Abstract
Field-scale simulation of flow in porous media in presence of incomplete mixing demands for high-resolution computational grids, much beyond the scope of state-of-the-art simulators. Hence, the upscaling-based Todd and Longstaff (TL) approach is typically used, where coarse grid cells are employed with effective mixing fluid properties and parameters found by matching results obtained with fully resolved reference simulations. Dynamic local grid refinement (DLGR) techniques, on the other hand, only employ fine-scale grid resolution where the fully mixed assumption is not valid. The rest of the domain is then solved at coarser resolutions, where the fully mixed assumption is valid. Here, we assess the accuracy and the robustness of DLGR- and TL-based simulations of miscible displacements in homogeneous and heterogeneous porous media. Due to the intrinsic uncertainty within the unstable displacement nature of the studied incomplete mixing processes, the performance of the methods is also investigated based on a range of acceptable solutions rather than relying only on a single reference one. Systematic numerical results illustrate that the DLGR method is much more robust and accurate than the upscaling-based TL approach, and employs only a small fraction of fine-scale reference grids. Especially, the TL upscaling results (though history matched with computationally expensive fine-scale results) are very sensitive to the change of the simulation parameters. Based on this study, we propose a dynamic multilevel simulation strategy for efficient and reliable large-scale simulation of the complex incomplete mixing processes.
Highlights
The miscible and immiscible displacements in subsurface porous media can develop instabilities at the interfaces of the fluids with different properties [1]
Based on the results presented here, Dynamic local grid refinement (DLGR) should be preferred over the Todd and Longstaff (TL) model, since it allows to accurately and efficiently simulate the incomplete mixing displacement, and it shares the same sensitivities with respect to the input parameters compared with the fine-scale fully resolved simulation
It can be observed that the TL model shows low sensitivity to the variation in production and local solvent concentration distributions compared to the high-resolution and DLGR simulations
Summary
The miscible and immiscible displacements in subsurface porous media can develop instabilities at the interfaces of the fluids with different properties [1]. Similar to alternative upscaling-based models, a major disadvantage of TL approach is that the effective fluid properties are described by an undefined scalar mixing parameter, which must be obtained from either highresolution simulation or experimental data. The sensitivity of DLGR simulations to different error estimate strategies in order to refine or coarsen the grid is assessed. Important is that TL upscaling approach was employed after tuning parameters based on the fine-scale reference solution, its results are sensitive to changes of the simulation inputs (e.g., grid resolution and mobility ratio). Based on the results presented here, DLGR should be preferred over the TL model, since it allows to accurately and efficiently simulate the incomplete mixing displacement, and it shares the same sensitivities with respect to the input parameters compared with the fine-scale fully resolved simulation.
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