engineering design considerations to maximize carbon

The Pennsylvania State University

The Graduate School

Department of Energy and Mineral Engineering

ENGINEERING DESIGN CONSIDERATIONS TO MAXIMIZE CARBON DIOXIDE

INJECTIVITY IN DEEP SALINE FORMATIONS

A Thesis in

Energy and Mineral Engineering

by

Qian Sun

© 2013 Qian Sun

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

May 2013

ii

The thesis of Qian Sun was reviewed and approved* by the following:

Turgay Ertekin

Professor of Petroleum and Natural Gas Engineering

George E. Trimble Chair in Earth and Mineral Sciences

Thesis Advisor

Zuleima Karpyn

Associate Professor of Petroleum and Natural Gas Engineering

Mku. Thaddeus Ityokumbul

Associate Professor of Mineral Processing and Geo-Environmental Engineering

Luis F. Ayala H.

Associate Professor of Petroleum and Natural Gas Engineering;

Associate Department Head for Graduate Education

*Signatures are on file in the Graduate School

iii

Abstract

Geological sequestration of CO2 in deep saline formation plays an important role in greenhouse

gas reduction strategy. Mt. Simon sandstone formation located in the Midwest of United state appears to

be an excellent candidate for carbon dioxide sequestration. The pressure build-up during CO2 injection

will restrict the bottomhole injection pressure to achieve desirable injection rates. Brine production is

treated as an effective external pressure release mechanism. However, the produced brine has no value

and its treatment or disposal may increase the process cost. Thus, the primary target project is to generate

a solution for optimal injector type and arrangement of injector and brine producer to inject as much CO2

as possible while producing minimum amount of brine. This work uses horizontal injection wells to

generate higher injectivity values. The concept of CO2 injection pattern is introduced to take full

advantage of the formation capacity. Accordingly, the injection performance of different injection pattern

types is studied. A commercial simulator is employed as core numerical simulation tool. In order to

reduce the uncertainties from the various reservoir properties, the analysis is achieved via implementation

of the Monte Carlo simulation protocol. The model does multiple simulation runs and expresses the

output parameters within p90 and p50 ranges. In order to avoid the time-consuming high-fidelity

simulation runs, artificial neural network based model is employed in generating the data for the Monte

Carlo analysis. This work develops expert network systems and applies the developed network to

determine the optimal design of injection pattern. The expert systems are also applied to basin scale field

case studies.

iv

Table of Contents

List of Figures ............................................................................................................................................. IV

List of Tables ............................................................................................................................................ VIII

Acknowledgement ...................................................................................................................................... IX

Chapter 1 Introduction .................................................................................................................................. 1

Chapter 2 Literature Review ......................................................................................................................... 3

2.1 Deep Saline Formation (Background about Mt. Simon Sandstone) ......................................... 3

2.1.1 Characteristics of Seal Formation (Eau Claire Formation) ....................................... 5

2.1.2 Characteristics of Mt. Simon Sandstone Formation .................................................. 6

2.1.3 Formation Brine Characterization ............................................................................ 11

2.2 Horizontal Injection Well ........................................................................................................ 12

2.3 Carbon Dioxide Capture, Transportation and Injection Techniques ....................................... 14

Chapter 3 Problem Statement ..................................................................................................................... 17

Chapter 4 Artificial Neural Network .......................................................................................................... 20

4.1 Introduction ............................................................................................................................. 20

4.2 Transfer (Active) Functions ..................................................................................................... 22

4.3 Backpropagation Networks ...................................................................................................... 23

4.4 Overlearning and Underlearning .............................................................................................. 24

4.5 Training of the Artificial Neural Network ............................................................................... 25

Chapter 5 Monte Carlo method ................................................................................................................... 27

5.1 Introduction .............................................................................................................................. 27

5.2 P-value Approach..................................................................................................................... 28

Chapter 6 Studies on Injection Patterns ...................................................................................................... 29

6.1 Introduction .............................................................................................................................. 29

6.2 Model Setup ............................................................................................................................. 33

6.2.1 Reservoir Properties Range and Mesh Grid Dimensions ......................................... 33

6.2.2 Modeling of CO2- Brine Relative Permeability ....................................................... 34

6.3 Simulation Results ................................................................................................................... 35

6.4 Studies on Pressure Depletion Ratio ........................................................................................ 41

6.5 Summary of Observations ........................................................................................................ 44

Chapter 7 Development of Artificial Neural Networks (ANN) ................................................................. 45

7.1 Generation of Dataset for Training the Networks .................................................................... 45

7.2 Designing of artificial neural networks .................................................................................... 47

7.2.1 End-point Forward-looking Solution Network (EFSN) .......................................... 47

7.2.2 Injection Efficiency Profile Network (IEPN) ......................................................... 49

7.2.3 Injection Well Bottomhole Pressure Profile Network (BHPN) .............................. 51

7.3 Test and Validation of the Networks ....................................................................................... 53

7.3.1 Test and Validation of End-points Forward-looking Solution Network .................. 54

7.3.2 Test and Validation of Injection Profile Network .................................................... 58

7.3.3 Test and Validation of Bottomhole Injection Pressure Profile Network ................. 60

Chapter 8 Case Studies ............................................................................................................................... 63

v

8.1 Injection Depth Limitation ....................................................................................................... 64

8.2 Design of Regular 4-spot Injection Pattern with Horizontal Injector ...................................... 65

8.2.1 Characterization of reservoir properties inputs ........................................................ 65

8.2.2 Design of regular 4-spot injection pattern with horizontal injector ......................... 67

8.2.2.1 Statement of Design Criteria .................................................................... 67

8.2.2.2 Design Procedure ..................................................................................... 69

8.2.2.3 Design Results ......................................................................................... 73

8.3 Basin Scale Simulation ............................................................................................................ 75

8.3.1 Geology Modeling ................................................................................................... 75

8.3.2 Simulation Results ................................................................................................... 90

Chapter 9 Summary and Conclusion ....................................................................................................... 109

9.1 Summary of Findings ............................................................................................................. 109

9.2 Conclusion ............................................................................................................................ 111

Reference .................................................................................................................................................. 117

Appendix ................................................................................................................................................... 119

A.1 Tabulated Results of the Design Protocol ............................................................................. 119

A.2 Development of a Toolkit for Map Digitizing ..................................................................... 126

A.3 Program Codes of Digitizing the Map Boundary ................................................................. 128

A.4 Program Codes of Digitizing the Contour Lines ................................................................... 133

A.5 Program Codes of Drawing the Surface Map ....................................................................... 136

A.6 Program Codes of Implementation of EFSN ........................................................................ 140

A.7 Program Codes of the Searching Protocol ............................................................................ 143

vi

List of Figures

Figure 2-1: Location of Mt. Simon sandstone formation in MRCSP region (MRCSP, 2008) ..................... 3

Figure 2-2: Location of Mt. Simon sandstone formation in MGSC region (Finley, 2008) .......................... 4

Figure 2-3: Stratigraphic column through Ordovician to Cambrian rocks Illinois Basin and Michigan

Basin (Leetaru et al. 2009) .............................................................................................................. 5

Figure 2-4: Isopach map of Eau Claire formation in Michigan and Illinois basins ...................................... 6

Figure 2-5: Isopach map and elevation map of Mt. Simon formation in Michigan basin (Barnes, 2009) ... 7

Figure 2-6: Isopach map and elevation map of Mt. Simon formation in Illinois basin (ISGS, 2006) ......... 8

Figure 2-7: Site of East Bend injection test and pressure response showing fracture pressure (MRCSP

Battelle Lab, 2011)........................................................................................................................... 9

Figure 2-8: Porosity vs. depth (Medina et al. 2008) .................................................................................. 10

Figure 2- 9: Porosity vs. permeability (Medina et al. 2008) ...................................................................... 11

Figure 2-10: Salinity contour map of Mt. Simon formation in Illinois Basin (ISGS, 2006) ..................... 12

Figure 2-11: Workflow of treatment of post combustion gas from coal fire power plant (Global CCS

institute, 2012) .............................................................................................................................. 14

Figure 2-12: Workflow of MEA (Global CCS institute, 2012) ................................................................. 14

Figure 2-13: Workflow of CO2 dehydrates and compression system (Finley, 2008) ................................ 15

Figure 4-1: A typical biology nervous neuron .......................................................................................... 20

Figure 4-2: An example of simple artificial neuron network ..................................................................... 21

Figure 4-3: Transfer functions ................................................................................................................... 22

Figure 4-4: Network overlearning.............................................................................................................. 25

Figure 4-5: Workflow of training the artificial neuron network ................................................................. 26

Figure 6-1 (a): Regular 4-spot injection pattern .......................................................................................... 29

Figure 6-1 (b): Inverted 4-spot injection pattern ......................................................................................... 30

Figure 6-1 (c): Regular 5-spot injection pattern .......................................................................................... 31

Figure 6-1 (d): Inverted 5-spot injection pattern ......................................................................................... 31

vii

Figure 6-1 (e): Regular 7-spot injection pattern .......................................................................................... 32

Figure 6-1 (f): Inverted 7-spot injection pattern ......................................................................................... 33

Figure 6-2: Relative permeability curve generated by Corey’s formulation .............................................. 35

Figure 6-3 (a): P90 cumulative CO2 injection vs. injection rate for 4-spot patterns ................................... 36

Figure 6-3 (b): P90 cumulative CO2 injection vs. injection rate for 5-spot patterns ................................... 36

Figure 6-3 (c): P90 cumulative CO2 injection vs. injection rate for 7-spot patterns ................................... 37

Figure 6-4 Comparison of peak P90 cumulative injection.......................................................................... 38

Figure 6-5 (a): P90 injection efficiency vs. injection rate for 4-spot patterns ............................................ 39

Figure 6-5 (b): P90 injection efficiency vs. injection rate for 5-spot patterns ............................................ 39

Figure 6-5 (c): P90 injection efficiency vs. injection rate for 7-spot patterns ............................................ 40

Figure 6-6: Comparison of peak p90 injection efficiency .......................................................................... 40

Figure 6-7: P50 pressure depletion ratio surface ........................................................................................ 42

Figure 6-8: Top view of “pattern size-injection rate” plane ....................................................................... 42

Figure 6-9: P90 injection efficiency surface .............................................................................................. 43

Figure 7-1: 2-D simulation model ............................................................................................................... 45

Figure 7-2: Architecture of EFSN .............................................................................................................. 49

Figure 7-3: Architecture of IEPN ............................................................................................................... 51

Figure 7-4: Architecture of BHPN ............................................................................................................. 52

Figure 7-5: Different performances for multiple trainings of EFSN. ........................................................ 54

Figure 7-6: Test errors distributions of EFSN ........................................................................................... 55

Figure 7-7 (a): Comparison of EFSN prediction and numerical model results of cumulative brine

production ...................................................................................................................................... 56

Figure 7-7 (b): Comparison of EFSN prediction and numerical model results of cumulative CO2 injection

....................................................................................................................................................... 56

Figure 7-7 (c): Comparison of EFSN prediction and numerical model results of stabilized injector block

pressure .......................................................................................................................................... 57

Figure 7-8: Tests error distributions of injection efficiency of three sample sets ....................................... 58

Figure 7-9 (a): Injection efficiency profile predicted by IEPN and numerical model, Case 1 ................... 59

viii

Figure 7-9 (b): Injection efficiency profile predicted by IEPN and numerical model, Case 2 ................... 60

Figure 7-10: Tests error distributions of bottomhole pressure of three sample sets ................................... 61

Figure 7-11 (a): Bottomhole pressure profile predicted by BHPN and numerical model, Case 1 .............. 62

Figure 7-11 (b): Bottomhole pressure profile predicted by BHPN and numerical model, Case 2 ............. 62

Figure 8-1: CO2 phase diagram (Medina, 2008) ......................................................................................... 64

Figure 8-2: Workflow of design protocol ................................................................................................... 70

Figure 8-3: Conceptual illustration of design protocol results .................................................................... 71

Figure 8-4: Illustration of four key definitions ........................................................................................... 72

Fig 8-5(a): Original isopach contour lines of Mt. Simon formation, Michigan Basin (Barnes, 2009) ...... 76

Fig 8-5(b): Digitized isopach contour lines of Mt. Simon formation, Michigan Basin .............................. 76

Fig 8-6: Thickness surface map of Mt. Simon formation, Michigan basin ................................................ 77

Fig 8-7(a): Original elevation contour lines of Mt. Simon formation, Michigan basin (Barnes, 2009) .... 78

Fig 8-7(b): Digitized elevation contour lines of Mt. Simon formation, Michigan Basin ........................... 79

Fig 8-8: Elevation distribution of Mt.Simon formation in Michigan Basin in 3-D view ........................... 80

Fig 8-9(a): Original isopach contour lines of Mt. Simon formation, Illinois Basin (ISGS, 2006) ............ 81

Fig 8-9(b): Digitized isopach contour lines of Mt. Simon formation, Illinois Basin .................................. 82

Fig 8-10: Thickness surface map of Mt. Simon formation, Illinois Basin .................................................. 83

Fig 8-11(a): Original elevation map of Mt. Simon formation, Illinois Basin (ISGS, 2006) ....................... 84

Fig 8-11(b): Digitized elevation map of Mt. Simon formation, Illinois Basin ........................................... 85

Fig 8-12: Elevation distribution of Mt. Simon formation in Illinois Basin in 3-D view ............................ 86

Fig 8-13: Permeability distribution map of Mt. Simon formation, Michigan Basin ................................... 87

Fig 8-14: Porosity distribution map of Mt. Simon formation, Michigan Basin .......................................... 88

Fig 8-15: Permeability distribution map of Mt. Simon formation, Illinois Basin ....................................... 89

Fig 8-16: Porosity distribution map of Mt. Simon formation, Illinois Basin .............................................. 90

Fig 8-17: Cumulative CO2 injection distribution map of Michigan Basin ................................................. 91

Fig 8-18: Stabilized reservoir pressure distribution map of Michigan Basin ............................................. 92

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Fig 8-19: Pressure depletion ratio distribution map of Michigan Basin ..................................................... 93

Fig 8-20(a): Injection efficiency distribution map of Michigan Basin at the end of 2012.......................... 94

Fig 8-20(b): Injection efficiency distribution map of Michigan Basin at the end of 2014 ......................... 95

Fig 8-20(c): Injection efficiency distribution map at the end of 2017 ........................................................ 96

Fig 8-21(a): Injection well bottomhole pressure distribution map at the end of 2012 ................................ 97

Fig 8-21(b): Injection well bottomhole pressure distribution map at the end of 2014 ................................ 98

Fig 8-21(c): Injection well bottomhole pressure distribution map at the end of 2017 ................................ 99

Fig 8-22: Cumulative CO2 injection distribution map of Illinois Basin ................................................... 100

Fig 8-23: Stabilized reservoir pressure distribution map of Illinois Basin ............................................... 101

Fig 8-24: Pressure depletion ratio distribution map of Illinois Basin ....................................................... 102

Fig 8-25(a): Injection efficiency distribution map of Illinois Basin at the end of 2012 ........................... 103

Fig 8-25(b): Injection efficiency distribution map of Illinois Basin at the end of 2014 ........................... 104

Fig 8-25(c): Injection efficiency distribution map of Illinois Basin at the end of 2017 ........................... 105

Fig 8-26(a): Injection well bottomhole pressure distribution map of Illinois Basin at the end of 2012 ... 106

Fig 8-26(b): Injection well bottomhole pressure distribution map of Illinois Basin at the end of 2014 ... 107

Fig 8-26(c): Injection well bottomhole pressure distribution map of Illinois Basin at the end of 2017 ... 108

Fig 9-1(a): Injection sweet spot shown in cumulative CO2 injection distribution map of Michigan Basin

..................................................................................................................................................... 113

Fig 9-1 (b): Injection sweet spot shown in Michigan state territory map (www.digital-topo-

maps.com/county-map/)............................................................................................................... 114

Fig 9-2(a): Injection sweet spot shown in cumulative CO2 injection distribution map of Illinois Basin .115

Fig 9-1 (b): Injection sweet spot shown in Illinois state territory map (www.digital-topo-

maps.com/county-map/) .............................................................................................................. 116

Figure A-1: Searching directions .............................................................................................................. 127

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List of Tables

Table 2-1: Summary of reservoir parameters from literature ....................................................................... 9

Table 2-2: CO2 injection pump parameters (Flowserve® Corporation, 2011) ......................................... 16

Table 7-1: Summary of training data ranges ............................................................................................... 46

Table 7-2: Input and output neurons of EFSN ........................................................................................... 48

Table 7-3: Output neurons and functional links of IEPN .......................................................................... 49

Table 7-4: Output neurons and functional links of BHPN ......................................................................... 51

Table 8-1: Summary of reservoir properties ranges .................................................................................... 67

Table 8-2: Summary of engineering design parameters ............................................................................. 67

Table 8-3: Summary of optimal design of different geology cases ............................................................ 74

Table A-1 ................................................................................................................................................. 119

Table A-2 .................................................................................................................................................. 121

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Acknowledgement

First and foremost, I would like to express my sincere gratitude to my advisor Dr. Turgay Ertekin

for his patient, steady support and assistance throughout this work. Working with Dr. Ertekin was an

invaluable experience for me. His guidance helped me gain a lot of insight into the subject matter. More

importantly, his great personality deeply influenced me and changed the way I think about life and

science. I appreciate the US Department of Energy for the providing support funding for this study. I

thank to Dr. Zuleima Karpyn and Dr. M. Thaddeus Ityokumbul for their great contributions as committee

members. I thank to Dr. Li Li and Dr. Shimin Liu for their recommendations and helps in this work.

I would like to thank to my parents, my father Baojiang Sun and my mother Xiaoping Zhang, for

their support and encouragement in my life.

I thank my girlfriend Miao Zhang for her encouragement when I came across difficulties and was

discouraged. I thank Ihsan Burak Kulga for his help in introducing me to the key concepts in artificial

neural network. In addition, my friends and colleagues; Nithiwat Siripatrachai, Jiahang Han and Junjie

Yang thanks to all of you for being very supportive during my college life.

