Hydraulic Fracturing and Flow-Back Simulation in Unconventional Tight Reservoirs

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2016 Hydraulic Fracturing and Flow-back Simulation in Unconventional Tight Reservoirs

Lin, Menglu

Lin, M. (2016). Hydraulic Fracturing and Flow-back Simulation in Unconventional Tight Reservoirs (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/26401 http://hdl.handle.net/11023/2965 master thesis

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Hydraulic Fracturing and Flow-back Simulation in Unconventional Tight Reservoirs

Menglu Lin

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, 2016

Abstract

At present, combination of the multistage hydraulic fracturing and horizontal wells has become a widely used technology in stimulating unconventional tight reservoirs in Western Canadian

Sedimentary Basin (WCSB). It is important to understand hydraulic fracture propagation mechanism, effects of their properties and controlling factors affecting flow-back recovery.

In this thesis, based on tight reservoir models in WCSB, firstly we examine different fracture geometry distributions and further discuss their effects on well productions. Then reservoir simulation coupled with rock geomechanics is employed to perform dynamic hydraulic fracturing for predicting hydraulic fracture dimensions and simulating fracturing liquid distribution. At last,

Design of Experiments and response surface methodology are conducted to explore well operational parameters affecting flow-back recovery and net present value (NPV).

This study provides new insights on the hydraulic fracturing and can be a reference for fracturing treatments in unconventional tight reservoirs.

Acknowledgements

I would like to thank my nice supervisor, Dr. Shengnan (Nancy) Chen and my generous co- supervisor, Dr. Zhangxing (John) Chen for their guidance, patience and support during my master study at the University of Calgary. I would also like to thank my respectable committee members:

Dr. Christopher Clarkson, Dr. Hossein Hejazi and Dr. Laurence R. Lines for reviewing my thesis and giving insightful comments.

I would like to acknowledge the support from the Natural Sciences and Engineering Research

Council (NSERC) of Canada and Seven Generations Energy Ltd. I also want to acknowledge the help from Reservoir Simulation Group (RSG) and Department of Chemical and Petroleum

Engineering.

In addition, I would like to extend the gratitude to all my great friends for making the experience at UCalgary wonderful. In particular, thank you to Mr. Jinze Xu, Mr. Mingxu Ma, and my officemates, Mr. Francisco J. Pacheco and Mr. Muhammad Fowaz Ikram, for their help on my master research.

Last but not the least, I appreciate the love, encouragement and support from my family.

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Table of Contents

Abstract ...... ii Acknowledgements ...... iii Table of Contents ...... iv List of Tables ...... vi List of Figures and Illustrations ...... vii List of Symbols, Abbreviations and Nomenclature ...... xi

CHAPTER ONE: INTRODUCTION ...... 1 1.1 Background ...... 1 1.1.1 Tight Resource in Western Canadian Sedimentary Basin ...... 1 1.1.2 Hydraulic Fracturing in Tight Reservoirs ...... 8 1.2 Research Objectives ...... 14 1.3 Thesis Organization ...... 14

CHAPTER TWO: EFFECT OF FRACTURE GEOMETRY ON WELL PRODUCTION16 2.1 Abstract ...... 16 2.2 Introduction ...... 17 2.3 Geological Model ...... 18 2.4 Numerical Simulation Model ...... 20 2.4.1 Reservoir and Fluid Properties ...... 20 2.4.2 Relative Permeability Curves and Initial Condition ...... 22 2.4.3 Hydraulic Fracture – Local Grid Refinement ...... 23 2.4.4 History Matching ...... 24 2.4.5 Microseismic Data ...... 25 2.4.6 Hydraulic Fracture Geometry Scenarios ...... 27 2.4.6.1 Scenario 1 ...... 28 2.4.6.2 Scenario 2 ...... 29 2.4.6.3 Scenario 3 ...... 30 2.5 Results and Discussion ...... 32 2.5.1 The Effect of Non-Darcy Flow in Hydraulic Fractures ...... 32 2.5.2 Ideal Planar Fractures - Effect of Main Fracture Length and Conductivity ....33 2.5.3 Effect of Fracture Geometry ...... 35 2.5.4 Effect of Secondary Fracture Permeability ...... 37 2.6 Flow Regime Analysis ...... 40 2.7 Conclusions ...... 43

CHAPTER THREE: APPLICATION OF RESERVOIR FLOW SIMULATION COUPLED WITH ROCK GEOMECHANICS ...... 45 3.1 Abstract ...... 45 3.2 Introduction ...... 46 3.3 Coupled Reservoir Simulation and Barton-Bandis Model ...... 48 3.4 Field Background ...... 50 3.4.1 Recombined Fluid Analysis ...... 51

3.5 Fracturing Simulation ...... 52 3.6 Reservoir Simulation ...... 57 3.7 Results and Discussion ...... 60 3.7.1 Effect of Non-Darcy Flow in Hydraulic Fracture ...... 60 3.7.2 Effect of Pressure-Dependent Permeability of Natural Fractures ...... 62 3.7.3 Effect of Well Bottom-hole Pressure ...... 65 3.8 Conclusion ...... 66

CHAPTER FOUR: SENSITIVITY ANALYSIS ON FLOW-BACK RECOVERY AND NPV IN LIQUID RICH GAS WELL ...... 68 4.1 Abstract ...... 68 4.2 Introduction ...... 69 4.3 Injection and Flow-back of Fracturing Fluid ...... 72 4.4 The Effect of Capillary Pressure and BHP ...... 77 4.5 The Effect of Well Shut-in Time ...... 79 4.6 Sensitivity Study of Flow-back Recovery and NPV ...... 81 4.7 Conclusion ...... 87

CHAPTER FIVE: SUMMARY AND FUTURE WORK ...... 89 5.1 Summary of Completed Research ...... 89 5.2 Future Work ...... 91

REFERENCES ...... 92

APPENDIX A: COPYRIGHT PERMISSION ...... 104

List of Tables

Table 1-1 Categorization of tight oil play in WCSB (Clarkson and Pedersen, 2011) ...... 4

Table 2-1 Properties of formation and reservoir fluid ...... 21

Table 3-1 Recombined analysis at gas-oil ratio 1198 Sm3/Sm3 ...... 52

Table 3-2 Typical treatment schedule of hydraulic fracturing (taken one stage as example) ...... 55

Table 3-3 Fracturing model properties ...... 55

Table 3-4 Reservoir model properties...... 58

Table 4-1 Variables and their value range ...... 83

List of Figures and Illustrations

Figure 1-1 Basinal elements of the WCSB (AER, 2015) ...... 1

Figure 1-2 Canadian production from tight resources (NEB, 2015) ...... 2

Figure 1-3 Location of tight oil activity in the WCSB (NEB, 2011) ...... 3

Figure 1-4 Cardium fairway, showing field locations (Reynolds, 2015) ...... 5

Figure 1-5 Distribution of tight gas resources (Heffernan, 2010) ...... 6

Figure 1-6 Lower-Middle Triassic sequence stratigraphic framework (Mederos, 1995) ...... 7

Figure 1-7 1). Stratigraphic groups on generalized stratigraphic column of Alberta (Dixon, 2010); 2). Zones of dry gas, wet gas and oil within Montney Formation (Ferri, 2013) ...... 8

Figure 1-8 Schematic of hydraulic fractured wells (NEB, 2015) ...... 9

Figure 1-9 Microseismic clouds data from Barnett Shale example (Wu, R., et al, 2012) ...... 12

Figure 1-10 Different types of fracture growth (Warpinski, Norman, et al., 2008) ...... 12

Figure 1-11 Illustration of water distribution in fracture network (Fan, L., 2010) ...... 13

Figure 2-1 Location of Willesden Green Oil Field (NEB, 2011) ...... 19

Figure 2-2 Three horizons and well location ...... 20

Figure 2-3 Properties of geological model...... 20

Figure 2-4 Relative permeability curves: 1) oil and water relative permeability curve and 2) Liquid and gas relative permeability curve ((Ghaderi, 2011 and 2012)) ...... 22

Figure 2-5 Zoom-in picture on local refined grids at and near the hydraulic fracture ...... 23

Figure 2-6 Oil production (constraints) of two vertical wells ...... 25

Figure 2-7 History matched gas production rates of two vertical wells ...... 25

Figure 2-8 Different stages microseismic event view of a horizontal well ...... 27

Figure 2-9 Different fracture geometries in microseismic data map ...... 27

Figure 2-10 scenario 1 with Ideal bi-wing planar fractures ...... 29

Figure 2-11 Scenario 2 with two branches in planar fractures ...... 30

vii

Figure 2-12 Scenario 3 with complex fractures ...... 32

Figure 2-13 Comparison of Darcy flow and non-Darcy flow in main fractures with conductivity of 500D•mm ...... 33

Figure 2-14 Cumulative oil production of different fracture half-lengths and conductivities (scenario 1) ...... 35

Figure 2-15 Cumulative oil productions with different fracture conductivity (secondary-main fracture permeability ratio: 1/4; conductivity ratio: 1/8) ...... 37

Figure 2-16 Pressure distribution after 10 years (main fracture conductivity: 500 D·mm; secondary-main fracture permeability ratio: 1/4; conductivity ratio: 1/8) ...... 37

Figure 2-17 Cumulative oil production of three scenarios at different fracture conductivities in the ratio of one-half ...... 39

Figure 2-18 Pressure distribution after 10 years in the 500 D·mm under the ratio of ...... 40

Figure 2-19 Rate-normalized pressure (RNP) and its derivative signature for MFHW ...... 43

Figure 3-1 Flowchart of iterative coupled approach (GEM 2013) ...... 49

Figure 3-2 Barton-Bandis permeability model (adapted from GEM User’ Guide, 2013) ...... 50

Figure 3-3 Generalized map showing the location and rock types of the Montney Formation (NEB, 2013) ...... 51

Figure 3-4 Grid dimensions in fracturing model ...... 54

Figure 3-5 Fracture profile (pressure: KPa) during the fracturing liquid injection (HL: half length) ...... 56

Figure 3-6 Water distribution in the fracture ...... 57

Figure 3-7 Reservoir model of a horizontal well with 21-stage fractures ...... 58

Figure 3-8 Matrix: a. oil and water relative permeability curve b. liquid and gas relative permeability curve ...... 59

Figure 3-9 Hydraulic fracture: a. oil and water relative permeability curve b. liquid and gas relative permeability curve...... 59

Figure 3-10 Schematic of natural fracture distribution ...... 60

Figure 3-11 History matching results ...... 60

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Figure 3-12 Darcy and non-Darcy flow with hydraulic fracture conductivity of 11.6 D·mm ..... 62

Figure 3-13 Pressure-dependent permeability of natural fracture ...... 63

Figure 3-14 Cumulative productions at hydraulic fracture conductivity 11.6 D·mm ...... 64

Figure 3-15 Cumulative productions at hydraulic fracture conductivity 1.16 D·mm ...... 64

Figure 3-16 Cumulative productions at hydraulic fracture conductivity of 1.16 D·mm with high conductive natural fracture (0.1 md) ...... 65

Figure 3-17 Production comparison of different bottom-hole pressures at conductivity of 11.6 D·mm ...... 66

Figure 4-1 Distribution of producing horizontal wells, Western Canada (Dixon K.R., Flint D., 2014) ...... 69

Figure 4-2 Phase envelope of simulated condensate reservoir ...... 72

Figure 4-3 Two-D schematic of a multi-fractured horizontal well in tight reservoir (Zanganeh, B. Ahmadi M. et. al., 2015) ...... 73

Figure 4-4 Permeability distribution (md) of reservoir model (taken one stage as an example) .. 74

Figure 4-5 Fracture profile (pressure: KPa) during the fracturing liquid injection (HL: half length) ...... 75

Figure 4-6 Water saturation in hydraulic fracture during injection ...... 75

Figure 4-7 Flow back at different conductivities ...... 77

Figure 4-8 Capillary pressure curves and corresponding cumulative water production ...... 77

Figure 4-9 Well production contrast at different BHP...... 78

Figure 4-10 Flow sequence of a typical fractured well (Alkouh, A., Mcketta, S. et. al., 2014) ... 79

Figure 4-11 Oil and gas rate of shut-in ...... 80

Figure 4-12 Cumulative production of shut-in ...... 81

Figure 4-13 Pressure (KPa) in the hydraulic fracture ...... 81

Figure 4-14 Cumulative oil production...... 83

Figure 4-15 Cumulative gas production ...... 84

Figure 4-16 Cumulative water production ...... 84

Figure 4-17 Tornado plot of recovered fluid ...... 85

Figure 4-18 Tornado plot of NPV ...... 86

List of Symbols, Abbreviations and Nomenclature

Symbol Definition

풂ퟏ Adjustable constants for calculating capillary pressure

풂ퟐ Adjustable constants for calculating capillary pressure

풂ퟑ Adjustable constants for calculating capillary pressure

푪풘풆풍풍 Cost of horizontal well, $

푪풇풓풂풄풕풖풓풆 Cost of hydraulic fracture, $

풅풑 Proppant diameter, mm

frs Fracture opening stress, KPa

fcd Fracture conductivity, D·mm

Fcd Dimensionless fracture conductivity

FC Total fixed cost, $

j Interest rate

k Absolute permeability, md

kccf Hydraulic fracture closure permeability, md

kf Proppant pack permeability, md

km Matrix permeability, md

ke Permeability of pseudoized fracture block in simulation model, mD

n Number of periods

N Number of horizontal wells

푷풄 Capillary pressure, psi

q(t) Oil production rate, STB/d

Q(t) Cumulative oil production, STB

RNP Rate-normalized pressure, psi·d/STB

푺풘 Wetting phase saturation, decimal

te Balance time, day

푽푭 Future value of revenue, $

Wf Hydraulic fracture width, mm

Wblock Width of pseudoized fracture block in simulation model, mm

∅ Pack porosity, fraction

흋 Sphericity

흀풎 Friction factor multiplier

µ Viscosity, cp

β Non-Darcy factor, ft-1

υ Velocity, cm·s-1

흈 Surface tension, dynes/cm

휽 Wettability contact angle, degree

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Chapter One: Introduction

1.1 Background

1.1.1 Tight Resource in Western Canadian Sedimentary Basin

The Western Canadian Sedimentary Basin (WCSB) is a vast sedimentary basin located in Western

Canada including the southwest corner of the Northwest Territories, northeastern British Columbia,

Alberta, southern Saskatchewan and southwestern Manitoba, shown as Fig 1-1.

