A rigorous yet simple technique for coupled reservoir and geomechanics simulation

Many applications in the petroleum industry require both an understanding of the porous flow of reservoir fluids and an understanding of reservoir stresses and displacements. Historically reservoir simulation has accounted for geomechanical effects by simple use of a rock compressibility. This assumption results in pore volume to change only with pore pressure. On the other hand, according to the poroelasticity theory, pore volume should change not only with pore pressure but also with confining stresses or volumetric strains induced by rock deformation. This difference in the governing equations poses a great challenge when coupling reservoir flow and geomechanics models. In this study, we develop a mathematical expression that relates the pore volume compressibility used in the porous flow equation to poroelasticity parameters defined in the geomechanics model. Secondly, in order to implement consistent pore volume changes between the reservoir flow and geomechanics models, we derive a pore volume correction term for the porous flow equation, which accounts for volumetric strain changes and rock matrix deformation. As demonstrated in the paper, the correction term can be easily implemented in sink/source terms (or "fictitious well" term), which are readily available for most commercial reservoir flow models. With this simple implementation, virtually any existing commercial reservoir simulation models can account for geomechanical effects via modular coupling techniques. In this work, we compare three different techniques for coupling reservoir flow and geomechanics. One technique uses an explicit algorithm to couple reservoir flow and displacements in which flow calculations are performed every time step followed by displacement calculations (i.e., One-way coupling method). A second technique uses an iteratively coupled algorithm in which flow calculations and displacement calculations are performed sequentially for the nonlinear iterations during each time step (i.e., Iterative partitioned coupling method). The third technique uses a fully coupled approach in which the program's linear solver must solve simultaneously for fluid-flow variables and displacement variables (i.e., Monolithic coupling method). Using Mandel's problem, example simulations are presented to highlight accuracy and computational efficiencies in these coupling techniques. To the best of the author's knowledge, this is the first paper to present a coupling technique to consider rigorous geomechanical effects in the porous flow equations. The coupling method proposed in this study can be applicable for virtually any existing reservoir and geomechanics simulation models. The proposed coupling techniques are easily extended to multiphase flow and poroelastoplastic problems. All problems in this paper are described in detail, so the results presented here may be used for comparison with other geomechanical / porous-flow simulators.