A Coupled Reservoir and Geomechanical Simulation System

Abstract

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.

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

“…Fluid-flow characteristics of reservoir rocks, such as permeability and pore compressibility, can be very sensitive to effective stress changes caused by changes in pore pressure. Settari and Mourits (1998) behavior. Also, Raghavan and Chin (2004) presented correlations to evaluate productivity losses owing to permeability changes in stress-sensitive reservoirs.…”

Investigation of possible wellbore cement failures during hydraulic fracturing operations

“…Sequential methods can offer the use of existing robust flow and geomechanics simulators only by constructing an interface between them (Settari and Mourits, 1998). According to Kim et al (2011), the fixed stress sequential method can provide unconditional stability and high accuracy, comparable to the fully coupled methods.…”

Disposal systems evaluations and tool development : Engineered Barrier System (EBS) evaluation.

“…For porous deformable media, two models for mechanically induced porosity changes are implemented in the most recent version linking FLAC 3D to TOUGH+ (i) A poroelastic model (based on the approach proposed by Settari and Mourits (1998) that considers macroscopic stress/strain changes and grain deformability…”

“…It is a delicate operation to correctly change the porosity of the reservoir simulator upon a change in stress or strain in the mechanical code. The ideas of Settari and Mourits (1998) have been implemented in TOUGH-FLAC coupling as one alternative poro-elastic model. The correct poro-elastic consideration is important when comparing simulation results to that of fully coupled poro-elastic finite element models of the Biot type.…”

“…The correct poro-elastic consideration is important when comparing simulation results to that of fully coupled poro-elastic finite element models of the Biot type. However, as described by Settari and Mourits (1998), in practice it is more important to consider the nonlinear stress-dependent effects on porosity and permeability over the range of stress expected in a problem. Such properties may be derived directly from laboratory data and fitted to theoretical or empirical functions (e.g., Liu et al, 2009) or by calibration to field experiments (e.g., Rutqvist et al, 2008).…”