Multiscale Methods and Non-Uniform Coarsened Grids for Reservoir Simulation Without Upscaling

Background: Standard reservoir simulators are seldom able to utilize the detailed description of the reservoir geology and petrophysical charateristics available in high-resolution geomodels. Indeed, to simulate the flow of reservoir fluids, it is common to upscale the geological model to a coarser simulation model that contains much less details. Modern multiscale methods seek to automate or bypass entirely the time-consuming and inaccurate upscaling process. In this project, we consider a particular multiscale methods, the multiscale mixed finite-element method (MsMFEM). This method is based on a two-grid approach: a fine grid on which the rock parameters are given and a coarse grid in which each block is a collection of cells from the fine grid. By solving flow problems locally for each pair of coarse blocks, we obtain a set of representative elementary solutions (basis functions) that can be patched together to solve the global flow problem on the coarse grid. This way, we obtain a detailed flow patterns on the fine grid without having to solve the full fine-grid system. The efficiency of MsMFEM appears for multiphase simulations where one for each time step only needs to solve a coarse-grid problem if the basis functions have been computed once initially.

Project goals: Develop methods for generating coarse grids that adapt to features in the flow field (barriers, high-flow regions, wells, etc) in such a way that a detailed and accurate flow pattern can be computed with as few coarse blocks as possible

Automatic coarsening: In the project we have developed multiscale methods capable of handling fully unstructured coarse grids in which each block consists of any connected collection of cells from the fine grid. Lessons learned in the project is that coarse blocks should follow geological layers and adapt to flow barriers to maximize accuracy and robustness of MsMFEM. The project also contributed to developing simple guidelines to be used in automated coarsening methods in order to improving the resulting coarse blocks.

Near-well flow: In the project we also studied multiscale methods for more accurate simulations of near-well flow. Specifically, we studied the coupling of a multi-segment drift-flux well model with a standard two-phase, incompressible reservoir model. We observed that the quality of the simulation results is strongly influenced by the choice of grids in the near-well region, and we developed simple gridding strategy that gave very good results.

Key Publications

1. J. E. Aarnes, S. Krogstad, and K.-A. Lie. Multiscale mixed/mimetic methods on corner-point grids. Computational Geosciences, Special issue on multiscale methods. DOI: 10.1007/s10596-007-9072-8
2. J. E. Aarnes, S. Krogstad, and K.-A. Lie. A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids, Multiscale Modelling and Simulation, Vol. 5, No. 2, pp. 337-363, 2006.
3. S. Krogstad and L.J. Durlofsky.Multiscale mixed finite element modeling of coupled wellbore/near-well flow. SPE 106179. 2007 SPE Reservoir Simulation Symposium, Houston, Texas, U.S.A. 26-28 February 2007. DOI: 10.2118/106179-MS.