application of dilation-recompaction model in hydraulic

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Graduate Studies The Vault: Electronic Theses and Dissertations

2015-04-30

Application of Dilation-Recompaction Model in

Hydraulic Fracturing Simulation

Huang, Xuemin

Huang, X. (2015). Application of Dilation-Recompaction Model in Hydraulic Fracturing Simulation

(Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/24959

http://hdl.handle.net/11023/2199

master thesis

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UNIVERSITY OF CALGARY

Application of Dilation-Recompaction Model in Hydraulic Fracturing Simulation

by

Xuemin Huang

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF SCIENCE

GRADUATE PROGRAM IN CHEMICAL AND PETROLEUM ENGINEERING

CALGARY, ALBERTA

APRIL, 2015

© Xuemin Huang 2015

Abstract

Production of unconventional oil and gas resources has played a significant role on the global

energy supply, of which tight oil and gas reservoirs are drawing greater focus. The key enabler

behind tight oil and gas production has been multi-stage hydraulic fracturing along extended reach

horizontal wells. Despite many advances in multistage fracturing, it still remains unclear how to

model the hydraulic fracturing process to provide the basis to optimize and predict the properties

of fracture networks and associated enhancement of fluid production. This is especially difficult

since it is not possible to directly image the fracture network since the length scales of the network

can be relatively small. In typical reservoir simulation practice, the conventional way to represent

the hydraulic fracture is to place transverse plane around the horizontal well – this means that the

user has prescribed the orientation and length scale of the fracture before the simulation has started.

In the research documented here, we explore a dynamic fracturing approach that uses a dilation-

recompaction model in a reservoir simulator to model hydraulic fracturing. The key strength of the

approach is that the geometry and length scale of the fracture is not prescribed a priori. This means

that the model can be relatively easily constructed and matched to field data. The results of the

simulation show that dilation-recompaction model is capable of modeling the hydraulic fracturing

process prior to the flow-back and production. The oil, gas, and water rates of the model are well

matched to the field data and the extent of the fractured zone predicted by the model is reasonable.

A sensitivity analysis using the history-matched model reveals that the design of hydraulic

fracturing operation suggests that a larger number of stages and fracture fluid volume injected will

raise oil and gas rates, but it remains unclear if the incremental oil and gas will provide enough

revenues to offset the additional costs from increases of stages and fluid injection volume.

.

ii

Acknowledgements

I would like to express the deepest appreciation to my supervisor Dr. Ian D. Gates and my co-

supervisor Dr. Shengnan (Nancy) Chen. They have conveyed to me the enthusiasm and a spirit of adventure

in academic research. They also taught me how to think out of the box and the truth that everything is

possible. And for the most, they guide me through the three years of study and pursuit on Master degree of

chemical and petroleum engineering.

In addition, I also want to thank Jacky (Jingyi) Wang and Da Zhu for the assistance. They help me out when

I was puzzled with simulation problems and mathematical issues.

I also would like to thank Schulich School of Engineering at University of Calgary for providing a

magnificent environment for studying and researching.

At the end, I also want to thank Accumap (for input data), CMG for use of its reservoir simulator

STARSTM, and Schlumberger for use of its geological modelling package Petrel.

iii

Table of Contents

Abstract ............................................................................................................................... ii Acknowledgements ............................................................................................................ iii Table of Contents ............................................................................................................... iv List of Table ....................................................................................................................... vi List of Figures ................................................................................................................... vii

CHAPTER ONE: INTRODUCTION ..................................................................................1 1.1 Tight Rock as a Source of Petroleum ........................................................................1 1.2 Hydraulic Fracturing ..................................................................................................3 1.3 Predictive Models for Hydraulic Fracturing ..............................................................7 1.4 Research Questions ....................................................................................................8 1.5 Thesis Organization ...................................................................................................9

CHAPTER TWO: LITERATURE REVIEW ....................................................................10 2.1 Introduction ..............................................................................................................10 2.2 Rock Mechanics and Fracturing Mechanism ...........................................................11 2.3 Analytic Theories for Hydraulic Fracturing ............................................................15 2.4 Flow within Fractures: Conceptual Models .............................................................20 2.5 Flow within Fractures: Numerical Models ..............................................................24 2.6 Stimulated Reservoir Volume, SRV Approach .......................................................26 2.7 Dilation-Recompaction Approaches ........................................................................29 2.8 What is missing in the literature? ............................................................................34 2.9 What are the limitations of dilation recompaction model? ......................................34

CHAPTER THREE: CASE STUDY OF DILATION RECOMPACTION MODEL IN THE CARDIUM FORMATION .......................................................................................35

3.1 Introduction ..............................................................................................................35 3.2 Description of Geological and Reservoir Simulation Models .................................37 3.3 Fluid and Rock Properties........................................................................................47 3.4 Well Completion and History Match of Production ................................................52 3.5 Results ......................................................................................................................55

3.5.1 Case 1: Production history match of Well-1 with hydraulic fracturing .........55 3.5.2 Case 2: Production history match of Well-1 without hydraulic fracturing .....62

3.6 Fractured Zone of Well-1 ........................................................................................67 3.7 Discussions ..............................................................................................................78 3.8 Conclusions ..............................................................................................................79

CHAPTER FOUR: IMPACT OF HYDRAULIC FRACTURING DESIGN ON PRODUCTION .........................................................................................................80

iv

4.1 Introduction ..............................................................................................................80 4.2 Model Description ...................................................................................................81 4.3 Results and Discussion ............................................................................................81

4.3.1 Scenario 1 ........................................................................................................81 4.3.2 Scenario 2 ........................................................................................................83 4.3.3 Scenario 3 ........................................................................................................85 4.3.4 Scenario 4 ........................................................................................................87 4.3.5 Scenario 5 ........................................................................................................89

4.4 Conclusions ..............................................................................................................91

CHAPTER FIVE: CONCLUSIONS AND RECOMMENDATIONS ..............................93 5.1 Conclusions ..............................................................................................................93 5.2 Recommendations ....................................................................................................94

REFERENCES ..................................................................................................................96

APPENDIX: RESERVOIR SIMULATION MODEL LISTING FOR HISTORY-MATCHED MODEL................................................................................................99

v

List of Table

Table 1: Table 3.1: Parameters used in reservoir simulation model (the parameters A and B are defined in Figure 2.13). ................................................................................................... 47

vi

List of Figures

Figure 1.1: Tight oil and gas formations in North America (Cattaneo, 2012). .............................. 3

Figure 1.2: Multi-Stage Hydraulic Fracturing (Zhao et al. 2013). ................................................. 5

Figure 1.3: Multi-Stage Hydraulic Fracturing (Theming, 2011). ................................................... 5

Figure 2.1: Geometry of a single fracture. .................................................................................... 11

Figure 2.2: Linear elastic and plastic behaviours of rock deformation. ........................................ 13

Figure 2.3: The PKN Model (Perkins and Nordgren, 1972). ....................................................... 17

Figure 2.4: The KGD Model (Geertsma and Klerk, 1969). .......................................................... 18

Figure 2.5: Settari’s (1985) Leak-off model. ................................................................................ 20

Figure 2.6: Schematic of fracture linear flow regime. .................................................................. 21

Figure 2.7: Schematic of bilinear flow regime. ............................................................................ 22

Figure 2.8: Schematic of formation linear flow. ........................................................................... 22

Figure 2.9: Schematic of pseudo-radial flow. ............................................................................... 23

Figure 2.10: An example of micro-seismic mapping data and the interpretations of the fracture network (Mayerhofer and Lolon, 2010 ................................................................................. 27

Figure 2.11: An example of seismic events that suggest the layout of SRVs surrounding a hydraulically fractured reservoir along a horizontal well (Mayerhofer and Lolon, 2010). .. 28

Figure 2.12: Simulation result of a SRV domain (Mayerhofer et al. 2010). The injection well is below the base of the image. ............................................................................................. 29

Figure 2.13: The quad dilation-recompaction model (Beattie et al. 1991). .................................. 33

Figure 3.1: Map of the Cardium Formation (Duhault, 2012). ...................................................... 36

Figure 3.2: Location of the Harmattan Pool (Angle, 2013). ......................................................... 37

Figure 3.3: Three examples of logs used to construct geological model (Accumap, 2014). ........ 38

Figure 3.4: Contour map of the top of the Cardium Formation. ................................................... 39

vii

Figure 3.5: Contour map of the bottom of the Cardium Formation.............................................. 40

Figure 3.6: Porosity and Permeability Correlation obtained from core data. ............................... 41

Figure 3.7: Description of different areas used to create the reservoir simulation model (Accumap, 2014). .................................................................................................................. 42

Figure 3.8: Porosity of the geological model (vertical to horizontal aspect ratio is 1:1). ............. 43

Figure 3.9: Absolute permeability of the geological model (vertical to horizontal aspect ratio is 1:1). ................................................................................................................................... 44

Figure 3.10: Distribution of porosity in the reservoir simulation model (vertical to horizontal aspect ratio is 24:1). .............................................................................................................. 45

Figure 3.11: Distribution of horizontal permeability in the reservoir simulation model (vertical to horizontal aspect ratio is 24:1). .......................................................................... 46

Figure 3.12: Correlation between oil viscosity and temperature. ................................................. 48

Figure 3.13: Oil-water relative permeability curves. .................................................................... 50

Figure 3.14: Liquid-gas relative permeability curves. .................................................................. 50

Figure 3.15: Three phase relative permeability ternary diagram. ................................................. 51

Figure 3.16: Well trajectories of Well-1, Well-2 and Well-3 (vertical to horizontal aspect ratio is 24:1). ......................................................................................................................... 54

Figure 3.17: History match of Well-1’s daily oil rate. .................................................................. 56

Figure 3.18: History match of Well-1’s cumulative oil production.............................................. 56

Figure 3.19: History match of Well-1’s daily gas rate.................................................................. 58

Figure 3.20: History match of Well-1’s cumulative gas production. ........................................... 58

Figure 3.21: History match of Well-1’s daily water production rate. ........................................... 60

Figure 3.22: History match of Well-1’s daily water production rate (zoomed in view). ............. 60

Figure 3.23: History match of Well-1’s cumulative water production. ........................................ 61

Figure 3.24: History match of Well-1’s production gas-to-oil ratio. ............................................ 62

Figure 3.25: Prediction of Well-1’s daily oil rate without hydraulic fracturing. .......................... 63

viii

Figure 3.26: Prediction of Well-1’s cumulative oil production without hydraulic fracturing. ..... 64

Figure 3.27: Prediction of Well-1’s daily gas rate without hydraulic fracturing. ......................... 65

Figure 3.28: Prediction of Well-1’s cumulative gas production without hydraulic fracturing. .... 65

Figure 3.29: Prediction of Well-1’s daily water rate without hydraulic fracturing. ..................... 66

Figure 3.30: Prediction of Well-1’s cumulative gas production without hydraulic fracturing. .... 66

Figure 3.31: Horizontal permeability after injecting 2050 m3 (vertical-to-horizontal aspect ratio equal to 0.5). ................................................................................................................. 68

Figure 3.32: Horizontal permeability after injecting 4100 m3 (vertical-to-horizontal aspect ratio equal to 0.5). ................................................................................................................. 68

Figure 3.33: Pressure after hydraulic fracturing with 2050 m3 of fluid injected (vertical-to-horizontal aspect ratio equal to 0.5). ..................................................................................... 69

Figure 3.34: Pressure after hydraulic fracturing with 4100 m3 of fluid injected (vertical-to-horizontal aspect ratio equal to 0.5). ..................................................................................... 70

Figure 3.35: Cross-well view of the porosity evolution during hydraulic fracturing operation (cross-section taken at mid-point of horizontal well). .......................................................... 72

Figure 3.36: Cross-well view of the horizontal permeability evolution during hydraulic fracturing operation (cross-section taken at mid-point of horizontal well). ........................ 73

Figure 3.37: Cross-well view of the pressure evolution during hydraulic fracturing operation (cross-section taken at mid-point of horizontal well). .......................................................... 74

Figure 3.38: Cross-well view of the oil saturation evolution during hydraulic fracturing operation (cross-section taken at mid-point of horizontal well). .......................................... 75

Figure 3.39: Cross-well view of the oil saturation evolution after hydraulic fracturing operation (cross-section taken at mid-point of horizontal well). ......................................... 77

Figure 4.1: Oil rate and cumulative oil production profiles for Scenario 1 and the history-matched model. ..................................................................................................................... 82

Figure 4.2: Gas rate and cumulative gas production profiles for Scenario 1 and the history-matched model. ..................................................................................................................... 82

Figure 4.3: Water rate and cumulative water production profiles for Scenario 1 and the history-matched model. ......................................................................................................... 83

ix













x

Chapter One: Introduction

1.1 Tight Rock as a Source of Petroleum

Production of unconventional oil and gas resources has played a significant role on the global

energy supply, of which tight oil and gas reservoirs are drawing greater focus. The key technology

behind tight oil and gas production has been multi-stage hydraulic fracturing along extended reach

horizontal wells. Hydraulic fracturing dramatically increases reservoir permeability in the near

wellbore region and enlarges the connectivity between wellbore and formation. Despite many

advances in multi-stage hydraulic fracturing, it still remains unclear how to model this process to

provide the basis to optimize and predict the layout and geometry of fracture network and

associated enhancement of fluid production. This is especially difficult since it is not possible to

directly image the fracture network because the length scales of the network can be relatively

small. Although transient analysis can provide estimates of fracture width, half length,

conductivity, and closure time, it does not provide measures of the fracture network connectivity

and complexity.

