Coupled Geomechanics and Reservoir Simulation
- L.K. Thomas (ConocoPhillips) | L.Y. Chin (ConocoPhillips) | R.G. Pierson (ConocoPhillips) | J.E. Sylte (ConocoPhillips)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2003
- Document Type
- Journal Paper
- 350 - 358
- 2003. Society of Petroleum Engineers
- 5.1.5 Geologic Modeling, 4.6 Natural Gas, 5.5.3 Scaling Methods, 5.5.8 History Matching, 1.2.2 Geomechanics, 5.3.2 Multiphase Flow, 5.4.2 Gas Injection Methods, 5.8.6 Naturally Fractured Reservoir, 4.3.4 Scale, 6.5.2 Water use, produced water discharge and disposal, 5.4.1 Waterflooding, 5.5.1 Simulator Development, 5.2.1 Phase Behavior and PVT Measurements, 5.3.4 Integration of geomechanics in models, 5.5 Reservoir Simulation
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An iterative procedure is presented in this paper to couple geomechanics and reservoir simulation models for the simulation of weaker rock formations with complex constitutive behavior. Parallel computing is employed in the coupled model to reduce run time in the compute intensive geomechanics model. The procedures developed here are general, and can be applied to any reservoir simulation and geomechanics model.
Field and example problems under a variety of exploitation scenarios are presented to demonstrate the utility and robust nature of the coupled model. For example, a large-scale field case was simulated using the coupled model with 16 processors for the geomechanics model. The total CPU time for a 30-year simulation run was approximately 2 hours. These results indicate that it is both economical and practical to use the proposed procedure and parallel computing for analyzing field-scale problems that integrate reservoir and geomechanics simulation.
Conventional reservoir simulators calculate the effect of rock compaction on pore volume change through the concept of rock compressibility under a defined loading condition (hydrostatic or uniaxial strain). This approach is usually appropriate for reservoirs with competent rock. However, for weaker formations and complicated rock-compaction behavior, coupled analysis of geomechanics and multiphase fluid flow may be required for obtaining more accurate solutions from reservoir simulation (for example, Refs. 1 through 7). Also, coupled analysis may be beneficial when key reservoir properties such as permeability are strongly influenced by the stress state and the loading conditions in the reservoir formation during fluid production.6,7
Reservoir simulation with coupled geomechanics for largescale, full-field, 3D simulation problems can be quite time consuming. Consequently, computational efficiency and convergence of numerical solutions are critical factors required to make coupled analysis economically and numerically feasible for practical field applications. In this paper, an improved iterative procedure and parallel computing are used to extend previous work7 to the simulation of large-scale, full-field, 3D problems. The procedure is general and effective for handling reservoir rock with complicated (elastic-plastic, etc.) constitutive behavior of rock compaction and permeability change while simulating various reservoir production scenarios. The constitutive behavior of reservoir rock that can be simulated includes nonlinear stress strain relations, the water-weakening effect, and compaction hysteresis (i.e., irrecoverable strain caused by plasticity). Previous investigators have dealt with this problem by using approximate relationships based on linear elastic functions.
Descriptions of model formulations, constitutive equations, solutions procedures, and strategies for enhancement of computational efficiency are presented in the paper. Field and example problems are presented to demonstrate the capability of the developed procedure for iterative, coupled analysis. These coupled problems include the impact of stress and water saturation on compaction in water-sensitive formations and the effect of stress-sensitive permeability on field productivity.
Coupled Model Formulation
An iterative, fully coupled procedure8 is used to integrate the reservoir simulation and geomechanics models in a generalized fashion. Discretized equations of these two models contain state variables that are shared by both models. These shared variables are porosity, pressure, and water saturation.
A flow chart illustrating the iterative, coupled procedure is shown in Fig. 1. The procedure consists of an initialization phase and a solution phase. At time zero, both reservoir and geomechanics models are set to their initial conditions. The initialization procedure used in this paper is at the upscaled model grid level. It is an iterative process to make both the reservoir and geomechanics simulators start from the same initial porosity distribution. Based on the initial pressure and saturation distributions provided by the reservoir model, the geomechanics model solves its governing equations to establish the initial stress state in the reservoir, overburden, underburden, and sideburden under the prescribed initial conditions. Then, the geomechanics model sends initial porosity values and initial derivatives of porosity with respect to pressure and water saturation to the reservoir model. At this stage, the initialization phase is complete, and the reservoir model is ready to start the first timestep calculation.
The reservoir model operates as the primary or controlling software in the coupled model. Pressures and water saturations for cases with water-sensitive rock are passed to the geomechanics model each Newton iteration of each timestep. The geomechanics model in turn iterates on its solution, taking as many Newton iterations as required, until convergence is reached. Porosities and porosity partial derivatives with respect to pressure and water saturation are then returned to the reservoir model for use on its next Newton iteration. This sequence is continued until convergence is reached, based on criteria in the reservoir simulation model.
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