Figure 1-1 Basinal elements of the WCSB (AER, 2015)

WCSB contains huge reserves of oil and natural gas (e.g. oil sands, conventional resources, and unconventional resources). Unlike conventional resources, unconventional resources are found in rocks with very low porosity and permeability and do not flow through rocks naturally. Without special stimulation treatments (e.g. massive hydraulic fracturing), they are difficult to be produced at economic flow rate. Based on the classification of unconventional resources by Alberta Energy

Regulator, unconventional resources include coalbed methane, tight gas, tight oil and shale gas.

This thesis focuses on tight resources (tight oil and tight gas), which are found in low permeability

rock including sandstones, siltstones and carbonates and have to be produced with the stimulation assistance. Tight plays in the WCSB has seen a significant increase in activity during the last few years due to the successful application of multi-fractured horizontal wells. In terms of statistics by

National Energy Board, tight oil production grew from zero in 2005 to 350,000 barrels per day by

2013 and tight gas production grew from three billion cubic feet per day in 2000 to seven billion cubic feet per day in 2013, shown in Fig 1-2.

a). Canadian shale and tight gas production

b). Canadian tight oil production

Figure 1-2 Canadian production from tight resources (NEB, 2015)

Development of tight oil in the WCSB began from the Bakken Formation and later extended to other plays in the WCSB. In terms of statistics by National Energy Board, the emerging tight oil resource plays include Bakken/Exshaw Formation, Cardium Formation, Viking Formation, Lower

Shaunavon Formation, Montney/Doig Formation, Duvernay/Muskwa Formation, Beaverhill Lake

Group and Lower Amaranth Formation. The location of tight oil land activity in the WCSB is shown in Fig 1-3.

Figure 1-3 Location of tight oil activity in the WCSB (NEB, 2011)

Tight light oil play can be classified into three categories, that is, halo oil, tight oil and shale oil, shown in Table 1-1.

Table 1-1 Categorization of tight oil play in WCSB (Clarkson and Pedersen, 2011)

Category Halo oil Tight oil Shale oil

Formation Source ≠ reservoir Source ≠ reservoir Source = reservoir

Perm More than 0,1 md Less than 0.1 md Nano-darcy

Characteristic Bypassed pay Analogous to tight gas Analogous to shale gas

Example Cardium, Viking Bakken, Montney Duvernay, Muskwa

In this thesis, relevant study is based on Cardium tight oil play. Specially, the Cardium Formation in WCSB contains the largest conventional oil reserves. Only 17% of the original oil in place has been produced since development begun in 1950s (Ghaderi, 2011). In recent several years, the applications of multi-fractured horizontal wells have significantly boosted development activities in the areas that do not meet traditional petrophysical cutoffs or pay criteria. The current areas has extended to the entire Cardium fairway, from the Lochend Field in the south to the Wapiti Field in the northwest, shown in Fig 1-4 (Reynolds, 2015). In terms of data by National Energy Board, the Cardium Formation in Alberta is estimated to have contained 10.6 billion barrels of oil originally in place, 9.4 billion barrels of which was in the Pembina Field. Since its discovery in the 1950s, 1.5 billion barrels of Cardium oil has been produced by 2010. With successful application of fractured horizontal well in target play with marginal reservoir properties, there could be an additional 1 to 3 billion barrels of oil in place around these unconventional reservoirs.

And so far, 130 million barrels of proved and probable reserves from these new areas have been publicly reported (NEB, 2011). Since Cardium play has a long development history, much abundant core and well log data have been acquired. The overall reservoir quality is quite poor,

with low porosity and permeability, typically 5%-12% and 0.1 to 10 md air permeability, determined at ambient conditions (Krause, 1994). The predominant rock types in the Cardium are mudstone and sandstone, with small conglomerate fractions. The reservoir facies mainly include upward coarsening, offshore marine muddy sandstones. Depths of Cardium reservoirs are generally from 1200 to 2800 m, deepening towards the foothills to the southwest. Pore pressure varies with depth, with the much shallower east Pembina area having a significantly lower pressure than the deeper west Pembina area. Most Cardium pools are slightly over-pressured compared to a water gradient at discovery (Reynolds, 2015).

Figure 1-4 Cardium fairway, showing field locations (Reynolds, 2015)

In addition to tight oil reserves, widespread deployment of horizontal drilling and reservoir stimulation technologies has also brought vast additional natural gas resources from tight gas reservoirs. Fig 1-5 illustrates tight gas resources in Canada.

Figure 1-5 Distribution of tight gas resources (Heffernan, 2010)

Among these tight gas plays, Montney formation has rapidly evolved into one of the hottest natural gas plays in recent years. Production volumes from Montney have been rising to over 117 million sm3/d and 9800 m3/d of oil and condensate by November 2014 (Zinselmeyer, 2015). The Montney formation stretches over approximately 55,000 square miles from north-east British Columbia to north-west Alberta and was deposited in the Peace River Basin during the Lower Triassic

(Zonneveld, 2012), shown in Fig 1-6.

Figure 1-6 Lower-Middle Triassic sequence stratigraphic framework (Mederos, 1995)

Montney facies range from mid to upper shoreface sandstones, to middle and lower shoreface hummocky cross-stratified sandstones and course siltstones, to finely laminated lower shoreface sand and offshore siltstones, and to turbidites. The Montney is primarily dominated by siltstone with subordinate very fine-grained siltstone and several ‘coquina’ horizons (Popp, 2015). Recent successful drilling for unconventional Montney reservoirs in Alberta shows that the Montney production fairway follows the over-pressure edge and extends South and Ease from Dawson and

Swan in British Columbia, across into Alberta, down through the Elmworth, Karr, Kakwa and into

Resthaven fields. For example, for the greater Kakwa area, the Montney is unconformably overlain by the Doig formation and unconformably overlies the Belloy. The top of the Montney ranges from 2800 to over 3500 meters in true depth from surface. In addition, the Montney has a complex maturation and migration history in this area, showing over-pressuring and variable liquid/gas

ratios. Shown in Fig 1-7, Montney Formation has a complex hydrocarbon system. It can be classified into deep-basin, over-pressured, mixed-hydrocarbon-saturated reservoirs (Kuppe, 2012).

Figure 1-7 1). Stratigraphic groups on generalized stratigraphic column of Alberta (Dixon,

2010); 2). Zones of dry gas, wet gas and oil within Montney Formation (Ferri, 2013)

1.1.2 Hydraulic Fracturing in Tight Reservoirs

Since reservoir properties (e.g. matrix permeability) in tight formation are extreme low, oil and gas cannot flow to the wellbore naturally without stimulation treatment. In recent years, as the successful application of multi-stage hydraulic fracturing treatments, unconventional energy revolution is initialed in North America. The technologies and relevant research of hydraulic fracturing have improved significantly since its introduction to the industry in 1947. Shown in Fig.

1-8, even though cost of one multi-fractured horizontal well is much higher than that of one vertical well, the additional production resulting from large drainage area can offset extra cost.

Figure 1-8 Schematic of hydraulic fractured wells (NEB, 2015)

Hydraulic fracture is created when fracturing liquid is pumped into the pay zone at high enough rate. First, a neat fluid, called a ‘pad’, is pumped to initiate the fracture and to establish propagation.

This is followed by a slurry of fluid mixed with a propping agent (often called a ‘proppant’). This slurry continues to extend the fracture and concurrently carries the proppant deeply into the fracture. After the materials are pumped, the fluid chemically breaks back to a lower viscosity and flows back out of the well, leaving a highly conductive propped fracture for oil or gas to flow easily from the tight formation into the well. Hydraulic fracture propagation is affected

significantly by rock mechanics. The theoretically identified factors affecting fracture propagation include 1) variation of in-situ stresses existing in different layers of rock, 2) relative bed thickness of formations in the vicinity of the fractures, 3) bonding between formations, 4) variations in mechanical rock properties (e.g. elastic modulus, Poisson’s ratio, toughness, or ductility), 5) fluid pressure gradients in the fracture, and 6) variations in pore pressure from one zone to the next. In addition, horizontal fractures have been reported at shallow depths and it is believed that vertical fractures are usually generated at depths below 305 to 601 m. Vertical fracture growth can be inhibited by the higher lateral stresses in the formations above and below the target zone. And fracture configuration can be influenced by stress changes between rock layers. Fracture height has a significant effect on fracture length and accurate predication of fracture dimensions. Methods of accurately estimating the growth profiles have to be developed (Veatch, R.W., Jr.; Moschovidis,

Z. A., Fast, C.R., 1989).

To predict the fracture properties (e.g. half-length, height and conductivity), many fracture models have been developed, which include two dimensional models, pseudo three dimensional models, and fully three dimensional models. With a 2 D model, one of three dimensions, usually the fracture height, is fixed. Fracture width and length can then be calculated. 2 D models can be used in certain formations with confidence, assuming the created fracture height can be estimated accurately. Perkins-Kern-Nordgren (PKN) and Kristonovich-Geertsma-de Klerk (KGD) models are widely used 2 D models in the industry, where PKN model is usually applied when the fracture length is much greater than the fracture height, while KGD model is more reliable if fracture height is more than the fracture length (Geertsma, J. and Haafkens, R., 1979). Pseudo-3 D models modify the PKN model by adding height variation along fracture length and its effect on the fracture width

(Rahman, M. M., and Rahman, M. K., 2010), while full 3 D models consider the variation of

fracture geometry in a three-dimensional space. Although being more realistic, computation costs of fully 3 D models are often high, which limits their applications. Even though above conventional hydraulic fracture propagation models are still popular in hydraulic fracturing design, they are mainly used for bi-wing planer fracture design. However, in tight reservoirs, multiple hydraulic fracture are closely spaced along horizontal wellbores. And hydraulic fractures of adjacent wells may also affect with each other. So growing fractures perhaps are influenced by other hydraulic fractures from stages of own well or adjacent well, resulting in complex fracture network rather than simple bi-wing planar fracture (Olson, 2012). In addition, natural fractures are often present in tight formation and affect propagation direction of induced fractures, which causes complex fracture networks (Wu, 2014). The presence of natural fracture alters the way induced fracture propagates through the rock. Affected by natural fractures, hydraulic fracture may propagate asymmetrically or in multiple strands or segments. When hydraulic fractures encounter natural fracture, possible modes of fracture propagation are 1) crossing of the natural fracture, which occurs when normal stress on natural fracture is high relative to the fracture toughness of the rock

2) Dilation of the natural fracture then propagation from the tip of natural fracture 3) Dilation of the natural fracture, then breakout of a fracture from along natural fracture (Potluri, N.K., and Zhu,

D., 2005). Shown in Fig 1-9, complex fracture geometries can be observed in microseismic mapping data. It shows one horizontal well with four stage hydraulic fractures in the Barnett shale.

It can be seen stage 1 and 2 show less complexity and stage 3 and 4 demonstrate more fracture divergence. This is because toe section (stage 1 and 2) of the lateral has higher stress anisotropy compared to the heel part (stage 3 and 4). Fig 1-10 illustrates various types of fracture growth, ranging from simple fractures to complex fracture networks. Complex fracture geometry brings about new challenges in reservoir modeling. It has become a big concern that what the effect of

different fracture geometries on well production. Understanding this problem can provide guidance for filed operation.

Figure 1-9 Microseismic clouds data from Barnett Shale example (Wu, R., et al, 2012)

Figure 1-10 Different types of fracture growth (Warpinski, Norman, et al., 2008)

In addition, a huge amount of water is injected in the tight reservoir to create fracture and flow- back is one necessary stage in hydraulic fracturing. However, much injected fracturing fluid cannot be recovered. Low flow-back recovery is thought to be one factor resulting in poor performance.

It is thought frac-water is imbibed into tight matrix during hydraulic fracturing, which lowers flow- back recovery and reduces fluid relative permeability. Other explanation (Fan, L., 2010) has also been proposed, shown as Fig 1-11. Complex fracture network is generated around one perforation cluster. It shows much water is filled inside fractures without proppant instead of being imbibed into tight matrix. Water in this space is trapped and never be returned. In this scenario, even though flow-back recovery is low, well still has better production performance. Thus it is necessary to investigate flow-back characteristics and clarify the controlling mechanism.

Figure 1-11 Illustration of water distribution in fracture network (Fan, L., 2010)

Based on above discussion, we can conclude such problems as follows:

1) Unlike shale reservoirs, matrix permeability of tight reservoir (micro-Darcy) is much higher than that in shale formation (nano-Darcy). The effect of fracture property variation (e.g. fracture conductivity and fracture half-length) and their contribution to well production are still unclear.

2) Hydraulic fracture may demonstrate geometry complexity, ranging from simple bi-wing planar geometry to complex network. Predicting fracture geometry is still very challenging topic. What is the effect of fracture complexity on well production? Which type of fracture geometry should be recommended?

3) Tons of fracturing liquid are injected into tight formation during hydraulic fracturing but flow- back recovery is low. A thorough understanding of this problem requires analysis combined with reservoir flow, geomechanics and fracture modeling. What is the mechanism of flow-back characteristics? What is controlling factors affecting flow-back recovery and NPV?

1.2 Research Objectives

In this thesis, the research objects are shown as follows:

1) Build a geological model based on the actual tight oil block in WCSB, perform the history matching using field production data and model different geometries and corresponding reservoir properties appropriately.

2) Examine the different fracture geometry distributions and further discuss the effects of geometry distribution on well productions. Understand the role of different parameters and their contribution to reservoir performance.

3) Present a simulation framework that can combine reservoir flow simulation with rock geomechanics together, perform dynamic hydraulic fracturing and predict fracture dimensions.

4) Conduct sensitivity analysis on flow-back recovery and NPV in tight liquid rich gas, clarify controlling factors affecting these response and related mechanism.

1.3 Thesis Organization

This thesis includes five chapters.

The first chapter introduce general background of hydraulic fractured tight reservoirs in WCSB, research problems and objects.

The second chapter builds a geological model and heterogeneous reservoir model based on

Cardium tight oil block, performs history matching by field data, examines the different fracture geometry distributions and further discuss the effects of geometry distribution on well production.

In addition, Rate Transient Analysis (RTA) is employed to analyze flow regime of different fracture properties.

The third chapter presents a novel approach to predict hydraulic fracture properties, which combines reservoir flow simulation with rock mechanics together. The dynamic hydraulic fracturing is performed based on Barton-Bandis model integrated in the geomechanics module of

CMG-GEM. Also, the effect of stress-dependent natural fracture on well performance is discussed.

