Production Optimization of a Tight Sandstone Gas Reservoir with Well Completions: A Numerical Simulation Study

Transcription

1 Production Optimization of a Tight Sandstone Gas Reservoir with Well Completions: A Numerical Simulation Study by Cyrille W. Defeu, B.S. A Thesis In PETROLEUM ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCES IN PETROLEUM ENGINEERING Approved Dr. M. Rafiqul Awal Chair of Committee Dr. Shameem Siddiqui Dr. Habib K. Menouar Peggy Gordon Miller Dean of the Graduate School December, 2010

2 Copyright 2010, Cyrille Defeu

3 DEDICATION To the Almighty God giver of life and wisdom, To my parents, who never had a college education, but understood its importance, and sacrificed everything in their life for our education, To my sisters and brothers for their unconditional support and love, To my grandmother for her encouragement, To the rest of my family and friends for prayers and continual support.

4 ACKNOWLEDGEMENTS I would like to express my sincere gratitude to Dr. Mohammad Rafiqul Awal, Chairperson of my committee for igniting this study, for guiding my steps through this work and for his endless support. I am also grateful to the members of my committee Dr. Shameem Siddiqui and Dr. Habib Menouar for co-advising this project and always making sure my work was on track. To Dr. Lloyd R. Heinze for encouraging me to enroll in Graduate School, I would like to graciously say thank you. I would like to express my thanks to my colleagues and friends specially Mr. Amao Abiodin (Matthew) and Stacey Amamoo, for going out of their way to help me on this work. I would like to express my thanks to Dr. Thomas Tan, President of T. T. & Associate for providing academic license at no cost to use the commercial 3D black oil simulator, Exodus and also for his technical assistance and support. Thanks to the staff and faculty of Bob L. Herd Department of Petroleum Engineering for providing me close assistance since day one here at Texas Tech University, I could not imagine my journey here without your support. Finally I would like to thank my very supportive fiancée Sandrine Ngamo for being by my side all along this journey. ii

5 TABLE OF CONTENTS ACKNOWLEDGEMENTS... ii ABSTRACT... vi LIST OF TABLES... vii LIST OF FIGURES... viii LIST OF ABBREVIATIONS... xi 1 INTRODUCTION Background Unconventional Hydrocarbon Resources Tight Gas Definition Reservoir Characterization Reserve Estimation Scope of the Work and Objectives REVIEW OF LITERATURE Tight Gas Reservoir Properties Porosity and Permeability Capillary Pressure and Relative Permeability Tight Gas Reservoir Type Completions (tight gas production methods) Tight Gas Hydraulic Fracture Simulation Well Model Combination of Fractures Simulators to Reservoir Simulator Literature Search on Tight Gas Sand Reservoir Optimization Statement of Problem Description of Tasks Assumptions and Considerations METHODOLGY Base Case: Simple Vertical Wells iii

6 3.2 Vertical Wells with Hydraulic Fractures Well Architecture Analysis Distance between Fractures Planes Distance Between Transverse Fractures Distance Between Hydraulic Fractures Planes of two Vertical Wells NUMERICAL SIMULATION General Description of Commercial Simulator Used Validation of the Simulator Base Case Simulation and Model Description Modeling Well Completion Features Well Model Hydraulic Fractures Modelling Case Studies Vertical Wells Comparison Architecture Analysis Potential and Streamline Analysis Application RESULTS AND DISCUSSION Vertical Wells Completion Architecture Special Well Completion Studies Collinear Fractures in Vertical Wells for Mitigating Flow Convergence Optimizing Spacing between two Consecutive Transverse Fractures (horizontal well completion) Optimizing spacing between two consecutive vertical well fractures (vertical well completion) Development of a New, Optimized Field Development Concept for Tight Gas Sandstone Reservoir Economic Analysis CONCLUSIONS and RECOMMENDATIONS iv

7 6.1 Conclusions Recommendations REFERENCES A ECONOMIC ANALYSIS B MODELING DATA FILES v

8 ABSTRACT Tight gas sands have significant gas reserves, which require cost-effective well completion technology and reservoir development plans for viable commercial exploitation. In this study, a new approach for well completion method coupled with a suitable reservoir development plan is proposed. Several well completion and well placement options are examined for optimum gas recovery and maximum economic returns. A commercially available numerical reservoir simulator (Exodus version 6.00) has been used extensively to study the various reservoir development scenarios. A novel hydraulic fracturing configuration involving a pair of vertical wells is proposed and is found to show excellent performance compared to more traditional hydraulic fracturing and horizontal well configurations. vi

9 LIST OF TABLES 1.1 Reserve Estimate Comparison of Conventional Gas Reservoir and Tight Gas Sand Numerical Reservoir Simulation Validation Data from SPE Simulation Model Data Hydraulic Fractures Properties Economic Data A.1 Economic Analysis Spreadsheet for Base Case. 65 A.2 Economic Analysis Spreadsheet 9 Vertical Wells with Hydraulic Fractures A.3 Economic Analysis Spreadsheet 8 Wells with Hydraulic Fractures 67 A.4 Economic Analysis Spreadsheet 6 Wells with Hydraulic Fractures 68 A.5 Economic Analysis Spreadsheet 5 Wells with Hydraulic Fractures 69 A.6 Economic Analysis Spreadsheet 4 Wells with Hydraulic Fractures 70 A.7 Economic Analysis Spreadsheet 2 Vertical Wells with Parallel Hydraulic Fractures Planes 71 A.8 Economic Analysis Spreadsheet 2 Vertical Wells with Collinear Hydraulic Fractures Planes vii

