Flow-based coarsening for multiscale simulation of transport in porous media

Abstract

Geological models are becoming increasingly large and detailed to account for heterogeneous structures on different spatial scales. To obtain simulation models that are computationally tractable, it is common to remove spatial detail from the geological description by upscaling. Pressure and transport equations are different in nature and generally require different strategies for optimal upgridding. To optimize the accuracy of a transport calculation, the coarsened grid should generally be constructed based on a posteriori error estimates and adapt to the flow patterns predicted by the pressure equation. However, sharp and rigorous estimates are generally hard to obtain, and herein we therefore consider various ad hoc methods for generating flow-adapted grids. Common for all is that they start by solving a single-phase flow problem once and then continue to form a coarsened grid by amalgamating cells from an underlying fine-scale grid. We present several variations of the original method. First, we discuss how to include a priori information in the coarsening process, e.g. to adapt to special geological features or to obtain less irregular grids in regions where flowadaption is not crucial. Second, we discuss the use of bi-directional versus net fluxes over the coarse blocks and show how the latter gives systems that better represent the causality in the flow equations, which can be exploited to develop very efficient nonlinear solvers. Finally, we demonstrate how to improve simulation accuracy by dynamically adding local resolution near strong saturation fronts.

Numerical Assessment Of Water Alternating Gas Practices In The Presence Of Hysteresis Effects On Relative Permeability

“…We take advantage of non-uniform coarsening (NUC) tools (Hauge et al, 2012) available in MRST environment to amalgamate (grouping) cells from the fine numerical grid described above. We do so to prevent numerical convergence issues.…”

Accelerating multiscale simulation of complex geomodels by use of dynamically adapted basis functions

“…These partitions could be constructed by increasing the coarse-grid resolution near features of interest such as fractures and well paths, and/or by ensuring that block interfaces follow geological layers, fault surfaces, boundaries between different rock types, flow units, and depositional environments, etc. One effective way to generate such partitions is to agglomerate cells into blocks according to user-defined cell/face indicators and partitioning rules [13,12,24,23]. Several partition examples are shown in [25].…”

Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs

“…The distance-based partition is defined by a predefined coarse grid resolution parameter and a distance indicator (measuring the distance between the cell center of a fine cell and the closest fracture). The coarse cells can be merged and refined in an iterative loop in order to obtain a coarse grid with preferred properties [13]. The focus of this work is not to obtain an optimal coarse grid, but rather to design a coarse scale discretization that works well also for highly irregular coarse grids.…”

“…Following [13], a control volume discretization of the advective term is obtained by integrating the (known) fine scale fluxes to net fluxes on the coarse scale,…”

“…While the advective term can be discretized from the known fine-scale velocity field in the manner of [13], the complex grid poses challenges for the discretization of the heat conduction term.…”