machine learning applications for production prediction
TRANSCRIPT
University of Calgary
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2020-12-09
Machine Learning Applications for Production
Prediction and Optimization in Multistage
Hydraulically Fractured Wells
Chaikine, Ilia
Chaikine, I. (2020). Machine Learning Applications for Production Prediction and Optimization in
Multistage Hydraulically Fractured Wells (Unpublished doctoral thesis). University of Calgary,
Calgary, AB.
http://hdl.handle.net/1880/112817
doctoral thesis
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UNIVERSITY OF CALGARY
Machine Learning Applications for Production Prediction and Optimization in Multistage
Hydraulically Fractured Wells
By
Ilia Chaikine
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
GRADUATE PROGRAM IN CHEMICAL AND PETROLEUM ENGINEERING
CALGARY, ALBERTA
DECEMBER, 2020
© Ilia Chaikine 2020
ii
Abstract
Due to improvements in horizontal drilling and completion technologies over the past several
decades, multistage hydraulic fracturing has become very popular and has led to an explosive
growth of the shale and tight oil and gas production worldwide. Even though the completion
techniques are well known and relatively simple, the dynamics of fracture formation and
hydrocarbon flow within the reservoir are extremely complex. Even with the recent
developments, little is known about how the rock mechanical properties, completion design and
well spacing affect the morphology of fracture networks and the production of hydrocarbons at
the wellhead. Because of this lack in understanding there are no models as of yet that are capable
of forecasting production performance with good accuracy. The focus of the thesis is the
Montney Formation in Alberta. The research presented in this thesis describes a method to use a
convolutional-recurrent neural network (c-RNN) to generate synthetic shear sonic logs with high
accuracy and to link a broad range of input parameters, both geological and stimulation, at every
stage along a horizontal well bore to the production performance at the well head. The results
show that the production performance is driven more by the rock mechanical properties
surrounding the perforation clusters than the design of the hydraulic fracture. The results also
show that well spacing has affect on production performance. The outcomes of the research
provide tools for improving the accuracy of rock mechanical models, optimizing hydraulic
fracturing operations with respect to water usage and the placements future wells in the reservoir
to maximize gas production.
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Acknowledgements
I would like to thank my supervisor Dr. Ian Gates for taking me in as his student. His knowledge,
encouragement and support has made me passionate about research and its limitless potential.
I would also like to thank Sproule Associates Limited for providing me the financial support
needed to pursue my goals. Special thanks also go to my colleagues at Sproule, firstly to my
mentor and boss Scott Pennell, for always making time to listen and discuss ideas and for always
supporting my goals, without your help this research project would have not happened. I would
also like to thank Irina Baisitova for mentoring me since the start of my engineering career and
helping me get through some of those tough graduate courses; Alexey Romanov for always
making time to show me how to work Petrel and build geomodels and teaching me all about
statistics; Surya Karri for teaching me all I needed to know about petrophysics and sonic logs;
Victor Verkhogliad for teaching me all about Montney geology and geology in general; and
Richard Holst for your enthusiasm about my project and always being there to answer any
question I had.
I give my greatest thanks to my wife and best friend Kaitlyn Johnson, you have made this
graduate school experience wonderful and your unfaltering love, faith and support
has made my life the only life I want to live.
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Dedication
To my wife Kaitlyn, thank you for being there for me through thick and thin and supporting me in
all my goals and dreams.
v
Table of Contents
Abstract ........................................................................................................................................... ii
Acknowledgements ........................................................................................................................ iii
Dedication ...................................................................................................................................... iv
Table of Contents ............................................................................................................................ v
List of Tables ................................................................................................................................. ix
List of Figures ................................................................................................................................ xi
Chapter 1: Introduction ................................................................................................................... 1
1.1 Background ......................................................................................................................................... 1
1.2 Montney Formation and Study Area .................................................................................................. 4
1.3 Problem Statement ............................................................................................................................. 6
1.4 Organization of Thesis ......................................................................................................................... 8
Chapter 2: Literature Review ........................................................................................................ 10
2.1 Multi-Stage Hydraulic Fracturing ...................................................................................................... 10
2.2 Variables Affecting Post Fracture Production Performance ............................................................. 11
2.2.1 Geological properties surrounding a wellbore location ............................................................ 12
2.2.2 Completion design ..................................................................................................................... 13
2.2.3 Well spacing and completion order ........................................................................................... 14
2.3 Hydrocarbon Production Forecasting ............................................................................................... 17
2.3.1 Forecasting ................................................................................................................................. 17
2.3.2 Forecasting Hydrocarbon Production ........................................................................................ 18
2.4 Time Series Forecasting and Machine Learning Algorithms ............................................................. 21
2.4.1 Parametric Models ..................................................................................................................... 23
2.4.2 Supervised Machine Learning and Artificial Neural Networks .................................................. 24
2.5 History of Machine Learning in Production Forecasting and Optimization ...................................... 34
2.6 What is Missing in Literature? .......................................................................................................... 35
vi
Chapter 3: A New Neural Network Procedure to Generate Highly Accurate Synthetic Shear
Sonic Logs in Unconventional Reservoirs .................................................................................... 37
3.1 Preface .............................................................................................................................................. 37
3.2 Abstract ............................................................................................................................................. 38
3.3 Introduction ...................................................................................................................................... 39
3.4 Study Area and Data Processing ....................................................................................................... 42
3.4.1 Study Area and Structure Model ............................................................................................... 42
3.4.2 Data Preparation ........................................................................................................................ 44
3.5 Experimental Setup and Types of Neural Network Algorithms ........................................................ 47
3.5.1 Experimental Setup .................................................................................................................... 47
3.5.2 Comparisons .............................................................................................................................. 49
3.5.3 Networks used in the experiments ............................................................................................ 50
3.5.4 Overfitting .................................................................................................................................. 51
3.5.5 Stopping procedure ................................................................................................................... 53
3.5.6 Summary of Procedure .............................................................................................................. 57
3.6 Results and Discussion ...................................................................................................................... 59
3.7 Conclusions ....................................................................................................................................... 72
Chapter 4: A Convolutional-Recurrent Neural Network Model for Predicting Multi-Stage
Horizontal Well Production .......................................................................................................... 74
4.1 Preface .............................................................................................................................................. 74
4.2 Abstract ............................................................................................................................................. 75
4.3 Introduction ...................................................................................................................................... 76
4.4 Input Data Preparation ..................................................................................................................... 78
4.4.1 Geological Properties ................................................................................................................. 80
4.4.2 Completion Variables ................................................................................................................. 81
4.4.3 Well spacing and completion order ........................................................................................... 83
4.4.4 Production Data ......................................................................................................................... 84
4.5 Experimental Setup ........................................................................................................................... 88
4.5.1 Networks used in the experiments ............................................................................................ 88
4.5.2 Input shape and normalization .................................................................................................. 89
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4.5.3 Experimental Setup .................................................................................................................... 91
4.5.4 Hyperparameter Tuning ............................................................................................................. 95
4.6 Results and Discussion ...................................................................................................................... 97
4.7 Conclusions ..................................................................................................................................... 105
Chapter 5: Optimizing Water Usage during Multi-Stage Hydraulic Fracturing with a
Convolutional-Recurrent Neural Network .................................................................................. 107
5.1 Preface ............................................................................................................................................ 107
5.2 Abstract ........................................................................................................................................... 108
5.3 Introduction .................................................................................................................................... 109
5.4 Study Area and Proposed Wells ...................................................................................................... 114
5.4.1 Well spacing and completion order ......................................................................................... 115
5.4.2 Rock mechanical properties ..................................................................................................... 116
5.4.3 Completion Parameters ........................................................................................................... 116
5.4.4 Input shape and normalization ................................................................................................ 117
5.5 Neural Network Algorithms and Experimental Setup..................................................................... 118
5.6 Results and Discussion .................................................................................................................... 120
5.7 Conclusions ..................................................................................................................................... 134
Chapter 6: Using a Convolutional-Recurrent Neural Network Forecasting Model to Optimize the
Positioning of New Wells in a Partially Developed Field .......................................................... 136
6.1 Preface ............................................................................................................................................ 136
6.2 Abstract ........................................................................................................................................... 137
6.3 Introduction .................................................................................................................................... 138
6.4 Study Area and Completion Scenarios ............................................................................................ 141
6.4.1 Well spacing and completion order ......................................................................................... 141
6.4.2 Rock mechanical properties ..................................................................................................... 142
6.4.3 Completion Parameters ........................................................................................................... 143
6.5 Neural Network Algorithm for Gas Production Forecasting ........................................................... 143
6.6 Well Combinations and Procedure ................................................................................................. 145
6.7 Results and Discussion .................................................................................................................... 150
6.8 Conclusions ..................................................................................................................................... 159
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Chapter 7: Conclusions and Recommendations ......................................................................... 161
7.1 Conclusions ..................................................................................................................................... 161
7.2 Recommendations .......................................................................................................................... 163
References ................................................................................................................................... 166
Appendix A: Temperature Transient Analysis of the Steam Chamber during a SAGD Shutdown
Event ........................................................................................................................................... 175
A.1 Abstract ........................................................................................................................................... 175
A.2 Introduction .................................................................................................................................... 176
A.3 Literature Review ............................................................................................................................ 178
A.4 Temperature Transient Analysis ..................................................................................................... 179
A.4.1 Non-Condensing Model for SAGD Start up ............................................................................. 180
A.4.2 Condensing Model for SAGD Ramp up .................................................................................... 184
A.4.3 Variable Thermal Diffusivity .................................................................................................... 189
A.5 Results and Discussion .................................................................................................................... 192
A.5.1 Constant Thermal Diffusivity ................................................................................................... 192
A.5.2 Variable Thermal Diffusivity .................................................................................................... 196
A.6 Conclusions ..................................................................................................................................... 198
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List of Tables
Table 2.1: Completion variables. .................................................................................................. 14
Table 2.2: Parametric and non-parametric algorithms for analyzing time series data. ................. 22
Table 3.1: Total number of data points in each well used for the study. ...................................... 47
Table 3.2: Starting hyperparameters for the c-RNN developed in this study. .............................. 57
Table 3.3: Results of the study comparing the performance of the various methods of generating
synthetic DTS curves. ................................................................................................................... 60
Table 4.1: The stage variables that were used as inputs in the experiments. ................................ 80
Table 4.2: Completion variables ................................................................................................... 81
Table 4.3: Starting hyperparameters for the c-RNN developed in this study ............................... 96
Table 4.4: Results of the leave-one out experiments performed on only the geological variables
....................................................................................................................................................... 97
Table 4.5: Results of the leave-one out experiments performed on only the completion variables
....................................................................................................................................................... 97
Table 4.6: Results of the leave-one out experiments performed on geological, completion and
spacing variables ........................................................................................................................... 97
Table 5.1: The stage variables that were used as inputs in the sensitivity experiment. .............. 115
Table 5.2: The ranges of all the variable input parameters and the increments used for the
sensitivity experiment. ................................................................................................................ 117
Table 5.3: Results from the sensitivity analysis using the crosslinked gel as the fracture fluid . 121
Table 5.4: Results from the sensitivity analysis using the slickwater as the fracture fluid. ....... 123
Table 6.1: Results from the sensitivity analysis using crosslinked gel as the fracture fluid. ...... 151
x
Table 6.2: Results from the sensitivity analysis using slickwater as the fracture fluid. ............. 154
xi
List of Figures
Figure 1.1: Resource triangle: the top region of the triangle represents conventional resources
available on the planet whereas the larger bottom region represents unconventional resources.
(Holditch, 2013). ............................................................................................................................. 1
Figure 1.2: Areal extent of the Montney Formation (Canadian Energy Regulator, 2018). ............ 5
Figure 1.3: Location of Study Area (Canadian Energy Regulator, 2018). ..................................... 6
Figure 2.1: Diagram of a hydraulic fracturing operation ( US Environmental Protection Agency,
2013). ............................................................................................................................................ 10
Figure 2.2: Example of multiple horizontal wells drilled form a pad (Energy Essentials, 2015). 15
Figure 2.3: Showing bounded and unbounded wells. Here well B is bounded from both sides, A
and C are bounded from one side, and well D is unbounded. (Belyadi et al., 2017) .................... 17
Figure 2.4: The accuracy of forecasts increases with the amount of system understanding. ....... 18
Figure 2.5: A schematic diagram of two bipolar neurons. (Mohaghegh, 2000). .......................... 25
Figure 2.6: Schematic diagram of a typical artificial neuron (Mohaghegh, 2000). ...................... 26
Figure 2.7: Structure of a three-layer ANN (Neville et al. 2004). ................................................ 27
Figure 2.8: ANN training model using PSO (adapted from Panja et al. 2017). ........................... 28
Figure 2.9: Visualization of overfitting (Bhande, 2018). .............................................................. 32
Figure 2.10: A plot showing how training and validation error evolves over the amount of
epochs. .......................................................................................................................................... 32
Figure 2.11: Dropout Neural Net Model. Left: A standard neural net with 2 hidden layers. Right:
An example of a thinned net produced by applying dropout to the network on the left. Crossed
units have been dropped (Srivatava et al., 2014). ......................................................................... 33
xii
Figure 3.1: Plot of shear slowness (DTS) versus compressional slowness (DTP) measurements
for 14 wells in the Montney Formation. ....................................................................................... 41
Figure 3.2: A 3D visualization of all wells in the study area. Red = horizontal, blue = deviated,
and black = vertical. ...................................................................................................................... 43
Figure 3.3: 3D generated Montney and Belloy surfaces in Petrel. The vertical axis is 25x
exaggerated compared to the X and Y scales and represent the subsea depth. ............................ 44
Figure 3.4: Areal view of the study area generated in Petrel. Black points with no labels are wells
with no DTS logs, labeled wells have the DTS logs..................................................................... 45
Figure 3.5: Architecture of the ANN (A) and c-RNN (B) used in the study. ............................... 50
Figure 3.6: Format of input and output data of the c-RNN. ......................................................... 51
Figure 3.7: Effect of batch size on the evolution of the validation error for blind well VT_42. .. 52
Figure 3.8: Training and validation error for two blind well tests. ............................................... 54
Figure 3.9: Validation error for all blind well tests, results are split into two graphs for clarity. 55
Figure 3.10: 20,000 iterations of the blind well DV_28 experiment. ........................................... 55
Figure 3.11: A zoomed in plot showing the training and blind well error tremor. ....................... 56
Figure 3.12: General procedure for training the synthetic DTS tool that can be applied to any
formation. ...................................................................................................................................... 58
Figure 3.13: Process for using the training tool to generate synthetic DTS curves. ..................... 59
Figure 3.14: Synthetic logs generated by the cheat ANN (left) and the average of three c-RNN
(right) runs compared to the true logs for one of the worst blind wells – VT_10. ....................... 64
Figure 3.15: Synthetic logs generated by the cheat ANN (left) and the average of three c-RNN
(right) runs compared to the true logs for the best blind well – VT_18. ...................................... 65
xiii
Figure 3.16: Synthetic logs generated by the cheat ANN (left) and the average of three c-RNN
(right) runs compared to the true logs for the most important well - VT_42. .............................. 66
Figure 3.17: Synthetic logs generated by the c-RNN for wells VT_26 and VT_29 compared to
the true logs. .................................................................................................................................. 68
Figure 3.18: Synthetic logs generated by the c-RNN for wells VT_69 and VT_108 compared to
the true logs. .................................................................................................................................. 69
Figure 3.19: Sequence of synthetic well logs generated for well VT_18 at different number of
epochs. Y-axis is DTS (µs/ft) and x-axis is the thickness steps from the top of the formation. ... 72
Figure 4.1: Areal extent of the 74 horizontal wells used in the study. ......................................... 79
Figure 4.2: An example of the long-range rock mechanical profiles surrounding the horizontal
wells. .............................................................................................. Error! Bookmark not defined.
Figure 4.3: A visual representation the Arps decline overlaying the true production. This is
shown on the rate-cumulative production plot for one of the wells. The red line represents the gas
rate assuming 100% on time every month, the orange line represents gas rate scaled down to
account for the actual on time during the month. ......................................................................... 85
Figure 4.4: A plot showing the differences in rate restrictions between the actual production and
that of the Arps decline curve. ...................................................................................................... 85
Figure 4.5: The three common types of plots used to describe the production performance of a
well. Cumulative versus time (top), rate versus cumulative (middle), rate versus time (bottom).
These plots were generated using one of the wells in the study. .................................................. 87
Figure 4.6: c-RNN structure that was used in the study. .............................................................. 89
Figure 4.7: Format of input and output data of the c-RNN model ............................................... 90
xiv
Figure 4.8: Plot showing the numerous predictions that a model trained on the same dataset could
make. ............................................................................................................................................. 93
Figure 4.9: Plots showing how the average prediction changes based on the number of runs ..... 94
Figure 4.10: Distribution of individual well MAPE from the best case. .................................... 100
Figure 4.11: Plot the worst (left) and best (right) well production profiles created by the best-case
model. The red line is the average of the 30 runs, the green line is the true profile. .................. 100
Figure 4.12: Plot the best-case aggregate production profile of all 74 wells vs time. ................ 102
Figure 4.13: Plot how aggregating well together affects the mean average percent error (MAPE).
..................................................................................................................................................... 103
Figure 5.1: 40 proposed well locations (blue) added to the existing 74 wells (red) in the study
area generated in Petrel. .............................................................................................................. 114
Figure 5.2: Aggregated cumulative 5-year production vs proppant amount and fluid amount per
stage using 15 stages per well and the crosslinked gel (top) and the slickwater (bottom) as the
fracture fluid................................................................................................................................ 127
Figure 5.3: Affect of stage count per well on the aggregated cumulative 5-year production using
crosslinked gel (top) and slickwater (bottom) as the fracture fluid. ........................................... 128
Figure 5.4: crosslinked gel vs slickwater results for 15 stage count. .......................................... 129
Figure 5.5: Aggregated cumulative production versus the total water injected for various stage
counts of crosslinked gel and slickwater wells using 120 tonnes of proppant per stage. ........... 130
Figure 5.6: injection efficiency for different stage count and fluid types versus total fluid injected
..................................................................................................................................................... 131
Figure 5.7: 5-year cumulative production (top) and injection efficiency (bottom) for the 74
existing crosslinked gel and slcikwater wells versus total fluid injected.................................... 133
xv
Figure 6.1: One random combination of 20 wells (top), another random combination of 20 wells
(bottom)....................................................................................................................................... 147
Figure 6.2: Best and worst 20 well positions found in the 40 well prediction using the slickwater
(water intense) stimulation. ......................................................................................................... 149
Figure 6.3: Best and worst 20 well positions found in the 40 well prediction using the crosslinked
gel (water conservative) stimulation. .......................................................................................... 150
Figure 6.4: Results of the 104 combinations presented in a histogram using both crosslinked
(top) and slickwater (bottom) as the stimulation fluid. ............................................................... 157
Figure A.1: Cross sectional schematic of a typical SAGD process (Gotawala and Gates, 2010).
..................................................................................................................................................... 177
Figure A.2: Schematic diagram of a three zone non-condensing model used for SAGD start
up (modified from Zhu et al., 2012). ........................................................................................ 181
Figure A.3: Discretization domain for one-dimensional radial heat transfer - temperature grid
layout. ......................................................................................................................................... 183
Figure A.4: Schematic diagram of a three-zone condensation model used for SAGD ramp up
(modified from Zhu and Zeng, 2014). ...................................................................................... 185
Figure A.5: Decision tree for steam quality grid calculation. .................................................... 187
Figure A.6: Decision tree for steam temperature grid calculation. ............................................. 187
Figure A.7: Discretization domain for one-dimensional radial phase change - steam quality
grid layout. ................................................................................................................................. 188
Figure A.8: Non-condensing model evolution of radial temperature profile. ............................ 193
Figure A.9: Condensing model evolution of radial temperature profile. .................................... 194
xvi
Figure A.10: Condensing model evolution of radial steam quality profile. ............................... 194
Figure A.11: Temperature change with time at the center of the well bore during start up and
ramp up. ...................................................................................................................................... 195
Figure A.12: Slope of temperature plotted against time at the center of the well bore during star
up and ramp up............................................................................................................................ 196
Figure A.13: Non-condensing radial temperature profile after 2 weeks for variable and constant
kh cases. ....................................................................................................................................... 197
Figure A.14: Non-condensing temperature evolution at the center of the wellbore for variable
and constant kh cases. .................................................................................................................. 197
1
Chapter 1: Introduction
1.1 Background
Unconventional hydrocarbon resources differ from conventional ones in that they reside in tight,
low quality formations and are more difficult to extract (Cander, 2012). Unconventional
resources are also much more abundant on the planet than conventional ones as shown in Figure
1.1.
Figure 1.1: Resource triangle: the top region of the triangle represents conventional resources
available on the planet whereas the larger bottom region represents unconventional resources.
(Holditch, 2013).
Many types of geological formations are classified as bearing unconventional resources
including tight gas sands, gas shales, heavy oil sands, coalbed methane, oil shales, and gas
hydrates. The focus of this research is on tight sands and shale, which are low permeability and
the methods and technology required to extract hydrocarbons from these reservoirs is different
from that of conventional reservoirs. For production, tight sands and shale reservoirs require
higher well density. Furthermore, the wells drilled will not produce economically until they are
stimulated using methods such as hydraulic fracturing (Ma et al., 2016)
Conventional Resources
Unconventional Resources
2
Hydraulic fracturing has become the most widely used technique of producing hydrocarbons
from low permeability reservoirs. The process includes pumping massive amounts of sand, water
and chemicals at a high rate and pressure into the formation to induce and prop open fractures
that increase the surface area of the reservoir that is connected to the wellbore (Belyadi et al.,
2017). Modern hydraulic fracturing is typically performed in multiple stages along the entire
horizontal wellbore. Advancements in hydraulic fracturing and horizontal drilling techniques
over the past several decades have made producing hydrocarbons from unconventional reservoirs
economically feasible – this has led to the shale boom in North America and now throughout the
world (Morton, 2013; Trembath et al., 2012).
The geological heterogeneity and flow mechanisms in unconventional reservoirs are not well
understood especially in the context of the geomechanical dynamics during the fracturing
process and during production of fluids from the reservoir. Furthermore, stimulation adds
complexity stemming from interactions between pre-existing natural fracture networks and
fractures that are formed during the stimulation. Fracture dynamics are extremely complex and
exact fracture morphology before and after stimulation is not possible to observe although
passive and microseismic provides options to visualize aspects of the fractured reservoir rock.
The injection of proppant during stimulation only adds to these complexities. One of the
challenges that the industry is facing today is the lack of understanding of unconventional
reservoir stimulation mechanisms and their effect on production as well as the impact of pre-
existing hydraulic fractures within the formation. The development of robust and reliable tools
would allow to forecast production from these types of reservoirs with reasonable certainty
3
(Cohen et al., 2012). Accurate forecasts would allow for better economic evaluations of assets,
implementation of optimization strategies, minimizing expenditures, and lowering environmental
impact of oil and gas operations.
Over the past 15 years, the drastic increase of hydraulic fracturing activity was paralleled with
significant advances in digital data capture and storage (Canvanillas et al., 2016). The
combination has generated a massive, ever-expanding dataset of information on hydraulic
fracturing. Over the same period computing power has increased exponentially and innovations
in machine learning models have made them well positioned in finding hidden patterns in data
and making accurate predictions (Goel et al., 2019).
Machine learning is a subset of artificial intelligence which utilizes computer algorithms capable
of improving performance automatically through experience (Tom, 1997). There are three broad
categories of machine learning: supervised learning, unsupervised learning and reinforcement
learning. In supervised learning both the inputs and outputs are presented with the goal of finding
their general correlations and being able to make prediction when only inputs are shown.
Supervised learning is used for classification and regression problem. In unsupervised learning
no outputs are presented and the algorithm is left to try and find similarities in the inputs.
Unsupervised learning is most commonly used for clustering, association, anomaly detection and
dimensionality reduction (Leung and Leckie, 2005). In reinforced learning the algorithm
interacts with a dynamic environment and learns to achieve goals through rewards
(Chandramouli et al., 2018). The research presented in this thesis deals with forecasting and
regression and the supervised learning approach was utilized.
4
The motivation for this research was driven by three factors:
1. the lack of current understanding of unconventional reservoirs,
2. the very large and largely unexplored digital data set generated from hydraulic
fracturing operations in unconventional reservoirs, and
3. recent advances in machine learning models and computing power.
By utilizing new machine learning techniques, we may be able to increase the understanding of
unconventional reservoirs and how hydraulic fracturing affects production by exposing patterns
and input-output relationships that have not been identified before in physics-based modelling.
The application of machine learning algorithms could lead to significant opportunities for
increasing production, lowering costs and lowering the environmental impact of oil and gas
operations.
1.2 Montney Formation and Study Area
The Montney formation shown in Figure 1.2 is a tight siltstone/shale oil and gas play that spans
over 500 km from Alberta in the southeast to British Columbia in the northwest and covers over
130,000 km2. The quality of reservoir varies significantly over the formation, with the general
trend of conventional sandstone in the southeast to pure shale in the northwest. The thickness and
depth also vary greatly from less than 1 m thickness and 500 m depth in the southeast to over
350 m thickness and 4,000 m depth in the northwest. The in-place resource volumes for the play
are estimated at over 2,000 trillion cubic feet of gas and over 150 billion barrels of oil and
condensate. (Reynolds et al., 2014; Wang and Chen, 2016).
5
Figure 1.2: Areal extent of the Montney Formation (Canadian Energy Regulator, 2018).
Due to the enormous volumes of in-place hydrocarbons and the major developments in
horizontal drilling and multi-stage hydraulic fracturing technologies, the Montney Formation has
become a major gas and natural gas condensate producer. With thousands of multistage
horizontal wells drilled to date, it accounts for over 38% of total Canadian natural gas production
(Canadian Energy Regulator, 2018). Due to its size and expected production growth, the
Montney Formation was chosen for the research documented in this thesis.
The study area is a small section of the Montney Formation and is show in Figure 1.3. It is
located near Dawson Creek in the province of British Columbia, Canada, covering an area of
around 30 km by 30 km with an average thickness of 300 m. In this area, the Montney Formation
6
underlies the Doig Formation and overlays the Belloy Formation. This particular study area was
chosen because it contains the highest density of vertical and horizontal wells – this creates a
large data set. The study area contains 145 vertical, 35 deviated wells and 255 horizontal wells
that penetrate the Montney Formation with only 60 of these wells penetrating all the way to the
Belloy Formation. Most of the horizontal and vertical wells are drilled in the middle of the study
area with some horizontal wells located in the northwest. All the horizontal wells in the study
target the Montney Formation with the majority drilled in the top 20% of its thickness.
Figure 1.3: Location of Study Area (Canadian Energy Regulator, 2018).
1.3 Problem Statement
The overall objective of the research presented in this thesis is to explore the use of machine
learning algorithms for understanding relationships between geology, geomechanical properties,
completion design, and fluid injection properties and the production performance of the well.
7
From this analysis, models can be devised to predict the production performance of multistage
hydraulically fractured horizontal wells. The approach makes minimal assumptions about the
exact structure of the reservoir and fluid flow mechanisms within the reservoir but instead
attempts to link the horizontal well input parameters and surround geology and geomechanical
properties to its production profile. As there are a myriad of variables driving production
behavior, machine learning was applied in the research documented in this thesis. More
specifically, the convolutional recurrent neural network (c-RNN) was chosen for its ability to
process large amount of data as well as find patterns in sequential data. This machine learning
method also needs to have the ability to aid in optimization problems such as optimizing
completion strategies and well placements. In general, for the research conducted, the approach
was developed following these steps:
1. With a machine learning model, create synthetic shear sonic logs to get a better
understanding of rock mechanical properties within a formation.
2. Create a three-dimensional (3D) rock mechanical model of the study by using the
density, compressional sonic and shear sonic (real and synthetic) logs of vertical and
deviated wells in the study area.
3. Use the rock mechanical properties, completion design, well spacing and timing
parameters as inputs to the machine learning algorithm to predict the five-year
cumulative gas production profiles of horizontal wells.
4. Use the machine learning model to minimize water usage while maximizing
production during hydraulic fracturing in future wells.
