induced fractures and hydraulic fractures study
TRANSCRIPT
Induced Fractures Modelling in
Reservoir Dynamic Simulators
Khaldoon AlObaidi Institute of Petroleum Engineering
MSc Petroleum Engineering
Project Report 2013/2014
Supervisor β Heriot Watt University
This study was completed as part of the Masters of Science in Petroleum Engineering at the Heriot Watt University.
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| Declaration
Declaration
I, Khaldoon AlObaidi, confirm that this work submitted for assessment is my own and is
expressed in my own words. Any uses made within it of the works of other authors in any form
(e.g. ideas, equations, figures, text, tables, programs) are properly acknowledged at the point of
their use. A list of the references employed is included.
Signedβ¦β¦β¦β¦K.A.β¦β¦β¦β¦β¦β¦..
Date 27 August 2014
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| Dedication
Dedication
To my family for their support.
To my uncle for his continuous encouragement.
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| Acknowledgements
Acknowledgments
Thanks also go to NSI Technologies Inc. for providing me with StimPlan software and licenses
which helped me establishing the basis of this work.
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| Abstract
Abstract
Since the middle of the twentieth century, hydraulic fractures and fractures created due to
injection under fracturing conditions have been proven to be effective in increasing the
productivity and injectivity factors of wells considerably. In this work, an algorithms for
determining the optimum hydraulic fracture dimensions, the growth of induced fractures
created due to injection under fracturing conditions and modelling fractures in dynamic
reservoir simulators are introduced. Additionally, the optimum dimensionless conductivity is
derived to be 1.6363 and is used in addition to practical limitations and economic considerations
to determine the optimum hydraulic fracture dimensions result in maximum folds of increase
in production. Also in this work, an algorithm adopting Perkins-Kern-Nordgren-Ξ± (PKN-Ξ±) and
Ahmed and Economides notation after Simonson analysis is adopted to determine the
dimensions of the induced fractures created due to injection under fracturing conditions. The
induced fractures are implemented in reservoir dynamic simulators using gridblocks refinement
and properties multiplications to increase net to gross, porosity and permeability to mimic the
fracture properties. For two simple box models, only approximately 42% increase in run time
due to implementing this algorithm in reservoir dynamic simulator is resulted. Therefore, the
algorithm presented provides a good approximation for modelling induced fractures growth
with reduced simulation run time and storage capacity compared to three-dimensional fracture
models. Also, it provides more accurate results compared to the simple two-dimensional models
that assumes fixed fracture height. The advantage of the algorithms presented is they combine
the fracturing physics with the reservoir dynamic simulator constraints. Therefore,
implementing this work provides robust reserves estimation and forecasts for wells with
induced fractures warning of fractures propagation into unintended with relatively fast running
simulation models.
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| Abstract
Table of Contents
Declaration ................................................................................................................................ ii
Dedication .................................................................................................................................iii
Acknowledgments .................................................................................................................... iv
Abstract ..................................................................................................................................... v
Table of Contents ..................................................................................................................... vi
List of Figures ........................................................................................................................viii
List of Tables ............................................................................................................................ ix
Nomenclature ............................................................................................................................ x
1 Project Scope and Objectives .......................................................................................... 1
1.1 Induced Fractures ....................................................................................................... 1
1.1.1 Fracture Orientation ................................................................................................ 3
1.1.2 Leak-off Test .......................................................................................................... 4
1.1.3 Hydraulic Fracturing Procedure ............................................................................. 6
1.1.4 Analytical and Numerical Models for Estimating Fracture Dimensions,
Propagation and Recession ................................................................................................. 7
1.1.4.1 PKN-Ξ± Model ................................................................................................. 8
1.1.4.2 Fracture Height Growth .................................................................................. 9
1.2 Dynamic Simulation of Hydraulic Fractures ............................................................ 10
1.3 Objectives ................................................................................................................. 11
2 Methodology .................................................................................................................... 12
2.1 Determining the Optimum Hydraulic Fracture Dimensions for a Well ................... 12
2.1.1 Cases Input for Testing the Procedure Used to Determine the Optimum Hydraulic
Fracture Dimensions for a Well........................................................................................ 19
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| Table of Contents
2.1.1.1 Low Permeability Reservoir Case ................................................................ 20
2.1.1.2 High Permeability Reservoir Case ............................................................... 20
2.2 Incorporating Hydraulic Fractures in Reservoir Dynamic Simulators ..................... 21
2.3 An Algorithm for Modelling Induced Fractures Created During Injection under
Fracturing Conditions in Reservoir Dynamic Simulators .................................................... 24
2.3.1 Fracture Height Growth ........................................................................................ 24
2.3.2 Fracture Width and Half-Length .......................................................................... 27
3 Results and Discussion ................................................................................................... 33
3.1 Determining the Optimum Hydraulic Fracture Dimensions for a Well ................... 33
3.1.1 Low Permeability and High Permeability Case Results ....................................... 33
3.1.1.1 Low Permeability Reservoir Case ................................................................ 34
3.1.1.2 High Permeability Reservoir Case ............................................................... 36
3.2 Incorporating Hydraulic Fractures in Reservoir Dynamic Simulators ..................... 38
3.3 Algorithm for Modelling Induced Fractures Created During Injection under
Fracturing Conditions in Reservoir Dynamic Simulators .................................................... 40
4 Conclusions and Recommendations.............................................................................. 42
References ................................................................................................................................ 43
Appendices ................................................................................................................................ I
A.1 Fracture Height Equations ...........................................................................................I
A.2 Meeting Agendas and Progress Reports ................................................................... III
A.2.1. Period 1 ............................................................................................................. III
A.2.1. Period 2 ........................................................................................................... XII
A.2.1. Period 3 .......................................................................................................... XIX
A.2.1. Period 4 ......................................................................................................XXVII
A.2.1. Period 5 .................................................................................................... XXXIV
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| List of Figures
List of Figures
Figure 1. Principal stresses (Anon. g 2014) ................................................................................ 3
Figure 2. Extended leak-off results (Crain 2013) ....................................................................... 5
Figure 3. Fracture geometry (a) PKN type (b) KGD type (c) Pseudo 3D cell approach (d) Global
3D, parameterised (e) Full 3D, meshed (Yang 2011) ................................................................. 8
Figure 4. Warpinski and Smith analysis and notation (Valko and Economides 1995) ............ 10
Figure 5. Cinco-Ley and Samaniego graph for Hydraulic Fracture Performance with f = sf + ln
(xf/rw) (Valko 2005) ................................................................................................................ 13
Figure 6. Pratβs dimensionless effective wellbore radius (Valko 2005) ................................... 17
Figure 7. Low permeability case model ................................................................................... 22
Figure 8. Hydraulic fracture for low permeability case ............................................................ 22
Figure 9. High permeability case model ................................................................................... 23
Figure 10. Hydraulic fracture for high permeability case ........................................................ 23
Figure 11. Ahmed and Economides notation for fracture height (Valko and Economides 1995)
.................................................................................................................................................. 24
Figure 12. Algorithm for estimating fracture dimensions created due to injection under
fracturing conditions ................................................................................................................. 32
Figure 13. Folds of increase and fracture volume vs. folds of increase for low permeability case
.................................................................................................................................................. 35
Figure 14. Folds of increase and fracture volume vs. folds of increase for high permeability case
.................................................................................................................................................. 37
Figure 15. Increase in cumulative oil production for low permeability case ........................... 38
Figure 16. Increase in cumulative oil production for high permeability case .......................... 38
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| List of Tables
List of Tables
Table 1: Low permeability case input ...................................................................................... 20
Table 2: High permeability case input ...................................................................................... 20
Table 3: Model dimensions summary ...................................................................................... 21
Table 4: Low permeability case results .................................................................................... 34
Table 5: High permeability case results ................................................................................... 36
Table 6: Run time and storage capacity requirement for base cases and cases with induced
fracture modelling ..................................................................................................................... 40
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| Nomenclature
Nomenclature
A = the fracture surface area at any instant during injection, ft2
Ae = the fracture surface area at the end of pumping, ft2
Bo= the oil formation volume factor, rb/STB
CL = leak-off coefficient ft/s0.5
Eβ = strain modulus, psi
Fcd = the fracture dimensionless conductivity, dimensionless
FOI = folds of increase, dimensionless
h = the flow unit height, ft
hd = the lower height growth, ft
hds = the dimensionless thickness, dimensionless
hf = fracture height, ft
hp = the perforation interval length, ft
hs = the thickness of a symmetry element, ft
hu = the upper height growth, ft
i = half injection rate, ft3/s
k = permeability, mD
k00 = the pressure at the middle of the crack, psi
k1 = the slope of net pressure, psi
K(C,2) = fracture toughness in the upper layer, psi.ft0.5
K(C,3) = fracture toughness in the lower layer, psi.ft0.5
kf = the fracture permeability, mD
kh = the horizontal permeability, mD
kv = the vertical permeability, mD
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| Nomenclature
Nprop = the dimensionless proppant number, dimensionless
pbhpf = the bottom-hole flowing pressure, psi
pcp = the pressure at mid perforation, psi
pn,w = the net wellbore pressure, psi
re = the drainage radius, ft
rw = the wellbore radius, ft
rwβ is the effective wellbore radius, ft
Sf = the skin factor due to fracture, dimensionless
Sp = spurt loss coefficient, ft
t = time, second
vf = the total fracture volume of both wings, ft3
vL = leak-off velocity, ft/s
w = average fracture width, ft
wf = fracture width, ft
ww,0 = the maximum fracture width at the wellbore, ft
xf = fracture half-length, ft
Ξ± = the exponent of fracture length growth (constant), dimensionless
Β΅ = the viscosity, cP
Ο = density, lb/ft3
Ο1 = the minimum horizontal stress in the targeted layer, psi
Ο2 = the minimum horizontal stress in the upper layer, psi
Ο3 = the minimum horizontal stress in the lower layer, psi
Οmin = the minimum horizontal stress, psi
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| Chapter 1 β Project Scope and Objectives
1 Project Scope and Objectives
1.1 Induced Fractures
Induced fracturing is a stimulation method used to accelerate the production and increase the
ultimate recovery of hydrocarbon reservoirs by fracturing the reservoir rock (Anon. a 2013).
Fracturing the rocks creates high conductivity channels growing into the reservoir away from
the wellbore, providing communication between the two (Anon. b 2013). These fractures are
called induced fractures since they are introduced to the reservoir and are not formed due to
natural causes (e.g. tectonic activities).
Since the 1940s, induced fracturing has proven to be an effective method for developing low
permeability reservoirs and increasing the commercial viability of the development of
conventional reservoirs (Taleghani et al. 2013). Also, induced fractures have made it possible
to produce hydrocarbon from shale formations (tight reservoirs) where conventional
technologies are ineffective (Anon. c 2014). Progress in hydraulic fracturing technologies has
resulted in a huge increase in the oil and gas reserves worldwide by making the development
of unconventional reservoirs feasible (Anon. d 2014).
There are three types of induced fractures: hydraulic fractures; fractures created by fluid
(usually water and/or polymer) injection under fracturing conditions; and thermal fracturing
(Taleghani et al. 2013). Hydraulic fractures are created by injecting specially engineered fluid
under high pressure for a short period of time to break the rocks. The created fractures are kept
open after treatment using proppant (a material similar to sand grains) of a particular size, which
is mixed with the treatment fluid (Anon. e 2014).
Another type of induced fracture is created by the continuous injection of fluid under high
pressure into the reservoir (greater than the fracture initiation pressure to create the fracture,
greater than the closure pressure to keep the fracture open and greater than the fracture
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| Chapter 1 β Project Scope and Objectives
propagation pressure to extend the fracture). These fractures are closed once the fluid injection
stops or the injection pressure becomes less than the fracture closure pressure (Moreno et al.