In typical reservoir simulation practice, the conventional way to represent the hydraulic fracture is

to place transverse plane around the horizontal well – this means that the simulator has prescribed

the orientation and length scale of the fracture before the simulation has started. In the research

documented here, we explore a dynamic hydraulic fracturing approach that uses a dilation-

recompaction model in a reservoir simulator to model hydraulic fracturing. The key strength of the

1

approach is that the geometry and length scale of the fracture is not prescribed a priori. We also

investigate the impact of reservoir heterogeneity on multistage hydraulic fracturing along a

horizontal well.

Tight oil and gas reservoirs are specified as reservoirs that have extreme low permeability which

are less than 0.5 mD. Tight oil and gas reservoirs can vary in lithology both in vertical and

horizontal directions. For instance, a tight formation can be composed of shale, siltstone, tight

sand, dolomite and other complex mixing lithology.

Over the past fifteen years, tight oil and gas recovery have been increased and improved. A lot of

oil and gas companies explore and produce from tight reservoirs located in Asia, Europe, Oceania,

North and South America and Africa, which continuously improve the related technology. North

America has many tight oil and gas formations including the Bakken Formation, the Barnett Shale

Formation, and the Eagle Ford formation as shown in Figure 1.1. Tight oil and gas deposits have

become a key contributor to the fossil fuel energy supply in North America. In the United States,

shale gas accounts for over 20% of the national natural gas production and the oil produced from

tight oil regions accounts for over 90% of the oil production growth (Stevens, 2012)). The

estimated global recoverable tight oil and gas reserve is roughly around 3 trillion barrels. Thus,

tight oil and gas formations are playing a crucial role in the global oil and gas supply, and will

become more important in the future.

2

1.2 Hydraulic Fracturing

In the 1970’s, the technology of hydraulic fracturing was invented to crack tight formations and

extract greater volumes of oil and gas. In the early days, before the advent of horizontal well and

directional drilling, the industry typically used vertical wells to transport the fracturing fluid, often

brine, to the formation. With further investment in the tight oil and gas business, the technology

of hydraulic fracturing has been improved significantly especially after 1990s with the growth of

the use of horizontal wells and directional drilling. Nowadays, the application of hydraulic

fracturing technology is not limited to reservoirs with low permeability, but also to some high-

permeability reservoirs with poor surface and underground environment, for example, oil fields

located in deserts, oceans, and swamps.

Figure 1.1: Tight oil and gas formations in North America (Cattaneo, 2012).

3

Physically, hydraulic fracturing induces fractures in the rock leading to either enhanced

permeability channels or a fracture network with relatively high permeability. For implementing

hydraulic fracturing in tight reservoirs, a horizontal well is usually used to inject fluids which

fractures the rock and significantly increases the contact area between the well bore and productive

formation. Conceptual examples are shown in Figures 1.2 and 1.3. In the case for a vertical well

perforated over a 20 ft interval, the total contact area between formation and well bore is 160 ft2 if

a vertical well is used. If a 2,000 ft horizontal well is used, the contact area will be increased by

over 1,000 times. Thus, fracturing a horizontal well will lead to a much larger fracture network

within the rock surrounding the well than that achieved with a vertical well. The length of

horizontal wellbore can vary from hundreds of meters to thousands of meters depending on the

formation condition and the company’s drilling requirement. Because of the improvement of

drilling technology, the industry is now capable of drilling wells with horizontal section of 11,000

meters or more.

Hydraulic fracturing can be used in both open-hole and cased completions. Additionally, due to

the length of the horizontal well, the wellbore can be separated into several stages so that hydraulic

fracturing can be implemented in the horizontal well bore at various points along its trajectory.

This process is called multi-stage hydraulic fracturing. In a multi-stage hydraulic fracturing

operation, typically, at first all the stages will be shut in except for the stage at the toe of the

horizontal wellbore. Then the fracturing process will be conducted for the opened stage. And after

that, the neighbor stage will be opened and fractured with all the other stages being shut in. The

point of conducting the fracture job for only one stage at a time is to assure the formation can be

4

fractured under the target pressure so that fractures with high quality will be created within the

formation at each stage. According to different conditions of formation and well trajectory, the

length of stage can be tens of meters or even greater than a hundred meters. The number of stages

can be varied as well. Currently in industry, up to 40 stages are created in some horizontal wells.

Figure 1.2: Multi-Stage Hydraulic Fracturing (Zhao et al. 2013).

Figure 1.3: Multi-Stage Hydraulic Fracturing (Theming, 2011).

5

With the improvement of the hydraulic fracturing technology, nowadays it is possible to crack the

formation at very high pressure. Typically, for a formation less than 2,500 m deep, the fracturing

pressure can be achieved as high as 70 MPa at the rock face. In deeper formations, the fracturing

pressure can exceed 100 MPa. Under such high fracturing pressure, to finish the fracturing

operation successfully and efficiently, as well as maintaining the stability of the formation, the

injection fluid must be specially designed. In industry, current injection fluids include fracking

fluid and proppants. The function of the fracking fluid is to initialize the fracture and to extend the

fractures as far into the formation as possible as well as carry the proppant into the fractures. The

proppants stay within the new fractures and support them against the rock compression when the

system depressurizes. There are two ways for the fracking fluids to carry the proppants. The first

is by using high fluid viscosity to fluidize the proppant particles. The second is by using high flow

rates so the hydrodynamics forces on the particles are large and can support them in the fluid.

Proppants are designed to withstand high compression stress and thus the material they are

constructed from is very important. In practice, for shallow formations, usually the proppant

consists of sand. In deep formations, special materials such as ceramic beads are used as proppants.

Due to high injection rate and pressure, often additional chemical additives are mixed in the

fracking fluid. These additives have several functions such as lubrication, increasing viscosity,

maintaining pH, and antibiotic biocides. In most cases, the fracking fluids are water based and will

be injected together with chemical additives and proppants. Usually the total injecting fluid volume

will contains about 90% water, 9% proppants, and 1% chemical additives. In some cases, gas-

based fluids such as nitrogen and liquefied petroleum gas are used as fracking fluid.

6

After the fluids are injected into the formation and the hydraulically-induced fractures and fracture

networks are created, on production, fluid is produced from the reservoir. This stage of the

operation is referred as flow-back where produced fluid consisting of the injected fracking fluids,

formation gas, formation water, and in some cases the proppant will be produced to surface.

After hydraulic fracturing, there may be a damaged zone surrounding the wellbore which may

significantly affect the production performance. In some operations, an acidizing treatment is used

combined with hydraulic fracturing to reduce wellbore damage.

1.3 Predictive Models for Hydraulic Fracturing

Currently in the industry there are two different viewpoints to model the fracture network created

by hydraulic fracturing process. One focuses on single fractures and its shape, extent (height,

width, and length), and effective permeability. These types of models are often analytical in nature

and permit the calculation of the aperture, pressure, and effective permeability of the fracture as

the rock is hydraulically fractured. Other models use finite element and discrete element models

to examine how the rock is dilated and eventually fractured by injected fluids (Mayerhofer et al.

2010). A key issue of these models is that they are complex and take huge amounts of simulation

time to model the single fracturing events. At this point, none of these models have captured the

behaviour of injection period of multi-stage hydraulic fracturing operations. In many cases, these

models are used to model the stimulated reservoir volume (SRV) that surrounds the wellbore after

7

the hydraulic fracture operation is complete. Other models use discrete fracture networks to model

the formation of hydraulic fractures (Kazemi and Kurtoglu, 2012). All of these approaches have

different strengths and limitations. With the exception of the finite element and discrete element

methods, dynamic fracture models are not available that can deal with multiple-stage hydraulic

fracturing process. A full description of models for hydraulic fracturing will be described in the

literature review.

1.4 Research Questions

The research questions tackled by the research documented in this thesis are as follows:

1. Can hydraulic fracturing be modelled dynamically by using a simple pore pressure dilation-

recompaction model?

2. What is the extent and dimensions of the hydraulically fractured zone surrounding the

wellbore?

3. What is the optimum size of fracture fluid volume and number of stages to improve the

performance of hydraulically fractured reservoir?

8

1.5 Thesis Organization

Chapter 2 contains a detailed literature review on hydraulic fracturing and what basic models used

to prescribe fracture shape, to explain the flow within fracture zone, and to simulate hydraulic

fracturing process. Chapter 3 describes a new dilation-recompaction method to model hydraulic

fracturing using a case study in Cardium formation. Chapter 4 describes the optimization of the

design of hydraulic fracturing for a wellbore, examining the size of the fracturing fluid as well as

the number of stages used. The final chapter lists the conclusions of the research and

recommendations for further research.

9

Chapter Two: Literature Review

2.1 Introduction

It remains unclear as to the extent, shape, and nature of hydraulically fractured rock. The fractures

created underground are complex in geometry, morphology, and properties especially since the

state of stress often varies spatially in the reservoir rock. To describe the fractures more specifically

and accurately, the characteristics required include the fracture length (more often used is the

fracture half length), fracture width (aperture), fracture height, closure pressure, orientation,

fracture volume, fracture density, fracture porosity, fracture permeability and fracture

compressibility.

The fracture half length (L), width (W) and height (H) which determine the geometry of an

idealized fracture are shown in Figure 2.1. The fracture porosity, volume, density, contact area

with the formation and permeability represent the transportability and productivity of the fracture,

the larger these parameters are, the faster the fluid can be transported through the fracture. Fracture

orientation represents the extension direction of the fracture and the closure pressure indicates the

pressure under which the fracture will be closed due to compression.

Over the years, there have been many theories developed to model hydraulic fracturing and most

are based on individual fractures.

10

Figure 2.1: Geometry of a single fracture.

2.2 Rock Mechanics and Fracturing Mechanism

After fluid is injected into formation at high pressure or high rate, the formation will be fractured

and complex fracture network will be created (Aziz and Wan, 2002). Although the operation

constraints including injecting pressure, injecting temperature and injection rate, will affect the

results of hydraulic fracturing job, the properties really controlling the orientation, propagation,

dimension and characteristics of fracture network are rock and injected fluids properties (Starch

and Vozniak, 1989). Injected fluids will have different impacts on the formation rock if they

possess different properties including density, viscosity, and PH value (Starch and Vozniak, 1989).

11

However in contrast with team fracturing or acid stimulation, the injected fluids in hydraulic

fracturing operation are usually water based so that the impact from fluids properties may not play

a significant role as they are in steam injection or acid stimulation (Starch and Vozniak, 1989).

The geomechanical properties of formation rock including Young’s modulus, Poisson’s ratio and

state of stress, are significant for the creation of fracture network (Holder et al. 2011). Figure 2.2

displays the deformation process of the rock. Typically, when fluid is injected on the surface of a

rock, it creates a pressure on that surface, which will initiate the deformation of the rock (Han et

al. 2011). Firstly, the rock will be deformed elastically, then at some point the deformation will

change to be plastic, at last the rock will be fractured (Han et al. 2011). Young’s modulus which

is the slope of the elastic line is defined as the ratio of stress to strain for an elastic deformation of

a rock (Han et al. 2011). The Poisson’s ratio is defined as the ratio of transverse strain to axial

strain. And the state of stress is consists of two parts, one is normal stress which is perpendicular

to the rock surface and the other is shear stress which is parallel to the rock surface. And typically

the equation used to calculate total compressibility from Young’s modulus and Poisson’s ratio is

(De Jong and Chen, 2015):

𝑐𝑐𝑡𝑡 =3(1 − 2𝑣𝑣)

𝐸𝐸… … … … … … … … … … … … … … … … … . (2.1)

Where 𝑐𝑐𝑡𝑡 is total compressibility in unit of 1/kPa, 𝑣𝑣 is Poisson’s ratio and 𝐸𝐸 is Young’s modulus

in unit of kPa.

12

Figure 2.2: Linear elastic and plastic behaviours of rock deformation.

After hydraulic fracturing operation starts, the reservoir pressure increases and changes the

pressure within the rock pore system, which will lead to changes in pore geometry of the rock

especially the shape and dimension of the pore and pore throats (Du and Wong, 2007). Typically

in consolidated reservoir, there are two main mechanisms for deformation of the rock. One is from

tensile failure and the other is from shear failure (Han et al. 2011). Tensile failure occurs when the

effective pressure of the rock, which is the pressure difference between overburden pressure and

pore pressure, exceeds the tensile stress of the rock (Han et al. 2011). On the other hand, shear

failure occurs when the effective pressure overcome the shear stress of the rock to initiate the

deformation (Han et al. 2011). From a macroscopic perspective, the mechanism for creating

induced fracture network can vary with the depth of the formation, the lithology especially the

shale content of the rock, and the level of consolidation (Han et al. 2011).

13

In an ideal formation where the lithology is consistent within the formation, the leak off of injected

fluids is zero and there is no presence of naturally fractures or micro fractures, there will be only

one induced fracture per perforation (Aziz and Wan, 2002). However, in reality, usually a complex

fracture network is thought to exist in a shale formation as evidenced by micro-seismic technology

or underground image technology (Holder et al. 2011). One reason is that there are natural

horizontal fissures or extensive fractures with no tensile and cohesive strength in shale formation,

so that new fractures will be initiated at these in situ horizontal fracture tips if the stresses and

deformation induced by the injection are excessive (Chau and Wong, 2004). Another reason is that

the leak-off of injected fluids will induce new fractures when they encounter with weaker

formation rock (Settari, 1985). The last reason is the presence of naturally fractures or micro

fractures (Chau and Wong, 2004). These fractures will be initiated by injected fluids and then

continue to create a new fracture network.