The fourth chapter employs Design of Experiment (DoE) and response surface methodology to clarify controlling factors affecting flow-back recovery and NPV.

The fifth chapter summarizes research results and potential improvements in the future study.

Chapter Two: Effect of Fracture Geometry on Well Production1

2.1 Abstract

Tight oil production is emerging as an important new source of energy supply and has reversed a decline in U.S. crude oil production and Western Canadian light oil production. At present, combination of the multistage hydraulic fracturing and horizontal wells has become a widely used technology in stimulating tight oil reservoirs. However, the ideal planar fractures used in the reservoir simulation are excessively simplified. Effects of some key fracture properties, such as facture geometry distributions and the permeability variations, are usually not taken into consideration during the simulation. Over simplified fractures in the reservoir model may fail to represent the complex fractures in reality, leading to significant errors in forecasting the reservoir performance. In this paper, we examined the different fracture geometry distributions and further discussed the effects of geometry distribution on well productions. All fracture geometry scenarios were confined by the microseismic mapping data. To make the result more reliable and relevant, a geo-model was first constructed for a tight oil block in Willesden Green oil field, AB, Canada.

The simulation model was then generated based on the geo-model and history-matched to the production history of vertical production wells. A horizontal well was drilled in the simulation model and different fracture geometry scenarios were analyzed. Results indicated that the simulation results of simple planar fractures overestimated the oil rate and led to higher oil recoveries. In addition, if the secondary fracture can achieve the same permeability as that of the main fracture, hydraulic fracture with branches can increase the well production (e.g. scenario 2

1 Menglu Lin, Shengnan Chen, Wei Ding, Zhangxin Chen, and Jinze Xu. Effect of Fracture Geometry on Well Production in Hydraulic Fractured Tight Oil Reservoirs. SPE 167761-PA, Journal of Canadian Petroleum Technology, Vol. 54, No. 03, pp. 183-194, 2015. 16

under the conductivity ratio of one-half), owing to a larger effective contact area between matrix and fracture. Secondary fractures with low permeability can decrease the well productivity compared to that of the wells with bi-wing planar fractures. Furthermore, the effect of hydraulic fracture geometries on the cumulative production of the wells with higher main fracture conductivity was more significant compared to those with lower main fracture conductivity.

2.2 Introduction

Tight oil plays in the Western Canadian Sedimentary Basin have recently seen a significant increase in activity through advances in horizontal drilling and fracturing technology (Kabir, et al,

2011; Legrand, et al., 2011; Priyantoro, et al., 2012). The Cardium Formation in the Pembina field of Alberta is an example of a reservoir, where 454 multistage fracture stimulated horizontal wells were rig-released in 2011; Horizontal well with multistage hydraulic fracturing technology has breathed new life into sustainable development of these plays, where hydraulic fractures provide high permeable conduits, improve reservoir percolation ability, increase the drainage area and the oil recovery.

Many researches have been conducted on flow regimes (Bahrami et al. 2013), primary recovery and enhanced oil recovery (Ghaderi et al. 2011; Iwere et al. 2012), reservoir modeling (Wang et al. 2013) and stimulation optimization (Woo et al. 2011) in hydraulic fractured tight oil reservoirs using reservoir simulation methods. However, in these works, different hydraulic fracture geometries are not taken into consideration. Hydraulic fractures are represented by parallel planes that are vertical to the horizontal well. In reality, the geometry of hydraulic fractures can be complex. For example, a hydraulic fracture diverted into the natural fracture can advance either by continued growth in the natural fracture or by kicking out of the natural fracture into the formation

rock (Taleghani, 2014). In layered sedimentary rocks, opening-mode fractures have been observed to abut against bedding contacts, causing fractures to terminate (abutment) at contacts or step-over at bedding contacts (Cooke and Underwood, 2001). Microseismic monitoring technology has been used to study the fracture geometry (Quirk et al. 2012; Liu et al 2004; Fischer et al. 2007). But these studies do not integrate the fracture geometry distribution into the reservoir simulation process. Stalgorova et al. (2012; 2013) proposed analytical models for horizontal wells with multiple fractures. However, many assumptions have to be made in order to apply the analytical models in practice. In this study, we first used Petrel to construct a geological model for an actual block in the Cardium Formation of Willesden Green oil field, AB, Canada. CMG IMEX was then employed to construct a dynamic simulation model based on the geological model and historical- matching was conducted. Local grid refinement was generated near the hydraulic fractures.

Microseismic data was utilized to confine and describe the characteristics of hydraulic fractures in tight oil reservoirs. Horizontal wells with different fracture geometries and conductivities were finally simulated and compared.

2.3 Geological Model

The Cardium Formation consists of interbedded sandstone, shale, and some local conglomerate, which spreads over much of western Alberta (Krause et al. 1994). Oil production in Cardium started more than half a century ago and activities in the tight formations in Cardium began in

2005. The Willesden Green oil field is located in south-central Alberta, and covers an area of

50,827 hectares (Varga et al., 2007). In Willesden Green field (as shown in Figure 2-1), the average vertical depth of formation is 1900-2300 m and the formation has significant amount of solution gas. The net pay thickness is 5-18 m resulting in large original oil in place (OOIP)

(Mageau et. al., 2012).

Figure 2-1 Location of Willesden Green Oil Field (NEB, 2011)

To build the geological model, a block with two vertical production wells, one horizontal production well and one observation well are selected to build the geological model. Structural surfaces are built based on well tops where three horizons CARD, CARDSD and BLACKSTN, are generated. These three horizons include the interval of CARD and CARDSD formation. The horizontal well is at the top of CARDSD formation, which can be seen in Fig 2-2, Vertical wells produce from the CARDSD zone and stimulated horizontal well produces from both CARD and

CARDSD zone. Since the reservoir is not supported by aquifer or gas cap, solution gas drive is the main driving force. The length of model is 1770m and width is 810m. The model is consisted of

143,370 grids. The properties, such as matrix permeability and porosity, are derived from

Sequential Gaussian Simulation using the core data, as shown in Fig 2-3. Specifically, the matrix horizontal permeability ranges from 0.06 md to 0.94 md, with an average value of 0.2 md. Matrix

vertical permeability is 1/10 of its horizontal value, and the porosity range in the model is between

7.8% and 15%.

Figure 2-2 Three horizons and well location

a. Matrix Permeability of geological model b. Matrix Porosity of geological model

Figure 2-3 Properties of geological model

2.4 Numerical Simulation Model

2.4.1 Reservoir and Fluid Properties

Numerical simulation model is constructed based on the geological model. Unlike simulating shale gas reservoirs, adsorption effect is not considered in this model as such effect is not equally significant in tight oil reservoirs. Effect of the Non-Darcy fluid flow is examined. Since liquid

flow rate is relatively lower compared to gas flow rate in hydraulic fractures in shale gas formations, non-Darcy effect on oil cumulative production rate is insignificant. Details are present in the results and discussion section. Geological model constructed by Petrel is exported directly into CMG

IMEX. There are 177 grids in I direction, 81 grids in J direction and 10 grids in K direction. In K direction, there are 10 layers where CARD formation consists of 5 layers (layer 1 to 5) and

CARDSD formation includes the rest 6 to 10 layers. The grid size of I and J direction is 10 meters.

The grid top ranges from 1945 m to 1988 m. Properties of the tight oil formation and reservoir oil properties are all obtained from field data, as shown in Table 2-1.

Table 2-1 Properties of formation and reservoir fluid

Reservoir temperature(℃) 65

Bubble point pressure(MPa) 22.8

Oil density at Stock Tank Condition(API) 30

Gas density at Stock Tank Condition 0.776

(Air=1)Formation compressibility(KPa-1) 6.41 x 10-7 Total compressibility(KPa-1) 2.28 x 10-5

Reference pressure(KPa-1) 26,880.7

Reference depth(m) 2,010

Water-Oil contact(m) 2,040

Solution gas/oil ratio at 23 MPa (Sm3/Sm3) 185

Average production gas/oil ratio (Sm3/Sm3) 1470

2.4.2 Relative Permeability Curves and Initial Condition

The initial pressure of each grid block is determined by a reference pressure and a reference depth shown in table 2-1. Both water/oil and gas/oil contacts have been set outside the boundary of the reservoir model, as there are no signs of a bottom water zone and the reservoir initial pressure is higher than the bubble point pressure (i.e., no gas cap). The initial phase saturations are imposed as the endpoint saturations in the relative permeability curves. Relative permeability curves are obtained from two reference papers (Ghaderi, 2011 and 2012) on Cardium tight formation and further tuned to match the production history of the two vertical wells, as depicted in Figure 2-4.

Rock wettability of oil wet, mixed-wet and water-wet have all been found in Cardium formation.

In our simulation model, based on the history matching results, the reservoir rocks is likely to be water-wet, which is in accordance with the reference papers. In this situation, no transition zone is assumed to exist in the reservoir. A test run is performed for 5 years without source/sink terms (i.e. injectors/ producers) and no pressure and saturation changes are observed which implied that the model reached the equilibrium state.

0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 Kr Krw Kr Krg 0.4 Kro 0.4 Krog 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sw Sl (Liquid saturation)

Figure 2-4 Relative permeability curves: 1) oil and water relative permeability curve and

2) Liquid and gas relative permeability curve ((Ghaderi, 2011 and 2012))

2.4.3 Hydraulic Fracture – Local Grid Refinement

In any reservoir simulator, it is a challenging task to simulate its actual width and permeability of a hydraulic fracture due to the unaffordable computational cost and the convergence issue.

Alternatively, grids with an equivalent permeability and width are used to represent the fracture in the simulator. It is assumed that conductivity of an actual hydraulic fracture is equal to that of the pseudoized fracture block in the model (Rubin, 2010).

푘푓 × 푤푓 = 푘푒 × 푤푏푙표푐푘 (2-1)

For example, if the fracture width is 10 mm and actual fracture permeability is 15,000 md, fracture conductivity, which is the product of the fracture permeability and width is 150 D·mm. If the grid width representing hydraulic fracture in the model is 60 cm, then the effective permeability in the grid block representing hydraulic fracture can be calculated as following:

푘푓 × 푤푓 15000 푚푑 × 0.01푚 푘푒 = = = 250 푚푑 푤푏푙표푐푘 0.6 푚

A zoom-in plot of the local grid refinement of a hydraulic fracture is shown in Fig. 2-5. Grid blocks in the middle represent the hydraulic fracture. The width of pseudoized fracture grid is 2 feet.

Figure 2-5 Zoom-in picture on local refined grids at and near the hydraulic fracture

2.4.4 History Matching

Three producers (one horizontal well and two vertical wells) are simulated in the numerical model.

Well 1 and 2 are two vertical producers, producing since February 1968 and September 1976, respectively. History matching process was performed where the oil rates were applied as constraints and gas rates of the two vertical wells were matched. A pressure build-up test of well

1 was conducted on July 15th, 2009 and the average reservoir pressure was measured to be 22.8

MPa. This pressure builder test was performed in order to obtain the formation pressure before drilling the horizontal well. Unfortunately the well flowing bottom-hole pressure was not reported and water production was negligible due to the primary production and no connected aquifers. The oil rates of the two vertical wells are used as inputs (shown in Fig 2-6) and the simulated average pressure is 21.6 MPa. The simulated gas rates of the two vertical wells are shown in Fig 2-7. In addition, our model can be regarded as a ‘conceptual’ model with realistic data collected from the field. Well 3 is a newly drilled horizontal well with multistage hydraulic fractures. Confined by the microseismic mapping data, different fracture geometry scenarios are simulated along the horizontal well. Effect of the hydraulic fracture geometries on the cumulative oil production is analyzed and sensitivity of fracture conductivity is performed for various fracturing scenarios.

Minimum bottom-hole pressure (BHP) of the horizontal well is kept at 7 MPa.

a). Oil rate of well 1 b). Oil rate of well 2

Figure 2-6 Oil production (constraints) of two vertical wells

a). Simulated gas rate of well 1 b). Simulated gas rate of well 2

Figure 2-7 History matched gas production rates of two vertical wells

2.4.5 Microseismic Data

Microseismic imaging is a monitoring technique that is used in the oil and gas industry to monitor and map fracture geometries created by hydraulic-fracturing stimulations. A microseismic event occurs when the rock beneath the ground surface fails (Mohammad and Miskimins, 2012). Data collected during well stimulations in tight shale generally reveal a wide spread of microseismic

events, as shown in Fig 2-8. In this figure, there are microseismic events from eight stages. The fracture half lengths and heights are not constant values and half lengths on both sides of every stage are not symmetry. Based on the map, it can be seen that, the event cloud shows a clear orientation, yet still covers a much wider area than the hydraulic fracture geometry. In many reservoirs, propagation of the hydraulic fractures may be complex because of interaction with pre- existing natural fractures, fissures, and other geologic heterogeneities (Cipolla, 2008; Mayerhofer,

2008; Potluri, 2005). In addition, complex fracture geometries may be created when there is no significant difference between the minimum and maximum principal stresses in the reservoir (Fan,

2010). Fig. 2-9 depicts a microseismic map from one stage of the horizontal well. When complex fracture network is expected in the formation, it is still impossible to predict an exact fracture network geometry in the area of event cloud. In this study, multiple different cases on geometry of hydraulic fractures, ranging from simple planar fractures to complex fractures are studied in reservoir simulation, which is demonstrated in Figure 2-9. These geometries represent scenario 1: planar fracture; scenario 2: branched fracture; and scenario 3: complex fracture. In our model, four fracture half-lengths ranging from 100 m to 250 m are simulated, and fracture height is the same as the height of the oil zone.

Figure 2-8 Different stages microseismic event view of a horizontal well

a. b. c.

Figure 2-9 Different fracture geometries in microseismic data map

2.4.6 Hydraulic Fracture Geometry Scenarios

Local refinement grids (LGR) are used to represent hydraulic fractures in the simulation model.

The horizontal length of well 3 is 1000 m. The 1000 m lateral which in layer 6 is completed with five stages and fracture spacing is 200 m. The fracture height is equal to vertical height of simulation model. It is assumed that the horizontal well is drilled along the direction of minimum horizontal stress.

As aforementioned, propagation of hydraulic fracture may be complex because of the interaction with pre-existing natural fractures, fissures, cleavage, and rock mechanical heterogeneities. Three

different hydraulic fractures are modeled. In the first scenario, the hydraulic fractures are ideal parallel planar fractures. In the second scenario, branches are added in the planar fractures. In the third scenario, complex hydraulic fractures are modeled according to the characteristics of microseismic events cloud. Sensitivity of fracture half-length, fracture conductivity and fracture geometry distribution are analyzed. For all three scenarios, a no flow boundary is assumed and bottom-hole pressure of the horizontal well is set to be 7 MPa. Average reservoir pressure has dropped to below the bubble point pressure when the horizontal well is put into production.