1

Chapter 1 Introduction

Geological sequestration of CO2 in deep saline formation has the potential of playing an

important role in greenhouse gas reduction strategy. Mt. Simon sandstone formation located in the

Midwest of United state appears to be an excellent candidate for carbon dioxide sequestration. It is an

extremely huge formation covering several territories. The reservoir properties of Mt. Simon sandstone

formation also vary considerably.

Rapid pressure build up is the main challenge in deep saline CO2 sequestration. Brine production

is considered as an effective method to provide external mechanism to release the reservoir pressure.

However, the produced brine has practically no value and treating or disposing it may introduce

considerable expenditure to the process. Thus, the primary goal of the project is to determine the

engineering design yielding maximum CO2 injection with minimum brine production. Another significant

concern is the resulting formation pressure after the stabilization of CO2-brine system. In designing the

injection operation, one has to ensure that the reservoir pressure after stabilization is lower than a

prescribed safety level to minimize the risk of CO2 leakage and upwards migration. Horizontal injection

well is applied in the design to increase the injectivity. Analogous to water flood pattern studies in

petroleum recovery projects, the concept of CO2 injection pattern is visited.

The output of the project is determined by multiple variables including reservoir properties and

engineering design parameters. Injection rate, pattern size, horizontal well length and brine producer’s

sandface pressure are considered as the engineering design parameters in this study. The study employs

CMG1-GEM

2, which is a compositional reservoir simulator to model CO2- brine fluid flow in porous

medium. Monte Carlo simulation protocol is employed for multiple simulation runs to reduce the

uncertainties from the reservoir properties. CMG-GEM is a high-fidelity model. If the study totally relies

on CMG-GEM, the simulation runs could be very time consuming. In order to address this issue, an

artificial neural network (ANN) model is developed and employed to generate data for Monte Carlo

1 CMG: Computer Modeling Group, a numerical reservoir simulator developed by Computer Modeling Group

Ltd, Calgary, Canada.

2 GEM: Generalized Equation-of-State Model, a compositional reservoir simulator in CMG software suit.

2

simulation. MATLAB1 neural network toolbox is employed in developing the artificial neural networks.

This work aims at training an expert neural network in this study area and then applying it to generate

large number of simulation results within short periods of time. The expert system will help determine the

optimal design of injection pattern and to conduct runs for basin scale simulation.

Chapter 2 briefly discusses critical literature review on the reservoir characterization of Mt.

Simon sandstone formation from previous geological studies. Chapter 3 presents the problem statement of

the work described here. Chapters 4 and 5 briefly introduce the background and typical algorithms of

ANN and Monte Carlo method. Chapter 6 focuses on study of different injection patterns. In Chapter 7,

the development and validation of the expert network is discussed. Field case studies of Mt. Simon

formation applying the expert system are shown in Chapter 8. In Chapter 9, a summary and

considerations derived from this work are presented.

1 MATLAB, MATrix LABoratory, a language for technical computing, by MathWorks inc, US

3

Chapter 2 Literature Review

2.1 Deep Saline formation (Background about Mt. Simon sandstone)

Mount Simon, which is a Middle-Upper Cambrian basal sandstone formation, has been

recognized as an important subsurface saline reservoir for carbon dioxide storage in the Midwest of

United States. It is an extremely huge reservoir covering Illinois, Indiana, Kentucky, Michigan and Ohio

states.

The United States Department of Energy (DOE) assigned the research work of geological

characterization and injection validation of Mt. Simon sandstone formation to two different partnerships:

Midwest Regional Carbon Sequestration Partnership (MRCSP) and Midwest Geological Sequestration

Consortium (MGSC). The red zone in Figure 2-1 shows the study region of MRCSP. The pink zone in

Figure 2-2 shows the study region of MGSC.

Figure 2-1: Location of Mt. Simon sandstone formation in MRCSP region (MRCSP, 2008)

http://sequestration.org/

http://sequestration.org/

4

Figure 2-2: Location of Mt. Simon sandstone formation in MGSC region (Finley, 2008)

Reservoir properties of Mt. Simon formation in the Illinois and Michigan basins have been

extensively carried out in the past. More importantly, the large scale carbon dioxide storage potentials of

these two reservoirs have been verified by the corresponding partnerships. Therefore, Mt. Simon

sandstone formation in the Illinois and Michigan basins are chosen as targets of reservoir simulation in

this study. Figure 2-3 shows the stratigraphic map of rocks through Ordovician to Cambrian. Mt. Simon is

overlaid by a low permeability formation, Eau Claire formation, which is recognized as a cap seal.

5

SYSTEM GROUP FORMATION

Ordovician

Maquoketa

Brainard

Ft. Atkinson

Scales

Galena Kimmswick

Decorah

Platteville

Ancell Joachim

St. Peter

Praire du Chien

Shakoppee

New Richmond

Oneota

Gunter

Cambrian Knox

Eminence

Postosi

Franconia

Ironton-Galesville

Eau Claire

Mt. Simon

Figure 2-3: Stratigraphic column through Ordovician to Cambrian rocks in Illinois and

Michigan basins (Leetaru et al. 2009)

2.1.1 Characteristics of Seal Formation (Eau Claire Formation)

Cap seal is one of the most important concerns in selecting a carbon dioxide sequestration

reservoir. An effective seal formation could prevent injected CO2 from migrating upwards during long-

term post injection period.

Eau Claire formation has been identified as an effective capstone overlaying Mt. Simon sandstone

formation. It consists of low-porosity crystalline dolomite, sandy dolomite, dolomitic and feldspathic

sandstone, siltstone, and shale (Wickstrom et al., 2005). Figure 2.4 shows the isopach maps of Eau Claire

formation in Michigan and Illinois basins.

6

Figure 2-4: Isopach map of Eau Claire formation in Michigan and Illinois basins

The thickness of Eau Claire formation could be as thick as 800 feet in Michigan Basin and 1,000

feet in Illinois Basin. Thus, Eau Claire formation has substantial thickness to be considered an effective

seal. More importantly, Lahann et al. (2012) state that Eau Claire formation displays slight silty and

carbonate lithofacies in Michigan and Illinois basins, which is a strong indication of low permeability and

inertia with acid CO2 gas. Besides, the absence of faults and natural fractures of Eau Claire formation in

Michigan and Illinois basins increases its sealing capacity significantly.

2.1.2 Characteristics of Mt. Simon Sandstone Formation

Reservoir properties of Mt. Simon sandstone formation vary considerably. The objective of this

section is to explore the existing technical documents and reports for key parameters that would be used

in simulation studies presented in this report.

7

Reservoir thickness and depth

Mt. Simon formation thickness and depth have been well studied during the past decades. Thus,

sufficient reliable data could be found for basin-scale simulation. Figure 2-5 shows the isopach and

elevation maps of Mt. Simon formation in Michigan Basin while Figure 2-6 shows the same maps in

Illinois Basin.

Figure 2-5: Isopach map and elevation map of Mt. Simon formation in Michigan basin (Barnes, 2009)

8

Reservoir temperature and pressure parameters

Reservoir pressure and temperature parameters are often expressed as pressure and temperature

gradients. The following parameters are the three important components for defining the reservoir initial

condition and also the injection bottomhole pressure limitation:

Formation pressure gradient is used to calculate the initial reservoir pressure, in psi.

Formation fracture pressure gradient is used to calculate the reservoir fracture pressure, in psi,

which also represents the bottomhole injection pressure limitation.

Formation temperature gradient is used to calculate the initial reservoir temperature, in °F.

Figure 2-6: Isopach map and elevation map of Mt. Simon formation in Illinois basin (ISGS, 2006)

9

Table 2-1 below summarizes these key parameters and the corresponding sources and those values of

reservoir pressure and temperature gradients will be applied in the simulation studies.

Table 2-1: Summary of reservoir parameters from literature

Reservoir Parameters Value Region Source Note

Formation pressure

gradient, psi/ft

0.46 MI David A. Barnes et al, 2009 Assumption of simulation

study

0.455 IL Scott M. Frailey et al, 2011 Field test at depth of 7045 ft

Formation fracture

pressure gradient, psi/ft

0.8 MI David A. Barnes et al, 2009 UIC Default Permission

0.855 KY MRCSP Battelle Lab, 2011

East Bend brine injection test

result at depth of 3,230 to

3,532 ft, shown in Figure 2-7

0.751 IL

UIC

(www.epa.gov/r5water/uic/uic-

permit-applicaions.htm)

UIC official data

Formation temperature

gradient, °F/1000 ft

11 MI David A. Barnes et al, 2009 Assumption of simulation

study

10 IL Q. Zhou, Scott M. Frailey Assumption of simulation

study

Figure 2-7: Site of East Bend injection test and pressure response showing fracture pressure

(MRCSP Battelle Lab, 2011)

10

Reservoir porosity and permeability

Reservoir permeability could be as large as several Darcies or as small as less than 1 md. Porosity

could be larger than 25% or smaller than 1%. Indiana Geology Survey (IGS), which is a member of

MRCSP, provides their research result in 2008 describing general characteristics of permeability and

porosity of Mt. Simon sandstone formation. Figure 2-8 shows the plot of porosity vs. depth. This figure is

generated through core analysis results and well log data from over 3,714 investigation wells in Michigan,

Kentucky, Ohio and Illinois.

Figure 2-8: Porosity vs. depth (Medina et al. 2008)

A regression equation which expresses reservoir porosity as a function of depth could be written as

(Medina et al. 2008):

Reservoir porosity trends to decrease as formation depth increases. At depths lower than 7,500 feet,

reservoir porosity would be smaller than 7%. Thus, regions of Mt. Simon formation with depths larger

than 7,500 feet will not be suitable as CO2 geology sequestration candidate (Medina et al. 2008).

11

IGS applied k/ and R35 approach (Pittman, 1992) to study reservoir permeability and porosity

simultaneously. Figure 2- 9 shows the cross plots of porosity and permeability values.

A regression equation which expresses reservoir permeability as a function of porosity could be written as

(Medina et al. 2008):

2.1.3 Formation Brine Characterization

Mt. Simon sandstone formation is an important underground water resource in the Midwest.

Formation brine in Michigan basin is not well characterized. MRCSP reported in their phase Ι final report

that brine samples were collected from only 18 wells. Thus, a salinity contour map for the Michigan basin

cannot be generated. But the available data in MRCSP region show that brine salinity trends to increase

with the formation depth.

Brine in Mt. Simon formation in the Illinois basin has been well studied in past decades by

Illinois State Geology Survey (ISGS) and Illinois Ground Water Quality (IGWQ). Figure 2-10 shows the

salinity contour map of Mt. Simon formation in the Illinois Basin. In general, brine salinity increases with

the formation depth.

Figure 2- 9: Porosity vs. permeability (Medina et al. 2008)

12

2.2 Horizontal Injection Well

Carbon dioxide injection well for long term geology sequestration is a relatively new concept

introduced by United State Underground Injection Control (UIC) program. UIC define CO2 injection well

as:

“Class VI injection well, which is used to inject Carbon Dioxide (CO2) for long term storage,

also known as Geologic Sequestration of CO2. Commercial wells are expected to come online by

2016 (EPA official definition, http://water.epa.gov/type/groundwater/uic/wells.cfm).”

Figure 2-10: Salinity contour map of Mt. Simon formation at Illinois Basin (ISGS, 2006)

13

There exists little on shore industrial large scale experience of the performance of horizontal CO2 injector

for geological sequestration purposes. But a number of simulation studies have been done focusing on

injectivity of horizontal injection well in geological CO2 sequestration projects. Jikich et al. (2006)

studied the injectivity of horizontal injection well to brine formation in Ohio Valley sandstone formation,

and concluded that:

“Horizontal well can significantly increase CO2 injectivity in brine formations of lower

permeability. Injection rates can be increased 4-5 times over that for a vertical for realistic injector

lengths with no increase in injection pressure. For deeper formations, or Northern West Virginia

formations with higher than normal fracture gradients even higher injection rates can be achieved.”

Jikich’s study proved that horizontal injector has better injectivity compared with vertical injection wells,

which indicates that higher injection rate could be achieved by using horizontal injection well without

increasing bottomhole pressure. Kumar (2007) makes two important statements in his master’s thesis:

1. “Due to lower velocity, gravity force is more influential and the flow has a greater vertical

component, thus contacting less brine/rock in the horizontal direction. In other words, for a

given injection rate the horizontal well allows more trapping along the well but cannot take

much advantage of permeability anisotropy to enhance trapping in the horizontal direction.”

2. “Trapping along the well length direction and in the transverse direction roughly balances

each other’s effect unless the well length is very long. Thus for given injection rate there is no

benefit in sequestration efficiency for horizontal wells unless they are very long.”

The first statement implies that using horizontal injection well may have negative influence on the

transport of CO2 plume along lateral directions. Kumar’s study indicated that horizontal injection well

may not be always as efficient as imagined. The injectivity of the horizontal injection well strongly

depends on the horizontal well length. Thus, the horizontal well length (Lw) will be treated as a significant

parameter in this study.

14

2.3 Carbon Dioxide Capture, Transportation and Injection Techniques

CO2 emission from retrofit coal-fired energy plant plays an important role in total greenhouse gas

emission. CO2 capture technique from post-combustion gas stream is mature. Figure 2-11 shows a

workflow of treatment of post combustion gas from coal fire power plant.

MEA in the last box represents a system which captures CO2 by absorption. Figure 2-12 shows the

workflow of MEA.

Figure 2-12: Workflow of MEA (Global CCS institute, 2012)

Figure 2-11: Workflow of treatment of post combustion gas from coal fire power plant (Global CCS institute, 2012)

15

The CO2 post combustion facility produces wet CO2 gas at low pressure and temperature. Figure

2-13 shows the workflow procedure to dehydrate and compress the CO2 gas stream before it enters long

distance pipeline or injection well head. This system output dry CO2 at relatively high pressure and

temperature.

CO2 injection pump is an important facility to generate bottom hole injection pressure to achieve

a certain flow rate. Typically, it is preferred to inject CO2 as a non-gaseous form. Therefore, the pump

discharging pressure and temperature are important parameters in designing a CO2 injection process.

Fortunately, modern pump manufactures provide powerful and heavy-duty CO2 injection pump models.

Table 2-2 summarizes typical pump models with their corresponding pressure and temperature limitations.

Table 2-2 CO2 injection pump parameters (Flowserve® Corporation, 2011)

Pump Model Pressure

Limitation, psi

Temperature

Limitation, °F

DVSR 3,750 400

DMX 4,000 400

HDO 9,500 840

Figure 2-13: Workflow system to dehydrate and compress CO2 (Finley, 2008)

16

These injection pumps could provide discharging pressures up to 9,500 psi and temperatures up to 840 °F,

which would be feasible for CO2 injection projects.

17

Chapter 3 Problem Statement

In CO2 deep saline sequestration projects, reservoir pressure build up is one of the main

restrictions. Although the application of horizontal injection well would improve the injectivity, it could

not increase the capacity of the reservoir unless there is external mechanism to dissipate pressure. The

effect of pressure build up would be especially important when multiple injection wells are used. One of

the feasible methods to decrease the reservoir pressure is to extract the brine in the formation to create

more available volume for CO2 injection. The target formation of this study is Mt. Simon sandstone

formation. The large nature of the reservoir and variation of key storage and transport characteristics of

Mt. Simon sandstone formation are also two of the challenges of this study. Besides, as brine production

is used to reduce the injection pressure limitation, CO2 breakthrough may happen at the production well

prematurely, which potentially can reduce the efficacy of the CO2 injection operation. More importantly,

the post injection stabilized reservoir pressure should be another important concern. The post injection

stabilized reservoir pressure should be maintained below a safety level to prevent the injected CO2 from

migrating upwards through the formation seal.

Similar to typical patterns used in waterflooding of petroleum reservoirs, the concept of “CO2

injection patterns” is visited. Different types of injection patterns including 4-spot, 5-spot and seven spot

injection patterns are studied. The goal of this study is to examine the relationship between the carbon

dioxide injectivity and the injection pattern parameters and brine production by using numerical reservoir

simulation techniques, and finally to generate a solution for optimal arrangement of injector and brine

producer to inject as much CO2 as possible while producing minimum amount of brine.

An injection efficiency (IE) term is introduced, which can be described as the ratio of cumulative

carbon dioxide injection to the cumulative brine production, to evaluate the enhancement effectiveness of

a brine production pattern in a carbon dioxide injection scenario. A pressure depletion ratio (PDR) term is

also introduced, which is calculated as the ratio of the stabilized pressure at injector block after shut in of

18

injection well to the initial reservoir pressure, to evaluate the long term safety of the sequestration

projects.

In parallel to the aforementioned goals and challenges, a mathematical model is built allowing the

numerical simulation of the study area. Instead of simulating the entire reservoir, the model studies an

injection-pattern-based unit of the reservoir. The injection-pattern-based unit has the same reservoir

properties range to represent one small part of the entire reservoir. In order to reduce the uncertainties

from the various reservoir properties, the analysis is achieved by implementing the Monte Carlo

simulation protocol. The input of the model consists of two sets of data; one is the reservoir properties

including permeability (k), porosity ( ), thickness (h), depth (D), initial reservoir temperature (Ti), initial

reservoir pressure (Pi) and formation fracture pressure (Pfrac). The second set includes engineering design

parameters including injection rate (Q), size of the pattern (A), horizontal well length (Lw) and brine

producer specification. The output of the model is cumulative CO2 injection within the injection period,

injection efficiency and pressure depletion ratio. Input arrays are generated within the property ranges

applicable to the study area. The model does multiple simulation runs with the elements of input arrays.

The outputs parameters are expressed within the p90, p50 and p10 confidence intervals.