8
5. Apply the machine learning model to find optimal positioning of future drills to
maximize production
1.4 Organization of Thesis
Chapter 2 is a literature review of multistage hydraulic fracturing, the variables that affect
postproduction performance, machine learning tools, as well as forecasting and optimizing post
fracture production performance.
In Chapter 3, a procedure is developed that can generate highly accurate synthetic shear sonic
logs. This procedure utilizes a c-RNN as it is capable of learning patterns in sequential data and
links the deviation survey along with the compressional and bulk density logs to the shear sonic
log. This procedure is a cost effective and fast alternative to running shear sonic (DTS) logs and
provides a greater insight into the rock mechanics of a formation.
In Chapter 4, a model is proposed that utilizes a c-RNN to predict the five-year cumulative gas
production profiles in multistage hydraulically fractured wells. The model was trained by linking
the cumulative production to a combination of completion parameters, rock mechanical
properties and well spacing for every stage of a well of 74 wells in the Montney Formation. The
accuracy of the model’s predictions was found to increase exponentially as the production of
multiple wells was aggregated.
9
In Chapter 5, we use the model developed in Chapter 4 to forecast the production of 40
proposed wells to be drilled alongside existing producers. 1,080 sensitivities were run to explore
how different combinations of stage count, fluid type, water amount, and proppant amount affect
the aggregated 5-year cumulative gas production of the 40 proposed wells. The study focuses on
reducing water usage while maximizing production and shows that it is possible to achieve a
cumulative production that is 76% of the maximum by injecting only 3% of the total water
volume required to achieve this maximum.
In Chapter 6, we use the model developed in Chapter 4 to forecast the production of 20
proposed wells. These 20 wells can only be drilled in the 40 fixed well locations identified in
Chapter 5, and the objective is to find the best placement for these wells. This resembles a
situation where budget constrains have forced a partial field development to be the only option.
Optimal combinations were found using two types of completion strategies, the water intense 30-
stage slickwater treatment and a water conservative 15-stage crosslinked gel treatment.
Chapter 7 highlights the major findings and conclusions of the thesis as well as
recommendations for future work.
Appendix A is a separate study not directly related to the research that was completed over the
course of the degree. Here, temperature fall-off from steam chambers where injection has
stopped is examined and a new three-zone model is designed with heat losses taking into account
temperature-dependent thermal conductivity. The model solves the transient heat conduction
and steam condensing equations.
10
Chapter 2: Literature Review
2.1 Multi-Stage Hydraulic Fracturing
First used in 1947, hydraulic fracturing has become the most widely used technique of producing
hydrocarbons from low permeability reservoirs. The process includes pumping massive amounts
of sand, water and chemicals at a high rate and pressure into the formation in order to induce and
prop open fractures that increase the surface area of the reservoir that is connected to the
wellbore. This in turn, increases the volumes that can be recovered (Belyadi et al., 2017). Figure
2.1 shows a visualization of the hydraulic fracturing process.
Figure 2.1: Diagram of a hydraulic fracturing operation ( US Environmental Protection Agency,
2013).
11
In the field, the two most popular methods to hydraulically fracture a formation are the plug and
perf and the sliding sleeve. Although there is no overall recommendation on which method is
better, typically the choice between the two is driven by economics as well as an operator’s
success in a particular formation. The plug and perf method is typically used for cased holes and
offers more flexibility in adjusting the position of the perforations. The sliding sleeve is used in
open hole wells and contains pre-perforated sleeves, so that a perforating gun is not needed
(Belyadi et al., 2017). Most hydraulic fluids are water-based and contain 90 to 97% water by
volume (U.S. Environmental Protection Agency, 2016). Two of the most common water-based
fluids used today are slickwater and crosslinked gel (Montgomery, 2013). Modern hydraulic
fracturing is typically performed in multiple stages along the entire horizontal wellbore.
Advancements in hydraulic fracturing and horizontal drilling techniques over the past several
decades have made producing hydrocarbons from unconventional reservoirs economically
feasible which lead to a unconventional boom in North America and throughout the world
(Morton, 2013).
2.2 Variables Affecting Post Fracture Production Performance
The production performance of a horizontal well that has been hydraulically fractured is
influenced by a multitude of variables, in this study we identify three major categories:
1. geological properties of the formation surrounding the perforations,
2. completion design of each stage, and
3. well spacing and completion order.
12
2.2.1 Geological properties surrounding a wellbore location
The geological properties surrounding the perforations in a horizontal well have arguably the
greatest influence on the production performance. Geological properties include the volume of
hydrocarbons in place, the permeability, the natural fracture geology, in situ stresses, and rock
mechanical properties. The selection of the right place to drill a well is critical to ensure an
ongoing expanding commercial operation.
The geological properties of a formation can be described as a mixture of both the properties of
the matrix and the morphology of the fracture network. The matrix properties include the gas and
fluid saturation, porosity, as well as matrix permeability. These properties cannot be altered to
any meaningful extent. Fractures, whether natural or induced are not static and evolve with
changing conditions. (Holland et al., 2009). Fractures on the other hand do have a significant
effect on fluid flow within a reservoir, either in the form of increased reservoir permeability or
increased permeability anisotropy (Nelson, 2001). The fracture morphology, distribution and
connectivity to a wellbore will significantly impact the production that is measured at the
wellhead. Mechanical rock properties are a major driver of how the fracture network evolves and
are especially important during a hydraulic fracture treatment, when the natural fracture network
gets drastically altered.
The horizontal wells in this study area are drilled within a small areal extent of the Montney
Formation and are all located at a similar depth near the top of the formation. The Montney
Formation was deposited in a shallow marine shelf environment which makes the geological
13
properties of the matrix fairly constant through the study area (Moslow, 2000). The rock
mechanics, which govern fracture networks differ significantly both areally and vertically. This
gives each horizontal well a unique rock mechanical profile. Mechanical properties can be
estimated using three sets of log measurements: shear sonic travel time (DTS), compressional
sonic travel time (DTP) and bulk density (RHOB) (Fjar et al., 2008). Horizontal wells do not
usually have these logs and the only reasonable way to estimate these horizontal logs is by
constructing a 3D rock mechanical model upscaled and interpolated using logs from nearby
vertical wells.
2.2.2 Completion design
After a well has been drilled, the completion design is the only thing the operator can control.
Completion design is a complicated process with many variables. A typical completion is
divided into multiple stimulation stages along the wellbore that are isolated from each other,
each stage can contain one or more perforation clusters. Since each stage is stimulated
separately, the stimulation process may differ between stages.
The stage count and spacing are one of the first decisions to be made during a completion design,
the idea is to contact as much surface area as possible while minimizing fracture interference
within clusters (Belyadi et al., 2017). The optimal spacing is difficult to determine and is tied to
both economics and the geology of the formation. The amount of proppant and water pumped
per stage are also very important variables as they dictate how large the fracture network will get
and how efficiently the fractures will stay propped open once the well starts to flowback. There
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are many other variables in the design of a completion that influence production, some of the
common variables are described in Table 2.1.
Table 2.1: Completion variables.
Service company performing the stimulation Amount of foam
Sliding sleeve or plug and perf Proppant concentration
Gun diameter Proppant size and type
Charge size Size of flush stage
Number of perforations per cluster Amount of crosslinked gel
Distance of the cluster from the well head Flowrate of each stage
Amount of acid used in spearhead stage Pressure of each stage
Fluid type (slickwater or gelled) Length of time of each stage
Size of pad stage Flowback design
Amount of energizer (CO2 or N2)
2.2.3 Well spacing and completion order
Whether a well is bounded or unbounded, the distance between producing wells, and the length
of time one well has been on production before an offsetting well is drilled all influence
production performance (Belyadi et al., 2017). During the early stages of field development,
many single wells are drilled. These primary wells usually produce unbounded, meaning that
they have no offsetting wells to interact with. As production data is gathered from the primary
wells it makes more economical sense to drill infill wells beside them, this type of drilling is
done from a pad which is shown in Figure 2.2.
15
Figure 2.2: Example of multiple horizontal wells drilled form a pad (Energy Essentials, 2015).
The production performance from primary wells is known to be better than that of the secondary
infill wells. This is because primary wells produce for the original reservoir which has been
unaltered for millions of years. The primary well production causes a depletion in original
reservoir pressure known as the drainage area that propagates away from it. As the pressure in
the drainage area drops so too does the flow rate to the wellbore. The reservoir stresses along
with the geological properties such as porosity and permeability also get altered. If drilled close
enough, the primary and secondary well will share a drainage area leading to lower production
rates in the secondary well. Lindsay et al. (2018) analyzed 564 wells in the Wolfcamp Formation
in the Permian’s Delaware Basin and found that 66% of the time the primary wells outperformed
16
secondary wells that were drilled within 300 m. When the results were adjusted for the more
modern, larger completions of the secondary wells, 79% of the primary wells performed better.
It is not just the distance between wells that has an affect on production, but the length of
unbounded depletion time and consequently the amount of volume that one well had already
produced before a nearby secondary well was drilled. Defeu et al. (2018) showed both of these
effects in an optimization study on wells from the Wolfcamp formation. Wells with unbounded
depletion time of 6 months had the same minimal impact on the production performance of
secondary wells drilled at 180, 230 and 275 m away from the primary. Wells with unbounded
depletion time of 36 months or more showed a 50% reduction in production performance of
secondary wells drilled 180 m away versus a 15% reduction for wells drilled 275 m away.
A primary well produces unbounded until a secondary infill well is drilled nearby making both
wells bounded. Wells can be bounded from one or both sides, as more wells are drilled in a field,
more wells become bounded from both sides. The spacing and completion order impacts the
overall performance of a field and needs to be carefully selected before a field is developed.
Figure 2.3 depicts typical bounded and unbounded configurations. Accounting for the distance
between neighboring wells and the length of time and volume that each neighbor produced is an
indirect way to account for changes in the geological properties and reservoir stresses which are
caused by well production.
17
Figure 2.3: Showing bounded and unbounded wells. Here well B is bounded from both sides, A
and C are bounded from one side, and well D is unbounded. (Belyadi et al., 2017)
2.3 Hydrocarbon Production Forecasting
2.3.1 Forecasting
Forecasting is a useful tool that is used in many situations that require decision making: a city
decides on the width of highways based on forecasts of population growth and vehicle usage;
stores decides on how much stock to buy based on forecasts of customer purchases. The length
of forecasts differs based on what they are used for, telecommunication routing only requires
forecasting several minutes ahead, large capital investments require multiyear forecasts
(Brockwell and Davis, 1996).
18
Certain things are easy to predict while others are extremely difficult. The trajectory of a comet
can be forecasted thousands of years into the future with extreme accuracy; however, forecasting
even one day of a stock market price with any degree of certainty is nearly impossible. This is
because the accuracy of a prediction depends on our understanding of the system, as show in
Figure 2.4
Figure 2.4: The accuracy of forecasts increases with the amount of system understanding.
2.3.2 Forecasting Hydrocarbon Production
Forecasting the production of oil and gas has been a major part of petroleum engineering for
most of the industry’s history. This is because having a forecast that can reasonably predict
future oil production grant the ability to estimate the assets remaining value and to optimize the
operation of existing wells and future drilling programs.
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Forecasting production is possible because reservoirs behave in a manner that is driven by the
underlying physics and geology. The oil rate at the well head is a function of drawdown pressure,
quality of the wellbore, porosity, permeability, net pay, oil saturations and several other
variables. Further to that many reservoirs around the world have been on production for several
decades and have produced a large dataset of reservoir geology, drilling and production and
pressure data. Even though reservoir physics is well understood and there are large data sets
available, the error in many forecasts still remains high, this is because
• reservoirs are very large,
• reservoir geology is very heterogenous,
• reservoirs contain vast complex natural fracture networks,
• reservoirs are deep underground and are not visible,
• the only direct measurement of the reservoir comes from vertical well bores which only
cover a tiny fraction of the entire reservoirs, and
• reservoir geology can change as hydrocarbons are produced and pressures drop.
For a long time, forecasting oil production for existing producers was done empirically by
decline curve analysis (DCA) or material balance (Aldeman and Jacoby, 1979). Forecasting
production for undeveloped (not yet drilled) wells was only done by analogy and by volumetric
calculations taking recovery efficiencies into account. The problem with traditional methods is
that they are based on subjective interpretation of the data, for example picking the proper slope
for DCA. Traditional methods suffer from human cognitive biases and because of this, long-term
production forecasts have been inaccurate and have to be revised through time as the reservoir is
20
produced. This is the reason why the volumetric accumulation in petroleum reservoirs (e.g. the
original oil or gas in place) have tended to be updated every few years as the petroleum resource
is produced.
Numerical simulation is another popular method to forecast production, based on historical data
and physics-based models. Numerical simulation develops a dynamic model using available
static and dynamic data. The dynamic model is based on a static geological model which is built
by upscaling interpreted data from vertical well logs. The flow model is developed using the
well-known engineering fluid flow principles followed by the history matching process. Despite
handling complex physics and chemistry, phase behavior, and approximations to the
heterogeneity of the geological system, numerical methods tend to do even worse than empirical
methods at long-term forecasting (Mohaghegh, 2017).
Numerical reservoir simulators build a model from the bottom-up by combining historical data
measurements (flowing bottom hole pressure, production rates, etc.) and geological
interpretations (static geological model of faults, porosity, permeability, etc.) with functional
relationships (heat and mass transfer, multiphase flow in porous media with fluid constitutive
equations and thermodynamics). In most cases, reservoir simulation modelers assume that field
measurements and geological models are uncertain and the functional relationships are certain
and fundamentally true. To match historical data the geological model is tuned until a good
historical match is achieved. It is then assumed that the model provides a reasonable
representation of the reservoir system and the model is suitable for forecast. The problem is that
the geological model is highly uncertain and the functional relationships that are assumed to be
21
true are nowhere close to being able to model the entire complexity of nature (Mohaghegh,
2017).
Empirical and numerical methods have proven to be bad at forecasting long-term, yet today they
are still the most widely used methods for forecasting oil production, reserves, and resources.
Governments, operators and investors rely heavily on these forecasts to make major decisions,
and that is why an improvement in the forecast accuracy may be of high practical value. Since oil
and gas plays such a large role with respect to global energy supply and economics, these
decisions not only affect the industry but the entire global economy, the environment, and overall
quality of human life on this planet. To reduce the amount of bad decisions made there is a need
for more accurate way of long-term forecasting reserves and resources that is driven by data.
2.4 Time Series Forecasting and Machine Learning Algorithms
Time series (TS) modeling saw its beginning from the work of Yule (1927). A time series is a set
of data recorded over a period of time, most commonly taken in regular intervals to insure
uniformity. Hourly power consumption, monthly product sales or daily oil production are all
examples of a time series. The importance of time series is twofold: firstly, it can be used to
identify patterns or behaviors in the past and secondly it can be used to make predictions about
the future. The latter has gained much popularity because of its vast applications in nearly every
field from forecasting sales to predicting the weather. Time series analysis is important since it
has the ability to identify causal factors, and these factors can then be manipulated to optimize
the future. Today, it is heavily used by investors, statisticians, meteorologists, engineers,
22
governments and has countless applications in any field that requires decision making. Due to its
usefulness and high popularity in industry it has also become a highly active field of research.
(Kumura et al. 2013).
Most time series analytics in the past were done manually but due to the recent trend of data
digitization, ease of storage and transition the amount of raw data available has made manual
processing an impossible task (De Gooijer and Hyndman, 2006). Today most data processing is
done automatically making use of modern computing power.
As described in detail by Chen et al. (1997), time series algorithms fall mainly into two classes:
parametric and non-parametric. A summary of these is listed in Table 2.2. Early methods were
mostly parametric approaches with the goal of fitting a statistical model to time series data.
Parametric approaches make certain assumptions and tend to suffer from severe limitations. Due
to this, most models used today are non-parametric which make no assumptions about the
underlying structure of the process (Meir, 2000).
Table 2.2: Parametric and non-parametric algorithms for analyzing time series data.
Time Series Forecasting
Parametric Non-parametric
• Exponential Smoothing
• Autoregressive Moving Average
• Autoregressive Integrated Moving
Average (ARIMA)
• Multivariate Local Polynomial Regression
• Functional Coefficient Autoregressive
• Adaptive Function Coefficient Autoregressive
• Additive Autoregressive
• Artificial Neural Networks (ANN)
• Support Vector Machines (SVM)
• Genetic and Evolutionary Approaches (GA)
• Particle Swarm Optimization (PSO)
• Simulated Annealing (SA)
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2.4.1 Parametric Models
Exponential smoothing was first proposed in the late 1950s (Brown 1959; Holt 1957; Winters
1960) and has been the foundation of most successful forecasting methods. Forecasts produced
using exponential smoothing are simple moving averages of past observations which are
weighted equally. Exponential functions are used to assign exponentially decreasing weights
over time. Exponential smoothing models are based on a description of the trend and seasonality
in the data and can quickly generate fairly reliable forecasts for a wide variety of time series. The
AutoRegressive Integrated Moving Average (ARIMA) model is the most popular and frequently
used stochastic time series model (Box and Jenkins, 1970). ARIMA models aim to describe the
autocorrelations in the data and provide a complimentary approach to exponential smoothing.
Some other examples of parametric models include the autoregressive conditional
heteroscedasticity (ARCH) method introduced by Engle (1982) which captures the time-varying
conditional variance or volatility. The generalized autoregressive conditional heteroskedasticity
(GARCH) (Bollerslev, 1986) represents the variance of the error term as a function of its
autoregressive terms, thereby allowing a more parsimonious representation of the time series.
Krishnamurthy and Yin (2002) combined a hidden Markov model and AR models under a
Markov regime where AR parameters switch in time according to the realization of a finite-state
Markov chain, for nonlinear time series forecasting. These parametric models tend to be limited
when modeling nonlinear and stationary time series forecasting by assuming local linearity with
an AR-type structure.
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2.4.2 Supervised Machine Learning and Artificial Neural Networks
Most non-parametric time approaches utilize supervised machine learning. The goal in
supervised machine learning is to learn how the outputs are connected to the input. During
supervised learning the algorithm is presented with training data that contains both the inputs and
outputs, the samples are presented multiple times and gradually the machine begins to learn the
patterns and reduce its forecast error. During the training round a validation dataset is also
monitored to see how accurate the algorithm is performing on data it has not seen and to monitor
overfitting (Chandramouli et al., 2018).
Out of the non-parametric methods of forecasting, Artificial Neural Networks (ANNs) have
become the most popular (Agrawal and Adhikari, 2013). ANNs are information processing
systems inspired by biological neural networks found in the brains of animals and allow for
complex nonlinear relationships between the input and response variables. ANNs have the ability
to both memorize and reason and are a method in which a computer can learn or train itself to
solve a problem it was not programmed to solve. ANNs are trained by reading a large number of
input patterns and have been applied to forecasting problems in various disciplines including
finance, sociology, medicine, engineering and many others (Cartwright, 2015). To understand
how an ANN works a basic understanding of the workings of a biological neural network is
required.
25
2.4.2.1 Biological Neural Networks
A very simple explanation of biological neurons is as follows. Typical biological neurons contain
three main parts: cell body in which the nucleolus is contained, dendrites and an axon. Figure 2.5
depicts two bipolar neurons. Information enters the cell body through the dendrites in the form of
electrical pulses or signals. Depending on the nature of the input signal the cell body will activate
in either an excitatory or inhibitory way, the cell body will then send an output signal through the
axon to the surrounding neurons. The electrical signal travels from one neuron and activates a
train of signals in another. A neural pathway is the point between two neurons and a synapse is
the point where the ends of an axon of one neuron come into close contact with the dendrites of
another. Neurons are the basic building blocks of neural networks.
Figure 2.5: A schematic diagram of two bipolar neurons. (Mohaghegh, 2000).
26
Biological neural networks can contain up to 100,000,000,000 neurons and are extremely
complex. In a neural network, one neuron is usually connected to thousands of other neurons.
Although individual electrical pulses in a neuron travel much slower than a signal in a computer,
the parallel structure of the brain allows for extremely fast processing; hundreds of times faster
than the capabilities of household computers (Mohaghegh, 2000).
2.4.2.2 Basic Structure of ANNs
Like biological neural networks, ANNs are composed of basic processing elements known as
perceptrons or artificial neurons (Mohaghegh, 2000). ANNs are composed of multiple neurons
that pass signals between one another, each neuron has connections to multiple other neurons.
Each input signal carries an associated weight which multiplies the signal being transmitted. The
neuron applies an activation function to the weighted sum of all the inputs to determine the
output signal. The output of one neuron then becomes an input to another. The neurons have
multiple inputs but only one output. Figure 2.6 is a schematic of a typical artificial neuron.
Figure 2.6: Schematic diagram of a typical artificial neuron (Mohaghegh, 2000).
27
Individual neurons in an ANN are arranged in rows or layers known as a multilayer feed-forward
network (Hyndman and Athanasopoulos, 2017). As depicted in Figure 2.7 the basic feed-forward
ANN has three layers: an input layer, hidden layer and an output layer. The hidden layer enables
the network to model nonlinear and complex functions and is responsible for feature extraction
and provides increased dimensionality. ANNs can have multiple hidden layers, and the more
hidden layers that are added, the more complex and nonlinear the model becomes (Mohaghegh,
2000). The number of neurons in the input layer corresponds to the number of parameters
presented to the network.
Figure 2.7: Structure of a three-layer ANN (Neville et al. 2004).
28
2.4.2.3 ANN training methods
Training is an optimization process where the weights of the inputs between neurons along with
the biases are calibrated until a desired output is reached. Once the network is trained it can
predict with greater accuracy (Ahmadi et al. 2015). A widely used training technique is the
backward propagation of errors (backpropagation). In backpropagation the difference between
desired and actual output (error) is calculated from the output layer backwards to the input layer
and makes small incremental adjustments in the input weights (Cheng et al. 2012).
Backpropagation is an iterative procedure that takes a certain time until the weights have been
calibrated. Other methods to make adjustments to the weights include genetic algorithms (GA),
particle swarm optimization (PSO), unified particle swarm optimization and imperialist
competitive algorithms. Their ability to optimize makes them not only a valuable tool in training
but also optimizing an objective function of a field. Figure 2.8 shows how PSO can be used to
train an ANN.
Figure 2.8: ANN training model using PSO (adapted from Panja et al. 2017).
29
2.4.2.4 Deep Neural Networks
Deep neural networks (networks with many successive layers) were introduced in the early
1990s and due to their impressive performance have become one the most popular machine
learning tools today. With each successive layer in the network, more complex representations
are developed, through this they completely automate the task of feature engineering which in
the past was a very time consuming a laborious process. There are many types of network layers
with more discoveries being made year over year. The studies in this thesis make use of three
types of layers (Chollet, 2017):
1. Densely connected – this is the simplest type of layer, every node in one layer is fully
connected to every node in the next. The traditional ANN uses only densely connected
layers as shown in Figure 2.7. The main problem with a network that uses only densely
connected layers is that it cannot capture sequential information in the input data. ANNs
suffer from the vanishing and exploding gradient problem which is associated with the
backpropagation algorithm. This problem appears if a network has too many hidden
layers. If the derivates of the error in the output layer are too large, the gradient will
increase exponentially with each layer and eventually explode, if the derivates of the
output layer error are too small, they will decrease exponentially with each layer and
eventually disappear (Pykes, 2020).
2. Recurrent – this type of layer is used for sequence-based data such as time series or logs.
It iterates through a sequence of a sample while maintaining a state of memory relative to
what has already been seen before. A network that uses recurrent layers is known as a
30
recurrent neural network (RNN). The two most popular types of recurrent layers are Long
Short-Term Memory (LSTM) and the gated recurrent unit (GRU). Both units have
similar performance and are related in that they gate information to prevent the vanishing
gradient problem. The GRU was chosen for this thesis because of its simpler structure
and is higher computational efficiency over the LSTM (Chung et al., 2014). RNNs also
suffer from the vanishing and exploding gradient problem.
3. Convolutional – this is a layer that learns spatial hierarchies of patterns. When staked
together, these layers make a convolutional network (CNN), they are able to capture both
local and global patterns. Filters (or kernels) are the building block of CNNs, and are
used to extract relevant features from the input using the convolutional operation. Due to
this, they are mostly used for image identification tasks; however, they have also found
success in processing sequence data. Their performance is competitive with recurrent
layers and is usually computationally less intensive. As with the other type of networks
the CNN suffers from the vanishing and exploding gradient problem.
Deep networks are able to combine many different types of layers, which opens nearly
unlimited potential for experimenting with configurations to find an optimal structure for a
certain type of problem. There is no optimal network structure since it depends largely on the
problem at hand. Some rules of thumb exist that can be used as a starting guide. However,
the only way to find the optimal configuration is by manually tuning hyperparameters and
running many experiments. Hyperparameters are parameters whose value is set before the
31
training occurs. Important hyperparameters are the type and number of layers, number of
nodes in each layer, dropout (which introduces randomness), batch size and optimizer.
2.4.2.5 Convolutional Recurrent Neural Network
For the experiments presented in this thesis a convolutional recurrent hybrid (c-RNN) network
was chosen. This is because it is able to combine the speed and ability to process large amounts
of data of a convolutional network (CNN) with the sequence processing ability of a recurrent
network (RNN). The study presented in Chapter 3 of this thesis required forecasting a sequence
4,000 steps long, but standalone RNNs are able to memorize patterns in only a few hundred steps
and would not be able to predict this long a sequence with great accuracy. Convolutional
networks are able to convert long sequences into shorter ones of higher-level features, which
gives a c-RNN hybrid the ability to process sequences with thousands of steps (Chollet, 2017).
2.4.2.6 Overfitting
Deep neural networks are good at learning complicated relationships between inputs and outputs;
however, if trained too long the networks start to confuse noise with signals and start to overfit to
the training set which results in lower generalization capabilities (Srivatava et al. 2014). This is
especially problematic when the amount of training data is limited as in the studies presented in
this thesis. A visual of overfitting is shown below in Figure 2.9.
32
Figure 2.9: Visualization of overfitting (Bhande, 2018).
Most machine learning experiments are run with three sets of data: training, validation and test.
The model is trained on the training set, the validation set is used to monitor overfitting and the
test set is then run after network has finished training. The typical approach is to limit overfitting
stop the training at the point where validation error is at a minimum as shown in Figure 2.10.
Figure 2.10: A plot showing how training and validation error evolves over the amount of
epochs.
33
This approach is good when there are at least a few hundred samples available. The studies in
this thesis had a maximum of 74 samples and running multiple experiments showed that the
point at which the validation error was at a minimum was inconsistent with different samples in
the training data. After numerous experimentations we found that the best way to limit
overfitting with the small sample sizes was to maximize the batch size and apply dropout.
Dropout is one of the most effective and commonly used methods to reduce overfitting (Chollet,
2017). The term “dropout” refers to the temporary removal (setting to zero) of a fraction of
nodes from a network along with their incoming and outgoing connections during training. The
units to drop are chosen at random with a probability of p which is known as the dropout rate
which is usually set between 0.2 and 0.5 (Chollet, 2017). At test time, no units are dropped,
instead layer output values are scaled down by p. At its core, dropout adds randomness which
breaks up patterns that are not significant (Srivatava et al. 2014). A visualization of dropout is
shown in Figure 2.11.
Figure 2.11: Dropout Neural Net Model. Left: A standard neural net with 2 hidden layers. Right:
An example of a thinned net produced by applying dropout to the network on the left. Crossed
units have been dropped (Srivatava et al., 2014).
34
Batch size refers to the number of training examples that are seen before a network update is
made. Batch size comes in three options (Brownlee, 2017):
• Batch mode: batch size is equal to the total number of samples in the training set,
• Mini-batch mode: batch size is smaller than that in batch mode but greater than one, and
• Stochastic mode: batch size is equal to one.
2.5 History of Machine Learning in Production Forecasting and Optimization
Time series forecasting in the petroleum engineering is relatively new with mostly parametric
models being used. Ayeni and Pilat (1992) used the ARIMA technique to forecast crude oil
reserves in South Louisiana. Ediger and Akar (2007) used ARIMA and S-ARIMA models to
forecast total primary energy demand over time in Turkey.
Machine learning-based, non-parametric forecasting have also been used: He et al. (2001) used
ANN forecasting to predict existing and infill oil well production using only production data.
The experiments included two data sets (for existing and infill wells prediction) of 9 wells each.