Increase in permeability is a great enhancement from hydraulic fracturing, the following equations

are used to calculate fracture permeability and the bulk permeability which is the permeability of

a combined system of matrix and fracture (Aguilera, 1998):

𝑘𝑘𝑓𝑓 = 54 × 106𝑤𝑤𝑜𝑜2 … … … … … … … … … … … … … … (2.2)

𝑘𝑘2 =𝑘𝑘𝑓𝑓𝑤𝑤𝑜𝑜𝐷𝐷

… … … … … … … … … … … … … … … … … . (2.3)

14

Where 𝑘𝑘𝑓𝑓 is fracture permeability in unit of Darcy. 𝑘𝑘2 is bulk permeability in unit of Darcy, 𝑤𝑤𝑜𝑜 is

fracture aperture in unit of inch and 𝐷𝐷 is fracture spacing in unit of inch.

2.3 Analytic Theories for Hydraulic Fracturing

Analytic models can be divided into two-dimensional (2D) and three-dimensional (3D) models.

These models rely on knowledge of the mechanical properties of the rock including the Young’s

modulus and Poisson’s ratio. Also, knowledge of the state-of-stress of the reservoir rock is

required.

In 2D models, the geometry of the fracture needs to be presumed and usually the fracture height

is estimated at first (often from the thickness of the reservoir rock), then the fracture half length,

width and pressure within fracture can be calculated. Among the most used models, the two earliest

and simplest are the Perkins-Kern-Nordgren (PKN) model (Perkins and Nordgren, 1972) and

Kristonovich-Geertsma-Daneshy (KGD) model (Geertsma and Klerk, 1969). Basically, the PKN

model considers the horizontal cross section of the fracture as an elliptical tube and the vertical

cross section as an eclipse, shown in Figure 2.3. Then the PKN model combines the Darcy’s

equation with continuity equation to calculate the fracture half length (Perkins and Nordgren,

1972), Fracture width and fracture pressure respect to time. The results of PKN model are shown

as the following equations:

15

𝐿𝐿 = 0.68 �𝐺𝐺𝑄𝑄3

(1 − 𝜈𝜈)𝜇𝜇ℎ4�1/5

𝑡𝑡4/5 … … … … … … … … … … … … … (2.4)

𝑤𝑤 = 2.52 �(1 − 𝜈𝜈)𝜇𝜇𝑄𝑄2

𝐺𝐺ℎ�1/5

𝑡𝑡1/5 … … … … … … … … … … … … … (2.5)

𝑝𝑝 = 2.5 �𝜇𝜇𝐺𝐺4𝑄𝑄2

(1 − 𝜈𝜈)4ℎ6�1/5

𝑡𝑡1/5 … … … … … … … … … … … … … … (2.6)

where G is the shear modulus in unit of psi, 𝜈𝜈 is the Poisson’s ratio, Q is the injection rate in unit

of bbl/min, h is the fixed fracture height in unit of ft, 𝜇𝜇 is the viscosity of the injected fluid in unit

of cp, and t is the injection time in unit of min. Equation (1) is used to calculate fracture half-length

in unit of ft, Equation (2) is to calculate fracture width in ft. and Equation (3) provides an estimate

of the fracture pressure change respect to time and the pressure is in psi. In general, the PKN model

will provide accurate results when the fracture half-length is much larger than the fracture height

(Perkins and Nordgren, 1972).

16

Figure 2.3: The PKN Model (Perkins and Nordgren, 1972).

In contrast with the PKN model, the KGD model provides accurate results when the fracture height

is close to or larger than the half-length (Geertsma and Klerk, 1969). Theoretically, the KGD model

assumes the horizontal cross section of the fracture as an elliptical tube (same as the PKN model),

but for the vertical cross section of the fracture, the KGD model assumes that it has a rectangular

cross section, as shown in Figure 2.4. Then by applying the same calculating procedure as the PKN

model, the following equations are obtained:

𝐿𝐿 = 0.48 �8𝐺𝐺𝑄𝑄3

(1 − 𝜈𝜈)𝜇𝜇ℎ3�1 6⁄

𝑡𝑡2 3⁄ … … … … … … … … … … … … … (2.7)

17

𝑤𝑤 = 1.32 �8(1 − 𝜈𝜈)𝜇𝜇𝑄𝑄3

𝐺𝐺ℎ3�1 6⁄

𝑡𝑡1 3⁄ … … … … … … … … … … … … … (2.8)

𝑝𝑝 = 0.96 �2𝐺𝐺3𝜇𝜇𝑄𝑄2

(1 − 𝜈𝜈)3𝐿𝐿2�1 4⁄

𝑡𝑡1/4 + 𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚 … … … … … … … … … … … (2.9)

where 𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚 is the minimum stress of the rock in unit of psi, G is the shear modulus in unit of psi,

𝜈𝜈 is the Poisson’s ratio, Q is the injection rate in unit of bbl/min, h is the fixed fracture height in

unit of ft, 𝜇𝜇 is the viscosity of the injected fluid in unit of cp, t is the injection time in unit of min,

𝐿𝐿 is fracture half-length in unit of ft, 𝑤𝑤 is fracture width in unit of ft and 𝑝𝑝 is the fracture pressure

in unit of psi.

Figure 2.4: The KGD Model (Geertsma and Klerk, 1969)

Instead of 2D models, pseudo 3D (P3D) models, models that are 2D with limited 3D assumptions,

are more often applied in industry (Pitakbunkate et al. 2011). P3D models require the rock

properties for multiple layers of the reservoir rock with 2D models used within each layer. This

18

then provides estimates of fracture extent, direction, and geometry including half length, height

and width, and also productivity within each layer.

There are several limitations of 2D models. Both PKN and KGD models do not take fluid leak-

off into consideration. Fluid leak-off is the phenomenon occurring during the hydraulic fracturing

process where some of the injected fracturing fluid penetrates the permeable formation rocks and

is not recovered during flow-back. There are some models built to describe the leak-off

phenomenon (Settari, 1985). Settari’s (1985) leak-off model describes that the leak-off of fluid

into the reservoir rock matrix will go through three stages: 1. mud cake, 2. filtrate, and 3. reservoir,

illustrated in Figure 2.5. This model indicates that while flowing into permeable formation, the

fracturing fluid carrying a lot of additives and solids will firstly accumulate the most of the heavy

ingredients at the formation surface near the wellbore, then the light component called filtrate will

continue move into reservoir. Finally, the filtrate will mix with the formation water, flow deep into

the reservoir and become unrecoverable.

Another limitation of 2D models is that the height of the fracture usually needed to be presumed.

However, under the complex condition of formation geomechanics, the height will vary with time

and location during injection. The prescription of fracture height usually comes from experience

or empirical correlation, which is not accurate enough to predict the shape and propagation of

fracture network.

19

Figure 2.5: Settari’s (1985) leak-off model.

2.4 Flow within Fractures: Conceptual Models

Fractures within rock are complicated both respect to geometry and characteristics, which makes

the description of fluid flow including single phase flow and multi-phase flow difficult. In some

ways, fractures span from bulk flow for example in pipes to flows within narrow gaps with many

rock contacts that resemble more of a porous medium. For most models governing flow in

fractures, the common assumptions as follows (Wattenbarger et al. 1998). First, the flow rate

across the cross-well area of the fracture is constant. Second, the pressure across the cross-section

of the fracture is uniform. Under these two assumptions, the flow can be described one-

dimensional flow. For perfectly propped open fractures (ones with no cementation, mineralization,

20

or physical damage within the fracture), the major resistance is the flow into the rock matrix, so

that within fracture the pressure will be considered to be constant at every location at a time.

After the near wellbore region is fractured, there are different conceptual flow patterns that occur

at different times (Cinco-Ley, 1981). The first flow pattern is fracture linear flow, illustrated in

Figure 2.6, which occurs at early times just after the formation is fractured (Wattenbarger et al.

1998). In this flow regime, the pressure changes only within fracture so that the produced fluid

will be the liquid that originally resides inside the fracture. Depending on the extent of the

fractures, this period can be short relative to the production life of the reservoir.

Figure 2.6: Schematic of fracture linear flow regime.

After the pressure reduction during production has been sensed by the formation but not by the

fracture tip, there will be additional fluid flowing from the formation to the fracture. This is

conceptually represented by linear flow in the fracture and linear flow from the matrix to the

fracture as shown in Figure 2.7. These dual flows only occur under the assumption that the fracture

21

has finite conductivity. If the fracture has very high conductivity and is depleted rapidly, then the

flow within the fracture may be solely sourced from the formation as shown conceptually in Figure

2.8.

Figure 2.7: Schematic of bilinear flow regime.

Figure 2.8: Schematic of formation linear flow.

22

After the formation fluid has been produced for a sufficiently long period, the pressure change will

be felt by the near wellbore formation and the fractured near wellbore formation will appear as

effectively an expanded wellbore. The flow pattern can be approximated as the pseudo-radial flow

as depicted in Figure 2.9.

Figure 2.9: Schematic of pseudo-radial flow.

When an oil or gas formation is fractured, there are two components that contribute to flow: matrix

and fracture. A classic standpoint describes the matrix as largely the storage component of the

formation containing the majority of the reservoir fluids, and the fractures as the highly permeable

conduits that transmit the formation fluid within the reservoir (Raiga-Clemenceau et al. 1984).

Before production begins, the formation fluid is stored largely within the matrix. After production

starts, the fluid flows from the matrix to the fracture and eventually enters the wellbore. Based on

this “storage and conduit” presumption, two classic models have arisen to simulate fluid flow in

the matrix-fracture systems: one is called dual-porosity model and the other one is dual-

permeability model (Denney, 2011). The dual porosity model indicates that there exist two

overlapping media: fracture and matrix. These two media are continuous in space. The fractures

provide the main flow path, and the matrix provides the main storage region for fluid. There is no

23

flow between neighbored matrices so that the formation fluid is simply flowing from the formation

to the fracture, then moving to the wellbore. For the dual permeability model, the main difference

compared to dual porosity model is that dual permeability model allows the intersecting flow

between the neighbored matrices (Denney, 2011). When the formation has extremely low

permeability, the inter-flow between matrices can be ignored, which makes the dual porosity

accurate enough to simulate the matrix-fracture flow. Instead, the dual permeability model will be

required to accurately simulate matrix-matrix and matrix-fracture flows for some high

permeability formation.

2.5 Flow within Fractures: Numerical Models

For hydraulic fractured reservoirs, several numerical methods have evolved to model the injection

and production behavior of the system. In most cases, these models have not provided full

predictive capability and have exhibited, in some cases, severe assumptions to make the discretized

version of the governing equations solvable. The key limitations of these models are that they are

generally over simplified and are not predictive, and in some cases are not founded on rigorous

rock and fluid mechanics. In some cases, they assume 2D geometry for the fracture and solve a

lubrication equation for the flow in the fracture. Also, in most of these models, the geomechanical

models are very limited with idealized one-dimensional solution for the fracture process with linear

elastic constitutive equations for the rock.

24

Several reservoir simulators have the ability to use the dual-porosity and the dual-permeability

methods (Manual of STARSTM, 2014; Manual of EclipseTM, 2013). By using these approaches,

hydraulic fracturing can be modeled but these models have no means to include aspects of the

mechanical properties of the reservoir rock, since the fracture orientation is fixed within these

models to be aligned with the grid blocks of the reservoir simulation code. In some approaches in

the literature, the fracture part of the dual-porosity or dual-permeability model is assumed based

on the experience of the simulator and only production from the reservoir is modeled (Edwards et

al. 2013). These models face severe limitations since the dynamic fracturing process is not

modeled at all and thus they cannot be predictive. In other models, a discrete fracture network

code is used to generate a fracture network surrounding the well (Kazemi and Kurtoglu, 2012).

Then, it is converted into a dual-porosity or dual-permeability model with equivalent overall

storage and flow properties. These models are not generally predictive since the discrete fracture

network must be specified by the user. In some cases, micro-seismic data is used to guide the size

of the fracture network (Mayerhofer et al. 2010). This approach also does not take into account

any mechanical properties of the reservoir rock. Also, it is typically computationally expensive

requiring a lot of user input for interfacing between the discrete fracture network code and the

reservoir simulator.

Other models have evolved to use integrated multiphase fluid as is done in a reservoir simulator

with loose coupling with a geomechanical finite element code. The key limitation of these models

is that historically they have been devised by totally different industries with different needs. In

most cases, reservoir simulators use the finite volume approach, dividing the domain into grid

25

blocks, which is well suited to solve multiphase flow equations especially for front-like behavior

as would be seen for example in a one-dimensional Buckley-Leverett displacement of oil by water.

These solvers are capable of having complex geology integrated into their structures with variable

porosity, permeability, phase saturations, and other properties (e.g. thermal properties) assigned

on the individual grid blocks (Manual of STARSTM, 2014). On the other hand, solid mechanics

codes have typically evolved from the finite element method (Tran et al. 2005). To merge these

approaches to simultaneously solve the governing rock mechanics equations and the multiphase

flow equations is difficult and at this point, most reservoir simulation codes that integrate rock

mechanics do so by iterating between the reservoir simulator and the rock mechanics code.