2005). The final type of induced fracture is thermal fracturing. Thermal fractures are created
due to the difference between the temperature of the reservoir rock and that of the injected fluid,
with the latter being colder (Anon. f 2013). Only the first two types of induced fractures will be
considered in this work.
Fracture dimensions are considered the most important factor in induced fracturing for three
main reasons: the incremental increase of production/injection rates is directly dependent on
the fracture dimensions; the cost of creating the fracture is directly proportional to the fracture
volume; and there is the possibility of induced fractures growing into unintended zones like
fresh water zones.
The environmental impacts associated with hydraulic fracturing are the main reason for it being
a controversial topic among the public (Shukman 2013). Therefore, it is necessary to simulate
the induced fracture propagation, dimensions and recession before the actual operations take
place (Xiang 2011). Extensive work has been done to simulate the fracture propagation and
dimensions. There are multiple analytical and numerical models available in the literature for
estimating fracture dimensions, propagation and recession with different geometries. They
include two-dimensional, three-dimensional and pseudo three-dimensional models (Yang
2011).
The advantage of simulating fracture dimensions and propagation using the algorithms and
methods introduced in this work is that they incorporate the actual reservoir dynamic simulator
constraints and pressure data for the whole life of the field. Also, they take into account the
practical limitations to estimate the optimum fracture dimensions, resulting in the maximum
possible increase in production or injection rates for the wells. Therefore, this results in robust
production and injection forecasts for reservoirs with induced fractured wells, and thus more
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| Chapter 1 β Project Scope and Objectives
representative economics for field development. Estimating the optimum hydraulic fracture
dimensions, modelling hydraulic fracture dimensions, induced fracture propagation in reservoir
dynamic simulators, and estimating the height growth of induced fractures are all covered in
this work. Over the past 70 years, extensive work has been done on induced fracturing. This
work is documented and can be found in the literature. The following sections discuss topics
related to induced fracturing available in the literature.
1.1.1 Fracture Orientation
Based on rock mechanics, there are three principal stresses acting on underground formations.
These are the overburden stress, the maximum horizontal stress, and the minimum horizontal
stress, as shown in Figure 1.
Figure 1. Principal stresses (Anon. g 2014)
These stresses are usually anisotropic in that they differ in magnitude based on direction (Anon.
a 2013). Fractures propagate in a direction which is perpendicular to the least stress (i.e. opening
in the direction of the least resistance) (Anon. h 2010). The overburden stress acting on a
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| Chapter 1 β Project Scope and Objectives
formation is due to the weight of the rocks above that formation, which depends on the
formation depth (Golf-Racht 1980).
Based on practical experience, for formations deeper than 2000 ft, the overburden stress is the
largest principal stress, followed by the maximum horizontal stress; minimum horizontal stress
is the smallest principal stress and the fractures are more likely to be vertical (Anon. h 2010).
For formations shallower than 2000 ft, the maximum horizontal stress is the largest stress,
followed by the minimum horizontal stress, and the overburden stress is the smallest principal
stress (Anon. h 2010). Therefore, for such formations, the fractures will be horizontal, opening
in the vertical direction with an environmental risk, since it may propagate to the surface.
It can be concluded that the magnitude and direction of the principal stresses play a major role
in determining the required pressure for fracture creation and propagation (Hudson 2005). The
interaction between the fluid pressure in the fracture and the principal stresses defines the shape,
the vertical extent and the propagation direction of the fracture (Dubey et al. 2012).
1.1.2 Leak-off Test
This is a test performed to measure the formation fracturing pressure usually carried
immediately after drilling below a new casing shoe. The test is performed by shutting-in the
well and pumping fluid, usually mud, into the wellbore to gradually increase the pressure
experienced by the formation. At some pressure, the fluid enters the formation (or leaks-off) by
fracturing the rock (Anon. e 2014).
If the test is stopped just after the leak-off happens then it is called a leak-off test (LOT). If the
test is extended longer until several iterations of pumping and discontinuing pumping have been
performed then it is called an extended leak-off test (XLOT). From the XLOT, more important
parameters can be estimated and used in the propagation and recession models. Figure 2 depicts
XLOT results.
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| Chapter 1 β Project Scope and Objectives
Figure 2. Extended leak-off results (Crain 2013)
From XLOT results, vital parameters for simulating the fracture propagation, opening and
closure are estimated. These include the fracture initiation pressure, fracture propagation
pressure, fracture reopening pressure and fracture closure pressure (which is synonymous with
minimum in-situ stress and minimum horizontal stress) (Anon. a 2013). These data will be used
as an input to modelling induced fractures created due to injection under fracturing conditions
using the PKN-Ξ± method.
Time
ΞP friction
Bottomhole Pressure
Injection Rate
1
3
5
2
3
6 4
1. Hydrostatic pressure
2. Breakdown pressure
3. Fracture extension pressure
4. Initial shut-in pressure (fracture gradient)
5. Fracture closure pressure (closure stress gradient)
6. Fracture reopening Pressure
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| Chapter 1 β Project Scope and Objectives
1.1.3 Hydraulic Fracturing Procedure
The process of hydraulic fracturing consists of injecting specially engineered fluid at high
pressure to break the formations and create high permeability channels extending away from
the wellbore into the formation and establishing communication between the two. To keep the
fracture open, proppant with specific grain diameter is used.
The stages of hydraulic fracturing, as covered in the literature (Anon. h 2010), include:
i. Spearhead stage or acid stage which consists of water mixed with acid. The purpose
of this stage is to remove the debris and clean the wellbore. This will provide a clean
wellbore and an open path for the fluid to be injected in subsequent stages.
ii. Pad stage which consists of slick water that is used to initiate the hydraulic fracture
in the formation. If the pressure stopped during this stage, the fractures would close
since no proppant material has yet been used.
iii. Proppant stage which consists of injecting water and proppant material into the
fractured formation to keep the fractures open. Proppant is a non-compressible
material, like sand grains, that is carried into the fractured formation to be left there
after the job has been completed. Once the pressure drops, the proppant will prevent
the fractures from closing, thus maintaining the enhanced permeability channels,
created in the pad stage, throughout the wellβs life.
iv. Flush stage which consists of fresh water being pumped into the wellbore to flush out
and remove the excess proppant from the wellbore.
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| Chapter 1 β Project Scope and Objectives
1.1.4 Analytical and Numerical Models for Estimating Fracture Dimensions, Propagation and
Recession
There are multiple analytical and numerical models in the literature for estimating fracture
dimensions, propagation and recession. These include two-dimensional, three-dimensional and
pseudo three-dimensional models (Yang 2011). Geometries of these models are shown in
Figure 3. The fracture geometry in reality is more complicated than the simple geometries
described in these models and is governed by many parameters related to rock mechanics, in-
situ stresses and the fluids used (Warpinski 1989). However, these models are commonly used
in industry and are widely accepted as providing an acceptable approximation for the estimation
of fracture dimensions.
The two famous 2D analytical models - PKN, developed by Perkins, Kern and Nordgren in
1961, and KGD, developed by Khristianovitch, Zheltov, Geertsma and de Klerk in 1955 - are
widely used and often referred to in the oil and gas industry (Yang 2011). The PKN model
assumes an elliptical cross-section fracture shape; fracture height is constant and fracture length
is significantly greater than fracture height. The KGD model assumes a rectangular cross-
section fracture shape, constant fracture height and fracture height significantly greater than
fracture length (Valko and Economides 1995). The plane strain direction assumption differs
between the two; a vertical direction for PKN and a horizontal direction for KGD (Xiang 2011).
Based on these assumptions, the KGD model could be used to estimate fracture dimensions and
shape for small fracture treatments and/or when fracture height is uncontrolled and significantly
greater than fracture length. PKN-type fractures are more interesting from a production point
of view since reservoir layers are usually contained by shale layers. Therefore, it represents a
case of an elongated fracture whose length is significantly greater than its height (Valko and
Economides 1995).
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| Chapter 1 β Project Scope and Objectives
Figure 3. Fracture geometry (a) PKN type (b) KGD type (c) Pseudo 3D cell approach (d)
Global 3D, parameterised (e) Full 3D, meshed (Yang 2011)
1.1.4.1 PKN-Ξ± Model
As mentioned in Section 1.1.4, the PKN model assumes the fracture has constant height and
that fracture length is significantly greater than fracture height. The PKN geometry depicted in
Figure 3(a), which shows an approximately elliptical shape in the vertical and the horizontal
directions, is more interesting from the production point of view. The PKN-Ξ± model assumes
the power law surface growth and Carter I leak-off to perform the material balance at any time
during injection.
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| Chapter 1 β Project Scope and Objectives
The power law surface growth assumes that the fracture surface grows according to a power
law relating the area of the fracture at any time during injection to the area of the fracture at the
end of the injection with an exponent, Ξ±, that is constant during the period of injection (Nolte
1986). Carter introduced the leak-off velocity by relating a leak-off coefficient to the elapsed
time since the start of the leak-off process and spurt loss based on the concept of Howard and
Fast (Howard 1957). Equations related to both assumptions are discussed in details in chapter 2.
1.1.4.2 Fracture Height Growth
The two-dimensional models suggested in the previous sections are simplified approximation
of the fracture dimensions and geometry. These models assume constant fracture height and
leave the half-length and fracture width to be estimated from injected fluid volume. However,
practical experience showed that fractures in some cases grow into unintended zones up and
down the targeted interval (Valko and Economides 1995).
This observation triggered the attempts to develop models able to simulate the fracture height.
Since there are many variables in the system of equations, simplifying the approach is essential
to result in an acceptable approximation used the simplest case by neglecting hydrostatic
pressure inside the fracture and using similar properties for the upper and lower layers for
approximating fracture height growth (Simonson et al. 1978). Another analysis that is widely
acceptable in oil and gas industry is Warpinski and Smith analysis with a more complex case
(Warpinski and Smith 1989). The notation used by them is shown in Figure 4. Alternative
notation is used by Ahmed and Economides which is discussed in chapter 2.
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| Chapter 1 β Project Scope and Objectives
Figure 4. Warpinski and Smith analysis and notation (Valko and Economides 1995)
The assumptions of Warpinski and Smith analysis (Valko and Economides 1995) are:
i. The minimum horizontal stress of the upper and lower layers can be different, but
higher than minimum horizontal stress of the targeted layer.
ii. The critical stress intensity factor (stress intensity near the tip) can be different for the
upper and lower layers.
iii. The density of the fluid is considered in the analysis
The notation will be used in this work is Ahmed and Economides notation and the set of the
equations used to determine the fracture height growth is presented in the methodology chapter.
1.2 Dynamic Simulation of Hydraulic Fractures
As for modelling the effects of induced fractures in the reservoir dynamic simulators, there are
multiple approaches, which include: using a negative skin factor, creating channels of enhanced
permeability gridblocks in the direction of fracture orientation, using non-neighbourhood
connections and/or a local increase of absolute permeability near the wellbore (Carlson 2006;
Owen1983).
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| Chapter 1 β Project Scope and Objectives
These approaches are helpful to a certain extent for increasing productivity, but they do not
incorporate the physics behind fracture propagation and recession (Carlson 2006; Owen1983).
Also, some of the routines used for 3D pseudo models result in long run times, making them
impractical for large reservoir models (Economides 2000).
1.3 Objectives
The objectives of this work are:
i. To develop an algorithm for determining the optimum hydraulic fracture dimensions of
a well and incorporating hydraulic fractures in reservoir dynamic simulators.
ii. To model induced fractures in fluid (usually water and/or polymer) injectors created
during injection under fracturing conditions using reservoir dynamic simulators.
iii. To develop an algorithm for modelling the height growth of induced fractures during
injection under fracturing conditions using reservoir dynamic simulators.
These algorithms and methods are simple and easy to incorporate in the reservoir dynamic
simulators to provide robust production and injection forecasts. This work is of great economic
and environmental benefit because the fracture dimensions are the single most important factor
which determines the increase of production/injection rates, the volume and cost of used
fracturing material, and the zones into which fractures propagate.