2.4.6.1 Scenario 1

In scenario 1, we assume the transverse hydraulic fractures propagate symmetrically in a plane perpendicular along the minimum principal stress. Ideal planar fractures are modeled and 1000 m lateral is completed with 5 parallel identical fractures (See Fig 2-10). The grid top value is calculated by the well’s true vertical depth subsea. According to Meyer (2013), a fracture with dimensionless conductivity higher than 10 should be targeted while designing a stimulation job and such fracture is close to infinite conductive. However, it should be noted that, the effective fracture conductivity in the reservoir can be as much as 90% lower than their lab measured values due to the effects of multiphase flow, proppant embedment, uneven proppant concentration (Terry

Palisch, 2007). In our model, four fracture conductivities: 100 D·mm 150 D·mm, 200 D·mm and

500 D·mm are examined. The fracture width is assumed to be 10 mm and thus the values of fracture permeability are between 10 D and 50D, respectively. Four fracture half-lengths of 100 m, 150 m, 200 m, and 250 m, are also studied.

Figure 2-10 scenario 1 with Ideal bi-wing planar fractures

2.4.6.2 Scenario 2

In this scenario, branches are added to the planar hydraulic fractures, which are shown in Fig 2-

11. For scenarios 1 and 2, the total fracture volume (summation of all fractures) are kept the same, which can be estimated by the usage (and flow back) data of the fracturing fluid and proppant.

Secondary fractures are typically created by activating the pre-existing natural fractures and thus they are likely to be narrower than the main hydraulic fractures. In this study, the width of a secondary fracture is assumed to be half of the main fracture width. Further, the width of a tertiary fracture (locates at the tip of each branch) will be half of the width of a secondary fracture, which makes it a quarter of that of the main fracture. It should be noted that, as the total fracture volume for scenario 1 and 2 are the same, adding secondary and tertiary fractures in scenario 2 implies the length for main fracture is decreased accordingly.

In addition, if the secondary fractures are propped well, permeability of the secondary fracture may be close to the main fracture permeability. Otherwise, if secondary fractures are not well propped due to its narrow width, and/or severe proppant crush/embedment, permeability of such

fracture can be less than main fracture permeability. In this study, two secondary fracture permeabilities are analyzed: its value to be the same as and one quarter of the main fracture permeability, making the secondary - main fracture conductivity ratio one half and one eighth. At the same time, four cases with main fracture conductivity values of 100 D·mm, 150 D·mm, 200

D·mm and 500 D·mm are simulated respectively. If the secondary fracture permeability is the same as that of the main fracture, corresponding conductivity of the secondary fractures are 50

D·mm, 75 D·mm, 100 D·mm and 250 D·mm; while if the secondary fracture permeability is a quarter of the main fracture permeability, conductivity of secondary fractures are 12.5 D·mm,

18.75 D·mm, 25 D·mm and 62.5 D·mm.

Figure 2-11 Scenario 2 with two branches in planar fractures

2.4.6.3 Scenario 3

In scenario 3, geometry of the hydraulic fractures is more complex to account for the interaction with fissures and natural fractures, as shown in Fig 2-12. There are three different directions a hydraulic fracture could propagate when encountering a closed and cemented natural fracture. a)

The natural fracture may have no influence and hydraulic fracture propagates in plane without

interruption. The fracture crossover may be because of the high strength cement (comparable to matrix), or fracturing pressure lower than the normal stress perpendicular to natural fracture; b)

Hydraulic fracture is deflected and the fluid is completely diverted into natural fracture system; and c) Natural fracture stops or at least slows down hydraulic fracture growth in the presence of high stress anisotropy and enhanced leak off (Taleghani, 2014). In addition, hydraulic fractures with complexity also tend to be created when there is no significant difference between the maximum and minimum principal horizontal stress. Total fracture volume of scenario 3 is again kept the same as those in scenarios 1 and 2. More secondary and tertiary fractures are added in scenario 3 to represent a complex fracture network. Thus, length of the main fracture in scenario

3 is the shortest among all three scenarios. Similar to scenario 2, two secondary to main fracture permeability ratio of 1 and 1/4 (i.e., secondary to main fracture conductivity ratios of one-half and one-eighth) are simulated. Different main fracture conductivity values of 100 D·mm, 150 D·mm,

200 D·mm and 500 D·mm are simulated for scenario 3 respectively.

Figure 2-12 Scenario 3 with complex fractures

2.5 Results and Discussion

2.5.1 The Effect of Non-Darcy Flow in Hydraulic Fractures

Non-Darcy flow effects were simulated in the high conductive hydraulic fractures and results were

shown in Figure 2-13. It can be seen that there was no noticeable difference between the oil rates

with and without non-Darcy flow effects (Fig. 2-13(a)), while slight differences were found in the

corresponding gas production rates, as shown in Fig. 2-13(b). In addition, Reynolds number was

also examined to confirm that non-Darcy flow didn’t exist in the liquid flow in the hydraulic

fractures. The Reynolds numbers of all the scenarios were calculated and results showed that for

the highest Reynolds number for oil flow was 1.02 and that for gas was 18.30. Different critical

Reynolds numbers for non-Darcy flow have been reported in the literature (Bear, 1972;

Hassanizadeh and Gray, 1987; Blick and Civan, 1988), ranging from 3 to 100. Thus, non-Darcy

flow was not expected for oil flow but may appear in gas flow, which was in accord with the

simulation results.

350 31 Non-darcy 29 Non-darcy flow

300

/d) 3

flow /d)

3 Darcy flow 27

Darcy flow m

250 3 25

200 Oil Oil rate(m 23 150 Gas Gas rate(10 21

100 19

50 17

0 15 0 365 730 1095 0 365 730 1095 Time (days) Time (days) a). Comparison of Darcy flow and non-Darcy flow for oil phase b). Comparison of Darcy flow and non-Darcy flow for

gas phase

Figure 2-13 Comparison of Darcy flow and non-Darcy flow in main fractures with

conductivity of 500D•mm

2.5.2 Ideal Planar Fractures - Effect of Main Fracture Length and Conductivity

Effects of the half-length and conductivities of the main fractures are examined first in this study.

The cumulative oil productions of scenario 1 with four different fracture half lengths (i.e., 100m,

150m, 200m, and 250m) and four different conductivities (100 D·mm 150 D·mm, 200 D·mm and

500 D·mm) are plotted in Fig 2-14 a to 2-14 d. It can be seen that, the larger fracture half-length under the same conductivity, the higher cumulative oil production. Similarly, for the same fracture half length, the higher fracture conductivity is, the higher cumulative oil production will be, especially during the first 2 years. The difference among different fracture half lengths is smaller under low fracture conductivity. For example, when fracture conductivity is 100 D.mm, cumulative oil production at the 1825th day (5th year) is increased by 31.7 % (13,000 m3) when fracture half- length increases from 100 m to 250 m, and its value increased by 52.3 % (23,000 m3 ) when fracture

conductivity is 500 D.mm. It can also be seen from Figure 2-14 that, the differences among different conductivities increase as production time proceeds, and reaches a peak value occurs in the fifth year and then differences become relative smaller during later production. If one wants to increase the early production rate, hydraulic fractures with high conductivity are needed. For example, when fracture half-length is 250 meters, first year’s production will be increased by 73.6 % if increasing fracture conductivity from 100 D.mm to 500 D.mm.

80 80

)

3 3 60 60

40 40 100 m 100 m 150 m 150 m 20 200 m 20 200 m

250 m 250 m Cumulative oil production(10 0 Cumulative oil production(10 0 0 730 1460 2190 2920 3650 0 730 1460 2190 2920 3650 Time (days) Time (days) a. Different half-lengths of fracture conductivity 100 D.mm b. Different half-lengths of fracture conductivity 150 D.mm

80 80

)

m 3

60 3 60

40 40 100 m 100 m 150 m 150 m 20 200 m 20 200 m 250 m 250 m

Cumulative oil production(10 0 0 Cumulative oil production(10 0 730 1460 2190 2920 3650 0 730 1460 2190 2920 3650 Time (days) Time (days)

c. Different half-lengths of fracture conductivity 200 D.mm d. Different half-lengths of fracture conductivity 500 D.mm

Figure 2-14 Cumulative oil production of different fracture half-lengths and conductivities

(scenario 1)

2.5.3 Effect of Fracture Geometry

Cumulative oil production for three scenarios with different fracture conductivities are simulated and shown in Fig 2-15. Permeability of the secondary fracture is assumed to be a quarter of that of the main fracture for both scenario 2 and 3. As secondary fractures are much narrower compared to the main fracture, uneven proppant distribution, crash and embedment in the secondary fractures are more significant than those in the main fractures. It can be seen that cumulative production differs from each other slightly among three scenarios in the first 180 days, but such difference increases as production proceeds and the main fracture conductivity increases. At the end of the

10th year, cumulative production of scenario 3 with complex fractures is 15% less than that of scenario 1 with ideal parallel planar fractures. This implies simulations using parallel planar fractures overestimate the well productivity when a fracture network is created in tight oil formations. Due to the reduction of secondary fracture conductivity, these fractures cannot effectively transit reservoir fluids to the main fracture and wellbore. Take the case with conductivity of 500 D·mm for example, when the main fracture is 500 D·mm, its dimensionless fracture conductivity is 25, which can be regarded as infinite conductive (Meyer, 2013). However, the dimensionless conductivity of secondary fracture is reduced to about 3. Secondary fractures with low conductivity values are non-effective to transport the fluids. In addition, as the total fracture volume are kept the same, main fracture half-length of scenarios 2 and 3 are shorter than that of scenario 1, even though the contact area between matrix and fracture are increased. Fig 2-

16 depicts the reservoir pressures distribution after 10 years’ production. It can be seen that, complex fracture scenario with finite conductivity limits the pressure conduction. Even though the

contact area of complex fracture with matrix increases significantly, the qualities of the sub- fractures become poor. In other words, if complex fractures are targeted to be created in the formation, efforts must be made to guarantee sufficient conductivity of the secondary and tertiary fractures.

80 80

)

3 3 60 60

40 40

Scenario 1 Scenario 1 Scenario 2 Scenario 2

20 Scenario 3 20 Scenario 3

Cumulative oil production(10 Cumulative oil production(10 0 0 0 730 1460 2190 2920 3650 0 730 1460 2190 2920 3650 Time (days) Time (days)

a. Fracture conductivity of 100 D·mm b. Fracture conductivity of 150 D·mm

80 80

)

3 3 60 60

40 40

Scenario 1 Scenario 1 Scenario 2 Scenario 2 20 20

Scenario 3 Scenario 3

Cumulative oil production(10 Cumulative oil production(10 0 0 0 730 1460 2190 2920 3650 0 730 1460 2190 2920 3650 Time (days) Time (days) c. Fracture conductivity of 200 D·mm d. Fracture conductivity of 500 D·mm

Figure 2-15 Cumulative oil productions with different fracture conductivity (secondary-

main fracture permeability ratio: 1/4; conductivity ratio: 1/8)

Figure 2-16 Pressure distribution after 10 years (main fracture conductivity: 500 D·mm;

secondary-main fracture permeability ratio: 1/4; conductivity ratio: 1/8)

2.5.4 Effect of Secondary Fracture Permeability

In the previous section, secondary fracture permeability is assumed to be a quarter of the main fracture permeability. To analyze its effects on well performance, secondary fracture permeability is then assigned to be the same as that of the main fracture for scenario 2 and 3. Under such circumstance, we assume the secondary fractures are propped well without severe proppant uneven distribution, embedment and crush. Secondary fracture width is kept as half of that of the main fracture again, which makes the conductivity of secondary to main fracture is 1:2. Cumulative

production over 10 years for 3 different fracture geometries are plotted in Fig 2-17. Unlike previous results with low secondary fracture permeability, scenario 2 shows an optimal performance, while scenario 3 still has the lowest production. Initial productions (e.g., at the end of 6 month) among the three scenarios are almost the same, which could be because the reservoir fluids produced for all the scenarios are mainly from the reservoir matrix near the main fractures during early production time. During year 1 and 6, cumulative production of scenario 2 is higher than that of scenario 1, especially under high main fracture conductivity. The ability of secondary fractures to transmit fluid has been improved significantly by keeping the permeability of the main and the secondary fractures the same. Compared with bi-wing fractures in scenario 1, fractures in scenario

2 with branches have larger contact areas between matrix and fractures and can also transport all the fluids effectively. In other words, if the effective conductivity of second fracture can be achieved, it is recommended to add some complexity in fractures. For long term production, the matrix around the fracture has been depleted and fluids from the matrix in the distance begin to contribute to the production. If main fractures can connect more remote reservoir area away from the wellbore, that is, having longer fracture half-length, well production rate can be maintained better compared to scenarios with shorter main fracture half lengths. As there are no secondary fractures in Scenario 1, the half-length of the main fractures are the longest. This leads to a highest overall cumulative production rate in 10 years. However, for a more complicated fracture geometry shown in scenario 3, cumulative production of 10 years are lower than the other two scenarios. As the total facture volume are the same for all three scenario, well-developed secondary and tertiary fractures in scenario 3 limits the length of the main fractures, and thus has a smaller drainage area.

Pressure distributions for different scenarios are shown in Fig 2-18.

80 80

)

3 3 60 60

Scenario 1 40 Scenario 1 40 Scenario 2 Scenario 2 Scenario 3 Scenario 3

20 20 Cumulative oil oil (10 Cumulative production 0 Cumulative oil production(10 0 0 730 1460 2190 2920 3650 0 730 1460 2190 2920 3650 Time (days) Time (days)

a. Main fracture conductivity of 100 D·mm b. Main fracture conductivity of 150 D·mm

) 80

)

m 3 60 60

40 40 Scenario 1 Scenario 1 Scenario 2 Scenario 2

20 Scenario 3 20 Scenario 3

Cumulative oil production(10 Cumulative oil production(10 0 0 0 730 1460 2190 2920 3650 0 730 1460 2190 2920 3650 Time (days) Time (days)

c. Main fracture conductivity of 200 D·mm d. Main fracture conductivity of 500 D·mm

Figure 2-17 Cumulative oil production of three scenarios at different fracture

conductivities in the ratio of one-half

Figure 2-18 Pressure distribution after 10 years in the 500 D·mm under the ratio of

one-half

2.6 Flow Regime Analysis

It is important to understand the flow regime caused by the stimulated hydraulic fractures. In this

study, the bottom-hole pressure of the horizontal well is held constant and the simulated well

production rates are regarded as the production data. For the horizontal well with multiple

transverse fractures (MTFW) in tight reservoirs, straight-line analysis method and a series of

diagnostic signature can be used to analyze the flow regimes (Clarkson, 2010, 2013). Rate-

normalized derivative signature analysis (Song and Ehlig-Economides, 2011) is employed to

identify the flow regime. Rate-normalized pressure (RNP) and its derivative are shown in Eq. (2-

2) and (2-3). The horizontal ordinate te is material balance time, shown in Eq. (2-4).