One and a half years of production history was used to train the ANN, the authors conclude good
predictive capacities for short term (1-2 year) forecasts. Chakra et al. (2013) applied a higher
order neural network (HONN) using limited reservoir data to predict the production of oil, gas
and water. Qiao et al (2017) used least square-SVM coupled with PSO to predict the production
of oil and gas. These studies although having shown promising results in short-term forecasting,
have had significant errors in forecasts of two or more years.
35
Aizenberg et al. (2016) applied a complex multilayer network with multi-value neurons
(MLMVN) was constructed to forecast oil production for 12 years into the future on 14 long
producing wells using their own production history for an oil field in Mexico. The forecasts
where then compared with actual production and the results had an average symmetric mean
absolute percentage error (SMAPE) of 17% with one 12-year forecast having an SMAPE of only
6.14%.
In terms of optimization, algorithms such as GA or PSO have been used mostly as a
complimentary tool to speed up the training process in ANNs and SVMs (Ahmadi et al., 2015).
However there have been numerous studies that employed these algorithms for optimizing field
development and operations. GAs were used to maximize NPV by optimizing the schedule and
location of horizontal wells with fixed orientations (Abukhamsin, 2009); GAs were also
employed in large-scale field development optimization involving the placement of several
hundred wells (Tanaka et al., 2018). PSO has been applied to geophysical inverse problems
(Fernández-Martínez et al., 2010) as well as determining the optimum well location and types
(Onwunalu and Durlofsky, 2010).
2.6 What is Missing in Literature?
There are many models that have been built to forecast production from horizontal oil and gas
wells of which many of them employ new and complex machine learning models. The overall
trend in these studies is that they do not sufficiently cover the broad spectrum of inputs that
affect production especially for the case of hydraulically fractured reservoirs. Many studies on
36
hydraulically fractured reservoirs train a network to link production to completion parameters
and top hole x,y coordinates; however, they miss the fundamental fact that geology is
heterogenous and the proper inputs, the entire geological profile that surround a 2 km long
horizontal wellbore needs to be taken into account. Also, horizontal wells are completed in
multiple stages (sometimes up to 100) and many studies take the average completion parameters
of the entire well bore. Taking the average is a huge oversimplification because each stage is
unique. Some stages are completed quickly, some take longer. Some stages only place partial
amounts of the proppant or fail to break the rock at all. The stages are also spaced far apart (60
meters or more) which means each stage has a unique surrounding geology leading to every
stage having extremely different fracture networks. Furthermore, many studies do not account
for the distance between producing wells and the interaction effects that occur if wells are
sharing a common drainage area.
To the author’s knowledge there are currently no studies that have attempted to link the
completion and geological parameters at a stage level (instead of averaging to a well level) along
with well spacing information to the production performance of horizontal wells. The research
documented in this thesis attempts to fill this gap.
37
Chapter 3: A New Neural Network Procedure to Generate Highly Accurate Synthetic Shear
Sonic Logs in Unconventional Reservoirs
3.1 Preface
This chapter has been published as an SPE paper 201453-MS after presenting at the SPE Annual
Technical Conference and Exhibition, October 26-29, 2020. https://doi.org/10.2118/201453-MS.
This manuscript is co-authored by Ian D. Gates.
38
3.2 Abstract
Shear sonic travel time (DTS), along with compressional sonic travel time and bulk density are
required in order to estimate rock mechanical properties which play an important role in fracture
propagation and the success of hydraulic fracture treatments in horizontal wells. DTS logs are
often missing from the log suite due to their costs and time to process. The following study
presents a machine learning procedure capable of generating highly accurate synthetic DTS
curves. A hybrid convolutional-recurrent neural network (c-RNN) was chosen in the
development of this procedure as it can learn sequential data which a traditional neural network
(ANN) cannot. The accuracy of the c-RNN was superior when compared to that of the ANN,
simple baselines and empirical correlations. This procedure is a cost effective and fast alternative
to running DTS logs and with further development, has the potential to be used for predicting
production performance from unconventional reservoirs.
39
3.3 Introduction
Mechanical rock properties such as the Young’s modulus and Poisson’s ratio are important to
understand the way fractures propagate within reservoir rocks during hydraulic fracturing.
Furthermore, the mechanical properties of the rocks in an unconventional reservoir are
anisotropic and heterogenous, which makes the production performance of a horizontal well
highly dependent upon its location and orientation within the reservoir. It remains unclear how
fractures propagate within these tight reservoirs especially in the context of the state-of-stress but
a better understanding of the mechanical properties can yield insights that enable the ability to
ultimately predict the production performance of each stage and cumulatively, of the well.
In typical practice, measuring mechanical properties is done through direct and indirect methods
(Maleki et al., 2014). Direct methods involve taking core samples from the reservoirs and
performing laboratory tests, for example, triaxial stress tests, to understand the stress-strain
behavior of the rock sample as well as the stress at which the rock fails. Due to the high costs
and difficulty of rock sample extraction, typically only a few core samples are retrieved from the
formation of interest. Also, laboratory tests are expensive and time consuming (Maleki et al.,
2014). Even when obtained, core data only provides point-value (discrete) information on the
formation of interest – the fraction of the reservoir sampled is typically under 1%. Discrete data
is not very useful when describing the entire formation since the mechanical properties of rock
vary greatly with depth and the loading conditions of the surrounding formations which can vary
areally due to variable thickness and densities of the formations and unconformities. A
continuous mechanical property measurement along the thickness of the formation is desired.
40
Fortunately, mechanical rock properties can be derived indirectly from a combination of three
sets of log measurements, specifically: bulk density (RHOB), compressional slowness (DTP),
and shear slowness (DTS) (Fjar et al., 2008). The dynamic Young’s modulus dynamic and
Poisson’s ratio can be derived from the compression and shear wave velocity (which are the
inverse of the DTP and DTS log measurements) along with the bulk density using the following
formulas:
𝐸𝑀𝐷𝑌𝑁 =𝜌𝑉𝑠
2(3𝑉𝑝2 − 4𝑉𝑠
2)
𝑉𝑝2 − 𝑉𝑠
2
ν𝐷𝑌𝑁 =𝑉𝑝
2 − 2𝑉𝑠2
2(𝑉𝑝2 − 𝑉𝑠
2)
Where EMDYN is the dynamic Young’s modulus (pascals); νDYN is the dynamic Poisson’s ratio;
Vp is the compression wave velocity (m/s); Vs is the shear wave velocity (m/s); ρ is bulk density
(kg/m3).
The problem is that shear sonic data is often missing from a well log suite due to its high cost
and length of time to acquire. Without log or core data, the only way to estimate the shear sonic
value is either through empirical correlations or statistical methods (Hadi and Nygaard, 2018).
Most empirical correlations attempt to express the relationship between the DTP and DTS
measurements obtained from the wells with DTS logs. Empirical correlations were the main way
to estimate DTS for many years with the more familiar works from Caroll et al. (1969), Castagna
et al. (1985), and Han et al. (1986). The difficulty is that although DTS is highly correlated to
DTP, multiple variables influence the DTS including pore pressure, fluid saturation, clay and
shale content, stress profiles and other factors (Barre, 2009). Empirical correlations are also
41
highly dependent upon the location and size of the study area, and result in poor estimates if
taken outside that area.
Figure 3.1: Plot of shear slowness (DTS) versus compressional slowness (DTP) measurements
for 14 wells in the Montney Formation.
It is easy to see the highly nonlinear, seemingly uncorrelated nature of the relationship which
makes predicting DTS difficult. Since it is impossible to know all of the causal factors
contributing to DTS, the better approach is to apply statistical methods. Machine learning
algorithms have capabilities to integrate subtleties between data sets more than simple regression
models. These algorithms work by learning patterns between input and output variables that are
too complex and subtle for regular statistics to capture. There have been multiple studies
applying various machine learning techniques to DTS prediction. Eskandari et al. (2004) used
artificial neural networks (ANN) and showed that they performed better than empirical
correlations. Rajabi et al. (2010) used genetic algorithms (GA) and fuzzy logic (FL) which were
able to capture the general shape of the log but did not perform well on localized variations.
Maleki et al. (2014) used both support vector regression (SVR) and ANN and found that
although SVR was a better predictor its accuracy was limited and was not a good replacement to
42
the true log. Al-Anazi and Gates (2015) used support vector regression (SVR) to predict
Poisson’s ratio and Young’s modulus with a fuzzy-based ranking algorithm to select the most
significant input variables and filter out dependency. Their results demonstrated that the learning
and predictive capabilities of SVR was similar or superior to that of a backpropagation neural
network depending on the control parameters of the SVR. There is no single algorithm that is
superior to others and several types should be used in a particular study; however, ANNs have
recently become the popular choice (Parapuram et al. 2018; Hadi and Nygaard, 2018). Recurrent
neural networks (RNNs) are of particular interest as they are useful for sequence data such as
logs as they retain a memory of previous patterns. RNNs have shown to overperform ANNs
(Zhang et al. 2018). Studies to date have been able to capture the general trend of the
relationship; however, they do not adequately capture smaller localized variations. These
localized variations are important since they can play a major role in the mechanical properties
which in turn can affect the way fractures propagate.
In the following, we present a procedure that uses a hybrid variation of the RNN to generate
synthetic DTS curves from DTP and RHOB logs and well deviation survey. The procedure is
applied to a set of wells in the Montney Formation in Alberta, Canada.
3.4 Study Area and Data Processing
3.4.1 Study Area and Structure Model
The study area is the same for all research chapters and is described in Chapter 1: introduction of
this thesis and shown in Figures 1.2 and 1.3. A three-dimensional (3D) structural model of the
43
study was constructed to get a better visual understanding of the reservoir and to serve as a
placeholder for data. Figure 3.2 shows the model along with the Montney and Belloy tops.
Figure 3.2: A 3D visualization of all wells in the study area. Red = horizontal, blue = deviated,
and black = vertical.
The geological model was constructed in the Petrel geological modelling package
(Schlumberger, 2018) using well information, deviation surveys, formation tops as well as logs
from public data sources. Public data requires quality checks which are performed on deviation
surveys, surface coordinates, surface elevation and well tops. It was found that most publicly
reported well top depths needed correction. This was done by using the gamma ray (GR) and
resistivity logs. The Montney formation top surface was generated by using ~400 well tops. Due
to the high number and density of penetrations, the Montney surface is believed to have
relatively low uncertainty. The Belloy Formation on the other hand only had 60 penetrations.
The Montney has a much lower variation in thickness as compared to the variation in true
vertical depth, so a thickness map should have more certainty than a Belloy surface generated
using only 60 penetrations. The thickness map was generated using Montney thickness data from
44
the 60 wells that penetrate the entire formation and the Belloy surface was generated by adding
the thickness map to the Montney surface map. In this way, the uncertainty of the Belloy surface
is low. The 3D map of the generated Montney and Belloy tops is shown in Figure 3.3.
Figure 3.3: 3D generated Montney and Belloy surfaces in Petrel. The vertical axis is 25x
exaggerated compared to the X and Y scales and represent the subsea depth.
Having a 3D model not only helps with visualization of the study area but also provides a means
of estimating the reservoir thickness for the 85% of wells that do not penetrate the entire
formation. The Montney Formation has a dip and varies in its true vertical depth, so a geological
layer or feature at location x1, y1 and a given depth z would not necessarily be present at the
same depth z at location x2, y2. The same layer is likely however to be present along the same
thickness interval, so this type of measurement is a better baseline for comparison than true
vertical depth.
3.4.2 Data Preparation
Estimating rock mechanical properties requires three sets of logs: RHOB, DTP, and DTS. The
majority of the 180 vertical and deviated wells have RHOB and DTS logs but only 14 (8% of the
45
wells) have all three sets of logs that covered >90% of the reservoir thickness. Figure 3.4 shows
all the vertical and deviated wells without DTS marked by black points and the wells with DTS
marked by a label. If accurate synthetic DTS logs could be generated for the remaining 166
vertical and deviated wells with no DTS, the certainty of a rock mechanical model could
potentially increase significantly.
Figure 3.4: Areal view of the study area generated in Petrel. Black points with no labels are wells
with no DTS logs, labeled wells have the DTS logs.
46
The following data was extracted for the 14 wells in the Montney Formation: deviation survey,
RHOB, DTP, and DTS logs. Initially, GR logs were also extracted, however through much
preliminary testing it was found that GR did not improve model accuracy and, in some cases,
even worsened the performance. Even after the GR log was converted to a volume of shale (Vsh)
log, it was still found to be unhelpful since the GR reaction for similar layers of shale varied
greatly from well to well.
Log measurements for each well have a specific resolution or measurement frequency that
ranges from 1 to 6 inches (2.5-15 cm). This caused some wells to have 6 times more
measurements than others for an interval of equal thickness. This is a problem since all wells
need to carry the same weight to have an unbiased analysis. To combat this discrepancy all logs
were converted to a resolution of 4,000 steps per 100% reservoir thickness, which is 0.025% per
step. The 4,000 step scale was chosen since it represented the average number of measurements
in the well logs and did not lower the resolution for the majority of the wells. Wells that did not
penetrate the entire Montney Formation had an estimated formation thickness which was
calculated using the top and bottom surfaces. As a result, every well had 4,000 measurements of
RHOB, DTP, and DTS from top to bottom. Each step also contained x and y coordinates
(constant for vertical wells). Deviated well coordinates for every step were calculated from the
deviation survey. Finally, the data was checked for quality and consistency, sections of the
formation that had missing values of one log were removed. Although not frequent, anomalies in
measurement (such as a sudden 40% spike in density) were also removed. This cleaning of data
reduced the total number of points per well; however, the step change of 0.025% thickness
47
remained the same leaving the experiment unbiased towards a certain well. Table 3.1
summarizes the number of data points for each of the 14 wells.
Table 3.1: Total number of data points in each well used for the study.
Well # of data points % thickness coverage
VT_02 3,913 98%
VT_10 3,543 89%
VT_18 3,999 100%
VT_26 3,574 89%
VT_29 3,999 100%
VT_42 3,520 88%
VT_49 3,988 100%
VT_69 3,845 96%
VT_108 3,904 98%
VT_132 4,000 100%
VT_137 3,946 99%
DV_16 3,952 99%
DV_19 3,372 84%
DV_28 3,999 100%
Total 53,554 96%
3.5 Experimental Setup and Types of Neural Network Algorithms
3.5.1 Experimental Setup
The synthetic DTS curve was generated by using the following five inputs: x coordinate, y
coordinate, depth measured in true vertical depth subsea (TVD subsea), RHOB and DTP for
every available point along the Montney thickness. Since there are only 14 wells in the data set,
the only suitable method to determine accuracy is the “leave-one-out” cross-validation method.
In this method, 13 wells are used as training data with one well to validate (blind), the
48
experiment is then run a total of 14 times (one for each blind well) and the results of all 14
experiments are examined. This “blind” well is not truly blind as its performance can be
measured. However, it is important that an individual blind well does not change the way the
tests are performed. This means the network structure and training procedure must be fixed
throughout the evaluation. The network can be tuned after all 14 experiments are completed to
see if an improvement is made. As the network makes 4,000-point sequence predictions, multiple
metrics are required to understand the accuracy of the prediction. For this study we compare four
types of accuracy metrics:
1. MAPE – Mean Absolute Percentage Error,
2. MaxPE – Maximum Percentage Error,
3. amount of points with >3% error, and
4. amount of points with >5% error.
MAPE is an indicator of the network performance on all points in the sequence. It does not
reveal how much of the sequence has poor accuracy, or what the maximum error is. MaxPE
shows the maximum error in the entire predicted sequence, but does not give insight into the
average performance (Zhang et al. 2015). The amount of points greater than (3 or 5%) is a metric
between MAPE and MaxPE and gives insight into what fraction of the predicted sequence is
reliable. These metrics although helpful, are not very intuitive and the best way to compare
algorithm performance is by plotting the entire synthetic log generated by the algorithm overtop
the measured log. Visually comparing synthetic logs generated by different algorithms can more
49
easily point to how well each algorithm predicts small variations and which log sections are
predicted better than others.
Consistency is also important, if network performance differs too much for the same blind well
experiment, there is a problem and the network cannot be trusted for true blind wells. To
measure consistency, each of the 14 blind well experiments were reset and trained three times,
without modifying any network parameters or training procedures. Metrics including the
maximum minus minimum error and the standard deviation of errors of the three runs were
measured. Running multiple experiments on each blind well is also a good way to average the
results by removing really good or really bad results.
3.5.2 Comparisons
To test if an algorithm has statistical significance, it must be compared to a baseline such as:
1. Taking the average DTS/DTP ratio of training wells and applying it to the blind well, or
2. Taking the average DTS minus DTP value of training wells and applying it to the blind
well.
The networks are also compared to the DTS estimates of two popular empirical correlations:
1. Castagna et al. (1985) for shales:
Vs (km/s) = 0.77 Vp – 0.8674
2. Han et al. (1986) for shaly sandstones:
Vs (km/s) = 0.85 Vp – 1.14
50
3.5.3 Networks used in the experiments
Two types of networks were chosen to run experiments: a simple feedforward network (ANN)
and c-RNN. The networks were programmed in Python using the keras library (Chollet, 2015).
The ANN was chosen as it is the simplest type of network and a good baseline to compare to the
more complicated c-RNN. The c-RNN hybrid network was chosen because it combines the
speed and ability to process large amounts of data of a convolutional network with the sequence
processing ability of a recurrent network. Traditional RNNs are only able to hold memory a few
hundred steps and since each of the wells has 4,000 steps in the input sequence, a standalone
RNN would not be able to predict with great accuracy. Convolutional networks are able to
convert long sequences into shorter ones of higher-level features, which gives a c-RNN hybrid
the ability to process sequences with thousands of steps (Chollet, 2017). For both the ANN and
the c-RNN hybrid the activation function was chosen to be the mean absolute error (MAE), this
activation function was found through trial and error and was chosen because it was able to train
the network faster other activations function such as the root mean square error (RMSE) or the
MAPE. The architecture of the networks is shown in Figures 3.5 and 3.6 is a visual
representation of the input and output data format of the c-RNN.
Figure 3.5: Architecture of the ANN (A) and c-RNN (B) used in the study.
51
Figure 3.6: Format of input and output data of the c-RNN.
3.5.4 Overfitting
Deep neural networks are good at learning complicated relationships between inputs and outputs;
however, if trained too long the networks start to confuse noise with signals and start to overfit to
the training set which results in lower generalization capabilities (Srivatava et al. 2014). This is
especially problematic when the amount of training data is limited as in the case in this study.
Since the aim of this study is to generate synthetic DTS for wells with no actual DTS there
should be a way to determine the stopping point of the training without looking at blind well
performance. Most machine learning experiments are run with three sets of data: training,
52
validation and test. The model is trained on the training set, the validation set is used to monitor
overfitting and the test set is then run after network has finished training. The typical approach is
to stop the training at the point where validation error is at a minimum. This approach is good
when there are at least a few hundred samples available; this study only has 14 wells in total.
Running multiple experiments showed that the point at which the validation error was at a
minimum was inconsistent between different blind wells and in repeat trials of the same blind
well; this implied that a way to limit overfitting was needed. To limit overfitting, we maximized
the batch size and applied dropout.
Figure 3.7 plots how the validation error evolves with different batch sizes (as a percent of the
maximum batch size) for the VT_42 blind well test. The plot reveals that fluctuations in blind
error become less aggressive and overfitting becomes less of an issue with larger batch sizes. For
these reasons it was decided to run all experiments in full batch mode.
Figure 3.7: Effect of batch size on the evolution of the validation error for blind well VT_42.
53
3.5.5 Stopping procedure
3.5.5.1 ANN
The ANN is meant to serve as a baseline to compare the c-RNN too. If the c-RNN performs
better than the best possible ANN results than the complexity and longer run time of the c-RNN
are justifiable. To reach the best possible result of the ANN a cheat run was performed for every
blind well. In the cheat run, the blind well error was observed during training and the network
was forced to stop when the blind error value was at its lowest. The point at which the blind error
is minimum was unique for every blind well and the only way to find it was to observe the blind
error rate at every epoch. Each blind well test was reset and run multiple times and the run with
the lowest blind error was used to generate a synthetic DTS log. This type of procedure is only
meant to test the maximum potential of the network and is not applicable when generating
synthetic DTS for wells with no DTS since the error on these wells cannot be observed.
3.5.5.2 c-RNN
54
Figure 3.8: Training and validation error for two blind well tests.
Figure 3.8 shows how the training and validation error evolves over 1,000 training epochs for
two of the blind well experiments. “Tremors” in both the training set and blind well error start to
occur at fairly regular intervals after ~400 epochs and the error rate seems to stabilize at a very
low constant error between them. These tremors were found to be universal across all wells, as
can be seen in Figure 3.9.
55
Figure 3.9: Validation error for all blind well tests, results are split into two graphs for clarity.
A long run was performed on one of the wells to see if this trend continued. Figure 3.10 shows
the train and test error for 20,000 iterations of data.
Figure 3.10: 20,000 iterations of the blind well DV_28 experiment.
56
Overfitting seemed to have stopped and the blind well error is more or less constant between
tremors. After about 2,000 iterations the tremors in test data get very large but still converge
back to a low and stable error rate. The tremors in the blind well point to a possibility for
improvement in accuracy if a way to stop the algorithm at the low point of the blind tremor is
found.
Since the validation error does not exist when generating synthetic DTS curves for wells with no
DTS, one can only use the training error to determine when to stop the network. From the figures
it is seen that the tremors in both the training set and blind well occur nearly at the same time
(validation tremor starts a bit earlier and ends a bit later than the training tremor). Figure 3.11
presents a zoom into one of the tremors.
Figure 3.11: A zoomed in plot showing the training and blind well error tremor.
57
Since the training and validation tremors where found to coincide with one another, a simple
empirical procedure was developed to determine the stopping criteria for the c-RNN:
A. Run network for 1,000 epochs (when network has stopped improving results).
B. If training error is stable and far enough away from the previous tremor, stop training.
C. If training error is experiencing a tremor or very close to previous tremor, continue
running network for 50-100 more epochs (but before next tremor occurs) until you reach
a state in step B, stop training.
D. If another tremor occurs, repeat C until you reach a state of B.
Finally, to see how close this procedure comes to the maximum potential of this network, a cheat
run was performed for every blind well. Like the ANN cheat run, the blind well error was
observed during training and the network was stopped at the lowest blind value.
3.5.6 Summary of Procedure
Table 3.2 presents the architecture and hyperparameters used for the c-RNN network used in this
study. Figure 3.12 shows the procedure required to generate a trained version of the synthetic
DTS tool presented in this study.
Table 3.2: Starting hyperparameters for the c-RNN developed in this study.
Layer Input Conv Conv
Max
Pooling Conv GRU GRU Output
Number of
nodes 5 32 32 - 32 100 100 1
Activation
Function -
rectified
linear unit rectified
linear unit - rectified
linear unit rectified
linear unit rectified
linear unit -
Recurrent
Dropout - - - - - 0.5 0.5 -
58
Figure 3.12: General procedure for training the synthetic DTS tool that can be applied to any
formation.
Generate top and bottom surfaces for the formation of interest
Load all pertinent data into Petrel (well tops, logs and deviation surveys)
Extract RHOB, DTP and DTS logs as well as deviation surveys in formation of interest for
all wells with DTS logs
Convert well logs to a set number of points per 100% formation thickness
Select 1 DTS well as validation set and remaining as training set
Train c-RNN network on training set using recommended starting architecture and
hyperparameters listed in Table 2
Retrain network with previous hyperparameters on different train/validation sets to ensure
network is generalizing to other wells (if generalization poor, re-tune hyperparameters)
Save network hyperparameters
Run network for 10,000 epochs on several validation wells to confirm overfitting has been
removed
Tune network hyperparameters until best validation accuracy is achieved
Take note at which epoch validation error is stable for most validation wells; this is the
stopping point (a stopping point of 1,000 epochs was chosen for this study)
59
Figure 3.13 shows how to use the trained tool to generate synthetic DTS curves. The training and
generating procedures are not limited to the Montney and can be applied to any formation of
interest.
Figure 3.13: Process for using the training tool to generate synthetic DTS curves.
3.6 Results and Discussion
Tables 3.3a to 3.3f summarize the results of the leave-one-out experiments. Tables 3.3a to 3.3d
compare the four different metrics for the two empirical correlations, the two simple baselines,
the best possible results achieved with the ANN cheat run, the average of the three c-RNN runs
along with the best possible result achieved with the c-RNN cheat run. Tables 3.3e and 3.3f show
the consistency of the three c-RNN runs. These metrics are the difference between maximum and
minimum error values and the standard deviation of the three runs for each blind well. The
MAPE and MaxPE (Tables 3.3a and 3.3b) are not the best metrics as they do not describe the
amount of local errors, but they do provide more information about the results. The more
revealing metric is the fraction of points >3% error (Table 3.3c) and the visual comparison.
60
Table 3.3: Results of the study comparing the performance of the various methods of generating
synthetic DTS curves.