However, a significant issue may show up, as explained below, if Monte Carlo simulation

protocol is applied. Obviously, there are thousands of combinations of input parameters. Conducting

simulation runs using a high fidelity model can become extremely time-consuming if data collection for

Monte Carlo analysis totally relies on hard-computation based runs. In order to address this issue, an

artificial neural network (ANN) based proxy model is developed to minimize computational work and

time requirements. If an artificial neural network could be well trained by using enough number of

training data, it could be used to generate large number of runs within fractions of a second. Three

networks are designed and used in this simulation study.

19

1. End-point forward-looking solution network (EFSN), with input of reservoir properties

and engineering design parameters and output of cumulative CO2 injection, injection

efficiency and pressure depletion ratio at the end of the injection period.

2. Injection efficiency profile network (IEPN), with input of reservoir properties and

engineering design parameters and output of injection efficiency profile at different

times.

3. Injector bottomhole pressure profile network (BHPN), with input of reservoir properties

and engineering design parameters and output injector bottom hole pressure profile at

different time.

These three networks help not only in determining the optimal design of the injection procedure but also

in simulating basin scale case of Mt. Simon sandstone formation and generating high resolution injection

potential maps. The injection period considered in this study is from 2012 to 2018.

20

Chapter 4 Artificial Neural Network

4.1 Introduction

Artificial neural network is a data mining technique inspired from biological central nervous

systems. The biological nervous systems respond to external stimulations by certain reactions. Artificial

neural networks mimic this behavior by learning the structure between the input neurons and output

neurons. The external stimulations for a biological nervous system are represented by input datasets for an

artificial neural network. Artificial neural network will respond to their external stimuli with an output

dataset to the input dataset. The modern concept of artificial neural network is first introduced by

McCulloc and Pitts in 1943.

As can be seen in Figure 4.1, a typical biological nervous neuron consists of dendrites, a soma, an

axon and another neuron’s dendrite is connected to the end of the axon through a terminal button or a

synapse. Dendrites collect the signals and soma sums them and output these signals through axon. In an

artificial neuron network system, the input neurons mimic the dendrites to provide input information.

Figure 4-1: A typical biology nervous neuron (www. pharmaworld.pk.cws3.my-hosting-

panel.com/BodySystemDetail )

)

http://pharmaworld.pk.cws3.my-hosting-panel.com/BodySystemDetail.asp?tId=59

http://pharmaworld.pk.cws3.my-hosting-panel.com/BodySystemDetail.asp?tId=59

21

Transfer functions mimic soma to sum the input information. Output neurons represent the axon.

Artificial neuron network is capable to deal with non-linear and multi-dimensional data systems. It is

widely used in weather forecasting, stock price prediction and investment decision making.

Figure 4.2 shows a typical structure of simple artificial neural network. The input information

from input neurons needs to be weighted and summed by a certain transfer function before being

transmitted to other neuron. The training of the network is a procedure that determines the optimal weight

of each input neuron. The reliability of the network is usually evaluated by internal random tests. Once

the errors from the test are found to be within tolerance levels, the network can be considered as “learned”

network or an expert system.

Figure 4-2: An example of simple artificial neuron network

22

4.2 Transfer (Active) Functions

Transfer function or active function is an important component of an artificial neural network.

The artificial neural network toolbox employed in this work couples more than ten different transfer

functions for users to choose. The following three types of transfer functions are widely used in reservoir

simulation studies.

1. Log-sigmoid transfer function (LOGSIG)

LOGSIG transfer function can be expressed as:

( )

Figure 4-3: Transfer functions

23

As shown in Figure 4.3 (a), LOGSIG takes input data and transfers them to output within the

range of 0 to 1. It is a differential network and is used in dealing with multiple layer networks.

2. Hyperbolic tangent transfer function (TANSIG)

TANSIG transfer function can be expressed as:

( )

or ( )

As shown in Figure 4.3 (b), TANSIG takes input data and transfers them to output within the

range of -1 to 1.

3. Purelin transfer function (PURELIN)

Purelin transfer function can be expressed as:

( )

As shown in Figure 4.3 (c), Purelin is the simplest linear transfer function which multiple

the input data by a constant k. The outputs of Purelin function do not need to be denormalized

because they are not expected to be in a certain specified range. Purelin transfer function is used

in the output layer in this study.

4.3 Backpropagation Networks

The network type used in this study is a backpropagation network. Backpropagation network,

which implies for backwards propagation of errors, is a supervised learning method to train artificial

neural networks. Backpropagation network consists of at least three layers: one input, one hidden and one

output layer. It has a wide application in reservoir simulation studies. According to Rojas (1996), typical

backpropagation training algorithm includes three steps:

“Step one: Feed-forward computation

24

Forward propagation of a training pattern's input through the neural network in order to generate

the propagation's output activations

Step two: Backpropagation to the output layer and hidden layers

Backward propagation of the propagation's output activations through the neural network using the

training pattern's target in order to generate the deltas of all output and hidden neurons

Step three: Weight updates

Multiply its output delta and input activation to get the gradient of the weight. Bring the weight in

the opposite direction of the gradient by subtracting a ratio of it from the weight”

In this study, the four aforementioned networks are multiple-layer backpropagation networks with

different structures.

4.4 Overlearning and Underlearning

Overlearning and underlearning are two major challenges encountered in training an artificial

neural network. Overlearning means that the artificial neural network memorizes too much information

from given input and output datasets and ignores the general data structure. If overlearning happens, the

error reflected from training set would be small but the network may fail to make predictions with new

input datasets. Overlearning always happens when relative simple datasets are fed to a complex network

or a network is trained unnecessarily long for times. Underlearning always indicates large error from

training sets. It happens if the training time is not long enough or there are not enough data sets for

training. The solution to these two issues is to apply “early-stopping technique” to the training.

The datasets used for training are divided into three parts: (1) training set (2) validation set (3)

test set. The validation set and test set are independent from the training set. The error from validation set

is recorded and it should decrease with the error from the test set. When validation error starts to increase,

it indicates that overlearning is taking place and the training must stop. As shown in Figure 4.4,

overlearning occurs when validation error starts to increases. At that point the training should stop.

25

4.5 Training of Artificial Neural Networks

Training of the artificial neural network is a procedure of trial and error. The performance of the

network is determined by the design of neural network. The transfer functions and training algorithms

selected have been discussed in previous sections. The following paragraphs summarize the key

parameters of artificial neural network:

Numbers of hidden layers

Numbers of hidden neurons in each hidden layers

Functional links

Backpropagation network is employed in this study to train the networks developed. The artificial

neural network tool box monitors the error of the weights of each input neurons for every training

iteration. A “performance” term is used to track the error of the weights. Therefore, the training procedure

can start by defining one hidden layer with neurons of same number of input neurons. Then, one trains the

artificial neural network and observes the performance and the error generated from the internal tests.

Figure 4-4: Network overlearning

Overlearning occurs when

validation error starts to

increase

26

Empirically, networks with bad performances will also have large internal test errors. Then, by adding

hidden layers and hidden neurons the performance of the network can be improved. However, a network

with good performance does not necessary have small internal test error. If this happens, it is

recommended to add functional links to output layers and input layers until the internal test error is within

the tolerance range.

Functional links are neurons of input or output layers. They help the network to learn the

structure of the data but the functional links in output layers will not be tested in internal tests. Functional

links could be defined by random combination of input and output neurons with random mathematical

operations such as multiplication, division and eigenvalues, etc. A point that should be emphasized here is

that the functional links in input layer cannot include any neurons in output layers. Figure 4.5 shows the

workflow of the training procedure.

Figure 4-5: Workflow of training the artificial neuron network

27

Chapter 5 Monte Carlo Method

5.1 Introduction

Monte Carlo method, which is also known as Monte Carlo experiment, is a computational

algorithm that does repeating calculations of randomly distributing data samples. Monte Carlo method

was introduced by J.v. Neumann, S.Ulam and N. Metropolis in 1945. It is developed for a nuclear weapon

project. The algorithm was named after the Monte Carlo Casino, a famous casino where Ulam's uncle

often gambled. There exists thousands of ways to apply Monte Carlo method. Generally, it follows the

steps listed below (Metropolis, 1987):

1. Define the domain of the possible inputs

2. Generate input arrays by uniform random distribution within the certain domain

3. Perform repeating computation for every element of the input array

4. Analyze the outputs

There are two major applications of Monte Carlo method in engineering: First one is sensitivity

and quantitative probabilistic analysis in process design. Monte Carlo method relies on repeating

computation of randomly distributing data samples. Thus, the outputs are arrays with the same dimension

of the input arrays. Sensitivity and quantitative probabilistic analysis could be done by generating

frequency distribution of the outputs.

The second one is process design optimization. For example, assume that Monte Carlo method is

applied to study an engineering design optimization problem. The inputs are thousands of combinations

of design parameters and repeating computations are processed based on these inputs. The outputs

represent the performance of the corresponding combination of engineering design. If certain analysis

with restriction and design criterion could be performed on the outputs of Monte Carlo runs, an optimal

output could be found and the corresponding design parameter group would be the optimal combination

of engineering design.

http://en.wikipedia.org/wiki/John_von_Neumann

http://en.wikipedia.org/wiki/Stanislaw_Ulam

http://en.wikipedia.org/wiki/Nicholas_Metropolis

http://en.wikipedia.org/wiki/Monte_Carlo_Casino

http://en.wikipedia.org/wiki/Sensitivity_analysis


http://en.wikipedia.org/wiki/Probabilistic

http://en.wikipedia.org/wiki/Process_design_(chemical_engineering)


http://en.wikipedia.org/wiki/Probabilistic

28

5.2 P-value Approach

P-value is a statistical definition which indicates that the cumulative probability of a random

number within a domain may fall within a range. For example, for a certain dataset, P90= 2,000 indicates

that 90 % data of the dataset is less than 2,000. As aforementioned in previous chapters, formation

reservoir properties vary within large ranges. Therefore, with Monte Carlo simulation protocol, p-value

approach is employed to study the probability of the output to reduce the uncertainty from the various

reservoir properties. The model developed in this study describes the output parameters by p90, p50 and

p10 confidence intervals.

29

Chapter 6 Studies on Injection Patterns

6.1 Introduction

The objective of this section is to study the injection performance of different injection patterns.

In this study, the followings injection patterns are studied:

1. Regular 4-spot injection pattern

Regular 4-spot injection pattern is a triangle-shaped injection pattern. A typical well arrangement of

regular 4-spot injection pattern is shown in Figure 6.1 (a). The injector to producer ratio is two.

2. Inverted 4-spot injection pattern

Inverted 4-spot injection pattern is also triangle-shaped injection pattern. A typical well arrangement

of regular 4-spot injection pattern is shown in Figure 6.1 (b). The injector to producer ratio is one half.

Figure 6-1 (a): Regular 4-spot injection pattern

30


Regular 5-spot injection pattern is a rectangular-shaped injection pattern. A typical well arrangement

of regular 5-spot injection pattern is shown in Figure 6.1 (c). The injector to producer ratio is 1.


Inverted 5-spot injection pattern is equivalent to a regular 5-spot injection pattern. The well

arrangement of inverted 5-spot injection pattern is shown in Figure 6.1 (d)

Figure 6-1 (b): Inverted 4-spot injection pattern

31

Figure 6-1 (c): Regular 5-spot injection pattern

Figure 6-1 (d): Inverted 5-spot injection pattern

32


Regular 7-spot injection pattern is a hexogen-shaped injection pattern. A typical well arrangement of

regular 7-spot injection pattern is shown in Figure 6.1 (e). The injector to producer ratio is one half.


Inverted 7-spot injection pattern is a hexogen-shaped injection pattern. A typical well arrangement of

regular 7-spot injection pattern is shown in Figure 6.1 (f). The injector to producer ratio is two.

Figure 6-1 (e): Regular 7-spot injection pattern

33

Monte Carlo simulation protocol will be applied in this simulation study. The simulation study

will focus on pattern-based-unit with the reservoir properties of Mt. Simon sandstone formation. The

output will be P90 confidence interval of cumulative injection of CO2 and injection efficiency. At this

stage, the simulation totally relies on high-fidelity model.

6.2 Model Setup

This section briefly discusses mesh grid dimension, reservoir property ranges and relative

permeability inputs to the numerical simulator.

6.2.1 Reservoir Properties Range and Mesh Grid Dimensions

The input of the reservoir properties are within the following ranges:

Porosity (5% - 20%)

Figure 6.1 (f): Inverted 7-spot injection pattern

34

Permeability (0.1 md - 150 md)

Depth (3,500 ft - 6,000 ft)

Thickness (1,600 ft - 2,000 ft)

Formation pressure gradient: 0.433 psi/ft

Formation fracture gradient: 0.6 psi /ft

A 2-D model with grid blocks of 20×20 is used for the numerical simulation runs, the well locations

are shown in Figure 6.1 (a)- 6.1 (f). At this stage, 500 Monte Carlo simulation runs are used to determine

the P90 confidence interval of cumulative injection of CO2 and injection efficiency. The CO2 injector

could be either horizontal injector or vertical injector. If horizontal injector is used, the length of wellbore

is set to 800 feet. The model is run based on different injection rates to observe the change of cumulative

CO2 injection and injection efficiency. The size of all the patterns is fixed at 160 acres. Brine producers

are operated at constant bottom-hole pressure, which is fixed at half of the initial reservoir pressure.

In case of dealing with CO2 breakthrough, the “TRIGGER” subroutine in CMG-GEM is employed.

TRIGGER allows user to change the well boundary condition and well activity for some certain threshold

values. In this study, TRIGGER is used to shut in the producer when the gas production rate at the brine

producer is larger than 1,000 SCF/day.

6.2.2 Modeling of CO2- Brine Relative Permeability

Relative permeability is an important parameter in modeling multiphase fluid flow in porous

medium. Corey’s formulation (Corey, 1956) for two phase flow is employed to model the relative

permeability of CO2- brine system. Corey’s formulation is described as:

(

)

(

)

(

)

35

where Sg is gas saturation, Sw is water saturation, Swirr is irreducible water saturation. The irreducible

water saturation is supposed to be 5% in this study. Figure 6.2 show the relative permeability curve

generated using Corey’s relative permeability model.

6.3 Simulation Results

Based on the model setup discussed in section 6.2, P90 cumulative injection curves changing with

injection rate for different injection patterns and different injector types are generated. Figure 6.3 (a) to

Figure 6.3 (c) show these P90 cumulative injection curves.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Rel

ati

ve

Per

mea

bil

ity

Sg

Gas Curve Water Curve

Figure 6-2: Relative permeability curve generated by Corey’s formulation

36

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250 300 350 400

P 9

0 C

um

ula

tiv

e In

ject

ion

, M

M m

etri

c T

on

Injection Rate, MMSCFD

Regular Pattern with

Horizontal Injector


Vertical Injector

Inverted Pattern

with Horizontal

Injector

Inverted Pattern

with Vertica Pattern

Peak P90 cumulative injection

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100 120 140P9

0 C

um

ula

tiv

e In

jecti

on

ra

te, M

M M

etri

c T

on

s


Inverted Pattern with

horizontal injector

Regular pattern with

horizontal injector


Vertical injector


Regular and Inverted

pattern with vertical

injector

Figure 6-3 (a): P90 cumulative CO2 injection vs. injection rate for 4-spot patterns

Figure 6-3 (b): P90 cumulative CO2 injection vs. injection rate for 5-spot patterns

37

The observation is that first P90 cumulative CO2 injection increases linearly as the injection rate

increases. When injection rate reaches a certain value, the path of cumulative CO2 injection curve

departures from the straight line and enters a plateau and later starts to decrease. The reasons are as

follows: first of all, if injection rate is high, a high bottomhole injection pressure is required. If the

bottomhole pressure exceeds the formation fracture pressure, the boundary condition of injector will

switch to injection with constant bottomhole pressure, which restricts the injectivity. The other reason is

that the CO2 may breakthrough at the brine producer prematurely, if that happens, brine producer will be

shut in and the formation pressure will build up faster and exceed the injection pressure limitation.

Another important observation is that: for certain 4-spot, 5-spot or 7-spot injection patterns, the

regular patterns with horizontal injector always have the best performance. Peak p90 cumulative

injections are shown in figure 6.3 (a) to (c).

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100 120 140

P9

0 C

um

ula

tiv

e In

ject

ion

ra

te, M

M M

etri

c T

on

s


Inverted Pattern

With Horizontal

Injector

Inverted Pattern

with Vertical

Injector

Regular Pattern

with Horizontal

Injector

Regular Pattern

with Vertical

Pattern


Figure 6-3 (c): P90 cumulative CO2 injection vs. injection rate for 7-spot patterns

38

Figure 6.4 shows the comparison of peak p90 cumulative injection among 4-spot, 5-spot and 7-

spot injection pattern. The observation at this stage is that regular 4-spot injection pattern with horizontal

injector has the best injectivity considering the cumulative CO2 injection.

Since regular patterns with horizontal injector has the best injectivity, Figures 6.5 (a) to 6.5 (c)

plot the p90 injection efficiency profile changing with injection rate. Peak p90 injections efficiency values

are shown in Figure 6.5 (a) to (c).