Examples of these numerical models are the CMG STARSTM (Manual of STARSTM, 2014) and

Schlumberger EclipseTM (Manual of EclipseTM, 2013) reservoir codes and their geomechanics

codes. These methods tend to be extremely computationally expensive with iterations not always

converging as the flow simulator and rock mechanics solvers being used sequentially.

2.6 Stimulated Reservoir Volume, SRV Approach

Other methods that have been of interest in the literature are those that treat the fractured zone as

an equivalent porous medium with an effective permeability and porosity. These methods try to

provide an equivalent underground environment that has the same impact on the production. One

of these methods is to use LGR (Local Grid Refinement) to refine the near wellbore region and

assign new properties including permeability, porosity, compressibility, and capillary pressure to

the refined zones (Iwere, 2012). These new properties are meant to represent the average effective

26

properties of the fracture and rock properties which yield good matches to the field production

response.

Another method similar to the LGR concept is called SRV (Stimulated Reservoir Volume) method

(Mayerhofer et al. 2010). To apply the SRV method, often micro-seismic mapping data is used to

constrain the size of the SRV. Figure 2.10 shows an example of micro-seismic mapping data and

the interpretation of the data to create a potential realization of a fracture network. Inside the SRV,

uniformly distributed fractures with the same properties are added to the model. Figure 2.11 is an

example of dividing the fractured near wellbore region into several SRVs. Figure 2.12 shows a

simulated image inside a SRV where there are equivalent fractures distributed uniformly. The

equivalent fracture spacing and properties of each SRV are calibrated from the real fracture data

points within the SRV region.

27

Figure 2.10: An example of micro-seismic mapping data and the presence of the fracture network (Mayerhofer et al. 2010).

Figure 2.11: An example of seismic event that suggests the layout of SRVs surrounding the wellbore (Mayerhofer et al. 2010).

28

Figure 2.12: Simulation result of a SRV domain (Mayerhofer et al. 2010). The injection well is below the base of the image.

At this point, it remains unclear what is the best method among existing analytical and numerical

models to represent hydraulic fracturing process and how to construct truly predictive dynamic

models for this process. All models require a complete set of data that characterizes the fracture

network including geophysical data to calibrate the model. For example, Computer Modelling

Group (Manual of STARSTM, 2014) in their prescriptive hydraulic fracturing models in their black

oil model (IMEX) requires all of the dimensions of the fractured zone to model hydraulic fracturing

including the half-length, width, permeability, porosity and compressibility of fracture. However,

in the reality, this data are not always available.

2.7 Dilation-Recompaction Approaches

In the research documented in this thesis, a new dynamic simulating method using a dilation-

recompaction model is introduced and evaluated, for the first time, to model hydraulic fracturing.

The dilation-recompaction model, also referred as Beattie-Boberg model (Beattie et al. 1991), was

first developed to describe the steam fracturing process in heavy oil and oil sands reservoir under

29

Cyclic Steam Stimulation (CSS). In CSS, steam fracturing occurs since the steam injection

pressure is greater than the fracture pressure of the reservoir. The first utilization of the dilation-

recompaction model was to model the CSS operation in Esso’s Cold Lake reservoir where the

initial reservoir pressure is around 3,000 kPa, the depth of oil sands is equal to 450 m and the

reservoir fracture pressure is equal to about 9,900 kPa (Cokar et al. 2012). During steam injection,

steam was injected at pressure of 11,000-13,000 kPa which caused steam fractures to occur in the

oil sand (Cokar et al. 2012).

There is one important difference between the oil sands reservoir and tight rock formation. The

oil sands reservoir in the Cold Lake deposit is an unconsolidated oil sands formation which means

during production the fracture will close due to the compaction from pressure depletion. As for

tight rock formations, the rock is consolidated and due to the presence of the proppant that fills the

fractures, hydraulic fractures are unlikely to heal after the production is initiated. The dilation-re-

compaction model can be adjusted so that re-compaction is inhibited to reflect the placement of

proppants within the fractures.

As high pressure fluid is injected into the reservoir, fracturing will happen and cause reservoir

deformation. As a consequence of the rise of the pore pressure, the mean effective stress falls and

the pore volume will increase – this is referred to as dilation. At some point, the pore pressure is

sufficient to fracture the reservoir rock and the pore volume in the reservoir rock increases at a

relatively fast pace. After fluid injection stops, the propagation of the fractured zone stops and the

pressure falls as fluids leak into the reservoir rock. This may lead to a reduction of the pore volume

30

– this part of the process is referred to as re-compaction. The key geomechanical properties that

control the process are the formation compressibilities during each of dilation and re-compaction

(Beattie et al. 1991). For linear elastic solids, the compressibility is directly related to Young’s

modulus that higher compressibility indicates a lower Young’s modulus.

Usually the formation compressibility will increase by orders of magnitude when the formation

effective stress decreases. Some experiments indicate for consolidated sandstone formations, the

formation compressibility will be one or two orders of magnitude larger than the original value

when the effective stress drops from 1 MPa to nearly 0 MPa. In this model in steam fracturing, to

achieve the high injectivity after the fracturing or dilation pressure is reached, a larger formation

compressibility is used instead of the original one after the dilation process starts. This will also

be done for modelling hydraulic fracturing.

The quad dilation-recompaction model is described in Figure 2.13. As shown in Figure 2.13, when

fluid is injected into the formation, the pore pressure (the x-axis in Figure 2.13) starts to increase

from the initial reservoir pressure and porosity (labelled as Point a in Figure 2.13). As a

consequence the mean effective stress, defined as the difference between the overburden stress and

the pore pressure, declines and as a consequence, the porosity rises. If the changes of the pore

pressure are small, then the system acts elastically, that is in a reversible manner, meaning that if

the pore pressure was reduced, then the porosity would traverse the same trajectory as it did when

the pore pressure was increasing but now in the opposite direction. In the elastic portion of the

31

porosity response (line marked by Points a and b), the change of the porosity with pore pressure is

relatively small. The equation governing the porosity during a to b is:

∅ = ∅𝑟𝑟𝑒𝑒𝑐𝑐(𝑝𝑝−𝑝𝑝𝑟𝑟) ≈ ∅𝑟𝑟[1 + 𝑐𝑐(𝑝𝑝 − 𝑝𝑝𝑟𝑟)]... … … … … … … … … … … (2.10)

where 𝑐𝑐 is the compressibility, 𝑝𝑝𝑟𝑟 is reference pressure and ∅𝑟𝑟 is the porosity at the reference

pressure. It is known that the absolute permeability of reservoir rock depends on the porosity of

the rock – the higher the porosity, the greater the permeability. However, since the change of the

porosity during the elastic response of the system is small, so too is the permeability. The

relationship used here between the porosity, φ, and the permeability, k, is given by:

𝑘𝑘𝑘𝑘0

= 𝑒𝑒𝑘𝑘𝑚𝑚𝑚𝑚𝑚𝑚𝜙𝜙−𝜙𝜙01−𝜙𝜙0 … … … … … … … … … … … … … … … … (2.11)

where k0 is the original permeability, kmul is a multiplier that is tuned from the history match

between field production and simulation production, and φ0 is the original porosity.

At some point, as the pore pressure is raised, it reaches the fracture pressure (labelled as Point b in

Figure 2.13). Thereafter, further increase in the pore pressure due to fluid injection leads to a

profound change of the porosity – as shown in Figure 2.13, the porosity now rises according to the

line connecting Points b and c. In this part of the process, the permeability enlarges significantly

as the porosity grows.

32

Figure 2.13: The quad dilation-recompaction model (Beattie et al. 1991).

At some point of time, fluid injection stops and the pore pressure stops climbing and as a

consequence, so does the porosity. After production starts, the pressure begins to fall. In steam

fracturing processes in oil sands since the oil sand is unconsolidated, as described above, the

fracture can “heal” and as a result, the porosity of the fractured domain drops. Consequently, the

absolute permeability also falls. However, it never falls to the original values of the reservoir as

shown in Figure 2.13. In consolidated rock, the situation is quite different. Here, when hydraulic

fracturing is halted, the pore pressure may fall and there may be a small reduction of the fracture

porosity but due to the presence of the proppants and shear failure during the fracturing process

(which moves the fractured rock faces past each other), the fractures do not heal significantly and

the fractured rock state is largely preserved with its elevated porosity and absolute permeability.

Thus, the lines connecting Points c, d and e, for consolidated rock, would be nearly horizontal.

33

2.8 What is missing in the literature?

The key capability that is missing in the literature is a relatively rapid dynamic fracturing model

that can be directly used in multiphase reservoir simulators that account for phase behavior and

heterogeneity of the reservoir geology. There is a need for relatively simple models that can

incorporate heterogeneity of both geological and mechanical rock properties. In the research

documented here, the formation of interest is the Cardium Formation. The dilation-recompaction

model will be applied and evaluated in a reservoir simulation model developed for the Cardium

formation for the first time.

2.9 What are the limitations of dilation recompaction model?

Although the dilation recompaction model is able to rapidly create a fractured zone and have a

similar equivalent impact on oil and gas production, there are still limitations. Firstly, this model

provides a fractured zone rather than creating actual fractures, so that this model is not capable of

simulating individual fractures. And, different fluid flow models cannot be applied to different

flow system (flow within fracture and flow within matrix). Secondly, as to different simulators,

the shape of fractured zone may be altered with the change of grid size. At last, since the dilation

recompaction model does not take state of tresses of formation rock into consideration, so that the

model is not able to predict the propagation of fractures.

34

Chapter Three: Case Study of Dilation Recompaction Model in the Cardium Formation

3.1 Introduction

The formation selected as the research target in this thesis is the Cardium Formation. This

formation is located in the center area of the Province of Alberta and stretches from the Northwest

to the Southeast. It overlies the Blackstone Formation and is overlain by the Wapiabi Formation.

The map of Cardium formation is shown in Figure 3.1.

The Cardium formation was deposited during the late Cretaceous age in the Western Canada

Sedimentary Basin and is divided into Pembina and Cardium zones. The lithology in Cardium

Formation is mainly fine-grained sandstone separated by shale layers. Typical sandstone members

in the Cardium Formation include the Sturrock Member, Cardinal Member, and Ram Member.

There are some shale layers separating the sand stone members, for instance the Leyland shale

layer, Kiska shale layer, and Moosehound shale layer.

The Pembina zone of the Cardium formation has the longer exploration history with respect to oil

and gas than that of Cardium zone. Natural gas was produced from the Pembina zone since 1953

and then light oil production was started. After oil and gas companies enlarged the area of

exploration, the vast amount of oil resource in Cardium zone, estimated at 7,780 MMbbls (Ghaderi

et al. 2011), was unlocked. In the Cardium zone, the lithology is more muddy sandstones than fine-

grained sandstone, which leads to a low permeability in the tenths of millidarcy and the porosity

35

is from 4 to 12%. The reservoir in Cardium zone consists of many sand-filled trace fossils, thin

shale barriers, and other complex facies, which leads to high heterogeneity of the reservoir. The

area selected as the basis for building the geological model is the Harmattan Cardium pool with

location shown in Figure 3.2.

Figure 3.1: Map of the Cardium Formation (Duhault, 2012).

36

Figure 3.2: Location of the Harmattan Pool (Angle, 2013).

3.2 Description of Geological and Reservoir Simulation Models

The Schlumberger Petrel geological modelling software package was used to construct the

geological model. Well logs from 9 vertical wells in Cardium formation were interpreted to obtain

reservoir porosity and fluid saturation, 3 examples out of 9 logs are shown in Figure 3.3. Also, to

finalize the domain beyond the reservoir model, 437 wells were used to determine the top and

bottom surfaces of the Cardium Formation. This represents a significant amount of data to

constrain the geological model.

37

Figure 3.3: Three examples of Logs used to construct geological model (Accumap, 2014).

38

Figures 3.4 and 3.5 display the contour maps of the top and bottom surfaces of the Cardium

Formation, where each black curve is an isobaths representing one formation top that at the same

depth. And there are too many different depths to show so that only isobaths are shown in map.

The contour map shows that the Cardium Formation in the area of interest has a North-South

channel. From an analysis of the formation tops in Cardium, the average depth of the Cardium

formation is equal to about 1,960 m and the average thickness of the unit is equal to about 10 m.

Figure 3.5 also shows the locations of horizontal wells within the area of interest.

Figure 3.4: Contour map of the top of the Cardium Formation.

39

Figure 3.5: Contour map of the bottom of the Cardium Formation.

For constructing the permeability distribution in the geological model, the core data from three

wells were examined and a correlation between permeability and porosity was fitted to the data

points displayed in Figure 3.6. In Figure 3.6, the green triangle points are data from core samples.

A log-linear permeability-porosity transform was fitted to the core sample data.

40

Figure 3.6: Porosity and Permeability Correlation obtained from core data.

There are three different area sizes: the data collection area (consisting of the 437 wells in total for

tops and 9 wells for logs), the geological model area, and the reservoir simulation model area

which are all displayed in Figure 3.7. The extent of the area used in the geological model is equal

to about 4.8 km by about 5.2 km. The number of grid blocks in each direction used in the geological

model is equal to 479 in the East-West direction, 519 in the North-South direction, and 44 in the

vertical direction. In total, the geological model consists of 10,938,444 grid blocks. The

dimensions of the grid blocks in the geological model were equal to 10 m in the horizontal

directions and 0.5 m in the vertical direction.

