Flow-based Grid Coarsening for Transport Simulations

Abstract

Geological models are becoming increasingly large and detailed to account for heterogeneous structures on different spatial scales. To obtain computationally tractable simulation models, it is common to remove spatial detail by upscaling. Pressure and transport equations are different in nature and generally require different strategies for optimal upgridding. To optimize accuracy of a transport calculation, the coarsened grid should be constructed based on a posteriori error estimates and adapt to the flow patterns predicted by the pressure equation. Sharp and rigorous estimates are generally hard to obtain; herein we consider various adhoc methods for generating flow-adapted grids. Common for all, is that they start by solving a single-phase flow problem once and continue by agglomerating 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 where flow-adaption is not crucial. Second, we show how different algorithmic choices can simplify the matrix structure of the discretized system and lead to reduced computational complexity. Finally, we demonstrate how to improve simulation accuracy by dynamically adding local resolution near strong saturation fronts.