10 LIST OF FIGURES 1.1 Natural Gas Resource Triangle U.S. Tight Gas Sand Basins (Law, 2003) Decline Curve - Rate vs. Time - exponential, harmonic, hyperbolic Illustration of Capillary Pressure and Relative Permeability Relationships in Conventional Gas Reservoir and in Tight Gas Sand Reservoir (Shanley et al., 2004) Conceptual Representation of Hydraulically Fractured Reservoir Model that Uses Separate Objects - DCN Model (Hoffman and Chang, 2009) Example of Fracture Model Output Showing Fracture Conductivity Distribution and Fracture Dimensions (Shaoul et al., 2007) Detail of Fracture Properties for two Longitudinal Fractures along a Horizontal Wellbore, corresponding to the Fracture Model Result from Figure 2.3 (Shaoul et al., 2007) Integrated Reservoir Modeling and Decision Making Tools for Spacing Optimization (Turkarslan et al. 2010) Thermodynamic Properties of the Gas (Volume Formation Factor and Viscosity) Relative Permeability of Tight Gas Sand from Brooks and Corey Equations Base Case 16 Vertical Wells with 40 Acres Spacing (Exodus ) Schematic Illustration of Scenarios with Vertical Wells Schematic Illustration of 2 Vertical Wells with 500 ft half-length Hydraulic fracture placed in parallel -Top View Schematic Illustration of 2 Vertical Wells with 500 ft half-length Hydraulic fracture placed on the same line Top View Schematic Illustration of 2 Horizontal Wells with 3 Transverse Hydraulic Fractures each Transverse Hydraulic Fracture Moving along the Horizontal Well Length Wells and Hydraulic Fractures Displaced Horizontally Production Performance for Hydraulically Fractured well in a Single-layer Reservoir (Cheng et al., 2008) Reservoir Simulation Validation Results Exodus Base Case Scenario Showing Well Locations and Porosity viii

11 Distribution Illustration of Hydraulic Fracture Local Grid Refinement Top View and 3-D View Gas Rate of the 5 Cases with 500 ft Half-length Hydraulic Fracture and the Base Case Cumulative Gas Production of the 5 Cases with 500 ft Half-length Hydraulic Fracture and the Base Case Cumulative Gas Production as function of the Number of Wells with Hydraulic Fractures Cumulative Gas Production as function of the Number of Wells with Hydraulic Fractures Semilog Gas Recovery as function of the Number of Wells with Hydraulic Fractures Gas Recovery as function of the Number of Wells with Hydraulic Fractures Semilog Pressure Distribution after 30 years of Production for all the Cases Mentioned in Section Pressure Distribution for 2 Wells Analysis after Production Gas Production Rate for 2 Wells Analysis Gas Cumulative Production for 2 Wells Analysis Radial Flow Around the Well Potential lines and Streamlines for Pressure after 30 years of production Schematic Illustration of Fracture Distance Effect Cumulative Gas Production at Various Fracture Distance Relationship of Cumulative Gas and Distance Between 2 Transverse Fractures on a Horizontal Well Schematic Illustration of Fracture Distance Effect between 2 Fractured Vertical Wells Cumulative Production at Various Distances between 2 Vertical Fractured Wells Relationship of Cumulative Gas Production and Distance between Fracture Planes of 2 Vertical Wells Schematic Illustration of the Proposed Scheme Pressure Distribution of the Proposed Scheme at the End of the Project Lifetime.. 54 ix

12 5.21 Cumulative Discounted Cash Flow for Vertical Wells Cumulative Discounted Cash Flow Comparing Completions Cumulative Cash Flow for the Proposed Case Showing Payout Time.. 58 x

13 LIST OF ABBREVIATIONS b: Arps decline curve constant or decline exponent B g : volume gas formation factor CBM: Coalbed Methane cp: centipoise D: Non-Darcy gas flow constant DCN: Discrete connection of nodes D p : diameter of the pipe ECL: Economic limit FOI: Folds of increase ft: feet h: thickness of the net pay zone k: absolute permeability K f : fracture permeability K fi : grid block fracture permeability K f W f : fracture conductivity k rg : gas relative permeability K rw : water relative permeability LGR: Local grid refinement md: millidarcy Mscf/d: thousand standard cubic feet per day NPV: Net Present Value P: Pressure PI: Productivity index psi: pounds per square inch psia: pounds per square inch, absolute PVT: Pressure, Volume and Temperature P wf : bottom hole flowing pressure q g : gas production rate xi

14 q i : Initial gas production rate q t : Gas production rate at time t rcf: Reservoir cubic feet R e : Equivalent drainage radius R w : Wellbore radius s: Skin factor scf: standard cubic feet S gc : Critical gas saturation S w *: Normalized water saturation S w : Water saturation S wc : Critical water saturation S wirr : Irreducible gas saturation or S wr T: Reservoir temperature t: Time Tcf: Trillion cubic feet T w : Well transmissibility W f : Fracture width WPI mult : Productivity index multiplier X f : Fracture half length Z pg : Gas compressibility factor at pressure P λ: Pore distribution index ϕ: Porosity ϕ fi : Fractured gridblock porosity y f : Gridblock fracture width µ: Viscosity µ g : Gas viscosity xii

15 CHAPTER 1 INTRODUCTION 1.1. Background Unconventional Hydrocarbon Resources Since tight sand gas is known as an unconventional resource, it is important to understand the concept, the context and the importance of unconventional resources with respect to energy supply in the world. Initially considered as a marginal product in the energy industry for economical reasons, hydrocarbon gas (natural gas) has become an important source of energy significantly contributing to the world energy supply. Hydrocarbon gas has grown to be one of the most favored source energy thanks to environmental concerns and development in technology in both its production and its consumption. Unconventional in the case of hydrocarbon energy is a term used to define those resources that are not easily accessible and can only be produced at a higher cost than those other resources that are considered conventional. To best illustrate the difference between conventional and unconventional resources, the natural gas resource triangle shown below (Figure 1.1) was devised based on the concept developed by Masters and Grey in the 1970 s 1

16 Figure 1.1 Natural Gas Resource Triangle Easily accessible resources are at the top of the triangle and are small in quantity as compared to unconventional resources which are available in large quantities but very challenging with respect to exploration and production. Unconventional gas provides over half of the US gas production As far as natural gas is concerned, unconventional resource includes: a) Gas Hydrates: the most abundant source of natural gas yet the most challenging production-wise and most untapped. Gas Hydrates are ice-like crystal structure solids formed from mixture of water and natural gas (usually methane) at high pressure and low temperature. They are generally formed on most continental margins near the sea floor below about 1600 ft of water depth, they can also be found on land in Polar Regions. Estimates range anywhere from 7,000 Tcf to over 73,000 Tcf b) Coalbed Methane (CBM): natural gas absorbed in coal matrix, due to technology development in the early 1990 s has become an important source of energy in countries with abundant deposits of coal such as USA, for which it contributes 2

