Abstract:

Modeling and simulation of multiphase flow have been used extensively by petroleum engineers to manage existing petroleum fields and to develop new oil and gas reservoir. One basic requirement for accurate and robust modeling and simulation of multiphase flow is to have the predicted physical quantities sit within a physically meaningful range. For example, the predicated saturation should sit between 0 and 1 in immiscible multiphase flow models. Unfortunately, popular simulation methods used in petroleum industries do not preserve physical bounds. Bound violation may crash the simulator, as saturations are often applied to a function involving logarithm in order to get the capillary pressure. A commonly used fix in industry to this problem is to simply apply a cut-off operator. However, this cut-off practice does not only destroy the local mass conservation but it also damages the global mass conservation, which seriously ruins the numerical accuracy and physical interpretability of the simulation results. In the talk, we will present our recent work on bound-preserving discretization and solvers for subsurface flow models based on a fully implicit framework. We reformulated subsurface multiphase flow using variational inequalities that naturally ensure the physical feasibility of the physical quantities including saturations (and concentrations if modeling composition). We applied a mixed finite element method and the implicit backward Euler scheme with adaptive time stepping. The resultant nonlinear system arising at each time step was then solved by a generalized Newton method, i.e., active-set reduced-space method, and then the ill-conditioned linear Jacobian systems were solved with a Krylov subspace method combined with a nonlinear preconditioner based on overlapping additive Schwarz type domain decomposition and nonlinear elimination. Numerical results will be presented to examine the performance of the newly developed algorithm on parallel computers. This presentation is based on the joint work [CMAME, 330: 334-350, 2018; JCP, 332: 1-20, 2017; and SISC, 38(4): B593–B618, 2016] with Haijian Yang (Hunan University), Chao Yang (Beijing University), and Yiteng Li (KAUST).