Dynamic Local Grid Refinement for Incomplete Mixing in Reservoir Simulation

Abstract

Reservoir simulation is a key tool to get insight in complex fluid flow phenomena occurring in many petroleum reservoirs, creating the possibility to quantify fluid productions and their uncertainty regarding many unknown properties. It has been shown by experimental and theoretical research that under certain criteria immiscible (multiphase) and miscible (single-phase) displacements can develop instabilities. These instabilities cause the displacing fluid to finger though the displaced oil, which is referred to as viscous fingering. Moreover, reservoir rock heterogeneity has shown to be capable to amply these phenomena. However, to limit computational costs, reservoir simulations typically use far lower grid resolution than the scale at which incomplete mixing phenomena occur. Numerical truncation errors imposed by large grid blocks will conceal small scale physical phenomena that contribute to unstable displacements. These sub-grid flow features are what is called incomplete mixing, as opposed to the fully mixed scenario inherent to the use of low resolution grids. To cope with this problem, effective models have been developed that make use of effective fluid properties in order to capture the sub-grid effect of incomplete mixing. Todd and Longstaff’s model is the most widely utilized model in the petroleum industry. Like similar models, one major disadvantage is that this effective model depends on an undefined scalar mixing parameter, which must be obtained from either high resolution simulation or experimental data. Dynamic local grid refinement (DLGR) is a simulation technique that can adapt the spatial grid resolution to the scale at which the physical phenomena occur without refining the grid over the entire domain. This can be achieved by means of local refinement and coarsening of the computational grid dynamically at every time step where small scale, local phenomena occur using predefined error criteria. This way DLGR could provide the means to solve for complex flow phenomena arising from instabilities at fluid fronts, while preserving complex geological features that could amplify this phenomena. This report investigates the use of state-of-the-art DLGR as an alternative to the effective model developed by Todd and Longstaff (TL). As DLGR is capable of adapting the spatial grid resolution locally where physical phenomena of incomplete mixing occur, this technique potentially allows for computational efficient and accurate results. The first part of this report studies and compares the results obtained using DLGR with that of the TL model and reference fine scale simulations for miscible transport in homogeneous media. Elaboration on DLGR's efficiency in term of CPU time, accuracy and consistency regarding scalability in terms of reservoir domain size and mobility ratio of the displaced and displacing fluid. Also a comparison is made for a secondary polymer flooding. The second part of this report investigates the accuracy of DLGR for miscible flow in heterogeneous reservoirs, and comparing the consistency of DLGR and the TL model.