Summary Current simulation models do not account for the interactions among the geomechanical behavior, formation fracturing and multiphase flow, and heat tnansfer in porous media. This paper describes a method for modular coupling of a commercial reservoir simulator with a three-dimensional (3D) stress code and fracture-propagation model. The iteratively coupled system is equivalent to a fully coupled solution of flow and stress. The iterative method is very robust. An experience with acceleration of the iteration is described, and the utility of the method is demonstrated on examples. The comparison with an uncoupled solution shows that significantly different (and more realistic) answers are obtained with the coupled modeling. The current limitations and future work are also discussed. Introduction Many commercial processes and technical problems in hydrocarhon production and environmental cleanup involve interactions between multiphase flow and heat transfer with stress/strain behavior in porous media. Examples are cyclic steam recovery of heavy oil and bitumen, hydraulic fracture propagation in water- flooding, waste disposal in deep deposits by injection above fracturing pressure, reservoir compaction during production and resulting subsidence, wellbore stability under multiphase flow conditions, cleanup of shallow hydrocarbon contaminants, and others. Numerical modeling of such coupled processes is extremely complex, and has been historically carried out in three separate areas: geomechanical modeling (with the primary goal of computing stress/strain behavior), reservoir simulation (essentially modeling multiphase flow and heat transfer in porous media), and fracture mechanics (dealing in detail with crack propagation and geometry). Each of these disciplines makes simplifying assumptions about the part of the problem that is not of primary interest. These approaches are discussed in detail below. However, such approaches are unacceptable in situations where there is strong coupling. For example, in reservoir modeling of unconsolidated porous media, the changes of porosity and permeability because of stress changes and failure of the soil cannot be represented by rock compressibility. This paper describes an approach to coupling the above three modeling components in such a manner that the already highly developed modeling techniques for each component can be used fully. The key idea is the reformulation of the stress-flow coupling such that the conventional stress-analysis codes can be used in conjunction with a standard reservoir simulator. This is termed a partially coupled approach because the stress and flow are solved separately for each time increment. However, the method solves the problem as rigorously as a fully coupled (simultaneous) solution, if iterated to full convergence. The advantages of the partially coupled approach are its flexibility in choosing different components and the full, cost-effective use of the existing sophisticated models. Comparison of Modeling Approaches The requirements for a comprehensive geomechanical and reservoir-simulation system are best established by examining the limitations of existing models in the three areas involved. Reservoir Simulators. Reservoir modeling technology is highly developed in the treatment of multiphase flow and heat transfer in porous media. Models handle three-phase immiscible flow and miscible flow. Complex hydrocarbon-type pressure/volume/temperature (PVT) can range from two-component (black oil) to multicomponent (including CO2, N2, and surfactants). Darcy flow, turbulence, and non-Newtonian fluids (polymers) can be modeled. Multiphase flow characteristics are generally described by relative permeability functions, which are complex functions of saturations, flow history, and PVT (through surface tension). Alternately, the reservoir models generally represent the porosity change of the solid by a simple function of pressure and temperature (e.g., Ref. 1).Equation (1) where p0, T0, and f0 are the reference values. The coefficient, cp, is referred to as rock compressibility and is treated as a constant. Only few authors attempted to consider stress changes.2 Ref. 3 includes the effect of pressure on the local effective stress and on the average stress change caused by depletion. Most current simulators use pressure-dependent compressibility cp=f(p) to approximate geomechanical effects or directly manipulate porosity.4 Permeability is similarly related to change in pressure only. Recently,5 effects of shear failure (again pressure dependent) were introduced. Stress Models. The majority of stress models for porous media use the theory of consolidation.6 They are advanced in terms of a variety of element shapes and orders of approximation, and in representing various types of constitutive behavior.7,8 Both hard rock and granular material behavior can be represented. Although the majority of the codes use the finite-element approach, finite differences, boundary elements, and discrete elements have also been used. Some models capture certain features of multiphase flow, such as gas dissolution in oil sands,9,10 but they are very simplistic compared to reservoir simulators. Also, numerical treatment of multiphase flow poses problems in finite-element setting unless low order elements are used. Fracture Propagation Models. Classical fracture mechanics deals mostly with problems in impermeable rock and has been adapted to porous media in the petroleum industry (see Ref. 11 for review). Many of the codes make two simplifying assumptions. First, the fluid flow from