푃 −푃 (푡) 푅푁푃 = 푖 푤푓 (2-2) 푞(푡)

푑 푅푁푃 푅푁푃′ = (2-3) 푑 푙푛푡푒

푄(푡) 푡 = (2-4) 푒 푞(푡)

For the RNP derivative signature, a 0.5 slope trend implies linear flow regime, a 0 slope trend suggests radial flow regime, and a unit slope indicates pseudo-steady state (dominated by the boundary). As shown in Fig 2-19, pseudo-linear flow, early radial flow, compound linear flow and pseudo-steady state flow can be identified for the fractured horizontal well. Flow regimes of scenario 1 (bi-wing fracture) with half-length 250 m is shown in Fig 2-19 a. Take main fracture conductivity of 100 D·mm for example, pseudo-linear flow which arises at the beginning of the production lasts for a short time and then the early-radial flow lasts for over ten days. These two flow regimes happen before fracture interference occurs. After fracture interference, the compound linear flow appears and the fluids flow into the fractures from the reservoir matrix beyond the fracture tip. Finally, the pseudo-steady state flow dominates the fluid flow in the middle and late period. As fracture conductivity increases, time for flow regime to change becomes relatively earlier. Pseudo-steady state flow regime resulting from fracture interference (seen as a nearly unit slope) and late pseudo radial flow (seen as a 0 slope) do not appear in the horizontal well. It may be due to a large fracture spacing and a short distance from fracture tip to the reservoir boundary.

Fig 2-19 b depicts flow regimes of different fracture geometries and similar flow regimes are shown in terms of RNP derivative signatures. Similarly, early linear flow and early radial flow appear before fracture interference occurs and compound linear flow (late linear flow) arises after fractures start to interfere with each other. At last, the boundary dominated flow (pseudo-steady

state flow) happens in the middle and late production period. Except the early linear flow, other flow regimes are similar in all three fracture geometry scenarios. In this study, the flow regimes for complex fracture include compound linear flow, early radial flow and pseudo-steady state flow

(dominated by a closed reservoir boundary), whereas for the bi-wing fractures, the flow regimes consist of pseudo-linear flow, early radial flow, compound linear flow and pseudo-steady state flow (dominated by a closed boundary). In summary, their dominant flow regimes are linear flow and radial flow in the early period and pseudo-steady state flow in the middle and late production period.

a. Rate-normalized pressure derivative signature for bi-wing fracture (scenario 1)

b. Rate-normalized pressure derivative signature for three scenarios (fracture conductivity of 500

D·mm)

Figure 2-19 Rate-normalized pressure (RNP) and its derivative signature for MFHW

2.7 Conclusions

1. Three fracture geometries, simple planar fractures, branching fractures, and fracture network

are simulated in this study. All three scenarios, have the same fracture volume and are all

confined by the same microseismic mapping data and it is found that commonly used simple

planar fractures overestimate the well productivity if a complex fracture network is created in

the reservoir. The differences increase as the fracture conductivity increases. On the other

hand, as geometry of fractures becomes more complex, the computational time increases.

2. For the ideal bi-wing fractures, main fracture conductivity plays an essential role in the early

period, while fracture half-length can significantly affect the long term production. For

different fracture geometries, the early production is similar (e.g. cumulative production of the

first 6 months) and the differences arise around the end of the first year. The differences of

complex fracture and ideal bi-wing fracture become large as the fracture conductivity

increases.

3. Conductivity of the secondary fracture plays an important role on the after-stimulation well

productivity. Secondary fractures with low conductivity can decrease the well productivity

compared to that of the wells with bi-wing planar fractures.

4. If a fracture network is intended to be created in the reservoir, especially at the presence of

natural fractures, efforts must be made to achieve high conductivity of the secondary fractures.

Under such circumstance, adding some complexity to the fracture geometry can increase well

production (e.g. scenario 2 under the conductivity ratio of one-half), which is due to a larger

contact area between matrix and fracture. However, even with high secondary fracture

conductivity, a complicated fracture geometry (scenario 3) still leads to a low long term

production. This is owing to the shortened length of the main fracture.

5. Linear flow and radial flow (or elliptical flow) are dominant flow regimes in early period and

pseudo-steady state flow is the most important regime in the mid and late periods. The flow

regimes are similar between ideal bi-wing fracture and fracture with complexity, except the

difference in early linear flow, that is, compound linear flow arising in complex fractures and

pseudo-linear flow appearing in ideal bi-wing fractures.

Chapter Three: Application of Reservoir Flow Simulation Coupled with Rock Geomechanics 2

3.1 Abstract

Multistage hydraulic fracturing technique now applied with horizontal wells and over large areas has enabled commercial production of oil and gas from unconventional tight rock formations, changing the energy landscape in North America. During fracturing process, tons of fracturing fluid and proppants are pumped into the reservoir matrix to create the hydraulic fractures. It is important to understand the propagation mechanism of hydraulic fractures and further optimize their properties. In addition, natural fractures are often present in the tight formations, which might be activated during the fracturing process and contribute to the after-stimulation well production rates.

In this study, reservoir simulation is coupled with rock geomechanics to predict the well after- stimulation production performance. A dual-permeability geological model is built first based on field data collected from a well pad in Montney formation, western Canada. Fracturing fluid injection in the formation coupled with rock geomechanics and tensile failure criteria is then employed to simulate dynamic hydraulic fracturing process. More specifically, as the continuous injection of fracturing slurry, the effective stress exerted on the rock matrix will decrease accordingly. When the effective stress reaches the rock failure criteria, hydraulic fractures will be generated, allowing the fracturing liquid to flow along the fractures. Based on the fracturing operational schedule, dynamic hydraulic fracturing simulation is conducted and results show that pad step contributes much to the propagation of hydraulic fractures, nearly 40%. Early production

2 Menglu Lin, Shengnan Chen, Zhangxin Chen, 2015, Application of Reservoir Flow Simulation Coupled with Rock Geomechanics in Unconventional Tight Play, Journal of Rock Mechanics and Rock Engineering, under review. 45

history of the stimulated well is then matched to valid the simulated fracture geometries. Finally, the effects of natural fractures and well bottom-hole pressure on well production are studied. It is found that if natural fractures can be propped or partially propped by the proppants, the production will be increased significantly for unconventional tight plays. This paper provides a significant insights on the fracture propagation and can be a reference for fracturing treatments in unconventional tight reservoirs.

3.2 Introduction

The world’s traditional hydrocarbon reserves are in rapid decline and will be unable to meet the future demand for energy. At present, multistage hydraulic fracturing technique together with horizontal wells has been the key to unlock the vast reserve in tight formations with very low permeability. In such process, fluid (e.g., water) is pumped into the formation to create enough pressure to fracture the rock layer. The fluid usually contains a “proppant,” like sand, that helps keep the fractures open to allow oil and gas to be produced to the well. With tons of fracturing fluid and proppants injected continually into formation, the created hydraulic fractures would propagate to more than hundreds of feet away from the wellbore. It is necessary to study the fracture propagation model as induced fractures grow in size and complexity. To predict the fracture properties (e.g. half-length, height and conductivity), many fracture models have been developed, which include two dimensional models, pseudo three dimensional models, and fully three dimensional models. With a 2D model, one of three dimensions, usually the fracture height, is fixed. Fracture width and length can then be calculated. 2D models can be used in certain formations with confidence, assuming the created fracture height can be estimated accurately.

Perkins-Kern-Nordgren (PKN) and Kristonovich-Geertsma-de Klerk (KGD) models are widely used 2D models in the industry, where PKN model is usually applied when the fracture length is

much greater than the fracture height, while KGD model is more reliable if fracture height is more than the fracture length (Geertsma. J, 1979). Pseudo-3D models modify the PKN model by adding height variation along fracture length and its effect on the fracture width (Rahman, 2010), while full 3D models consider the variation of fracture geometry in a three-dimensional space. Although being more realistic, computation costs of fully 3D models are often high, which limit their applications. At present, commercial and research fracture design software are usually developed based on Pseudo-3D models, which have robust capabilities to simulate fluid leak-off, fracture initiation, propagation and closure. However, such models on the other hand cannot handle the reservoir flow behavior in a rigorous way. The modeling of reservoir fluid flow with rock geomechanics has been applied to simulate field problems, such as subsidence in a steam assisted gravity drainage(SAGD) process, well stability or formation deformation in CO2 sequestration

(Tran, 2009). Unlike traditional reservoir simulation in hydraulic fractured reservoirs, the reservoir fluid flow coupled with rock geomechanics can not only investigate the formation fluid flow in the matrix-fracture system, but also be able to predict hydraulic fracture dimensions (e.g., height and half length), fracturing fluid flow back, and in-situ pressure distribution near the wellbore after stimulation. Padmakar (Padmakar, 2013) simulated reservoir fluid flow with geomechanical deformation for mini-fracture tests, providing a new way to model hydraulic fracturing. There are three coupling approaches of reservoir flow and rock geomechanics, which are fully coupled approach, iterative coupled approach and explicit coupled approach (Tran, 2005).

In this study, the iterative coupled approach of reservoir simulation and rock geomechanics is used to simulate the dynamic hydraulic fracturing process. The early production of stimulated wells in a tight liquid rich gas reservoir are then compared and matched with the actual production data collected from the well. The dynamic fracturing process is simulated based on the Barton-Bandis

fracture permeability model (GEM, 2013). The relationship of fracture permeability and effective stress is defined. As the pressure increases in the injection grid block, the normal fracture effective stress decreases accordingly. The hydraulic fracture will be created when rock tensile failure criteria is met, which allows fracturing fluid to flow along the fractures. Effects of non-Darcy flow, pressure dependent permeability of the activated natural fractures, and effects of well bottom-hole pressure on well cumulative production are finally presented.

3.3 Coupled Reservoir Simulation and Barton-Bandis Model

In our model, the iterative coupled approach between reservoir fluid flow and rock geomechanics is adopted due to its flexibility. An advanced general equation-of-state compositional simulator

(GEM, 2013), is applied for reservoir simulation. The flow chart of this coupling method is shown in Fig 3-1. In each time step, pressure and temperature of every grid are calculated by reservoir simulator and then sent to geomechanics module to calculate strain, stress and displacement. The updated stress and strain will be used to determine new pore compressibility and absolute permeability. This coupling iterative algorithm is repeated until the convergence criteria is met.

Thus, the properties computed in the reservoir simulator and geomechanics module are exchanged back and forth, which not only save computation time significantly but also ensure the accuracy.

Figure 3-1 Flowchart of iterative coupled approach (GEM 2013)

The Barton-Bandis model is depicted in Fig 3-2. When a fracturing job starts (point A), pore pressure in the injection grid increases and the normal effective stress decreases. Once the normal effective stress meets the rock tensile failure criteria (point B, frs), the hydraulic fracture will be initiated and hydraulic fracture permeability increases to its maximum value (point C, khf). Once the fracturing job comes to an end, the pumps on the ground surface stop injection. The pore pressure begins to decrease and normal fracture effective stress will increase, leading to the reduction of fracture width. Then the fracture permeability will be reduced to closure value (point

F, kccf). The hydraulic fracture cannot fully close because the proppants have been placed within the fracture and its permeability is decreased to the residual value (point G, krcf), which will serve as an effective conduit to transmit reservoir fluids from the formation to the wellbore.

Figure 3-2 Barton-Bandis permeability model (adapted from GEM User’ Guide, 2013)

3.4 Field Background

The geological model in this study is built for a tight liquid-rich gas reservoir in Montney formation, as seen in Fig 3-3. The Montney Formation is a sedimentary wedge that was deposited during the Early Triassic in the Western Canadian Sedimentary Basin. The Montney depositional fairway stretched over approximately 55,000 square miles from north-east British Columbia to north-west Alberta (Schmitz, 2014). Resources in place in Alberta consists of 2,113 Tcf of natural gas, 28.9 billion bbl. of natural gas liquids, and 136.3 billion bbl. of oil (P50 estimate) and the estimate of natural gas resources in British Columbia is 450 Tcf (Reynolds, Bachman, 2014). The

Montney strata consist of interbedded fine grained sandstones, siltstone and dark grey shale and can be divided into upper, middle and lower units. Upper and middle units are composed of dolomitic siltstones interbedded with shales, while lower units is mainly made of blocky siltstones with interlaminated fine grain sands (Wust, 2014). Montney formation lies between Doig formation and the Belloy formation. The depth of Montney top to the surface ranges from 2800 m

to 3500 m and average formation thickness is 200 m, which tilts from the North East to the South

West (Schmitz, 2014). Reservoir porosity is about 5% and matrix permeability is around 1000 nano-darcy. Natural fractures are developed in the studied area, with a direction perpendicular to the direction of the minimum horizontal stress.

Figure 3-3 Generalized map showing the location and rock types of the Montney

Formation (NEB, 2013)

3.4.1 Recombined Fluid Analysis

The area of interests is located in a liquid rich gas zone. In this study, oil and gas samples collected at the wellhead are recombined to analyze the phase behavior of the reservoir fluids. Compositions of the separator oil and separator gas, and recombined reservoir fluid are shown in Table 3-1. The calculated phase envelope of the recombined reservoir fluid confirms its type to be liquid rich gas.