0

2

4

6

8

10

12

14

16

18

20

4-spot 5-spot 7-spot

Pea

k P

90

Cu

mu

lati

ve

Inje

ctio

n,

MM

met

ric

ton

nn

es

Figure 6-4: Comparison of peak P90 cumulative injection

39

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 50 100 150 200 250 300 350 400 450 500

P9

0 I

nje

ctio

n E

ffic

ien

cy,

met

ric

ton

/bb

l


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 20 40 60 80 100 120 140

Inje

ctio

n E

ffic

ien

cy,

met

ric

ton

/bb

l

Injection Rate MMSCFD

Figure 6-5 (a): P90 injection efficiency vs. injection rate for 4-spot patterns

Figure 6-5 (b): P90 injection efficiency vs. injection rate for 5-spot patterns

Peak p90 injection efficiency


40

Figure 6.6 shows the comparison of peak p90 injection efficiency among regular 4-spot, 5-spot

and 7-spot injection patterns with a horizontal injector. The observation is that regular 4-spot injection

pattern with horizontal injector again has the best injectivity in terms of the injection efficiency.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 20 40 60 80 100 120 140

Inje

ctio

n E

ffic

ien

cy,

met

ric

ton

/bb

l


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

4-spot Pattern 5-spot Pattern 7-spot Pattern

Pea

k P

90

In

ject

ion

Eff

icie

ncy

, m

etri

c to

n/

ba

rrel

Figure 6-5 (c): P90 injection efficiency vs. injection rate for 7-spot patterns


Figure 6-6: Comparison of peak p90 injection efficiency

41

6.4 Studies on Pressure Depletion Ratio

The observation from Section 6.3 is that regular 4-spot injection pattern with horizontal injector

has the best injectivity considering both cumulative CO2 injection and injection efficiency. The study runs

simulation on regular 4-spot injection pattern with horizontal injector with pattern areas of 70, 160, 320

and 640 acres. Pressure depletion ratio values from those runs are tracked. In this case, the production

wells are producing brine at half of initial reservoir pressure and horizontal wellbore length is fixed at 800

ft. Thus, the pressure depletion ratio is controlled by pattern area and injection rate. Accordingly, an

implicit expression of pressure depletion ratio can be written as:

( )

where Q is the injection rate, in MMSCFD and S is the pattern area, in acres.

Then, the p50 pressure depletion ratio surfaces can be plotted as shown in Figure 6.7. After

inserting a plane cutting the P50 pressure depletion ratio surface parallel to the “pattern size—injection

rate” plane (as shown in Figure 6.7), it can be seen that all the pattern size and injection rate design data

below this plane are yielding smaller stabilized injection block pressures than initial reservoir pressure.

The plane has an intersection line with the PDR surface. Then, one can determine the projection of the

intersection line on the “pattern size- injection rate” plane, as shown in Figure 6.8. The projection line is

defined as “safety-limit line”. The red area in Figure 6.8 highlights the region for the safe injection rate

and pattern size design. However, the design criteria on the safety-limit line not only represent safe

injection practices; but more importantly, imply that injection design parameters on the limitation line

take full advantage of the capacity of the formation for storage purposes. Note that the safety -limit line is

not necessarily a straight line. At this phase of the study, the database is not large enough to generate a

smooth curve.

42

Plane at p50 PDR=1

Figure 6-7: P50 pressure depletion ratio surface

Figure 6-8: Top view of “pattern size-injection rate” plane

43

Figure 6.9 shows the p90 injection efficiency surface. One can apply the safety-limit line to this

surface to find the highest injection efficiency and the corresponding injection rate and pattern size. The

protocol to apply the safety-limit line to find the optimal injection rate and pattern size as shown in Figure

6.9 is as follows: Draw a plane containing the safety-limit line and at the same time perpendicular to the

“pattern size-injection rate” plane. Then, find the highest injection efficiency on the intersection line of

these two planes and the corresponding injection rate and pattern size. Since the data is not dense enough

to get the exact solution, the optimal injection efficiency appears at ranges: Pattern area: [510, 525] acres,

Injection rate [105, 115] MMSCFD.

Studies in this section is inspiring. The observations can be summarized as follows:

1. Pressure depletion ratio is an important constraint in designing the injection pattern. The

optimal design should consider both pressure depletion ratio and injectivity.

Figure 6-9: P90 injection efficiency surface

44

2. The injectivity of a 4-spot injection pattern with horizontal injector is controlled by multiple

engineering design parameters including injection rate, pattern area , horizontal wellbore

length and brine producer specifications. Determining the optimal design needs to generate

large amount of simulation results.

3. Running simulation totally relying on high-fidelity model is not the best way to determine the

optimal design.

6.5 Summary of Observations

In this section, different injection patterns with horizontal or vertical injector are studied in

consideration of injection efficiency and cumulative CO2 injection. Monte Carlo simulation protocol is

employed to output the p90 value of injection efficiency and cumulative CO2 injection. One of the most

significant observation is that 4-spot injection pattern with horizontal injector has the best injectivity

considering both cumulative CO2 injection and injection efficiency.

However, there exist several deficiencies in this analysis. The horizontal well length and the brine

producer specification are fixed at certain values. More importantly, all the simulations totally rely on

high-fidelity compositional simulation runs, which raises two concerns: 1. the simulation run times are

long; 2. the required hard drive space to restore the output files of the simulation runs is extremely large.

Therefore, if one desires to do simulation study on the influence of pattern size, horizontal well length and

brine production to the CO2injectivity, a more effective approach has to be introduced.

Artificial neural network technology is recognized as an effective approach to achieve the overall

goals of this study. An artificial expert system can generate large number of Monte Carlo simulation runs

within a short period of time. In the following chapters, the development of artificial neural network and

more extensive simulation studies applied to the network development will be discussed.

45

Chapter 7 Development of Artificial Neural Networks (ANN)

This chapter will discuss the development and validation of three networks aforementioned. The

study in Chapter 6 comes to the conclusion that the regular 4-spot injection pattern with horizontal

injector has the best performance compared with other patterns. Thus, the study of this section will focus

on designing of artificial neural network with variables of regular 4-spot injection pattern with horizontal

injector. Then, once an expert artificial neural network is developed, it will help in generating large

number of Monte Carlo simulation runs to determine the optimal design of regular 4-spot injection

patterns with horizontal injector. More importantly, ANN will be applied to basin-scale simulation.

7.1 Generation of Dataset for Training the Networks

A 2-D model with grid dimension of 30×30 is built to model the 4-spot injection pattern, as

shown in Figure 7-1.

Figure 7-1: 2-D simulation model

46

The input layer includes two groups of input parameters. The first group is reservoir properties

group which includes formation permeability (k), porosity ( ), reservoir thickness (h), depth (D), initial

reservoir temperature (Ti), initial reservoir pressure (Pi), formation fracture pressure (Pfrac). Reservoir

temperature, initial reservoir pressure and formation fracture pressure is calculated using temperature and

pressure gradients. The second input layer group involves the injection operation related design

parameters including injection rate (Q), pattern size (A), horizontal well length (Lw) and brine producer

sandface pressure (Pwf). Table 7-1 shows the input neurons and corresponding ranges that are used in

generating the training data sets.

Reservoir

Property and

Design Parameter Training Data Range

k(md) 0.5-150

h(ft) 50-2600

(fraction) 0.01-0.25

D(feet) 2000-8500

(psi/ft) 0.433-0.5

(ºF/1,000 ft) 9.5-12

(psi/ft) 0.6-0.9

A(acres) 70-640

Q (MMSCFD) 1-250

Lw (feet) 500-1500

Pwf , fraction of Pi 0.5~0.95

1,000 input data arrays are generated within certain ranges and to generate 1,000 input files for

the high fidelity model. Different output parameters are picked from those 1,000 CMG output files for

training of different networks:

The end-point forward-looking solution network (EFSN), the selected output parameters are

cumulative CO2 injection at the end of injection period, cumulative brine production at the end of

injection period and the post injection well block stabilized pressure.

Table 7-1: Summary of training data ranges

47

The injection efficiency profile network (IEPN): the selected output parameters are injection

efficiency at different time points.

The injector bottomhole pressure profile network (BHPN): the selected output parameters are

injection well bottomhole pressure at different time points.

Those 1,000 output data files need to be cleaned up before using for ANN training. The data cleaning

up criterion are as follows (the runs ignored):

Cumulative injection after 6 years < 0.1 MM metric tons

Pressure depletion ratio > 2

7.2 Designing of Artificial Neural Networks

This section discusses the architecture design of the three networks aforementioned.

7.2.1 End-point Forward-looking Solution Network (EFSN)

As can be seen in Table 7-2, there are 11 neurons in input layers of this network. A set of 16

functional links are used in the output layer.

48

Inputs (11

neurons)

Reservoir

properties , k, h, D, Ti, Pi, Pfrac

engineering

design

parameter

A, Q, Lw, Pwf

Outputs(20

neurons)

Tracked data Cumulative CO2 injection(CumGas), cumulative brine production (CumBrine),

stabilized injector block pressure(Pr)

17 Functional

links

Injection efficiency, pressure depletion ratio, kh/A, k× ×CumGas,

,

,

,

,

,

,

,

,

,

,

,

Figure 7-2 shows the structural design of EFSN. A cascade feed-forward backpropagation

network is designed with 5 hidden layers. The transfer functions between hidden layers are TRANSIG.

Purelin transfer function is used on the output layer.

Table 7-2: Input and output neurons of EFSN

49

7.2.2 Injection Efficiency Profile Network (IEPN)

The injection efficiency profile network (IEPN) is developed to track the injection efficiency at

different times after the injection well becomes active. The input layer is the same as EFSN. In the output

layer, 13 data points of injection efficiency are tracked. Table 7-3 shows the neurons in output layers. The

subscript numbers of the injection efficiency represent the injection efficiency at the end of the injection

duration.

Table 7-3.Output neurons and functional links of IEPN

Injection Efficiency Points IE30, IE180, IE360, IE540 IE720, IE900, IE1080, IE1260,

IE1440, IE1620, IE1800, IE1980, IE2192

Functional links

∑

, √

,

∑

, ,

,

,

,

Figure 7-2: Architecture of EFSN

50

Notes on Table 7-3:

is the larger eigenvalue of matrix[

]


] (same as the previous network)

is the value of determinant|

|


|


|


|

Figure 7-3 shows the design of architecture of injection efficiency profile network (IEPN). There

are 5 hidden layers with 15 neurons on each hidden layers.

http://dict.youdao.com/w/determinant/




51

7.2.3 Injection Well Bottomhole Pressure Profile Network (BHPN)

Similar to the injection efficiency profile network, another network, which is injection well

bottomhole pressure profile network (BHPN), is developed to track 13 injection well bottom pressure

after the injection well is put in operation. The subscript numbers of the injection well bottomhole

pressure variable represent the pressure values being on stream for a specified number of days. Table 7-4

shows the output neurons in output layer of the network.

Table 7-4: Output neurons and functional links of BHPN

Pressure Points P30, P180, P360, P540 P720, P900, P1080, P1260, P1440,

P1620, P1800, P1980, P2192

Functional links

∑

, √

,

∑

, ,

,

,

,

Figure 7-3: Architecture of IEPN

52

Notes on Table 7-4:


]


]

is the value of the determinant|

|

Figure 7-4 shows the structure of BHPN. There are 4 hidden layers with 15 neurons on each of

them.

Figure 7-4: Architecture of BHPN


53

7.3 Test and Validation of the Networks

This section discusses testing and validation of the three neural networks aforementioned. Each

network is tested by random internal tests. The test error for a certain variable predicted by ANN is

defined as:

One of the most important observations in training these networks is that the training results, including

training performance, epoch when overlearning occurs and the test error vary every time when one runs

the training program. This is expected as the training program divides the datasets for training into

training set, validation set and testing set randomly every time. In other words, the datasets used for

training, validation and testing of a certain ANN can vary for different training sessions. Thus, one cannot

prove the reliability of a network by training it for only one time. In the following sections, all the errors

are generated from repeated trainings. As can be seen in Figure 7-5, the best performance varies for the

three sample trainings of EFSN. Similar observations can happen in the training of the other two

networks.

54

7.3.1 Test and Validation of EFSN

Figure 7-5 (a) to (c) shows the tests errors of the three tracking parameters from 12 repeating

training runs of EFSN. More than 65% of the test errors of prediction of cumulative brine production are

within 10% error margin. More than 60% of the test errors of prediction of cumulative CO2 injection are

within 10% error margin. More than 75% of test errors of the stabilized injector pressure error are within

10% error margin.

Figure 7-5: Different performances for multiple trainings of EFSN

55

To further prove the reliability of the network, 96 random test dataset are picked to compare the

EFSN prediction to the high-fidelity model results of certain parameter, as shown in Figure 7-7 (a) to (c).

Figure 7-6: Test errors distributions of EFSN

56

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 10 20 30 40 50 60 70 80 90 100

Cu

mu

lati

ve

Bri

ne

Pro

du

ctio

n, M

M b

bl

Test Sets

ANN Prediction CMG ResultsNumerical model results

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 10 20 30 40 50 60 70 80 90 100

Cu

mu

lati

ve

Carb

on

Dio

xid

e In

ject

ion

, M

M

Met

ric

ton

nes

Test Sets

ANN Prediction CMG Results

Figure 7-7 (a): Comparison of EFSN prediction and numerical model results of cumulative brine production

Figure 7-7 (b): Comparison of EFSN prediction and numerical model results of cumulative CO2 injection

EFSN Prediction

EFSN Prediction Numerical model results

57

The tests results from the repeated training sessions indicate the success of the network in

predicting the cumulative brine production, cumulative CO2 injection and the stabilized injector block

pressure.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 10 20 30 40 50 60 70 80 90 100

Post

In

ject

ion

In

ject

or

Blo

ck S

tab

iliz

ed P

ress

ure

, p

si

Test Sets

ANN Prediction CMG Results

Figure 7-7 (c): Comparison of EFSN prediction and numerical model results of stabilized injector block pressure

EFSN Prediction Numerical model results

58

7.3.2 Test and Validation of IEPN

Repeating the training approach is also applicable to IEPN. A total of 13 injection efficiency

values are tracked in this network. Instead of plotting the error distribution of each injection efficiency

value, the model outputs the error distribution of all the 13 injection efficiency points comprehensively.

For each training session, 250 internal tests are used to record the error. This network is trained for 12

times to observe the error distributions. Figure 7-8 shows the error distribution of three sample tests sets.

Figure 7-8: Tests error distributions of injection efficiency of three sample sets

59

Figure 7-7 displays that about 40 % of the error is within less than 5% error margin and 60% of the error

is found to be within the 10% error margin.

Figures 7-9 (a) and 7-9 (b) show the injection efficiency values as predicted by the IEPN against

high-fidelity model results. In Figure 7-9 (a), the relative permeability to CO2 also increases with gas

saturation. Thus, the brine production rate will decrease at a constant production rate. The injection

efficiency enters a plateau region due to CO2 breakthrough. The producers are shut in and the reservoir

pressure builds up. Therefore, the cumulative CO2 injection will change slightly after breakthrough

(cumulative brine production will not change any more). Figure 7-9 (b) shows the case when the producer

is strong but the CO2 injection rate is comparatively small. The injection efficiency keeps decreasing due

to large brine production.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 500 1000 1500 2000 2500

Inje

ctio

n e

ffic

ien

ct,

Met

ric

ton

ne/

bb

l

time, days

CMG ANN

Figure 7-9 (a): Injection efficiency profiles predicted by IEPN and numerical model, Case 1

IEPN

60

7.3.3 Test and Validation of BHPN

Similar to IEPN, 12 successive training sessions are used to test the network. Figure 7-10 shows

the error distribution of three test set samples. These test results show that more than 60% of the errors are

within the 5% error margin. This is an indicative of the success of the network in predicting the

bottomhole pressure of the injection well.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 500 1000 1500 2000 2500

Inje

ctio

n e

ffic

ien

ct,

Met

ric

ton

ne/

bb

l

time, days

CMG ANN

Figure 7-9 (b): Injection efficiency profiles predicted by IEPN and numerical model, Case 2

IEPN

61

Figures 7-11 (a) and (b) show the comparison between predictions from BHPN and the results from the

numerical simulator. First, observation from Figure 7-11 (a) is that the blue line from the numerical model

shows a sudden bottom-hole pressure increase around 1550 days. This is indicative of CO2 breakthrough.

The brine producers are shut in, thus, the pressure build up is rather quick. Another important observation

is that the ANN shows worst performance at the CO2 breakthrough time. Figure 7-11 (b) shows a

different scenario. The bottomhole pressure builds up quickly and enters a plateau zone. This is indicative

of large injection rates and small production volumes. The bottomhole pressure reaches the formation

bursting pressure and the injection process has to be switched to constant pressure injection. The key

Figure 7-10: Tests error distributions of bottomhole pressure of three sample sets

62

observation here is that BHPN again shows a relatively poor performance at the discontinuity point on the

profile (when the switch of the boundary condition takes place).

2000

2500

3000

3500

4000

4500

5000

0 500 1000 1500 2000 2500

Inje

cto

r b

ott

om

ho

le p

ress

ure

, p

si

Time, days

CMG ANN

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

0 500 1000 1500 2000 2500

Inje

cto

r b

ott

om

ho

le p

ress

ure

Time, days

CMG ANN

Figure 7-11 (a): Bottomhole pressure profiles predicted by BHPN and numerical model, Case 1

Figure 7-11 (b): Bottomhole pressure profiles predicted by BHPN and numerical model, Case 2

BHPN

BHPN

63

At this stage, three expert ANN systems are developed and their reliabilities are tested by repeating

the training experiments. The following bullets summarize some conclusions that are from the study of

this section:

EFSN can effectively predict the cumulative CO2 injection, cumulative brine production at the

end of the injection period. The stabilized injector block pressure can also be accurately predicted.

EFSN will be applied to determine the optimal design of the injection pattern in different

geologies cases.

IEPN can effectively predict the trends encountered at the injection well in terms of bottom-hole

pressure and the injection efficiency profile.

BHPN performs rather poorly at the discontinuity points of the bottomhole pressure profile (when

the boundary condition of injection well switches from flow rate specification to bottomhole

pressure specification).

64

Chapter 8 Case Studies

The objective of this section is to apply the three expert networks developed in Chapter 7 to

design a regular 4-spot injection pattern with horizontal injector. Monte Carlo simulation protocol will

also be coupled in the design workflow. The geological sites cases selected are Mt. Simon sandstone

formation in the Illinois Basin and Michigan Basin.

8.1 Injection Depth Limitation

The objective of this section is to verify the injection depth limitation. The injection protocol aims

to keep the injected CO2 to be in non-gaseous form during the sequestration period. As can be seen in

Figure 8-1, the critical pressure of CO2 is 1073 psi and critical temperature is 88 °F. The formation

pressure gradient is assumed to be 0.433 psi/ft and the formation temperature gradient is assumed to be 11

°F/1000 ft. Thus, in order to keep the CO2 in liquid phase or super critical phase, the minimum injection

constraint becomes: 1073 psi/0.433 psi/ft≈2,500ft. For injection the maximum depth is already defined in

Chapter 1. The maximum depth to inject is constraint at 7,500 feet due to a sharp porosity decrease at

that depth.