Table 3.3a - MAPE
well
Castagna et
al. Han et al. DTS/DTP DTS-DTP ANN Cheat
Ave of 3
c-RNN Runs c-RNN Cheat
VT_02 2.80% 2.19% 1.24% 1.03% 0.91% 1.00% 0.83%
VT_10 2.31% 3.17% 1.61% 1.53% 1.88% 1.76% 1.27%
VT_18 1.79% 3.47% 1.35% 0.93% 0.62% 0.66% 0.50%
VT_26 3.39% 2.55% 1.80% 2.29% 1.12% 1.02% 0.83%
VT_29 3.80% 1.89% 1.87% 2.15% 1.16% 1.27% 1.09%
VT_42 7.05% 3.27% 4.07% 3.11% 1.17% 1.02% 0.85%
VT_49 1.53% 3.95% 1.66% 1.01% 1.81% 1.40% 0.66%
VT_69 6.41% 2.84% 3.29% 2.11% 1.28% 1.20% 0.91%
VT_108 2.05% 3.01% 1.43% 1.31% 0.92% 0.99% 0.82%
VT_132 2.73% 2.73% 1.36% 1.37% 1.01% 0.95% 0.75%
VT_137 4.59% 2.93% 2.17% 1.37% 1.26% 1.99% 1.31%
DV_16 1.60% 4.11% 2.17% 1.75% 0.74% 1.01% 0.75%
DV_19 2.57% 4.92% 2.95% 2.32% 1.59% 1.27% 1.18%
DV_28 2.67% 3.12% 1.78% 2.15% 1.62% 1.52% 0.85%
Total 3.21% 3.14% 2.03% 1.73% 1.23% 1.22% 0.89%
Table 3.3b - MaxPE
well
Castagna et
al. Han et al. DTS/DTP DTS-DTP ANN Cheat
Ave of 3
c-RNN Runs c-RNN Cheat
VT_02 8.37% 9.50% 4.96% 4.06% 4.36% 4.18% 3.52%
VT_10 10.44% 14.00% 12.90% 13.32% 14.63% 14.00% 12.98%
VT_18 6.85% 10.93% 5.87% 5.71% 4.72% 4.44% 3.82%
VT_26 14.76% 11.14% 8.45% 6.15% 5.09% 5.32% 5.52%
VT_29 11.42% 7.70% 7.03% 6.59% 5.11% 4.87% 4.12%
VT_42 16.84% 13.59% 9.34% 7.61% 5.66% 6.07% 5.18%
VT_49 6.02% 10.54% 6.31% 5.50% 4.79% 7.18% 4.32%
VT_69 15.84% 12.57% 8.54% 6.31% 3.87% 4.43% 3.73%
VT_108 6.79% 11.06% 7.10% 5.93% 3.97% 4.03% 3.77%
VT_132 12.15% 11.89% 6.65% 8.88% 6.07% 7.08% 6.75%
VT_137 14.48% 11.36% 7.13% 7.47% 6.15% 5.98% 6.74%
DV_16 8.73% 13.20% 6.73% 5.88% 5.71% 5.05% 5.51%
DV_19 10.59% 14.82% 10.53% 7.53% 7.32% 6.32% 5.67%
DV_28 11.49% 14.23% 8.64% 9.65% 10.07% 10.36% 11.32%
Total 16.84% 14.82% 12.90% 13.32% 14.63% 14.00% 12.98%
61
Table 3.3c – Percentage of points above 3% error
well
Castagna et
al. Han et al. DTS/DTP DTS-DTP ANN Cheat
Ave of 3
c-RNN Runs c-RNN Cheat
VT_02 41.53% 27.17% 5.39% 2.12% 1.97% 1.92% 0.43%
VT_10 32.30% 50.65% 10.33% 9.37% 19.00% 15.50% 8.58%
VT_18 14.60% 53.84% 4.25% 1.18% 0.15% 0.18% 0.13%
VT_26 47.01% 34.42% 18.33% 25.63% 3.19% 2.63% 1.15%
VT_29 61.24% 19.55% 19.08% 25.81% 4.80% 7.87% 4.20%
VT_42 94.29% 42.67% 69.03% 56.65% 3.55% 4.01% 1.99%
VT_49 13.59% 65.92% 11.69% 1.71% 10.88% 2.96% 0.68%
VT_69 92.09% 32.35% 49.67% 18.99% 3.07% 3.34% 0.60%
VT_108 23.95% 44.54% 8.97% 5.84% 2.38% 1.71% 0.54%
VT_132 35.08% 43.78% 6.70% 7.08% 0.78% 0.97% 1.20%
VT_137 62.19% 38.55% 28.08% 5.22% 3.57% 24.84% 5.25%
DV_16 13.36% 68.09% 21.18% 16.37% 0.89% 3.13% 1.01%
DV_19 35.29% 67.53% 42.41% 28.32% 13.14% 5.13% 5.46%
DV_28 31.48% 48.66% 13.05% 17.75% 8.35% 5.50% 2.10%
Total 42.30% 45.42% 21.45% 15.37% 5.26% 5.66% 2.31%
Table 3.3d – Percentage of points above 5% error
well
Castagna et
al. Han et al. DTS/DTP DTS-DTP ANN Cheat
Ave of 3
c-RNN Runs c-RNN Cheat
VT_02 14.16% 5.49% 0.00% 0.00% 0.00% 0.00% 0.00%
VT_10 8.98% 16.23% 3.81% 3.13% 5.51% 4.64% 3.11%
VT_18 2.13% 21.71% 0.15% 0.10% 0.00% 0.01% 0.00%
VT_26 20.03% 9.26% 5.65% 1.71% 0.03% 0.09% 0.08%
VT_29 25.81% 3.85% 4.95% 4.93% 0.08% 0.00% 0.00%
VT_42 75.28% 21.73% 26.90% 5.40% 0.17% 0.49% 0.06%
VT_49 0.85% 25.53% 0.53% 0.13% 0.00% 0.05% 0.00%
VT_69 65.80% 15.14% 16.33% 0.52% 0.00% 0.00% 0.00%
VT_108 2.87% 19.19% 0.38% 0.41% 0.00% 0.00% 0.00%
VT_132 14.03% 10.55% 0.25% 0.68% 0.20% 0.30% 0.60%
VT_137 39.38% 17.82% 6.06% 0.23% 0.10% 0.74% 0.15%
DV_16 1.77% 32.82% 0.63% 0.51% 0.25% 0.03% 0.10%
DV_19 12.51% 42.26% 16.96% 4.51% 1.99% 0.34% 0.33%
DV_28 16.35% 16.33% 0.90% 3.20% 1.15% 0.52% 0.53%
Total 21.09% 18.22% 5.67% 1.76% 0.63% 0.49% 0.34%
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Table 3.3e – Maximum minus minimum error of the three c-RNN runs
well MAPE MaxPE
Percentage of
points > 3% error
Percentage of
points > 5% error
VT_02 0.29% 1.24% 2.58% 0.00%
VT_10 0.78% 1.36% 11.94% 0.62%
VT_18 0.18% 1.07% 0.08% 0.03%
VT_26 0.14% 0.70% 0.39% 0.11%
VT_29 0.07% 0.32% 0.95% 0.00%
VT_42 0.42% 2.14% 4.89% 1.25%
VT_49 0.57% 4.67% 3.06% 0.05%
VT_69 0.50% 1.28% 5.28% 0.00%
VT_108 0.03% 0.55% 0.56% 0.00%
VT_132 0.52% 0.89% 0.08% 0.03%
VT_137 0.29% 0.21% 8.64% 0.30%
DV_16 0.32% 0.76% 1.49% 0.05%
DV_19 0.06% 0.84% 0.50% 0.06%
DV_28 0.16% 0.49% 1.20% 0.03%
Average 0.31% 1.18% 2.97% 0.18%
Table 3.3f – Standard deviation of errors of the three c-RNN runs
well MAPE MaxPE
Percentage of
points > 3% error
Percentage of
points > 5% error
VT_02 0.14% 0.68% 1.32% 0.00%
VT_10 0.41% 0.76% 6.39% 0.36%
VT_18 0.10% 0.54% 0.04% 0.01%
VT_26 0.07% 0.35% 0.22% 0.06%
VT_29 0.04% 0.18% 0.50% 0.00%
VT_42 0.22% 1.11% 2.55% 0.72%
VT_49 0.33% 2.34% 1.53% 0.03%
VT_69 0.25% 0.67% 2.65% 0.00%
VT_108 0.01% 0.30% 0.30% 0.00%
VT_132 0.26% 0.46% 0.04% 0.01%
VT_137 0.15% 0.11% 4.42% 0.18%
DV_16 0.16% 0.38% 0.78% 0.03%
DV_19 0.03% 0.48% 0.26% 0.03%
DV_28 0.08% 0.28% 0.61% 0.01%
Average 0.16% 0.62% 1.54% 0.10%
63
The results show that the empirical correlations did not work for this study. The likely reason for
this is because the empirical correlations were developed from a very broad (global) set of
reservoirs and do not translate well to specific (local) reservoirs well. The simple baselines
performed about twice as well as the empirical formulas. This is no surprise as they were derived
from the average of 13 training wells, making them very local and only applicable to this
particular study area. Both neural networks show statistical significance as they outperformed the
simple baselines and the empirical correlations.
The metrics show that the c-RNN performance is similar that of the ANN cheat run; however, a
visual comparison reveals that the c-RNN has much better predictive capabilities. Figures 3.14,
3.15 and 3.16 compare the ANN cheat and average c-RNN synthetic logs for one of the worst
wells (VT_10), the best well (VT_18) and the most central well VT_42 respectively. The visual
comparison shows how the average c-RNN run can predict the small variations much better than
the best result achieved by the cheat ANN run.
64
Figure 3.14: Synthetic logs generated by the cheat ANN (left) and the average of three c-RNN
(right) runs compared to the true logs for one of the worst blind wells – VT_10.
MAPE = 1.76% MAPE = 1.88%
65
Figure 3.15: Synthetic logs generated by the cheat ANN (left) and the average of three c-RNN
(right) runs compared to the true logs for the best blind well – VT_18.
MAPE = 0.62% MAPE = 0.66%
66
Figure 3.16: Synthetic logs generated by the cheat ANN (left) and the average of three c-RNN
(right) runs compared to the true logs for the most important well - VT_42.
Depth of majority of
nearby horizontal wells
MAPE = 1.17% MAPE = 1.02%
67
Wells VT_10 and VT_137 had the highest error rate in the c-RNN runs. As shown in Figure 3.4
these wells are located near the edge of the study area where not many wells have been drilled,
so their accuracy is not of great importance for the purpose of this study. Most of the vertical and
horizontal wells are drilled near the center of the study area closest to well VT_42 and four other
nearby wells: VT_26, VT_29, VT_69 and VT_108. It is important to focus on these wells as they
dictate the success of the network to generate synthetic curves for the majority of wells with no
DTS. From the results, VT_42 had a MAPE of only 1% and only ~7% of the points had an error
>3% error, the other four wells also performed fairly well with an MAPE close to 1%. Figures
3.17 and 3.18 show the synthetic curves generated by the c-RNN compared to the true DTS
curves for the more centrally located wells VT_26, VT_29, VT_69 and VT_108. The cheat run
of the c-RNN had the best performance. This suggests potential for improvement in the stopping
criteria and design of the c-RNN network.
68
Figure 3.17: Synthetic logs generated by the c-RNN for wells VT_26 and VT_29 compared to
the true logs.
MAPE = 1.27% MAPE = 1.02%
69
Figure 3.18: Synthetic logs generated by the c-RNN for wells VT_69 and VT_108 compared to
the true logs.
MAPE = 1.20% MAPE = 0.99%
70
Figure 3.19 shows how the synthetic curves generated for blind well VT_18 improve in accuracy
with the number of training iterations. The results show that the broad trend of the DTS log is
captured early in the network training and more detailed variations are captured with more
training iterations.
Epoch 1:
Epoch 10:
71
Epoch 40:
Epoch 70:
Epoch 120:
72
Epoch 380:
Figure 3.19: Sequence of synthetic well logs generated for well VT_18 at different number of
epochs. Y-axis is DTS (µs/ft) and x-axis is the thickness steps from the top of the formation.
3.7 Conclusions
A procedure to generate highly accurate synthetic DTS curves has been developed. This
procedure can act as a cost effective and fast alternative to running actual DTS logs. This does
come with the condition that the area of interest is small enough and that there are enough wells
with true DTS measurements available. Generation of a synthetic DTS measurement at a given
point along the reservoir thickness only required five inputs: x and y coordinates, depth subsea,
RHOB and DTP. The GR log was tested and was found to not improve the performance of the
network. As shown by the cheat run, the procedure does still have room for improvement. Some
potential reasons for the error in the synthetic DTS curves are:
• 13 training wells are not enough to learn every possible signal.
• Some signals are caused by variables not captured in the study (ie. fractures, stress
profiles, pore fluids, high porosity, shale, thin beds, gas presents, high total organic
content (TOC)).
73
• DTS measurement error is caused by the tool itself or poor borehole conditions.
Although the network did perform poorly on two of the blind well tests (VT_137 and VT_10) it
is more important to look at the performance of wells located closer to the majority of vertical
and horizontal wells. As there is no real way to measure synthetic DTS curve accuracy for wells
with no DTS one can only rely on the results of the network for nearby wells. Most wells are
located in the center of the study area and most of the horizontal wells reside in the top 25%
thickness and the network has shown to be able to generate fairly accurate curves for that region
of the study. The c-RNN has also shown to have fairly consistent results between the runs, but it
is still suggested to take the average of three runs when generating synthetic curves for wells
with no DTS. This procedure is not limited to the Montney Formation. As long as the area is
small enough and contains enough wells with DTS logs it could be applied to any other
formation. Even in this small window of the Montney, the 250 existing horizontal wells only
cover a small fraction of the thick reservoir and there is remaining opportunity for further
development.
Having a predictive procedure like this could potentially give the user a way to optimize where
to drill and how to complete a horizontal well before it is actually drilled. If the number of wells
per area is large enough the procedure could be applied to any other formation.
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Chapter 4: A Convolutional-Recurrent Neural Network Model for Predicting Multi-Stage
Horizontal Well Production
4.1 Preface
This Chapter has been published as a manuscript in the Journal of Petroleum Science &
Engineering on November 21, 2020. This article is co-authored by Ian D. Gates.
75
4.2 Abstract
In this study, a hybrid convolutional-recurrent neural network (c-RNN) is evaluated for making
predictions of the five-year cumulative production profiles in multistage hydraulically fractured
wells. The model was trained by using a combination of completion parameters, rock mechanical
properties, and well spacing and completion order for each stage of 74 wells in the Montney
Formation in British Columbia. The prediction accuracy of the various combinations was
measured by using the mean average percent error (MAPE) generated through the leave-one-out
method. The best combination of inputs was found to be the rock mechanical properties
surrounding each perforation cluster, the proppant amount used for every stage, and the spacing
and completion order of neighboring wells. The novelty of this study is that the input variables
used are at the stage level rather than the average of the entire well. The accuracy of the model
was found to increase exponentially as the production of multiple wells was aggregated. The
approach yields insights for planning new well drills in fields with existing development since it
provides the ability to run multiple field development scenarios without having to spend capital.
76
4.3 Introduction
The post hydraulic fracture production performance of a horizontal well is influenced by a
multitude of variables, in this study we identify three major categories:
3. Geological properties of the formation surrounding the perforations,
4. Completion design of each stage, and
5. Well spacing and completion order.
The geological properties surrounding the perforations in a horizontal well have arguably the
greatest influence on the production performance. Geological properties include the volume of
hydrocarbons in place, the permeability, the natural fracture geology, in situ stresses, and rock
mechanical properties. The selection of the right place to drill a well is critical to ensure an
ongoing expanding commercial operation.
A model that predicts the production profile of a well before it is drilled with reasonable
accuracy would help to ensure a commercial operation allowing an operator to run multiple
scenarios of well placements and completion types and give the ability to optimize the
development of the field to their needs. Such a model could only predict the production
performance given a set of input parameters at each perforation cluster along the wellbore; it
would be difficult to predict how much each individual cluster parameter contributes to the
output. This is partly because the production in a horizontal wellbore is measured as a sum of the
production coming into each perforation cluster. The wells in our study had between 5 and 47
clusters that were spaced from 58 to 300 m apart and the completion design of each stage in the
77
same well was not identical. This results in each cluster having a unique post stimulation
fracture network making each cluster contribute non-equal amounts to overall production.
Furthermore, fracture stimulation is far from a perfect process: sometimes the reservoir never
reaches breakdown pressure and/or a plug breaks down and the fluid meant for one stage goes
into another. In other cases, the injected fluid may only flow into one thick natural fracture
thereby not really increasing the contact surface area. If there are multiple clusters in one stage,
there is no guarantee that the total stage fluid would divide itself evenly into each cluster and
create identical copies of fracture networks. This non-uniformity in production is well known,
He et al. (2017) and Al-Shamma et al. (2014) showed that up to 30% of fracture clusters in a
horizontal wellbore are non-productive.
The typical way to predict production from hydraulically fractured wells is to use numerical
reservoir simulators. Numerical simulation develops a dynamic model using available static and
dynamic data. The dynamic model is based on a static geological model which is built by
upscaling interpreted data from vertical well logs. The flow model is developed using the well
known engineering fluid flow principles followed by the history matching process. Fracture
propagation is modeled in various 2D or 3D geometries: some common types include the
Kristianovich-Geertsma-de Klerk (KGD) and the Perkins-Kern-Nordgren (PKN) geometry as
well as the pseudo-three-dimensional (P3D) model. Traditional numerical simulation to predict
production is known as a bottom-up approach (Mohaghegh, 2017). This is because these models
assume that all of the reservoirs complexities and fracture networks are known. Typically, the
geological models are upscaled from single wells and have large uncertainty (Mohaghegh, 2011).
Furthermore, the models that describe the morphology of fractures are grossly oversimplified:
78
real hydraulic fracture networks rarely resemble perfect ellipsoids and are impossible to perfectly
model. Due to these assumptions, numerical simulators are usually poor estimators of actual
production performance.
An alternative approach is to use an empirical, top-down approach using machine learning
algorithms. In this approach, minimal assumptions are made about the structure of the reservoir
or how fluid flows through it. Rather the input variables of each stage are presented to a machine
learning algorithm that attempts to link them to the production. The purpose of this study is to
develop a model that can predict, with reasonable accuracy the five-year production
performance, post hydraulic fracture of horizontal wells that targets a field with existing
development. The model utilizes a convolutional-recurrent neural network (c-RNN) hybrid to
link the input variables of each stage to a well’s production performance. The input variables are
highly detailed and include the rock mechanical properties surrounding each perforation interval,
the type and size of stimulation of each stage along with the spacing, and completion order of
neighboring wells. Different combinations of inputs are tested to find which combination leads to
the best predictions. The study focuses on 74 horizontal wells located in the Montney Formation
in Alberta, Canada.
4.4 Input Data Preparation
The study area is the same for all research chapters and is described in Chapter 1: introduction of
this thesis and shown in Figures 1.2 and 1.3. To make sure that matrix properties are similar in
the wells, the study focuses only on the top layer of the Montney, Figure 4.1 shows an areal
extent of the 74 wells in the study area.
79
Figure 4.1: Areal extent of the 74 horizontal wells used in the study.
For this study we gathered the geological properties and completion variables of each stage and
perforation interval for all 74 wells. We also gathered the well spacing and completion order.
Table 4.1 shows the stage input variables that were used in the experiments. The five-year
production profile of the wells was used to train the network.
80
Table 4.1: The stage variables that were used as inputs in the experiments.
Rock mechanical properties Completion Well spacing and completion order
RHOBnear Type of fluid Length of unbounded time
DTSnear Total proppant placed Unbounded gas production
DTPnear Total fluid injected Length of time each offset well
produced before well is drilled
RHOBfar Total CO2 injected Volume of gas each offset well
produced before well is drilled
DTSfar Distance between
perforation clusters
Percentage of length that each offset
well covers this well
DTPfar Average perpendicular distance from
each offset well to this well
The number of clusters per stage was typically only one. However, some of the newer wells had
up to three clusters per stage. The clusters in a stage share the total proppant and fluid amounts
of the stage. This makes it difficult to allocate the amount of proppant and fluid entering each
cluster. To account for this, the rock mechanical variables of those stages were taken as the
average of all the clusters in that stage.
4.4.1 Geological Properties
Both the matrix and the natural fracture network contribute to the overall geological properties.
As previously mentioned, the matrix properties are expected to be similar between wells.
Fracture networks which are based on the rock mechanics would be expected be vastly different
not only between wells but between perforation clusters along the wellbore. The rock mechanical
properties were used to describe the geology surrounding each perforation cluster. Rock
mechanics are a function of the DTS, DTP and RHOB logs. As shown in Figure 3.4, only 14/180
of the vertical and deviated wells in the study area had DTS measurements. In Chapter 3 a
procedure was described that generates accurate synthetic shear sonic logs (with an average
MAPE of 1.2%). For this study, this procedure was used to generate DTS logs for 166 of the
81
vertical and deviated wells that were missing one. The Petrel software (Schlumberger, 2019) was
used to upscale and interpolate each of the three logs from all 180 wells throughout the
formation, generating a 3D model of each of the three logs enabling an estimation of the DTS,
DTP and RHOB log profiles along the horizontal wellbores. Two types of profiles were built: the
near and the far. The near profiles were used to estimate the rock mechanical properties at the
wellbore; they would be expected to directly influence how the fractures start to propagate. The
far profiles shown were built using 50 m3 cubes that follow the wellbore profile. Each cube
resembled the average of the properties within that cube. The cubes were an attempt to describe
the how hydraulic fractures would propagate through the cube after they were initiated. The
measured depth (MD) of each cluster was used to get the corresponding rock mechanics
surrounding it. Each perforation cluster in each well had 6 rock mechanical values: (DTS, DTP,
RHOB)near and (DTS, DTP, RHOB)far.
4.4.2 Completion Variables
Table 4.2: Completion variables
Completion Variable Range per stage
Service company performing the stimulation Numerous companies
Type of completion Sliding sleeve or plug and perf
Gun diameter 73 mm – 86 mm
Charge size 15 - 31
Number of perforations per cluster 11 - 42
Distance between successful stages 27 m – 875 m
Amount of acid used in spearhead stage 0 m3 – 9 m3
Fluid type slickwater or crosslinked gel
Size of pad stage 1 m3 – 138m3
Amount of energizer (CO2) 20 m3 - 560 m3
Proppant concentration 25 – 1,920 kg/m3
82
Proppant size and type 50/40, 30/50, 20/40 mesh
Total proppant placed 0 tonnes – 300 tonnes
Total proppant inejcted 10 m3– 1400 m3
Size of flush stage 0.5 m3 – 98 m3
Amount of crosslinked gel 0 m3 – 8 m3
Flowrate of each stage 1 m3/min - 13 m3/min
Pressure of each stage 5 – 75 MPa
All of the completion variables that are listed in Table 4.2 were gathered for each stage of the 74
horizontal wells in the study using publicly available completion reports. Not every well had all
these variables publicly available. From the various stage variables gathered, to limit the number
of variables, the experiments were conducted with the following variables: the type of fluid, total
proppant placed, total fluid injected, total CO2 injected, and the distance between perforation
clusters. These variables were chosen since they were available at every well.
The 74 horizontal wells in the study were completed between 2006 and 2017, the amount of
stages per well ranged from 5 to 31. In total there was 943 attempted stages for all 74 wells.
Some of the stages failed due to pump problems, screen off or the breakdown pressure never
being reached. There were a total of 23 (about 2%) failed stages and all of the failed stages
resulted in minimal amounts of proppant entering the formation (maximum 3 tonnes). For the
purposes of this study the failed stages were ignored, thus the total amount of stages used was
920. Each successful stage has completion variables as well as rock mechanical properties linked
to it.
83
4.4.3 Well spacing and completion order
Well spacing and completion order were considered at a well level not a stage level. Because of
this, the input values representing spacing and completion order for the well would be equal
every stage in that well. The following inputs were gathered for each well:
a) The length of time the well produced unbounded;
b) The volume of gas the well produced unbounded;
c) The length of time that each offset well produced before this well began production
(could be positive or negative depending on the order);
d) The volume of gas that each offset well produced before this well began production;
e) The percentage of length that each offset well covers this well;
f) The average perpendicular distance from each offset well to this well.
Each well in the study could have up to three offsetting wells (one on one side and two wells
sharing a portion of the length of another). The reason that (c) above could be positive or
negative is because the number of offsets each well has during field development is not constant,
a negative value in (c) means that this well was drilled before the offset was drilled. This is
important to account for as future offsetting wells may negatively impact the production of the
current well. If we use the model to predict the production performance of a new well,
accounting for when a new offset would be drilled beside this well would require some
forecasting; however, this decision is fully controlled by the operator and for all of the wells in
this study, the timing is already known. Having the ability to tell the network when a future
offset well would be drilled would enable the model to run various sensitivities.
84
4.4.4 Production Data
Predicting the gas production profile is the focus of this study. Gas production data, along with
the operational hours were gathered from the public database on a monthly basis for each well
from the start of production to January 2020. The 74 wells in this study produced mainly dry gas,
condensate production was rare and only reported in a few wells for a small portion of their
production history. The condensate production made up only 0.01% of the total barrel of oil
equivalent (BOE) production of the 74 wells and due to this the condensate production was
ignored for this study and all wells were assumed to produce dry gas.
The amount of gas that a well produces in a month is controlled by the reservoir and operating
conditions. Reservoirs conditions behave in a somewhat predictable manner, but well operation
is human driven which makes it impossible to predict. For example, most of the wells in the
study had rate a restriction between 5,000 and 8,000 Mscf/day and most of the wells did not
produce 100% percent of the time for every single month. In order to have a model that predicts
reservoir behavior, the operating conditions needed to be constant. To do this, we created an
Arps decline curve that mimicked the true production data in the rate cumulative plot. The rate
restriction for all wells was set at 5,000 Mscf/day and the production time was set to 100%. An
example of the Arps overlaying process for one of the wells is shown in Figure 4.2. Figure 4.3
shows how the Arps overlay rate restriction is lower than the actual for some of the wells. The
Arps decline is a smooth curve and represents what the production trend would look like under
perfect conditions.
85
Figure 4.2: A visual representation the Arps decline overlaying the true production. This is
shown on the rate-cumulative production plot for one of the wells. The red line represents the gas
rate assuming 100% on time every month, the orange line represents gas rate scaled down to
account for the actual on time during the month.
Figure 4.3: A plot showing the differences in rate restrictions between the actual production and
that of the Arps decline curve.
Production trends can be described by volume produced, time produced or the production rate
which is a derivative of the two. Figure 4.4 shows the various ways to visualize a production
trend. The most commonly used are the cumulative production versus time plot, rate versus
86
cumulative production plot and rate versus time a plot. This study focuses on the cumulative
versus time plot, specifically a five-year cumulative production curve at one-year increments.
The cumulative versus time plot was chosen because it provides a simple, high level view of
production performance that can aid an operator when running sensitivities on where to drill a
new well and how to complete it. Although the rate-based plots provide much more detail such
as the initial rate, decline rate, decline exponents, shut down time and flush production, these
would add unnecessary complexity and cause the network to make less accurate predictions.
87
Figure 4.4: The three common types of plots used to describe the production performance of a
well. Cumulative versus time (top), rate versus cumulative (middle), rate versus time (bottom).
These plots were generated using one of the wells in the study.
Some wells in the study have not yet reached five years of production, which creates a problem
when training the network. For these wells, the Arps decline curve was used to forecast out
production beyond the end of historical data. Only 16 out of the 74 wells required to have their
production to be forecasted between 1 and 30 months beyond January 2020. Although this
inevitability introduced some uncertainty to the analysis it was very useful in that it allowed the
experiment to be run on all 74 wells. The experiment was also run using only the 58 wells with
no forecasted production to see if forecasting production for the 16 well lead to better prediction
accuracy.
88
4.5 Experimental Setup
4.5.1 Networks used in the experiments
Two types of networks were used in this study: a simple feedforward network (ANN) and a multi
headed convolutional-recurrent hybrid (c-RNN). The networks were programmed in Python
using the keras library (Chollet, 2015).
The ANN was chosen as it is the simplest type of network and serves as good baseline to
compare the performance to the more complicated c-RNN. The c-RNN hybrid network was
chosen because it combines the speed and ability to process large amounts of data of a
convolutional network with the sequence processing ability of a recurrent network. The c-RNN
also uses a 3D input which allows it to use a stage level input. In Chapter 3, the c-RNN was
found to have superior performance to that of the ANN.
In multi-headed architectures each input variable is handled by a separate convolutional network
(head) and the output of each of these networks (heads) are merged and inputted into a recurrent
network before a prediction is made; these types of models are known to offer better
performance in some instances (Bagnall, 2015). The architecture of the multi-headed c-RNN is
shown in Figure 4.5.
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Figure 4.5: c-RNN structure that was used in the study.
4.5.2 Input shape and normalization
An ANN requires a 2D input (sample, variable). Since the output of the networks (production
profile) is forecasted on a well level, the input into an ANN must be on a well level as well. The
problem is that the input variables are different for every stage in a well, so the only way to use
an ANN for these experiments is to average an input variable along all stages in a well. The
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expectation then is that this would lead to higher error rates because certain variables such as
rock mechanical properties can change drastically from stage to stage over a 2 km horizontal
wellbore.
The c-RNN on the other hand uses a 3D input (step, variable, sample). The c-RNN input shape
works much better with our study because our input data is on a stage level, each stage goes into
the step axis. The input shape is depicted in Figure 4.6 as a series of tables, where the columns
represent the input variables and the rows represent the stages and each table is a different well.
Figure 4.6: Format of input and output data of the c-RNN model
Each value in the tables represents a particular input variable at a particular stage. The maximum
number of successful stages per well in this study was 31. The input shape cannot change during
an experiment so wells with less than 31 successful stages simply had a “0” value associated
with the stages it did not have. This made the total size of the training input = (n, 31, 73) and the
total size of the test = (n, 31, 1), where n is the number of input parameters chosen for the
experiment. Because the number of stages in a well is in a different axis than the rest of the
variables, it can be thought of as a baseline parameter that is always present no matter what
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combination of input parameters are shown to the network. The c-RNN was used as the main
network in the experiment because of its 3D input shape. The ANN performance was compared
to the c-RNN in the last experiment which used the best configuration of input parameters.
All the input variables along with the 5-year predictions where normalized to values between 0
and 1, where 0 represents the minimal value in that parameter and 1 represents the maximum.
Normalizing the inputs and outputs is a very common step in pre-processing of data, as it
removes the differences in the scales across variables that may decrease model performance. For
example, the RHOB values in this study ranged between 2.45 g/cc and 2.66 g/cc but the total
fluid placed in a stage ranged from 66 m3 to 1,805 m3 if the data was presented in its raw form.
The network would put more bias on the fluid placed per stage as the numerical values are orders
of magnitude larger than RHOB.
4.5.3 Experimental Setup
The study only contained 74 wells. In machine learning this is considered to be a small sample
size. The best method to determine model accuracy for limited sample sizes is the “leave-one-
out” cross-validation method. In this method, 73 wells are used to train the network and one well
known as the blind well is used to evaluate. The network is trained 74 time using 74 different
blind wells and the average accuracy of all 74 wells are examined.