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| Chapter 2 β Methodology
2 Methodology
This chapter represents the methodology followed to achieve the stated objectives. Derivation,
calculations and Eclipse modelling are shown in this chapter for each objective.
2.1 Determining the Optimum Hydraulic Fracture Dimensions for a Well
For the first objective of determining the optimum hydraulic fracture dimensions, the optimum
fracture conductivity for pseudo-steady state and steady state flow conditions is calculated. For
conventional reservoirs, since most wells spend the majority of their lifetime in a pseudo-steady
state flow regime, the solution reached should represent the optimum hydraulic fracture
dimensions of a well (Richardson 2000).
The analysis starts with the use of Darcy law for pseudo-steady state flow conditions, as shown
in Eq.1:
π = 2ππβ/ππ΅π
ππππππ€
β34 + ππ
β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦(1)
where: k is permeability, h is the flow unit height, Β΅ is the viscosity, Bo is the oil formation
volume factor, re is the drainage radius, rw is the wellbore radius and Sf is the skin factor due to
fracture.
It needs to be noted that the assumption here is that the skin due to damage is not a part of the
optimum fracture dimension calculations since it happens due to drilling, production and/or
completions. However, skin will be used later as a check that the wellbore radius, due to damage
(rs), is less than half the length of the fracture (xf), to confirm that the hydraulic fracture bypasses
the damage zone.
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| Chapter 2 β Methodology
In order to maximise the production rate, the denominator of Eq. 1 has to be minimised.
Defining function G as the denominator of Eq.1, as shown in Eq.2, which has to be minimised
to increase rate.
πΊ = ππππππ€
β3
4+ ππ β ππππππ’π β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦ (2)
Now, defining function A, as shown in Eq.3.
π΄ = πππ₯π
ππ€+ ππ β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦β¦β¦β¦(3)
Based on Figure 5, A is the y-axis of the Cinco-Ley and Samaniego graph (Valko and
Economides 1995).
Figure 5. Cinco-Ley and Samaniego graph for Hydraulic Fracture Performance with f =
sf + ln (xf/rw) (Valko 2005)
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| Chapter 2 β Methodology
As shown in Eq. 4, function G becomes:
πΊ = ππππππ€
β3
4+ π΄ β ππ
π₯π
ππ€ β ππππππ’π β¦β¦β¦β¦β¦ . . (4)
Simplifying function G, as shown in Eqs. 5 through 7.
πΊ = ππππ β ππ ππ€ β3
4+ π΄ β πππ₯π + ππ ππ€ β¦β¦β¦β¦ .β¦ . (5)
πΊ = ππππ β πππ₯π + π΄ β3
4β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦ . (6)
πΊ = πππππ₯π
+ π΄ β3
4β¦β¦β¦ .β¦β¦β¦β¦β¦β¦ . . β¦β¦β¦β¦β¦ . . (7)
Two functions should be introduced here: the fracture dimensionless conductivity and the
fracture volume as shown in Eqs. 8 and 9.
πΉππ = πππ€π
ππ₯πβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦(8)
where Fcd is the fracture dimensionless conductivity, kf is the fracture permeability, wf is the
fracture width, k is the matrix permeability and xf is the fracture half-length.
The fracture dimensions are related to each other by the fracture volume, as shown in Eq. 9.
π£π = 2βππ₯ππ€π β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . (9)
where vf is the total fracture volume of both wings and hf is the fracture height.
By combining Eqs. 8 and 9, the fracture half-length can be estimated using Eq. 10.
ππ = βπ£πππ
2βππΉππβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . (10)
By substituting Eq.10 in Eq. 6, as shown in Eq. 11, the G function becomes:
πΊ = ππππ β ππβπ£πππ
2βππΉππ+ π΄ β
3
4 β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . (11)
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| Chapter 2 β Methodology
where A is defined in Eq. 12, as shown in Figure 5 as:
π΄ =1.65 β 0.328 πππΉππ + 0.116 (ππ(πΉππ))2
1 + 0.18 πππΉππ + 0.064(ππ(πΉππ))2 + 0.005(ππ(πΉππ))3β¦β¦β¦β¦β¦β¦β¦ .β¦β¦β¦β¦β¦(12)
To determine the Fcd value that will result in the minimum function G, the function is derived
with respect to Fcd. Substitution of function A in function G and the derivation is shown in Eqs.
13 and 14.
πΊ = ππππ β ππβπ£πππ
2βππΉππ+
1.65 β 0.328 πππΉππ + 0.116 (ln(πΉππ))2
1 + 0.18 πππΉππ + 0.064(ln(πΉππ))2 + 0.005(ln(πΉππ))3
β3
4β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦ (13)
ππΊ
ππΉππ
= 1
2πππΉππ
β23.2 [(πππΉππ)4 β 5.6552(πππΉππ)3 β 29.521(πππΉππ)2 β 35.862πππΉππ + 1077.59]
πππΉππ[(πππΉππ)3 + 12.8(πππΉππ)2 + 36πππΉππ + 200]2β¦ . (14)
By setting the derivative equal to zero and solving for the fracture dimensionless conductivity,
Fcd that results in minimum value of the G function can be found;
Fcd = 1.6363.
Thus, the optimum fracture dimensionless conductivity value for a fracture in a well flowing
under pseudo-steady state flow conditions is 1.6363.
The partial penetration skin is the function of two parameters; the penetration ratio and
dimensionless thickness (b and hds) (Brons et al. 1961). The penetration ratio (b) is assumed to
be set dependent upon given facts of a specific reservoir to ensure reduction in water and/or gas
production and that the best part of the reservoir is targeted. Thus, the only variable to be
considered for the calculation of the optimum hydraulic fracture dimensions is the
P a g e 16
| Chapter 2 β Methodology
dimensionless thickness (hds). Brons and Marting defined the hds of a fractured well as shown
in Eq. 15.
βππ = βπ
ππ€β²β
πβ
ππ£β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ β¦β¦β¦β¦β¦ .β¦β¦ (15)
where hds is the dimensionless thickness, hs is the thickness of a symmetry element, rwβ is the
effective wellbore radius, kh is the horizontal permeability and kv is the vertical permeability
(Brons et al. 1961).
By analysing Eq. 15, the goal of minimising hd can be achieved by increasing rwβ. Since Sf is
inversely proportional to rwβ, determining the minimum Fcd using Sf, as above, results in the
maximum rwβ.
The method described in this work includes starting from the minimum additional economic
value gain required from a hydraulic fracturing project. Let us assume that the screening
criterion of a small project for a company is a net present value of x $. Based on the oil price,
the production forecast without hydraulic fracturing and hydraulic fracturing job cost, the
additional increase in oil production rate results in a net present value of x$ due to accelerated
production can be estimated.
Thus, the minimum required folds of increase (FOI) for the project to pass the screening
criterion are calculated. To estimate the optimum fracture dimensions, relating FOI to the
fracture half-length would provide a tool to directly determine the optimum fracture dimensions
from a known or targeted FOI value. This is shown by relating the effective wellbore radius to
FOI and using Pratβs dimensionless effective wellbore radius, as explained below.
FOI and skin due to fracture are related, as shown in Eq. 16.
πΉππΌ = ππ
ππππ€
ππππππ€
+ ππ
β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦ .β¦β¦β¦β¦(16)
P a g e 17
| Chapter 2 β Methodology
where the skin due to fracture is related to the effective wellbore radius, as shown in Eq. 17.
ππ = βππππ€
β²
ππ€β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦(17)
Thus, FOI can be related to the effective wellbore radius, as shown in Eqs. 18 and 19.
πΉππΌ = ππ
ππππ€
ππππ β ππππ€ + ππππ€ β ππππ€β²β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦(18)
πΉππΌ = ππ
ππππ€
ππππππ€β²
β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦(19)
Using Eq. 19, a table of rwβ vs. FOI can be developed with the FOI value of the minimum
estimated from economics or greater.
Using Pratβs dimensionless effective wellbore radius and knowing the optimum Fcd is 1.6363,
rwβ/xf can be found, as shown in Figure 6.
Figure 6. Pratβs dimensionless effective wellbore radius (Valko 2005)
Thus, the optimum rwβ/xf value is 0.2534, which can be used for finding the optimum xf results
in the maximum FOI value. It is important to note that there is a maximum theoretical value of
P a g e 18
| Chapter 2 β Methodology
xf that is equal to the drainage radius (re), which is used as a maximum constraint for the fracture
half-length calculation.
It is also important to mention that the work thus far only assumes the theoretical value and
does not include the practical aspect of hydraulic fracturing. For example, is it possible to
achieve a fracture half-length equal to the drainage radius of the reservoir? Is it possible to have
all of the injected fluid contained in the pay zone, or intended zone? Valko introduced a
parameter called the dimensionless proppant number (Nprop) as shown in Eq. 20 (Valko 2001).
πππππ = 4πππ₯ππ€π
ππππ2β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦ (20)
According to Valko, since the proppant cannot be contained in the pay zone and within the
drainage area and for large treatments there is a great uncertainty as to where the proppant goes
in both horizontal and vertical directions, there is a practical limit to the dimensionless proppant
number (Valko 2001). The practical N number is less than or equal to 0.1 for medium and high
permeability formations (50 mD and above), while for low permeability reservoirs a
dimensionless proppant number more than 0.5 is rarely realised. Therefore, another condition
is applied in this work to the calculation performed, which is the use of N of 0.1 or less for
formations with a permeability of 50mD and above, and 0.5 or less for the formations with a
permeability of less than 50mD (Valko 2001).
Also, it is preferable to have the fracture half-length longer than the damage radius to eliminate
the impact of damage on production. If the fracture half-length is increased, the width also has
to be increased to maintain the optimum Fcd value. Thus, the proppant volume required is
increased so that the economic value resulted from increasing production by increasing the
volume of the fracture versus the economic saving made on the proppant cost by keeping the
fracture half-length less than the damaged radius has to be evaluated. Finally, Eq. 8 is used to
calculate the fracture width, since everything else is known.
P a g e 19
| Chapter 2 β Methodology
In the case of low permeability reservoirs, the fracture width calculated by the method above
can be small. Practically, the fracture width has to be large enough for the proppant to be placed
in the fracture to keep it open. Therefore, another condition to be applied is that the fracture
width has to be at least two to three (2-3) times the mesh proppant grain diameter. In such a
case, starting with a fracture width of 2-3 times the proppant grain diameter, the length can be
calculated using N value of 0.5 or lower (applying the condition that the calculated half-length
fracture is equal to or less than drainage radius). By analysing Eq.8, for low permeability
reservoirs, it can be inferred that a long fracture is required for a certain minimum width
determined to result in optimum Fcd value. Thus, in cases of low permeability low drainage
radius reservoirs, the theoretical limitation on the maximum possible fracture half-length in
addition to the practical limitations previously mentioned may result in Fcd values more than
1.6363.
An excel workbook is developed to perform all the calculations mentioned in this section.
Further work can be performed by linking this workbook to Eclipse Dynamic Simulator so that
refinements and calculations are performed automatically.
2.1.1 Cases Input for Testing the Procedure Used to Determine the Optimum Hydraulic Fracture
Dimensions for a Well
For the first objective, two cases from literature (Valko and Economides 1995) are used to test
the analysis of this work, perform the calculations for the optimum fracture dimensions and
perform the Eclipse Dynamic Simulation. The results match very well, as shown in the results
and discussion chapter.
The two cases are for a low permeability reservoir and a high permeability reservoir. Each
reservoir has six water injectors and one oil producer. The oil producer is to be hydraulically
P a g e 20
| Chapter 2 β Methodology
fractured to increase the reservoirβs production rate. It is necessary to determine the optimum
hydraulic fracture dimensions, estimate the increase in production rate and develop the new
production forecast.
2.1.1.1 Low Permeability Reservoir Case
Input data for the low permeability reservoir case are shown in Table 1.
