A finite element-finite volume approach for multiphase poromechanics

Modeling the hydromechanical behavior of geological materials infiltrated by one or more types of fluids is critical in many scientific and engineering applications, including geologic carbon sequestration, hydrocarbon recovery, and geotechnical analysis. For some of these applications, it is sufficient to consider only the solid deformation problem or the fluid flow problem separately. Even then, the solution could encounter difficulties, both theoretically and numerically. Other applications require simultaneous solution of solid deformation and fluid flow phenomena, thus creating enormous computational challenges in that one needs to solve different physical problems at the same time. This thesis addresses some of the computational challenges associated with modeling coupled multiphase and multi-physical systems in poromechanics. The first part of this thesis focuses on how to improve the solution accuracy for a particular type of discretization that uses the finite element method to solve the solid deformation problem and the finite volume scheme for the fluid flow. This type of approximation is quite common; however, it may lead to unphysical oscillations in the pore pressure field. To suppress the spurious oscillations, we devise a stabilized formulation. This work is one of very few studies of stabilization procedures addressing multiphase poromechanics in the context of mixed finite element-finite volume method. The designed stabilization supplements the mass balance equations with stabilizing fluxes inside patches of elements called macroelements. The method is simple to implement in an existing code and conserves mass within the macroelements. We show that the stabilization effectively treats the pervasive oscillations associated with the presence of near-singular modes. Additionally, a direct result of removing the near-singular modes is the dramatical improvement on the convergence of iterative linear solvers. The second part of this work aims to develop an efficient solver for coupled solid deformation-fluid flow problems where capillarity forces are strong. For these cases, the saturation of the invading fluid spreads more diffusively. This change in the behavior of saturation variables has to be taken into account in the design of efficient solvers. In a coupled simulation, a major part of the overall computational time is devoted to solving the large system of linear equations that arises from the discretization of the governing equations. By designing a more efficient iterative linear equation solver for the problem, we reduce the computational cost of large-scale coupled simulations. In this work, the efficiency of the iterative linear solver is improved by designing three preconditioning approaches that are more suitable to the strong capillary pressure regime. The approaches are based on a block factorization of the coupled system with sparse Schur complement approximations. The strategies differ on how they approximate the Schur complement used to correct the saturation unknowns. When the approximation relies on a multilevel preconditioner, we show that the linear solver reduces the computing time by a factor of two relative to the base case strategy, which uses a Jacobi approximation. The final part of this work builds upon the previously developed numerical framework to analyze a potential offshore carbon storage site in the Gulf of Mexico. The goal of the study is to assess appropriate deformation monitoring techniques that have sufficient sensitivity to measure the seabed uplift induced by fluid injection into the reservoir. Before deploying such measuring instruments in an offshore environment, it is essential that we first simulate the coupled solid deformation-fluid flow phenomena as realistically as possible to gain some insight into the precision of instruments needed for such field study. To this end, we create a finite element-finite volume model of a potential offshore site that incorporates a spatially heterogeneous permeability distribution expected at this site. We conduct a sensitivity analysis on the geomechanical parameters and investigate the influence of fault sealing on the fluid flow. Results of the simulations suggest that the reservoir has a remarkable injectivity, allowing for a large amount of fluid to be injected without a substantial increase in pore pressure. The computed seabed deformations are equally small and could be monitored with distributed fiber optic cables and ocean bottom pressure recorders

Advisor: Borja Ronaldo I. (Ronaldo Israel) 
Linder Christian (Engineering professor) 
White Joshua (Joshua A.)