Figure 8-1: CO2 phase diagram (Medina, 2008)

65

8.2 Design of Regular 4-spot Injection Pattern with Horizontal Injector

8.2.1 Characterization of Reservoir Properties Inputs

The injection depth limit of Mt. Simon sandstone formation is defined as 2,500 ~ 7,500 feet.

There is no thickness limitation for CO2 injection in this study. (See the isopach and elevation maps of

Illinois and Michigan Basins, Figures 2-5 and 2-6, which are duplicated here for ease of reference.)

As can be seen in Figure 2-5, the contour values of elevation maps reflects that the depth of Mt.

Simon formation within the injection depth limits is 3,500~ 7,500 feet and the formation thickness is

100~ 1,300 feet. Within the acceptable depth range, porosity range is 6.5%~20%, and permeability range

is 4.8- 100 md. Recall the formation pressure and temperature gradients from literatures: For Michigan

Basin as 0.46 psi/ft, temperature gradient as 11 °F/1,000 ft; and fracture pressure gradient as 0.8 psi/ft.

Figure 2-5: Mt. Simon Formation isopach map and elevation map at Michigan basin (Barnes, 2009)

66

Figure 2-6 shows that contour values of elevation maps reflects that the depth of Mt. Simon

formation within the injection limitation is 2,500~ 7,500 feet and formation thickness is 500~ 2,250 feet.

Within the acceptable depth range, porosity range is 6.5%~20% and permeability range is 4.8- 100 md.

The formation pressure gradient of Illinois Basin is 0.45 psi/ft; temperature gradient is 10 °F/1,000 ft and

fracture pressure gradient is 0.751 psi/ft. Table 8-1 summarizes the reservoir property ranges in the

Michigan and Illinois basins.

Figure 2-6: Mt. Simon Formation isopach map and elevation map at Illinois basin (ISGS, 2006)

67

Michigan Basin Illinois Basin

Properties Units min max min max

fraction 6.5 20 6.5 20

k md 4.8 100 4.8 100

thickness ft 100 1300 500 2250

depth ft 3500 7500 2500 7500

Pi psi 1610 3450 1127.5 3382.5

Ti °F 98.5 142.5 85 135

Pfrac psi 2800 6000 1877.5 5632.5

8.2.2 Design of a regular 4-spot injection pattern with horizontal injector

The objective of this section is to apply one of the expert system (EFSN) developed in Chapter 7

to determine the optimal design of regular 4-spot injection pattern with horizontal injector. The design

will couple Monte Carlo simulation protocol to express the output in p90 and p50 values.

8.2.2.1 Statement of Design Criteria

The EFSN network requires inputs of reservoir properties and engineering design parameters.

The reservoir property ranges of the two basins are summarized in Table 8-1. The engineering design

parameters includes injection rate (Q), pattern area (A), length of horizontal well bore (Lw) and brine

producer sandface pressure (multiplier of Pi). Table 8-2 summarizes the ranges of design parameters.

Design Parameters min max unit

Q 1 200 MMSCFD

A 70 640 acres

Lw 800 1500 feet

Pi multiplier for Pwf 0.5 0.95 fraction

Table 8-1: Summary of reservoir properties ranges

Table 8-2: Summary of engineering design parameters

68

As is discussed previously, the goal of the project is to find the optimal design yielding maximum

CO2 injection and minimum brine production. In achieving this, the post injection reservoir stabilized

pressure needs to be maintained at a safe level. Thus, the best way to determine the optimal project design

parameters is to establish a one-to-one relationship between the project performance parameters, and

project design parameters and reservoir properties.

The pressure depletion ratio (PDR), which is defined earlier as the ratio of reservoir stabilized

pressure to the initial reservoir pressure, is an important safety constraint in the design protocol. The

network developed in this study tracks the block pressure of the injection well after the injector is shut in

for 50 years to represent the stabilized reservoir pressure. PDR needs to be maintained below a safety

level to prevent the CO2 gas from migrating upwards through the seal formation. More importantly, PDR

is not only a safety constraint factor but also a measure of the reservoir intake capacity. Low PDR

represents that the overall capacity of the formation is not fully used or too much brine is produced.

Monte Carlo simulation protocol helps solve the dilemma of dealing with the PDR. In this design,

a model is developed to use the EFSN to run the Monte Carlo simulation. The four design parameters will

be combined randomly for thousands for cases for the ranges shown in Table 8-2. Each individual case of

design parameters will be combined with 500 groups of combinations of reservoir properties of a certain

basin case. Thus, 500 input arrays are generated; EFSN is employed to generate 500 outputs. Then, 500

groups of PDR could be calculated. The model will express the PDR value in p50 confidence interval of

these 500 values from each simulation run. The design criterion is to select the design parameter

combination with p50 PDR approximately equals to one for further calculation. The p50 value of PDR

equals to one addresses the issue of capacity usage and safety.

The pattern area is considered as a parameter in the design. It is not reasonable to compare the

cumulative CO2 injection in a small pattern against a large pattern. An “area justification factor” is

introduced. This area justification factor is defined as:

69

Area justification factor 6 0

Pattern size, in acres

All the cumulative CO2 injections are multiplied by this area justification factor for comparison amongst

different design combinations.

8.2.2.2 Design Procedure

The design of the regular 4-spot injection pattern with a horizontal injector follows the protocol

summarized below:

1. Generate 10,000 groups of design parameters and group them randomly. The design parameters

and corresponding ranges are shown in Table 8-2.

2. Generate 500 groups of reservoir parameters and group them randomly. The reservoir properties

and corresponding ranges for Illinois and Michigan Basin are shown in Table 8-1.

3. Starting with this step, the simulation run will focus on individual basins. Now, combine one of

the design parameter groups of those 10,000 cases with the 500 groups of reservoir parameters.

Then, 500 groups of datasets for the input layer of the EFSN will be generated.

4. Employ the expert network to run simulation for the 500 groups of input dataset generated from

step 3. Thus 500 groups of output will be generated, including cumulative CO2 injection,

cumulative brine production, and injection well block stabilized pressure.

5. Calculate the p90 cumulative CO2 injection, p90 cumulative brine production, p90 injection

efficiency and p50 pressure depletion ratio. Note: Steps 4 and 5 are aiming at test the injection

performance of one of the randomly generated combinations of the design parameters.

6. Restore the confidence interval data from Step 5 and go back to Step 3 until all of the 10,000

groups of combinations are studied.

The workflow of the design protocol is shown is Figure 8-2.

70

The design algorithm produces a one-to-one relationship between the design parameters and p90

corresponding confidence intervals, which can be displaced in an 8×10,000 matrix. Figure 8-3

conceptually shows the product of the design algorithm.

Figure 8-2: Workflow of the design protocol

71

The next step is to search the column of p50 PDR and select the rows with p50 PDR values close

enough to one. The design parameters groups in these selected rows are candidates of future designs. The

selected rows of Michigan and Illinois Basin are shown separately in appendix.

The optimal design should comprehensively consider the injection efficiency and the cumulative

CO2 injection. The next step is to select rows with the highest p90 cumulative CO2 injection and the

highest injection efficiency from the candidate rows. Define the highest p90 cumulative CO2 injection as

“gmax”, and the p90 injection efficiency of the row with highest p90 cumulative CO2 injection as “e”.

Define the highestp90 injection efficiency as “emax”, the p90 cumulative CO2 injection of the row with the

highest p90 injection efficiency as “g”. These definitions are illustrated in Figure 8-4.

Figure 8-3: Conceptual illustration of design protocol result

72

Define:

G gmax

g

g

E emax e

e

If G and E are identical, choose the corresponding design combination as the optimal design. If they are

not identical:

If G>E, choose the design group with the highest p90 cumulative CO2 injection as the optimal design.

If G<E, choose the design group with the highest p90 injection efficiency as the optimal design.

The application of G and E helps in consideration of the injection efficiency and cumulative CO2

injection in a comprehensive manner to determine the optimal design.

Figure 8-4: Illustration of the four key definitions

73

8.2.2.3 Design Results

For Michigan Basin:

Design group with highest p90 cumulative CO2 injection:

Q(MMSCFD) A(Acres) Lw(ft) Pwf p90

cumGas

p90

CumBrine p90 Pr p90 IE

P50

PDR

93.14 588.50 1118.34 0.54 11.174 86.121 2513.753 0.119 0.995

Design group with highest p90 injection efficiency:


cumGas

p90


P50

PDR

4.52 70.68 1196.02 0.57 10.456 8.734 2531.327 0.14028 0.99709

Here according to the definition, gmax=11.174 MM metric tons, g= 10.456 MM metric tons; emax=0.14028

metric tons/bbl, e= 0.119 metric tons/bbl.

G gmax

g

g

0. 56

E emax e

e 0. 028 0.

0.

Since E>G, the optimal design for Michigan basin is


cumGas

p90


P50

PDR

4.52 70.68 1196.02 0.57 10.456 8.734 2531.327 0.14028 0.99709

For Illinois basin:

Design group with highest p90 cumulative CO2 injection:


cumGas

p90


P50

PDR

156.470 397.877 808.783 0.679 25.011 104.526 2321.627 0.132 1.002

74

Design group with highest p90 injection efficiency:


cumGas

p90


P50

PDR

198.3172 497.0403 805.545 0.767543 24.15998 117.65742 2297.74090 0.13712 0.99864

Here according to the definition, gmax=25.011 MM metric tons, g= 24.16 MM metric tons;

emax=0.137metric tons/bbl, e= 0.132 metric tons/bbl.

Since E>G, the optimal design for Illinois basin is


cumGas

p90


P50

PDR

198.3172 497.0403 805.545 0.767543 24.15998 117.65742 2297.74090 0.13712 0.99864

Table 8-3 summarizes the optimal design in Michigan and Illinois basins.

Optimal

design Michigan Illinois units

Q 4.52 198.3172 MMSCFD

A 70.68 497.0403 acres

Lw 1196.02 805.545 ft

Pwf 0.57 0.767543 times of Pi

Table 8-3: Summary of optimal design of different geology cases

75

8.3 Basin Scale Simulation

In Chapter 8.2, the optimal design considering injection rate (Q), pattern size (A), horizontal well

length (Lw) and brine producer sand face pressure is determined. The objective of the study in this section

is to employ the EFSN as coupled to the optimal design results of Section 8.2 to generate the injection

potential maps of Illinois and Michigan Basin. The isopach and elevation map of these two geological

basins are available. Moreover, the geo-statistic formulation can be used to estimate the reservoir porosity

and permeability as a function of depth. If the isopach and elevation maps of these two basins can be

digitized in a matrix form, the value of porosity ( ), permeability (k), initial reservoir pressure (Pi), initial

reservoir temperature (Ti) and formation fracture pressure (Pfrac) of each block of the digitized map can be

calculated. Coupled with the optimal design determined from Section 8.2, input dataset for each grid

block on the digitized maps can be generated for ANN simulation runs. The ANN could output the

cumulative CO2 injection over 6 years, injection efficiency, and reservoir stabilized pressure surface at the

basin scale.

8.3.1 Geological Modeling

In order to digitize the contour maps, a toolkit is developed to transfer the contour maps to high

resolution matrix form for simulation study. The detail about the toolkit is shown in appendix. The

contour maps are digitized in 350× 350 meshed grid system.

For Michigan Basin, each block has the following dimensions:

Width (West-East direction)= 248/350=0.709 miles

Length (North-South direction)= 328 miles/350= 0.937 miles

Area covered by any block= 0.709×0.937 =0.664 squaremiles= 425.24 acres

Figure 8-5 (a) and (b) shows the original and digitized isopach maps of Michigan Basin.

76

Fig 8-5(b): Digitized isopach contour lines of Mt. Simon formation, Michigan Basin

Fig 8-5(a): Original isopach contour lines of Mt. Simon formation, Michigan Basin (Barnes, 2009)

77

The thickness values in between the contour lines are calculated thus the thickness distribution

map of Michigan Basin can be generated, as shown in Figure 8-6.

Similarly, the elevation map is also digitized using the same grid. Note in this study only the

depths within the injection limitation (2500~ 7500 feet) are digitized. Figure 8-7(a) and (b) shows the

original and digitized maps. Figure 8-8 shows the elevation map of Michigan Basin in 3-D view.

Fig 8-6: Thickness surface map of Mt. Simon formation, Michigan Basin

78

Fig 8-7(a): Original elevation contour lines of Mt. Simon, Michigan Basin (Barnes, 2009)

79

Fig 8-7(b): Digitized elevation contour lines of Mt. Simon, Michigan Basin

80

Fig 8-8: Elevation distribution of Mt.Simon in Michigan basin in 3-D view

81

For the Illinois Basin, each block has the following dimensions:

Width (West-East direction)= 297.5miles/350=0.85 miles;

Length (North-South direction)= 406 miles/350= 1.16 miles;

Area covered by any block= 1.16×0.85 =1.00 mile square=640 acres.

Figure 8-9 (a) and (b) show the original and digitized isopach maps of Mt. Simon formation in Illinois

Basin. Figure 8-10 shows the thickness surface map of Mt. Simon formation in Illinois Basin.

Fig 8-9(a): Original isopach contour lines of Mt. Simon formation, Illinois Basin (ISGS, 2006)

82

Fig 8-9(b): Digitized isopach contour lines of Mt. Simon formation, Illinois Basin

83

Fig 8-10: Thickness surface map of Mt. Simon formation, Illinois Basin

84

Figure 8-11 (a) and (b) show the original and digitized elevation maps of Mt. Simon formation in Illinois

Basin. Figure 8-12 shows the elevation distribution map of Mt. Simon in Illinois in 3-D view.

Fig 8-11(a): Original elevation map of Mt. Simon formation, Illinois Basin (ISGS, 2006)

85

Fig 8-11(b): Digitized elevation map of Mt. Simon formation, Illinois Basin

86

The reservoir porosity and permeability values can be estimated using the regression equations as

a function of depth as discussed in Chapter 2. The porosity and permeability regression equation were

given as (C. Medina et al. 2008):

6. 6 e 0.000 2d, R2 0.

k 0. 68 e0.5 5 , R2 0.6 57

Fig 8-12: Elevation distribution of Mt.Simon formtion in Illinois Basin in 3-D view

87

Figure 8-13 to Figure 8-16 show the reservoir porosity and permeability distribution of Mt. Simon in

Michigan and Illinois basin.

Fig 8-13: Permeability distribution map of Mt. Simon formation, Michigan Basin

Depth >7500 feet

88

Fig 8-14: Porosity distribution map of Mt. Simon formation, Michigan

Basin

Depth >7500 feet

89

Fig 8-15: Permeability distribution map of Mt.Simon formation, Illinois Basin

Depth >7500

feet

Depth < 2500 feet

90

8.3.2 Simulation Results

In this section, EFSN is employed to generate the cumulative CO2 injection potential maps and

stabilized reservoir pressure maps for Michigan and Illinois basins. IEPN and BHPN are employed to

generate the injection efficiency and injector bottomhole pressure surface maps at different times.

Figure 8-17 shows the cumulative CO2 injection at the end of injection period of Michigan Basin.

Fig 8-16: Porosity distribution map of Mt. Simon formation, Illinois Basin

Depth >7500 feet

Depth < 2500 feet

91

Fig 8-17: Cumulative CO2 injection distribution map in Michigan Basin

Depth >7500 feet

92

Figures 8-18 to 8-19 show the stabilized reservoir pressure and the PDR value distributions in

Michigan Basin.

Fig 8-18: Stabilized reservoir pressure distribution map in Michigan Basin

Depth >7500 feet

93

Fig 8-19: Pressure depletion ratio distribution map in Michigan Basin

Depth >7500 feet

94

Figure 8-20 (a) to (c) shows the injection efficiency distribution an estimated by the IEPN at the

end of the first, third and sixth years in Michigan Basin.

Fig 8-20(a): Injection efficiency distribution map in Michigan Basin at the end of 2012

Depth >7500 feet

95

Fig 8-20(b): Injection efficiency distribution map in Michigan Basin at the end of 2014

Depth >7500 feet

96

Figure 8-20(c): Injection efficiency distribution map in Michigan Basin at the end of 2017

Depth >7500 feet

97

Figures 8-21 (a) to (c) show the injection well bottomhole pressure distribution estimated by

BHPN at the end of the first, third and sixth years in Michigan Basin.

Fig 8-21(a): Injection well bottomhole pressure distribution map at the end of 2012

Depth >7500 feet

98

Fig 8-21(b): Injection well bottomhole pressure distribution map at the end of 2014

Depth >7500 feet

99

Fig 8-21(c): Injection well bottomhole pressure distribution map at the end of 2017

Depth >7500 feet

100

Figure 8-22 shows the cumulative CO2 injection distribution map at the end of the

injection period in Illinois Basin.

Fig 8-22: Cumulative CO2 injection distribution map in Illinois Basin

Depth >7500 feet

Depth < 2500 feet

101

Figures 8-23 to 8-24 show the stabilized reservoir pressure and the PDR value distributions in

Illinois Basin.

Fig 8-23: Stabilized reservoir pressure distribution map in Illinois Basin

Depth >7500 feet

Depth < 2500 feet

102

Fig 8-24: Pressure depletion ratio distribution map in Illinois Basin

Depth >7500 feet

Depth < 2500 feet

103

Figure 8-25 (a) to (c) show the injection efficiency distribution map of Illinois Basin at the end of

the first, third and sixth years.

Fig 8-25(a): Injection efficiency distribution map of Illinois Basin at the end of 2012

Depth >7500 feet

Depth < 2500 feet

104

Fig 8-25(b): Injection efficiency distribution map of Illinois Basin at the end of 2014

Depth >7500 feet

Depth < 2500 feet

105

Fig 8-25(c): Injection efficiency distribution map of Illinois Basin at the end of 2017

Depth >7500 feet

Depth < 2500 feet

106

Figure 8-26 (a) to (c) show the injection well bottom hole pressure distribution maps of Illinois

Basin at the end of the first, third and sixth years.