17 over 1.6 trillion cubic feet of natural gas per year. In June 2009, the Potential Gas Committee estimated that 163 Tcf of technically recoverable coalbed methane existed in the United States, which made up 7.8 percent of the total natural gas resource base. c) Shale Gas, this is natural gas produced from shale generally considered as source rock, it is stored in shale in various forms: free gas in porous regions, free gas in natural fractures and gas absorbed in the matrix. Shale gas is expected to contribute about half of the natural gas production in the next decade. A study has suggested that shale gas resource in the U.S. range from 1,500 Tcf to 1,900 Tcf. As of November 2008, FERC estimated there were 742 Tcf of technically recoverable shale gas resources in the United States. d) Tight sand gas: generally found in low permeability sand formation, tight sand account for about half of natural gas production in the US with 7,406 Tcf of reserve worldwide. Tight sand gas will be our main focus in this report. Figure 1.2 U.S. Tight Gas Sand Basins (Law, 2003) 3

18 1.2. Tight Gas Definition Tight sand gas is referred to as gas that is stuck in a very tight formation underground, trapped in uncommonly low permeability hard rock, or in a sandstone formation in most cases, however they could also be found carbonates such as limestone that is unusually impermeable and non-porous (tight sand). Typically, these formations contain net pay zone ranging from 25 to over 250 feet, original reservoir pressure from 1500 to 15,000 psi and porosity from 3 to 10 percent. Tight sand gas reservoir was first defined by US government in the 1970 s for political use in an attempt to define which gas wells will receive government incentive for producing gas from deemed tight reservoirs. As such, a tight sand gas reservoir is defined as any reservoir with a value of permeability to gas flow less than 0.1 md. However political, this definition intrinsically combines fundamental fluid and reservoir parameters in the well known Darcy s equation of fluid flow in porous media applied to gas as follows (Holditch, 2006): (1.1) In equation 1.1 reservoir properties are accounted for, as well as fluid properties. Well stimulation is represented by composite skin, s Reservoir Characterization One of the particularities of tight gas reservoir is the versatility of its characteristics as such; in the characterization of the reservoir one must consider the following: a) Geology: this defining regional thermal gradients, the regional pressure gradients as well as the stratigraphy of the region. b) Reservoir Continuity: this affects particularly the characteristics of the drainage area, and the orientation of hydraulic fractures as it is 4

19 conditioned by horizontal stresses in all of the reservoir layers. Reservoir continuity depends essentially on regional tectonics. c) Reservoir data acquisition: this is done in two ways, and the most important and the most economical being the openhole well logging that helps determine the volumetric (porosity, saturation), and the petrophysical (resistivity, density) properties of the reservoir, some cases may include special logs such wellbore image and nuclear magnetic resonance. The second type of data acquisition is coring, this provides essentially fluid flow properties and mechanical properties of the rock d) Mechanical Properties: Most tight gas reservoir must be stimulated before it is economically produced; the most popular method is hydraulic fractures. For such procedure to be successful one must be aware the mechanical properties of the pay zone and its surroundings, these properties include: in-situ stress, Young s modulus and Poisson s ratio. e) Permeability Distribution: This is an important concept to be considered when it comes to forecasting gas flow. Holditch determined that most tight gas reservoir follow the similar log normal permeability distribution pattern. Therefore, the median permeability value is the best approximation for central tendency as opposed to the arithmetic mean values which tend to overestimate permeability values Reserve Estimation Estimating reserves in tight gas reservoir is a delicate task as conventional well known methods such as volumetric method, and material balance method rarely apply due to assumptions used in developing these methods, Table 1.1 below elaborates on each and their range of application. Literature abound with variations of material balance methods adapted to tight gas reservoir most of them are based compartmental reservoir approach these include the Payne (1996) method and the Hagoort and Hoostra (1999) method. The most common methods as far as tight gas reservoirs are concerned are curve analysis 5

20 (decline and type) and reservoir models when simulators are available. The focus in this section is decline curve analyses since readily available and less cumbersome than others. Table 1.1 Reserve Estimate Comparison of Conventional Gas Reservoir and Tight Gas Sand (Holditch, 2006) Method Volumetrics Material Balance Decline Curves Reservoirs Models Conventional Gas Reservoir Accurate in blanket reservoirs Accurate in depletion drive reservoirs Exponential Decline usually accurate Used to simulate the field Tight Gas Sand Reservoir Used only when n wells have been drilled Should never be used Must use Hyperbolic Decline Used to simulate individual wells Declines curve analysis is based on production history and uses plots of flow rate vs. time and cumulative production (Cartesian or log-log scale) to determine reservoir parameters, reserves and predict future production. Arps in the 1940 s determined that production rate decline behaviors were similar to one of the hyperbolic family of curves. Depending on the curvature, decline behavior can be group as follow: exponential, harmonic and hyperbolic. These behavior are illustrated in the figure below 6

21 Figure 1.3 Decline Curve - Rate vs. Time - exponential, harmonic, hyperbolic Tight gas reservoirs decline predominantly as hyperbolic decline type and are analyzed with semi-log plot of production rate vs. time and obey to the following relationships (1.2) (1.3) Di and b are determined iteratively from historical production data. Where 0 < b < 1, 1.3. Scope of the Work and Objectives After elaborating on the background and the evolution of unconventional resources, it is clear that unconventional resources are contributing increasingly and in a fast rate to our energy supply, therefore the future of our energy supply lies essentially on unconventional resources among which is tight sand gas. The affordability of 7

22 unconventional resources is conditioned by how cost effective its development and its extraction are. It is important to develop adequate extraction methods and techniques to effectively produce tight sand gas reservoir. Planning the development of the field is one of the most important steps in the extraction process after geological, geophysical and petrophysical study of the field have been executed. Nowadays numerical simulators have become handy tools to accomplish such purpose. Conventionally, a lot of wells must be drilled to get most of the gas out of these tight formations. This study is using a reservoir simulation approach to optimize the potential of a hypothetical gas field by comparing various completion methods ranging from simple vertical wells to multistage hydraulically fractured horizontal wells and also by determining the optimum number of wells to be drilled. 8