Table 1: Low permeability case input
Horizontal Permeability 0.5 mD
Formation Height 105 ft
Fracture Height 35 ft
Fracture Permeability 60000 mD
Proppant Mesh Diameter 70 mesh (420 Β΅m)
Drainage radius 2100 ft
Wellbore radius 0.328 ft
Damage skin 0
2.1.1.2 High Permeability Reservoir Case
Input data for the high permeability reservoir case is shown in Table 2.
Table 2: High permeability case input
Horizontal Permeability 500 mD
Formation Height 150 ft
Fracture Height 30 ft
Fracture Permeability 100000 mD
Proppant Mesh Diameter 40 mesh (840 Β΅m)
Drainage radius 1000 ft
Wellbore radius 0.328 ft
Damage skin 0
P a g e 21
| Chapter 2 β Methodology
2.2 Incorporating Hydraulic Fractures in Reservoir Dynamic Simulators
To estimate the impact of hydraulic fracturing on reservoir production and/or injection rates, a
high permeability channel in a refined box model is simulated using Eclipse Reservoir
Simulator. The results of the optimum dimensions for hydraulic fracture (Section 2.1) are used
to create a high permeability channel near the wellbore, extending away from it by fracture
half-length in each direction. In the two cases of this work, the model is refined to have the
width of the gridblocks equal to the hydraulic fracture width, as shown in Figure 8 and Figure
10.
In both cases, the models have six water injectors and one hydraulically fractured oil producer,
as shown in Figure 7 and Figure 9. A permeability multiplier, NTG multiplier and porosity
multiplier are used for the gridblocks representing the fracture to mimic the hydraulic fracture
permeability, increase the porosity of the gridblocks to 100% and increase NTG to 100%. Table
3 summarises the Eclipse dimensions used for the two cases.
Table 3: Model dimensions summary
Item Low permeability case High permeability case
Number of gridblocks 11 x 1000 x 3 11 x 10000 x 5
Model dimensions (ft) 410.8 x 0.014 x 35 87.2 x 1.783 x 30
P a g e 22
| Chapter 2 β Methodology
Figure 7. Low permeability case model
Figure 8. Hydraulic fracture for low permeability case
P a g e 23
| Chapter 2 β Methodology
Figure 9. High permeability case model
Figure 10. Hydraulic fracture for high permeability case
In other cases, models can be refined so that the gridblock width is less than the fracture width
(i.e. the fracture channel includes more than one gridblock in the width direction). In the case
of large models, local gridblock refinement can be performed instead to mimic the same
P a g e 24
| Chapter 2 β Methodology
procedure followed in this work. Also, fracture half-length should be taken into consideration
of refinement in case fracture half-length estimated is less than gridblock length.
2.3 An Algorithm for Modelling Induced Fractures Created During Injection under
Fracturing Conditions in Reservoir Dynamic Simulators
The following sections introduce the methodology used in this work to develop an algorithm to
be used to simulate the propagation, recession and dimensions induced fractures created due to
injection under fracturing conditions.
2.3.1 Fracture Height Growth
As mentioned in the Section 1.1.4.2, Ahmed and Economides notation (Economides 1992) is
used in this work. The variables to be estimated as shown in the notation (Figure 11) are the
upper (βhu) and lower (βhd) height growth.
Figure 11. Ahmed and Economides notation for fracture height (Valko and Economides
1995)
The solution can be achieved by solving for two unknowns in two equations (Eqs. 21 and 22).
P a g e 25
| Chapter 2 β Methodology
πΎπΌ, π‘ππ
= ββπ
π(π¦π’ β π¦π) . {ππ‘[π¦π , π00 β π3, π1] β ππ‘[β1, π00 β π3, π1] + ππ‘[π¦π’, π00 β π1, π1]
β ππ‘[π¦π, π00 β π1, π1] + ππ‘[+1, π00 β π2, π1] β ππ‘[π¦π’, π00 β π2, π1]}
= πΎ(πΆ, 2) [πππππ‘π’ππ π‘ππ’πβπππ π ππ π‘βπ π’ππππ πππ¦ππ]β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦ (21)
πΎπΌ, πππ‘
= ββπ
π(π¦π’ β π¦π) . {ππ[π¦π, π00 β π3, π1] β ππ[β1, π00 β π3, π1] + ππ[π¦π’, π00 β π1, π1]
β ππ[π¦π, π00 β π1, π1] + ππ[+1, π00 β π2, π1] β ππ[π¦π’, π00 β π2, π1]}
= πΎ(πΆ, 3) [πππππ‘π’ππ π‘ππ’πβπππ π ππ π‘βπ πππ€ππ πππ¦ππ]β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦ (22)
where:
π¦π’ = 1 β 2ββπ’
βπ + ββπ’ + ββπβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦β¦(23)
π¦π = β1 + 2ββπ
βπ + ββπ’ + ββπβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦β¦ (24)
π00 = πππ + ππββπ β ββπ’
2β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦β¦ (25)
π1 = β ππ 2βπ
π¦π’ β π¦πβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦β¦(26)
ππ‘ = β1 + π¦
1 β π¦ . {βππ β π1 +
(2π0 + π1). π¦
2+
π1π¦2
2}
+(2π0 + π1)
2. tanβ1(
π¦β(1 + π¦) (1 β π¦)β
1 + π¦)β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦ (27)
P a g e 26
| Chapter 2 β Methodology
ππ = β
1 β π¦
1 + π¦ . {ππ β π1 +
(2π0 β π1). π¦
2+
π1π¦2
2}
β(2π0 β π1)
2. tanβ1 (
π¦β(1 β π¦) (1 + π¦)β
β1 + π¦)β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . . (28)
It should be noted that the following limits (Eqs. 29 through 32) are required to perform the
calculation:
ππ‘[+1, π0, π1] = π
4 (2π0 + π1)β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦ (29)
ππ‘[β1, π0, π1] = π
4 (β2π0 β π1)β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦ (30)
ππ[+1, π0, π1] = π
4 (2π0 β π1)β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦ (31)
ππ[β1, π0, π1] = π
4 (β2π0 + π1)β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦β¦ (32)
where: hp is the perforation interval length, hu is the upper height growth, hd is the lower height
growth, Ο is the density, Ο1 is the minimum horizontal stress in the targeted layer, Ο2 is the
minimum horizontal stress in the upper layer, Ο3 is the minimum horizontal stress in the lower
layer, K(C,2) is fracture toughness in the upper layer, k0 is a constant, k1 is the slope of net
pressure, k00 is the pressure at the middle of the crack, K(C,3) is fracture toughness in the lower
layer and pcp is the pressure at mid perforation.
All of the parameters in these two equations are inputs except hd and hu are the variables to be
solved for. These two variables are calculated at each time step and the fracture height results
is used in PKN-Ξ± calculation for determining the fracture half-length and width.
In this work, these two equations were combined and simplified. The final complete version of
these two equations with two unknowns are shown in appendix A.1.
P a g e 27
| Chapter 2 β Methodology
2.3.2 Fracture Width and Half-Length
As mentioned in Chapter 1, the PKN geometry assumes an elliptical shape in the vertical and
the horizontal directions for the hydraulic fracture. It assumes that the height, hf, is constant and
that the half-length, xf, is considerably greater than the width, wf. The method used in this work
to simulate induced fractures developed due to injection under fracturing conditions is the PKN-
Ξ± method, which assumes:
i. The power law surface growth, which is represented in Eq. 33.
π΄
π΄π= (
π‘
π‘π)πΌ β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦β¦β¦β¦ . (33)
where A is the fracture surface area at time t, Ae is the fracture surface area at the end of
pumping, t is time, te is the time at the end of pumping, and Ξ± is the exponent of fracture length
growth and is constant during the injection period.
ii. Carter equation I for leak-off, which is shown by Eqs. 34 and 35.
π£πΏ = πΆπΏ
βπ‘β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .β¦β¦β¦β¦β¦ .β¦ . . (34)
which has an integrated form of:
π£πΏ = 2πΆπΏβπ‘ + ππ β¦β¦β¦β¦β¦ .β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦ . . (35)
where π£πΏ is leak-off velocity, πΆπΏ is the leak-off coefficient and t is the time elapsed since the
start of leak-off.
iii. Ξ± is the exponent and is assumed to be known. It is equal to 4/5 for the case with no
leak-off and it is reasonable to assume that the exponent remains the same in the
presence of leak-off.
P a g e 28
| Chapter 2 β Methodology
With the above assumptions, the material balance at any time during injection can be written as
Eq. 36.
π€__ =
ππ‘ π΄
β2πΆπΏ πΌβπβ(πΌ)
β(3 2β + πΌ) βπ‘ β 2ππ β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . (36)
where A is the fracture surface area at time t, which equals xf.hf; i is half of the injection rate or
the injection rate for one wing of the fracture, hf is fracture height, π€__ is the average width of
the fracture, Sp is the spurt-loss coefficient, CL is the leak-off coefficient, t is time, Ξ± is the
exponent of fracture length growth and β is the Euler Gamma Function, which can be calculated
using Eq. 37.
β(t) = β« π₯π‘β1πβπ₯ππ₯
β
0
β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦(37)
Substituting for the fracture surface area to incorporate fracture half-length and fracture height,
the material balance can be written as shown in Eq. 38.
π€__ =
ππ‘ π₯πβπ
β2πΆπΏ πΌβπβ(πΌ)
β(3 2β + πΌ) βπ‘ β 2ππ β¦β¦β¦β¦β¦β¦β¦β¦β¦(38)
To solve for fracture half-length, Eq. 35 can be re-arranged as shown in Eq. 39.
π₯π =
ππ‘βπ
π€__ + 2ππ + 2πΆπΏ βπ‘ [
πΌβπβ(πΌ)
β(3 2β + πΌ)]
β¦β¦β¦β¦β¦β¦ .β¦ . . (39)
The procedure to be followed for the calculations consists of using the input data in simple
calculations and testing conditions at each time step. In the beginning, at each time step a
comparison of bottom-hole flowing pressure to the fracture initiation pressure is performed and
fracture is only initiated if the former is greater than or equal to the latter. Once the fracture is
initiated, it either closes, remains open, closes then reopens, or propagates. At each time step
following the fracture initiation, condition testing is performed and a decision is made on the
P a g e 29
| Chapter 2 β Methodology
fracture simulation for the next time step. In case the bottom-hole pressure is greater than or
equal to the fracture propagation pressure, the PKN-Ξ± calculation method is performed and the
half-length and width of the fracture are estimated. For the PKN-Ξ± model, the fractureβs
dimensions can be estimated as shown in Eqs. 40 through 43.
ππ,π€ =ππβππβ ππππβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . (40)
where pn,w is the net wellbore pressure, pbhpf is the bottom-hole flowing pressure and Οmin is the
minimum horizontal stress.
Once the net wellbore pressure is calculated, the maximum fracture width at the wellbore can
be found thus:
ππ,π€ =
πΈβ²
2βπ π€π€,0
β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . . β¦ (41)
where Eβ is the plane strain modulus (which can be calculated from Youngβs modulus and
Poissonβs ratio) and ww,0 is the maximum fracture width at the wellbore.
To solve the maximum fracture width at the wellbore, Eq. 41 can be re-arranged as shown in
Eq. 42.
π€π€,0 = 2βπ (ππβππ β ππππ)
πΈβ²β¦β¦β¦β¦β¦β¦β¦ .β¦β¦β¦β¦β¦(42)
The average fracture width is related to the maximum fracture width at the wellbore, as shown
in Eq. 43.
π€__ = 0.628319 π€π€,0 β¦β¦β¦β¦β¦ .β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ . (43)
where π€__ is the average fracture width and 0.628319 is the shape factor (Ο/5). The shape factor
contains Ο/4 because the vertical shape is an ellipse. Also, it contains another factor (4/5) which
accounts for the lateral variation of the width for the PKN model (Yang 2011). Once the average
fracture width has been estimated, the fracture half-length is related to it as shown in Eq. 39.