The metrics used to measure the accuracy of the model was the mean absolute percentage error
(MAPE) and mean absolute error (MAE):
𝑀𝐴𝑃𝐸 = 1
𝑛∑
|𝐴𝑡−𝐹𝑡|
𝐴𝑡
𝑛𝑡=1 𝑀𝐴𝐸 =
1
𝑛∑ |𝐴𝑡 − 𝐹𝑡|𝑛
𝑡=1
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Where At is the actual value, Ft is the forecasted value and n is the number of samples. MAPE is
the most common accuracy metric and works best if there are no extremes in data. The MAPE
was used as the main metric in this study because it scales the error to the data and give the
ability to compare the results between wells with different cumulative productions. Due to the
scaling of errors, each individual well MAPE contributes an equal amount to the entire field
MAPE, which removes bias towards wells with larger production volumes. For this study the
individual well MAPE was calculated by averaging the volumetric error of every year in the 5-
year cumulative production trend. The field MAPE (average of all 74 wells) was then used as the
ultimate metric when comparing the results of various combinations of input variables and
network hyperparameters. The MAE was used as a secondary measure of accuracy to make sure
that the MAPE is not affected by extreme outliers, the MAE is a volumetric measurement and
represents the average error of all 74 wells in all 5 years of production forecast. If there are no
extremes in data, the total field MAE and MAPE are expected to follow similar trends.
The outcomes of a neural network are not only dependant on the training data, but also the
starting values of the weight parameters. In machine learning, a model is typically initiated with
random weights, so the model can have a range of predictions while using the same training data,
an example of this is shown in Figure 4.7. Having a range of outcomes is problematic as it is not
consistent and makes the model less trustworthy. The only way to have consistent predictions is
by taking the average of multiple runs. The more times a model is restarted and run the less the
average prediction will differ, Figure 4.8 shows how the average prediction changes with the
amount of runs for a well. We chose to use 30 runs per blind well because the average did not
change much with additional runs which required more computing time. Each run had a total of
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300 training epochs, this value was chosen since the blind test error for all 74 wells no longer
decreased at that point.
Figure 4.7: Plot showing the numerous predictions that a model trained on the same dataset could
make.
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Figure 4.8: Plots showing how the average prediction changes based on the number of runs
1
run
2 runs
5 runs 10 runs
30 runs 100 runs
500 runs
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4.5.4 Hyperparameter Tuning
Network hyperparameters such as the number of nodes and layers, and number of epochs can be
tuned after all 74 experiments are completed to see if an improvement is made. The network
hyperparameters used for the experiments were chosen by a trial and error procedure that
includes the following steps:
1. Choose which hyperparameters can be modified – in our case this was the number of filters
and pooling layers in the convolutional heads as well as the number of nodes and layers in
the RNN part.
2. Define a range for these hyperparameters (ie, maximum and minimum number of nodes and
layers)
3. Run sensitivities using the same experimental setup but changing the hyperparameters. First
change one hyperparameter at a time then run different combinations of each to see which
configuration yields the best result.
The amount of combinations is infinite, so finding the optimal hyperparameters is impossible;
however, this approach does help tune the network to produce fairly accurate results. The tuned
hyperparameters used for the network are presented in Table 4.3.
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Table 4.3: Starting hyperparameters for the c-RNN developed in this study
Same for every head
Layer Input Conv Conv
Max
Pooling Merge Conv GRU GRU Output
Number of
nodes 1 64 64 -
32 50 50 1
Activation
Function -
rectified
linear
unit
rectified
linear
unit -
rectified
linear
unit
rectified
linear
unit
rectified
linear
unit -
Recurrent
Dropout - - - -
- 0.5 0.5 -
Once the network hyperparameters were chosen, multiple experiments were run on different
combinations of stage input parameters to see how they affected the error metrics. The first
experiment was a base case prediction which was run using zero stage variables. In this case the
input shape of the training data was (1, 31, 73) where the x-axis was either a 1 or a 0 representing
a stage being present or not. By doing this, the only information presented to the network was the
number of stages in a well. Next, the experiments were run on individual factors, followed by a
combination of factors from the geological and completion categories. Finally, once the best
combination of parameters was found the well spacing and completion order information was
added to see if it had any affect on the outcome.
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4.6 Results and Discussion
Table 4.4: Results of the leave-one out experiments performed on only the geological variables
Variables Used Average MAPE Maximum MAPE Minimum MAPE MAE (MMcf)
No variables (base case) 21.18% 112.31% 1.73% 685
RHOBnear 19.60% 84.49% 1.82% 648
DTSnear 19.56% 83.44% 2.08% 663
DTSfar, DTPfar and RHOBfar 19.08% 89.79% 1.63% 634
DTPnear and DTSnear 18.74% 91.22% 0.90% 629
DTPnear 18.39% 91.71% 1.72% 612
RHOBnear and DTSnear 17.91% 68.86% 1.56% 606
RHOBnear and DTPnear 16.73% 85.17% 1.74% 565
(DTS, DTP, RHOB)far and (DTS, DTP, RHOB)near 16.60% 84.91% 1.64% 563
DTSnear, DTPnear and RHOBnear 16.57% 84.42% 1.78% 562
Table 4.5: Results of the leave-one out experiments performed on only the completion variables
Variables Used Average MAPE Maximum MAPE Minimum MAPE MAE (MMcf)
No variables (base case) 21.18% 112.31% 1.73% 685
Distance between successful stages m 23.07% 100.84% 2.00% 757
Total CO2 injected 21.96% 124.02% 1.94% 737
Total proppant injected and total fluid injected 21.14% 105.50% 1.72% 687
Total fluid injected 21.08% 124.23% 1.17% 682
Type of fluid used 20.68% 118.72% 1.36% 658
Total proppant injected 20.43% 99.04% 1.88% 662
Total proppant, fluid and CO2 injected 19.38% 100.55% 0.95% 636
Total proppant, fluid, CO2 injected, and type of fluid used 19.21% 100.30% 0.80% 633
Table 4.6: Results of the leave-one out experiments performed on geological, completion and
spacing variables
Variables Used Average MAPE Maximum MAPE Minimum MAPE MAE (MMcf)
No variables (base case) 21.18% 112.31% 1.73% 685
(DTS, DTP, RHOB)near, total proppant, fluid, CO2
injected, and type of fluid used 17.34% 79.88% 1.41% 583
(DTS, DTP, RHOB)near, total proppant and fluid injected 16.37% 84.95% 1.85% 563
(DTS, DTP, RHOB)near and total proppant injected 16.27% 89.99% 0.82% 556
(DTS, DTP, RHOB)near, total proppant injected, well
spacing and completion order 14.90% 83.12% 0.97% 534
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Tables 4.4 through 4.6 summarize the results of the leave-one-out experiments using the c-RNN
network. Each table has the base case prediction included for comparison; the MAPE and MAE
of the base case came out to be 21.18% and 685 MMcf respectively. The MAE was used as a
secondary check to make sure the MAPE is not affected by very large or very small
measurements. From the tables it is clear that the MAE and MAPE follow similar trends,
because of this we will only comment on the MAPE for the remainder of the study.
Table 4.4 shows the results using combinations of only rock mechanical variables. Using all
three near profile logs resulted in average prediction error of 16.57% which is lower than the
19.08% error resulting from the far profile logs. Also, using both far and near profile logs as
inputs did not have any improvements on the prediction performance over using just the near
profile logs. This is likely because the far profile logs were averages of 50 m3 blocks, that ended
up being poor representations of how fractures propagate through a formation whereas the near
profile logs were not averaged and describe the conditions at fracture initiation. Predictions were
also made using individual near profile logs, out of the individual well logs, the DTP log lead to
a better prediction than the DTS or RHOB. Using all three rock mechanical logs as inputs
resulted in better performance than just one or two; this suggests that using all three logs is
important when describing the rock mechanics.
Table 4.5 shows the results using only completion variables. Runs were done on individual
variables as well as combinations of variables. Out of the individual variables, the total proppant
injected had the lowest average error of 20.43%. The combination of total proppant, fluid, CO2
injected, and the type of fluid used had the lowest error of 19.21%. Using the distance between
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successful stages as the only input made the model predict with and error of 23.07% which was
worse than that of the base case. The prediction accuracy of the model was greater using only the
rock mechanical properties versus only the stimulation variables. This suggests that the rock
mechanics surrounding a well have a greater effect on production performance than the
stimulation design.
Table 4.6 shows the results from the combination of rock mechanical properties and completion
variables as well as the addition of the well spacing and completion order. The best prediction
with an average error rate of 16.27% was made by using the three near profile logs in
combination with the total proppant injected. Adding more stimulation variables to the input
such as total fluid/CO2 injected, or type of fluid used did not improve the accuracy of the model.
Finally, when information about the well spacing and completion timing was added to the input,
the network was able to make even better predictions with an average error rate of 14.90%, this
was the best case in this study. This points to the fact that this information plays an important
role in production performance. The difference between the best case and the base case was only
6.28%, this suggest that the number of stimulation stages in a well (which is the input of the base
case) has a large affect on production.
Figure 4.9 shows the distribution of the individual well MAPE values for the best case, 47 out of
the 74 wells had a MAPE <15%, and almost all the wells had a MAPE <50%, only one well had
an error rate of 83%. Figure 4.10 shows the production profiles of the best and worst wells.
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Figure 4.9: Distribution of individual well MAPE from the best case.
Figure 4.10: Plot the worst (left) and best (right) well production profiles created by the best-case
model. The red line is the average of the 30 runs, the green line is the true profile.
There were 16 wells used in the training set that have not yet reached five years of on production
time, and their trend had to be forecasted out to using Arps decline. To see if this forecasting of
production had an impact on results the best case was also run with the 16 wells removed. The
average error rate for the 58 non-forecasted wells was 15.2% when the 16 forecasted wells were
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included in the training set. When the 16 forecasted wells were removed from the training set,
the average error rate for the 58 non-forecasted wells turned out to be 18.0%, this suggests that
using more wells in the training set is beneficial even if production from these wells needed to be
partially forecasted.
The input parameters for the best-case experiment were also used to test ANN accuracy. Since
the ANN can only take a 2D input, the input variable had to be averaged along the stages. The
MAPE from the ANN turned out to be 20.6%. This demonstrates that the c-RNN is the better
network to use.
Predicting individual well production before it is drilled is difficult, and it comes at no surprise
that the best case MAPE of the model was 14.9%. There are several reasons for this. Firstly, the
information about the geology surrounding a horizontal well comes with great uncertainty.
Secondly, the process of how hydraulically induced fractures propagate through a formation is
extremely complex and depends on a myriad of factors that cannot be measured; the possibilities
of network structures are endless. Also, the inability of measuring production coming out of each
perforation interval makes it impossible to link the rock mechanics and stage parameters directly
to the stage production. Finally, the interaction affects between wells are difficult to quantify and
add more complexity to the problem.
An interesting observation was that the accuracy of the model increased if the individual well
predictions were added together and compared to the actual. Adding up the best-case production
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profiles of all 74 wells resulted in an average MAPE of only 0.8%, the aggregated production
profile of the 74 wells is depicted in Figure 4.11.
Figure 4.11: Plot the best-case aggregate production profile of all 74 wells vs time.
This reduction in MAPE is due to the network underpredicting the performance of some wells
and overpredicting the performance of others. When these differences are added they begin to
cancel each other out. To see how the number of wells in aggregated group affect the MAPE, we
chose aggregate numbers of 2, 3, 5, 10, 30 and 50 wells and ran 500 different combinations of
randomly chosen wells for each aggregate amount and recorded each combinations MAPE. The
aggregate MAPE was taken as the average of the 500 runs. Doing 500 runs on each aggregate
amount produces a statistical representation of the average of all possible combinations of wells
in that aggregate. The results of this analysis is shown in Figure 4.12.
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Figure 4.12: Plot how aggregating well together affects the mean average percent error (MAPE).
The MAPE drops exponentially with the increase in the number of aggregated wells. By
predicting the summed production profile of 10 wells the prediction accuracy drops to 4.5%,
which is a significant improvement over the 15% error rate of individual wells. Due to this, the
model developed in this study becomes more useful with larger development plans. The
aggregated production profile assumes all wells will come on production at the same time, which
is not the case in real life development, but it would still be of use to provide an overall picture
of total production that would be expected from the new wells.
Since the DTP was an important input it is important to understand how the DTP at the
perforation intervals affect the cumulative production at the wellhead. The DTP affects the
brittleness of a rock which dictates the way fractures form within a reservoir. A more brittle
104
reservoir is expected to produce more hydrocarbons than a ductile one since brittle rock forms
more complex fracture networks which increase the contact area between reservoir and wellbore.
Brittleness is related to the mechanical properties and rocks with a large Young’s modulus and
small Poisson’s ratio are more brittle than those with a small Young’s modulus and large
Poisson’s ratio (Wang and Gale, 2009). When the DTP is increased and all other variable
including the DTS are held constant both the Poisson’s ratio and the Young’s modulus decrease;
however, the Poisson’s ratio decreases more drastically. Conversely when the DTP is lowered
both the Poisson’s ratio and the Young’s modulus increase, however the Poisson’s ratio increases
more drastically. Because of this, the brittleness increases with increasing DTP and since
brittleness is related to production increase in DTP is expected to increase production as well. To
test this a sensitivity was run to see what affect the DTP input has on cumulative production. In
this sensitivity all input variables for all 74 wells were held constant and only the DTP stage
inputs were multiplied by a factor ranging between 0.5 and 1.5 to see how this affected the
aggregated 74 well 5-year cumulative production. Figure 4.13 shows the results of the
sensitivity. The results show a linear correlation between DTP and cumulative production and
that the cumulative production increases with increased DTP as expected.
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Figure 4.13: Results of a sensitivity showing how the 5 year cumulative production from all 74
wells is affected with changes in the DTP.
4.7 Conclusions
In this study we developed a machine learning model to predicts the five-year cumulative
production profiles in multistage hydraulically fractured wells. The novelty of this study is that it
uses not just the completion variables of a well but also the rock mechanical properties
surrounding perforation clusters along with well spacing and completion timing of wells. The
model was able to predict individual well production profiles with an average error rate of
14.9%, with the best well having an error of only 1% and the worst well having an error of 83%.
The average error rate decreases exponentially as the production of multiple wells is aggregated.
There are many ways to improve this model’s performance, arguably the biggest would be to
have a flow rate measuring tool installed at every perforation cluster. Having this tool would
345
350
355
360
365
370
375
380
385
50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150%
5 y
ear
Cum
ula
tive
Pro
duct
ion o
f 74 w
ells
(B
cf)
% of oiginal DTP
106
enable linking the completion variables and the rock mechanics of each stage directly to the
amount of production coming from that stage. Having more vertical wells with actual DTS logs
would lessen the need to generate synthetics which would improve the accuracy of the 3D
models of the DTS logs. Also, it would be useful to have a 3D seismic survey of the formation
since it can be used to identify faults which could be used as inputs into the network as well.
Finally, it is unlikely that the neural network used in this study has the optimal configuration.
Finding this optimal would improve the accuracy but would require many more tests. Installing
this many measuring devices and having DTS logs on every well would most likely be
uneconomic and would probably never occur in a profit driven industry.
Unfortunately, even if economics was not a factor, there is no way to build a model capable of
predicting the production performance of each well with 100% certainty. This is because we are
not able to see with full clarity what goes on under the ground. Geological formations are very
heterogenous and any computer model will fall short of describing their true structure, in
addition to that, fracture dynamics are extremely complex and the exact fracture configurations
before and after stimulations are not possible to observe.
That being said, this model would be of great use to anyone planning on drilling multiple wells
in fields with existing development. This is because the model accuracy was shown to increase
exponentially if it is used for predicting production of more than one well. The lower error gives
the ability to run multiple field development scenarios without having to spend capital. This
would grant the ability to optimize well placement and completion which would lower overall
costs and potentially lower the environmental impact of hydraulic fracture operations.
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Chapter 5: Optimizing Water Usage during Multi-Stage Hydraulic Fracturing with a
Convolutional-Recurrent Neural Network
5.1 Preface
This Chapter has been submitted as a manuscript to the Journal of Petroleum Science &
Engineering in 2020. This article is co-authored by Ian D. Gates.
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5.2 Abstract
A machine learning model was developed and trained on 74 existing wells in the Montney
formation in Canada, to run sensitivities on 40 proposed wells that are to be drilled alongside the
existing producers with the objective of minimizing water usage. 1,080 sensitivities were run to
explore how different combinations of stage count, fluid type, water amount, and proppant
amount affect the aggregated 5-year cumulative gas production of the 40 proposed wells. The
results from the machine learning analysis finds that the injection efficiency (cumulative
gas/total fluid injected) drops exponentially when more water is injected. The results show that it
is possible to achieve a cumulative production that is 76% of the maximum by using only 3% of
the water required to achieve this maximum. This represents a significant reduction of the water
usage which supports cleaner and more efficient drilling operations as well as lower costs
associated with water treatment and disposal as well as potential induced seismicity.
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5.3 Introduction
Currently, hydraulic fracturing has become the most common method for producing
hydrocarbons from ultra-low permeability reservoirs. Advancements in hydraulic fracturing and
horizontal drilling techniques over the past several decades have made producing hydrocarbons
from unconventional reservoirs economically feasible which lead to a shale boom in North
America and throughout the world (Morton, 2013). In hydraulic fracturing, large amounts of
water and sand are pumped down a wellbore and injected into a target formation at high rates
and pressures (Montgomery and Smith, 2010). The injected fluid creates new fracture networks
starting at the well within the formation that are propped open by the sand effectively increasing
the surface area of the reservoir that is connected to the wellbore (Yew, 1997). Modern hydraulic
fracturing is typically performed in multiple stages along the entire horizontal wellbore. After
hydraulic fracturing, the well is put on production with relatively short peak production period
with a rapid decline to a plateau value that can be maintained for an extended period of time (Tan
et al., 2018).
Most hydraulic fluids are water-based and contain 90 to 97% water by volume (U.S.
Environmental Protection Agency, 2016). Two of the most common water-based fluid used
today are slickwater and crosslinked gel (Montgomery, 2013). Crosslinked fluids were
introduced in the 1960s after it was found that fractures heal unless a propping agent was co-
injected with the water (Palisch et al., 2010). Crosslinked gel is a relatively viscous fluid
(compared to that of water) typically used in ductile formations with higher permeability.
Commonly, guar gum is used as the thickening agent and borate ions as the crosslinking agents.
The advantage of using crosslinked gel is that they exhibit low fluid leak off, low pump rate, low
110
water usage and ability to pump high sand concentrations (Fink, 2015). The biggest concern with
this type of fluid is that the gel residue that remains in the formation may block the newly created
fractures (Belyadi et al., 2017). Slickwater fluid is typically used in low-permeability, high net
pay reservoirs. Slickwater is water that has had its viscosity reduced by the addition of polymers
such as polyacrylamides (Montgomery, 2013). The lower viscosity of slickwater leads to a
reduction of viscous effects (friction). From a pumping point of view, this lowers the energy
required to move the fluid but on the other hand, this reduces the ability of the liquid to suspend
and transport the proppant from the surface to the reservoir (Palisch et al., 2010). This also leads
to narrower fracture aperture which in turn results in lower hydraulic conductivity of the fracture
(Barati and Liang 2014). To offset this, slickwater is pumped at relatively higher rates (100+
bbl/min) and relatively low concentrations of proppant resulting in massive water requirements
(Barati and Liang 2014). The primary technical advantage of slickwater is the reduced damage
within fractures and reduced fracture height growth (Fink, 2015). Depending on water
availability and costs, low concentration slickwater treatments may also be lower cost than
crosslinked gel since they require less chemicals (Ba et al., 2019). Given the relatively large
volume of water for slickwater stimulation, there is a pressing need to reduce the amount of
water injected into the formation. Furthermore, there might be advantages of low volume
hydraulic fracturing due to the lower chance of induced seismicity (Schultz et al., 2018).
Although there has been a lot of research on which fluid is better for a particular type of tight
formation, for the most part, the choice of fluid is driven by the actual production data and the
operator’s success in a particular formation (Belyadi et al., 2017). Lately, slickwater treatments
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have become the more popular choice for hydraulic fracturing stimulation. The three main
reasons for this are as follows (Palisch et al., 2010):
1. industry’s need to cut costs (via use of less chemicals),
2. reservoirs being fractured today have lower permeability and gel clean-up from the
induced fractures have become a stimulation challenge, and
3. fractures created by crosslinked gel were not performing as well as expected due to
formation damage.
Based on a data survey of around 40,000 wells in the United States, the average volume of water
used to create a hydraulic fracture is about 9,500 m3 (Freyman, 2014) with around 30,000 wells
being fractured per year between 2011 and 2014 (U.S. Environmental Protection Agency, 2016).
The fracture intensity, well length and stage count of multi-stage horizontal wells have also
increased over time which has led to an increased water usage. Kondash et al. (2018) found that
between 2011 to 2016, the average water injected along with the average flowback per well has
increased in all six of the major shale producing regions in the Unites States. The large amounts
of water injected during hydraulic fracturing impacts surrounding water resources and requires
more wastewater management (U.S. Environmental Protection Agency, 2016). The greater the
water used, the larger the impacts (Schultz et al., 2018).
The water that is used in hydraulic fracture fluid is typically sourced from groundwater and
surface water resources (U.S. Environmental Protection Agency, 2016). The water may also be
sourced from reused wastewater from previous fracture jobs however this is not widely practiced
and only ~5% of fracture jobs use recycled wastewater (U.S. Environmental Protection Agency,
112
2016). Groundwater and surface water resources are also the main source of drinking water,
household processes, irrigation, livestock and industrial processes. Water used for a hydraulic
fracture on a single well does not usually impact local water resources; however, if multiple
treatments for many wells are being performed in a single area, the total volume of fluid needed
to fracture the wells may take up a significant portion of locally available water resources
(Scanlon et al., 2014). Areas that are prone to drought or hot weather are significantly impacted
since high withdrawals of local surface and ground water may reduce drinking water availability
(U.S. EPA, 2015). For example, in 2011, water wells overlying the Haynesville Shale used for
extracting drinking water were excessively drained due to local hydraulic fracture operations and
drought (Louisiana Ground Water Resources Commission, 2012). Hydraulic fracturing may also
impact groundwater levels: a study conducted by Scanlon et al. (2014) in Texas showed that
groundwater levels dropped by 31 meters to 61 meters after hydraulic fracturing activity
increased in 2009. High local water withdrawal may lead to erosion, sedimentation, and habitat
fragmentation (Lin et al., 2018).
Large volumes of injected water result in large volumes of flowback wastewater which needs to
be treated, handled, transported, and disposed of (Veil, 2015). Wastewater is typically reinjected
or disposed of above ground. Reinjecting can either be done via injection wells or in other
hydraulic fracture operations. To handle the wastewater above ground, it can either be processed
in wastewater treatment facilities and released back into rivers or evaporated in evaporation
ponds (U.S. Environmental Protection Agency, 2016).
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Wastewater handling carries risks and reinjecting water can potentially contaminate freshwater
aquifers (Faruque and Goldowitz, 2017) or cause inducing seismicity (Eaton et al., 2018). The
choice to reuse wastewater in hydraulic fracturing is rarely practiced since it depends on the
quality, quantity and cost associated with reusing the wastewater. Inadequate wastewater
treatment has been known to impact drinking water resources. For example, in Pennsylvania,
wastewater from Marcellus Shale gas wells was treated and released to surface waters. The
wastewater treatment facilities were unable to properly remove the high levels of total dissolved
solids and the discharged wastewater contributed to elevated levels of total dissolved solids
(particularly bromide) in the Monongahela River Basin (Pennsylvania Department of
Environmental Protection, 2015).
The literature suggests that there is a compelling desire to reduce the amount of water used in
hydraulic fracturing jobs. In this study, we use the model developed and trained in Chapter 4 to
run sensitivities on a proposed future field development scenario. In this scenario, 40 additional
wells are to be drilled adjacent to the existing 74 wells and are scheduled to all come on
production at the same time. 1,080 sensitivities are run to explore how different combinations of
stage count, fluid type, water amount, and proppant amount affect the aggregated 5-year
cumulative gas production of the 40 proposed wells. The ultimate purpose of the study is to see if
injected water can be minimized without having a large negative impact on the 5-year
cumulative production.
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5.4 Study Area and Proposed Wells
The study area is the same for all research chapters and is described in Chapter 1: introduction of
this thesis and shown in Figures 1.2 and 1.3. Figures 4.1 shows the areal extent of the 74
producing wells that currently exist in the area. The 40 proposed wells chosen to be drilled are
shown in Figure 5.1.
Figure 5.1: 40 proposed well locations (blue) added to the existing 74 wells (red) in the study
area generated in Petrel.
The positioning of these 40 locations represent a full field infill drilling plan that would take
place in a field with existing development. The length of the proposed wells was fixed at 2 km as
this was the representative length of existing wells. Variable stage counts of 10, 15 and 30 per
115
well were used for the sensitivities. This range was chosen as it represents the minimum, average
and maximum number of completion stages that were done in the existing 74 producers.
The model used in this study uses three groups of input parameters at every stage along the
wellbore to make a prediction about the gas production. These 3 groups are:
• well spacing and completion order,
• rock mechanical properties, and
• completion parameters
The individual parameters of each group are listed in Table 5.1.
Table 5.1: The stage variables that were used as inputs in the sensitivity experiment.
Rock mechanical properties Completion Well spacing and completion order
Density (RHOB) Type of fluid Length of unbounded time
Compressional Sonic (DTP) Total fluid injected Unbounded gas production
Shear Sonic (DTS) Total proppant placed Length of time each offset well
produced before well is drilled
Volume of gas each offset well
produced before well is drilled
Percentage of length that each offset
well covers this well
Average perpendicular distance from
each offset well to this well
5.4.1 Well spacing and completion order
Existing producers in this study are drilled close to each other so the production of gas from one
well affects the production of its neighbors. This was shown in Chapter 4 where the individual
well error rate of the model decreased from 16.3 to 14.9% when well spacing and completion
order parameters (time and gas volume that a well produced in an unbounded state, time and gas
volume that offset wells produced before a well was drilled, percentage of length that each offset
well covers a well, average perpendicular distance between offsetting wells) were taken into
116
account. Because the well spacing and completion order was important, they were also used for
the 40 proposed wells in this study. The spacing parameters were based on distance from a
proposed well location to existing producers as well the distance between the proposed wells
themselves. Well spacing and completion order makes more sense on a well level not a stage
level, so the input values representing spacing and completion order for the well would be
constant at every stage in that well. This group of input parameters was also constant for every
sensitivity run as the trajectory of the wells was fixed.
5.4.2 Rock mechanical properties
The rock mechanical properties at each stage of the proposed wellbore trajectory where extracted
using the rock mechanical model built in Chapter 4. Briefly, this model was developed by
upscaling and 3D interpolating the density (RHOB), compressional sonic (DTP) and shear sonic
(DTS) logs of 180 vertical and deviated wells located in the study area. The DTS log was present
in only 14 of these wells and had to be synthetically generated for the other 166 using the neural
network developed in Chapter 3. Because stage count per well can be either 10, 15 or 30
depending on the scenario, the rock mechanical properties are different depending on the stage
count. For each proposed well we extracted 3 sets of rock inputs based on the number of stages.
5.4.3 Completion Parameters
For this study the fluid type, fluid amount and proppant amount are the completion parameters.
Just like the stage count, the completion parameters had a range of values in the sensitivity
analysis. The range of fluid and proppant amount as well as the proppant density was limited to
within the values of the existing 74 wells. This was done because the model was trained on the
117
input parameters of the 74 existing wells and extrapolating values outside the ranges that already
exist may lead to large errors. Table 5.2 shows the ranges of all the variable input parameters
used for the sensitivities as well as the increments used. On average, the 26 existing slickwater
wells used 650 m3 of liquid per stage while the 40 existing crosslinked gel wells used 145 m3.
Due to the much higher stage water volumes of the slickwater wells we split the input water
amount into two ranges, one for each fluid type.
Table 5.2: The ranges of all the variable input parameters and the increments used for the
sensitivity experiment.