23 CHAPTER 2 REVIEW OF LITERATURE 2.1. Tight Gas Reservoir Properties Tight gas reservoirs are characterized by small pore throats and crack-like interconnection between pores. These microscopic features result in some macroscopic features such as high capillary pressure, low porosity, high irreducible wetting phase saturation and low permeability Porosity and Permeability Porosity in tight gas sand reservoir is made of a complex combination of various pore shapes and the matrix cracks. Smith et al. (2009) demonstrated using sonic log that velocities profile could not be analyzed without considering microcracks on the matrix. Most of the permeability in tight sand reservoirs is attributed to cracks or microfractures. It has been proven that permeability in tight sand reservoir is log normally distributed. Low permeability in tight gas reservoirs results from the combine effects of stress distribution, matrix composition and partial brine saturation Capillary Pressure and Relative Permeability The most significant differences between conventional reservoirs and low-permeability reservoirs lie in the low-permeability structure itself, the response to overburden stress, and the impact that the low-permeability structure has on effective permeability relationships under conditions of multiphase saturation (Naik, 2006). Shanley et al. (2006) demonstrated that low permeability reservoir are generally characterized with high capillary pressure at relatively low wetting-phase saturations as compare to conventional reservoir. This trend is illustrated in the figure below where capillary pressure and relative permeability of both conventional reservoir and low permeability reservoir are compared. 9

24 Figure 2.1 Illustration of Capillary Pressure and Relative Permeability Relationships in Conventional Gas Reservoir and in Tight Gas Sand Reservoir (Shanley et al., 2004) Critical water saturation (S wc ), critical gas saturation (S gc ), and irreducible water saturation (S wirr ) are shown. In conventional reservoirs, irreducible water saturation and critical water saturation are similar. In low-permeability reservoirs, however, irreducible 10

25 water saturation and critical water saturation can be significantly different. Conventional reservoirs are dominated with a wide range of water saturation for which multi phase flow is observed. On the other hand, in low-permeability reservoirs such tight gas, there is a broad range of water saturations in which neither gas nor water can flow. In some very low-permeability reservoirs, there is virtually no mobile water phase even at very high water saturations (Shanley et al., 2004). Since relative permeability data are not readily available, and based on the above observations, relative permeability can be calculated using computational technique as indicated by Brooks and Corey equation and the lab measured capillary pressure. This technique uses the following equations: (2.1) (2.2) Where: (2.3) - λ represents the characteristics of the pore structure is the slope of the log-log plot of S * w versus P c Based on the desorption measurements, Ward and Morrow (1987) suggested that irreducible water saturation for tight formation should be set at 30% Tight Gas Reservoir Type Completions (tight gas production methods) The successful exploitation of tight gas reservoirs relies on some combination of horizontal drilling, multi-stage completions, innovative fracturing, and fracture mapping to engineer economic completions (Warpinski et al., 2008). Unless faults are present, tight gas reservoirs are known to yield relatively simple and planar fractures pattern after hydraulic fracturing treatments. As oppose to shale gas reservoir, heavy network of 11

26 hydraulic fractures are not required, instead marginal existing natural fractures most be preserved and not damage in the process of fracturing Tight Gas Hydraulic Fracture Simulation Experience have shown that artificially fractured low permeability reservoir can yield up to 10 folds of increase in production (FOI) compare to non-fractured reservoir. This contribution due to artificial fractures is significantly high not to be included in reservoir management. In such cases, artificial fractures should be properly included in the reservoir simulation models and the question is how should we do that? To answer this question various methods varying from analytical (skin) to numerical (LGR) have been documented in the literature. We will be discussing some of these methods Well Model Hoffman and Chang (2009) proposed to treat the hydraulic fracture as a discrete object that is neither gridded nor included in the skin term of a traditional well model. Fractures are modeled as a discrete connection of nodes (DCN). Practically hydraulic fracture is represented as a well that does not produce to the surface. Since well can be connected to any number of gridblocks, fractures are represented as shut-in wells that allow crossflow. (Figure 2.2) 12

27 Figure 2.2 Conceptual Representation of Hydraulically Fractured Reservoir Model that Uses Separate Objects - DCN Model (Hoffman and Chang, 2009) Two basic features of wells in common reservoir simulators help to tune the well to fit physical and flow capacity of the fracture: a) Well friction factor: this depends on well diameter and is used to account for permeability in the fracture, as such; permeability can be sized by varying well diameter. Knowing the permeability of the fracture, Hoffman and Chang proposed to solve the following equation 2.4 for diameter of the pipe D p to get the right value to be input in the simulator. (2.4) Where k f is fracture permeability and is porosity b) Well productivity index (PI) multipliers allow flow from the reservoir to the fracture to be modeled differently than flow to a well. This parameter allows us to modify fracture transmissibility to suit hydraulic fractures, it is quantified as well productive index multiplier (WPI mult ) and is calculated from equation 2.5 assuming well transmissibility (T w ) equals fracture transmissibility, the effective drainage radius is e (exponential), the well radius is one and skin is 0. 13

28 (2.5) Hoffman and Chang concluded that the use of wells to model fractures is more fundamental. From a mathematical standpoint, wells are simply source/sink terms that remove or add fluids to the grid at specific locations. Source/sink terms do not have to remove fluid or add new fluid to the reservoir (although they usually do that when modeling wells). They can simply move fluid from one gridblock to another as needed for a fracture Combination of Fractures Simulators to Reservoir Simulator Noticing that predicting production from hydraulically fractured wells has always been a challenge and approximated through three basic approaches such as analytical solutions to fracture conductivity, negative skin factor to represent fracture stimulation and manual grid refinement to represent hydraulic fractures, all of which are not physical representation of the hydraulic fractures. Shaoul et al. (2007) opted for a different approach by building a tool that consists of generating models of fractures using hydraulic fracture simulator and combining them with commercial or any numerical reservoir simulator. Fracture model. This is built based on a 3D commercial fracture simulator which can handle both proppant and acid fractures; the advantage of such method is that all physical properties of the fractures are available for transmission to the reservoir simulator. The most important outputs for reservoir simulation are fracture dimension and fracture conductivity; these properties are illustrated in Figure