Fig 8-26(a): Injection well bottomhole pressure distribution map of Illinois Basin at the end of 2012

Depth >7500 feet

Depth < 2500 feet

107

Fig 8-26(b): Injection well bottomhole pressure distribution map of Illinois Basin at the end of 2014

Depth >7500 feet

Depth < 2500 feet

108

Fig 8-26(c): Injection well bottomhole pressure distribution map of Illinois Basin at the end of 2017

Depth >7500 feet

Depth < 2500 feet

109

Chapter 9 Summary and Conclusions

9.1 Summary of Findings

Mt. Simon sandstone formation in Michigan Basin and Illinois Basin are considered as two

potential geological structures in this study. The optimal design which involves injection rate (Q), pattern

area (A), horizontal well length (Lw) and brine producer bottom hole pressure (Pwf) is determined by

establishing one-to-one relationship between the design parameters and the project outputs. This goal is

achieved by applying the EFSN and Monte Carlo simulation protocol in a coupled manner. The design

parameter groups have to yield p50 pressure depletion ratio close to one in order to be selected as optimal

design candidates. Once the optimal design parameter group is determined, it helps the expert network to

run basin scale simulation. Thus cumulative CO2 injection distribution maps, injection efficiency

distribution maps and pressure distribution maps could be generated by different expert network.

One may compare the cumulative CO2 injection distribution map of Illinois Basin and Michigan

Basin. Figure 8-22 shows that the highest cumulative CO2 injection point in Illinois Basin map yields

value equals to 34.2 MM metric tons over 6 years. That value is equaled to about 6.5 MM metric tons in

Michigan Basin. The pressure depletion ratios at the highest cumulative CO2 injection points are slight by

less than one at both Michigan and Illinois Basin. This observation could also prove that taking p50 PDR

equal to one is an effective design criterion. The highest cumulative CO2 injection of Illinois Basin is

much higher than that of Michigan Basin. The disparities in performance indicators are caused by

different geology characteristics of the two basins, as shown is Table 8-1, which is duplicated here for

easy reference.

110

Table 8-1 Summary of reservoir properties ranges

Michigan Basin Illinois Basin

Properties Units min max min max

fraction 6.5 20 6.5 20

k md 4.8 100 4.8 100

thickness feet 100 1300 500 2250

depth feet 3500 7500 2500 7500

Pi psi 1610 3450 1127.5 3382.5

Ti °F 98.5 142.5 85 135

Pfrac psi 2800 6000 1877.5 5632.5

Illinois basin essentially has greater formation thickness within the injection depth constraint.

More importantly, the thicker formation appears either in shallow depth or deep depth, as displaced in

Figure 2-5. The pressure tolerance at shallow formation is low, which restricts the bottomhole injection

pressure. The reservoir permeability and porosity values are low in deep formations. Those two factors

limit the injectivity at the thickest section of the Mt. Simon formation in Michigan basin.

111

9.2 Conclusion

This study in a comprehensive manner applies Monte Carlo simulation protocol and artificial

neural network to design a regular 4-spot injection pattern with horizontal injector for an optimal CO2

injection process. Monte Carlo simulation and artificial neural network are two complementary tools to

each other. The Monte Carlo simulation protocol helps in reducing the risk that can arise from the error

margins of the data generated by ANN. On the other hand, ANN helps to generate a large amount of

Monte Carlo simulation data within very short period of time. Three expert networks systems, including

Figure 2-5: Mt. Simon Formation isopach map and elevation map at Michigan basin (Barnes, 2009)

D=7000 ~7500

feet

D<3500 feet

112

end-point forward-looking solution network (EFSN), injection efficiency profile network (IEPN) and

injection well bottomhole pressure profile network (BHPN), are developed to ease the extremely

computational time required in high-fidelity simulation studies. All of these three networks are validated

through repeated training experiments. The tests errors are within reasonable margins. An important

observation is that even though the injection well bottomhole pressure profile network yields small tests

error, it performs rather poorly at the discontinuity points of the pressure profile (when the boundary

condition switch takes place).

The concept of “injection sweet spot” is introduced. Injection sweet spot could be found through

the following steps:

1. Pick the blocks with PDR values close to one on the PDR distribution maps.

2. Select the blocks yielding the highest cumulative CO2 injection from blocks picked in Step 1

as the injection sweet spots.

The star in Figure 9-1 (a) shows the injection sweet spot of Michigan Basin. Coupled with the territory

map of Michigan Basin, the injection sweet spot is located at Eaton and Calhoun County. Figure 9-2 (a)

to (b) shows the injection sweet spot of Illinois Basin. The injection sweet spot located at De Witt and

Macon County.

113

Fig 9-1(a): Injection sweet spot shown in cumulative CO2 injection distribution map of Michigan Basin

114

Fig 9-1 (b): Injection sweet spot shown in Michigan state territory map(www.digital-topo-maps.com/county-

map/)

115

Fig 9-2(a): Injection sweet spot shown in cumulative CO2 injection distribution map of Illinois Basin

116

Fig 9-1 (b): Injection sweet spot shown in Illinois state territory map (www.digital-topo-maps.com/county-

map/)

117

References:

Battelle Laboratory, “CO2 Injection Test in the Cambrian-Age Mt. Simon Formation Duke Energy East

Bend Generating Station, Boone County, Kentucky”, 20 .

Battelle Laboratory, “Michigan Basin phase II geologic CO2 sequestration field test”, Report prepared for

the U.S. Department of Energy, National Energy Technology Laboratory, 2011

Beeland Group, LLC “UIC permit application, Class non-hazardous injection well”, 200 .

A.T. Corey, C.H. Rathjens, J.H. Henderson, and M.R.J. Wyllie, “Three-Phase Relative Permeability”,

Journal of Petroleum Technology, Vol. 8 (11), 1956

C. Medina et al, “A regional characterization and assessment of geologic carbon sequestration

opportunities in the upper Cambrian mount Simon sandstone in the Midwest region”, MRCSP

Phase II Topical Report, 2010.

C. Medina et al, “Depth Relationships in Porosity and Permeability in the Mount Simon Sandstone (Basal

Sand) of the Midwest Region: Applications for Carbon Sequestration”, Indiana Geology Survey,

2009.

David A. Barnes et al, “Geological sequestration of carbon dioxide in the Cambrian Mount Simon

Sandstone: Regional storage capacity, site characterization, and large-scale injection feasibility,

Michigan Basin”, Environmental Geosciences, v. 6, no. (September 200 ), pp. 6 –183.

Deepanshu Kumar, “Optimization of well settings to maximize residually trapped CO2 in Geologic

Carbon Sequestration”, report submitted to the department of energy resources engineering of

Stanford university; in partial fulfillment of the requirements for the degree of master of science,

2007

Flowserve®, “Pumps for CO2 Capture, Transportation and Storage”.

Global CSS institute “CO2 capture technologies”, 20 2.

H. Leetaru and J. McBride, “Reservoir uncertainty, Precambrian topography, and carbon sequestration in

the Mt. Simon Sandstone, Illinois Basin”, Environmental Geosciences, Vol. 6, No. (December

2009), pp. 235–243.

Howard Herzog et al, “Advanced Post-Combustion CO2 Capture”, Report prepared for Clean Air Task

Force, 2009.

M. Dorofki, “Comparison of Artificial Neural Network Transfer Functions Abilities to Simulate Extreme

Runoff Data”, IPCBEE, vol.33, 2012

National Water Summary, “Illinois ground water quanlity”, 86.

N. Metropolis, “The beginning of the Monte Carlo method”, Los Alamos Science Special Issue 1987.

Peter H. Kobos et al, “Storing Carbon Dioxide in Saline Formations: Analyzing Extracted Water

Treatment and Use for Power Plant Cooling”, Sandia National Laboratories, 2010.

118

Quanlin Zhou et al, “On scale and magnitude of pressure buildup induced by large-scale geological

storage of CO2”, Earth Sciences Division, Lawrence Berkeley national laboratory, 20 0.

R. Lahann et al, “A regional lithostratigraphic model of the Eau Claire formation (Cambrian): How much

shale is in the confining unit?” AAPG, 2012.

Randall l. Milstein et al, “Subsurface stratigraphy of Cambrian rocks in the southern peninsula of

Michigan: Michigan basin”, 8 .

Robert J. Finley, “Demonstrating Geological Carbon Sequestration in the Mt. Simon Sandstone of the

Illinois Basin”, Illinois State Geological Survey, 2008.

R. Rojas, Neural Networks, 1996.

Schlumberger Carbon Services, “Summary Results for: Carbon Storage Feasibility Study Taylorville

Energy Center (TEC)”, 20 0

Sinisha A. Jikich et al, “Carbon dioxide injectivity in brine reservoirs using horizontal wells”, NETL,

2006.

Scott M. Frailey et al, “Reservoir characterization of the Mt. Simon Sandstone, Illinois Basin, USA”,

Energy Procedia, Vol.4 (2011), pp. 5487–5494.

Tracy L. Vaught, “An assessment of the geothermal resources of Illinois based on existing geologic data”,

DOE/NV, Dec. 1980.

The Midwest Regional Carbon Sequestration Partnership (MRCSP), “Phase I Final Report”, Report

prepared for the U.S. Department of Energy, National Energy Technology Laboratory, 2005.

The Midwest Regional Carbon Sequestration Partnership (MRCSP), “Phase II Final Report”, Report

prepared for the U.S. Department of Energy, National Energy Technology Laboratory, 2011.

119

Appendix

A-1 Tabulated Data of the Design Protocol

Table A-1 shows the results generated by the design protocol discussed in Chapter 8.2.3 for

Michigan Basin

Table A-1

NO. Q(MMSCFD) A(Acres) Lw(ft) Pwf P90

CumGas

P90

CumBrine P90 Pr P90 IE

P50

PDR

1 70.06 519.7 1231.96 0.66 10.32 66.47 2551.41 0.127 1

2 61.68 636.28 1067.65 0.87 7.83 57.4 2557.59 0.14 1.002

3 50 462.58 1157.77 0.79 8.66 49.9 2554.11 0.129 0.996

4 30.18 267.06 1342.97 0.62 9.17 34.84 2563.14 0.113 1.004

5 42.32 388.49 1346.65 0.76 8.71 43.35 2583.04 0.126 0.997

6 4.52 70.68 1196.02 0.57 10.46 8.73 2531.33 0.14 0.997

7 11.84 130.51 919.51 0.91 7.61 12.95 2672.35 0.127 1.001

8 50.72 507.02 1163.64 0.84 8.09 50.02 2579.7 0.133 0.995

9 39.78 415.45 826.17 0.88 7.64 40.39 2583.74 0.129 1.002

10 49 514.09 1306.25 0.86 7.7 48.3 2589.13 0.134 0.997

11 94.09 602.87 863.86 0.57 11.09 85.32 2540.44 0.123 0.999

12 36.49 296.83 840.74 0.66 9.62 39.21 2571.76 0.116 1.004

13 50.63 439.19 1178.25 0.77 9.19 49.82 2584.68 0.129 1.003

14 85.45 562.65 918.13 0.59 11.03 78.86 2550.09 0.124 1.002

15 43.42 336.05 994.92 0.59 10.07 46.99 2547.53 0.113 1.002

16 66.65 545.61 1187.87 0.75 9.68 62.81 2565.81 0.134 1.003

17 47.87 552.74 840.44 0.91 6.93 46.55 2572.91 0.134 1.002

18 47.55 465.2 1305.04 0.82 8.25 47.57 2574.17 0.13 0.997

19 81.52 620.31 986.57 0.73 10.12 73.33 2561.46 0.136 1.002

20 45.06 504 889.43 0.89 7.17 44.79 2557.01 0.132 0.996

21 33.37 409.37 1072.74 0.94 6.62 34.22 2607.15 0.132 1.003

22 87.66 606.86 1132.59 0.65 10.71 78.95 2539.13 0.131 1

23 27.25 319.77 993.35 0.92 6.91 28.71 2619.77 0.128 0.999

24 66.42 485.75 1012.41 0.63 10.38 64.6 2542.47 0.123 0.995

25 52.81 381.15 941.22 0.55 10.4 56.15 2531.87 0.111 0.999

26 43.35 442.22 888.98 0.85 7.84 43.85 2580.85 0.13 0.996

27 84.42 533.57 833.15 0.53 11.06 80.15 2546.72 0.116 1.001

28 71.56 476.25 1056.67 0.52 10.82 72.04 2519.64 0.112 0.998

120

Table A-1 (Continued)

29 79.97 560.34 1381.71 0.64 10.55 73.79 2534.76 0.126 1.003

30 53.43 506.24 1315.85 0.8 8.46 52.5 2561.3 0.132 0.996

31 34.2 303.04 1277.63 0.68 9.09 37.23 2572.03 0.118 0.998

32 44.19 537.8 1105.41 0.93 6.68 43.64 2589.54 0.136 1.003

33 69.32 633.1 821.81 0.81 8.59 63.35 2537.35 0.136 1.002

34 14.32 145.01 813.79 0.76 8.39 16.8 2626.82 0.119 0.999

35 93.14 588.5 1118.34 0.54 11.17 86.12 2513.75 0.119 0.995

36 70.86 552.65 946.95 0.71 9.96 66.3 2554.71 0.131 0.995

37 71.91 541.54 1333.66 0.69 10.17 67.11 2547.78 0.129 1.002

38 57.66 579.92 1160.22 0.86 8.04 54.75 2582.57 0.138 1.003

39 60.44 473.45 995.02 0.71 9.95 58.16 2574.83 0.129 1.003

40 45.42 630.74 1177.48 0.95 5.85 44.51 2593.51 0.137 1.002

41 81.63 576.89 1088.61 0.66 10.62 74.79 2543.64 0.13 0.998

42 78.66 594.94 1005.47 0.72 10.2 71.52 2564.48 0.135 1.003

43 30.68 384.94 1202.68 0.94 6.51 31.84 2604.1 0.13 0.997

44 57.5 592.3 805.39 0.86 7.68 54.36 2530.43 0.135 0.998

45 76.85 615.16 1037.06 0.76 9.8 69.62 2553.02 0.137 1.003

46 80.12 552.25 1170.57 0.62 10.73 74.53 2531.12 0.126 1.001

47 62.09 434.46 922.9 0.58 10.62 62.29 2553.29 0.117 0.998

48 45.98 403.47 852.26 0.76 9 46.6 2567.51 0.125 0.997

49 40.37 507.22 1358.96 0.94 6.47 40.42 2598.02 0.135 1.003

50 56.54 398.25 905.85 0.54 10.53 59.2 2531.6 0.111 1.002

51 95.07 627.93 1322.23 0.61 10.93 84.37 2506.26 0.127 1

52 65.81 599.57 1320.89 0.82 8.78 60.84 2576.74 0.138 1.005

53 58.3 507.62 1332.25 0.77 9.15 56.11 2575.33 0.132 1.003

54 12.83 148.07 1145.86 0.88 7.29 14.12 2646.63 0.126 0.996

55 42.89 452.76 1121.78 0.88 7.7 42.71 2609.54 0.134 1.005

56 52.82 620.32 880.87 0.91 6.83 50.36 2570.94 0.137 1.002

57 27.53 240.47 1139.08 0.52 9.31 35.11 2532.12 0.103 0.998

58 33.73 403.55 1197.22 0.92 6.82 34.7 2605.5 0.131 0.998

59 23.83 227.5 897.32 0.78 8.47 26.18 2621.5 0.12 1.003

60 44.31 425.14 1113.38 0.81 8.42 44.95 2570.98 0.128 0.999

121

Table A-2 shows the results generated by the design protocol discussed in Chapter 8.2.3 for