Parameter Range Stage Count 10, 15 or 30 Fluid Type Slickwater or crosslinked gel Proppant Density 85-1,050 kg/m3 Proppant Amount per stage 40-300 tonnes (20 tonne increments) Fluid Amount per Stage Crosslinked: 90-260 m3 (10 m3 increments)
Slickwater: 250-1,000 m3 (50 m3 increments)
5.4.4 Input shape and normalization
As depicted in Figure 4.7, the input to the neural network is a series of tables where the columns
represent the stage variables and rows represent the stages. Each value in this table represents a
particular input variable at a particular stage. The maximum number of successful stages per well
in the existing 74 wells was 31. Since the network was trained on existing wells the input shape
cannot, so wells with less than 31 successful stages simply had a “0” value associated with the
stages it did not have. All the input variables along where normalized to values between 0 and 1,
where 0 represents the minimal value in that parameter and 1 represents the maximum from the
existing 74 wells.
118
5.5 Neural Network Algorithms and Experimental Setup
The neural network used in this study was developed in Chapter 4. In this work, the network was
trained using the 74 existing producers in the area with the supervised learning approach. During
supervised learning both the inputs and the outputs are provided to the network. The inputs are
the well spacing and completion order, rock mechanical properties and the completion
parameters. The output was the 5-year cumulative production profile in one-year increments. The
network predicts an output given the inputs, this predicted output is compared to the actual and
the error is backpropagated back through the system adjusting the weight parameters. The weight
parameters are started with random values but get adjusted as more of the well inputs and outputs
are shown to network. Once the network sees the entire data hundreds of times over the network
beings to find general trends and patterns within the study area and the overall prediction error
rate drops (Reed and Marks, 1998). Once the network is trained to a sufficiently low error rate it
can be used to make predictions.
The trained network cannot distinguish between existing or proposed wells, as long as the input
data is in the correct format the network will make a prediction. The trained network can be used
to see how the 5-year cumulative production of a proposed well is affected when the inputs are
changed, i.e. it can be used to run sensitivities. As long as the proposed wells are located within
the study area (the geology is similar to what the network has been trained on), of similar length
and of similar completion designs the aggregate error rate should be similar to that of the existing
producers. Figure 4.13 shows how the error of the model drops as more wells are aggregated, at
40 wells the error rate should be around 2%.
119
The model consists in this study is a multi-headed convolutional-recurrent hybrid network (c-
RNN). The c-RNN hybrid network was chosen because it combines both the speed and ability to
process large amounts of data of a convolutional network with the sequence processing ability of
a recurrent network. The c-RNN hybrid has been shown to outperform traditional neural
networks in Chapter 3. In multi-headed architectures each input variable is handled by a separate
convolutional network (head) and the output of each of these networks (heads) are merged and
inputted into a recurrent network before a prediction is made; these types of models offer better
performance (Bagnall, 2015). The network was programmed in Python using the keras library
(Chollet, 2015). The architecture of the network is shown in Figure 4.6 and the network
hyperparameters are shown in Table 4.3.
As depicted in Figure 4.7, the inputs to the neural network are a series of tables where the
columns represent the stage variables and rows represent the stages. Each value in this table
represents a particular input parameter at a particular stage. The maximum number of successful
stages per well in the existing 74 wells was 31. Since the network was trained on existing wells
the input shape cannot change, so wells with less than 31 successful stages simply had a “0”
value associated with the stages it did not have. All the input variables were normalized to values
between 0 and 1, where 0 represents the minimal value in that parameter and 1 represents the
maximum from the existing 74 wells.
The network was used to run 1,080 sensitivities to explore how different combinations of stage
count, fluid type, water amount, and proppant amount affect the aggregated 5-year cumulative
gas production of the 40 proposed wells.
120
5.6 Results and Discussion
Tables 5.3 and 5.4 show the results from the 1,080 sensitivity runs, the tables depict how the
aggregated 5-year cumulative production (known from now as “the output”) from the proposed
40 wells is affected by changes in the input. Tables 5.3a, 5.3b and 5.3c depict the crosslinked gel
results using 10, 15 and 30 stages per well respectively. Table 5.4a, 5.4b and 5.4c depict the
slickwater results using 10, 15 and 30 stages per well respectively.
Out of the existing 74 existing wells, 48 were completed using the crosslinked gel and 26 were
completed using the slickwater. Crosslinked gel was the original fluid choice and was used from
2006 to 2014 after which point all wells were fractured using slickwater. Since the slickwater
stimulations used newer technology, they tended to have more stages. The stage count for the
crosslinked gel wells had a range of 5 to 17 with an average value of 10. The stage count for the
slickwater wells had a range of 9 to 31 with an average value of 18. For this study, the
cumulative production is forecasted using stage counts of 10, 15 and 30 for both fluids. Since the
largest crosslinked gel stage count was 17, forecasting using 30 stages per crosslinked gel well
would be an extrapolation. Only two of the existing slickwater wells stages counts are lower than
14 and because of this forecasting using 10 stages per slickwater well is also an extrapolation. 15
stages per well should be used when comparing the results of the two types of fluids as these are
not extrapolations and would be have the best basis for comparison.
121
Table 5.3: Results from the sensitivity analysis using the crosslinked gel as the fracture fluid
Table 5.3a – 10 Stages Crosslinked Gel (Results in Bcf)
Proppant
amount
per stage (tonnes)
Well
proppant
amount (tonnes)
Row 1 - Fluid injected per stage (m3), Row 2 - Fluid injected per well (m3)
90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260
900 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500 2,600
40 400 193.0 193.1 193.2 193.3 193.5 193.6 193.8 194.1 194.4 194.7 195.0 195.3 195.5 195.7 195.9 196.1 196.3 196.5
60 600 194.0 194.1 194.2 194.3 194.5 194.6 194.8 195.1 195.4 195.7 196.0 196.3 196.5 196.8 197.0 197.2 197.4 197.6
80 800 197.0 197.1 197.2 197.3 197.4 197.6 197.8 198.1 198.4 198.7 199.0 199.3 199.5 199.7 200.0 200.2 200.4 200.6
100 1,000 203.8 203.9 204.0 204.1 204.2 204.4 204.8 205.1 205.4 205.7 205.9 206.2 206.4 206.6 206.8 207.1 207.3
120 1,200 204.6 204.7 204.8 205.0 205.3 205.7 206.0 206.3 206.5 206.8 207.0 207.2 207.4 207.6 207.8
140 1,400 202.4 202.6 202.9 203.2 203.5 203.8 204.1 204.3 204.5 204.8 205.0 205.2 205.4
160 1,600 200.4 200.7 201.0 201.3 201.5 201.7 202.0 202.2 202.4 202.6 202.8
180 1,800 198.6 198.9 199.1 199.4 199.6 199.8 200.0 200.2 200.4
200 2,000 197.0 197.3 197.5 197.7 197.9 198.1 198.3
220 2,200 195.4 195.6 195.8 196.0 196.2 196.4
240 2,400 194.0 194.2 194.4 194.6
260 2,600 192.8 193.0
Table 5.3b – 15 Stages Crosslinked Gel (Results in Bcf)
Proppant
amount
per stage (tonnes)
Well
proppant
amount (tonnes)
Row 1 - Fluid injected per stage (m3), Row 2 - Fluid injected per well (m3)
90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260
1,350 1,500 1,650 1,800 1,950 2,100 2,250 2,400 2,550 2,700 2,850 3,000 3,150 3,300 3,450 3,600 3,750 3,900
40 600 195.2 195.4 195.5 195.6 195.8 195.9 196.2 196.5 196.9 197.3 197.6 197.9 198.2 198.4 198.7 198.9 199.1 199.4
60 900 198.9 199.1 199.2 199.3 199.5 199.6 199.8 200.2 200.6 201.0 201.3 201.6 201.8 202.1 202.4 202.6 202.8 203.1
80 1,200 204.8 204.9 205.1 205.2 205.3 205.5 205.7 206.1 206.5 206.8 207.1 207.4 207.7 208.0 208.2 208.4 208.7 208.9
100 1,500 214.8 214.9 215.0 215.2 215.3 215.5 215.9 216.3 216.6 216.9 217.2 217.4 217.7 217.9 218.1 218.4 218.6
120 1,800 217.5 217.6 217.8 218.0 218.3 218.7 219.0 219.3 219.6 219.8 220.1 220.3 220.5 220.7 221.0
140 2,100 216.8 217.1 217.4 217.7 218.1 218.4 218.6 218.9 219.1 219.3 219.6 219.8 220.0
160 2,400 216.2 216.6 216.9 217.2 217.5 217.7 218.0 218.2 218.4 218.6 218.8
180 2,700 215.8 216.0 216.3 216.5 216.8 217.0 217.2 217.4 217.6
200 3,000 215.2 215.5 215.7 215.9 216.1 216.3 216.5
220 3,300 214.5 214.7 214.9 215.1 215.3 215.5
240 3,600 213.9 214.1 214.3 214.5
260 3,900 213.4 213.6
Out of existing proppant density range
Out of existing proppant density range
122
Table 5.3c – 30 Stages Crosslinked Gel (Results in Bcf)
Proppant Amount
per stage
(tonnes)
Well proppant
amount
(tonnes)
Row 1 - Fluid injected per stage (m3), Row 2 - Fluid injected per well (m3)
90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260
2,700 3,000 3,300 3,600 3,900 4,200 4,500 4,800 5,100 5,400 5,700 6,000 6,300 6,600 6,900 7,200 7,500 7,800
40 1,200 222.7 222.9 223.0 223.2 223.3 223.5 223.8 224.2 224.7 225.1 225.5 225.9 226.3 226.7 227.0 227.4 227.7 228.1
60 1,800 226.8 226.9 227.0 227.2 227.4 227.5 227.8 228.2 228.6 229.0 229.4 229.8 230.1 230.5 230.8 231.2 231.5 231.8
80 2,400 232.5 232.6 232.7 232.9 233.0 233.1 233.4 233.7 234.1 234.5 234.9 235.2 235.5 235.8 236.1 236.4 236.7 237.0
100 3,000 241.3 241.4 241.5 241.6 241.7 241.9 242.1 242.5 242.7 243.0 243.3 243.5 243.8 244.0 244.2 244.5 244.7
120 3,600 243.9 244.0 244.1 244.3 244.5 244.8 245.1 245.3 245.5 245.8 246.0 246.2 246.4 246.6 246.8
140 4,200 245.1 245.3 245.5 245.8 246.1 246.3 246.6 246.8 247.0 247.2 247.5 247.7 247.9
160 4,800 246.5 246.8 247.0 247.3 247.5 247.7 248.0 248.2 248.4 248.6 248.9
180 5,400 247.7 248.0 248.2 248.4 248.7 248.9 249.1 249.3 249.5
200 6,000 248.9 249.2 249.4 249.6 249.8 250.0 250.2
220 6,600 249.8 250.1 250.3 250.5 250.7 250.9
240 7,200
250.9 251.1 251.3 251.5
260 7,800 251.8 252.0
Out of existing proppant density range
123
Table 5.4: Results from the sensitivity analysis using the slickwater as the fracture fluid.
Table 5.4a – 10 Stages Slickwater (Results in Bcf)
Proppant
amount per stage
(tonnes)
Well
proppant amount
(tonnes)
Row 1 - Fluid injected per stage (m3), Row 2 - Fluid injected per well (m3)
250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1,000
2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 6,500 7,000 7,500 8,000 8,500 9,000 9,500 10,000
40 400 225.2 226.1 226.7 226.7 226.5 226.1 225.6 225.0 224.3 223.7 223.0 222.3 221.6 221.0 220.3 219.7
60 600 225.5 226.4 227.0 227.1 226.9 226.5 226.1 225.5 224.8 224.2 223.5 222.9 222.2 221.6 220.9 220.3
80 800 227.5 228.4 229.0 229.1 228.9 228.6 228.2 227.6 227.0 226.4 225.7 225.1 224.5 223.9 223.3 222.7
100 1,000 232.9 233.7 234.3 234.5 234.3 234.0 233.6 233.1 232.5 231.9 231.4 230.8 230.2 229.6 229.1 228.5
120 1,200 232.7 233.5 234.1 234.2 234.1 233.8 233.4 232.9 232.4 231.8 231.2 230.7 230.1 229.6 229.1 228.5
140 1,400 229.6 230.4 231.0 231.2 231.0 230.7 230.4 229.9 229.3 228.8 228.2 227.6 227.1 226.6 226.0 225.5
160 1,600 226.3 227.1 227.7 227.8 227.7 227.4 227.1 226.5 226.0 225.5 224.9 224.4 223.8 223.3 222.8 222.3
180 1,800 223.0 223.8 224.4 224.5 224.4 224.1 223.8 223.3 222.8 222.2 221.7 221.2 220.7 220.2 219.7 219.2
200 2,000 219.8 220.6 221.2 221.4 221.2 221.0 220.7 220.2 219.7 219.2 218.7 218.2 217.7 217.3 216.8 216.4
220 2,200 216.9 217.7 218.3 218.4 218.3 218.1 217.8 217.4 216.9 216.4 216.0 215.5 215.1 214.7 214.2 213.8
240 2,400 214.1 214.9 215.5 215.7 215.6 215.4 215.1 214.7 214.3 213.9 213.4 213.0 212.6 212.2 211.8 211.5
260 2,600 211.5 212.3 213.0 213.1 213.1 212.9 212.6 212.3 211.9 211.5 211.1 210.7 210.3 210.0 209.6 209.3
280 2,800 209.9 210.6 210.8 210.7 210.6 210.3 210.0 209.6 209.2 208.9 208.5 208.2 207.8 207.5 207.2
300 3,000 207.7 208.3 208.5 208.5 208.4 208.1 207.8 207.5 207.1 206.8 206.5 206.2 205.9 205.6 205.4
124
Table 5.4b – 15 Stages Slickwater (Results in Bcf)
Proppant
amount per stage
(tonnes)
Well
proppant amount
(tonnes)
Row 1 - Fluid injected per stage (m3), Row 2 - Fluid injected per well (m3)
250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1,000
3,750 4,500 5,250 6,000 6,750 7,500 8,250 9,000 9,750 10,500 11,250 12,000 12,750 13,500 14,250 15,000
40 600 199.6 200.7 201.6 202.0 202.1 202.2 202.2 202.1 202.0 201.9 201.8 201.7 201.6 201.5 201.4 201.3
60 900 203.2 204.3 205.2 205.5 205.7 205.8 205.8 205.7 205.6 205.5 205.4 205.3 205.3 205.2 205.1 205.0
80 1,200 208.8 209.9 210.7 211.1 211.3 211.4 211.4 211.3 211.3 211.2 211.1 211.0 210.9 210.8 210.8 210.7
100 1,500 218.1 219.1 219.9 220.3 220.4 220.5 220.6 220.5 220.4 220.3 220.3 220.2 220.1 220.0 220.0 219.9
120 1,800 220.4 221.4 222.2 222.6 222.7 222.8 222.9 222.8 222.7 222.7 222.6 222.5 222.4 222.4 222.3 222.2
140 2,100 219.6 220.6 221.4 221.7 221.9 222.0 222.0 222.0 221.9 221.8 221.7 221.7 221.6 221.5 221.4 221.4
160 2,400 218.5 219.5 220.3 220.7 220.9 220.9 221.0 220.9 220.9 220.8 220.7 220.6 220.5 220.5 220.4 220.3
180 2,700 217.5 218.5 219.3 219.6 219.8 219.9 219.9 219.9 219.8 219.7 219.6 219.6 219.5 219.4 219.4 219.3
200 3,000 216.5 217.5 218.3 218.6 218.8 218.9 218.9 218.9 218.8 218.7 218.7 218.6 218.5 218.5 218.4 218.4
220 3,300 215.6 216.6 217.4 217.7 217.9 218.0 218.0 218.0 217.9 217.9 217.8 217.7 217.7 217.7 217.6 217.6
240 3,600 214.7 215.7 216.5 216.8 217.0 217.1 217.2 217.1 217.1 217.0 217.0 216.9 216.9 216.8 216.8 216.8
260 3,900 213.9 214.8 215.6 216.0 216.2 216.3 216.3 216.3 216.3 216.2 216.2 216.1 216.1 216.1 216.0 216.0
280 4,200 214.0 214.8 215.2 215.3 215.4 215.5 215.5 215.4 215.4 215.4 215.3 215.3 215.3 215.3 215.3
300 4,500 213.2 214.0 214.4 214.5 214.6 214.7 214.7 214.7 214.7 214.6 214.6 214.6 214.6 214.6 214.6
125
Table 5.4c – 30 Stages Slickwater (Results in Bcf)
Proppant
amount per stage
(tonnes)
Well
proppant amount
(tonnes)
Row 1 - Fluid injected per stage (m3), Row 2 - Fluid injected per well (m3)
250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1,000
7,500 9,000 10,500 12,000 13,500 15,000 16,500 18,000 19,500 21,000 22,500 24,000 25,500 27,000 28,500 30,000
40 1,200 233.2 234.7 236.0 236.8 237.4 237.9 238.3 238.7 239.0 239.3 239.6 239.9 240.2 240.4 240.7 240.9
60 1,800 236.5 237.9 239.1 239.8 240.4 240.9 241.3 241.6 241.9 242.2 242.5 242.8 243.1 243.3 243.6 243.8
80 2,400 241.0 242.2 243.2 243.9 244.4 244.9 245.2 245.5 245.8 246.1 246.4 246.6 246.9 247.1 247.4 247.6
100 3,000 247.6 248.4 249.1 249.6 250.0 250.3 250.6 250.9 251.1 251.3 251.6 251.8 252.0 252.2 252.4 252.6
120 3,600 249.4 250.1 250.7 251.2 251.5 251.8 252.1 252.3 252.5 252.7 252.9 253.1 253.3 253.5 253.7 253.8
140 4,200 250.5 251.3 251.9 252.3 252.7 253.0 253.3 253.5 253.7 253.9 254.0 254.2 254.4 254.5 254.7 254.8
160 4,800 251.5 252.3 253.0 253.4 253.8 254.1 254.3 254.5 254.7 254.9 255.0 255.2 255.3 255.5 255.6 255.7
180 5,400 252.4 253.2 253.8 254.3 254.6 254.9 255.1 255.3 255.5 255.6 255.8 255.9 256.1 256.2 256.3 256.4
200 6,000 253.0 253.8 254.5 255.0 255.3 255.6 255.8 255.9 256.1 256.3 256.4 256.6 256.7 256.9 257.0 257.1
220 6,600 253.7 254.5 255.2 255.6 256.0 256.2 256.4 256.6 256.8 257.0 257.1 257.3 257.4 257.5 257.6 257.8
240 7,200 254.4 255.2 255.8 256.3 256.6 256.9 257.1 257.3 257.4 257.6 257.7 257.9 258.0 258.1 258.2 258.3
260 7,800 254.9 255.8 256.4 256.9 257.2 257.4 257.6 257.8 257.9 258.1 258.2 258.4 258.5 258.6 258.7 258.8
280 8,400 256.2 256.9 257.3 257.6 257.9 258.1 258.2 258.3 258.5 258.6 258.7 258.8 259.0 259.1 259.2
300 9,000 256.6 257.2 257.7 257.9 258.2 258.4 258.5 258.6 258.8 258.9 259.0 259.1 259.2 259.3 259.4
126
Figure 5.2 compares how the 15-stage output for both the crosslinked gel and slickwater is
affected by changes in proppant and fluid amounts. Crosslinked gel does see a small
improvement in the output when the fluid per stage is increased. The slickwater case peaks at
400 m3/stage with no further improvements to the output. The output for both the slickwater and
crosslinked gel peaks at 120 tonnes per stage; when more proppant is added the output beings to
drop.
Figure 5.3 shows how the stage count affects the output. Here each stage has different lines that
represent varying fluid amount. The output using the crosslinked gel increases with stage count.
The 10-stage slickwater output outperformed the 15-stage slickwater output. As mentioned
previously the 10 stages per well using slickwater are likely extrapolated and may be unreliable.
The 30 stage output for the crosslinked gel is also extrapolated. However, it does follow a similar
trend of the 30 stages using the slickwater.
Figure 5.4 compares the 15-stage output of crosslinked and slickwater wells. The results are
close between the two types of fluids, especially when the fluid amount per stage is similar
(example 260 m3/stage for crosslinked and 250 m3/stage for slickwater)
127
Figure 5.2: Aggregated cumulative 5-year production vs proppant amount and fluid amount per
stage using 15 stages per well and the crosslinked gel (top) and the slickwater (bottom) as the
fracture fluid.
Slickwater - 15 stages
Crosslinked gel - 15 stages
128
Figure 5.3: Affect of stage count per well on the aggregated cumulative 5-year production using
crosslinked gel (top) and slickwater (bottom) as the fracture fluid.
Crosslinked gel
Slickwater
129
Figure 5.4: Crosslinked gel vs slickwater results for 15 stage count.
To effectively observe how the injected water amounts affect the output, the cases where 120
tonnes of proppant per stage were used since this is the amount at which most of the cases hit
either the maximum or an inflection point. Figure 5.5 shows the output versus the total water
injected for various stage counts for both crosslinked gel and slickwater wells using 120 tonnes
of proppant per stage. From this result, it can be seen that output increases with stage count (with
the exception of the 10 stage slickwater treatment), also the output is minimally impacted when
more fluid is injected per stage and after a certain amount of fluid it no longer improves output.
130
Figure 5.5: Aggregated cumulative production versus the total water injected for various stage
counts of crosslinked gel and slickwater wells using 120 tonnes of proppant per stage.
The maximum output from the sensitivities was 259 Bcf. If maximum output was the ultimate
goal, then the best way to complete the 40 wells would be to be with slickwater, 30 stages, 1,000
m3 of fluid per stage and 300 tonnes of proppant per stage. This would result in a total injected
fluid of 1,200,000 m3 and 360,000 tonnes of proppant. If, however the goal is to minimize the
fluid input, the best strategy would be to complete with crosslinked gel, 10 stages, 120 m3 of
fluid per stage and 120 tonnes of proppant per stage. This would result in a total injected fluid of
48,000 m3 and 48,000 tonnes of proppant. This type of completion would result in an output of
205 Bcf which is 79% of the maximum possible output, the water usage is only 4% and the
proppant usage is 13% of the maximum possible case.
131
Since the goal of this study is to minimize water injection a new parameter can be identified
known as injection efficiency:
Injection Efficiency (Mcf
m3) =
Aggregated 5 year cumulative production (Mcf)
Total fluid injected in all wells (m3)
Figure 5.6 shows how the injection efficiency for different stage count and fluid types changes as
more fluid is injected. The results show that the crosslinked gel has a better injection efficiency
than slickwater and that the injection efficiency decreases as more stages are added to wells. This
makes sense since the crosslinked gel uses far less water injection than slickwater and the lower
the stage count, the less the water use.
Figure 5.6: injection efficiency for different stage count and fluid types versus total fluid injected
132
If the goal was to maximize injection efficiency, the best strategy would be to complete with
crosslinked gel, 10 stages, 90 m3 of fluid per stage and 80 tonnes of proppant per stage. This
would result in total injected fluid of only 36,000 m3 and 32,000 tonnes of proppant. This type of
completion would result in an output of 197 Bcf which is 76% of the maximum possible output,
the water usage is only 3% and the proppant usage is 9% of the maximum possible case.
With all proposed well forecasts, it is worth crosschecking the outputs with the existing wells.
Figure 5.7 shows the individual well 5-year cumulative production and injection efficiency for
the 74 existing crosslinked gel and slickwater wells versus total fluid injected. The injection
efficiency of the crosslinked gel is much higher than the slickwater, the results are also similar to
the injection efficiency curves generated from the sensitivity runs in Figure 5.5 and 5.6.
133
Figure 5.7: 5-year cumulative production (top) and injection efficiency (bottom) for the 74
existing crosslinked gel and slcikwater wells versus total fluid injected
134
5.7 Conclusions
In this study we used a machine learning model developed and trained on 74 existing wells in the
Montney formation in Canada, to run sensitivities on 40 proposed wells to be drilled adjacent to
the existing producers. 1,080 sensitivities were run to explore how different combinations of
stage count, fluid type, water amount, and proppant amount affect the aggregated 5-year
cumulative gas production of the 40 proposed wells.
The results of the sensitivities show that injecting greater amounts of water during a hydraulic
fracture does result in slightly more cumulative production in both slickwater and crosslinked gel
completions. The injection efficiency on the other hand drops exponentially with greater water
injection. The results show that it is possible to achieve a cumulative production that is 76% of
the maximum by using only 3% of the water required to achieve this maximum. The results also
show that after cumulative production peaks at about 120 tonnes of proppant per stage for wells
with 10 or 15 stages and only marginally higher for wells with 30 stages.
The model in this study can be used to find the optimal stage count, fluid type, water and
proppant usage when adding new wells to a field with existing development. The model can be
used for any formation as long as there are sufficient vertical wells with rock mechanical logs in
the area. The accuracy of the model increases when the field has more existing development.
Over the last decade the industry has shifted away from crosslinked gel in favor of slickwater, at
the same time, stage count per well along with water injected per stage has also increased. This
has led to a dramatic increase in water usage which has impacted local water resources and
increased the need for wastewater management. This study has shown that bigger is not
135
necessarily better and that using slickwater and many stages should not be the automatic choice
for completion design even though it the most popular. Conservation of water should be a top
consideration together with cost and profit, every aspect of completion design should be
carefully considered for every type of play. The choice should be driven by resulting production
history from the field and should evolve as more data is generated. Several types of completion
design should be experimented with to see which have the highest injection efficiency at the
lowest cost.
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Chapter 6: Using a Convolutional-Recurrent Neural Network Forecasting Model to Optimize the
Positioning of New Wells in a Partially Developed Field
6.1 Preface
This Chapter has been submitted as a manuscript to the Journal of Petroleum Science &
Engineering in 2020. This article is co-authored by Ian D. Gates.
137
6.2 Abstract
The ultimate recoverable hydrocarbon volumes and economic value of a partially developed field
is controlled by the positioning of future wells. The placement of wells involves aspects of the
understanding of the geology and heterogeneity of the resource as well as the costs of surface
pads and facilities. In this study, a convolutional-recurrent neutral network (c-RNN) developed
and trained to forecast shale gas production given well positions, spacing parameters, and
geomechanical properties within the reservoir, as well as the completion strategies: either a water
intense 30-stage slickwater treatment or a water conservative 15-stage crosslinked gel treatment.
The forecasting model is used to guide the optimal positioning of 20 new wells selected from 40
possible well positions; there are exactly 137,846,528,820 ways to position 20 wells in 40
predetermined positions; this defines the well placement space. To run this many positioning
combinations is computationally not feasible. Here, an approach is described to optimize well
placement using a subspace of the well placement space. The results show that with only 100
random combinations a normal distribution describing the entire well placement space begins to
form. The approach described permits a simple and intuitive method that can be used to find a
well placement combination with high aggregated 5-year cumulative gas production volume and
demonstrates a practical application of the c-RNN forecasting model.
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6.3 Introduction
Maximizing hydrocarbon recovery while minimizing costs has always been a priority of the oil
and gas industry and with green fields becoming increasingly rare, optimization of developed
fields has become of great interest to organizations. If completion design is held constant in a
particular area, two factors drive the production performance of a future well: 1. geology and 2.
well placement (location, orientation, and depth or trajectory). The geological properties of a
reservoir, such as permeability, porosity, fluid saturation, rock mechanical properties, in-situ
stresses, etc., have a large effect on how fracture networks form and interact during stimulation
and how fluids flow through the formation during production. Geological properties are also
heterogenous and can vary dramatically even over distances of order of one hundred meters.
Thus, no two wells in a formation will have the exact same geological profile along the wellbore.
Well placement – which gives rise to well spacing – is another important factor because wells
drilled to near each other can share drainage areas which can negatively impact the production of
both wells. This is especially true in multi-stage hydraulically fracture horizontal wells since the
fracture networks from neighboring wells can easily link up. Well spacing depends ultimately on
geology: in less permeable rock, wells can be drilled closer together than in reservoirs with high
permeability. Because of geological heterogeneity, the position of a wellbore path within a
reservoir plays an important role in the future production performance of that well. Most fields
are only partially developed which implies that the amount of hydrocarbon volume left in the
reservoir to produce is driven by the position of future wells. Therefore, a method that can
optimize future well placement would be of great use in field development.