41

Figure 3.7: Description of different areas used to create the reservoir simulation model

(Accumap, 2014).

The porosity obtained from the logs was used to populate the porosity within geological model.

The population of the porosity within the geological model was accomplished by using sequential

Gaussian method (Manual of EclipseTM, 2013). For this work, a single geological model was

constructed; it is shown in Figure 3.8.

42

Figure 3.8: Porosity of the geological model (vertical to horizontal aspect ratio is 1:1 and legend is from 0 to 0.08 with a color scale of 0.01)

The porosity-permeability transform described by the equation inset in Figure 3.6 was then used

to populate the absolute horizontal permeability distribution within the geological model; the

distribution of the absolute horizontal permeability is displayed in Figure 3.9. It is not possible to

obtain reliable oil saturation values for the reservoir from log and core data. Based on the data

43

available from Accumap, the oil saturation was set equal to 0.8. The remaining fluid within the

formation is entirely water, in other words, there is no free gas zones within the formation.

Figure 3.9: Absolute permeability of the geological model (vertical to horizontal aspect ratio is 1:1).

44

As shown in Figure 3.7, the reservoir model area is extracted from the larger geological model

area; this prevents boundary effects that might occur. The dimensions of the reservoir simulation

model are equal to about 2 km in the East-West direction by about 2 km in the North-South

direction. The number of grid blocks in the reservoir simulation model is equal to 202 in the East-

West direction, 202 in the North-South Direction, and 25 in the vertical direction. This gives a

total number of grid blocks equal to 1,020,100. Figures 3.10 and 3.11 display the distributions of

the porosity and the permeability within the reservoir simulation model. The average porosity and

permeability of the domain is equal to 0.0622 and 0.219 mD, respectively. The ratio of vertical

permeability to horizontal permeability is 0.5. The locations of the three wells are also displayed.

Figure 3.10: Distribution of porosity in the reservoir simulation model (vertical to horizontal aspect ratio is 24:1).

45

Figure 3.11: Distribution of horizontal permeability in the reservoir simulation model (vertical to horizontal aspect ratio is 24:1).

For the reservoir simulation model, the reservoir pressure at a depth equal to 1,940 m was taken to

be equal to 17,848 kPa. The pressure distribution for the remainder of the model was determined

from hydrostatic pressure. The temperature of the formation was taken to be 61°C. In the

simulation, the temperature is maintained constant at the initial value of the temperature (the

ISOTHERMAL option was used in the reservoir simulator). Table 3.1 lists other input parameters

used in the reservoir simulation model. The compressibility controlling the elastic compaction line

is set to nearly zero to make the elastic compaction line nearly horizontal.

46

Table 3.1: Parameters used in reservoir simulation model (the parameters A and B are defined in Figure 2.13).

Variable Value

Initial Reservoir Pressure, kPa (at a depth equal to 1,940 m) 17,848 Compressibility for Elastic Compaction, 1/kPa 0.00000001 Compressibility for Dilation, 1/kPa 0.01 Residual Dilation Fraction, B/A 1 Maximum Percentage of Increase in Porosity 20 Fracture Pressure, kPa 35,000 Recompaction Pressure, kPa 200 Permeability Multipliers (in both horizontal and vertical directions) 200 Ratio of Vertical Permeability to Horizontal Permeability 0.5

3.3 Fluid and Rock Properties

The CMG reservoir simulator STARSTM was used for the research documented here. The

properties for water, both formation water and injection water, were taken from the internal

database within the CMG STARSTM reservoir simulator. The density of the oils was taken to be

equal to 834 kg/m3. A two oil component model is used to represent the oil phase: the first

component is the dead oil (oil without solution gas) and the second component is the solution gas

(represented by methane).

Even though the operation of the process at reservoir condition is considered isothermal, the

reservoir simulator requires viscosity data versus temperature. The viscosity versus temperature

data is shown in Figure 3.12. The live oil viscosity in the model was determined by using the log-

linear viscosity-mole fraction mixing rule (Manual of STARSTM, 2014):

47

ln µmix = xdead oil ln µdead oil + xsolution gas ln µsolution gas (3.1)

where µmix is the live oil viscosity, µdead oil is the dead oil viscosity (given by the correlation

displayed in Figure 3.12), µsolution gas is the liquid-equivalent solution gas viscosity, xsolution gas is the

mole fraction of solution gas in the oil phase.

Figure 3.12: Correlation between oil viscosity and temperature.

The solubility of solution-gas in oil was determined by a standard correlation for methane

solubility obtained from the reservoir simulation user’s manual (Manual of STARSTM, 2014):

48

𝑦𝑦𝑠𝑠𝑠𝑠𝑚𝑚𝑚𝑚𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑔𝑔𝑔𝑔𝑠𝑠

𝑥𝑥𝑠𝑠𝑠𝑠𝑚𝑚𝑚𝑚𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑔𝑔𝑔𝑔𝑠𝑠= K-value = �𝑘𝑘𝑣𝑣1

𝑃𝑃+ 𝑘𝑘𝑣𝑣2𝑃𝑃 + 𝑘𝑘𝑣𝑣3� 𝑒𝑒

𝑘𝑘𝑣𝑣4𝑇𝑇−𝑘𝑘𝑣𝑣5 (3.2)

where ysolution gas is the mole fraction of solution gas in the gas phase (equal to nearly one except

for the small amount of water vapour that would exist in the vapour phase due to thermodynamic

equilibrium), P is the absolute total pressure, and T is the temperature. The values of the

coefficients kv1, kv2, kv3, kv4, and kv5 are 56187.5 kPa, -0.00314675 kPa-1, 60.8839, -879.991°C, and

-265.99°C, respectively. The K-value correlation provides the relationship between the gas mole

fraction in the vapour phase versus that in the oil phase. The solubility of the solution gas in

formation and injected water was ignored.

Figure 3.13 displays the oil-water relative permeability curves used in the model. The end points

of the model were tuned to achieve the history match. Given the tightness of the reservoir rock,

the irreducible oil saturation with respect to water is equal to 0.4. The connate water saturation is

equal to 0.25. The liquid-gas relative permeability curves are displayed in Figure 3.14. The end

points of the liquid-gas curves was tuned to achieve the history match. The irreducible gas

saturation was found to be equal to 0.05.

49

Figure 3.13: Oil-water relative permeability curves.

Figure 3.14: Liquid-gas relative permeability curves.

0.00

0.20

0.40

0.60

0.80

1.00

Oil

and

Wat

er R

elat

ive

Per

mea

bilit

y

0.00 0.20 0.40 0.60 0.80 1.00Water Saturation

0.00

0.20

0.40

0.60

0.80

1.00

Liqu

id a

nd G

as R

elat

ive

Per

mea

bilit

y

0.00 0.20 0.40 0.60 0.80 1.00Liquid Saturation

50

Figure 3.15 displays the three-phase relative permeability ternary diagram for the oil phase. The

Stone 2 model was used to calculate the oil phase relative permeability. In this model, the water

and gas relative permeability are calculated from the two-phase curves. The diagram demonstrates

that the mobile region for the oil phase is relatively small. This is due to the tightness of the

reservoir rock.

Based on the literature research on Cardium formation, the compressibility of 2.2E-6 at the initial

reservoir condition (Clarkson and Pedersen, 2011) is used in the model.

Figure 3.15: Three phase relative permeability ternary diagram.

Kro by Stone #2 Model, SWSG

Sgas=1.00

Swater=1.00 Soil=1.00

0.00001

0.00003

0.00010

0.00032

0.00100

0.00316

0.01000

0.03162

0.10000

0.31623

1.00000

51

3.4 Well Completion and History Match of Production

Within the reservoir simulation model area, there are three wells (Well-1, Well-2, and Well-3)

coming with complete well trajectory, well completion and operation data. Figure 3.16 shows the

three wells. Well-1 is selected as the target well to do the history match. Well-1 is a horizontal

well at the depth equal to 1940 meters, the horizontal section is 1800 meters. Well-1 is completed

with 28 stages of hydraulic fracturing, each stage equally spaced along the length of the horizontal

well. According to the field data, about 143 m3 of fluid and ten tons of proppants were injected per

stage, which lead to the total amount of approximately 4000 m3 fluid and 280 tons proppants for

Well-1.

During hydraulic fracturing, Well-1 is operated under a constant injection pressure constraint of

80,000 kPa. Since a solid component cannot be injected through a well in the STARSTM reservoir

simulator, the volume of injected proppants will be added to the volume of injected water to get

the total injected volume. The volume of injected proppants is approximately 100 m3 (density of

sand as 2650 kg/ m3 is used to calculate the volume of injected proppants), so that about 4100 m3

of fluids were injected for Well-1 in the reservoir simulation model. In the model, Well-1 is called

“I1” during injection and named “P1” during production (both located at the same location). To

reflect the behaviour of the injected proppants as the well is fractured, as described above, the

fracture is not permitted to close when pore pressure decreases during production, which indicates

the recompaction line of the quad model is modified to horizontal. Thus, the hydraulically created

fractures remain open in the model after the fracture job is finished.

52

There are two key elements of the history match completed here. Firstly, the inputs of dilation

recompaction model including permeability multipliers, compressibility during dilation which is

controlling the time needed to inject 4100 m3 fluids and maximum percentage allowed to increase

in porosity are significant. These parameters are required to enable sufficient connectivity and

conductivity for formation to achieve the same peak rates as field data. And the other element is

the relative permeability curves controlling the oil and gas rates during the post-production.

Because the history production file does not include the water production during the flow-back

(the main water production after the hydraulic fracturing operation is from flow-back period), the

history match for water rate is not as essential as that for the oil and gas rates in this research. The

two elements mentioned above are not independent – the extent and enhanced permeability of the

hydraulically fractured zone around the well places a strict constraint on the ability of the reservoir

to deliver fluids to the well (and to surface). Also the relative flow of oil and water from the

hydraulically fractured zone and the adjacent connected reservoir controls the production rate.

After the hydraulic fracturing operation is completed, Well-1 is put on production. According to

the field data, the operational bottom-hole pressure for Well-1 during production is between 2,500

kPa and 4,000 kPa.

In the field operation, after about seven months of production, Well-2 which is closely adjacent to

the Well-1 started hydraulic fracturing operations and then was put into production. The well

spacing between Well-1 and Well-2 is from 200 meters to 350 meters and the permeability of

53

formation is about 0.2 mD which indicates is a relatively more permeable reservoir than typical

tight formation, so that it is reasonable to believe the injection in well-2 will affect the reservoir

condition of well-1. In the reservoir simulation model, the bottom-hole pressure for Well-1 is set

constant of 3000 kPa during production.

The first step is to history match oil production and gas production of Well-1. If the oil and gas

production can be reasonably history matched, it implies that the hydraulic fracturing job and

relative flow of oil and gas in the connected zone is reasonably well represented in the model.

Figure 3.16: Well trajectories of Well-1, Well-2 and Well-3 (vertical to horizontal aspect ratio is 24:1).

54

3.5 Results

3.5.1 Case 1: Production history match of Well-1 with hydraulic fracturing

To achieve the history match, firstly, the relative permeability curves, with the results displayed in

Figures 3.13 and 3.14, were tuned using the model without hydraulic fracturing which is shown in

the next section as case 2. And the purpose is to match the post production so that the tuned relative

permeability curves can well represent the relative fluids flow within matrix. Secondly, by

matching the injection including injecting time and total injected volume, the compressibility

during dilation can be tuned. At last, using the model with hydraulic fracturing operation, the

permeability multipliers can be tuned through history matching the production at the beginning.

Figures 3.17 and 3.18 display the daily oil rate verses time and cumulative oil production,

respectively. From the plots, we can see the oil rate is well matched and although the cumulative

oil production is about seven percent less than the history file at the beginning but it is still

considered to be a reasonable match. The notable features about the history match are the peak oil

rate, the decline rate of the oil rate, and the asymptote. The hydraulic fracturing operation is

expected to affect the early behaviour of the well and the flow from the matrix to the fractures is

expected to dominate the later time behaviour of the well. The results demonstrate that both the

early and later time behaviours are well matched and thus, the reservoir model is providing a

reasonable response to the hydraulic fracturing operating as well as the matrix response.

55

Figure 3.17: History match of Well-1’s daily oil rate.

Figure 3.18: History match of Well-1’s cumulative oil production.

56

Figures 3.19 and 3.20 show the daily gas rate verses time and the cumulative gas production,

respectively. From the plots, the gas rate is well matched until the time of June 2012 when the

adjacent Well-2 was hydraulically fractured. After injection, the formation pressure surround

Well-1 has been increased and another gas rate peak occurs. But due to pressure depletion, the gas

rate rapidly decrease to the value close to that before Well-2 injection started. The long term gas

production rate after June 2012 of Well-1 is generally fifty percent less than that of the field data.

This is most likely because of the interference effect of the hydraulic fracturing of Well-2. But in

consideration of the fair match between the gas rate of Well-1 and field data before June 2012, and

the fact of the injection of Well-2 in June 2012, the history match of daily gas rate and cumulative

gas production are considered to be reasonable. The reservoir simulation result is an indication of

the gas rate had Well-2 not been hydraulically fractured. The results suggest that the gas rate is

more sensitive to the pressure change induced by injection at Well-2 than the oil rate. From Figure

3.17, at the time of June 2012, we can see a small increase of oil rate, although the increase

percentage cannot be comparable of that for gas rate, it is still an indication of pressurization at

that time.