P a g e 30
| Chapter 2 β Methodology
To determine the fracture half-length and width, fracture height is required as an input. From
fracture height calculation Section 2.3.2, the result is used as an input to the PKN-Ξ± calculation
to estimate the maximum fracture width near the wellbore which is then used to carry the of the
calculations to estimate the fracture average width and half-length.
To incorporate the fracture in the dynamic model, local grid refinement is performed based on
the new fracture height, width and half-length calculated after each time step. Also,
permeability, NTG and porosity multipliers should be applied to the gridblocks representing
the fracture. The logic behind that should be performing NTG and porosity multiplying to result
in gridblocks NTG of 1 and porosity of 100%. As for the permeability multipliers, analogues
can be used to relate the fracture width to certain fracture permeability value. Then,
permeability multiplier should be used to increase the gridblocks permeability to the fracture
permeability. The algorithm for the procedure described is shown in Figure 12.
P a g e 32
| Chapter 2 β Methodology
Figure 12. Algorithm for estimating fracture dimensions created due to injection under
fracturing conditions
P a g e 33
| Chapter 3 β Results and Discussion
3 Results and Discussion
This chapter introduces the results of the investigation to determine the optimum hydraulic
fracture dimensions for low and high permeability reservoir cases. Furthermore, it discusses the
results of modelling hydraulic fractures and induced fractures created due to injection under
fracturing conditions in reservoir dynamic simulators. For each of these topics, the results are
discussed and further improvements are suggested.
3.1 Determining the Optimum Hydraulic Fracture Dimensions for a Well
The optimum hydraulic fracture width and half-length are estimated using the Excel workbook
developed, based on the derived optimum dimensionless fracture conductivity, the practical
dimensionless proppant number constraint and the minimum possible hydraulic fracture width
related to proppant grain diameter.
3.1.1 Low Permeability and High Permeability Case Results
The results of the low permeability case and the high permeability case are tabulated and
discussed below. The same procedure can be followed to determine the optimum hydraulic
fracture dimensions for other cases, to which the issues discussed also apply.
P a g e 34
| Chapter 3 β Results and Discussion
3.1.1.1 Low Permeability Reservoir Case
The optimum hydraulic fracture dimensions estimated for the low permeability case are shown
in Table 4.
Table 4: Low permeability case results
Half-length (xf) 1027 (ft)
Fracture width (wf) 0.014 (ft)
Fracture volume (vf) 1010 (ft3)
FOI 4.2
Skin due to fracture (sf) -6.676
N 0.5
Fcd 1.643
Although the results shown in Table 4 represent the optimum fracture dimensions for the
maximum folds of increase, it can be inferred from Figure 13 and Figure 14 that reducing the
fracture volume to half will result in a reduction of only 0.5 in FOI. For a fracture volume of
about 1000 ft3, FOI of about 4.2 is calculated, while FOI of 3.7 is calculated for a fracture
volume of 570 ft3. Therefore, the cost of fracturing material and the expected increase in
production due to the larger FOI value should be taken in consideration when determining the
optimum hydraulic fracture dimensions for a well.
P a g e 35
| Chapter 3 β Results and Discussion
Figure 13. Net present bbls increase in production and fracture volume vs. folds of
increase for low permeability case
For economics to be calculated there are multiple factors that need to be taken into
consideration. These include:
i. Capacity of the production system and facilities. If additional equipment and/or larger
equipment sizes are required, there is an additional cost encountered for each barrel of
oil produced and the additional folds of increase also incur more cost. Thus, the
comparison should include this factor when estimating the saving versus the cost.
ii. Other small projects that require investment (e.g. artificial lift, increasing the injection
rate and/or deploying EOR methods). Ranking of the additional fracturing volume cost
and gain versus the cost and gain of other methods should be performed to facilitate the
selection of the best project for investment (the one with the highest net present value
index, the highest net present value and/or the highest internal rate of return).
iii. Additional investment in production facilities due to earlier water and/or gas
breakthrough. Since created hydraulic fractures are high permeability channels, they can
result in faster breakthrough of water and/or gas from aquifers, injectors and/or gas cap
P a g e 36
| Chapter 3 β Results and Discussion
to producers. The dimensions of the hydraulic fracture should be selected carefully to
delay breakthrough since this requires larger equipment sizes and/or additional
equipment for separation and treatment.
iv. Depth of damage due to drilling and/or completion phases. The depth of the damaged
zone near the wellbore might be longer than the optimum fracture half-length in a few
special cases. In such a case, the optimum fracture half-length can be increased (while
also increasing the width to result in the same optimum fracture conductivity) to bypass
formation damage.
All of these factors should be taken into account when selecting the optimum dimensions of the
hydraulic fracture.
3.1.1.2 High Permeability Reservoir Case
The optimum hydraulic fracture dimensions estimated for the high permeability case are shown
in Table 5 and Figure 14.
Table 5: High permeability case results
Half-length (xf) 218 (ft)
Fracture width (wf) 1.783 (ft)
Fracture volume (vf) 23322 (ft3)
FOI 2.77
Skin due to fracture (sf) -5.13
N 0.1
Fcd 1.6363
P a g e 37
| Chapter 3 β Results and Discussion
Figure 14. Net present bbls increase in production and fracture volume vs. folds of
increase for high permeability case
Similar to the low permeability case, it can be observed that for FOI of 2.5, a fracture volume
of 12500 ft3 is required. Increasing the fracture volume to 23300 ft3 (approximately double),
will result in only approximately 0.25 increase in FOI value. Therefore, the cost of the fracturing
material and the additional gain in oil production should be taken into consideration before
deciding the optimum fracture dimensions for a well, as has been shown in the two cases tested
above.
P a g e 38
| Chapter 3 β Results and Discussion
3.2 Incorporating Hydraulic Fractures in Reservoir Dynamic Simulators
The increases in production due to hydraulic fracture for the low permeability case and the high
permeability case are shown in Figure 15 and Figure 16.
Figure 15. Increase in cumulative oil production for low permeability case
Figure 16. Increase in cumulative oil production for high permeability case
P a g e 39
| Chapter 3 β Results and Discussion
It can be observed that the production increase for the low permeability case is higher than the
increase for the high permeability case. Creating a 600,000 mD channel inside a 0.5 mD
reservoir provides a high permeability pathway for the fluid to flow through, which significantly
impacts the production. On the other hand, for the high permeability case, the reservoir is able
to produce at a good rate and thus the impact of the high permeability channel is not as great as
for the low permeability case. Also, it can be observed that the average FOI is different from
the estimated FOI from the optimum hydraulic fracture calculations. The first reason for this is
that the calculations were based on the assumption of pseudo-steady state flow conditions, while
in a dynamic simulation the well flows under transient flow conditions followed by pseudo-
steady state conditions. The second reason is that water breakthrough can be expected to occur
earlier for the hydraulic fracture case, impacting the well-lifting ability and thus the oil
production rate. Once the water has created a path to the well, water production will increase
rapidly, since the fracture will act as a short circuit for water conducting. Therefore, it is
expected that for wells with hydraulic fractures, there is faster water and/or gas breakthrough
and a subsequent reduction in oil production.
P a g e 40
| Chapter 3 β Results and Discussion
3.3 Algorithm for Modelling Induced Fractures Created During Injection under
Fracturing Conditions in Reservoir Dynamic Simulators
The impact of implementing the algorithm shown in Figure 12 in the reservoir simulator is
examined using the injectors of the two cases from Section 3.1. The procedure followed
involved manually stopping the simulator after each time step to check the pressure and then
manually performing the calculations, refinement and properties multiplying. This resulted in
an average increase of 42% in run time for a simulation period of 200 days with an average
time step length of 10 days as shown in Table 6.
Table 6: Run time and storage capacity requirement for base cases and cases with
induced fracture modelling
It can be inferred that the run time and storage capacity for the low permeability case are more
than those for the high permeability case. The reason is the fracture dimensions of the low
permeability case is smaller than the fracture dimensions of the high permeability case and
therefore more gridblocks are required due to more refinement.
Additionally, the algorithm is not fully automated in the Eclipse Dynamic Simulator, but it can
be easily observed that such an increase in run time is not very significant. Still, there are other
Low Permeability Case High Permeability Case
Run Time for Case with No
Fracture (Minutes) 3.3 3.1
Run Time for Case with
Induced Fracture (Minutes) 4.9 4.1
Storage Required for Case with
No Fracture (Megabytes) 359 342
Storage Required for Case with
Induced Fracture (Megabytes) 573 512
P a g e 41
| Chapter 3 β Results and Discussion
factors that can increase the expected run time, such as performing the calculations within the
dynamic simulator and having a case of smaller fracture dimensions which results in increasing
the number of gridblocks due to more refinement.
The numerical three-dimensional fracture models are based on moving coordinate system
governed by partial differential equations with five unknowns that need to be solved for either
explicitly or implicitly (Xiang 2011). Such calculations are time consuming since for each time
step five unknowns are required to be solved for in addition mass and pressure. In contrast to
the numerical three-dimensional fracture models, the proposed algorithm has only two sets of
equations to be solved for the fracture three dimensions. Therefore, a reduction in both run time
and storage capacity is achieved by implementing the proposed algorithm compared to using
three-dimensional models. Still, due to the assumptions and simplifications in both PKN-Ξ±
model and Ahmed and Economides notation after Simonson analysis mentioned in
Section 1.1.4, the accuracy of the results of using this algorithm is expected to be lower than
those of the numerical three-dimensional fracture models. Therefore, the algorithm presented
provides a good approximation for modelling induced fractures growth with reduced simulation
run time and storage capacity compared to three dimensional fracture models. Also, it provides
more accurate results compared to the simple two-dimensional models that assumes fixed
fracture height.
P a g e 42
| Chapter 4 β Conclusions and Recommendations
4 Conclusions and Recommendations
The work presented is of significant economic and environmental importance for oil and gas
companies. In this work, optimum dimensionless hydraulic fracture conductivity is
mathematically determined for pseudo-steady state and steady state flow conditions. The
optimum Fcd is found to be 1.6363 and this value, in addition to the practical limitations, is then
used in an algorithm to determine and simulate the optimum hydraulic fracture dimensions.
Refinement and gridblock properties multiplying are then performed to incorporate the effect
of hydraulic fractures on production and injection forecasts from reservoir dynamic models.
Additionally, in this work an algorithm to simulate induced fractures created due to injection
under fracturing conditions is developed. The advantage of the algorithm is that it incorporates
the pressure data and field constraints from the dynamic simulator to simulate the fracture
progression, recession and dimensions for the full life of the field. Also, the algorithm acts as
an alerting tool for fracture growth into unintended zones. All in all, the results of this work
represent a thorough tool for determining the optimum hydraulic fracture dimensions and
simulating the impact of induced fractures on the fieldβs production and injection forecasts
using reservoir dynamic simulators.
Future work can include incorporating the algorithms in reservoir dynamic simulators so that
the calculations and induced fracture modelling can be performed automatically in the
background.
P a g e 43
| References
References
Anon. a 2013. Fracture mechanics. PetroWiki (16 September 2013 revision),
http://petrowiki.org/Fracture_mechanics (accessed 3 August 2014).
Anon. b 2013. Fracture. Schlumberger Oilfield Glossary, 14 November 2013,
http://www.glossary.oilfield.slb.com/en/Terms/f/fracture.aspx (accessed 20 July 2014).
Anon. c 2014. What is Fracking?. Energy From Shale, 27 June 2014,
http://www.energyfromshale.org/hydraulic-fracturing/what-is-fracking (accessed 14 July
2014).
Anon. d 2014. Natural Gas Extraction - Hydraulic Fracturing. EPA, 16 July 2014,
http://www2.epa.gov/hydraulicfracturing (accessed 4 August 2014).
Anon. e 2014. Hydraulic fracturing. Schlumberger Oilfield Glossary, 11 January 2014,
http://www.glossary.oilfield.slb.com/en/Terms/h/hydraulic_fracturing.aspx (accessed 21
July 2014).