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Historically, the most common way for industry to find the optimal well placements has been to
use exhaustive physics-based reservoir simulation methods together with a set of candidate well
locations which are typically defined by the user. In that approach, a geological model and a
numerical reservoir simulator are used to forecast production from all possible well placements
in the set of candidate well locations to see which combination of well placements result in the
highest cumulative field production or economic value or both (Jang et al., 2018). This approach,
however, is time consuming as full field simulation models typically contain tens of millions of
grid blocks requiring large compute time for evaluating multiple development options. To
overcome this limitation, various optimisation techniques have been developed including genetic
algorithms (GA), simulated annealing (SA), neural networks (ANN) and particle swarm
optimisation (PSO) (Bittencourt and Horne,1997; Centilmen et al., 1999; Yeten et al., 2002;
Emerick et al., 2009; Salmachi et al., 2013; Onwunalu and Durlofsky, 2010). Despite these
optimization methods, many being automated, the required computation time is still significant.
An optimized well placement strategy is only as good as the geological, reservoir, and
forecasting model used to produce it. If the geological or reservoir model is poor or the
forecasting model is inaccurate or uncertain, then it is likely that any well placements that are
chosen by the optimization algorithm will not produce optimal volumes. Numerical reservoir
simulators are a bottom up approach (Mohaghegh, 2017) where the geological model or an
ensemble of equiprobable models is defined and the system is optimized against an objective
function taking into account the set of candidate well locations. In most cases, a single geological
model is defined and the model is constructed from upscaled data from wells that are kilometers
away from each other yielding an oversimplification of a reservoir, its geological properties and
140
the complexities of its fracture networks. Thus, many operators have little confidence in the
ability to use numerical reservoir simulation optimization for forecasting and the placement of
wells to maximize future production.
An alternative approach that has been recently getting attention is by using machine learning
algorithms. These algorithms make minimal assumptions about the structure or geology of the
reservoir or how fluid flows through it. Rather, they are trained using existing data to find links
between the inputs (such as geology, completion type and spacing between wells) and the output
(such as cumulative production). The greater the richness of the input data, the better the
accuracy of the forecasting model, and the more capable the machine learning methods are able
to optimize well placements.
In this study, we use a machine learning algorithm to determine where best to locate 20 wells
amongst 40 potential locations. In the context of a company, this could be interpreted as having
40 well location options for a full field development but having a budget for a partial field
development that requires selecting only a subset of 20 of them. The objective function is to
maximize the aggregated 5-year cumulative gas production using only 20 of the well locations
taking into account the factors described above about geology and secondary wells drilled after a
first well and spacing from adjacent older wells and how cumulative production is impacted.
If done manually, there are 137,846,528,820 different combinations (the well placement space)
to position 20 wells in 40 predetermined positions. If done with a physics-based reservoir
simulator and if each simulation took 10 minutes to run, it would take over 2,000,000 years to
141
run all the cases. Even if only 1% of the well placement space was evaluated, this would take
20,000 years of simulations. Even with parallel processing capabilities, for example, with 1,000
cores, a 1% subset evaluation would take 20 years. Thus, options to do this in meaningful time,
say on the order of days to weeks would be desired. Machine learning offers an option to do this.
6.4 Study Area and Completion Scenarios
The study area is the same for all research chapters and is described in Chapter 1: introduction of
this thesis and shown in Figures 1.2 and 1.3. The 40 possible future well positions are shown in
Figure 5.1 and are the same as the 40 well positions that where used to run sensitivities on
completion designs in Chapter 5.
The forecasting model developed in this study uses three groups of input parameters at every
stage along the wellbore to make a prediction about the gas production. These 3 groups are:
• well spacing and completion order,
• rock mechanical properties, and
• completion parameters.
The individual parameters of each group are listed in Table 5.1.
6.4.1 Well spacing and completion order
The existing producers in this study are drilled close to each other so the production of gas from
one well affects the production of its neighbors. This was shown by Chapter 4 where the
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individual well error rate of the forecasting model decreased from 16.3 to 14.9% when well
spacing and completion order parameters (time and gas volume that a well produced in an
unbounded state, time and gas volume that offset wells produced before a well was drilled,
percentage of length that each offset well covers a well, average perpendicular distance between
offsetting wells) were taken into account. Because the well spacing and completion order was
important, they were also used for the proposed wells in this study. The spacing parameters were
based on distance from a proposed well location to existing producers as well as the distance
between the proposed wells themselves. Well spacing and completion order makes more sense
on a well level not a stage level, so the input values representing spacing and completion order
for the well would be constant at every stage in that well.
6.4.2 Rock mechanical properties
The rock mechanical properties at each stage of the proposed wellbore trajectory were extracted
using the rock mechanical model built in Chapter 4. Briefly, this model was developed by
upscaling and 3D interpolating the density (RHOB), compressional sonic (DTP) and shear sonic
(DTS) logs of 180 vertical and deviated wells located in the study area. The DTS log was present
in only 14 of these wells and had to be synthetically generated for the other 166 using the neural
network developed in Chapter 3. Because stage count per proposed well can be either 15 or 30
depending on the scenario, the rock mechanical properties are different depending on the stage
count. For each proposed well we extracted 2 sets of rock inputs based on the number of stages.
143
6.4.3 Completion Parameters
For this study the fluid type, fluid amount and proppant amount are used as the completion
parameters. Two completion cases are considered for each well: 1. water intense and 2. water
conservative. This makes the optimization problem more challenging. The completion
parameters for the two cases are as follows:
• Water intense:
o Fracture fluid - slickwater
o 30 stages per well
o 150 tonnes of proppant per stage
o 650 m3 of fluid per stage
• Water conservative:
o Fracture fluid - crosslinked gel
o 15 stages per well
o 100 tonnes of proppant per stage
o 150 m3 of fluid per stage
The stage count, proppant amount, and fluid amount for each of these cases were chosen based
on the average of the existing 26 slickwater wells and 40 crosslinked gel wells in the area of
interest.
6.5 Neural Network Algorithm for Gas Production Forecasting
The neural network used in this study was developed in Chapter 4. In this work, the network was
trained using the 74 existing producers in the area with the supervised learning approach. During
supervised learning both the inputs and the outputs are provided to the network. The inputs are
144
the well spacing and completion order, rock mechanical properties and the completion
parameters. The output was the 5-year cumulative production profile in one-year increments. The
network predicts an output given the inputs, this predicted output is compared to the actual and
the error is backpropagated back through the system adjusting the weight parameters. The weight
parameters are started with random values but get adjusted as more of the well inputs and outputs
are shown to network. Once the network sees the entire data hundreds of times over, the network
begins to find general trends and patterns within the study area and the overall prediction error
rate drops (Reed and Marks, 1998). Once the network is trained to a sufficiently low error rate it
can be used to make predictions.
The trained network cannot distinguish between existing or proposed wells, as long as the input
data is in the correct format the network will make a prediction. The trained network can be used
to see how the 5-year cumulative production of a proposed well is affected when the inputs are
changed, i.e. it can be used to run sensitivities. As long as the proposed wells are located within
the study area (the geology is similar to what the network has been trained on), of similar length
and of similar completion designs the aggregate error rate should be similar to that of the existing
producers. Figure 4.13 shows how the error of the model drops as more wells are aggregated, at
20 wells the error rate is expected to be around 2.8%.
The model consists in this study is a multi-headed convolutional-recurrent hybrid network (c-
RNN). The c-RNN hybrid network was chosen because it combines both the speed and ability to
process large amounts of data of a convolutional network with the sequence processing ability of
a recurrent network. The c-RNN hybrid has been shown to outperform traditional neural
145
networks in Chapter 3. In multi-headed architectures each input variable is handled by a separate
convolutional network (head) and the output of each of these networks (heads) are merged and
inputted into a recurrent network before a prediction is made; these types of models offer better
performance (Bagnall, 2015). The network was programmed in Python using the keras library
(Chollet, 2015). The architecture of the network is shown in Figure 4.6 and the network
hyperparameters are shown in Table 4.3.
As depicted in Figure 4.7, the inputs to the neural network are a series of tables where the
columns represent the stage variables and rows represent the stages. Each value in this table
represents a particular input parameter at a particular stage. The maximum number of successful
stages per well in the existing 74 wells was 31. Since the network was trained on existing wells
the input shape cannot change, so wells with less than 31 successful stages simply had a “0”
value associated with the stages it did not have. All the input variables were normalized to values
between 0 and 1, where 0 represents the minimal value in that parameter and 1 represents the
maximum from the existing 74 wells.
6.6 Well Combinations and Procedure
Although there are 137,846,528,820 ways to position 20 wells in 40 predetermined positions, in
the approach used here, a very small number is used for making predictions with the forecasting
model. Two steps are conducted to create the sample space for evaluating well placement as
follows:
146
Step 1: 100 combinations of the well placements were chosen at random and the gas volumes
were forecasted using the c-RNN model. Different positioning combinations of the 20 wells lead
to different well spacing and completion order parameters for each of the wells which must be
recalculated for each arrangement of the 20 wells relative to themselves as well as to the existing
wells. Recalculation of these parameters is important because the produced gas volume depends
on spacing. As an example, Figure 6.1 shows two random positioning combinations of the 20
wells illustrating how different arrangements lead to different spacings between all wells. To
generate the results the spacing input parameters were updated for every well in each
combination. For every combination the c-RNN generated a unique 5-year cumulative gas
production profile for every well, the production of all 20 wells was then aggregated. The 100
well location combinations were run with each of the slickwater (water intense) and cross-linked
gel (water conservative) stimulation methods. This gave rise to 200 total well location
combinations and stimulation designs. The purpose of the random combinations was to roughly
approximate what the true normal distribution curve of all possible combinations would look
like. This approximate distribution is meant to serve as a background on which to compare the
performance of other well combinations. It is also used to validate or falsify claims of optimal
well combinations.
147
Figure 6.1: One random combination of 20 wells (top), another random combination of 20 wells
(bottom).
148
Step 2: Given that there are over 100 billion combinations, it is unlikely that 100 random
combinations would give insights into which combination yields the highest or the lowest
cumulative gas. For this reason, a second set of combinations are examined using the following
procedure to generate 4 additional combinations:
1. Run a full field scenario using all 40 possible well positions with slickwater (water intense)
stimulation; denote this set of cases as SW40.
2. Identify subset of the 20 wells with the highest production volume from the SW40 set;
denote this subset as SW20H. The remaining subset of 20 wells become subset SW20L (the
lowest production volume wells). Figure 6.2 displays the SW20H and SW20L subsets.
3. Run a full field scenario using all 40 possible well positions with crosslinked gel (water
conservative) stimulation; denote this set of cases as CG40.
4. Identify subset of the 20 wells with the highest production volume from the CG40 set; denote
this subset as CG20H. The remaining subset of 20 wells become subset CG20L (the lowest
production volume wells). Figure 6.3 shows the CG20H and CG20L subsets.
This procedure generated 4 well combinations that were added to the 100 random combinations
generated in Step 1 giving a total of 104 positioning combinations for each stimulation method.
In total, 208 different aggregated 5-year cumulative gas production values were determined (104
per stimulation method). The point of generating these 4 additional well combinations is that it is
a shortcut which finds the “approximate” lowest and highest combinations when only 20 wells
are used. However, the shortcut is only approximate since it uses all 40 wells with spacing
parameters for all 40 wells involved in the calculation. The four additional cases from Step 2 are
149
then re-run using only the 20 wells with the slickwater and crosslinked gel stimulations using the
spacing parameters for the 20 wells.
Figure 6.2: Best and worst 20 well positions found in the 40 well prediction using the slickwater
(water intense) stimulation.
Existing
20 best wells
20 worst wells
150
Figure 6.3: Best and worst 20 well positions found in the 40 well prediction using the crosslinked
gel (water conservative) stimulation.
6.7 Results and Discussion
Tables 6.1 and 6.2 show the results of the 100 random positioning combinations along with the
four additional combinations found from forecasting the drilling of all 40 wells in scenarios
SW40 and CG40. The results in Table 6.1 are from the crosslinked gel (water conservative)
stimulation and the results in Table 6.2 are from the slickwater (water intense) stimulation.
Existing
20 best wells
20 worst wells
151
Table 6.1: Results from the sensitivity analysis using crosslinked gel as the fracture fluid.
20 Well Cumulative Gas Production (Bcf)
Combination Year 1 Year 2 Year 3 Year 4 Year 5
001 33 57 75 87 96
002 32 55 71 83 91
003 33 57 74 86 95
004 33 57 75 88 98
005 34 58 76 88 97
006 33 56 73 85 94
007 34 58 76 89 98
008 33 57 74 87 95
009 32 54 71 82 90
010 34 60 78 92 102
011 33 57 74 86 95
012 34 60 78 91 101
013 34 59 77 90 99
014 34 60 78 91 100
015 34 58 76 89 99
016 34 58 75 87 96
017 33 56 73 85 93
018 34 60 79 93 103
019 32 55 71 83 91
020 33 57 74 86 95
021 33 56 72 84 92
022 33 57 74 86 95
023 34 59 78 91 101
024 33 58 76 88 97
025 34 60 79 93 103
026 33 57 75 87 96
027 35 62 81 95 106
028 34 60 79 92 102
029 32 54 70 81 89
030 34 58 76 89 98
031 35 61 80 93 103
032 35 60 78 91 100
033 33 57 74 86 96
034 34 59 77 90 100
035 35 59 77 89 98
036 33 56 72 84 92
037 34 58 75 87 96
038 33 58 76 89 99
152
Table 6.1 continued 20 Well Cumulative Gas Production (Bcf)
Combination Year 1 Year 2 Year 3 Year 4 Year 5
039 33 56 73 85 93
040 32 56 72 84 93
041 34 59 77 90 100
042 32 55 72 84 92
043 33 58 77 91 100
044 34 59 77 89 99
045 34 59 77 91 100
046 35 60 79 92 101
047 34 58 74 86 95
048 33 56 72 84 92
049 35 60 78 92 101
050 32 55 71 83 91
051 34 60 78 92 101
052 33 58 76 89 99
053 34 59 77 90 99
054 33 58 76 90 100
055 35 61 81 94 104
056 32 55 72 84 92
057 34 59 77 90 99
058 33 56 73 85 94
059 34 59 77 90 100
060 33 58 76 89 98
061 34 59 77 91 100
062 33 57 74 86 95
063 33 57 75 87 96
064 35 62 82 96 106
065 34 60 79 93 103
066 35 60 78 91 100
067 34 58 76 89 98
068 33 56 73 84 93
069 32 55 71 82 91
070 34 59 78 91 100
071 34 58 76 89 98
072 34 59 77 90 100
073 34 58 76 88 98
074 34 59 77 90 99
075 33 58 77 90 100
076 33 56 73 85 93
077 1 59 78 91 101
153
Table 6.1 continued 20 Well Cumulative Gas Production (Bcf)
Combination Year 1 Year 2 Year 3 Year 4 Year 5
078 33 58 77 90 100
079 34 58 76 89 98
080 33 58 76 88 98
081 34 59 77 90 100
082 33 57 75 88 98
083 32 56 72 84 93
084 33 55 72 83 92
085 34 58 76 89 99
086 33 57 74 86 94
087 33 57 74 85 94
088 33 57 74 86 95
089 34 57 74 85 94
090 34 59 77 91 100
091 33 58 76 88 98
092 33 57 74 86 95
093 34 59 77 89 98
094 33 58 76 90 100
095 34 60 79 93 104
096 33 57 75 88 97
097 34 59 78 91 101
098 34 60 79 93 103
099 33 58 77 90 99
100 33 57 73 85 94
CG20H well combination 37 66 88 104 116
CG20L well combination 32 53 68 79 87
SW20H well combination 36 64 84 99 110
SW20L well combination 34 58 75 88 97
154
Table 6.2: Results from the sensitivity analysis using slickwater as the fracture fluid.
20 Well Cumulative Gas Production (Bcf)
Combination Year 1 Year 2 Year 3 Year 4 Year 5
001 34 62 84 102 115
002 34 60 80 96 109
003 33 59 81 98 111
004 33 59 80 97 110
005 35 64 86 104 118
006 34 60 81 97 109
007 33 60 82 99 113
008 34 61 82 99 111
009 32 57 77 92 104
010 34 63 86 105 119
011 34 61 82 100 113
012 34 62 85 103 117
013 34 61 83 101 114
014 34 61 84 102 116
015 35 63 86 105 119
016 35 62 85 103 117
017 33 60 82 99 112
018 35 63 87 106 120
019 34 60 81 97 109
020 35 62 84 101 115
021 33 59 80 97 110
022 34 61 82 99 112
023 33 60 83 100 114
024 33 59 81 98 111
025 35 64 87 106 120
026 33 59 81 97 110
027 35 64 87 106 121
028 34 61 83 101 115
029 32 58 79 95 107
030 35 63 86 104 118
031 35 64 87 106 120
032 36 65 89 108 123
033 32 58 79 96 109
034 33 60 81 98 111
035 35 62 84 101 115
036 34 61 83 99 112
037 35 61 82 99 112
038 33 60 82 100 114
155
Table 6.2 continued 20 Well Cumulative Gas Production (Bcf)
Combination Year 1 Year 2 Year 3 Year 4 Year 5
039 35 61 82 99 111
040 33 58 79 95 107
041 34 62 84 102 116
042 34 61 82 99 112
043 33 60 82 100 114
044 34 61 83 101 114
045 33 60 83 100 114
046 35 64 88 107 122
047 35 63 85 102 115
048 34 61 82 99 112
049 34 63 86 105 119
050 33 60 81 98 110
051 36 64 87 105 120
052 34 62 85 103 118
053 35 62 85 102 116
054 33 59 81 98 111
055 35 64 87 106 121
056 32 57 77 93 105
057 35 62 85 102 116
058 33 60 81 97 110
059 34 62 84 102 116
060 33 60 82 99 112
061 34 61 83 101 115
062 36 64 86 104 117
063 34 61 83 100 113
064 35 64 89 108 124
065 34 63 86 105 120
066 35 64 87 105 119
067 34 62 84 102 115
068 35 62 84 101 113
069 33 59 79 95 107
070 34 63 86 104 119
071 35 63 86 104 118
072 33 60 82 99 112
073 35 62 84 102 115
074 34 62 84 101 115
075 33 60 82 99 113
076 35 61 83 99 112
156
Table 6.2 continued 20 Well Cumulative Gas Production (Bcf)
Combination Year 1 Year 2 Year 3 Year 4 Year 5
077 34 61 83 101 114
078 33 59 80 97 110
079 34 62 84 101 115
080 32 58 79 96 110
081 35 63 86 104 119
082 33 59 80 97 111
083 32 58 79 96 108
084 33 59 79 94 106
085 34 61 84 102 117
086 34 60 81 98 111
087 34 61 83 100 113
088 34 60 82 99 112
089 34 61 83 99 112
090 34 61 83 101 114
091 33 59 81 98 111
092 34 61 82 99 113
093 35 63 86 104 118
094 33 60 83 100 114
095 34 61 84 102 116
096 33 60 81 98 111
097 35 63 87 105 119
098 34 62 85 103 117
099 34 62 85 103 117
100 35 62 84 101 114
SW20H well combination 36 66 91 111 127
SW20L well combination 34 61 83 100 114
CG20H well combination 36 66 91 112 129
CG20L well combination 34 60 80 96 108
Figure 6.4 shows two histograms (one for each stimulation case) which depict the distribution of
the aggregated 5-year cumulative gas production of the 100 random positioning combination
along with the 4 best/worst combinations generated by running the full field development
scenario in Step 2 of the procedure. The 100 random combinations in the histograms are rough
approximations of what the true normal distribution curve of all possible combinations would
look like.
157
Figure 6.4: Results of the 104 combinations presented in a histogram using both crosslinked
(top) and slickwater (bottom) as the stimulation fluid.
Bins of aggregated 5-year cumulative production of 20 wells (Bcf)
[87,
88
]
(88,
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94
]
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]
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Num
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Bins of aggregated 5-year cumulative production of 20 wells (Bcf)
[104
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10
12
14
Slickwater (water intense) case
Crosslinked gel (water conservative) case
CG20H SW20H
CG20L
SW20L
CG20H SW20H
SW20L
CG20L
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The average 5-year aggregated cumulative gas production was 104 Bcf for the water
conservative (crosslinked gel) case and 114 Bcf for the water intense (slickwater) case. The
histograms also show just how much better the best combination was than the average. The
combination that yielded the best results in both water intense and water conservative cases was
the CG20H combination. The CG20H combination performed 19% higher than the average and
34% higher than the worst combination in the water conservative case. In the water intense case
the CG20H combination performed 13% higher than the average and 24% higher than the worst
combination. The cost to drill and complete 20 wells should be the same no matter where they
are drilled in the area. By running these scenarios before drilling, for the same price it is possible
to achieve a 19% higher recoverable volume then average.
The CG20H combination subset outperformed the SW20H combination subset in terms of
cumulative gas produced in both the water conservative and water intense stimulation scenarios.
This is an interesting result because when slickwater was used as the stimulation fluid, the best
20 wells in the full field development (SW20H) were not the best 20 wells in a partial field
development but when crosslinked gel was used, the best 20 wells in the full field development
(CG20H) were the best 20 wells in a partial field development. Another interesting observation
is that the positioning combinations in subset CG20L was the worst positioning combination in
the water conservative case but neither subsets CG20L nor SW20L were the worst cases (in fact
they were closer to the average) in the water intense case.
The approximate best and worst combinations generated by running the full 40 well development
were not the best/worst for slickwater but were the best/worst for crosslinked gel. The only
159
difference between the 20 well scenario and the 40 well scenario is the well spacing. Since the
approximate best/worst combination ranking was affected between the 20 and 40 well scenarios
only when slickwater was used, this suggests that well spacing plays a larger role when
completing with slickwater. When crosslinked gel was used, the best/worst combination ranking
was not affected between the 20 and 40 well scenarios. These results are driven by the larger
well spacing of the 20 well field development versus the full field 40 well development. The
results suggest that the distance between wells is a large factor in production performance when
stimulating with slickwater. This makes intuitive sense as the amount of fluid injected during a
slickwater stimulation is much larger than a crosslinked stimulation and thus would be expected
to create fracture networks that extend further away from the wellbore then if crosslinked gel is
used. Also, the fact that the CG20H well combination performed the best in both water intense
and water conservative stimulation cases suggests that the rock mechanical profile near the
wellbore plays a greater role than completion type when it comes to choosing the best places to
drill locations.
On average, completing the same 20 wells with slickwater lead to the cumulative gas production
being 10% higher then when those wells were completed with crosslinked gel. However; for
10% more gas volumes the slickwater completions had to use 300% more proppant and 867%
more fluid then the crosslinked gel completions.
6.8 Conclusions
In this study, a convolutional-recurrent neural network previously developed and trained on 74
existing wells were used to find the aggregated 5-year cumulative gas production of various
160
positioning combinations of 20 new wells. The positioning of the 20 new wells was selected
from 40 predetermined positions that were chosen to be have similar length, depth and well
spacing as the existing wells in the field. The results show that with only 100 random
combinations a normal distribution describing the entire sample space of 137,846,528,820 begins
to form. This distribution is useful as it can be used to see how a particular positioning
combination compares to the average of all possible locations. The best combination in the study
was found to be the cross-linked gel well combination (shown in green in Figure 6.3). The results
also suggest that neither the well spacing nor the completion fluid affected the best well position
combination which suggests that the rock mechanical profile near the wellbore plays the greatest
role when it comes to choosing the best places to drill locations.
The method did not sample the complete space (consisting of 137,846,528,820 well
combinations) but rather examined a simple and intuitive method to use the c-RNN gas
production model to guide the decision for choosing the best 20 locations. The tool developed in
this study does not rely on the bottom-up approach of conventional simulators and instead links
well inputs to well performance using a machine learning algorithm. Because the algorithm was
trained and evaluated on existing wells in the study area and had a 5 year, 20 well aggregate
forecast error of only 2.8%, it is arguably more useful then forecast produced by numerical
simulators. Therefore, the optimized well positioning combination will also be more trustworthy.
The approach developed in this study is useful to anyone planning on optimizing the positioning
of new wells in a partially developed field. It allows the user to test how various well placements
would perform as well as provides a guideline to find the best possible well placement.
161
Chapter 7: Conclusions and Recommendations
The main objectives of this thesis were to improve production forecasting as well as optimize
completion and well placement of multi-stage horizontal wells by using machine learning
methods. The research in this thesis focuses on a 30 km by 30 km section of the unconventional
part of the Montney Formation in the province of Alberta, Canada. This area contains a large
number of vertical and horizontal wells thus providing a rich data set for analysis.
7.1 Conclusions
1. A procedure was designed that can generate highly accurate shear synthetic logs using a
convolutional recurrent network (c-RNN). This procedure can act as a cost effective and
fast alternative to running actual DTS logs in a field with prior development. The rock
mechanical properties surrounding a wellbore can be calculated using the density,
compressional and shear sonic logs of wells penetrating the formation. The rock
mechanical properties of the wells can also be upscaled and interpolated to construct a
three-dimensional (3D) model. Since shear sonic logs are missing from the majority of
wells, generating accurate shear synthetic logs helps increase the accuracy of the rock
mechanical model.
2. A 3D rock mechanical model of the study area was generated using the density and
compressional sonic logs along with the shear sonic (14 actual and 166 synthetic) logs of
162
the 180 vertical and deviated wells in the study area. This 3D model allowed to generate
rock mechanical profiles along the horizontal well bores.
3. The c-RNN was employed to generate five-year cumulative gas production profiles for
74 horizontal multistage hydraulically fractured wells in the study area. The model was
trained by using a combinations of completion parameters, rock mechanical properties,
and well spacing and completion order for each stage in the wells. The best combination
of inputs was found to be the rock mechanical properties surrounding each perforation
cluster, the proppant amount used for every stage, and the spacing and completion order
of neighboring wells. The novelty of this study is that the input variables used are at the
stage level rather than the average of the entire well. The accuracy of the model was
found to increase exponentially as the production of multiple wells was aggregated.
4. The model trained to predict the production performance of the 74 horizontal wells in the
area was used to predict the production performance of 40 new wells planned to be
drilled along side the existing producers. 1,080 sensitivities were run to explore how
different combinations of stage count, fluid type, water amount, and proppant amount
affect the aggregated 5-year cumulative gas production. The study finds that the injection
efficiency (cumulative gas/total fluid injected) drops exponentially when more water is
injected. The results show that it is possible to achieve a cumulative production that is
76% of the maximum by using only 3% of the water required to achieve this maximum.
163
5. The model trained to predict the production performance of the 74 horizontal wells in the
area was used to predict the production performance of 20 new wells that can be drilled
in 40 pre-determined well positions. The results show that with only 100 random
combinations a crude normal distribution describing the entire sample space of
137,846,528,820 begins to form which reveals the average of all possible combinations.
The best combination was found by taking the top 20 wells from the crosslinked gel full
field scenario. This combination performed better than all other combinations in the 20
well scenarios for both the water intense and water conservative cases. It was also found
that rock mechanical profile near the wellbore plays the greatest role when it comes to
choosing the best places to drill locations.
7.2 Recommendations
1. To investigate if the accuracy of the model used to generate synthetic shear logs can be
improved by training it on a field with more than 14 wells that contain actual shear sonic
logs. Also, to test if the accuracy can be improved by looking incorporating other logs
(training data) into the training set.
2. There are many ways to improve the accuracy of the production forecasting model.
Arguably the biggest way would be to have flowrate measuring tool installed at every
perforation cluster, a tool like this would enable linking the completion variables and the
rock mechanics of each stage directly to the amount of production coming from that stage
instead. Another way would be to add the microcosmic measurements at each stage of the
164
well as these would aid in the understanding of the fracture morphology at each stage
along the wellbore. Also, it is unlikely that the neural network used in this study has the
optimal configuration, finding this optimal would improve the accuracy but would
require many more tests. Of course, more installed devices requires additional cost and
since the industry is driven more by profit than scientific curiosity it is likely this will not
happen.
3. Construct the study area in a simulation model to see if the simulation model prediction
as better or worse than the machine learning model. Perhaps also see if the machine
learning model accuracy can be enhanced by incorporating the geology, fracture network
modeling and flow mechanics of the simulation model.
4. Run an economic analysis on water injection efficiency to see if using the water
conservative crosslinked gel fluid during a hydraulic fracture leads to a better or worse
net present value than fracturing with the water intense slickwater fluid.
5. Conduct a more in-depth investigation to see which inputs are driving the choice of the
top 20 well positions in Figure 6.2 and 6.3 to be located more in the bottom right corner
of the study area.
