Implicit coupling framework for multi-physics reservoir simulation [electronic resource]
Keywords: Energy Resources Engineering.

The growth in the complexity of the subsurface flow processes of interest and the continuous increase in computational power have created the need for simulation frameworks that can be extended to handle multi-physics problems. Having a generalized framework reduces the development cost of incorporating additional physical mechanisms and exploring new numerical formulations and solution algorithms. In addition, a general simulation framework is necessary as we the transition from the existing paradigm, in which a small number of specific process models are coupled in a very limited number of predefined combinations, to a new paradigm, where many different nonlinear processes can be coupled in arbitrary permutations. The flexibility of such a framework allows us to investigate new nonlinear coupling configurations across the different physics processes and improve our understanding of the nature of the interactions. Such a flexible simulation framework will allow us to improve the robustness and computational efficiency of modeling coupled systems by finding new configurations and more efficient solvers for a given physics process. The goal of this work is the development and implementation of a general sequential reservoir simulation framework for multi-physics problems. The limitations associated with existing `general-purpose' platforms include: (1) Limited coupling strategies for a predetermined small set of physical processes. (2) The absence of accurate and consistent comparisons between the different coupling strategies. (3) Highly specialized linear solvers for a predefined set of physical processes. (4) Limited paths for the extension to new physics and additional complex features. In contrast to the existing platforms, the new framework can accommodate any coupling strategy across the different nonlinear physics modules. This flexibility is achieved using a `sub-problem' tree structure and a global status table. These components are integrated with the subsets through an automatic differentiation layer (library). The exploration of different coupling strategies facilitates the study of new multi-physics preconditioners. The modular design with transparent subset-based interfaces greatly improves code extensibility. In addition, we developed a unique `mapping operators' concept that enables advanced coupling strategies, including (parallel) domain-decomposition and multiscale approaches. We have designed, developed, implemented, and tested a new GENeral Implicit Coupling framework for multi-physics problems (GENIC) that allows for rapid prototyping and customization. This GENIC framework is the next generation of the Automatic-Differentiation General-Purpose Research Simulator (AD-GPRS) at Stanford. GENIC represent a flexible and efficient `computational' laboratory for advanced reservoir simulation that allows researchers to try their ideas rapidly and specialize the preferred strategies efficiently. We demonstrate the power and flexibility of the GENIC framework in modeling complex multi-physics problems using several nonlinear problems that involve several mechanisms of flow and transport, and we show that the GENIC framework allows for investigating the full range of possible coupling strategies. We explore the use of existing and novel sequential coupling schemes for flow-thermal problems (i.e., multi-component multiphase flow and transport of mass and energy). We investigate the convergence properties of three different schemes: constant pressure, constant density, and a hybrid scheme where constant pressure is used for single-phase blocks, and constant density is used for two-phase blocks. The hybrid approach performed the best out of the three schemes tested. This hybrid method was able to avoid the divergent, or slow converging, behavior in the single-phase (constant density) and the two-phase (constant pressure) regions. Next, we present a new approach for coupling flow and thermal displacement processes -- modified sequential fully implicit (m-SFI) method. We demonstrate m-SFI method for several challenging examples where standard sequential approaches fail; specifically, we show that m-SFI takes a similar number of time steps as the full implicit method (FIM). In cases where accurate front prediction is possible and the two-phase region is limited, such as strictly injection or production problems, the m-SFI approach outperforms FIM. However, when most of the reservoir has two phases, the overall performance of the m-SFI method is more expensive than FIM due to the increased cost of the sequential iterations. We then demonstrate the applicability of the GENIC framework for flow-mechanics problems using three examples: (1) Mandel's problem; (2) Dean's problem; (3) an extended SPE 10 problem. We tested two existing `coupled properties': fixed-stress and fixed-strain. The results are consistent with published results, where the fixed-strain approach is only conditionally stable and the fixed-stress is unconditionally stable. In addition, we compare the performance of the sequential coupling strategy with FIM for the extended SPE 10 problem. For moderate and weak coupling, the sequential approach performs better than FIM. However, strongly coupled problems where both physics are highly nonlinear poses remains an open challenge for sequential schemes. We conclude with a solution for a flow-thermal-mechanics problem using three different coupling strategies: fully coupled, sequentially coupled, and nested sequentially coupled. This is the first example - to our knowledge - where both fully coupled and sequentially coupled approaches are applied to this three-physics problem. When the mechanics problem is linear, and the coupling strength is weak, the sequential coupling strategy performs faster than FIM; however, as the coupling strength involving mechanics increases, sequential coupling strategies become less effective.