Table 3-1 Recombined analysis at gas-oil ratio 1198 Sm3/Sm3

Component Separator oil Separator gas Recombined fluid CH4 0.2200 80.5077 70.0910 C2H6 0.6101 10.8434 9.5157 C3H8 1.9902 5.2003 4.7838 IC4 0.9901 0.7880 0.8142 NC4 2.9603 1.5675 1.7482 IC5 2.2702 0.3569 0.6052 NC5 3.1003 0.3771 0.7304 FC6 6.1606 0.2055 0.9781 C7+ 81.6982 0.1536 10.7334 Mole percent 12.9743 87.0257 Density, Kg/m3 715.5738 35.3957 57.6437

3.5 Fracturing Simulation

When the hydraulic pressure is removed from the well, small grains of hydraulic fracturing proppants hold the fractures open. The ability of the fracture to transmit fluid is represented by fracture conductivity, which is the product of fracture width and permeability. Permeability of the fracture equals the permeability of proppant pack within the fracture and is a function of pack porosity, proppant shape, proppant diameter and net stress. The proppant pack permeability

(Meyer, 2013) is calculated by Eq. 3-1.

3 2 −2 푘 ∅ 휑 휑푑푝 2 = 2 [1 + ] (3-1) 푑푝 72휆푚(1−∅) 3(1−∅)푤

Where k is proppant pack permeability (md), dp is proppant diameter (mm), φ is pack porosity, ϕ is sphericity, λm is friction factor multiplier and wf is fracture width (mm).

Dimensionless fracture conductivity (Fcd) is a key design parameter in well stimulation that compares the capacity of the fracture to transmit fluids down the fracture and into the wellbore with the ability of the formation to deliver fluid into the fracture (Pearson, 2001)

푘푓푤푓 퐹푐푑 = (3-2) 푘푚푥푓

Where kf is the fracture permeability; wf is the fracture width; km is the permeability of the matrix, and xf is the fracture half length.

The fracture opening conductivity is estimated by a fracture design and analysis software (Fracpro,

2015) and fracture residual permeability is calculated by Eq. 3-1. A model representing one stage of horizontal well is built to simulate the hydraulic fracturing process. The grid dimension is shown in Fig 3-4. In this study, it is assumed hydraulic fracture opening stress (frs) equals to zero. In other words, the hydraulic fractures will be initiated if the normal fracture effective stress decreases to zero, leading to a tensile failure (Tran, 2009). At the same time the hydraulic fracture permeability will increase to Khf. Effective stress will increase accordingly after fracturing slurry injection stops, resulting in the reduction of hydraulic fracture permeability. In addition, common fracture design software assume constant pressure drop and constant leak-off coefficient across the fracture length, which contradicts the actual leak-off into the formation (Padmakar, A. S. 2013). On the other hand, the coupled reservoir simulation with rock geomechanics has variable leak-off coefficients which are depended on the in-situ pressure in each grid.

Figure 3-4 Grid dimensions in fracturing model

Over 100 mini-frac tests in western Canada indicate that for large parts of the Alberta Plains, normal-fault stress regime Sv is larger than the maximum horizontal stress, SHmax, while the minimum horizontal stress Shmin is the smallest (Cui, 2013). In this model, vertical principal stress is calculated from density log data and the minimum principal stress is obtained from the diagnostic fracture injection test (DFIT). During the hydraulic fracturing process, the slick-water is used and the pumping schedule is shown in table 3-2. The detail model properties are shown in table 3-3. To simplify the hydraulic fracturing process, main fractures are assumed to have planar bi-wing geometries. Natural fractures might be activated during the fracturing process and serve as secondary fractures. The dynamic propagation profile of hydraulic fracture is shown in Fig 3-5 and the perforation is in the middle of the formation. Hydraulic fracture propagates along the least

principal stress direction, the final hydraulic fracture half-length is predicted to be 130 m and hydraulic fracture height is 40 m. In addition, it is found that the pad step has a larger contribution to the propagation compared with other steps.

Table 3-2 Typical treatment schedule of hydraulic fracturing (taken one stage as example)

Step Stage Flow Proppant Fluid Time Fluid Proppant No. Type Rate Concentration Volume (min) Type Type (m3/min) (kg/m3) (m3) 1 Frac pad 1.2 0 27 22.5 Slickwater 2 Frac 1.28 229 16.4 13.92 Slickwater CarboProp slurry 40/70 3 Frac 1.3 298 13.44 11.5 Slickwater CarboProp slurry 40/70 4 Frac 1.38 541 14.8 12.91 Slickwater CarboProp slurry 40/70 5 Frac 1.44 746 19.1 17 Slickwater CarboProp slurry 40/70 6 Frac 1.45 741 6.75 5.96 Slickwater CarboProp slurry 40/70 7 Frac 3.6 0 18.64 5.18 Slickwater flush

Table 3-3 Fracturing model properties

Reservoir temperature(℃) 92 Top depth (m) 3005 Thickness (m) 40 Formation compressibility (KPa-1) 6 × 10-7 Total compressibility(KPa-1) 5 × 10-5 Connate water saturation 30 % Porosity 5 % Matrix permeability (md) 0.001 Young’s modulus (GPa) 47 Poisson’s ratio 0.2 Principal stress (Sv, SH, Sh, MPa) 65, 53, 38 Stress gradient (Sv, SH, Sh, KPa/m) 26, 22.7, 16.6 Injection fluid Slickwater Hydraulic fracture closure conductivity (kccf·w f, D·mm) 60

Residual value of fracture closure conductivity (krcf·w f, D·mm) 11.6

Fig. 3-5 shows the dynamic propagation profile of hydraulic fracture, which corresponds to each step in the pumping schedule for a single stage. The matrix pressure is equal to initial pressure

(blue color) and pressure in hydraulic fracture increases significantly. It is shown that fracture propagates vertical to the direction of least principal stress and half-length grows to about 130 m at the end of pumping period, where fracturing pad step contributes 50 m, nearly 40%.

Figure 3-5 Fracture profile (pressure: KPa) during the fracturing liquid injection (HL: half

length)

The water distribution of each step is shown in Fig 3-6. It can be seen that water distribution is corresponding to the dimensions of fracture propagation. The profile (step No. 7) is the water distribution at the end of pumping schedule. It is also observed the penetration depth of fracture fluid into matrix is very shallow (less than 0.5 m). Thus in such tight formation, fracturing liquid is mainly distributed in the hydraulic fracture and some is placed in surrounding matrix near the fracture face.

Figure 3-6 Water distribution in the fracture

3.6 Reservoir Simulation

After obtaining the hydraulic fracture properties and fluid composition, the reservoir model is then utilized to simulate the multiphase flow (gas-water-condensate liquid) in the formation. The simulator of GEM (GEM, 2013) is used to simulate the well post stimulation performance of the horizontal well. In this model, the length of multi-fractured well is 1925 m with 21 stages. The perforation type is open-hole and average stage spacing is 85 m. The reservoir model with dimensions of 2125 m x 455 m x 40 m is set up to simulate the horizontal well. The grid number is 89 x 25 x 10, which corresponds to the reservoir length, width and thickness, which is shown in

Fig 3-7. The reservoir properties is assumed to be homogenous, shown in table 3-4, which are the same as those in the fracturing model. The fluid properties can be found in table 3-1.

Figure 3-7 Reservoir model of a horizontal well with 21-stage fractures

Table 3-4 Reservoir model properties

Horizontal well length (m) 1925 Stages 21 Reference pressure (KPa) 36,017 Reference depth (m) 3,025 Hydraulic fracture half-length (m) 130 Hydraulic fracture conductivity 11.60 (D.mm)Natural fracture spacing (m) 4.2

The relative permeability curves are shown in Fig 3-8 and 3-9, which is modified from the literature (Al Ghamdi, 2009). The natural fractures can be observed in the core and rose diagram.

The cleavage or natural fractures are distributed, parallel to the minimum principal stress, as shown in the Fig 3-10. Existence of natural fracture may pose an evident impact on the production of fractured well in tight formations (Lin, M., Chen. S, 2015). In this study, it is assumed that

horizontal well is drilled along the direction of the minimum principal stress, so that hydraulic fracture can propagate perpendicular to the minimum principal stress. The natural fractures are considered in the direction parallel to the minimum principal stress and horizontal well is assumed to be drilled along the minimum principal stress. Thus, the generated hydraulic fractures will be orthogonal to the natural fractures.

1 1

Krw Krg 0.75 Krow 0.75 Krog Kr Kr 0.5 0.5

0.25 0.25

0 0 0 0.2 0.4 0.6 0.8 1 Sw 0 0.2 0.4 Sg 0.6 0.8 1 Figure 3-8 Matrix: a. oil and water relative permeability curve b. liquid and gas relative

permeability curve

1 1 Krw Krg Krow Krog 0.75 0.75

Kr Kr 0.5 0.5

0.25 0.25

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 Sg 0.6 0.8 1 Sw Figure 3-9 Hydraulic fracture: a. oil and water relative permeability curve b. liquid and

gas relative permeability curve

Figure 3-10 Schematic of natural fracture distribution

History matching procedure was performed where the oil rates are selected as constraints and the gas rates are used as inputs and the simulated oil rates are shown in Fig 3-11. It can be seen that early production of the stimulated well are well matched, which might be a validation of the hydraulic fracture properties derived from the fracturing simulation.

Figure 3-11 History matching results

3.7 Results and Discussion

3.7.1 Effect of Non-Darcy Flow in Hydraulic Fracture

Non-Darcy flow is typically observed in high-rate gas wells when the flow converging to the wellbore reaches flow velocities exceeding the Reynolds number for laminar or Darcy flow, and

results in turbulent flow. For condensate gas reservoirs, once gas velocity exceeds the limit for

Darcy’s Equation application in the hydraulic fractures, an additional pressure loss will occur due to the non-Darcy effect. Two types of criteria, the Reynolds number and the Forchheimer number, have been used in the past for identifying the existence of non-Darcy flow (Zeng, 2006). In this study, Forchheimer equation, shown in the Eq. 3-3, is used to study the effect of non-Darcy flow in the hydraulic fracture (Rubin, 2010, Yu. 2014). As shown in Fig 3-12, the difference between

Darcy flow and non-Darcy flow is very small. So the effect of non-Darcy flow can be neglected in the hydraulic fracture with the hydraulic fracture conductivity of 11.6 D.mm. As discussed before, dimensionless fracture conductivity (11.6 D.mm) is around 90, which can be treated as infinite conductive. Because this conductivity value is the maximum in our simulations, the flow rate is the largest among all the simulations. Thus the effect of non-Darcy flow in other simulations can also be neglected.

휇 −∇푝 = 푣 + 훽𝜌푣2 (3-3) 푘

Where µ is viscosity, k is hydraulic fracture permeability, v is velocity, ρ is density of certain phase,

β is the non-Darcy Beta factor. And the correlation equation used in simulator is shown as follows, proposed by Evans and Civan (1994).

9 91.021 훽(푓) = 1.485 × 10 ⁄푘 (3-4)

20 100

) 3 ) 80

16 3

3 6

12 60

8 40 Cumulative Oil (10 Oil SC Cumulative

4 Non-Darcy flow (10 GasSC Cumulative 20 Non-Darcy flow Darcy flow Darcy flow

0 0 0 365 730 1095 1460 1825 0 365 730 1095 1460 1825 Time (Days) Time (Days)

a. Darcy and non-Darcy flow for oil phase b. Darcy and non-Darcy flow for gas phase Figure 3-12 Darcy and non-Darcy flow with hydraulic fracture conductivity of 11.6 D·mm

3.7.2 Effect of Pressure-Dependent Permeability of Natural Fractures

The natural fractures may be activated during hydraulic fracturing process, and contribute to the well post production. Once the stimulated well is put on production, pore pressure decreases and the permeability of natural fractures will be reduced. The permeability loss of natural fracture as reservoir pressure decrease is shown in Fig 3-13 (Bachman, 2011). Bachman defined 3 different scenarios for pressure-dependent permeability based on different Montney formation properties.

As can be seen from Fig 3-13, for low pressure-dependent permeability, its value drops by 20%, whereas, for high pressure-dependent permeability, permeability drops by about 70%.

0.8

0.6

0.4 Normalized permeability Normalized 0.2 Low perm loss High perm loss 0 0 10 20 30 40 Pressure, MPa

Figure 3-13 Pressure-dependent permeability of natural fracture

Reservoir simulations are conducted to investigate the effect of pressure-dependent permeability of natural fractures on well cumulative production in 2000 days and results are shown in Fig 3-14 and 3-15. The initial natural fracture permeability is 0.01 md. It is shown the differences between scenarios with constant natural permeability and pressure-dependent ones are significant. The cumulative oil production of high permeability loss is reduced by 22.8% and that of low permeability loss is reduced by 12.2 %, as shown in Fig 3-14. The similar trend can also be found for cumulative gas production, which is reduced by 18.4% and 10%, respectively. The similar trend can be seen if the hydraulic fracture conductivity is reduced to 1.16 D·mm, shown in Fig 3-

15. As dimensionless fracture conductivity is less than 10, it is regarded as limited conductive.

Cumulative production differences among such three scenarios are also significant. In addition, differences of cumulative production appear around 100 days if natural fracture permeability is highly dependent on reservoir pressure, compared to its value for constant permeability scenario.

For the scenario of low-permeability loss, the production difference between low permeability loss and constant natural fracture permeability appears around 500 days.

16 30

14 25

)

3 3

m 12

m 3 6 6 20 10

8 15

6 10

4 constant perm constant perm low perm loss 5 low perm loss Cumulative Oil (10 SC Cumulative 2

high perm loss (10 GasSC Cumulative high perm loss 0 0 0 400 800 1200 1600 2000 0 400 800 1200 1600 2000 Time (Days) Time (Days)

Figure 3-14 Cumulative productions at hydraulic fracture conductivity 11.6 D·mm

20 30

)

m 6

m 20 3 12 15

8 10

4 constant perm constant perm

low perm loss 5 low perm loss Cumulative (10 GasSC Cumulative Cumulative Oil (10 SC Cumulative high perm loss high perm loss 0 0 0 400 800 1200 1600 2000 0 400 800 1200 1600 2000 Time (Days) Time (Days)

Figure 3-15 Cumulative productions at hydraulic fracture conductivity 1.16 D·mm

If the proppants with small particles (100 mesh) are used in the fracturing, the activated natural fracture is probably propped or partly propped, resulting in the increase of natural fracture permeability. If the initial permeability of natural fracture is increased to the 10 times of the previous value when natural fracture is partly propped. The cumulative productions of increased natural fracture permeability at the hydraulic fracture conductivity 1.16 D·mm are shown in Fig

3-16. Compared with results of constant natural fracture in Fig 3-15, the productions are increased

significantly. Condensate oil increases by 28% and gas increases by 36%. Similarly, differences of early cumulative production are small and their differences increase with production time. So it is necessary to predict the accurate production considering the pressure-dependent permeability.

