Advanced Discretization Framework for Fully-Implicit Simulation of Multiphysics Flow in Porous Medi

This work covers several advances in numerical discretization methods for reservoir simulation. In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular Phase-Potential Upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iterations. Recently proposed methods address improved smoothness of the numerical flux. The objective is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases. We analyze the consistency property of the C1-PPU scheme, and derive saturation and pressure estimates, which are used to prove the solution existence. The numerical examples show that the C1-PPU scheme exhibits superior convergence properties for large time steps compared to the other alternatives.;The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit Cell-Centered Finite-Volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintaining robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance.;Although many works confirm the high accuracy of Embedded Discrete Fracture Model (EDFM) for the solutions of pressure and velocity field, very few results have been presented to examine its accuracy for the saturation solutions from multiphase flow problems. Our study shows that EDFM can induce large errors for multiphase displacement processes, due to its incapability to capture the proper flux split through a fracture. For the first time in the literature we present a systematic evaluation on the performances of EDFM for multiphase flow and provide a detailed analysis to illuminate when and why the method fails. The analysis motivates us to exploit the projection-based extension of EDFM (pEDFM) as an effective method to resolve the limitations associated with EDFM. Moreover, we make several improvements upon the original pEDFM method. A physical constraint on the preprocessing stage is proposed to overcome the limitation in a naive implementation of pEDFM. A number of test cases with different fracture geometries are presented to benchmark the performances of the improved pEDFM method for multiphase flow. Grid convergence studies are conducted for different numerical schemes. The results show that improved pEDFM significantly outperforms the original EDFM method.