29 Figure 2.3 Example of Fracture Model Output Showing Fracture Conductivity Distribution and Fracture Dimensions (Shaoul et al., 2007) The spatial variation (physical dimensions) observed on the fracture simulator output is converted to a rectangular grid for reservoir simulator. Due to heterogeneity of both the fracture width and fracture conductivity, the gridblocks width being constant, permeability of each fracture gridblock is adjusted to obtain equivalent fracture conductivity; an illustration is shown on Figure

30 Figure 2.4 Detail of Fracture Properties for two Longitudinal Fractures along a Horizontal Wellbore, corresponding to the Fracture Model Result from Figure 2.3 (Shaoul et al., 2007) The reservoir simulator interface. This is articulated in 5 important steps: a) Reservoir Data: the input file is created from the fracture growth model previously prepared b) Wellbore and Fracture Geometry: these options are readily available in most reservoir simulators, the well inflow is handled by the Peaceman approach c) Automatic Grid Generation: a grid generation algorithm is created to adapt the grid to the geometry of the reservoir, the fracture and the well; and also to optimize the gridblocks numbers with respect to the CPU usage. This step also include the optimization of the local grid refinement (LGR) d) Initialization of Grid Properties: every gridblock in the host grid and the LGR is assigned value of each distributed reservoir characteristic. This is done by using t equation 2.6 and equation 2.7 to convert fracture properties into corresponding gridblock values: 16

31 (2.6) (2.7) Where k and are permeability and porosity respectively, b is actual fracture width, y gridblock width, subscript f denotes gridblock property and subscript f i denotes actual fracture property. e) Model Run Time: the time it takes to generate input data for the reservoir simulator is very short ranging from 1 to 5 second, the execution of the final reservoir simulation depends on various factors such as the computer used, number of gridlocks and number of fractures. Additional inputs are needed in order to complete a successful simulation; these include PVT and relative permeability data, production wellbore configuration, and production constraints Literature Search on Tight Gas Sand Reservoir Optimization In the early days of tight gas sand reservoir exploitation, Holditch et al. study well spacing and fracture length and constructed a series of plots could be used to optimize tight formations. They found out that these tools depend essentially on the permeability of the reservoir. They concluded that for reservoir with permeability above 0.05 md the optimum length of the fracture should be about one-half of the optimum drainage radius whereas for reservoir below 0.01 md the focus should be long fracture and smaller well spacing. Holditch 1978 Warpinski et al. in attempt to maximize gas production warns that in tight gas reservoir, network fractures are not as likely to develop, so maximizing drainage efficiency probably involves minimizing damage of any natural fracture system by fluid damage which is the direct opposite to shale gas (Warpinski et al., 2009). According to Warpinski et al. tight reservoir optimization should focus should focus on fracture length, number fracture per well and fracture clean up. 17

32 After remarking that early planification of reservoir development through optimal spacing can help protect the environment and enhance profitability by avoiding overdrilling, Turkaslan et al. based their spacing optimization models on statistical approach. No generalized solution is proposed but a framework leading to spacing optimization is proposed and as illustrated in Figure 2.5 (Turkaslan et al., 2010) Figure 2.5 Integrated Reservoir Modeling and Decision Making Tools for Spacing Optimization (Turkarslan et al. 2010) 2.5. Statement of Problem A section of 640 acres and a net pay of 150 ft at a depth of 7200 ft was considered for this study. This is a dry gas reservoir with no aquifer pressure support (no liquid and condensate produced). This reservoir has an initial pressure of 5000 psia and is produced until economic limit set at 50 Mscf/d or, the duration of the project life set at 30 years, whichever is earlier Description of Tasks The purpose of this study is to develop several reservoir management and well completion scenarios, and study each using a commercially available numerical reservoir 18

33 simulator. Total field production data are used to run economic analysis and the best case is picked on the basis of relevant economic parameters for the project Assumptions and Considerations It assumed that this reservoir is homogeneous with porosity 8%, horizontal permeability 0.01 md and vertical permeability md. The thermodynamic properties of the gas are calculated using Standing s correlation (Figure 2.6). Relative permeability data are calculated using Brooks-Corey equations for gas and water. λ is assigned the value 2 and plug into equations 2.1 and 2.2 to obtain relative permeability values for gas and water that will mimic the permeability jail profile (see Figure 2.7). Figure 2.6 Thermodynamic Properties of the Gas (Volume Formation Factor and Viscosity) 19

34 Figure 2.7 Relative Permeability of Tight Gas Sand from Brooks and Corey Equations 20

35 CHAPTER 3 METHODOLGY Synthetic data are used to build the model used for this project as illustrated in the next chapter. Cumulative gas production is used to gauge each type of completion considered in this project and economic analysis is used for decision making. 3.1 Base Case: Simple Vertical Wells This case consist of 16 wells placed on equal spaces of 40 acres it is produced until economic limits or end of the project set at 30 years (10,950 days). These wells are completed vertically with no hydraulic fractures and connected on the entire pay zone. This is used benchmark for this project. This combines radial flow around the well and early potential interference between streamlines. 21

36 Figure 3.1 Base Case 16 Vertical Wells with 40 Acres Spacing (Exodus ) 3.2 Vertical Wells with Hydraulic Fractures A decreasing number of vertical wells hydraulic fractures are placed on the field so that the effect of hydraulic fractures could be analyzed and compared to the base case. The half-length of the fracture is set to 500 ft to remain conservative in the analysis. The different scenarios ran are chosen in such a way that drainage area is the same for each wells. The number wells chosen are respectively 9, 8, 5, 4, and 2. Figure 3.2 illustrate all these scenarios except 2 vertical wells scenario shown in Figure

37 Figure 3.2 Schematic Illustration of Scenarios with Vertical Wells The equivalent number of vertical wells with 500 ft half-length hydraulic fracture is obtained by plotting the recovery against the number of vertical wells with hydraulic fractures and fitting a trend line which is then used to calculate the equivalent number of vertical wells with hydraulic fractures knowing the recovery factor of the base case. 23