Michigan Basin

Table A-2

NO. Q(MMSCFD) A(Acres) Lw(ft) Pwf P90

CumGas

P90

CumBrine P90 Pr P90 IE

P50

PDR

1 163.69 504.13 1305.76 0.85 20.82 106.63 2307.88 0.131 0.996

2 92.45 291.4 931.2 0.79 21.88 69.01 2275.26 0.125 0.998

3 176.62 502.26 983.08 0.88 21.84 108.29 2309.37 0.135 1.004

4 161.68 472.9 1125.25 0.81 21.55 104.97 2292.2 0.129 0.997

5 191.02 484.75 876.76 0.77 23.67 114.53 2303.34 0.135 1.001

6 38.53 182.24 1348.4 0.89 17.87 37.71 2260.64 0.123 1.004

7 147.27 477.28 1299.07 0.93 20.63 98.05 2311.25 0.136 1.005

8 196.44 619.8 1284.08 0.91 19.84 123.54 2283.3 0.135 0.999

9 123.31 358.69 987.78 0.71 22.45 89.53 2304.86 0.125 1.001

10 199.17 515.91 1050.3 0.77 22.65 117.8 2301.15 0.132 1.001

11 154.19 439.82 1357.76 0.64 21.92 109.76 2320.7 0.122 1.002

12 197.96 630.98 1227 0.94 19.69 123.87 2293.82 0.137 1.002

13 91.73 294.78 1040.58 0.68 21.52 72.71 2283.71 0.119 0.998

14 189.71 508.06 1190.33 0.73 22.23 118.22 2296.82 0.129 0.999

15 129.14 385.12 1166.77 0.7 21.68 94.25 2306.84 0.123 0.996

16 108.9 356.52 1330.05 0.52 21.39 93.15 2265.02 0.108 0.999

17 137.46 393.33 1102.15 0.64 22.44 101.02 2324.96 0.121 1.003

18 17.47 104.86 1037.72 0.78 13.3 19.78 2200.58 0.102 1.001

19 76.86 267.14 1173.97 0.78 20.47 61.77 2287.03 0.122 1

20 138.93 456.68 1182.45 0.92 20.56 94.42 2287.33 0.133 0.998

21 174.47 478.21 1349.85 0.61 22.25 121.48 2324.98 0.12 1.002

22 162.63 460.21 1335.85 0.63 22.01 115.56 2323.5 0.12 0.995

23 149.71 425.1 1155.38 0.54 22.67 113.2 2301.3 0.115 1.003

24 169.48 495.7 1348.69 0.81 21.32 107.59 2307.23 0.131 1.004

25 159.27 444.52 1134.79 0.53 22.93 119.6 2305.94 0.115 1.003

26 139.3 445.69 1050.24 0.92 20.98 93.6 2295.48 0.133 0.998

27 105.34 324.83 971.49 0.62 22.31 82.93 2276.73 0.118 0.998

28 182.05 506.38 1272.28 0.52 22.24 136.08 2288.7 0.113 0.998

29 176.29 469.49 1138.51 0.68 22.5 114.15 2311.85 0.126 0.996

30 195.03 528.46 1172.68 0.79 21.73 116.7 2296.79 0.131 1.004

122


31 69.38 265.36 960.2 0.96 19.53 55.84 2276.89 0.128 0.998

32 163.56 473.79 1293.39 0.51 22.18 127.73 2284.73 0.111 0.996

33 37.4 177.43 1114.15 0.9 16.8 35.76 2230.49 0.119 0.998

34 178.41 535.06 964.14 0.92 21.06 111.17 2285.79 0.136 1.002

35 100.12 306.13 832.73 0.55 23.24 80.1 2242.24 0.117 1.003

36 119.45 391.31 1382.14 0.86 20.83 85.81 2321.73 0.131 1

37 181.67 471.45 982.43 0.61 23.86 122.02 2329.22 0.125 0.998

38 53.42 233.75 1369.71 0.93 18.7 48.46 2266.58 0.129 0.996

39 187.57 471.79 868.65 0.76 23.85 113.75 2305.14 0.135 1.002

40 147.16 419.63 1119.32 0.61 22.51 107.96 2312.59 0.12 0.997

41 72.68 247.81 1067.04 0.72 20.79 59.4 2293.63 0.119 1.004

42 55.57 233.02 1236.16 0.59 18.91 55.99 2160.71 0.105 0.996

43 179.59 496.92 854.99 0.86 22.63 110.03 2297.65 0.135 0.999

44 143.67 447.7 993.51 0.91 21.32 95.37 2293.52 0.133 0.996

45 169.93 505.92 1146.74 0.88 21.15 106.46 2307.31 0.132 1.003

46 33.16 168.09 1277.19 0.85 16.61 33.92 2220.35 0.118 0.997

47 121.73 372.53 1095.28 0.56 22.15 97.03 2244.36 0.114 0.997

48 153.56 428.96 1077.45 0.76 22.32 101.8 2291.98 0.129 1.003

49 173.41 486.5 1328.93 0.69 21.81 115.72 2298.47 0.125 0.998

50 62.36 253.78 1105.51 0.51 19.45 64.53 2132.02 0.1 0.995

51 180.8747 451.1356 820.065 0.698471 24.83647 114.0646 2285.337 0.133747 0.998

52 198.3172 497.0403 805.545 0.767543 24.15998 117.6574 2297.741 0.137117 0.999

53 36.3815 167.5816 1057.848 0.735638 16.99113 36.25107 2204.574 0.109606 0.999

54 111.5979 350.7368 1229.834 0.817517 21.16397 81.12429 2321.166 0.128315 1.005

55 129.7024 387.4055 1143.857 0.765355 21.65624 91.30274 2281.742 0.126424 1

56 176.661 570.0291 1090.102 0.954405 20.04807 114.019 2295.023 0.136144 1

57 141.8686 461.5929 1199.197 0.912612 20.66843 95.56919 2290.888 0.132821 1

58 177.3387 477.8707 1172.363 0.563776 22.85177 125.7278 2316.517 0.118238 1.002

59 119.7479 344.0498 860.6187 0.700108 23.32579 87.47702 2293.957 0.125761 1

60 184.2237 542.963 1203.666 0.879351 20.98617 112.884 2305.746 0.133219 1.005

61 84.10645 268.7618 842.6261 0.787183 21.88612 64.77861 2268.155 0.124577 0.997

123


62 156.4701 397.8774 808.7832 0.67929 25.01101 104.5259 2321.627 0.131777 1.002

63 198.9648 526.6755 1062.711 0.797268 22.14233 117.6585 2305.093 0.132548 1.003

64 142.5419 420.9663 1043.73 0.790112 21.80154 97.13029 2274.102 0.12819 0.996

65 188.7682 496.2352 953.6689 0.806101 22.87956 112.7106 2312.018 0.133954 1.003

66 49.0108 186.6626 825.4122 0.715669 19.19693 43.09058 2227.067 0.113742 1.002

67 184.9054 501.6547 1230.831 0.704246 22.15867 118.6553 2290.675 0.12647 0.998

68 165.456 448.8975 1106.92 0.572908 23.10468 119.2878 2318.502 0.119317 0.999

69 65.90142 259.2792 1316.208 0.879913 19.6357 56.17065 2301.956 0.126171 0.995

70 91.77921 319.49 1059.713 0.953521 20.41289 68.33305 2301.821 0.131574 1.001

71 172.8028 530.1028 1354.918 0.863625 20.70107 110.4471 2308.996 0.13302 1.001

72 105.426 312.4622 831.9038 0.793458 22.86847 75.28595 2285.995 0.128775 1.002

73 114.7311 361.385 1293.616 0.704964 21.07443 86.8688 2299.926 0.122067 1

74 136.6586 431.5132 939.5286 0.943416 21.44235 91.516 2299.232 0.13472 1.001

75 149.575 431.9606 1058.236 0.825952 21.90395 97.97889 2313.247 0.130607 1.004

76 114.6989 358.1283 1150.637 0.644699 21.5339 90.21331 2281.123 0.117951 0.997

77 60.23112 213.0643 805.7526 0.865675 20.34929 48.64289 2297.101 0.123598 0.999

78 168.0702 518.5169 1243.378 0.878137 20.70959 107.2896 2298.557 0.131754 0.998

79 117.4799 347.2073 901.8728 0.633813 23.01425 89.81389 2284.944 0.121281 0.996

80 81.08933 276.0441 1154.048 0.615058 20.98601 68.24908 2272.68 0.114002 1.001

81 177.4992 517.8033 1025.192 0.883886 21.25558 109.5952 2297.662 0.134183 1

82 77.93119 276.3882 1237.939 0.817211 20.31399 62.63626 2305.559 0.124374 1.002

83 122.409 382.8464 878.0584 0.930269 21.75573 85.3671 2302.889 0.133597 1.001

84 198.7599 554.1229 996.0577 0.844886 21.52443 118.295 2294.266 0.133552 0.997

85 106.668 326.5754 946.3311 0.637256 22.44913 83.19529 2273.17 0.119305 0.998

86 197.4834 597.3595 1268.761 0.897628 20.35232 121.0326 2293.069 0.134539 1.003

87 50.92464 192.6677 874.4525 0.691762 19.35743 44.7381 2232.985 0.113014 1.004

88 130.3806 396.9091 1258.2 0.58821 21.72382 103.0873 2282.789 0.115285 1

89 44.24154 183.3682 802.1077 0.885298 17.83043 38.76993 2234.603 0.118963 0.998

90 159.0672 442.9039 1124.479 0.571763 22.82244 117.221 2303.567 0.118089 0.999

91 183.9812 458.8962 869.8997 0.763002 23.9197 111.581 2314.413 0.135123 1.005

124


92 123.4426 368.0247 952.858 0.519508 23.1871 98.30227 2261.584 0.11412 0.996

93 141.1302 483.5325 1386.346 0.940169 20.08967 97.57482 2291.725 0.135898 0.999

94 129.7414 426.7086 1088.847 0.930771 20.76948 89.15205 2292.858 0.133146 1

95 140.1957 448.985 1170.1 0.900972 20.90477 94.43479 2297.541 0.131775 1

96 130.204 371.2408 841.3707 0.558162 24.15773 99.24189 2266.623 0.120741 0.996

97 97.30326 322.8208 1271.838 0.604359 20.88987 81.3746 2270.492 0.113852 0.996

98 98.7246 346.3352 1345.154 0.908455 20.4603 73.98204 2313.369 0.13211 1

99 183.6201 477.7358 1148.209 0.675161 22.63733 116.7476 2322.7 0.126647 1.001

100 180.582 496.9803 1123.685 0.794337 21.94736 111.3959 2291.409 0.130619 1.003

101 107.8982 343.1884 847.7129 0.929051 21.91492 77.14527 2299.934 0.13238 0.999

102 173.5507 502.521 1064.077 0.862182 21.47726 107.9761 2302.984 0.132698 1

103 139.1495 429.9157 1009.502 0.885067 21.33561 93.26747 2296.37 0.131622 0.996

104 159.4273 456.8546 1333.992 0.610438 21.94178 116.1211 2315.159 0.11893 0.996

105 190.1837 516.9228 1329.807 0.68241 21.97085 122.6091 2299.635 0.125272 0.998

106 63.5302 227.5691 967.0076 0.849546 20.18765 51.70774 2312.132 0.122798 1.003

107 171.0892 462.6318 1055.557 0.51159 23.58947 125.6895 2306.404 0.116131 1.004

108 144.3835 379.772 825.2543 0.711827 24.42132 96.95131 2308.741 0.131031 0.996

109 172.081 491.7393 948.788 0.889638 21.96462 106.3087 2306.113 0.134983 1.004

110 172.4685 466.3796 1101.665 0.543124 23.23767 125.0459 2307.928 0.117546 1.003

111 173.2711 494.9714 834.6425 0.908333 22.30073 107.962 2292.33 0.136853 1.001

112 87.01383 317.9074 1277.416 0.942005 20.22299 67.05836 2304.319 0.132281 1

113 92.4778 299.9348 1073.341 0.856032 21.31323 68.7446 2333.575 0.127391 1.003

114 167.9279 449.8037 1199.839 0.668935 22.48166 111.692 2327.894 0.125302 1.004

115 179.0554 500.1451 1349.443 0.532596 22.12551 132.8423 2295.093 0.113862 1.001

116 182.7734 465.8163 909.0804 0.596098 24.52358 123.2181 2331.604 0.125438 1.003

117 59.37173 242.1095 1169.048 0.936068 18.89564 50.64287 2274.773 0.126979 0.999

118 183.8829 518.5584 1243.414 0.801365 21.44325 113.0615 2294.592 0.130699 1.002

119 157.447 483.5686 1144.284 0.884085 20.9984 101.7966 2300.976 0.132048 0.999

120 183.3604 500.0928 1170.673 0.719934 22.13754 117.1405 2283.787 0.127507 0.997

121 149.1116 461.2492 1106.149 0.911649 21.1185 97.53404 2308.395 0.133387 1.004

122 181.8495 621.2121 1250.067 0.957336 18.98516 118.8053 2289.31 0.136415 0.995

125


123 86.61825 286.5443 1033.861 0.60919 21.2859 71.80782 2264.437 0.113883 0.995

124 43.57692 201.5694 1157.164 0.930435 17.36421 40.54861 2249.932 0.123178 0.995

125 108.4575 334.833 1092.414 0.590935 22.17323 85.9974 2283.602 0.115491 1.005

126 170.28 485.7837 1311.843 0.73992 21.58897 111.225 2287.8 0.127167 1

127 183.3674 492.1286 981.1927 0.786782 22.62987 112.1585 2286.221 0.132162 0.995

128 87.25881 299.8922 1289.783 0.833828 20.57573 68.38704 2323.879 0.126868 1.004

129 62.62393 261.106 1298.773 0.50331 19.42308 67.05947 2148.067 0.099737 0.997

130 199.3852 555.5206 1238.046 0.800312 21.39417 120.2813 2284.866 0.131203 0.998

131 159.5653 407.4969 852.2521 0.684417 24.53097 105.9966 2326.659 0.131079 1.003

132 181.3132 491.0974 1235.743 0.681608 22.14044 118.5924 2303.882 0.125056 0.997

133 171.5129 550.7888 1339.128 0.921495 20.25553 110.8604 2300.867 0.135458 1.001

134 53.92856 222.5523 1363.36 0.759184 19.16186 50.39655 2256.593 0.118638 0.998

135 140.4016 388.784 955.8266 0.766083 23.01905 94.24453 2300.434 0.129757 1.005

136 195.129 524.3947 1148.879 0.792241 21.88839 116.4911 2301.205 0.1314 1.005

137 189.5261 614.8401 1151.2 0.94366 19.60183 121.2068 2285.254 0.135686 0.997

138 135.412 415.3718 1139.951 0.846635 21.37034 92.15207 2319.629 0.129853 0.999

139 106.8555 331.1279 937.1642 0.869122 21.85571 76.20498 2330.218 0.129597 1.004

140 11.48949 77.71218 962.3811 0.806026 11.25549 13.32475 2224.767 0.097533 0.998

141 116.0999 368.1415 1315.879 0.696537 21.01244 88.7152 2289.752 0.121367 0.997

142 126.1078 372.079 984.8963 0.543903 23.12173 98.37583 2270.512 0.115252 1.001

143 128.8761 440.7592 1258.023 0.931063 20.30828 89.83986 2288.323 0.133901 0.996

144 172.7237 523.4827 1237.815 0.88189 20.83904 108.3841 2300.904 0.132445 1.003

145 120.8036 423.8699 1332.055 0.93055 20.27486 86.75358 2287.607 0.133718 0.996

146 66.92334 248.08 1270.344 0.680161 19.95903 59.35755 2263.537 0.115534 1.003

147 52.18713 219.8684 1297.062 0.85507 18.82786 47.42212 2281.455 0.122143 1

148 172.3233 449.4937 932.2917 0.581076 24.32727 120.5589 2320.444 0.123321 1.001

149 67.67591 233.7568 807.2722 0.909724 20.86854 52.98046 2307.223 0.126337 1.002

150 72.32603 282.6887 1343.996 0.512809 20.09059 72.42967 2188.307 0.102854 0.997

151 129.4699 369.911 1004.838 0.607128 23.023 96.71048 2319.015 0.120404 1.003

152 60.05218 234.6372 969.3167 0.521837 19.8403 58.63516 2162.961 0.103358 1.004

153 76.33524 265.9702 1155.925 0.774911 20.43946 61.72022 2283.354 0.12158 0.998

154 118.8299 356.4561 996.3541 0.825648 21.97872 83.54079 2315.463 0.129032 1.005

155 147.2785 446.9615 1139.842 0.838992 21.19898 98.2554 2307.393 0.130097 0.997

126

A.2 Development of a Toolkit for Map Digitizing

In typical reservoir engineering studies, contour maps, including isopach maps and elevation maps,

are significant references for reservoir characteristic descriptions. Contour maps are drawnthrough actual

data from investigation wells. There exist matured geo-statistic techniques to generate vector field from

available data resources (such as Kriging’s Interpolation). This forward drawing procedure could be done

by several softwares (SURFUR, MATLAB®, PETRAL

®, etc.). However, for reservoir simulation studies,

one may need information from contour maps to import elevation, thickness, permeability and porosity

distribution of the formation to a simulation model. This is a backward procedure to extract information

from maps. It is possible to read the contour values block by block, but such procedure would consume a

lot of labor and time. Even worse, the values between contour values would be eyeballing, which can

decrease the accuracy of the data compiled. The objective of the devvelopment discussed here is to

develop a toolkit to digitize the contour maps. With the assist of the toolkit, one could generate digitized

contour maps with any gridding dimension accurately and quickly. The toolkit is developed through the

following steps:

Step1. Define Boundary and Contour Lines

Before drawing any contour maps, one need to define the boundary of the formation and contour lines

with values. In a meshed cartesian coordinate system, the best way is to find the coordinate of the points

that lie on the target contour lines and boundary. If enough point coordinate information is available, one

could draw the contour lines and the boundary on the meshed system.

Step 2. Calculation of Values from Contour Lines

The theory of calculating the values out of the contour line is to generate data fields based on information

from the contour lines. Define the points on the contour lines as ‘valid point’, define the points located out

127

of the contour line as unknown points’. For any unknown points, search along the north (N), south (S),

west (W), east (E), north east (NE), south east (SE), north west (NW) and south west (SW) until reaching

any valid data points. Record the contour value from a certain direction as Z and direction from the

unknown point and the valid point as d. Thus the value of the unknown point could be calculated by the

following equation:

If search procedure touches the boundary, set the contour value and the reciprocal of the distance as zero.

Equation 1.1 helps to generate the contour value of all points within the formation boundary.