Anon. f 2013. Thermal and Hydraulic Fracturing. PETEX, 9 July 2013,
http://www.petex.com/products/?id=53 (accessed 5 August 2014).
Anon. g 2014. Mini-Frac (or DFIT) & Caprock Integrity. Big Guns Energy Services, 18 July 2014,
http://www.bges.ca/cat/engineering/mini_frac.php (accessed 13 August 2014).
Anon. h 2010. Hydraulic Fracturing: The Process. Fracfocus Chemical Disclosure Registry, 20
July 2010, http://fracfocus.ca/hydraulic-fracturing-how-it-works/hydraulic-fracturing-
process (accessed 19 July 2014).
Brons, F., Marting, V. 1961. The Effect of Restricted Fluid Entry on Well Productivity. Journal of
Petroleum Technology, 13 (2): 172-173.
Carlson, M.R. 2006. Practical Reservoir Simulation - Using, Assessing, and Developing Results.
Oklahoma, USA: PennWell Corporation.
Crain, E. 2013. Fracture Pressure Basics. Crainβs Petrophysical Handbook, 21 December 2013,
http://www.spec2000.net/10-closurestress.htm (accessed 8 August 2014).
P a g e 44
| References
Dubey, S., Gudmundsson, A. 2012. Field Study and Numerical Modeling of Fracture Networks: Application
to Petroleum Reservoirs. M&S: Schlumberger J. of Modeling, Design, and Simulation 3
(1): 5-9.
Economides, M.J. 1992. A Practical Companion to Reservoir Stimulation. Amsterdam: Elsevier.
Economides, M.J. and Nolte, K.G. 2000. Reservoir Stimulation, third edition. New York: John
Wiley and Sons.
Golf-Racht, T. 1982. Fundamentals of fractured reservoir engineering, First edition. Amsterdam:
Elsevier.
Howard G.C. and Fast, c.R.: Optimum Fluid Characteristics for Fracture Extension, Drilling and
Production Prac., API, 261-270, 1957 (Appendix by E.D. Carter).
Hudson, J., and Harrison, J. 2005. Engineering rock mechanics, First edition. Tarrytown, NY:
Pergamon.
Moreno, J., Ligero, E., and Schiozer, D. 2005. Effects of Water Injection under Fracturing
Conditions on the Development of Petroleum Reservoirs. International Congress of
Mechanical Engineering, Ouro Preto, MG, November 6-11.
Nolte, K.G.: Determination of Proppant and Fluid Schedules from Fracturing Pressure Decline,
SPEPE, (July), 225-265, 1986 (originally paper SPE 8341, 1979).
Owen, D. R. J. and Fawkes, A. J. 1983. Engineering Fracture Mechanics: Numerical Methods and
Applications. Swansea: Pineridge Press Ltd.
Richardson, M. 2000. A new and practical method for fracture design and optimisation. SPE 59736,
SPE/CERI Gas Technology Symposium, Calgary, Alberta, Canada, April 3β5.
Simonson, E., Abou-Sayed, AS., and Clifton, RJ. 1978. Containment of Massive Hydraulic
Fractures, SPEJ, (Feb.), 27-32, 1978.
Shukman, D. 2013. What is fracking and why is it controversial?.BBC NEWS, 27 June 2013,
http://www.bbc.com/news/uk-14432401 (accessed 2 August 2014).
P a g e 45
| References
Taleghani, A., Ahmadi, M., and Olson, J. 2013. Secondary Fractures and Their Potential Impacts
on Hydraulic Fractures Efficiency. In Effective and Sustainable Hydraulic Fracturing, first
edition, Andrew P. Bunger, John McLennan and Rob Jeffrey, Chap. 38, 785-789. Brisbane:
INTECH.
Valko, P. (2001). HF2D Frac Design Spreadsheet. Lecture conducted from Texas A&M
University, Houston, TX.
Valko, P. (2005). Hydraulic Fracturing Short Course. Lecture conducted from Texas A&M
University, Houston, TX.
Valko, P., and Economides, M. J. 1995. Hydraulic Fracture Mechanics, first edition. Chichester,
England: John Wiley & Sons.
Warpinski, N. R., and Smith, M. B. 1989. Rock mechanics and fracture geometry. In: Recent
Advances in Hydraulic Fracturing, Monograph Vol. 12, Gidley, J. L. et al. (Eds.).
Richardson, TX: SPE.
Xiang, J. 2011. A PKN Hydraulic Fracture Model Study and Formation Permeability
Determination. MS thesis, Texas A&M University, Houston, Texas (December 2011).
Yang, M. 2011. Hydraulic Fracture Optimization with a Pseudo-3d Model in Multi-Layered
Lithology. MS thesis, Texas A&M University, Houston, Texas (August 2011).
I
| Appendices β Fracture Height Equations
Appendices
A.1 Fracture Height Equations
Using Texas Instrument (TI-89) calculator, the two equations with the two unknowns to be solved
for are shown below:
πΎπΌ, π‘ππ =
β2 π2{(2.(βπ+βπ+βπ’).π΄πππ‘ππ
[ (βπ+βπ+βπ’).β
βπ+βπβπ’
2.(βπ+βπ)
]
β4.βπ’ββπ+βπ
βπ’βπ(βπ+βπ+βπ’)}
4βπ(βπ+βπ+βπ’)+
β2 π3{(2.(βπ+βπ+βπ’).π΄πππ‘ππ
[ (βπββπ+βπ’).β
βπβπ’+βπ
2.(βπ)
]
+4(βπ+βπ’)ββπ
βπ+βπ’βπ(βπ+βπ+βπ’)}
4.βπ(βπ+βπ+βπ’)β
0.399. π1β(βπ β βπ + βπ’) . π΄πππ‘ππ
[ (βπββπ+βπ’).β
βπβπ’+βπ
2.(βπ)
]
β
0.399. π1β(βπ + βπ + βπ’) . π΄πππ‘ππ [(βπ+βπββπ’).β
βπ+βπ
βπ’
2.(βπ+βπ)] β
0.798{π1(βπ+βπ’).ββπ
βπ+βπ’β π1.βπ’β
βπ+βπ
βπ’+25.27(βπ+βπ+βπ’).(π.βπ+2(π.βπ’β0.0311πππ))}
β(βπ+βπ+βπ’) β¦β¦β¦β¦ . (π΄. 1 β 1)
= πΎ(πΆ, 2)
II
| Appendices β Fracture Height Equations
πΎπΌ, πππ‘ =
β2 π2{(2.(βπ+βπ+βπ’).π΄πππ‘ππ
[ (βπ+βπββπ’).β
βπ’βπ+βπ
2.(βπ’)
]
+4(βπ+βπ)ββπ’
βπ+βπβπ(βπ+βπ+βπ’)}
4βπ(βπ+βπ+βπ’)+
β2 π3{(2.(βπ+βπ+βπ’).π΄πππ‘ππ
[ (βπββπ+βπ’).β
βπ’+βπβπ
2.(βπ+βπ’)
]
β4(βπ)ββπ’+βπ
βπβπ(βπ+βπ+βπ’)}
4βπ(βπ+βπ+βπ’)β
0.399. π1β(βπ + βπ + βπ’) . π΄πππ‘ππ [(βπ+βπββπ’).β
βπ’βπ+βπ
2.(βπ’)] β
0.399. π1β(βπ + βπ + βπ’) . π΄πππ‘ππ [(βπββπ+βπ’).β
βπ’+βπ
βπ’
2.(βπ’+βπ)] β
0.798{π1(βπ+βπ).ββπ’
βπ+βπβ π1.βπ’β
βπ’+βπ
βπβ25.27(βπ+βπ+βπ’).(π.βπ+2(π.βπβ0.0311πππ))}
β(βπ+βπ+βπ’) β¦β¦β¦β¦ . (π΄. 1 β 2)
= πΎ(πΆ, 3)
III
| Appendices β Meeting Agendas and Progress Report (Period 1)
A.2 Meeting Agendas and Progress Reports
A.2.1. Period 1
Heriot Watt University
Individual Project Weekly Progress Meeting
Induced Fractures Modelling in Reservoir Dynamic Simulators
Meeting Agenda
July 25, 2014
11 a.m β 12 p.m
Meeting Type Individual Project Weekly Progress Meeting
Meeting Facilitator Khaldoon AlObaidi
Invitees Dr. Khalik M. Sabil
1. Last Meeting Minutes Review/Summary: 11 a.m β 11:10 a.m
2. Previous Period Targets: 11:10 a.m β 11:20 a.m
a) Initial literature review
b) Draft write-up: summary, introduction, methodology and appendices
c) Optimum hydraulic fracture dimensions algorithm
3. Previous Period Open issues: 11:20 a.m β 11:30 a.m
a) Function Derivation Using Excel Sheet
b) StimPlan software Learning
4. Next Period Targets/Goals: 11:30 a.m β 11:40 a.m
a) Incorporating hydraulic fractures in reservoir dynamic simulator
IV
| Appendices β Meeting Agendas and Progress Report (Period 1)
5. Next Period Expected Issues: 11:40 a.m β 11:50 a.m
a) Model size/run time due to refinement near wellbore
b) Convergence issues due to small gridblocks
6. Action Items/ Close-out/ Feedback: 11:50 a.m β 12:00 p.m.
V
| Appendices β Meeting Agendas and Progress Report (Period 1)
MSc Petroleum Engineering
Individual Project Weekly Progress Report 1
Khaldoon AlObaidi
Induced Fractures Modelling in
Reservoir Dynamic Simulators
Heriot-Watt University
Institute of Petroleum Engineering
Supervisor - Dr. Khalik M. Sabil
VI
| Appendices β Meeting Agendas and Progress Report (Period 1)
Table of Contents 1. Periodic Progress Summary .................................................................................................. VII
Key Accomplishments for Last Period: ......................................................................... VII
Upcoming Tasks for This Period: .................................................................................. VII
Issues: ............................................................................................................................VIII
2. Major Task Completion for the Period .................................................................................. IX
3. Major Task for the Next Period ................................................................................................X
4. Conclusion .............................................................................................................................. XI
VII
| Appendices β Meeting Agendas and Progress Report (Period 1)
1. Periodic Progress Summary
To: Dr. Khalik M. Sabil From: Khaldoon AlObaidi
Subject: Individual Project Summary Progress Report Date: 25/07/2014
Project Name: Induced Fractures Modelling in
Reservoir Dynamic Simulators Report
Period:
July 15 - July 25
Student: Khaldoon AlObaidi Supervisor: Dr. Khalik M. Sabil
Progress Report
Number:
1 Copy: Restricted
Key Accomplishments for Last Period:
Thorough literature review for fracture design.
Analysis of literature data gathered.
Simple Excel Sheet to perform the calculation for optimum fracture design (Partially
completed).
Summary, introduction, methodology and appendices write up submission to UK
Documenting the results (Partially completed).
Upcoming Tasks for This Period:
Completed the excel sheet work for optimum fracture design.
Generate simple Eclipse box model.
Gather literature examples of hydraulic fractures.
Generate an algorithm for gridblocks refinement.
Test the algorithm and compare to StimPlan software results.
Document the results.
VIII
| Appendices β Meeting Agendas and Progress Report (Period 1)
Issues:
Difficulty in performing derivative using Excel sheet for finding absolute minimum
and maximum for a function.
Self-teaching of StimPlan is time consuming.
IX
| Appendices β Meeting Agendas and Progress Report (Period 1)
2. Major Task Completion for the Period
Project Name: Induced Fractures Modelling in Reservoir Dynamic Simulators
Status Date: 25/07/2014
Period Major
Tasks Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Actual
Complete
Date
%
Comp. Comments
Literature
Research 14/07 15/07 -- --
Ongoing
Work
This work continues as
ongoing work during the
project period. Initial
review is 100%
completed for the first
objective of the project
Write-up of
Summary,
Introduction,
methodology
and
appendices
14/07 15/07 21/07 21/07 100%
First draft is completed.