38 3.4 Well Architecture Analysis To analyze well patterns, two wells are considered and placed on the section with respect to the following patterns. a) 2 vertical wells with 500 ft half length hydraulic fractures placed parallel to each other. (see Figure 3.3) Figure 3.3 Schematic Illustration of 2 Vertical Wells with 500 ft half-length Hydraulic fracture placed in parallel -Top View b) 2 vertical wells with 500 ft half length hydraulic fractures placed on the same horizontal line. (see Figure 3.4) 24

39 Figure 3.4 Schematic Illustration of 2 Vertical Wells with 500 ft half-length Hydraulic fracture placed on the same line Top View c) 2 horizontal wells with well length of 1680 ft placed on the same line. Equivalent well length is determined using graphical method by Brown and Economides (1992). This method uses the fracture half-length of vertical wells to determine the corresponding horizontal well length for various permeability values. For this case permeability less than 0.1 md is used. d) 2 horizontal wells with 3 transverse fractures on each wells and fracture halflength 500 ft, both wells are placed on the same horizontal line. (see Figure 3.5) 25

40 Figure 3.5 Schematic Illustration of 2 Horizontal Wells with 3 Transverse Hydraulic Fractures each 3.4 Distance between Fractures Planes Distance Between Transverse Fractures Distance between 2 transverse fracture is analyzed by considering a single horizontal well with well length 1680 ft. One fracture is kept fix at the heel of the well and the other initially set close to the first one is moved towards the toe of the well as illustrated on Figure 3.6, at increment distance as could be allowed by grid cells size, in this case increments of 80 ft. 26

41 Figure 3.6 Transverse Hydraulic Fracture Moving along the Horizontal Well Length Distance Between Hydraulic Fractures Planes of two Vertical Wells Two wells with hydraulic fractures are initially placed at the centre of the section, 160 ft apart from each other with the fracture planes parallel to each other. The wells are then moved on the same horizontal in incremental distance to observe the effect of distance between fracture planes on the recovery. Figure 3.7 illustrates the mechanism of wells and fracture movement. 27

42 Figure 3.7 Wells and Hydraulic Fractures Displaced Horizontally 28

43 CHAPTER 4 NUMERICAL SIMULATION 4.1 General Description of Commercial Simulator Used The need to predict hydrocarbon reservoir performance is of a fundamental importance in petroleum industry decision making for reservoir management; the most accurate method in achieving such a goal is reservoir simulation. It is therefore very important that the model created be precise and as close as possible to the real reservoir. One of the challenges of reservoir simulation is modeling micro-systems such as fractures (generally hydraulically fractured reservoir) in the reservoir. In this project we will be using Exodus v from T. T. & Associates Inc. in Canada. Exodus v is K-compositional reservoir simulator. Exodus internally converts black oil data into compositional equivalents. It can simulate three dimensions problems in either Cartesian or cylindrical coordinates. Exodus v is fully implicit and uses Newton Raphson methods to ensure maximum stability and adaptability. Exodus is by default a block centered reservoir simulator. Exodus has functionalities such as: - Dual porosity/dual permeability modeling - Coarse grid modeling - Local grid refinement - Modeling single well hydraulic fractures More than just reservoir simulation, Exodus v has additional components such as a map digitizer and a Pre-Tax economic analysis tool. 4.2 Validation of the Simulator Before using the simulator for the planned studies, a level of confidence is required to ascertain the accuracy the simulator. This is usually done by a benchmark test. In this study, a benchmark test was performed using published data in a relevant SPE 29

44 comparative paper (Cheng et al., 2008). Table 4.1 shows the data used for the simulator validation and figure 4.1 shows the result from a different simulator used for the paper. Figure 4.2 represents the results of Exodus simulated data compared with the digitized results obtained from Figure 4.1. Given that, fracture width of 0.02 in and the minimum size of a cell on Exodus is 1 ft, Hydraulic fracture width on the simulator is represented by 1 ft width of local grid refined cell. The permeability of the refined cell is adjusted accordingly to reflect the conductivity of the actual fracture which is 100 md-ft. since relative permeability data were not provided by the authors, Brooks and Corey equations were used. Also gas volume formation factor and gas viscosity was calculated from gas gravity and using Standings correlations. Table 4.1 Numerical Reservoir Simulation Validation Data from Cheng et al. (2008) Reservoir and Fracture Properties Reservoir Temperature 250 o F Initial Reservoir Pressure 5,000 psi Net-pay Thickness 150 ft Drainage Area 80 Acres Gas Porosity 0.06 Gas Permeability md Fracture Length 450 ft Fracture Conductivity 100 md-ft Bottomhole Flowing Pressure 1,000 psi Fluid Properties Gas Gravity (air = 1.0) 0.65 Initial Gas Viscosity cp Initial Gas Compressibility 1.2 x 10-4 psi -1 Initial Gas Production Rate 2,000 Mscf/D 30

45 Figure 4.1 Production Performance for Hydraulically Fractured well in a Single-layer Reservoir (Cheng et al. 2008) Figure 4.2 Reservoir Simulation Validation Results 31

46 4.3 Base Case Simulation and Model Description The model for this project is created by using a section (640 acres) and net pay of 150 ft divided in 3 equal thickness layers. The grid sizes in x and y directions are chosen with respect to the wells distribution for each case. Table 4.2 below shows hypothetical data representative of a tight gas sandstone reservoir and grid size for the base case. (sample data file included in Appendix B) Table 4.2 Simulation Model Data Reservoir Model Model Size, feet 5280x5280x150 Model Area, Acres 640 Number of Layers 3 Net Thickness, feet/layer 50 Top Depth of the Reservoir, feet 7,200 Porosity, fraction 0.08 X Permeability, md 0.01 Y Permeability, md 0.01 Z Permeability, md Rock Compressibility, v/v/psi 3.00E-06 Initial Datum Pressure, psia 5,000 Datum Depth, feet 7,200 Gas-Water Contact, feet 7,500 Reservoir Temperature, o F 250 Fluid Properties Gas Gravity (air = 1.0) 0.72 Water Density, lbs/ft Water Viscosity, cp Well Flow Parameters Well Index Peaceman Well Radius, ft 0.3 Flowing Bottom Hole Pressure, psia 1,000 Minimum Gas Rate, Mscf/d 50 32