20 40

)

) 3

16 3

m m

3 30 6

12 25 20

8 15

constant perm 10 constant perm 4 low perm loss low perm loss Cumulative Oil (10 SC Cumulative 5 high perm loss (10 GasSC Cumulative high perm loss 0 0 0 400 800 1200 1600 2000 0 400 800 1200 1600 2000 Time (Days) Time (Days)

Figure 3-16 Cumulative productions at hydraulic fracture conductivity of 1.16 D·mm with

high conductive natural fracture (0.1 md)

3.7.3 Effect of Well Bottom-hole Pressure

The cumulative oil and gas condensate production rate from the stimulated well in the gas condensate reservoir is sensitive to the well flowing bottom-hole pressure (BHP). 5000-day simulations are conducted under different BHP pressures. BHP for the first scenario is 10 MPa for all 5000 days and BHP in the second scenario is 15 MPa in the first three years and 5 MPa in the following 12 years. As shown in Fig 3-17, both oil and gas productions in the early production period are higher in the first scenarios with BHP of 10 MPa. The cumulative production of the second scenario overtakes the first one in the 5th year. For the second scenario, the pressure difference in the first 3 years is small and thus the formation energy is kept at a high value. When the BHP of the second scenario is reduced to 5 MPa at the end of 3rd year, productions increase significantly and exceeds their values in scenario 1.

16 25 10 MPa 10 MPa 14 15 Mpa + 5MPa

) 15 Mpa + 5MPa

) 3

3 20 m

12 m

3 6

10 15 8

6 10

5 Cumulative (10 Oil SC Cumulative

2 (10 SC Gas Cumulative

0 0 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Time (Days) Time (Days)

Figure 3-17 Production comparison of different bottom-hole pressures at conductivity of

11.6 D·mm

3.8 Conclusion

1. In this paper, the reservoir flow simulation coupled rock geomechanics has been successfully

employed to predict the properties of the hydraulic fracture in the formation. The combination

of robust reservoir flow and geomechanical deformation improves the reservoir fluids flow

simulation in the matrix-fracture system by considering fracturing fluid leak-off and saturation

in the matrix, as well as an updated pressure distribution near the wellbore after stimulation

job.

2. It is found that in the tight gas reservoir with the permeability of 0.001 md, the penetration

depth of fracture fluid into matrix is very shallow, which is less than 0.5 m. Thus in such tight

formation, fracturing liquid is mainly distributed in the hydraulic fracture and leak-off is only

expected in surrounding matrix very close to the fracture surface.

3. In tight gas reservoirs (km=0.001 md), the effect of natural fractures on cumulative

production is significant. Natural fracture permeability can be sensitive to stress during the

production life, which can in-turn affects the well after-stimulation production profile. The cumulative oil production of high permeability loss is reduced by 22.8% and that of low permeability loss is reduced by 12.2 %, compared to the scenario with the constant natural fracture permeability. Similar trends can be seen for both high and low hydraulic fracture conductivity scenarios.

4. In liquid-rich gas reservoirs, liquid hydrocarbon (oil) production is critical to the profit of the project. It is found that, a higher BHP at the earlier production life, followed by a lower

BHP later yields more cumulative gas and oil, compared to the case with constant BHP.

Chapter Four: Sensitivity Analysis on Flow-back Recovery and NPV in Liquid Rich Gas Well

4.1 Abstract

Multi-stage hydraulic fracturing in horizontal wells is routinely used in commercial exploitation of oil and gas from unconventional reservoirs (e.g. tight liquid rich gas reservoir). In these reservoirs, tons of fracturing fluid are pumped into the reservoir matrix to create hydraulic fractures but much is trapped in tight formation, resulting in low flow-back recovery. In addition, condensate drops out of gas when pressure is below the dew point, which affects production and net present value. It has become a major concern to clarify cleanup characteristics of tight liquid rich gas well and further improve net present value (NPV).

In this paper, a simulation framework is established including hydraulic fracturing, flow-back and production based on a coupled reservoir flow/geomechanics simulator. First, hydraulic fracturing is simulated to inject fracturing liquid. Then the effects of parameters (e.g. well bottom-hole pressure, fracture conductivity, capillary pressure and well shut-in) on flow-back recovery are investigated. Then Design of Experiments and response surface methodology are conducted to explore well operational parameters affecting flow-back recovery and net present value.

Results indicate fracturing fluid is distributed in the hydraulic fracture and surrounding matrix near fracture face. Flow-back mainly occurs in the first two months, especially the first ten days. Much fracturing liquid cannot be recovered due to poor properties of tight formation instead of limitation of hydraulic fracture. In addition, well bottom-hole pressure (BHP) at production is the controlling factor affecting flow-back recovery and NPV. Well shut-in has the negative effect on both flow- back recovery and NPV. It is recommended short well shut-in period, low BHP during flow-back and relative high BHP at production. This paper not only offers an alternative method to predict

hydraulic fracture but also provides a novel approach to simulate flow-back and optimize condensate well performance, which can enhance the understanding of their mechanisms and provide guidance for the design of field operations.

4.2 Introduction

In recent years, the Western Canadian Sedimentary Basin (WCSB) has observed significant developments with fractured horizontal wells in unconventional tight reservoirs, which have been important sources of energy supply. The widely spread of producing horizontal wells in WCSB can be seen in Fig. 4-1, from the provinces of Saskatchewan, Alberta and British Columbia, and the ratio of multi-fractured horizontal wells is markedly improving recently and their contributions have reversed the decline in Canadian natural gas and light oil production.

Figure 4-1 Distribution of producing horizontal wells, Western Canada (Dixon K.R., Flint D.,

2014)

In terms of statistics from 2009 to 2013, light oil production from horizontal wells has doubled to over 600 mbopd and gas production from horizontal wells has more than a tripled to over 6 bcfd since 2009 (Dixon K.R., Flint D., 2014) . In terms of the investigation of Canada National Energy

Board (NEB, 2015), shale gas accounted for approximately 4% of total Canadian natural gas production while tight gas accounted for 47% in 2014. It is expected that unconventional gas production will represent 90% of Canada’s natural gas production by 2035. The Montney formation is a sedimentary wedge that was deposited during the Early Triassic in the Western

Canadian Sedimentary Basin. Montney formation lies between Doig formation and the Belloy formation. The depth of Montney top to the surface ranges from 2800 m to 3500 m, which tilts from the North East to the South West (Schmitz, 2014). Reservoir porosity is about 5% and matrix permeability is around 1000 nano-darcy. The target Montney play is from the Karr field located in the transition area of oil window and gas window. The liquid rich potential has made it prolific and more profitable compared with other resources. The Montney reservoirs in the Karr field, where complex fluids vary from rich gas/condensate of the west side to volatile oil of the east side, can be classified into deep-basin, over-pressured, mixed-hydrocarbon-saturated reservoirs. The depth of target formation is more than 2 miles and pressure gradient is more than 10 kPa/m, which can support improved deliverability (Kuppe, 2012).

The successful developments of these tight plays are significantly dependent on appropriate completions. The introduction of hydraulic fracturing with horizontal well has brought in noticeable production increase, and meanwhile, many problems arising from this process are needed to be solved. For example, in order to create massive hydraulic fractures, great quantities of water, proppant and small amounts of chemical lubricants are pumped into tight formations.

However, the recovery of fracturing liquid is not satisfying and much is trapped in the formation due to high capillary pressure. In tight formations, the gas relative permeability declines due to water saturation increase around the hydraulic fracture, which impairs gas production in a very long cleanup period. In addition, more complex challenges are presented in liquid rich gas

reservoir. As pressure decreases, condensate drops out of gas once pressure is below dew point. It is generally accepted three zones are present from well to reservoir boundary. 1) Mobile gas and mobile condensate region near the wellbore 2) Transition zone including mobile gas and immobile oil 3) One phase zone including mobile gas and no condensate drop-out ( Penuela G. Civan F.,

2000). Condensate drops out near hydraulic fracture during flow-back and production. And the condensate with trapped fracturing liquid together aggravates fluid mobility. For releasing potential productivity, it is necessary to investigate controlling factors affecting flow-back recovery and condensate production. In current literatures, when flow back is simulated, high conductive hydraulic fracture is added in the model and then water is injected in the reservoir through the high conductive fractures (Sharma, M., Agrawal, S., 2013). However, in the field, the frac-water is pumped into tight matrix and then hydraulic fracture is created, where stress and pressure vary drastically in a short time. The previous methods fail to capture hydraulic fracturing characteristics. In our paper, the coupled reservoir flow/geomechanics simulator can combine dynamic hydraulic fracturing with robust fluid flow simulation together, which is more appropriate to simulate hydraulic fracturing and flow back. The dynamic fracturing process is simulated based on the Barton-Bandis fracture permeability model (GEM, 2013). In terms of the defined relationship between fracture permeability and effective stress, as the injection of frac-water and increase of grid pressure, the normal fracture effective stresses (the effective stress that is applied normal to the fracture surface) decreases accordingly. When the normal fracture effective stress decreases and rock tensile failure criteria is met, the hydraulic fracture will be created, which allows fracturing fluid to flow along the fractures. Then flow back and well production can be simulated after injection of fracturing fluid.

4.3 Injection and Flow-back of Fracturing Fluid

The introduction of the coupled reservoir flow/geomechanics simulator and Montney formation description can be found in the last chapter. The calculated phase envelope of the recombined reservoir fluid is shown in Figure 4-2. It is shown that the reservoir condition is within the gas condensate side of the generated phase envelope, to the right of the critical point.

Figure 4-2 Phase envelope of simulated condensate reservoir

The multi-fractured horizontal well plays the critical role in the commercial development of unconventional reservoirs. Fig 4-3 shows a typical horizontal well with multiple stages in the unconventional reservoir. Oil and gas are produced through these high conductive hydraulic fractures. In our model, we assume vertical transverse fractures are identical and equally spaced and each fracture has symmetric no flow boundaries. If identical hydraulic fracture is assumed, one single fracture can be adopted to represent the whole horizontal well, which will reduce

simulation time significantly (Chaudhary, A. S. 2011, Sennhauser, E. S. 2011, Zhang, Z. 2013).

Single stage separated with blue dashed lines is chosen for reservoir simulation.

Figure 4-3 Two-D schematic of a multi-fractured horizontal well in tight reservoir

(Zanganeh, B. Ahmadi M. et. al., 2015)

Shown in Fig 4-4, the dimensions of the model are 83 m x 805 m x 30 m and the corresponding grid number is 25 x 57 x 11 (X, Y, Z). The width (83 m) of the model is equal to the fracture spacing. In any simulator, it is a challenging task to simulate the actual width and permeability of a hydraulic fracture because of the high computational cost and the convergence issue.

Alternatively, grids with an equivalent permeability, width and porosity are used to represent the hydraulic fracture in the simulator (Rubin 2010 and Lin, M., Chen, S., 2015). The width of grid that represents fracture is 2 ft. The grids of surrounding matrix near the fracture are logarithmically spaced in order to capture the drastic change of pressure and saturation.

Figure 4-4 Permeability distribution (md) of reservoir model (taken one stage as an

example)

The fracturing schedule and fracture model properties are shown in Table 3.2 and 3.3 of chapter three. The fracture propagation is shown in Fig 4-5. It shows that fracture propagates vertical to the direction of least principal stress and half-length grows to about 160 m at the end of pumping period, where fracturing pad step contributes 60 m, 37.5 %. Water saturation in the hydraulic fracture is shown in Fig 4-6, which correspond to fracture propagation dimensions.

Figure 4-5 Fracture profile (pressure: KPa) during the fracturing liquid injection (HL: half

length)

Figure 4-6 Water saturation in hydraulic fracture during injection

In the model, hydraulic fracture relative permeability is the same with that in Chapter 3. Matrix relative permeability are calculated based on Brooks and Corey relative permeability model

(Brooks, R. H. and Corey, A. T. , 1966). Matrix capillary pressure is generated in terms of the following correlation equation (Gdanski, R.D., 2009 and 2010).

휎 cos 휃 ∅ 푎3 푃푐 = 푎1 ( ) (4-1) 푎2 푆푤 푘

Where 푃푐 is capillary pressure, psi; 𝜎 is surface tension, dynes/cm; 휃 is wettability contact angle, degree; 푆푤 is water saturation, fraction; ∅ is porosity, fraction; k is absolute permeability, md; and

푎1 , 푎2 푎푛푑 푎3 are adjustable constants.

After hydraulic fracturing stimulation, high pressure in hydraulic fracture causes frac-water to rise to the surface. Shown in Fig 4-7, frac-water flows back at different fracture conductivities when well bottom-hole pressure (BHP) is kept constant (15 MPa). It shows frac-water flow-back mainly happens in the first 10 days. The final cumulative water production at about two months is 60 m3 and thus flow-back recovery is 51.67%. Although larger fracture conductivity has higher water production rate, final cumulative water production is similar. This is because hydraulic fracture conductivity in this range has enough ability to transport frac-water into the wellbore. If dimensionless fracture conductivity is calculated, its value (taken 10 D.mm for example) can be more than 40, which is infinite conductive. Since flow-back recovery is around 50%, it is possible that much injected water is trapped in the tight matrix. In addition, as pressure near hydraulic fracture declines below dew-point pressure, condensate begins to build up and reduces gas and water mobility.

100

) 3

60 40

60 D·mm 40 60 D·mm

20 D·mm 20 20 D·mm Water Cut SC (%) SC Cut Water

20 10 D·mm 10 D·mm Cumulative water(m SC Cumulative

0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 Time (Day) Time (Day)

Figure 4-7 Flow back at different conductivities

4.4 The Effect of Capillary Pressure and BHP

In order to study the effect of capillary pressure, several sets of capillary pressure are calculated according to the above correlation equation. For example, 푎1 = 1.86 푎2 = 6.42 and 푎3 is normally set to the value of 0.5. If rock is water wet, 휃 = 1 and cos 휃 = 1. All surface tensions are defined as 72 dynes/cm. Shown as Fig 4-8, three different capillary pressure curves are calculated.

500 100

Set 3 ) Set 1 3 400 80 Set 2 Set 2 Set 1 Pc, Pc, Psi Set 3 300 60

200 40

100 20 Cumulative water(m SC Cumulative

0 0 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 Sw Time (Day)

Figure 4-8 Capillary pressure curves and corresponding cumulative water production

It can be observed that cumulative water production decreases with increasing capillary pressure value. Much more water is trapped into tight formation due to higher capillary pressure. That

means higher pressure drawdown is required to overcome the resistance of capillary pressure.

