Parallel simulation of coupled flow and geomechanics in porous media

textIn this research we consider developing a reservoir simulator capable of simulating complex coupled poromechanical processes on massively parallel computers. A variety of problems arising from petroleum and environmental engineering inherently necessitate the understanding of interactions between fluid flow and solid mechanics. Examples in petroleum engineering include reservoir compaction, wellbore collapse, sand production, and hydraulic fracturing. In environmental engineering, surface subsidence, carbon sequestration, and waste disposal are also coupled poromechanical processes. These economically and environmentally important problems motivate the active pursuit of robust, efficient, and accurate simulation tools for coupled poromechanical problems. Three coupling approaches are currently employed in the reservoir simulation community to solve the poromechanics system, namely, the fully implicit coupling (FIM), the explicit coupling, and the iterative coupling. The choice of the coupling scheme significantly affects the efficiency of the simulator and the accuracy of the solution. We adopt the fixed-stress iterative coupling scheme to solve the coupled system due to its advantages over the other two. Unlike the explicit coupling, the fixed-stress split has been theoretically proven to converge to the FIM for linear poroelasticity model. In addition, it is more efficient and easier to implement than the FIM. Our computational results indicate that this approach is also valid for multiphase flow. We discretize the quasi-static linear elasticity model for geomechanics in space using the continuous Galerkin (CG) finite element method (FEM) on general hexahedral grids. Fluid flow models are discretized by locally mass conservative schemes, specifically, the mixed finite element method (MFE) for the equation of state compositional flow on Cartesian grids and the multipoint flux mixed finite element method (MFMFE) for the single phase and two-phase flows on general hexahedral grids. While both the MFE and the MFMFE generate cell-centered stencils for pressure, the MFMFE has advantages in handling full tensor permeabilities and general geometry and boundary conditions. The MFMFE also obtains accurate fluxes at cell interfaces. These characteristics enable the simulation of more practical problems. For many reservoir simulation applications, for instance, the carbon sequestration simulation, we need to account for thermal effects on the compositional flow phase behavior and the solid structure stress evolution. We explicitly couple the poromechanics equations to a simplified energy conservation equation. A time-split scheme is used to solve heat convection and conduction successively. For the convection equation, a higher order Godunov method is employed to capture the sharp temperature front; for the conduction equation, the MFE is utilized. Simulations of coupled poromechanical or thermoporomechanical processes in field scales with high resolution usually require parallel computing capabilities. The flow models, the geomechanics model, and the thermodynamics model are modularized in the Integrated Parallel Accurate Reservoir Simulator (IPARS) which has been developed at the Center for Subsurface Modeling at the University of Texas at Austin. The IPARS framework handles structured (logically rectangular) grids and was originally designed for element-based data communication, such as the pressure data in the flow models. To parallelize the node-based geomechanics model, we enhance the capabilities of the IPARS framework for node-based data communication. Because the geomechanics linear system is more costly to solve than those of flow and thermodynamics models, the performance of linear solvers for the geomechanics model largely dictates the speed and scalability of the coupled simulator. We use the generalized minimal residual (GMRES) solver with the BoomerAMG preconditioner from the hypre library and the geometric multigrid (GMG) solver from the UG4 software toolbox to solve the geomechanics linear system. Additionally, the multilevel k-way mesh partitioning algorithm from METIS is used to generate high quality mesh partitioning to improve solver performance. Numerical examples of coupled poromechanics and thermoporomechanics simulations are presented to show the capabilities of the coupled simulator in solving practical problems accurately and efficiently. These examples include a real carbon sequestration field case with stress-dependent permeability, a synthetic thermoporoelastic reservoir simulation, poroelasticity simulations on highly distorted hexahedral grids, and parallel scalability tests on a massively parallel computer.Engineering Mechanic