the fracture is assumed to be one-dimensional, and expressed through a simple parametric leak-off model based on single-phase flow theory. Second, the changes of stresses around the fracture caused by poroelastic and thermoelastic effects are estimated by use of simplified two-dimensional (D) analytical approaches. These two assumptions allow the fracture model to be decoupled from the reservoir flow and stress solution. Fully coupled models are rare12 and treat only single-phase flow. Ref. 13 shows the importance of the fracture-induced stresses for reservoir problems. Thus, none of the above three approaches is satisfactory for problems where strong coupling exists. An example is a steam injection into oil sands, which is an important commercial in-situ bitumen recovery process. Its economic success depends on maximizing recovery through better engineering. Another example is water or waste injection into stress-sensitive formations. These two applications are chosen as the basis for the discussion and for data used in the examples. Reservoir Simulators. Reservoir modeling technology is highly developed in the treatment of multiphase flow and heat transfer in porous media. Models handle three-phase immiscible flow and miscible flow. Complex hydrocarbon-type pressure/volume/temperature (PVT) can range from two-component (black oil) to multicomponent (including CO2, N2, and surfactants). Darcy flow, turbulence, and non-Newtonian fluids (polymers) can be modeled. Multiphase flow characteristics are generally described by relative permeability functions, which are complex functions of saturations, flow history, and PVT (through surface tension). Alternately, the reservoir models generally represent the porosity change of the solid by a simple function of pressure and temperature (e.g., Ref. 1).Equation (1) where p0, T0, and f0 are the reference values. The coefficient, cp, is referred to as rock compressibility and is treated as a constant. Only few authors attempted to consider stress changes.2 Ref. 3 includes the effect of pressure on the local effective stress and on the average stress change caused by depletion. Most current simulators use pressure-dependent compressibility cp=f(p) to approximate geomechanical effects or directly manipulate porosity.4 Permeability is similarly related to change in pressure only. Recently,5 effects of shear failure (again pressure dependent) were introduced. Stress Models. The majority of stress models for porous media use the theory of consolidation.6 They are advanced in terms of a variety of element shapes and orders of approximation, and in representing various types of constitutive behavior.7,8 Both hard rock and granular material behavior can be represented. Although the majority of the codes use the finite-element approach, finite differences, boundary elements, and discrete elements have also been used. Some models capture certain features of multiphase flow, such as gas dissolution in oil sands,9,10 but they are very simplistic compared to reservoir simulators. Also, numerical treatment of multiphase flow poses problems in finite-element setting unless low order elements are used. Fracture Propagation Models. Classical fracture mechanics deals mostly with problems in impermeable rock and has been adapted to porous media in the petroleum industry (see Ref. 11 for review). Many of the codes make two simplifying assumptions. First, the fluid flow from the fracture is assumed to be one-dimensional, and expressed through a simple parametric leak-off model based on single-phase flow theory. Second, the changes of stresses around the fracture caused by poroelastic and thermoelastic effects are estimated by use of simplified two-dimensional (D) analytical approaches. These two assumptions allow the fracture model to be decoupled from the reservoir flow and stress solution. Fully coupled models are rare12 and treat only single-phase flow. Ref. 13 shows the importance of the fracture-induced stresses for reservoir problems. Thus, none of the above three approaches is satisfactory for problems where strong coupling exists. An example is a steam injection into oil sands, which is an important commercial in-situ bitumen recovery process. Its economic success depends on maximizing recovery through better engineering. Another example is water or waste injection into stress-sensitive formations. These two applications are chosen as the basis for the discussion and for data used in the examples.

Coupled geomechanical and reservoir modeling is becoming feasible on a full-field scale. This paper describes the advances of the coupled model described previously, 1 its extensions for modeling compaction, and the application of the model in full-field studies. The advances of the theory and numerical implementation since the original work 1 make it practical to perform full-field coupled studies with complex, realistic descriptions of the geomechanical behavior of the reservoir and shales, which allows prediction of stress changes, reservoir compaction, and surface subsidence. These capabilities are demonstrated in field examples that analyze and predict classical pressure-induced compaction in a gas field and thermally induced compaction in a heavy-oil field. In both cases, the methodology of interpreting the geomechanical laboratory and field data and their integration in the coupled modeling process was the key to obtaining a realistic predictive tool. The examples demonstrate that the technology is maturing to the point that conventional studies can be converted to coupled modeling on a fairly routine basis.