57

Figure 3.19: History match of Well-1’s daily gas rate.

Figure 3.20: History match of Well-1’s cumulative gas production.

58

Figures 3.21 and 3.22 show the daily water rate from full view and zoom in view, and Figure 23

shows the cumulative water production, respectively. As mentioned above, the field water

production data does not include the water production during flow back period in which some of

the injected fluid will be produced. The difference between cumulative water production of Well-

1 and that of field data occurs at the beginning of production, which is consistent with the fact that

the water production field data does not include the amount of water that is produced during the

flow back period. If this water, roughly 20% of the water injected during the fracturing operation,

is added to the field data with flow back occurring in the few days after hydraulic fracturing, then

the match is quite reasonable. Figure 3.22 presents a zoomed-in view of the water production rate

data. In terms of long term water rate, it is still fairly to be considered as a reasonable match. The

secondary water rate peak is observed in Figure 3.22 in June 2012 which is consistent with the

observations from oil production and gas production.

The cumulative water produced plotted in Figure 3.23 demonstrates that the match is reasonable

with a similar shape between the field data and that of the reservoir simulation model. The step

event in June 2012 corresponds to the onset of hydraulic fracturing in Well-2. The reveal that

during the production interval, the volume of water produced from the reservoir is relatively small

compared to the oil and gas volumes.

59

Figure 3.21: History match of Well-1’s daily water production rate.

Figure 3.22: History match of Well-1’s daily water production rate (zoomed in view).

60

Figure 3.23: History match of Well-1’s cumulative water production.

Figure 3.24 displays the comparison of the production gas-to-oil ratio (pGOR) between the field

data and reservoir simulation data for Well-1. The results show that the match is reasonable until

injection is started in Well-2. The match is considered quite reasonable. Even though there is

some scatter of the field pGOR data, the reservoir simulation data is a reasonable match to the field

data prior to the hydraulic fracturing operation at Well-2. After Well-2 is fractured, due to the

level production of gas from Well-1, the pGOR starts to rise. The results suggest that if Well-2

had not been fractured, then the pGOR would have followed the trend indicated by the reservoir

simulation results in Figure 3.24.

61

Figure 3.24: History match of Well-1’s production gas-to-oil ratio.

3.5.2 Case 2: Production history match of Well-1 without hydraulic fracturing

In this Subsection, the impact of hydraulic fracturing is evaluated by using the history-matched

reservoir simulation model. Figures 3.25 and 3.26 display the daily oil rate verses time and

cumulative oil production, respectively, for the case where no hydraulic fracturing is done in the

reservoir model. From the plots, the results demonstrate that the peak oil rate and early time

response of the reservoir model with respect to oil production does not provide a good match with

the field data when the reservoir is not hydraulically fractured. However, the later time response

of the reservoir is well-matched. This is consistent with the idea that the late time behaviour of

62

the system represents the response of the matrix to production. The only parameters that were

tuned that would impact the matrix are the end points on the relative permeability curves. Thus,

the late time match of the behaviour displayed in Figure 3.25 as well as the match of the late time

behaviour for the case with hydraulic fracturing, shown in Figure 3.17, reveals that the matrix flow

response is reasonably represented by the model.

Figure 3.25: Prediction of Well-1’s daily oil rate without hydraulic fracturing.

63

Figure 3.26: Prediction of Well-1’s cumulative oil production without hydraulic fracturing.

Figures 3.27 and 3.28 show the daily gas rate verses time and the cumulative gas production,

respectively. The data shows that hydraulic fracturing is required to match the production data.

Figures 3.29 and 3.30 display the daily water rate verses time and cumulative water production,

respectively, for the case with no hydraulic fracturing operation. The field data file used here does

not include the water production from flow back period since there is no flow back because the

hydraulic fracturing job was not done. The results show that the water rate is nearly equal to zero

without hydraulic fracturing.

64

Figure 3.27: Prediction of Well-1’s daily gas rate without hydraulic fracturing.

Figure 3.28: Prediction of Well-1’s cumulative gas production without hydraulic

fracturing.

65

Figure 3.29: Prediction of Well-1’s daily water rate without hydraulic fracturing.

Figure 3.30: Prediction of Well-1’s cumulative gas production without hydraulic

fracturing.

66

3.6 Fractured Zone of Well-1

In this Section, the three-dimensional results from the history-matched reservoir simulation model

are examined to show the fractured zone around the wellbore. Well-1 was completed with 28

stages. Figures 3.31 and 3.32 display the horizontal permeability evolution surrounding Well-1

after 2,050 and 4,100 m3 of fluid injection during the hydraulic fracturing operation. The original

horizontal permeability of the formation averages about 0.219 mD. The results reveal that the

permeability of fractured zone increases with the increase of total injection volume. The size of

fractured zone increases with larger injected volume. The length of the fractured zone (cross-well)

is about 60 m.

In the dilation-recompaction model, the fractured rock is represented as a continuum with

enhanced permeability. In other words, the enhanced permeability of the fractured zone represents

the combined effects of the fracture network and the matrix in the dilated volume. The fractured

zone permeability reaches as high as 15 mD. This demonstrates a significant enhancement of the

fractured zone permeability from that of its original matrix permeability due to the hydraulic

fracturing operation.

67

Figure 3.31: Horizontal permeability in unit of mD after injecting 2050 m3 (vertical-to-horizontal aspect ratio equal to 0.5).

Figure 3.32: Horizontal permeability in unit of mD after injecting 4100 m3 (vertical-to-horizontal aspect ratio equal to 0.5).

68

Figures 3.33 and 3.34 display the formation pressure after hydraulic fracturing operation after 2050

m3 of injected fluid and 4100 m3 of injected fluid. The results show in the near well region, the

reservoir rock is fractured at just above 35 MPa. During the hydraulic fracturing, the pressure

climbs up to about 77 MPa especially directly at the perforation. At the edges of the fractured

zone, the pressure is at 36 MPa. After fracturing happens, the porosity of the reservoir rock

increases and as a consequence, the pressure falls slightly. With further injection, the pressure

rises.

Figure 3.33: Pressure in unit of kPa after hydraulic fracturing with 2050 m3 of fluid

injected (vertical-to-horizontal aspect ratio equal to 0.5).

69

Figure 3.34: Pressure in unit of kPa after hydraulic fracturing with 4100 m3 of fluid

injected (vertical-to-horizontal aspect ratio equal to 0.5).

Figures 3.35 to 3.38 display the evolution of the porosity, horizontal permeability, pressure, and

oil saturation, respectively, during the hydraulic fracturing operation. The results show that as the

hydraulic fracturing occurs, the porosity grows to as high as 0.08. The fractured zone (marked by

the yellow, orange, and red region in the reservoir) is roughly elliptical in shape. The evolution of

the horizontal permeabilty, displayed in Figure 3.36, shows that the permeability increases

significantly as the fluid is injected into reservoir. The shape of the dilated zone is elliptical but

then grows to a 60 m wide fractured zone surrounding the well. And the height of fractured zone

is about 8 meters. The area with the greatest dilation is in the near well region whereas at the edges

there is a decline from the highly dilated region to the original reservoir permeability. The pressure

distribution, displayed in Figure 3.37, shows how the pressure builds up and reaches the fracture

pressure of the reservoir. In the perforation, the pressure can reaches as high as 77,000 kPa, then

reduces to 36,000 kPa which is slightly above fracture pressure as the injected fluids propagating

70

towards the edge of fractured zone. And due to the presence of shale layer on both top and bottom

of the payzone, the permeability of the shale layers are set to zero so that the injected fluids will

not be able to propagate beyond the payzone. Figure 3.38 shows the evolution of the oil saturation

in the reservoir as it is fractured, As the fracture fluid is injected into the reservoir, it fills the

region which is dilated and since it raises the porosity (which nearly doubles), the injected water

fills in the newly created pore space, As a consequence, the oil saturation in the dilated region

drops due to the presence of the added water in the newly created pore space. Typically in cardium

formatoin, at depth of 2,000 m, the maximum stress of rock is at vertical direction, so that the

propagation of fracture should be vertical (McLennan et al. 1983). Hwoever, the fractured zone

shown in Figure 3.36 appears to be horizontal propagation. One reason is that in this reservoir

model, since the geomachanical properties especially the state of tresses are not considered, the

propagatation of fracture will be controlled by formation permeability. Because the vertical

permeability is half of the horizontal permeability, the propagation of the fracture network will be

faster at horizontal direction than at vertical direction. However, there are confinements for the

payzone. The permeability of top layer and bottom layer of the payzone is set to be zero due to the

presence of shale layers. So that in reality, although the fracture may propagate vertically at first,

it will reach top and bottom quickly since the payzone thickness is only 8 meters, then the fracture

will propagate horizontally to ultimately create a similar fractured zone as that created by

simulator.

71

Initial Porosity

After 1025 m3 injection




Figure 3.35: Cross-well view of the porosity evolution at the 6th stage during hydraulic


72

Initial Horizontal Permeability





Figure 3.36: Cross-well view of the horizontal permeability evolution at the 6th stage during

hydraulic fracturing operation (Permeability is in unit of mD).

73

Initial Pressure





Figure 3.37: Cross-well view of the pressure evolution at the 6th stage during hydraulic

fracturing operation (Pressure is in unit of kPa).

74

Initial Oil Saturation





Figure 3.38: Cross-well view of the oil saturation evolution at the 6th stage during hydraulic


75

Figure 3.39 displays the oil saturation distributions during the production period. The results show

that the oil saturation changes mainly in the region surround in the fracture zone. The oil saturation

distribution within the fractured zone does not change significantly. This does not indicate that oil

is not moving – rather the opposite. As the pressure falls on production, initially, oil is produced

from the fractured zone. The results shown in Figure 3.39 show that the deeper green region

shrinks – this is because of the oil flowing from the fractured zone to the well – thus the oil

saturation increases by a slight amount. The water in the zone, since a lot of it is below the

irreducible water saturation from the relative permeability curve, remains in the reservoir and thus

the oil saturation changes are subtle.

At later times (say beyond about 30 days), the outer contour of the oil saturation shown in Figure

3.39 is seen moving outwards from the fractured zone. This indicates the movement of oil from

the matrix beyond the fractured zone to the fractured zone which is then moved to the well and

produced to surface. This confirms the role of the matrix oil in the production process. Since the

pressure falls and the driving force for oil flow from the region beyond the fractured zone to the

fractured zone and to the well drops, the well rate eventually declines. However, the oil production

rates suggest that there is sufficient drive, from solution-gas induced displacement, to move oil

from the reservoir to the well. The results suggest an interesting dynamic behaviour for the

fractured rock and the interaction of the matrix beyond the fractured zone. In early times the

fractured zone yield the majority of production but in later times the matrix is the main contributor.

Since the fractured zone is a reduced pressure zone, the matrix continually supplies oil to it.

76

After 3 days of production





Figure 3.39: Cross-well view of the oil saturation at the 6th stage evolution after hydraulic fracturing operation.

77

3.7 Discussions

According to the inputs and results obtained from previous sections, for one stage, the total length

of fractured zone is 60 m, the height is 8 m and the width is 60 m which is equal to the length of a

stage. These numbers will give a total volume of 2,880 m3 for fractured zone surrounding one

stage. And given that 143 m3 of injected fluids for one stage, the formation volume being fractured

per unit of injected volume can be calculated as approximately 20 m3/ m3. This value gives us a

roughly estimate on how much fractured volume can be created by injecting 1 m3 of fluid into this

type of formation. It is can be expected that this value varies in formations with different

underground conditions and also changes with operation constraints, which will be shown in the

comparison with the value from another formation. Hoodley formation is a typical tight gas

formation with initial porosity of 15%, the initial permeability is about 0.07 mD, the total injectd

volume for one stage is 185 m3 and the injection bottom pressure is around 40 MPa during

hydraulic fracturing operation (Maulianda, 2015). The total length of fractured zone is 174 m and

the width is 60 m (Maulianda, 2015). The payzone thickness is about 6 m (Maulianda, 2015), so

that the total volume for fractured zone is approximately 62,640 m3. Then we can use the same

procedure to calculate the formation volume being fractured per unit of injected volume. The result

is 339 m3/ m3, which is higher than that from Cardium formation.

Since the fractured zone created by dilation recompaction model is not actually containing induced

fractures, it is interesting to back calculate the fracture spacing within the fractured zone. After

hydraulic fracturing, the average enhanced permeability within fractured zone is about 13 mD.

78

Then the equations 2.2 and 2.3 in Chapter 2 can be used to calculate fracture spacing using the

assumption that the aperture of a single fracture is 0.008 inch (0.2032 mm). The calculated result

is that the fracture spacing is about 54 m, which is nearly equal to the distance between the mid-

points of two neighbor stages.

3.8 Conclusions

The match between the reservoir simulation results using the dilation-recompaction hydraulic

fracturing model and field data for Well-1 regarding on oil, gas, water, and gas-to-oil ratio is

reasonable and demonstrates that the dilation-recompaction model is capable of providing a simple

and realistic model to represent hydraulic fracturing within the reservoir. The model is simple to

calibrate and provides a model where geomechanical properties of the reservoir, in the form of the

compressibility, are used to calibrate the model. The extent of the fractured zone, as predicted by

the dilation-recompaction model, is reasonable and compares well with expected fracture widths

from field operations and demonstrates that the model can provide insight into the nature of the

fractured zone in the reservoir.