Shown as Fig 4-9, well bottom-hole pressure is kept at a low value (7 MPa) and fracture conductivity is assumed at 60 D.mm. It shows that more frac-water can be recovered at a low bottom-hole pressure because of higher driving force. Gas production is also enhanced significantly at a low bottom-hole pressure.

100 1600 )

80 ) 3

3 1200 m

60 800 40

400

20 High BHP ( SC oil Cumulative

Cumulative water(m SC Cumulative High BHP Low BHP Low BHP 0 0 0 10 20 30 40 50 60 0 200 400 600 800 1000 Time (Day) Time (Day)

)

3 m

6 4

High BHP 1

Cumulative gas (10 SC Cumulative Low BHP 0 0 200 400 600 800 1000 Time (Day)

Figure 4-9 Well production contrast at different BHP

However, cumulative oil volumes are reduced in terms of long-term production even though early period demonstrates a higher trend from the low well bottom-hole pressure. In liquid rich gas

reservoir, higher bottom-hole pressure brings about increased oil production but restrains the gas production and recovered frac-water volume. Since the condensate oil is more valuable, increased oil recovery can increase the net present value (Holme, 2013). It is necessary to keep a balance between flow-back recovery and condensate oil production.

4.5 The Effect of Well Shut-in Time

Shown as Fig 4-10, a typical fractured well workflow includes fracturing job, flow-back, shut-in and production periods. After fracturing stimulation, frac-water starts to flow back directly in order to reduce formation damage. There is one shut-in or well resting period between flow-back and production due to delay in pipeline connection (Alkouh, A., Mcketta, S. et. al., 2014).

Figure 4-10 Flow sequence of a typical fractured well (Alkouh, A., Mcketta, S. et. al., 2014)

In this part, we compare the effect of shut-in period on production. It is assumed flow-back lasts for 10 days and then different shut-in times are investigated. Shown as Fig 4-11, initial production rates apparently increase when well is reopened and differences gradually disappear at 150 days.

As shut-in time is extended, the increase of initial production is larger. However, Fig 4-12 shows shut-in period almost has no positive effect on the long-term production. In addition, during shut- in period, more frac-water penetrates into the matrix, which lowers flow-back recovery. From Fig

4-13, well bottom-hole pressure is kept at 15 MPa and we can see fracture pressure begins to build up after well shut-in. The pressure build-up increases initial production rate. Because low matrix permeability limits pressure transition, this increase can only last for a short time and differences disappear at 150 days, which does not have the contribution to longer production any more. For example, for all cases, pressure distribution at 2000 days are almost the same. Since production is not enhanced by well shut-in, we recommend that well shut-in period should be as short as possible.

3 15

2.5 No shut-in ) No shut-in 3

) 12

3 m 2 4 Shut-in for 9 Shut-in for 7 days 7 days 1.5 Shut-in for Shut-in for 6

1 one month one month Oil rate (m SC Oil 3 0.5 (10 SC Gasrate

0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Time (Day) Time (Day)

Figure 4-11 Oil and gas rate of shut-in

500 1800

) 3

) 1500 3

m 400

4 4 m 1200 300 No shut-in No shut-in 900 Shut-in for 200 Shut-in for 7 days 600 7 days Shut-in for Shut-in for one month one month

100 300

Cumulative oil ( SC oil Cumulative Cumulative gas (10 SC Cumulative 0 0 0 500 1000 1500 2000 0 500 1000 1500 2000 Time (Day) Time (Day)

) 3 60

40 No shut-in

Shut-in for 20 7 days

Cumulative water(m SC Cumulative Shut-in for one month

0 0 20 40 60 80 100 Time (Day)

Figure 4-12 Cumulative production of shut-in

Figure 4-13 Pressure (KPa) in the hydraulic fracture

4.6 Sensitivity Study of Flow-back Recovery and NPV

For identifying the most important parameters affecting flow-back recovery and NPV, Design of

Experiment is employed to investigate the effect of different operational parameters, which is widely used to investigate main effect and interaction effect of factors.

As aforementioned, valuable condensate is sensitive to operational parameters, such as well bottom-hole pressure. Several parameters are picked out to conduct sensitivity analysis from

different operational periods. Five factors affecting flow-back recovery and net present value and their corresponding value range are shown in table 4-1, including fracture conductivity, BHP at flow-back, flow-back period time, well resting or shut-in period time and BHP at production. Their corresponding responses are recovered frac-water after sixty days and NPV after two thousand days, respectively. As one objective function, NPV is calculated as the following equation (Yu. W,

Sepehrnoori, K., 2014).

(푉 ) 푁푃푉 = ∑푛 퐹 푗 − [퐹퐶 + ∑푁 (퐶 + 퐶 )] (4-2) 푗=1 (1+푖)푗 푘=1 푤푒푙푙 푓푟푎푐푡푢푟푒

Where 푉퐹 is the future value of gas and condensation liquid revenue, 퐹퐶 is total fixed cost, 퐶푤푒푙푙 and 퐶푓푟푎푐푡푢푟푒 are cost of horizontal well and hydraulic fracture, N is number of horizontal wells, n is number of periods and j is discount rate or interest rate.

Fracture conductivity is from 6 D.mm to 60 D.mm, which is in the infinite conductive range. Fig

4-7 shows that water-cut has decreased below 20% after about one week. Thus flow-back simulation period is from one week to two weeks. Shut-in time is from 1 day to about 3 weeks after flow-back. As valuable condensate production is sensitive to reservoir pressure, large range

of BHP is investigated. The simulation responses are recovered frac-water after sixty days

(response 1) and NPV after 2,000 days (response 2), respectively.

Table 4-1 Variables and their value range

Factor Lower level Higher level Unit

A Fracture conductivity 6 60 D.mm

B Flow-back BHP 3,000 18,000 KPa

C Flow-back time 7 14 Day

D Production BHP 3,000 18,000 KPa

E Well resting time 1 23 Day

CMOST (CMOST, 2013) is used to perform Design of Experiment and the simulation results of well production are shown in Fig. 4-14, 4-15 and 4-16. It can be observed that cumulative oil and gas productions vary significantly among different variable values. Fig 4-16 shows that frac-water mainly flows back in the first two months and about half injected volume can be recovered.

Figure 4-14 Cumulative oil production

Figure 4-15 Cumulative gas production

Figure 4-16 Cumulative water production

Relationships between factors and responses can be explored by response surface methodology, which is to use designed experiments to build a proxy model. Common proxy models include a linear form or quadratic form of a polynomial function. After a proxy model is built, tornado plots

displaying a sequence of parameter can be used to assess the sensitivity of parameters (CMOST,

2013). Regarding the response 1 (R1, recovered frac-water at 60 days), linear proxy model can represent the original simulation model because no evident interaction effect is observed, shown as Equation 4-3, which can predict flow-back recovery.

−5 푅1 = 62.369 + 0.0176922퐴 − 7.6 × 10 퐵 + 0.200157퐶 − 0.0003075퐷 − 0.1389퐸 (4-3)

Fig 4-17 is tornado plot showing rank of different factors. Max and min are maximum and minimum values of objective function. We can see the difference about importance of five parameters is relatively small. If objective is to achieve high flow-back recovery, measures can be taken, such as increasing fracture conductivity and flow-back time, lowering well bottom-hole pressure and well-resting (shut-in) time.

Figure 4-17 Tornado plot of recovered fluid

Regarding response 2 (R2, NPV at 2000 days), it is assumed interest rate is 10%, condensate oil price is 40 $/Barrel and gas price is 2 $/Mscf. Quadratic proxy model is used due to the significant interaction effect, shown as Equation 4-4.

퐑ퟐ = ퟓퟗퟖퟖퟔퟓ − ퟏퟑퟑ. ퟎퟎퟖ푨 − ퟎ. ퟏퟏퟔퟒퟖퟗ푩 + ퟐퟐퟎ. ퟏퟑퟗ푪 + ퟒ. ퟖퟓퟕퟔퟐ푫 − ퟏퟕퟒ. ퟕퟗퟔ푬 +

ퟎ. ퟎퟎퟗퟏퟓퟐퟕퟒ푨 ∙ 푫 − ퟎ. ퟎퟎퟎퟐퟖퟑퟖퟏퟐ푫ퟐ (4-4)

Fig 4-18 is tornado plot about rank of different factors affecting NPV at 2000 days. It can be observed that BHP at production is one controlling factor affecting NPV. The effects of well bottom-hole pressure at flow-back (B), flow-back time (C) and well resting time (E) on objective function are relatively small. Results show that simulations with high NPV usually have short shut- in period, low flow-back BHP and high production BHP. For example, in the optimal case of max

NPV, fracture conductivity is 6 D.mm, flow-back BHP is 3 MPa, flow-back time is two weeks, production BHP is 13 MPa and well resting time is 1 day. Thus if objective is to achieve high NPV, such measures can be taken, 1) lowering BHP at flow-back for higher flow-back recovery 2) increasing BHP at production for more condensate oil volume 3) shorting well shut-in period.

Figure 4-18 Tornado plot of NPV

4.7 Conclusion

1. In this paper, a coupled reservoir flow/geomechanics simulator is employed to

investigate frac-water flow-back, which provides an alternating method to simulate

hydraulic fracturing, flow back and production in liquid rich gas reservoir..

2. In tight gas formation (about 0.001 md), if fracture conductivity keeps enough transport

ability (e.g. 6 D.mm), it can support enough ability to transport fluid to the wellbore.. Low

matrix permeability limits pressure transition, resulting in fast decline rate. Well shut-in

can increase initial production rate due to pressure build-up but does not have positive

contribution to long-term production.

3. Flow-back mainly happens in the first two months and simulation recovery is from 43.5%

to 60.3%. Although fracturing liquid is mainly distributed in the hydraulic fracture and

surrounding matrix very close to fracture face, much still cannot be recovered because

injected fluid is trapped by the tight matrix near hydraulic fracture, such as resistance of

capillary pressure. Low well bottom-hole pressure can recover more fracturing fluid

because high pressure drawdown can overcome capillary pressure. Well shut-in decreases

flow-back recovery because more frac-water with high pressure penetrates into deeper

matrix during shut-in.

4. In liquid rich gas well, NPV is highly affected by valuable condensate oil production. In

order to keep a balance of NPV and flow-back recovery, liquid rich gas well should begin

to flow back immediately after hydraulic fracturing. Flow-back BHP should keep low so

that large pressure drawdown can drive more frac-water out. After flow-back of one or two

weeks, we had better put wells on production directly because of negative effects of well

shut-in. For increasing NPV, BHP at production cannot be too low, especially in the early production period.

Chapter Five: Summary and Future Work

5.1 Summary of Completed Research

1. Three fracture geometries, simple planar fractures, branching fractures, and fracture network are simulated in this thesis. It is found that, in tight oil reservoirs, commonly used simple planar fractures overestimate the well productivity if a complex fracture network is created in the reservoir. The differences increase as the fracture conductivity increases

2. In the tight oil reservoir, for the ideal bi-wing fractures, main fracture conductivity plays an essential role in the early period, while fracture half-length can significantly affect the long term production. For complex fractures, conductivity of the secondary fracture plays an important role on the after-stimulation well productivity. If a fracture network is intended to be created in the reservoir, especially at the presence of natural fractures, efforts must be made to achieve high conductivity of the secondary fractures.

3. Based on the analysis of simulation data from tight Cardium formation, linear flow and radial flow (or elliptical flow) are dominant flow regimes in early period and pseudo-steady state flow is the most important regime in the mid and late periods. The flow regimes are similar between ideal bi-wing fracture and fracture with complexity, except the difference in early linear flow, that is, compound linear flow arising in complex fractures and pseudo-linear flow appearing in ideal bi- wing fractures.

4. The reservoir flow simulation coupled rock geomechanics has been successfully employed to predict the properties of the hydraulic fracture in the tight Montney formation. The combination of robust reservoir flow and geomechanical deformation improves the reservoir fluids flow simulation in the matrix-fracture system by considering fracturing fluid leak-off and saturation in the matrix, as well as an updated pressure distribution near the wellbore after stimulation job.

5. It is found that in the tight gas reservoir (0.001 md), the penetration depth of fracture fluid into matrix is very shallow, which is less than 0.5 m. Thus in such tight formation, fracturing liquid is mainly distributed in the hydraulic fracture and leak-off is only expected in surrounding matrix very close to the fracture surface.

6. In tight gas reservoirs (0.001 md), the effect of natural fractures on cumulative production is significant. Natural fracture permeability can be sensitive to stress during the production life, which can in-turn affects the well after-stimulation production profile.

7. The coupled reservoir flow/geomechanics simulator can simulate injection and flow-back of fracturing fluid more accurately. In tight gas formation (about 0.001 md), if fracture conductivity keeps enough transport ability (e.g. 6 D.mm), the compaction effect of hydraulic fracture (or stress- dependent conductivity) can be neglected.

8. Flow-back mainly happens in the first two months and simulation recovery is from 43.5% to

60.3%. Much cannot be recovered because injected fluid is trapped by tight matrix, such as resistance of capillary pressure. Low BHP at flow-back can recover more fracturing fluid because high pressure drawdown can overcome capillary pressure. Well shut-in decreases flow-back recovery as more high pressure frac-water penetrates into deeper matrix.

9. In liquid rich gas well, in order to keep a balance of NPV and flow-back recovery, fractured well should begin to flow back directly after hydraulic fracturing. Flow-back bottom-hole pressure should keep at a low value so that large pressure drawdown can drive more frac-water out. After flow-back of one or two weeks, shut-in period should be shorted because shut-in has the negative effects on flow-back recovery and NPV. Well bottom-hole pressure during production should keep relatively high for increasing NPV.

5.2 Future Work

In this thesis, different fracture geometries are built in the fractured tight oil model. If we consider high gas mobility in fractured tight gas reservoir, results may demonstrate different. Also, our dynamic hydraulic fracturing can only simulate ideal bi-wing planar fracture, which limits its application. In addition, we only study the scenario of injecting slick-water. Currently, other fracturing liquid is widely used in fracturing jobs of WCSB, such as nitrogen foam fracturing. In the future, the following research should be considered:

1) Investigate the effect of different fracture geometries based on actual tight gas block in WCSB and perform RTA analysis to study differences of their flow regimes.

2) Predict complex fracture geometry and its fracturing liquid distribution

3) Extend similar flow-back study into the following aspects: the first is injecting different fracturing fluid (e.g. foam fracturing liquid); the second is flow-back of complex fracture network.

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Appendix A: Copyright Permission

Chapter 2

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