Summary Coupled geomechanical and reservoir modeling is becoming feasible on a full-field scale. This paper describes the advances of the coupled model described previously,1 its extensions for modeling compaction, and the application of the model in full-field studies. The advances of the theory and numerical implementation since the original work1 make it practical to perform full-field coupled studies with complex, realistic descriptions of the geomechanical behavior of the reservoir and shales, which allows prediction of stress changes, reservoir compaction, and surface subsidence. These capabilities are demonstrated in field examples that analyze and predict classical pressure-induced compaction in a gas field and thermally induced compaction in a heavy-oil field. In both cases, the methodology of interpreting the geomechanical laboratory and field data and their integration in the coupled modeling process was the key to obtaining a realistic predictive tool. The examples demonstrate that the technology is maturing to the point that conventional studies can be converted to coupled modeling on a fairly routine basis. Introduction The geomechanical behavior of porous media has become increasingly important to hydrocarbon operations. Numerical modeling of such processes is complex and has been carried out historically in three separate areas: geomechanical modeling (with the primary goal of computing stress/strain behavior), reservoir simulation (essentially modeling multiphase flow and heat transfer in porous media), and fracture mechanics (dealing in detail with crack propagation and geometry). A modular system has been developed coupling these three modeling components in such a manner that the already highly developed modeling techniques for each component can be used fully.1 This model has been applied to several geomechanical/reservoir problems assisting in reservoir development. The paper will first discuss the theory of different degrees of coupling and its consequences for the formulation of the constitutive models and running efficiency of the software. Next, the modeling of compaction by rigorous means (plasticity) and its simplifications, which lead to a considerable increase of computational efficiency, will be presented. In addition to classical pressure-depletion-induced compaction, the paper will describe the theoretical and modeling aspects of thermal compaction phenomena, which have been observed in some applications. Methods of Coupling The key idea in the modular coupled system is the reformulation of the stress-flow coupling so that the conventional stress-analysis code can be used in conjuction with a standard reservoir simulator. This is termed a partially coupled approach because the stress and flow equations are solved separately for each time increment. However, the method solves the problem as rigorously as a fully coupled (simultaneous) solution if iterated to full convergence. The coupling takes place through the use of interface code developed to allow communication between simulators. In a geomechanics/reservoir problem, for instance, the pressure and temperature changes occurring in the reservoir simulator are passed to the geomechanical simulator. The updated strains and stresses are passed back to the reservoir simulator and used to compute coupled parameters in the reservoir formulation (i.e., porosity and permeability). An iterative method then must be used to obtain convergence. The interface is flexible enough to allow the user to choose several degrees of coupling. The degree of coupling may affect the accuracy of the solution as well as the computational efficiency; therefore, tradeoffs may be made to optimize run times. To see the different degrees of coupling, consider first the general formulation of the coupled problem in a finite-element setting. After discretization in space and time, such a system can be written in matrix form as2,3Equation 1 where [K]=the stiffness matrix, =the vector of displacements, [L]=the coupling matrix to flow unknowns, [E]=the flow matrix, and =the vector of reservoir unknowns (i.e., pressures, saturations, and temperatures). On the right side, =the vector of force boundary conditions, and =the right side of the flow equations. The symbol ?t denotes the change over timestep; i.e.,Equation 2aEquaton 2b Note that in the conventional reservoir simulation notation,4 [E]=[T]-[D], where [T]=the symmetric transmissibility matrix, [D]=the accumulation (block diagonal) matrix, and = -[T], where =the vector of boundary conditions (well terms). Decoupled. Consider now the flow part of the coupled system only, by assuming that ?t =0. This is the assumption made in reservoir simulation (i.e., stresses do not change), which gives the familiar matrix equationEquation 3 Conversely, if we assume that ?t =0, we obtain the classical elasticity equations. In many stress analysis packages, pressure and/or temperature can be imposed as external loads, which corresponds to assuming that ?t is known. Then the top half of Eq. 1 can be decoupled and written asEquation 4 In practice, decoupled simulations can be carried out in several ways.