79

Chapter Four: Impact of Hydraulic Fracturing Design on Production

4.1 Introduction

Even though hydraulic fracturing operation is a widely used technology to enhance production

from tight rock reservoirs, optimization of the number of stages and size of the injected fluid per

stage. However, the design and optimization of this process is not simple because of the many

variables involved in the system. The history matched model documented in Chapter 3 provides

a reasonable representation of the fracturing process in that the oil, water, and gas rates are well

matched to the field data as well as the extent of the fractured zone are within the expected fracture

zone extent. This model can be used to optimize the design of the hydraulic fracturing operation.

Here, the two key variables that will be evaluated are the number of stages assuming each stage

has the same length of 60 meters and the total inject volume for hydraulic fracturing job. For Well-

1, as described in Chapter 3, the number of stages was equal to 28 and the total injected volume

(for all of the stages) was equal to 4100 m3. In the history-matched model, the stages are equally

spaced along the horizontal well. Five scenarios are evaluated here as follows.

Scenario 1: 14 stages with total injected volume (for all stages) equal to 4100 m3.





80

In all scenarios, the stages are equally spaced along the horizontal well.

4.2 Model Description

The base case model used in the research documented in this Chapter is the history-matched model

described in detail in Chapter 3.

4.3 Results and Discussion

4.3.1 Scenario 1

In this scenario, 14 stages are completed in Well-1 and the total injected volume remains is equal

to 4100 m3. Figure 4.1 displays the daily oil rate verses time and cumulative oil production for

Scenario 1 and history-matched model. In Scenario 1, the peak oil rate drops by about 26% from

that of the matched model but beyond the initial few months of production, the oil rates are very

similar. The cumulative oil production volume profile reveals that the oil volume drops by about

6% after 2 year of production. The results show that despite the reduction of the number of stages,

since the total volume of fluid injected was the same, the oil rate profile is very similar. Figure

4.2 show the daily gas rate verses time and the cumulative gas production. Similar to the oil

profiles, the peak gas rate in Scenario 1 is reduced form that of the history-matched model (by

about 22%) which leads to a drop of about 6% of the cumulative volume of gas. Figure 4.3 displays

81

the daily water rate and cumulative water production for Scenario 1 and the history-matched

model. Similar to the oil and gas rates, the water profiles are reduced.

Figure 4.1: Oil rate and cumulative oil production profiles for Scenario 1 and the history-matched model.

Figure 4.2: Gas rate and cumulative gas production profiles for Scenario 1 and the history-matched model.

82

Figure 4.3: Water rate and cumulative water production profiles for Scenario 1 and the history-matched model.

4.3.2 Scenario 2

In this scenario, 14 stages are completed in the well with a total injected volume equal to 8200 m3.

Figure 4.4 shows the daily oil rate verses time and cumulative oil production comparing the

Scenario 2 and history-matched model. Figure 4.5 shows the daily gas rate verses time and

cumulative gas production. The results show that the oil and gas rates and cumulative volumes are

very similar. Figure 4.6 shows the daily water rate and cumulative water production for Scenario

2. The plots show that the water production rate from the reservoir is greater than that of the

history-matched model. This is because the total amount of water injected into the reservoir was

doubled during the hydraulic fracturing operation.

83



84


4.3.3 Scenario 3

In Scenario 3, the well is completed with 28 stages with the total injected volume reduced to 2050

m3. Figure 4.7 displays the daily oil rate verses time and cumulative oil production. The results

shows up to 38% reduction of oil rate at the earl production period but that the rates merge within

a few months. As a result, the cumulative oil produced is reduced by about 13% from that of the

history-matched model. This result is expected since the total amount of fracture fluid injected

into the reservoir was half that of the history-matched model. However, although an economic

analysis has not been done here, the process only suffered a 13% reduction in produced oil volume

versus a 50% reduction in the fracture fluid injection. Figure 4.8 shows the daily gas rate verses

time and cumulative gas production for Scenario 3 and the history-matched model. The results are

similar to the oil profiles – the cumulative gas produced from Scenario 3 is 11% lower than that

of the history-matched model. Figure 4.9 presents the daily water rate and cumulative water

85

production. The obvious observation is that the peak water production rate and cumulative

production volume is significantly reduced because of the reduction of the total fracture fluid

injection volume.



86


4.3.4 Scenario 4

In this scenario, the well is completed with 28 stages with a total fracture fluid injection volume

equal to 8200 m3. Figure 4.10 display the daily oil rate verses time and cumulative oil production

between Scenario 4 and that of the history-matched model. The resulst show that the early period

production rate is increased as a result, the incremental oil volume produced after two years is

equal to about 6% after 2 years of operation. The later time behaviour is eseentially the same

which is suggests that the matrix response from the system is similar in both cases. The gas rate

and cumulative volume, displayed in Figure 4.11, show a similar trend with 9% additional gas

after two years of production. Compared to 100% increase in the total injected fracture fluid

volume, the increase of the oil and gas rates and cumulative oil and gas production volumes for

Scenario 4 is minor which suggests that the efficiency of injecting more fluid to fracture formation

87

may have a limit. Figure 4.12 shows the daily water rate verses time and cumulative water

production for the two cases. The obvious observation is that, because of the doubling on total

injected fracture fluid volume, the peak water rate and cumulative water production of Scenario 4

are much larger than those of history-matched model.



88


4.3.5 Scenario 5

In Scenario 5, the well is completed with 7 stages with total injected fracture fluid volume equal

to 4100 m3. Figure 4.13 displays the daily oil rate verses time and cumulative oil production for

Scenario 5 and the history-matched model. The results show that the peak oil rate drops by 33%

and that the cumulative oil produced after two years of operation reduces by 15%. Figure 4.14

compares the daily gas rate verses time and cumulative gas production for the two cases. Similar

to the oil profiles, the peak gas rate of Scenario 5 is about 33% less than that of history-match

model and the cumulative gas production drops by about 13%. Figure 4.15 compares the daily

water rate verses time and cumulative water production. The results show that the peak water rate

of Scenario 5 is about 55% of that of the history-matched model because of the reduction on the

number of stage which shrinks the well interval through which the water can be produced. The

cumulative water production of Scenario 5 is about 50% of that of the history-matched model.

89



90


4.4 Conclusions

The results show that the lower the number of stages in the fracture operation, the smaller are the

oil and gas rates and the cumulative volumes produced. A reduction of the number of stages to

one-half and one-quarter of the history-matched model at constant total volume of fracture fluid

injected shows that a reduction to one-half of the number of stages appears to have a minor effect

on oil volume produced (after two years of operation) whereas a reduction to one-quarter of the

number of stages yields a significant impact. The results also show that at fixed number of stages,

the smaller is the injected total volume of fracture fluid into the reservoir, the smaller are the oil

and gas production rates and produced volumes. However, the results do not indicate that the

relationship is linear since even with doubling the injected fracture fluid volume, the oil and gas

rates were not doubled. There appears to be a point of diminishing returns the greater the volume

of fracture fluid injected. This suggests that the interaction between the fracture zone production

91

and matrix zone production are coupled and thus this should be taken into account for optimizing

the number of stages and volume of fracture fluid injected.

92

Chapter Five: Conclusions and Recommendations

5.1 Conclusions

Hydraulic fracturing operations have complex interactions between rock mechanics and

multiphase flow in porous media. The objective of the thesis was to determine if the dilation-

recompaction could be used to represent hydraulic fracturing and what insights the model could

yield on optimizing the fracture job operation. To the author’s knowledge, this is the first time

that this model has been used to model this complex process. The conclusions derived from the

results of the thesis are as follows.

• The history-matched dilation-recompaction model provides a reasonable representation of

the hydraulic fracturing operation with respect to matching field oil, gas, and water rates

and cumulative produced volumes.

• The dilation-recompaction model provides a reasonable prediction of the extent of the

fracture network and its enhancement of effective porosity and permeability. The model

thus provides another method to estimate the extent and effective properties of the

stimulated reservoir volume (SRV) created during hydraulic fracturing operations.

• The dilation-recompaction model is relatively easy to implement with few input parameters

(fracture pressure and compressibilities of the rock before and after fracturing occurs).

93

• Reservoir simulations with this model are relatively quick to run and thus this approach

has promise for rapid evaluation of tight rock reservoirs and estimation of the extent of the

SRV.

• The sensitivity analysis conducted on the history-matched model suggests that the larger

the number of stages and the greater the injected fracture fluid, the larger is the oil and gas

production rates. The produced water is directly linked to the amount of fracture fluid

injected. However, the number of stages and fracture fluid volume cost more and it remains

unclear whether the incremental oil and gas would provide sufficient revenues to cover the

increased costs of the added stages and larger fracture fluid volumes.

• The sensitivity analysis suggests that there might be a point of diminishing returns with

respect to increases of the number of stages and fracture fluid volume.

5.2 Recommendations

The conclusions and discussion derived from the research leads to the following recommendations.

• The dilation-recompaction model should be tested with other tight rock operations

including tighter rock formations than that which was tested here.

• An economic model should be used to evaluate the optimum number of stages and fracture

fluid volume given the incremental oil and gas produced from the well. This should also

include the cost of disposing and/or treating the produced water.

• The dilation-recompaction model should be compared to classic fracture model using dual

porosity model or dual permeability model.

94

• Sensitivity analysis should be conducted on the inputs of the simulation model including

porosity, permeability and initial oil saturation to examine the impact of variation on these

parameters on oil and gas production.

• The dilation-recompaction model should be compared to full reservoir simulation-

geomechanical models.

• If microseismic data is available, the extent of the SRV predicted by the dilation-

recompaction model should be compared to microseismic data to determine how well it

predicts the size and shape of the fractured zone.

95

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98

Appendix: Reservoir simulation model listing for history-matched model

GRID CORNER 202 202 25 CORNERS Grid block definition values removed since too long to list PINCHOUTARRAY ALL NULL ALL POR ALL Porosity values removed since too long to list mod 131 73:126 5 = 0 PERMI ALL Permeability values removed since too long to list mod 131 73:126 5 = 0 PERMJ EQUALSI PERMK EQUALSI * 0.5 END-GRID *ROCKTYPE 1 ** Matrix Heat Properties *PRPOR 3300.0 *CPOR 2.20E-06 *ROCKCP 2.35E+06 *THCONR 6.60E+05 *THCONW 5.35E+04 *THCONO 1.25E+04 *THCONG 3.20E+03 *THCONMIX *COMPLEX *HLOSST 60.0 *HLOSSTDIFF 0.1 *HLOSSPROP *OVERBUR 2.350E+06 1.496E+05 *UNDERBUR 2.350E+06 1.496E+05 *DILATION *PBASE 17000. *PDILA 35000. *PPACT 200. *CRD 0.01 *CPEPAC 0.0 *FR 1 *PORRATMAX 1.2 PERMULI CON 200 PERMULJ CON 200 PERMULK CON 200 THTYPE CON 1 ***********

99

**$ Model and number of components MODEL 3 3 3 1 COMPNAME 'Water' 'Dead_Oil' 'Soln_Gas' CMM 0 0.207 0.016 PCRIT 0 268.20 4388.06 TCRIT 0 833.81 24.7369 KV1 0 0 56187.5 KV2 0 0 -0.00314675 KV3 0 0 60.8839 KV4 0 0 -879.991 KV5 0 0 -265.99 PRSR 101 TEMR 100 PSURF 101 TSURF 16.85 MASSDEN 999.999 834.000 587.098 CP 7.3822e-007 1.272e-005 1.06e-006 CT1 6.01397e-005 -2.292E-04 0.00041332 AVG 0 0 3.79966e-005 BVG 0 0 1 VISCTABLE 5 0.00E+00 6.257338385 1.15E+02 10 0.00E+00 5.20618022 9.81E+01 20 0.00E+00 3.746179305 6.84E+01 30 0.00E+00 2.814999832 5.41E+01 40 0.00E+00 2.191527276 4.34E+01 50 0.00E+00 1.756804199 3.52E+01 60 0.00E+00 1.443172214 2.89E+01 70 0.00E+00 1.210267421 2.40E+01 80 0.00E+00 1.032993358 2.01E+01 90 0.00E+00 0.895174004 1.70E+01 100 0.00E+00 0.78604849 1.46E+01 110 0.00E+00 0.698256057 1.26E+01 120 0.00E+00 0.626635771 1.09E+01 VSMIXCOMP 'Soln_Gas' VSMIXENDP 0 0.34 VSMIXFUNC 0 0.0440116 0.0880231 0.132035 0.176046 0.233352 0.278791 0.308067