47 Figure 4.3 Exodus Base Case Scenario Showing Well Locations and Porosity Distribution 4.4 Modeling Well Completion Features As Indicated, the various reservoir development scenarios include several well completion options as follow: - Vertical well completion - Horizontal well completion - Vertical with fractures (by hydraulic fracturing) - Horizontal with transverse fractures or with longitudinal fractures (by hydraulic fracturing) 33

48 4.4.1 Well Model All vertical wells are completed on the entire thickness of the pay zone. For each wells there are three connections, one for each layers. Well productivity index is automatically calculated using Peaceman method. Horizontal wells are completed through the second (middle) layer and the x-direction. The number of connection is determined by the length. All the wells are block centered and flow data are included in the previous section Hydraulic Fractures Modelling Hydraulic fractures are simulated using local grid refinement (LGR). Actual fracture data are represented in the table below. A fracture width of 0.02 in is represented by 1 ft LGR fracture width since it is the minimum size of an LGR cell. The permeability of the LGR fracture is adjusted accordingly to the conductivity of the actual fracture. LGR hydraulic fracture is illustrated on Figure 4.4. (sample data file included in Appendix B) Table 4.3 Hydraulic Fractures Properties Hydraulic Fracture Half-length, X f 500 ft Width, W f 0.02 ft Conductivity K f W f 100 md-ft LGR Frac Width 1 ft 34

49 Figure 4.4 Illustration of hydraulic fracture Local Grid Refinement Top view and 3-D view 35

50 4.5 Case Studies The above well completion features are used in various ways to create several reservoir management plays as described below: Vertical Wells Comparison - Base Case 16 vertical wells - 9 vertical wells with 500 ft half length fracture (9 V Wells HF 500) - 8 vertical wells with 500 ft half length fracture (8 V Wells HF 500) - 5 vertical wells with 500 ft half length fracture (5 V Wells HF 500) - 4 vertical wells with 500 ft half length fracture (4 V Wells HF 500) - 2 vertical wells with 500 ft half length fracture parallel (2 V Wells HF 500) Architecture Analysis - 2 vertical wells with 500 ft half length fracture parallel (2 VP Wells HF 500) - 2 vertical wells with 500 ft half length fracture collinear (2 VL Wells HF 500) - 2 horizontal wells with 1680 ft well length collinear (2 H Wells 1680) - 2 horizontal wells with 1680 ft well length collinear and 3 transverse fracture of 500 ft (2 H Wells 3 HFT 500) Potential and Streamline Analysis - 2 vertical wells with 1,000 ft half length fracture collinear (2 VL Wells HF 1,000) Application - 6 vertical wells with 500 ft half length fracture ( V Wells HF 500) 36

51 Average Gas Rate, MMcf/d Texas Tech University, Cyrille Defeu, December 2010 CHAPTER 5 RESULTS AND DISCUSSION As elaborated in chapter 3, different types of completions were analyzed to both find the best well architecture for tight gas and also to understand the flow pattern for each completion setup. 5.1 Vertical Wells 16 vertical wells on equal spacing of 40 acres were compared to different numbers of vertical wells with hydraulic fractures of half length 500 ft and the results (Gas rate and cumulative gas produced) are graphed below Field Gas Rate Decline 16 V Wells 8 V Wells HF V Wells HF V Wells HF V Wells HF V Wells HF Time (Days) Figure 5.1 Gas Rate of the 5 Cases with 500 ft Half-length Hydraulic Fracture and the Base Case 37

52 Cum Gas Production, MMSCF Texas Tech University, Cyrille Defeu, December ,000 35,000 30,000 Field Gas Cummulative Production 16 V Wells 9 V Wells HF V Wells HF V Wells HF V Wells HF V Wells HF ,000 20,000 15,000 10,000 5, Time Days Figure 5.2 Cumulative Gas Production of the 5 Cases with 500 ft Half-length Hydraulic Fracture and the Base Case As could be seen on the plot above, the base case falls between 5 and 8 wells with 500 ft half length hydraulic fractures. In order to find the equivalent number of wells representing the base case, the cumulative gas produced at the end of 30 years is plotted against the number of wells with hydraulic fractures, below are the Cartesian and the semi-log representation respectively 38

53 Cum Production - Xf = 500' (MMcf) Cum Production - Xf = 500' (MMcf) Texas Tech University, Cyrille Defeu, December ,000 35,000 30,000 25,000 20,000 15,000 10,000 5,000 Cummulative Production vs. Number of HF V Wells (Xf = 500') 0 Gp = 14655ln(N hfw ) R² = Number of HF Wells (Nhfw) Figure 5.3 Cumulative Gas Production as function of the Number of Wells with Hydraulic Fractures 100,000 Cumulative Production vs. Number of HF V Wells (Xf = 500') 10,000 Gp = 14655ln(N hfw ) R² = , Number of HF Wells (Nhfw) Figure 5.4 Cumulative Gas Production as function of the Number of Wells with Hydraulic Fractures - Semilog 39

54 2 methods could be used obtained equivalent number of wells from the graph above: - Graphical method, knowing the cumulative production, number of equivalent could be obtained by extending a line from the cumulative gas production value on the y axis to the curve and reading the corresponding number of wells on the x axis. - Using the equation obtained from the trendline the number of equivalent wells could be calculated as follows: Given, G p = 14655ln(N hfw ) (5.1) Solving for N hfw gives, (5.2) A generalized method is obtained by using recovery factor instead of cumulative gas produced. Dividing cumulative gas produced by the original gas in place and plotting the result, the following pair of plot was obtained: 40

55 Recovery Factor Recovery Factor Texas Tech University, Cyrille Defeu, December Recovery vs. Number of HF V Wells (Xf = 500') R f = ln(N hfw ) R² = Number of HF Wells (N hfw ) Figure 5.5 Gas Recovery as function of the Number of Wells with Hydraulic Fractures 1 Recovery vs. Number of HF V Wells (Xf = 500') 0.1 R f = ln((N hfw ) R² = Number of HF Wells (N hfw ) Figure 5.6 Gas Recovery as function of the Number of Wells with Hydraulic Fractures - Semilog 41