Figure A-1: Searching directions

128

A.3 Program Codes of Digitizing the Map Boundary

%Read the file saving the coordinators of the discrete points

load Boundary.txt

num=length(Boundary(:,1));

Bi=350-Boundary(:,2);

Bj=Boundary(:,1);

indexB=zeros(350,350);

for i= 1:350

for j=1:350

indexB(i,j)=-999;

end

end

%The following loop introduce a term “index”. Set the index of points on the %map boundary as -1

for i=1:350

for j=1:350

for k=1:num

j1=abs(Bi(k)-i);

j2=abs(Bj(k)-j);

if j1==0 && j2==0

indexB(Bi(k),Bj(k))=-1;

else

end

end

end

end

% Connecting the discrete points on a meshed grid system

for k=1: num

k

if k~=num

BiN=Bi(k+1);

BjN=Bj(k+1);

else

BiN=Bi(1);

BjN=Bj(1);

end

di=BiN-Bi(k);

dj=BjN-Bj(k);

%% the next point is at the north of the prevoius point

if di<0&&dj==0

129

%% avoid the nearby points

if abs(di)~=1

for s=1:abs(di)

indexB(BiN+s,Bj(k))=-1;

end

else

end

%% the next point is at the Sorth of the prevoius point

elseif di>0&&dj==0


if abs(di)~=1

for s=1:abs(di)

indexB(Bi(k)+s,Bj(k))=-1;

end

else

end

%% the next point is at the West of the prevoius point

elseif di==0&&dj<0


if abs(di)~=1

for s=1:abs(dj)

indexB(Bi(k),Bj(k)-s)=-1;

end

else

end

%% the next point is at the East of the prevoius point

elseif di==0&&dj>0


if abs(di)~=1

for s=1:abs(dj)

indexB(Bi(k),Bj(k)+s)=-1;

end

else

end

%% the next point is at the north east of the prevoius point

elseif di<0&& dj >0

if abs(di)~=1 || abs(dj)~=1

cx=Bi(k);cy=Bj(k);

while BiN~=cx||BjN~= cy

dN=(BiN-cx+1)^2+(BjN-cy)^2;

dE=(BiN-cx)^2+(BjN-cy-1)^2;

if dN<dE

cx=cx-1;

else

cy=cy+1;

130

end

indexB(cx,cy)=-1;

end

end

%% the next point is at the north west of the prevoius point

elseif di<0&& dj<0


cx=Bi(k);cy=Bj(k);



dW=(BiN-cx)^2+(BjN-cy+1)^2;

if dN<dW

cx=cx-1;

else

cy=cy-1;

end

indexB(cx,cy)=-1;

end

end

%% the next point is at the South West of the prevoius point

elseif di>0&& dj<0


cx=Bi(k);cy=Bj(k);


dS=(BiN-cx-1)^2+(BjN-cy)^2;


if dS<dW

cx=cx+1;

else

cy=cy-1;

end

indexB(cx,cy)=-1;

end

end

%% the next point is at the South East of the prevoius point

elseif di>0&& dj>0


131

cx=Bi(k);cy=Bj(k);




if dS<dE

cx=cx+1;

else

cy=cy+1;

end

indexB(cx,cy)=-1;

end

end

end

end

disp('******Boundary Defined!!!!!!**********')

for i= 2:350

for j=2 :350

if indexB(i,j)~= -1

%% Search North

kN=1;

while (i-kN)>1||(i-kN)==1

if indexB(i-kN,j)==-1

MarkN=1;

break;

else

MarkN=0;

end

kN=kN+1;

end

%% Search South

kS=1;

while (i+kS)<350||(i+kS==350)

if indexB(i+kS,j)==-1

MarkS=1;

break;

else

MarkS=0;

end

kS=kS+1;

end

%% Search West

kW=1;

while (j-kW)>1||(j-kW)==1

132

if indexB(i,j-kW)==-1

MarkW=1;

break;

else

MarkW=0;

end

kW=kW+1;

end

%% Search East

kE=1;

while (j+kE)<350||(j+kE)==350

if indexB(i,j+kE)==-1

MarkE=1;

break;

else

MarkE=0;

end

kE=kE+1;

end

if MarkW==1&&MarkE==1&&MarkN==1&&MarkS==1

indexB(i,j)=0;

else

end

Str=sprintf('Block (%d, %d) is done.', i, j);

disp(Str);

else

end

end

end

tol=1e6;

while tol>10

tol

for i= 2:350

for j=2:350

if indexB(i,j)==0

if indexB(i-1,j)==-999 ||indexB(i+1,j)==-999 ||indexB(i,j-1)==-999||indexB(i,j+1)==-999||...

indexB(i-1,j-1)==-999||indexB(i+1,j+1)==-999||indexB(i+1,j-1)==-999||indexB(i-1,j+1)==-

999

indexB(i,j)=-999;

else

end

133

diff(i,j)=abs(indexB(i,j)-indexB(i-1,j))+abs(indexB(i,j)-indexB(i+1,j))+abs(indexB(i,j)-indexB(i,j-

1))+abs(indexB(i,j)-indexB(i,j+1))...

+abs(indexB(i,j)-indexB(i-1,j-1))+abs(indexB(i,j)-indexB(i+1,j+1))+abs(indexB(i,j)-indexB(i+1,j-

1))+abs(indexB(i,j)-indexB(i-1,j+1));

else

diff(i,j)=0;

end

end

end

tol=max(max(diff));

end

save Boundary_Michigan.txt indexB -ASCII

A.4 Program Codes of Digitizing the Contour Lines

function [ Oi,Oj ] = OpenPoly(isize, jsize,Bi,Bj,Index )

%% A function used to draw continuous contour lines

% 'Index' in input args is an identification for different

% Contour Values.

num=length(Bi);

indexB=zeros(isize,jsize);

for i=1:isize

for j=1:jsize

for k=1:num

indexB(Bi(k),Bj(k))=Index;

end

end

end

for k=1: num

k

if k~=num;

BiN=Bi(k+1);

BjN=Bj(k+1);

di=BiN-Bi(k);

dj=BjN-Bj(k);

%% the next point is at the north of the prevoius point

if di<0&&dj==0


if abs(di)~=1

for s=1:abs(di)

indexB(BiN+s,Bj(k))=Index;

end

else

end

134

%% the next point is at the Sorth of the prevoius point

elseif di>0&&dj==0


if abs(di)~=1

for s=1:abs(di)

indexB(Bi(k)+s,Bj(k))=Index;

end

else

end

%% the next point is at the West of the prevoius point

elseif di==0&&dj<0

%% Avoid the nearby points

if abs(di)~=1

for s=1:abs(dj)

indexB(Bi(k),Bj(k)-s)=Index;

end

else

end

%% the next point is at the East of the prevoius point

elseif di==0&&dj>0


if abs(di)~=1

for s=1:abs(dj)

indexB(Bi(k),Bj(k)+s)=Index;

end

else

end

%% the next point is at the north east of the prevoius point

elseif di<0&& dj >0

cx=Bi(k);cy=Bj(k);




if dN<dE

cx=cx-1;

else

cy=cy+1;

end

indexB(cx,cy)=Index;

end

%% the next point is at the north west of the prevoius point

elseif di<0&& dj<0

135

cx=Bi(k);cy=Bj(k);




if dN<dW

cx=cx-1;

else

cy=cy-1;

end


end

%% the next point is at the South West of the prevoius point

elseif di>0&& dj<0

cx=Bi(k);cy=Bj(k);




if dS<dW

cx=cx+1;

else

cy=cy-1;

end


end

%% the next point is at the South East of the prevoius point

elseif di>0&& dj>0

cx=Bi(k);cy=Bj(k);




if dS<dE

cx=cx+1;

else

136

cy=cy+1;

end


end

end

end

end

k=1;

for i=1:isize

for j=1:jsize

if indexB(i,j)==Index

Oi(k)=i;

Oj(k)=j;

k=k+1;

else

end

end

end

disp('******Contour Line is Drawn!!!**********')

end

A.5 Program Codes of the Drawing Surface Map

%This code is used to generate the elevation distribution map

%The following loop is used to define the contour value on the contour

%lines

for i=1: 350

for j=1 :350

if index(i,j)==75;

CoutourValue(i,j)=7500;

elseif (index(i,j)==70);

CoutourValue(i,j)= 7000;

elseif index(i,j)==65;








137







else

CoutourValue(i,j)=0;

end

end

end

% The following applies the protocol described in Section A.2 to draw the

% map

for i=1: 350

for j=1 :350

%%Search inside the boundary

if index(i,j)==0

%==Search the North

if index(i-1,j)~=-1

k=1;

while index(i-k,j)==0

k=k+1;

end

if index(i-k,j)>0

ZN(i,j)=CoutourValue(i-k,j);

DN(i,j)=1/(dy*k);

else

end

else

ZN(i,j)=0;

DN(i,j)=0;

end

%==Search the South

if index(i+1,j)~=-1

k=1;

while index(i+k,j)==0

k=k+1;

end

if index(i+k,j)>0

ZS(i,j)=CoutourValue(i+k,j);

DS(i,j)=1/(dy*k);

else

138

end

else

ZS(i,j)=0;

DS(i,j)=0;

end

%==Search the East

if index(i,j+1)~=-1

k=1;

while index(i,j+k)==0

k=k+1;

end

if index(i,j+k)>0

ZE(i,j)=CoutourValue(i,j+k);

DE(i,j)=1/(dx*k);

else

end

else

ZE(i,j)=0;

DE(i,j)=0;

end

%==Search the West

if index(i,j-1)~=-1

k=1;

while index(i,j-k)==0

k=k+1;

end

if index(i,j-k)>0

ZW(i,j)=CoutourValue(i,j-k);

DW(i,j)=1/(dx*k);

else

end

else

ZW(i,j)=0;

DW(i,j)=0;

end

%==Search the NorthEast

if index(i-1,j+1)~=-1

k=1;

while index(i-k,j+k)==0

k=k+1;

end

if index(i-k,j+k)>0

ZNE(i,j)=CoutourValue(i-k,j+k);

DNE(i,j)= 1/(k*((dx^2+dy^2)^0.5));

else

end

else

ZNE(i,j)=0;

DNE(i,j)= 0;

139

end

%==Search the NorthWest

if index(i-1,j-1)~=-1

k=1;

while index(i-k,j-k)==0

k=k+1;

end

if index(i-k,j-k)>0

ZNW(i,j)=CoutourValue(i-k,j-k);

DNW(i,j)= 1/(k*((dx^2+dy^2)^0.5));

else

end

else

ZNW(i,j)=0;DNW(i,j)=0;

end

%==Search the SouthEast

if index(i+1,j+1)~=-1

k=1;

while index(i+k,j+k)==0

k=k+1;

end

if index(i+k,j+k)>0

ZSE(i,j)=CoutourValue(i+k,j+k);

DSE(i,j)=1/(k*((dx^2+dy^2)^0.5));

else

end

else

ZSE(i,j)=0; DSE(i,j)=0;

end

%==Search the SouthWest

if index(i+1,j-1)~=-1

k=1;

while index(i+k,j-k)==0

k=k+1;

end

if index(i+k,j-k)>0

ZSW(i,j)=CoutourValue(i+k,j-k);

DSW(i,j)= 1/(k*((dx^2+dy^2)^0.5));

else

end

else

ZSW(i,j)=0;DSW(i,j)=0;

end

else

140

end

%%end of the search

end

end

for i=1: 350

for j=1 :350

if index(i,j)==0

% implementation of protocol discussed in Section A.2

Z(i,j)=-

((ZN(i,j)*DN(i,j)+ZE(i,j)*DE(i,j)+ZS(i,j)*DS(i,j)+ZW(i,j)*DW(i,j)+ZNE(i,j)*DNE(i,j)+ZNW(i,j)*DNW

(i,j)+ZSE(i,j)*DSE(i,j)+ZSW(i,j)*...

DSW(i,j))/(DN(i,j)+DS(i,j)+DW(i,j)...

+DE(i,j)+DNE(i,j)+DNW(i,j)+DSE(i,j)+DSW(i,j)));

elseif index(i,j)>0

Z(i,j)=-CoutourValue(i,j);

elseif index(i,j)<0

Z(i,j)=NaN;

end

end

end

A.6 Program Codes of Implementation of EFSN

%Read the original input and output for ANN train

load Tn.txt;

load Pn.txt;

Tn=Tn';

Pn=Pn';

%Find the max and minimum values of each columne for the use of rverse

maxT=max(Tn');

minT=min(Tn');

maxP=max(Pn');

minP=min(Pn');

%Normalize all the input and ouput within -1,1

[Pn,ps] = mapminmax(Pn,-1,1);

[Tn,ts] = mapminmax(Tn,-1,1);

[mi,ni] = size(Pn);

[mo,no] = size(Tn);

%Define key parameters of training

N_in = mi;

N_out = mo;

Tot_in = ni;

%Randomly divide the datasets into train, validation and test sets.

[Pn_train,Pn_val,Pn_test,trainInd,valInd,testInd] = dividerand(Pn,0.94,0.03,0.03);

[Tn_train,Tn_val,Tn_test] = divideind(Tn,trainInd,valInd,testInd);

val.T = Tn_val;

val.P = Pn_val;

141

test.T = Tn_test;

test.P = Pn_test;

%Define the hidden layers and hidden neurons.

NNeu1 = 20;

NNeu2 = 20;

NNeu3 = 20;

% Creating the cascade backpropagation network

net = newcf(Pn,Tn,[NNeu1,NNeu2,NNeu3,mo]...

,{'tansig','tansig','tansig','purelin'},'trainscg','learngdm','msereg');

%Setting training parameters for the network

%Stop the traininng when the error of weights is less than 0.0005 or when training iteration repeats for

10,000 times

net.trainParam.goal = 0.0005;

net.trainParam.epochs = 10000;

net.trainParam.show = 1;

net.trainParam.max_fail = 100000;

%Reduce memory requirements

net.trainParam.mem_reduc = 60;

[net,tr] = train(net,Pn_train,Tn_train,[],[],test,val);

plotperf(tr)

Tn_train_ann = sim(net,Pn_train);

Tn_test_ann = sim(net,Pn_test);

%denormalizing the data sets obtained

%output reversal

T_train = mapminmax('reverse',Tn_train,ts);

T_test = mapminmax('reverse',Tn_test,ts);

T_train_ann = mapminmax('reverse',Tn_train_ann,ts);

T_test_ann = mapminmax('reverse',Tn_test_ann,ts);

%input reversal

Pn_train = mapminmax('reverse',Pn_train,ps);

Pn_val = mapminmax('reverse',Pn_val,ps);

Pn_test = mapminmax('reverse',Pn_test,ps);

%Calculate the brine production, cumulative gas production and stabilized well block pressure predicted

from ANN

ANNbrine=exp(T_test_ann(1,:));

ANNGas=exp(T_test_ann(2,:));

ANNPressure=10.^(T_test_ann(3,:));

CMGbrine=exp(T_test(1,:));

CMGGas=exp(T_test(2,:));

CMGPressure=10.^(T_test(3,:));

%Calculate the errors of target parameters

error_a = abs((exp(T_test(1,:))-exp(T_test_ann(1,:)))./exp(T_test(1,:)))*100;

error_mean_a = mean(error_a);

error_b = abs((exp(T_test(2,:))-exp(T_test_ann(2,:)))./exp(T_test(2,:)))*100;

error_mean_b = mean(error_b);

error_c1 = 10.^(T_test(3,:));

error_c2 = 10.^(T_test_ann(3,:));

error_c=abs(error_c1-error_c2)./error_c1;

error_mean_c = mean(error_c);

%Read the reservoir properties arrays, 500 elements each

%Read the design parameter combinations, 10,000 combinations in total

142

load Design.txt;

load Case_1.txt;

nx=length(Design');

ny=length(Case_1');

for j=1:nx

for i=1: ny

% Calculate the brine production well bottomhole pressure, in log10 scale;

Pwf1(1,i)=log10(Design(4,j)*(10^Case_1(4,i)));

% Generate input arrays of EFSN;

Case1_In(1,i)=Case_1(1,i);




Case1_In(5,i)=Design(1,j);



Case1_In(8,i)=Pwf1(1,i);

% Normalize the input data within -1, -1;

for k=1 :8

Case1_In0(k,i)=Qian(Case1_In(k,i),maxP(k),minP(k));

end

end

%Call the EFSN for runs

%Output data

Case_1_output=net(Case1_In0);

Case_1_output= mapminmax('reverse',Case_1_output,ts);

Case_1_brine=exp(Case_1_output(1,:));

Case_1_gas=exp(Case_1_output(2,:));

Case_1_Pressure=10.^(Case_1_output(3,:));

Case_1_Ratio=Case_1_Pressure./(10.^Case_1(4,:));

Case_1_IE=Case_1_gas./Case_1_brine;

% Calculate p90 values for cumulative gas injection and p50 values for

% Injection efficiency

P90gas1=quantile(Case_1_gas,0.9);

P90brine1=quantile(Case_1_brine,0.9);

P90Pressure1=quantile(Case_1_Pressure,0.9);

P90Ratio1=quantile(Case_1_Ratio,0.9);

P90IE1=quantile(Case_1_IE,0.9);

%Collect the data

Data_collection1_90(j,1)=10^Design(1,j);



Data_collection1_90(j,4)=Design(4,j);

Data_collection1_90(j,5)=P90gas1;

Data_collection1_90(j,6)=P90brine1;

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Data_collection1_90(j,7)=P90Pressure1;

Data_collection1_90(j,8)=P90Ratio1;

Data_collection1_90(j,9)=P90IE1;

j

end

save Data_collection1_90.txt Data_collection1_90 -ASCII

A.7 Program Codes of the Searching Protocol

% Read the data generated from ANN

load Data_collection1_90.txt;

Brine=Data_collection1_90(:,6);

GasM=Data_collection1_90(:,5);

Pwb=Data_collection1_90(:,7);

IE=Data_collection1_90(:,9);

Ratio=Data_collection1_90(:,8);

Q=Data_collection1_90(:,1);

A=Data_collection1_90(:,2);

Lwf=Data_collection1_90(:,3);

Pwf=Data_collection1_90(:,4);

num=length(Data_collection1_90);

J=zeros(num,1);

%The following loop is used to search the p50 pressure depletion ratio(PDR) column to select the rows

%with PDR values closed enough to one.

for i=1:num;

if abs(Ratio(i)-1)<=0.001;

kc=kc+1;J(i)=1;

else

J(i)=2;

end

design=zeros(kc,9);LineC=zeros(kc,1);k_=1;

end

for i= 1:num;

if J(i)==1;

LineC(k_)=i; k_=k_+1;

else

end

end

%The following loop is used to find the design parameter combinations and outputs.

for i= 1:kc;

%Calculate the cumulative CO2 injection by muliply the CO2 amount by the area justification factor

design(i,1)=Q(LineC(i))/(640/A(LineC(i)));

design(i,2)=A(LineC(i));

design(i,3)=Lwf(LineC(i));

design(i,4)=Pwf(LineC(i));

design(i,5)=(640/design(i,2))*GasM(LineC(i));

design(i,6)=(640/design(i,2))*Brine(LineC(i));

144

design(i,7)=Pwb(LineC(i));

design(i,8)=IE(LineC(i));

design(i,9)=Ratio(LineC(i));

end

optimalIE=max(design(:,8));

for j=1 :kc;

if abs(design(j,8)-optimalIE)<=1e-20

opt_p=j;

else

end

end

engineering design considerations to maximize carbon

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