0.322072 0.32733 0.336331

100

ROCKFLUID RPT 1 WATWET **$ Sw krw krow ** Sw krw krow SWT 0.25 0 1 0.271875 1.52588e-006 0.772476 0.29375 2.44141e-005 0.586182 0.315625 0.000123596 0.435806 0.3375 0.000390625 0.316406 0.359375 0.000953674 0.223404 0.38125 0.00197754 0.152588 0.403125 0.00366364 0.100113 0.425 0.00625 0.0625 0.446875 0.0100113 0.0366364 0.46875 0.0152588 0.0197754 0.490625 0.0223404 0.00953674 0.5125 0.0316406 0.00390625 0.534375 0.0435806 0.00123596 0.55625 0.0586182 0.000244141 0.578125 0.0772476 1.52588e-005 0.6 0.1 0 **$ Sl krg krog ** Sl krg krog SLT 0.65 1 0 0.66875 0.772476 1.52588e-005 0.6875 0.586182 0.000244141 0.70625 0.435806 0.00123596 0.725 0.316406 0.00390625 0.74375 0.223404 0.00953674 0.7625 0.152588 0.0197754 0.78125 0.100113 0.0366364 0.8 0.0625 0.0625 0.81875 0.0366364 0.100113 0.8375 0.0197754 0.152588 0.85625 0.00953674 0.223404 0.875 0.00390625 0.316406 0.89375 0.00123596 0.435806 0.9125 0.000244141 0.586182 0.93125 1.52588e-005 0.772476 0.95 0 1 *swr 0.3 ** irreducible water saturation *sgr 0.05 ** critical gas saturation **sorg 0.01 **krwro 0.1 ** end point INITIAL VERTICAL DEPTH_AVE INITREGION 1 REFPRES 17848 ** average wellbore pressure gradient 9.19 kPa/m

101

REFDEPTH 1940 TEMP CON 61 SG CON 0.0 SW CON 0.20 MFRAC_OIL 'Soln_Gas' CON 0.53047 MFRAC_OIL 'Dead_Oil' CON 0.46953 NUMERICAL NORM PRESS 10000 SATUR 0.4 ISOTHERMAL RUN DATE 2011 11 24.00000 DTWELL 0.01 **$ **$ **$ ** ** WELL 'I1' INJECTOR MOBWEIGHT EXPLICIT 'I1' INCOMP WATER 1.0 0.0 0.0 TINJW 60.0 QUAL 0.0 OPERATE MAX BHP 80000.0 CONT OPERATE MAX STW 10000.0 CONT **$ rad geofac wfrac skin **$ UBA ff Status Connection **$ perf geometric data: UBA, block entry(x,y,z) block exit(x,y,z), length ** rad geofac wfrac skin GEOMETRY J 0.086 0.249 1.0 0.0 PERF GEOA 'I1' ** UBA ff Status Connection 119 154 12 1.0 OPEN FLOW-TO 'SURFACE' REFLAYER 119 153 12 1.0 OPEN FLOW-TO 1 119 152 12 1.0 OPEN FLOW-TO 2 119 151 12 1.0 OPEN FLOW-TO 3 120 151 12 1.0 OPEN FLOW-TO 4 120 150 12 1.0 OPEN FLOW-TO 5 120 149 12 1.0 OPEN FLOW-TO 6 120 148 12 1.0 OPEN FLOW-TO 7 120 147 12 1.0 OPEN FLOW-TO 8 121 147 12 1.0 OPEN FLOW-TO 9 121 146 12 1.0 OPEN FLOW-TO 10 121 145 12 1.0 OPEN FLOW-TO 11 121 144 12 1.0 OPEN FLOW-TO 12 121 144 13 1.0 OPEN FLOW-TO 13 122 144 13 1.0 OPEN FLOW-TO 14 122 143 13 1.0 OPEN FLOW-TO 15 122 142 13 1.0 OPEN FLOW-TO 16 122 141 13 1.0 OPEN FLOW-TO 17

102

122 140 13 1.0 OPEN FLOW-TO 18 123 140 13 1.0 OPEN FLOW-TO 19 123 139 13 1.0 OPEN FLOW-TO 20 123 138 13 1.0 OPEN FLOW-TO 21 123 137 13 1.0 OPEN FLOW-TO 22 123 137 12 1.0 OPEN FLOW-TO 23 124 137 12 1.0 OPEN FLOW-TO 24 124 136 12 1.0 OPEN FLOW-TO 25 124 135 12 1.0 OPEN FLOW-TO 26 124 134 12 1.0 OPEN FLOW-TO 27 124 133 12 1.0 OPEN FLOW-TO 28 125 133 12 1.0 OPEN FLOW-TO 29 125 132 12 1.0 OPEN FLOW-TO 30 125 131 12 1.0 OPEN FLOW-TO 31 125 131 13 1.0 OPEN FLOW-TO 32 125 130 13 1.0 OPEN FLOW-TO 33 126 130 13 1.0 OPEN FLOW-TO 34 126 129 13 1.0 OPEN FLOW-TO 35 126 128 13 1.0 OPEN FLOW-TO 36 126 127 13 1.0 OPEN FLOW-TO 37 126 126 13 1.0 OPEN FLOW-TO 38 127 126 13 1.0 OPEN FLOW-TO 39 127 125 13 1.0 OPEN FLOW-TO 40 127 124 13 1.0 OPEN FLOW-TO 41 127 123 13 1.0 OPEN FLOW-TO 42 128 123 13 1.0 OPEN FLOW-TO 43 128 122 13 1.0 OPEN FLOW-TO 44 128 121 13 1.0 OPEN FLOW-TO 45 128 120 13 1.0 OPEN FLOW-TO 46 128 119 13 1.0 OPEN FLOW-TO 47 129 119 13 1.0 OPEN FLOW-TO 48 129 118 13 1.0 OPEN FLOW-TO 49 129 117 13 1.0 OPEN FLOW-TO 50 129 116 13 1.0 OPEN FLOW-TO 51 129 115 13 1.0 OPEN FLOW-TO 52 130 115 13 1.0 OPEN FLOW-TO 53 130 114 13 1.0 OPEN FLOW-TO 54 130 113 13 1.0 OPEN FLOW-TO 55 130 112 13 1.0 OPEN FLOW-TO 56 130 111 13 1.0 OPEN FLOW-TO 57 131 111 13 1.0 OPEN FLOW-TO 58 131 110 13 1.0 OPEN FLOW-TO 59 131 109 13 1.0 OPEN FLOW-TO 60 131 108 13 1.0 OPEN FLOW-TO 61 131 108 14 1.0 OPEN FLOW-TO 62 132 108 14 1.0 OPEN FLOW-TO 63 132 107 14 1.0 OPEN FLOW-TO 64 132 107 15 1.0 OPEN FLOW-TO 65 132 106 15 1.0 OPEN FLOW-TO 66 133 106 15 1.0 OPEN FLOW-TO 67 133 105 15 1.0 OPEN FLOW-TO 68 133 104 15 1.0 OPEN FLOW-TO 69 133 103 15 1.0 OPEN FLOW-TO 70

103


104

143 64 16 1.0 OPEN FLOW-TO 124 144 64 16 1.0 OPEN FLOW-TO 125 144 63 16 1.0 OPEN FLOW-TO 126 144 62 16 1.0 OPEN FLOW-TO 127 144 61 16 1.0 OPEN FLOW-TO 128 145 61 16 1.0 OPEN FLOW-TO 129 145 60 16 1.0 OPEN FLOW-TO 130 145 59 16 1.0 OPEN FLOW-TO 131 145 59 17 1.0 OPEN FLOW-TO 132 145 58 17 1.0 OPEN FLOW-TO 133 145 57 17 1.0 OPEN FLOW-TO 134 146 57 17 1.0 OPEN FLOW-TO 135 146 56 17 1.0 OPEN FLOW-TO 136 146 56 18 1.0 OPEN FLOW-TO 137 146 55 18 1.0 OPEN FLOW-TO 138 146 54 18 1.0 OPEN FLOW-TO 139 147 54 18 1.0 OPEN FLOW-TO 140 147 53 18 1.0 OPEN FLOW-TO 141 147 53 19 1.0 OPEN FLOW-TO 142 147 52 19 1.0 OPEN FLOW-TO 143 147 51 19 1.0 OPEN FLOW-TO 144 148 51 19 1.0 OPEN FLOW-TO 145 148 51 20 1.0 OPEN FLOW-TO 146 148 50 20 1.0 OPEN FLOW-TO 147 148 49 20 1.0 OPEN FLOW-TO 148 148 48 20 1.0 OPEN FLOW-TO 149 149 48 20 1.0 OPEN FLOW-TO 150 149 47 20 1.0 OPEN FLOW-TO 151 149 47 19 1.0 OPEN FLOW-TO 152 149 46 19 1.0 OPEN FLOW-TO 153 149 45 19 1.0 OPEN FLOW-TO 154 149 44 19 1.0 OPEN FLOW-TO 155 150 44 19 1.0 OPEN FLOW-TO 156 150 43 19 1.0 OPEN FLOW-TO 157 150 42 19 1.0 OPEN FLOW-TO 158 150 41 19 1.0 OPEN FLOW-TO 159 151 41 19 1.0 OPEN FLOW-TO 160 151 40 19 1.0 CLOSED FLOW-TO 161 SHUTIN 'I1' **$ **$ ** ** WELL 'P1' PRODUCER 'P1' OPERATE MIN BHP 2000.0 CONT **$ rad geofac wfrac skin **$ UBA ff Status Connection **$ perf geometric data: UBA, block entry(x,y,z) block exit(x,y,z), length ** rad geofac wfrac skin GEOMETRY J 0.086 0.249 1.0 0.0 PERF GEOA 'P1' ** UBA ff Status Connection

105

119 154 12 1.0 OPEN FLOW-TO 'SURFACE' REFLAYER 119 153 12 1.0 OPEN FLOW-TO 1 119 152 12 1.0 OPEN FLOW-TO 2 119 151 12 1.0 OPEN FLOW-TO 3 120 151 12 1.0 OPEN FLOW-TO 4 120 150 12 1.0 OPEN FLOW-TO 5 120 149 12 1.0 OPEN FLOW-TO 6 120 148 12 1.0 OPEN FLOW-TO 7 120 147 12 1.0 OPEN FLOW-TO 8 121 147 12 1.0 OPEN FLOW-TO 9 121 146 12 1.0 OPEN FLOW-TO 10 121 145 12 1.0 OPEN FLOW-TO 11 121 144 12 1.0 OPEN FLOW-TO 12 121 144 13 1.0 OPEN FLOW-TO 13 122 144 13 1.0 OPEN FLOW-TO 14 122 143 13 1.0 OPEN FLOW-TO 15 122 142 13 1.0 OPEN FLOW-TO 16 122 141 13 1.0 OPEN FLOW-TO 17 122 140 13 1.0 OPEN FLOW-TO 18 123 140 13 1.0 OPEN FLOW-TO 19 123 139 13 1.0 OPEN FLOW-TO 20 123 138 13 1.0 OPEN FLOW-TO 21 123 137 13 1.0 OPEN FLOW-TO 22 123 137 12 1.0 OPEN FLOW-TO 23 124 137 12 1.0 OPEN FLOW-TO 24 124 136 12 1.0 OPEN FLOW-TO 25 124 135 12 1.0 OPEN FLOW-TO 26 124 134 12 1.0 OPEN FLOW-TO 27 124 133 12 1.0 OPEN FLOW-TO 28 125 133 12 1.0 OPEN FLOW-TO 29 125 132 12 1.0 OPEN FLOW-TO 30 125 131 12 1.0 OPEN FLOW-TO 31 125 131 13 1.0 OPEN FLOW-TO 32 125 130 13 1.0 OPEN FLOW-TO 33 126 130 13 1.0 OPEN FLOW-TO 34 126 129 13 1.0 OPEN FLOW-TO 35 126 128 13 1.0 OPEN FLOW-TO 36 126 127 13 1.0 OPEN FLOW-TO 37 126 126 13 1.0 OPEN FLOW-TO 38 127 126 13 1.0 OPEN FLOW-TO 39 127 125 13 1.0 OPEN FLOW-TO 40 127 124 13 1.0 OPEN FLOW-TO 41 127 123 13 1.0 OPEN FLOW-TO 42 128 123 13 1.0 OPEN FLOW-TO 43 128 122 13 1.0 OPEN FLOW-TO 44 128 121 13 1.0 OPEN FLOW-TO 45 128 120 13 1.0 OPEN FLOW-TO 46 128 119 13 1.0 OPEN FLOW-TO 47 129 119 13 1.0 OPEN FLOW-TO 48 129 118 13 1.0 OPEN FLOW-TO 49 129 117 13 1.0 OPEN FLOW-TO 50 129 116 13 1.0 OPEN FLOW-TO 51 129 115 13 1.0 OPEN FLOW-TO 52

106


107


108

150 41 19 1.0 OPEN FLOW-TO 159 151 41 19 1.0 OPEN FLOW-TO 160 151 40 19 1.0 CLOSED FLOW-TO 161 SHUTIN 'P1' DATE 2011 11 24.5 DTWELL 0.01 OPEN 'I1' DATE 2011 11 25.00000 DATE 2011 11 26.00000 DATE 2011 11 27.00000 DATE 2011 11 28.00000 DATE 2011 11 29.00000 DATE 2011 11 30.00000 SHUTIN 'I1' DATE 2011 12 1.00000 DTWELL 0.01 PRODUCER 'P1' OPERATE MIN BHP 20000.0 CONT OPEN 'P1' DATE 2011 12 2.00000 DATE 2011 12 3.00000 DATE 2011 12 4.00000 SHUTIN 'P1' DATE 2011 12 5.00000 DTWELL 0.01 PRODUCER 'P1' OPERATE MAX STO 135.0 CONT OPERATE MIN BHP 3000 CONT OPEN 'P1' DATE 2011 12 6.00000 DATE 2011 12 7.00000 DATE 2011 12 8.00000 DATE 2011 12 9.00000 DATE 2011 12 10.00000 Production dates removed since too long to list The end date of production is 2013 11 20 STOP

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application of dilation-recompaction model in hydraulic

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