It has been observed that the shale gas production modeled with conventional simulators/models is much lower than actually observed field data. Generally reservoir and/or stimulated reservoir volume (SRV) parameters are modified (without much physical support) to match production data. One of the important parameters controlling flow is the effective permeability of the intact shale. In this project we aim to model flow in shale nano pores by capturing the physics behind the actual process. For the flow dynamics, in addition to Darcy flow, the effects of slippage at the boundary of pores and Knudsen diffusion have been included. For the gas source, the compressed gas stored in pore spaces, gas adsorbed at pore walls and gas diffusing from the kerogen have been considered. To imitate the actual scenario, real gas has been considered to model the flow. Partial differential equations were derived capturing the physics and finite difference method was used to solve the coupled differential equations numerically. The contribution of Knudsen diffusion and gas slippage, gas desorption and gas diffusion from kerogen to total production was studied in detail. It was seen that including the additional physics causes significant differences in pressure gradients and increases cumulative production. We conclude that the above effects should be considered while modeling and making production forecasts for shale gas reservoirs.

Interactions of solid mechanics and fluid flow have been studied by numerous researchers for the past several years. Different methods of coupling such as full coupling, iterative coupling, etc., have been used. Nevertheless, the accuracy and the large run time of the coupled solid-mechanics fluid-flow model are outstanding issues that prevent the application of the coupled model in full-field studies. In this work, a novel relationship of porosity as a function of pressure, temperature and mean total stress is developed for iterative coupling of stress and flow. The new formula not only improves the accuracy of the coupling, but also reduces substantially the number of coupling iterations. The latter feature decreases significantly the CPU time. The new approach was implemented in a modular, iteratively coupled system. The rapid convergence provides the equivalent of a fully coupled method that is necessary to investigate complex coupled problems. The main advantage of this type of coupling is that a geomechanics module can be easily coupled with different reservoir simulators. The paper gives some comparisons of results obtained by the new porosity formula with another formulation. Introduction Reservoir simulation has a long history of development and it is used to model a wide variety of reservoir problems. However, using a conventional simulator still cannot explain some phenomena that occur during production such as subsidence, compaction, casing damage, wellbore stability, sand production, etc.1,2,3. Most conventional reservoir simulators do not incorporate stress changes and rock deformations with changes in reservoir pressure and temperature during the course of production. The physical impact from these geomechanical aspects of reservoir behavior is not small. For example, pore reduction or collapse leads to abrupt compaction of the reservoir rock, which in turn causes subsidence at the ground surface and damage to well casings. There are many reported cases of environmental impact due to fluid withdrawal from the subsurface. Well known examples include the sea floor subsidence in the Ekofisk field or Valhall field in the North Sea4; subsidence over a large area in the Long Beach Harbor, California5 or in the regions of the Bolivar Coast and Lagunillas in Venezuela6. In addition, production loss due to casing damage can be significant (e.g., in the Belridge Diatomite field in California7). The fundamentals of geomechanics are based on the concept of effective stress formulated by Terzaghi in 19368. Based on the concept of Terzaghi's effective stress, Biot9 investigated the coupling between stress and pore pressure in a porous medium and developed a generalized three-dimensional theory of consolidation. Skempton10 derived a relationship between the total stress and fluid pore pressure under undrained initial loading through the so-called Skempton pore pressure parameters A and B. Geerstma11 gave a better insight of the relationship among pressure, stress and volume. Van der Knaap12 extended Geertsma's work to nonlinear elastic geomaterials. Nur and Byerlee13 proved that the effective stress law proposed by Biot is more general and physically sensible than that proposed by Terzaghi. Rice and Clearly14 solved poroelastic problems by assuming pore pressure and stress as primary variables instead of displacements as employed by Biot. Yet, all the above work has been limited to the framework of linear constitutive relations and single-phase flow in porous media. Rapid progress in computer technology in recent years has allowed the tackling of numerically more challenging problems associated with nonlinear materials and multiphase flow. Due to the complexity of the solutions of multiphase flow and geomechanics models themselves, the solution of the coupled problem is even more complicated and needs further study to improve accuracy, convergence, computing efficiency, etc. In particular, researchers have been debating which coupling approach is best for computing fluid-solid interactions. The term ‘interaction’ is understood here as the mechanical force effect rather than the chemical reaction effect between fluid and solid.