However, further
refinement shall be
performed as more work
is accomplished
An algorithm
for defining
the optimum
hydraulic
fracture
dimensions
for a well
21/07 21/07 25/07 -- 70%
Needs further
investigation for defining
derivatives using Excel
Sheets and testing
StimPlan results
X
| Appendices β Meeting Agendas and Progress Report (Period 1)
3. Major Task for the Next Period
Next Period
Major Tasks
Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Comments
Literature
Research 25/07 25/07 07/08
This work continues as ongoing work during the
project period. Literature review for this task
should consider hydraulic fracturing modelling in
reservoir dynamic simulators.
Incorporating
hydraulic
fractures in
reservoir
dynamic
simulators
25/07 25/07 07/08
This task should include using Eclipse software
and some issues might raise from the size of the
model due to grid refinement and/or convergence
problems.
Comparison
of algorithm
results to
StimPlan
results
01/08 -- 07/08 Learning of StimPlan is already ongoing and some
support might be required for using the software.
XI
| Appendices β Meeting Agendas and Progress Report (Period 1)
4. Conclusion
The work is on track. Some issues rose from the ability to perform function derivation using excel
workbook and the time consuming process of self-teaching StimPlan software. Further
investigation to perform derivation using excel sheet is ongoing and expected to be completed in
one or two days at maximum. This is not expected to affect the timeline or the delivery of the
project. Next period will involve generating box model using Eclipse software and performing runs
to model hydraulic fractures using dynamic reservoir simulator. Expected issues for the next period
involve run time/model size and convergence issues.
XII
| Appendices β Meeting Agendas and Progress Report (Period 2)
A.2.1. Period 2
Heriot Watt University
Individual Project Weekly Progress Meeting
Induced Fractures Modelling in Reservoir Dynamic Simulators
Meeting Agenda
August 1, 2014
11 a.m β 12 p.m
Meeting Type Individual Project Weekly Progress Meeting
Meeting Facilitator Khaldoon AlObaidi
Invitees Dr. Khalik M. Sabil
1. Last Meeting Minutes Review/Summary: 11 a.m β 11:10 a.m
2. Previous Period Targets: 11:10 a.m β 11:20 a.m
a) Optimum hydraulic fracture dimensions algorithm.
b) Excel sheet for the calculation of optimum hydraulic fracture dimensions in cases of
low permeability and conventional permeability reservoirs.
c) Implementing findings and calculations this in reservoir dynamic simulator, Eclipse.
d) The literature review of PKN-Ξ± method and the write-up of the first objective.
3. Previous Period Open issues: 11:20 a.m β 11:30 a.m
Eclipse run time and difficulty of having runs completed.
Convergence issues.
4. Next Period Targets/Goals: 11:30 a.m β 11:40 a.m
a) Literature review of PKN-Ξ± method (the remaining of it).
XIII
| Appendices β Meeting Agendas and Progress Report (Period 2)
b) Defining an algorithm for fracture design for injection under fracture conditions.
c) Completing the write-up of first objective.
d) Completing the implementation of hydraulic fracturing in Eclipse.
5. Next Period Expected Issues: 11:40 a.m β 11:50 a.m
c) Adding equations to Eclipse as part of the run routine
d) Convergence and runtime issues.
6. Action Items/ Close-out/ Feedback: 11:50 a.m β 12:00 p.m.
XIV
| Appendices β Meeting Agendas and Progress Report (Period 2)
MSc Petroleum Engineering
Individual Project Weekly Progress Report 2
Khaldoon AlObaidi
Induced Fractures Modelling in
Reservoir Dynamic Simulators
Heriot-Watt University
Institute of Petroleum Engineering
Supervisor - Dr. Khalik M. Sabil
XV
| Appendices β Meeting Agendas and Progress Report (Period 2)
Table of Contents 1. Periodic Progress Summary ................................................................................................ XVI
Key Accomplishments for Last Period: ....................................................................... XVI
Upcoming Tasks for This Period: ................................................................................ XVI
Issues: ........................................................................................................................... XVI
2. Major Task Completion for the Period .............................................................................. XVII
3. Major Task for the Next Period ......................................................................................... XVIII
4. Conclusion ......................................................................................................................... XVIII
XVI
| Appendices β Meeting Agendas and Progress Report (Period 2)
1. Periodic Progress Summary
To: Dr. Khalik M. Sabil From: Khaldoon AlObaidi
Subject: Individual Project Summary Progress Report Date: 1/08/2014
Project Name: Induced Fractures Modelling in
Reservoir Dynamic Simulators Report Period: July 25βAugust 1
Student: Khaldoon AlObaidi Supervisor: Dr. Khalik M. Sabil
Progress Report
Number:
2 Copy: Restricted
Key Accomplishments for Last Period:
Defining optimum hydraulic fracture dimensions for well under pseudo-steady state
flow conditions.
Testing the algorithm on literature examples.
Eclipse simulation of hydraulic fracture (20% completed).
Literature review of PKN-Ξ± (50% completed).
Write-up of first objective (75% completed).
Upcoming Tasks for This Period:
Complete the literature review for PKN-Ξ±.
Complete Eclipse simulation for hydraulic fracture design.
Complete dynamic simulation routine for defining fracture dimensions during
injection under fracturing condition.
Issues:
Difficulty in incorporating the hydraulic fracture in Eclipse (run time and convergence
issues).
Eid holiday and library closed where targets had to be shifted to accommodate.
XVII
| Appendices β Meeting Agendas and Progress Report (Period 2)
2. Major Task Completion for the Period
Project Name: Induced Fractures Modelling in Reservoir Dynamic Simulators
Status Date: 1/08/2014
Period Major
Tasks Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Actual
Complete
Date
%
Comp. Comments
Literature
Research for
Second
Objective
25/07 01/08 -- -- Ongoing
Work
This work continues as
ongoing work during the
project period. Initial
review is 50% completed
for second objective of
the project.
Write-up of
the First
Objective
28/07 01/8 03/08 -- 75%
Few sections were
written. However, further
refinement shall be
performed and more
writing is required.
Implementing
Hydraulic
Fracture
algorithm in
Eclipse
27/07 01/08 05/08 -- 20%
Needs further work since
difficulty faced in
convergence and run
time. Also, close of
library where work station
are located due to Eid
holiday.
XVIII
| Appendices β Meeting Agendas and Progress Report (Period 2)
3. Major Task for the Next Period
Next Period
Major Tasks
Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Comments
Literature
Research for
Second
Objective
25/07 25/07 --
This work continues as ongoing work during the
project period. Literature review for this task
should consider PKN-Ξ± method and how to
incorporate that in Eclipse.
Write-up of
first objective 28/07 01/08 03/08
This task is about 75% completed. Still, further
review and more details to be added.
Implementing
Hydraulic
Fracture
algorithm in
Eclipse
27/07 27/07 05/08
This task is about 20% completed. Issues were
faced as expected in dynamic simulation due to
long run times and convergence issues.
4. Conclusion
The work is on track. Little delays are faced due to issues rising from dynamic simulation of the
hydraulic fractures. The two main issues where long run time and convergence issues. Literature
review for the approaches to achieve the second objective (using PKN-Ξ± for dynamic simulation
of fractures created due to injection under fracturing under conditions) is ongoing. Further write-
up of the first objective will be completed by the beginning of next week. Next period will involve
more dynamic simulation and Eclipse usage. Expected issues for the next period involve run
time/model size, convergence issues and difficulty in incorporating routine for calculating fracture
dimensions during injection under fracturing conditions in Eclipse simulation.
XIX
| Appendices β Meeting Agendas and Progress Report (Period 3)
A.2.1. Period 3
Heriot Watt University
Individual Project Weekly Progress Meeting
Induced Fractures Modelling in Reservoir Dynamic Simulators
Meeting Agenda
August 11, 2014
11 a.m β 12 p.m
Meeting Type Individual Project Weekly Progress Meeting
Meeting Facilitator Khaldoon AlObaidi
Invitees Dr. Khalik M. Sabil
1. Last Meeting Minutes Review/Summary: 11 a.m β 11:10 a.m
2. Previous Period Targets: 11:10 a.m β 11:20 a.m
a) Eclipse simulation of hydraulic fracture (70% completed).
b) Literature review of PKN-Ξ± (60% completed).
c) Literature review of fracture height growth (50% completed).
d) Write-up of first objective (100% completed).
3. Previous Period Open issues: 11:20 a.m β 11:30 a.m
a) Difficulty with incorporating the hydraulic fracture in Eclipse (run time, insufficient
memory and convergence issues).
b) Only one Petrel license is available which restricts using floViz for viewing the work.
XX
| Appendices β Meeting Agendas and Progress Report (Period 3)
4. Next Period Targets/Goals: 11:30 a.m β 11:40 a.m
a) Complete the literature review for PKN-Ξ±.
b) Complete the literature review for fracture height growth.
c) Complete dynamic simulation routine for defining fracture dimensions during
injection under fracturing condition.
d) Complete dynamic simulation for hydraulic fracturing.
e) Write-up of literature review and methodology and submit to Dr. Khalik.
5. Next Period Expected Issues: 11:40 a.m β 11:50 a.m
a) Adding equations to Eclipse as part of the run routine.
b) Solving two linear equations for two variables and implementing that in Eclipse.
c) Convergence, runtime issues, insufficient memory and restricted number of license.
6. Action Items/ Close-out/ Feedback: 11:50 a.m β 12:00 p.m.
XXI
| Appendices β Meeting Agendas and Progress Report (Period 3)
MSc Petroleum Engineering
Individual Project Weekly Progress Report 3
Khaldoon AlObaidi
Induced Fractures Modelling
in Reservoir Dynamic Simulators
Heriot-Watt University
Institute of Petroleum Engineering
Supervisor - Dr. Khalik M. Sabil
XXII
| Appendices β Meeting Agendas and Progress Report (Period 3)
Table of Contents 1. Periodic Progress Summary .............................................................................................. XXIII
Key Accomplishments for Last Period: ..................................................................... XXIII
Upcoming Tasks for This Period: .............................................................................. XXIII
Issues: ......................................................................................................................... XXIII
2. Major Task Completion for the Period ............................................................................ XXIV
3. Major Task for the Next Period .......................................................................................... XXV
4. Conclusion ........................................................................................................................ XXVI
XXIII
| Appendices β Meeting Agendas and Progress Report (Period 3)
1. Periodic Progress Summary
To: Dr. Khalik M. Sabil From: Khaldoon AlObaidi
Subject: Individual Project Summary Progress Report Date: 11/08/2014
Project Name: Induced Fractures Modelling in
Reservoir Dynamic Simulators Report Period: August1βAugust11
Student: Khaldoon AlObaidi Supervisor: Dr. Khalik M. Sabil
Progress Report
Number:
3 Copy: Restricted
Key Accomplishments for Last Period:
Eclipse simulation of hydraulic fracture (70% completed).
Literature review of PKN-Ξ± (60% completed).
Literature review of fracture height growth (50% completed).
Write-up of first objective (100% completed).
Upcoming Tasks for This Period:
Complete the literature review for PKN-Ξ±.
Complete the literature review for fracture height growth.
Complete dynamic simulation routine for defining fracture dimensions during
injection under fracturing condition.
Complete dynamic simulation for hydraulic fracturing.
Write-up of literature review and methodology and submit to Dr. Khalik.
Issues:
Difficulty in incorporating the hydraulic fracture in Eclipse (run time, insufficient
memory and convergence issues).
Only one Petrel license is available which restricts using floViz for viewing the work.
XXIV
| Appendices β Meeting Agendas and Progress Report (Period 3)
2. Major Task Completion for the Period
Project Name: Induced Fractures Modelling in Reservoir Dynamic Simulators
Status Date: 11/08/2014
Period Major
Tasks Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Actual
Complete
Date
%
Comp. Comments
Literature
Review of
PKN-Ξ± and
Fracture
Height
Growth
25/07 01/08 13/08 -- Ongoing
Work
This work continues as
ongoing work throughout
the project. Initial review
is 50%-60% completed
for the second and third
objectives of the project.