Doctor of Philosophy

dissertationFluid production from tight and shale gas formations has increased significantly, and this unconventional portfolio of low-permeability reservoirs accounts for more than half of the gas produced in the United States. Stimulation and hydraulic fracturing are critical in making these systems productive, and hence it is important to understand the mechanics of the reservoir. When modeling fractured reservoirs using discrete-fracture network representation, the geomechanical effects are expected to have a significant impact on important reservoir characteristics. It has become more accepted that fracture growth, particularly in naturally fractured reservoirs with extremely low permeability, cannot be reliably represented by conventional planar representations. Characterizing the evolution of multiple, nonplanar, interconnected and possibly nonvertical hydraulic fractures requires hydraulic and mechanical characterization of the matrix, as well as existing latent or healed fracture networks. To solve these challenging problems, a reservoir simulator (Advanced Reactive Transport Simulator (ARTS)) capable of performing unconventional reservoir simulation is developed in this research work. A geomechanical model has been incorporated into the simulation framework with various coupling schemes and this model is used to understand the geomechanical effects in unconventional oil and gas recovery. This development allows ARTS to accept geomechanical information from external geomechanical simulators (soft coupling) or the solution of the geomechanical coupled problem (hard coupling). An iterative solution method of the flow and geomechanical equations has been used in implementing the hard coupling scheme. The hard coupling schemes were verified using one-dimensional and two-dimensional analytical solutions. The new reservoir simulator is applied to learn the influence of geomechanical impact on unconventional oil and gas production in a number of practical recovery scenarios. A commercial simulator called 3DEC was the geomechanical simulator used in soft coupling. In a naturally fractured reservoir, considering geomechanics may lead to an increase or decrease in production depending on the relationship between the reservoir petrophysical properties and mechanics. Combining geomechanics and flow in multiphase flow settings showed that production decrease could be caused by a combination of fracture contraction and water blockage. The concept of geomechanical coupling was illustrated with a complex naturally fractured system containing 44 fractures. Development of the generalized framework, being able to study multiphase flow reservoir processes with coupled geomechanics, and understanding of complex phenomena such as water blocks are the major outcomes from this research. These new tools will help in creating strategies for efficient and sustainable production of fluids from unconventional resources

A Study of Interwell Interference and Well Performance in Unconventional Reservoirs Based on Coupled Flow and Geomechanics Modeling with Improved Computational Efficiency

Completion quality of tightly spaced horizontal wells in unconventional reservoirs is important for hydrocarbon recovery efficiency. Parent well production usually leads to heterogeneous stress evolution around parent wells and at infill well locations, which affects hydraulic fracture growth along infill wells. Recent field observations indicate that infill well completions lead to frac hits and production interference between parent and infill wells. Therefore, it is important to characterize the heterogeneous interwell stress/pressure evolutions and hydraulic fracture networks. This work presents a reservoir-geomechanics-fracturing modeling workflow and its implementation in unconventional reservoirs for the characterization of interwell stress and pressure evolutions and for the modeling of interwell hydraulic fracture geometry. An in-house finite element model coupling fluid flow and geomechanics is first introduced and used to characterize production-induced stress and pressure changes in the reservoir. Then, an in-house complex fracture propagation model coupling fracture mechanics and wellbore/fracture fluid flow is used for the simulation of hydraulic fractures along infill wells. A parallel solver is also implemented in a reservoir geomechanics simulator in a separate study to investigate the potential of improving computational efficiency. Results show that differential stress (DS), parent well fracture geometry, legacy production time, bottomhole pressure (BHP) for legacy production, and perforation cluster location are key parameters affecting interwell fracture geometry and the occurrence of frac hits. In general, transverse infill well fractures are obtained in scenarios with large DS and small legacy producing time/BHP. Non-uniform parent well fracture geometry leads to frac hits in certain cases, while the assumption of uniform parent well fracture half-lengths in the numerical model could not capture the phenomenon of frac hits. Perforation cluster locations along infill wells do not play an important role in determining whether an infill well hydraulic fracture is transverse, while they are important for the occurrence of frac hits. In addition, the implementation of a parallel solver, PETSc, in a fortran-based simulator indicates that an overall speedup of 14 can be achieved for simulations with one million grid blocks. This result provides a reference for improving computational efficiency for geomechanical simulation involving large matrices using finite element methods (FEM)