6. Another recommendation is to test the predictor models on different study areas both
conventional and unconventional to see how the prediction accuracy improves or
decreases.
165
166
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175
Appendix A: Temperature Transient Analysis of the Steam Chamber during a SAGD
Shutdown Event
A.1 Abstract
In 2015, major forest fires in Northeast Alberta Canada shut down nearly all major oil sands
extraction and mining operations leading to a loss of 47 million barrels of bitumen within four
weeks; at a $20 netback, this is equivalent to nearly $1 billion dollars in lost value. For in-situ
Steam-Assisted Gravity Drainage operations, the shutdown of operations meant that steam
injection stopped and as a consequence, with continued heat losses from the steam chambers to
the surrounding rock formations, the temperature of the steam chambers fell. This implies that
when the steam injection resumes, some fraction of the injected energy is consumed bringing the
steam chamber back to the temperature and pressure it was at prior to the shutdown. Here, we
examine temperature fall-off from steam chambers where injection has stopped by using a new
three-zone model with heat losses taking into account temperature-dependent thermal
conductivity. The model solves the transient heat conduction and steam condensing equations.
The results show that while the steam chamber collapses it heats the surrounding reservoir
through latent heat loss. A warmer reservoir leads to more mobile oil and less heat loss once
steam injection restarts.
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A.2 Introduction
The performance and efficiency of oil sands thermal recovery processes such as Steam-Assisted
Gravity Drainage (SAGD) is tied to heat transfer within the reservoir. As illustrated in cross-
section in Figure A.1, when the steam enters the oil sands formation through a horizontal steam
injection well, it flows to the outer edge of the steam chamber and releases its latent heat which
in turn is conducted and convected into the colder oil sands at the chamber’s edge (Butler, 1991).
The bitumen is heated to the steam’s temperature and as a consequence, its viscosity drops by
over five orders of magnitude until it is less than 10 cP. The mobilized bitumen then drains
under gravity to a horizontal production well at the base of the steam chamber (Butler, 1991).
The key to successful performance of SAGD is the conformance of steam along the horizontal
well pair. Providing the well pairs are parallel to each other and reasonably horizontal, steam
conformance is controlled in turn by the geological properties and heterogeneity of the oil sands
formation. In particular, since bitumen mobilization provides pore space for steam to invade,
steam conformance is controlled by the ability of the bitumen to be both mobilized and drained
from the reservoir. Thus, the key underlying mechanism of steam conformance is heat transfer
from steam to bitumen and bitumen drainage as illustrated by Austin-Adigio and Gates (2018).
This also implies that a continuous supply of steam must be provided to the reservoir to enable
continuous mobilization, drainage, and production of bitumen.
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Figure A.1: Cross sectional schematic of a typical SAGD process (Gotawala and Gates, 2010).
If steam injection stops, then the pressure of the steam chamber declines. If production were to
continue while steam injection was halted, the pressure would decline in the chamber simply
through the production of fluids from the chamber. The other consequence of a shutdown of
steam injection is that with the pressure declining, the saturation temperature of the steam would
also fall. Furthermore, with continued heat losses from the steam chamber to the surrounding
formation as well as to the overburden and understrata, together with the pressure decline, the
temperature of the steam chamber would drop. With sufficient time, the temperature of the
chamber would fall to the point that oil mobilization suffers and drainage declines lead to
potentially non-economic production. If long enough, to re-pressurize the chamber and get it
back to steam temperature may take an extended period of time of steam injection after the
shutdown period was done. A key question that arises is what is the evolution of the steam
chamber temperature after steam injection is stopped in the case with no production from the
chamber? Here, we examine this question.
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A.3 Literature Review
On temperature decline analysis, there are very few papers that describe methods or applications
of temperature decline methods or both. Duong (2008a) was the first to attempt using
temperature to model steam chamber development. Duong’s study introduced two novel
concepts of cooling time and heating ring and proposed a new technique that uses temperature
measurements taken during a shut in to estimate the effectiveness of conductive heating. The
mathematical model developed by Duong represents the horizontal well as a one-dimensional
radial-cylindrical heat flux equation for an infinite-acting formation. The model is considered
analogous to pressure transient analysis of a pressure build-up test. Temperature fall off data
during shut ins can be used to estimate cooling time and thermal diffusivity of the target
formation.
Zhu et al. (2012) developed semi analytical models that predict the change in steam chamber
temperature during a shut in for a two-dimensional system in the cross-well plane. The models
were developed for both the circulation (startup) and early steam injection (ramp up) phases of
SAGD. The study also developed an inverse model which interprets actual temperature falloff
data at a given location along the wellbore to back calculate the steam chamber size. The inverse
model works by generating hundreds of temperature profiles corresponding to different steam
chambers and iterating until the generated temperature profiles matches the input temperature
profile. In 2015, Zhu et al. showed that plotting the temperature falloff derivative curve against
time resulted in a straight line for the early stage of SAGD. Using numerical simulation, they
developed a correlation between steam chamber size and temperature falloff data, and also
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developed a practical method to estimate the steam chamber size variation along the horizontal
well bore. The models developed by Zhu et al. (2012) solve partial differential equations
analytically by using Laplace transforms. This approach, although accurate, limits the analysis to
simple linear systems where properties are constant. To deal with non-linear systems arising
from temperature-dependent properties, numerical methods such as the finite difference method
are required (Ketkar and Reddy 2003; Sarker and Ketkar 2013).
A.4 Temperature Transient Analysis
Temperature transient analysis uses the evolution of temperature to evaluate properties of a
system. For the case of SAGD, the decline of the temperature can be used to determine heat loss
rates or to determine the size of the steam chamber. Here, we derive a new transient temperature
numerical model that takes temperature-dependent thermal conductivity into account. During
the early life of a SAGD operation there are two types of stages which correspond to two types
of heating scenarios (Edmunds and Gittins, 1991). The first stage is the startup stage during
which steam is circulated in both well pairs to heat the surrounding formation via thermal
conduction. Circulation works by injecting steam into the tubing and circulating it out the
annulus. Once the bitumen around the wells has reached a sufficient temperature to be mobile
and a thermal communication between the well pairs is established the operation moves to Stage
2 which is known as ramp up. During ramp up, steam is injected into the formation and the steam
chamber expands upwards until it hits the overburden formation. While the steam chamber is
growing vertically the rate of oil production increases. After the steam chamber begins to expand
horizontally the production rate levels off, and conventional SAGD begins.
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If a shut in occurs during the circulation phase the dominant form of heat loss will be via
conduction with no latent heat transfer occurring. If the shut in occurs during ramp up the steam
chamber will lose energy to the surrounding reservoir both through sensible and latent heat
transfer. Although convection will exist when the steam chamber collapses it can be assumed
that the dominant form is still conduction.
The mathematical model developed here follows the model first proposed by Zhu et al. (2012).
The models were built on the following assumptions:
1. Beyond the edge of the steam chamber, heat transfer via conduction is the dominant
mode of heat transfer.
2. All temperature zones are modelled as circles with radial temperature distributions. If no
steam is present, then the center of the circle is the highest temperature. If steam is
present, the shape of the steam chamber is assumed to be a circle with constant
temperature until the radius where the steam reaches the saturation curve with zero
quality beyond which point the temperature drops with increasing radius.
3. The steam chamber is modelled as a radial system in the cross-well plane.
4. The reservoir has uniform thermal properties.
A.4.1 Non-Condensing Model for SAGD Start up
During the startup phase of a SAGD operation, steam is circulated through the well to establish
thermal communication between the injector and producer and also make the nearby oil mobile.
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In effect, the wells act as line heat sources. Since the steam is circulated into and out of the well,
no actual steam is injected into the reservoir so the SAGD process can be modeled as simple
conduction from the well to the reservoir. To model the start-up process of SAGD we employed
the non-condensing three zone model first proposed by Zhu et al. (2012) depicted in in Figure
A.2.
Figure A.2: Schematic diagram of a three zone non-condensing model used for SAGD start
up (modified from Zhu et al., 2012).
The three temperature zones are bounded by three circles of increasing radius. The innermost
circle is the steam injection well which is at steam temperature. Zone 1 is the region
immediately surrounding the well and is also at the steam temperature. Zone 2 is saturated liquid
water with its outer limit, and Zone 3, is at reservoir temperature. The three region model is also
useful when modeling a steam chamber since the hot inner zone contains wet steam and thus it is
at saturation conditions and thus its temperature is equal to the steam temperature.
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A.4.1.1 Mathematical form of non-condensing model
For heat transfer in a cylindrical geometry, the dimensionless heat transfer equation is given by
(Zhu et al.2012):
𝜕2𝑇𝐷
𝜕𝑟𝐷2 +
1
𝑟𝐷
𝜕𝑇𝐷
𝜕𝑟𝐷=
𝜕𝑇𝐷
𝜕𝑡𝐷
where TD, tD, and rD, are dimensionless temperature, time and radius, defined by:
𝑇𝐷 =𝑇−𝑇𝑟
𝑇𝑠−𝑇𝑟, 𝑟𝐷 =
𝑟
𝑟𝑤, 𝑡𝐷 = 𝑡
𝛼
𝑟𝑤2
and Ts is the steam temperature, Tr is the initial reservoir temperature, rw is the well bore radius,
and α is the thermal conductivity of the reservoir. The three zones have the following initial
conditions:
Zone 1 (hot zone): 𝑇𝐷(𝑟𝐷, 𝑡𝐷 = 0) = 1 at 0 < 𝑟𝐷 < 𝑅𝐷1
Zone 2 (intermediate zone): 𝑇𝐷(𝑟𝐷, 𝑡𝐷 = 0) =ln (
𝑟𝐷𝑅𝐷2
)
ln (𝑅𝐷1𝑅𝐷2
) at 𝑅𝐷1 < 𝑟𝐷 < 𝑅𝐷2
Zone 3 (cold zone): 𝑇𝐷(𝑟𝐷 , 𝑡𝐷 = 0) = 0 at 𝑅𝐷2 < 𝑟𝐷
The boundary conditions are as follows:
• Since all zones are in contact with each other the heat transfer rate is equal at the boundaries,
and
• The temperature at infinite radius is assumed to always be at Tr.
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A.4.1.2 Numerical solution of the non-condensing model
The finite difference method is used to solve the radial heat transfer equation. The
discretization grid is shown in Figure A.3.
Figure A.3: Discretization domain for one-dimensional radial heat transfer - temperature grid
layout.
The finite difference method can be solved either explicitly or implicitly. The explicit method
uses a forward difference approach and solves for temperature at a new time step using the
temperature at the previous time step. The implicit method uses both the previous time step and
the current time step to solve for temperature at the current time step using an iterative
procedure. The model designed in this study uses the implicit Crank-Nicholson method to solve
for temperature at the jth time and ith radial nodes (Sarker and Ketkar, 2004). Since the non-
condensing model assumes no latent heat transfer (condensation), the only form of heat transfer
is sensible heat transfer. The grid is built by first specifying RD1 and RD2 and the number of
nodes needed in the radial direction. Since RD1 and RD2 represent the size of the steam chamber
they are selected based on the length of steam injection prior to shut in and operator experience.
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It was found that the node representing the “infinite” boundary condition is far enough away so
that results are invariant when the boundary radius is at r > 5R2.
The first ‘i’ node is = 0 and represent the center of the SAGD injector well bore, the grid is
divided to contain the three zones described above. The population of the grid involves three
steps:
1. Filling in the temperature for all nodes in the top row at initial conditions tD = 0. TD in the
hot zone nodes is = 1, TD in the cold zones is = 0.
2. Filling in the temperature for all nodes in the first (rD=0) and last columns (rD->∞) the TD
at the infinite boundary node will always be = 0 since it assumed that no heat reaches it.
The finite difference equation for Node 0 is then (Sarker and Ketkar 2004):
𝑇0𝑗
=(1 − 2𝑃)𝑇0
𝑗−1+ 2𝑃𝑇1
𝑗−1+ 2𝑃𝑇1
𝑗
1 + 2𝑃
where 𝑃 = 𝛥𝑡
𝛥𝑟2
3. Solving for the temperature at the other nodes is given by (Sarker and Ketkar 2004):
𝑇𝑖𝑗
=𝑇𝑖
𝑗−1(1 − 𝑃) +𝑃2 [(1 +
12𝑖) 𝑇𝑖+1
𝑗−1+ (1 +
12𝑖) 𝑇𝑖+1
𝑗+ (1 −
12𝑖) 𝑇𝑖−1
𝑗−1+ (1 −
12𝑖) 𝑇𝑖−1
𝑗]
1 + 𝑃
A.4.2 Condensing Model for SAGD Ramp up
During the ramp up stage of SAGD, steam is injected into the reservoir and a steam chamber
grows within the reservoir. Since it loses its latent heat to the surrounding formation, steam
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needs to be continuously injected to maintain growth. If a shut in occurs, heat losses causes the
steam within the chamber to condense into liquid water. During condensation, the temperature of
the steam stays equal and only the overall quality of the steam decreases. To model a shut in
during the ramp up phase we used the condensing three system SAGD model first proposed by
Zhu and Zeng (2014) depicted in Figure A.4. Since the dominant form of heat transferred beyond
the chamber is conduction, the steam chamber can be modeled as a shrinking circle.
Figure A.4: Schematic diagram of a three-zone condensation model used for SAGD ramp up
(modified from Zhu and Zeng, 2014).
A.4.2.1 Mathematical form of condensing model
The governing equation for transient heat transfer, including the effect of latent heat, in 1D radial
coordinates is given by:
186
𝜕ℎ
𝜕𝑡=
1
𝑟
𝑘𝑇𝐻
𝜌
𝜕2𝑇
𝜕𝑟2− 𝜆
𝜕𝑓𝑠𝑡
𝜕𝑡
where h is the specific enthalpy, kTH is the thermal conductivity, ρ is density, is the specific
latent heat of vaporization, and fst is the steam quality. The three zones have the following
initial conditions:
Zone 1 (hot zone): 𝑓𝑠𝑡(𝑟𝐷 , 𝑡𝐷 = 0) = 1 at 0 < 𝑟𝐷 < 𝑅𝐷1
Zones 2 (intermediate zone) and 3 (cold zone): 𝑓𝑠𝑡(𝑟𝐷 , 𝑡𝐷 = 0) = 0 at 𝑅𝐷1 < 𝑟𝐷
The boundary condition is as follows: the steam quality at infinite radius is equal to 0.
A.4.2.2 Numerical solution of the condensing model
The finite difference solution to the latent heat transfer problem is more complex and requires
two mirror grids. The first grid calculates the steam quality (fst) and the second grid calculates T.
Both grids communicate with each other and are considered “mirrors” since the steam quality at
the radial node i and time node j is directly linked to the enthalpy and temperature at the same
node. Latent heat transfer is done before sensible heat transfer so if the steam quality > 0 at a
particular node, then the temperature at that node is equal to the injected steam temperature Ts.
To test if there is still steam left at each new time step and to solve for the steam quality at the
new time step, two decision trees are required: one tree for the steam quality grid and another
for temperature grid as depicted in Figures A.5 and A.6.
187
Figure A.5: Decision tree for steam quality grid calculation.
Figure A.6: Decision tree for steam temperature grid calculation.
A thorough search of the literature revealed that an implicit finite difference formula has not
been developed to solve for the transient radial steam quality. For the study, we developed a
Crank Nicholson scheme adapting the finite difference method for melting ice derived by
188
Zivkovic and Fujii (2001). The discretization domain for steam quality is shown in Figure
A.7.
Figure A.7: Discretization domain for one-dimensional radial phase change - steam quality
grid layout.
To populate both the temperature and steam quality grids, the following steps are taken:
1. Filling in the temperature for all nodes at initial conditions tD = 0. TD in the hot zone
nodes is equal to 1, TD in the cold zones is equal to 0.
2. Filling in the steam quality for all nodes in the top rows at initial conditions tD = 0.
3. Filling in the temperature for all nodes in the first (rD=0) and last columns (rD>∞) the TD
at the infinite boundary node is always equal to 0. The temperature at Node 0 is
calculated by using (Sarker and Ketkar 2004):
𝑇0𝑗
=(1 − 2𝑃)𝑇0
𝑗−1+ 2𝑃𝑇1
𝑗−1+ 2𝑃𝑇1
𝑗
1 + 2𝑃
4. The steam quality at the infinite boundary node is equal to 0. The steam quality at node 0
is calculated by using:
189
𝑓𝑠𝑡0𝑗
= 𝑓𝑠𝑡0𝑗−1
+𝑐𝑃
𝐿(𝑇1
𝑗−1+ 𝑇1
𝑗− 𝑇0
𝑗−1− 𝑇0
𝑗)
5. Using the decision tree in Figures A.5 and A.6, the steam quality and temperature at all
other node are calculated. The “Latent Heat Calc” referenced in the decision tree is given
by:
𝑓𝑠𝑡𝑖𝑗
= 𝑓𝑠𝑡𝑖𝑗−1
+𝑐𝑃
2𝐿[(1 +
1
2𝑖) (𝑇𝑖+1
𝑗−1− 𝑇𝑖
𝑗−1+ 𝑇𝑖+1
𝑗− 𝑇𝑖
𝑗)
+ (1 −1
2𝑖) (𝑇𝑖
𝑗−1− 𝑇𝑖−1
𝑗−1+ 𝑇𝑖
𝑗− 𝑇𝑖−1
𝑗)]
The finite difference model was encoded in Microsoft Excel. The code reads the user inputs
from the spreadsheet and simultaneously builds two finite difference grids, one for the
temperature and one for the steam quality. The grids are built by using three FOR loops, one for
the spatial nodes one for the time steps and one for the iterative nodes used in the implicit
method. The mirror grids communicate with each other using the decision trees in Figures A.5
and A.6.
A.4.3 Variable Thermal Diffusivity
One advantage of having a numerical solution over an analytical is that non-linear complexity
can be added to the problem. The model developed by Zhu et al. (2012) assumes a constant
thermal diffusivity as derived in classic SAGD models such as those developed by Butler (1997)
and Gates and Sharma (2010). In reality, however, the thermal diffusivity of an oil sands
reservoir changes with temperature and does play a role in the temperature profile. Thermal
190
diffusivity α as defined below is the quotient of the thermal conductivity kH (W/mC) and
volumetric heat capacity Ms (J/m3C):
α = 𝑘𝐻
𝑀𝑠
Irani and Cokar (2014) explain that the both density and heat capacity experience negligible
change during temperature changes and that the change in thermal diffusivity due to temperature
is dominated by the change in thermal conductivity. Oil sands are a mixture of various
components such as methane, steam, water bitumen and rock (quartz) which all have different
thermal conductivities. Irani and Cokar (2014) describe that the thermal conductivities of gas and
steam rise as temperature increases and that the thermal conductivities of bitumen and water
change little whereas the thermal conductivity of reservoir rock drops as temperature enlarges.
The bulk thermal conductivity of an oil sand is driven primarily by the rock and secondly by the
water and oil saturation. The thermal conductivity of gas and steam are very small and can be
ignored. Irani and Cokar (2014) explain that oil sands thermal conductivity is essentially a linear
function of temperature that can be written in the following form:
𝑘𝐻 = a + bϕ + c√𝑆𝑤 + 𝑑√𝑆𝑜 − 𝑒𝑇
where ϕ is the porosity, Sw is the water saturation, So is the oil saturation, T is temperature and a,
b, c, d and e are constants. Since the first four parts of the equation tend to remain constant, the
equation can be simplified to:
𝑘𝐻 = 𝑘𝐻𝑟𝑒𝑓 − 𝐵(𝑇 − 𝑇𝑟𝑒𝑓)
where kHref is the formation thermal conductivity at a reference temperature Tref and B is a
constant. From Irani and Cokar, the overall thermal conductivity of oil sands decreases linearly
with temperature with a slope (B) that varies between 0.001-0.002 K-1 and a changing y-intercept
191
of 1.7-2.7 W/mC. For our study we have used a reference temperature as the common SAGD
steam temperature of 250C. kHref was chosen as 1.8 W/mC. As suggested by Irani and Cokar
(2014) the coefficient “B” was set at 0.002 K-1. The formula for thermal diffusivity is then given
by:
α(W/mC) = 𝑘𝐻
𝑀𝑠=
𝑘𝐻𝑟𝑒𝑓 − 𝐵𝑇𝑟𝑒𝑓
𝑀𝑠=
1.8 − 0.002(𝑇(C) − 250)
𝑀𝑠
A.4.3.1 Incorporation into Numerical Model
To incorporate variable thermal diffusivity into the numerical model the equations must be
modified. For the non-condensing model, the temperature of grid block i and j is a function of
the temperature in the surrounding grid blocks and the parameter P (a function of 𝛥𝑡𝐷 and 𝛥𝑟𝐷2),
and 𝛥𝑡𝐷 is proportional to α, since α is now variable, P can be re-written as:
𝑃 = 𝛥𝑡
∆𝑟2𝛼 =
𝛥𝑡
∆𝑟2
1.8 − 0.002(𝑇 − 250)
𝑀𝑠
𝛥𝑡 and ∆𝑟2 are both constant. Since the thermal conductivity, over small temperature
differences, changes little with temperature, the P value used to calculate the temperature in grid
block i and j is based on the temperature from the previous time step grid block i and j-1:
𝑃𝑖𝑗
= 𝛥𝑡
∆𝑟2
1.8 − 0.002(𝑇𝑖𝑗−1
− 250)
𝑀𝑠
Consequently, to solve for the temperature in the i and j block, the following formulas are used:
For temperature:
𝑇𝑖𝑗
=𝑇𝑖
𝑗−1(1 − 𝑃𝑖
𝑗) +
𝑃𝑖𝑗
2 [(1 +12𝑖) 𝑇𝑖+1
𝑗−1+ (1 +
12𝑖) 𝑇𝑖+1
𝑗+ (1 −
12𝑖) 𝑇𝑖−1
𝑗−1+ (1 −
12𝑖) 𝑇𝑖−1
𝑗]
1 + 𝑃𝑖𝑗
For steam quality:
192
𝑓𝑠𝑡𝑖𝑗
= 𝑓𝑠𝑡𝑖𝑗−1
+𝑐𝑃𝑖
𝑗
2𝐿[(1 +
1
2𝑖) (𝑇𝑖+1
𝑗−1− 𝑇𝑖
𝑗−1+ 𝑇𝑖+1
𝑗− 𝑇𝑖
𝑗)
+ (1 −1
2𝑖) (𝑇𝑖
𝑗−1− 𝑇𝑖−1
𝑗−1+ 𝑇𝑖
𝑗− 𝑇𝑖−1
𝑗)]
A.5 Results and Discussion
A.5.1 Constant Thermal Diffusivity
Figure A.8 depicts how the radial temperature profile (in dimensional values) evolves during a
shut in that occurs while the SAGD operation is in the startup period. The hot zone radius R1 is
selected as 1 m and the intermediate zone radius R2 is taken to be 3 m. The well, steam and
reservoir properties used were reflective of typical parameters found for Athabasca oil sands
reservoirs where SAGD operations are practiced (rw = 0.084 m, Ts = 250C, Tr = 10C, kH =
1.8x10-3 kW/mC, Ms = 3,000 kJ/m3C). The results show that the temperature drops rapidly
after steam is stopped during the startup period. Within one month, the temperature at the well
has dropped to less than half its original value and after six months, the temperature is lower than
15% of the original temperature. This implies that if a SAGD well is in the startup period and if
steam injection is stopped, a substantial amount of heat will have to be injected to get the
interwell pair temperature distribution back to the target temperature (typically about 80C)
sufficient to mobilize bitumen from this part of the reservoir.
193
Figure A.8: Non-condensing model evolution of radial temperature profile.
Figure A.9 depicts the how the radial temperature profile evolves during a shut-in event that
occurs while the SAGD operation is in the ramp up period. In this period, the hot inner zone is at
steam temperature. Here, the hot zone radius R1 is taken to be 1 m and intermediate zone radius
R2 is equal to 3 m. The steam quality fst is equal to 0.9 which is reflective of typical SAGD
operations. The well, steam and reservoir properties used were the same as the non-condensing
model listed above. Figure A.10 shows how the radial steam quality evolves over time. The
results show that after steam injection stops, first, the latent heat within the system is largely
consumed and thereafter, the sensible heat in the water is then lost. The steam quality drops to a
maximum of 0.3 after 6 months of cooling with live steam only occupying a very small radius
around the well. The results show that the even though the hot and intermediate zone radii are
the same for both the condensing and non-condensing models, the steam chamber takes longer
too cool due to the extra energy stored as latent heat.
0
50
100
150
200
250
300
0 2 4 6 8 10
T (o
C)
Radial Distance from wellbore center (m)
0 Hours
1 week
2 weeks
1 month
2 months
6 months
194
Figure A.9: Condensing model evolution of radial temperature profile.
Figure A.10: Condensing model evolution of radial steam quality profile.
0
50
100
150
200
250
300
0 2 4 6 8 10
T (o
C)
Radial Distance from wellbore center (m)
0 Hours
1 week
2 weeks
1 month
6 weeks
2 months
6 months
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0 0.5 1.0 1.5 2.0
Stea
m Q
ual
ity
Radial Distance from wellbore center (m)
0 Hours
1 week
2 weeks
1 month
6 weeks
195
Figure A.11 depicts how the temperature evolves with shut in time in the center of the wellbore
during the start-up and ramp up phases. The temperature during start up is always less than ramp
up since there is no latent heat transfer, however, the change is much more gradual since the heat
has not had time to distribute throughout the reservoir. The temperature during the ramp up
phase remained constant for about 6 weeks until the steam chamber fully condensed and then
dropped very suddenly, this is because the heat had over 6 weeks to distribute. This sudden drop
is better visualized in Figure A.12 which shows the negative slopes of the temperature profiles
versus time. The startup phase reached maximum value of about 0.34C/hour whereas the ramp
up phase reached values of over 19C/hour the moment the steam chamber collapsed.
Figure A.11: Temperature change with time at the center of the well bore during start up and
ramp up.
0
50
100
150
200
250
300
0 20 40 60 80 100 120 140 160 180
T (o
C)
time (days)
start up
ramp up
196
Figure A.12: Slope of temperature plotted against time at the center of the well bore during star
up and ramp up.
The temperature at the center of the wellbore during the ramp up phased leveled off around 67C
whereas the temperature during the star up phase kept decreasing to close to initial reservoir
temperature of 10C. This is because the latent heat loss from the steam had warmed up the
surrounding reservoir much more than that of sensible heat transfer during start up. The
temperature will continue to drop until it reaches 10C but this will take orders of magnitude
longer to occur than sensible heat transfer.
A.5.2 Variable Thermal Diffusivity
Figure A.13 shows the results of incorporating the variable heat conductivity into the model.
From the results, it is clear that variable heat conduction plays a relatively small role in the
overall result, however it demonstrates the model’s ability to incorporate complexities. Figure
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 20 40 60 80 100 120 140 160 180
-dT/
dt
(oC
/ho
ur)
time (days)
start up
ramp up
197
A.14 shows how a variable kh speeds up the cooling time, this is because the formation kh
increases as temperature drops causing heat to dissipate faster.
Figure A.13: Non-condensing radial temperature profile after 2 weeks for variable and constant
kh cases.
Figure A.14: Non-condensing temperature evolution at the center of the wellbore for variable
and constant kh cases.
0
50
100
150
200
250
300
0 2 4 6 8 10
T (o
C)
Radial Distance from wellbore center (m)
2 weeks constant kh
2 Weeks variable kh
0
50
100
150
200
250
300
0.0 20.0 40.0 60.0 80.0 100.0 120.0
T (o
C)
time (days)
constant kh
variable kh
198
A.6 Conclusions
In this study, a heat transfer model was developed to analyze how SAGD steam chambers
respond when steam injection is stopped. The model was solved numerically by using the finite
difference method. The results have shown that once the steam chamber has fully condensed the
temperature drops rapidly, but levels off at a higher value than the initial reservoir temperature.
While the steam chamber shrinks, it heats the surrounding formation through latent heat loss, this
causes the change of temperature in the middle of the well bore to drop very gradually. Having a
higher reservoir temperature is helpful during SAGD restart since the reservoir takes less energy
to heat and the oil is more mobile. The effect of temperature-dependent thermal diffusivity is
relatively small and a constant thermal diffusivity provides a good estimate of the temperature
transients