Write-up of
the First
Objective
28/07 01/8 03/08 07/08 100%
First objective work is
completed and the first
draft is shared with Dr.
Khalik for his initial
review and feedback.
Some modifications is
required for separating
methodology from results
and discussions.
Implementing
Hydraulic
Fracture
algorithm in
Eclipse
27/07 01/08 05/08 -- 70%
Due to difficulties with
long run time,
insufficient memory and
convergence; further
work is required. Also,
only one license of
floViz is available.
XXV
| Appendices β Meeting Agendas and Progress Report (Period 3)
3. Major Task for the Next Period
Next Period
Major Tasks
Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Comments
Literature
Review of
PNK-Ξ± and
Fracture
Height
Growth.
25/07 25/07 --
This work continues as ongoing work throughout
the project. Literature review for this task should
consider PKN-Ξ± method and how to incorporate
that in Eclipse. Also, it should consider the
methodology for incorporating fracture height
growth in the routine.
Implementing
Hydraulic
Fracture
algorithm in
Eclipse
27/07 27/07 12/08
This task is about 70% completed. Issues were
faced as expected in dynamic simulation due to
long run times, insufficient memory and
convergence issues.
Complete
dynamic
simulation
routine for
defining
fracture
dimensions
during
injection
under
fracturing
condition.
08/08 08/08 15/08 This task is in progress and some literature review
is already performed.
Submission of
literature
review and
methodology
write-up to
Dr. Khalik.
07/08 07/08 13/08 This task is in progress.
XXVI
| Appendices β Meeting Agendas and Progress Report (Period 3)
4. Conclusion
The work is on track. Little delays are faced due to issues rising from dynamic simulation of the
hydraulic fractures. The main issues are long run time, restricted number of license for Petrel,
insufficient memory, and convergence issues. Literature review for the approaches, achieving the
objectives of modeling fracture generated due to injection under fracturing conditions and fracture
height growth simulation, is ongoing. Furthermore, the first objectiveβs write-up is completed and
discussed with project supervisor (Dr. Khalik). Next period will involve more dynamic simulation
and Eclipse usage in addition to literature reviews of the next objectives. Expected issues from the
next period involve difficulty with calculating fracture dimensions during injection under
fracturing conditions in Eclipse simulation. Some issues might rise from solving two linear
equations for two variables and implementing that in dynamic simulation.
XXVII
| Appendices β Meeting Agendas and Progress Report (Period 4)
A.2.1. Period 4
Heriot Watt University
Individual Project Weekly Progress Meeting
Induced Fractures Modelling in Reservoir Dynamic Simulators
Meeting Agenda
August 18, 2014
11 a.m β 12 p.m
Meeting Type Individual Project Weekly Progress Meeting
Meeting Facilitator Khaldoon AlObaidi
Invitees Dr. Khalik M. Sabil
1. Last Meeting Minutes Review/Summary: 11 a.m β 11:10 a.m
2. Previous Period Targets: 11:10 a.m β 11:20 a.m
a) Eclipse simulation of hydraulic fracture (100% completed).
b) Literature review of PKN-Ξ± (100% completed).
c) Literature review of fracture height growth (60% completed).
d) Write-up first draft of report (100% completed).
3. Previous Period Open issues: 11:20 a.m β 11:30 a.m
a) No issues for this period. Time can be used to discuss the report format.
4. Next Period Targets/Goals: 11:30 a.m β 11:40 a.m
XXVIII
| Appendices β Meeting Agendas and Progress Report (Period 4)
a) Complete a case test for PKN-Ξ±.
b) Write-up the height calculation section
c) Finalize the report and start writing SPE paper
d) Prepare the slide-pack for presentation
5. Next Period Expected Issues: 11:40 a.m β 11:50 a.m
a) No expected issues for next period. Time can be used to discuss generated algorithms.
6. Action Items/ Close-out/ Feedback: 11:50 a.m β 12:00 p.m.
XXIX
| Appendices β Meeting Agendas and Progress Report (Period 4)
MSc Petroleum Engineering
Individual Project Weekly Progress Report 4
Khaldoon AlObaidi
Induced Fractures Modelling in
Reservoir Dynamic Simulators
Heriot-Watt University
Institute of Petroleum Engineering
Supervisor - Dr. Khalik M. Sabil
XXX
| Appendices β Meeting Agendas and Progress Report (Period 4)
Table of Contents 1. Periodic Progress Summary ............................................................................................. XXXI
Key Accomplishments for Last Period: .................................................................... XXXI
Upcoming Tasks for This Period: ............................................................................. XXXI
Issues: ........................................................................................................................ XXXI
2. Major Task Completion for the Period ........................................................................... XXXII
3. Major Task for the Next Period ...................................................................................... XXXIII
4. Conclusion ...................................................................................................................... XXXIII
XXXI
| Appendices β Meeting Agendas and Progress Report (Period 4)
1. Periodic Progress Summary
To: Dr. Khalik M. Sabil From: Khaldoon AlObaidi
Subject: Individual Project Summary Progress Report Date: 18/08/2014
Project Name: Induced Fractures Modelling in
Reservoir Dynamic Simulators Report
Period:
August11βAugust18
Student: Khaldoon AlObaidi Supervisor: Dr. Khalik M. Sabil
Progress Report
Number:
4 Copy: Restricted
Key Accomplishments for Last Period:
Eclipse simulation of hydraulic fracture (100% completed).
Literature review of PKN-Ξ± (100% completed).
Literature review of fracture height growth (60% completed).
Write-up first draft of report (100% completed).
Upcoming Tasks for This Period:
Complete a case test for PKN-Ξ±.
Write-up the height calculation section
Finalize the report and start writing SPE paper
Prepare the slide-pack for presentation
Issues:
No issues for this period
XXXII
| Appendices β Meeting Agendas and Progress Report (Period 4)
2. Major Task Completion for the Period
Project Name: Induced Fractures Modelling in Reservoir Dynamic Simulators
Status Date: 18/08/2014
Period Major
Tasks Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Actual
Complete
Date
%
Comp. Comments
Literature
Review of
PKN-Ξ± 25/07 01/08 13/08 18/08 100%
Completed and first draft
report is written
Literature
Review for
Fracture
Height
Growth
25/07 01/08 13/08 -- 60%
This work is ongoing and
planned to be completed
in the next period.
Write-up of
the First
Draft Report
10/08 11/8 18/08 18/08 100% Completed and submitted
to Dr. Khalik on 18/08
Implementing
Hydraulic
Fracture
algorithm in
Eclipse
27/07 01/08 05/08 12/08 100%
Results are extracted from
runs and forecast is
shown in the report
XXXIII
| Appendices β Meeting Agendas and Progress Report (Period 4)
3. Major Task for the Next Period
Next Period
Major Tasks
Status
Planned
Start
Date
Actual
Start Date
Planned
Complete
Date
Comments
Complete a
case test for
PKN-Ξ±. 11/08 18/08 20/08
A case will be used to test the PKN- Ξ±
algorithm generated.
Write-up the
Height
Growth
Section
11/08 -- 20/08 Write-up the methodology and results sections
for the fracture height growth calculation.
Finalize the
report and
start writing
SPE paper
15/08 -- 22/08 Finalize the report write-up and write-up SPE
paper.
Prepare the
slide-pack for
presentation
15/08 -- 24/08 Prepare slide-pack for the presentation.
4. Conclusion
The work is on track. Draft report is submitted to Dr. Khalik for review. Next period will involve
more write-up and finalizing work. There were no issues for the last period and there are no
expected issues for the next period.
XXXIV
| Appendices β Meeting Agendas and Progress Report (Period 5)
A.2.1. Period 5
Heriot Watt University
Individual Project Weekly Progress Meeting
Induced Fractures Modelling in Reservoir Dynamic Simulators
Meeting Agenda
August 25, 2014
11 a.m β 12 p.m
Meeting Type Individual Project Weekly Progress Meeting
Meeting Facilitator Khaldoon AlObaidi
Invitees Dr. Khalik M. Sabil
1. Last Meeting Minutes Review/Summary: 11 a.m β 11:10 a.m
2. Previous Period Targets: 11:10 a.m β 11:20 a.m
e) Write-up of report
f) Finalize the missing sections
g) Review the write-up
3. Previous Period Open issues: 11:20 a.m β 11:30 a.m
b) No issues for this period. Time can be used to discuss the report format.
4. Next Period Targets/Goals: 11:30 a.m β 11:40 a.m
e) Finalize report write-up
XXXV
| Appendices β Meeting Agendas and Progress Report (Period 5)
f) Finalize the report and start writing SPE paper
g) Prepare the slide-pack for presentation
5. Next Period Expected Issues: 11:40 a.m β 11:50 a.m
b) No expected issues for next period. Time can be used to discuss write up.
6. Action Items/ Close-out/ Feedback: 11:50 a.m β 12:00 p.m.
XXXVI
| Appendices β Meeting Agendas and Progress Report (Period 5)
MSc Petroleum Engineering
Individual Project Weekly Progress Report 5
Khaldoon AlObaidi
Induced Fractures Modelling in
Reservoir Dynamic Simulators
Heriot-Watt University
Institute of Petroleum Engineering
Supervisor - Dr. Khalik M. Sabil
XXXVII
| Appendices β Meeting Agendas and Progress Report (Period 5)
Table of Contents 1. Periodic Progress Summary ........................................................................................ XXXVIII
Key Accomplishments for Last Period: ............................................................... XXXVIII
Upcoming Tasks for This Period: ........................................................................ XXXVIII
Issues: ................................................................................................................... XXXVIII
2. Major Task Completion for the Period ..........................................................................XXXIX
3. Major Task for the Next Period ......................................................................................XXXIX
4. Conclusion ......................................................................................................................XXXIX
XXXVIII
| Appendices β Meeting Agendas and Progress Report (Period 5)
1. Periodic Progress Summary
To: Dr. Khalik M. Sabil From: Khaldoon AlObaidi
Subject: Individual Project Summary Progress Report Date: 25/08/2014
Project Name: Induced Fractures Modelling in
Reservoir Dynamic Simulators Report
Period:
August18βAugust25
Student: Khaldoon AlObaidi Supervisor: Dr. Khalik M. Sabil
Progress Report
Number:
5 Copy: Restricted
Key Accomplishments for Last Period:
Write-up the height calculation section (100% completed)
Write-up of first draft of report (100% completed).
Write-up of second draft of report (100% completed).
Write-up of third draft of report (100% completed).
Upcoming Tasks for This Period:
Finalize the report and start writing SPE paper
Prepare the slide-pack for presentation
Issues:
No issues for this period
XXXIX
| Appendices β Meeting Agendas and Progress Report (Period 5)
2. Major Task Completion for the Period
Project Name: Induced Fractures Modelling in Reservoir Dynamic Simulators
Status Date: 25/08/2014
Period Major
Tasks Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Actual
Complete
Date
%
Comp. Comments
Write-up the
height
calculation
section
18/08 18/08 20/08 20/08 100% Completed and
reviewed
Complete
first, second
and third
draft of
report
10/08 11/08 18/08 25/08 100% Completed and
reviewed
3. Major Task for the Next Period
Next Period
Major Tasks
Status
Planned
Start
Date
Actual
Start
Date
Planned
Complete
Date
Comments
Finalize the
report 25/08 25/08 26/08 Finalize writing the report.
Prepare SPE
paper and
presentation
slide pack
25/08 25/08 28/08 Prepare SPE paper and presentation as first
draft.
4. Conclusion
The work is on track. Draft report is submitted to Dr. Khalik for review. Next period will
involve more write-up, finalizing work and preparing SPE paper & slide pack. There were no
issues for the last period and there are no expected issues for the next period.