Incomplete mixing in porous media: Todd-Longstaff upscaling approach versus a dynamic local grid refinement method

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. Keywords Incomplete mixing in porous media • Dynamic local grid refinement • Todd-Longstaff model • Algebraic dynamic multilevel method • Viscous fingering

Dynamic adaptive mesh optimisation for immiscible viscous fingering

“…Initial applications to viscous fingering involved the use of an underlying, fixed, structured mesh which was locally refined or coarsened depending on specified error metrics. These enabled the modelling of viscous fingering in both miscible [26,27] and immiscible [28] 2D systems. More recently, Lee and Wheeler [29] used adaptive enriched Galerkin methods on structured Cartesian grids to model miscible fingering in linear and radial displacements.…”

Scaling Analysis of Two‐Phase Flow in Fractal Permeability Fields

“…This finding is similar to the results of scaling analysis for miscible displacements reported by Sajjadi and Azaiez (2013). Despite recent advances in understanding the impact of heterogeneity on fluid mixing for miscible or partially miscible flows (Amooie et al, 2017; Connolly & Johns, 2016; Cusini et al, 2019; Nicolaides et al, 2015; Nijjer et al, 2019), few studies have explored self‐similarity of the evolution of mixing for both miscible and immiscible flows in fractal permeability fields.…”

Algebraic Dynamic Multilevel Method for Fractured Geothermal Reservoir Simulation

“…Even with EDFM-based strategy, the classical FIM systems become too expensive to be solved in realfield applications. Upscaling the nonlinear formulations does not lead to good approximate solutions and similarly sensitive systems with the user-defined error control strategies (Cusini et al, 2018b). In this work, a fully-implicit multilevel multiscale approach is presented to solve this challenge.…”