56 Similarly, the number of equivalent wells with hydraulic fracture is given by: (5.3) Pressure distribution profile after 30 years of production of each case is shown in Figure 5.7 Figure 5.7 Pressure Distribution after 30 years of Production for all the Cases Mentioned in Section Completion Architecture To optimize completion architecture, 4 completion scenarios were compared by coupling two wells ( 2 vertical wells with hydraulic fractures in parallel, 2 vertical wells with fracture in the same horizontal line, 2 horizontal wells and 2 horizontal wells with 3 transverse hydraulic fractures of half 500 ft) to better understand and measure interaction mechanisms. The respective results for both flow rates and cumulative production are plotted below, preceded by the top view of the reservoir for each case. 42

57 Figure 5.8 Pressure Distribution for 2 Wells Analysis after Production 43

58 Cum Prod MMscf Gas Production Rate (MMscf/d) Texas Tech University, Cyrille Defeu, December Gas Production Rate (2 wells) 2 H wells 3Layers H wells 3 HFT VP Wells HF VL Wells HF Time Days Figure 5.9 Gas Production Rate for 2 Wells Analysis 14,000 12,000 10,000 Cumulative Gas MMscf (2 wells) 2 H wells H wells 3 HFT VP Wells HF VL Wells HF 500 8,000 6,000 4,000 2, Time Days Figure 5.10 Gas Cumulative Production for 2 Wells Analysis 44

59 As could be seen from the figure 5.9 and figure 5.10, two horizontal wells with transverse hydraulic fractures are in a class of their own and yield a better recovery. 5.3 Special Well Completion Studies Collinear Fractures in Vertical Wells for Mitigating Flow Convergence As far vertical wells are concerned, one the factors that leads to poor performance is flow convergence around the well as shown in Figure 5.11, this type of flow in the reservoir should be avoided as flow competition around the wellbore leads to high drawdown. Wells with collinear hydraulic fractures yielded a better recovery than wells with parallel hydraulic fractures. Therefore wells with larger collinear hydraulic fractures were analyzed to understand the flow pattern and the following potential (pressure) and streamline map was obtained after 30 years of production. Figure 5.11 Radial Flow Around the Well 45

60 Figure 5.12 Potential lines and Streamlines for Pressure after 30 years of production Observing Figure 5.12, it is easily noticed that most of the flow through the reservoir is linear, and there is interference in the streamline. 46

61 5.3.2 Optimizing Spacing between two Consecutive Transverse Fractures (horizontal well completion) The effect of the distance between 2 transverse hydraulic fractures was analyzed by moving one of the hydraulic fractures along the horizontal well length as the other one is kept fix. The pressure distribution at the low, medium and high range distances was captured and shown on Figure 5.13 to illustrate flow interference between fractures. The graph on Figure 5.14 was then obtained after producing each case for 30 years. Figure 5.13 Schematic Illustration of Fracture Distance Effect 47

62 Figure 5.14 Cumulative Gas Production at Various Fracture Distance Cumulative gas production for each distance between fractures was then used to plot the following graph (figure 5.15) which shows a close to inverted parabolic relationship between transverse fractures distance and cumulative production or gas recovery. This plot can be used as tool to determine optimum distance between transverse fractures. 48

63 Cumulative Gas MMscf Texas Tech University, Cyrille Defeu, December 2010 Cumulative Gas Production vs. Transverse Fracture Distance 7,300 7,280 7,260 7,240 7,220 7,200 7,180 7,160 7, Fracs Distance Figure 5.15 Relationship of Cumulative Gas and Distance Between 2 Transverse Fractures on a Horizontal Well Optimizing spacing between two consecutive vertical well fractures (vertical well completion) Similarly as in section 5.3.1, distance between 2 wells with hydraulic fractures was analyzed and the pressure profile after 30 years of production is shown in Figure Interaction between the wells at lower distance is so strong that both wells act like a single well with a larger fracture. 49

64 Figure 5.16 Schematic Illustration of Fracture Distance Effect between 2 Fractured Vertical Wells The cumulative production after 30 years of production for each distance analyzed in summarized in Figure

65 Cumulative Gas MMscf Texas Tech University, Cyrille Defeu, December ,000 12,000 10,000 Cumulative Gas Production, Distance between 2 Fractured Wells 1440 ft 1280 ft 1120 ft 960 ft 640 ft 480 ft 320 ft 160 ft 8,000 6,000 4,000 2, Time, Days Figure 5.17 Cumulative Production at Various Distances between 2 Vertical Fractured Wells Cumulative gas production for each distance between fractures was then used to plot the graph on Figure 5.18, which shows a linear relationship between transverse fractures distance and cumulative production or gas recovery. This plot can be used as tool to determine optimum distance between transverse fractures. 51

66 Cumulative Gas MMscf Texas Tech University, Cyrille Defeu, December ,000 Cumulative Gas Production vs. Distance between 2 Fractures 12,000 10,000 8,000 6,000 y = x R² = ,000 2, Fracs Distance, ft Figure 5.18 Relationship of cumulative gas production and distance between fracture planes of 2 vertical wells 5.4 Development of a New, Optimized Field Development Concept for Tight Gas Sandstone Reservoir An application of the combination of results in the previous sections leads to the optimum completion architecture. The number of equivalent vertical wells with 500 ft half length hydraulic fractures was found by using equation 5.2 to be 6. In order to reduce flow interference in the space between fracture planes and favor linear flow, the best practice is to put the maximum number of wells in a linear pattern. The proposed architecture for the 640 acre section is shown in figure 5.18 below. The 6 wells are split into 2 groups of 3 fractured collinear wells. These groups are placed apart enough to minimize early interference. Economic analysis in the next section will help confirm it relevance of this scheme. 52

67 Figure 5.19 Schematic Illustration of the Proposed Scheme 53

68 Figure 5.20 Pressure Distribution of the Proposed Scheme at the End of the Project Lifetime After 30 years of production, the pressure distribution on Figure 5.19 shows most of the flow in the reservoir is linear. 5.5 Economic Analysis The data in Table 5.1 were used for economic analysis. These data were obtained from literature mainly SPE and SPE Cost for each case was derived from these basic data and multiply proportionally to obtained corresponding values. 54