Hjeij, Dawood (Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University) | Abushaikha, Ahmad (Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University)
Most commercially available simulators use the trivial two-point flux approximation (TPFA) method for flux computation. However, the TPFA only gives consistent solutions when used for K-orthogonal grids. In general, multi-point flux approximation (MPFA) methods perform better under both heterogeneous and anisotropic conditions. The mimetic finite difference (MFD) method is designed to preserve properties on unstructured polyhedral grids, and its development for simulating full tensor permeabilities is also crucial step. This paper compares the performance, accuracy, and efficiency of these schemes for simulating complex synthetic and realistic hydrocarbon reservoirs.
High-resolution discretizations can be advantageous in compositional simulation to reduce excessive numerical diffusion that tends to mask shocks and fingering effects. In this work, we outline a fully implicit, dynamic, multilevel, high-resolution simulator for compositional problems on unstructured polyhedral grids. We rely on four ingredients: (i) sequential splitting of the full problem into a pressure and a transport problem, (ii) ordering of grid cells based on intercell fluxes to localize the nonlinear transport solves, (iii) higher-order discontinuous Galerkin (dG) spatial discretization with order adaptivity for the component transport, and (iv) a dynamic coarsening and refinement procedure. For purely cocurrent flow, and in the absence of capillary forces, the nonlinear transport system can be perturbed to a lower block-triangular form. With counter-current flow caused by gravity or capillary forces, the nonlinear system of discrete transport equations will contain larger blocks of mutually dependent cells on the diagonal. In either case, the transport subproblem can be solved efficiently cell-by-cell or block-by-block because of the natural localization in the dG scheme. In addition, we discuss how adaptive grid and order refinement can effectively improve accuracy. We demonstrate the applicability of the proposed solver through a number of examples, ranging from simple conceptual problems with PEBI grids in two dimensions, to realistic reservoir models in three dimensions. We compare our new solver to the standard upstream-mobility-weighting scheme and to a second-order WENO scheme.
Accurate numerical modeling of fluid transport is essential in reservoir management. Higher-order methods help to improve accuracy by reducing the numerical diffusion, which is common for all first order methods. In this paper, we present an implementation of a MUSCL-type second-order finite volume method and demonstrate its capabilities on 2D and 3D unstructured grids. This includes corner point grids that are typically used in reservoir modeling.
A second order finite volume method is compared to standard first order method in terms of accuracy, performance and an ability to handle nonlinearities. There are several ways to build a second order finite volume method. In this paper we choose an optimization-based strategy to compute the steepest possible linear reconstruction. At the same time, a steepness-limiting procedure is included in the optimization as constraint. This ensures that the steepest possible reconstruction that does not lead to oscillations is computed. As a result, sharper fronts compared to standard schemes are obtained.
The paper demonstrates the described method on several benchmark cases with emphasis on relevant for practical reservoir simulation test cases. In particular, we use Norne field open data set, which enables cross validation with other implementations. We test the method on the transport case, where an analytical solution is known, to verify convergence behavior and to isolate the errors. Furthermore, the performance of first- and second-order methods is compared on multiphase flow problems typical for improved oil recovery: solvent and CO2 injection. The second order method shows superior performance in terms of accuracy.
This paper verifies the desirable properties of higher order method for reservoir simulation. Moreover, all the described implementations are available in an open source reservoir simulator Open Porous Media (OPM). As a result, these methods are accessible for reservoir engineers and can be used with industry standard modeling setups.
Modelling multiscale-multiphysics geology at field scales is non-trivial due to computational resources and data availability. At such scales it is common to use implicit modelling approaches as they remain a practical method of understanding the first order processes of complex systems. In this work we introduce a numerical framework for the simulation of geomechanical dual-continuum materials. Our framework is written as part of the open source MATLAB Reservoir Simulation Toolbox (MRST). We discretise the flow and mechanics problems using the finite volume method (FVM) and virtual element method (VEM) respectively. The result is a framework that ensures local mass conservation with respect to flow and is robust with respect to gridding. Solution of the coupled linear system can be achieved with either fully coupled or fixed-stress split solution strategies. We demonstrate our framework on an analytical comparison case and on a 3D geological grid case. In the former we observe a good match between analytical and numerical results, for both fully coupled and fixed-stress split strategies. In the latter, the geological model is gridded using a corner point grid that contains degenerate cells as well as hanging nodes. For the geological case, we observe physically plausible and intuitive results given the boundary conditions of the problem. Our initial testing with the framework suggests that the FEM-VEM discretisation has potential for conducting practical geomechanical studies of multiscale systems.