The Development of an Optimal Grid-Coarsening Scheme: Interplay of Fluid Forces and Higher Moments of Fine-Scale Flow Data

Abstract

Abstract The accuracy of upscaling procedures can be improved by using non-uniform grid cells at the coarse scale level. Several researchers have investigated objective methods of selecting the optimal coarse grid configuration for a particular fine grid model1–2. However, all of these works neglect the effect of fluid force balances and always assumed the model to be in viscous dominated flow. This paper describes a new optimal grid-coarsening scheme for two-phase flow in porous media based on the quantitative use of fine-scale simulation data. The main idea of this approach is to use fine-grid fluctuating moments to guide the choice of the coarse grid structure. These quantities are derived from the volume average saturation equation for different fluid force balances i.e. viscous, gravity and capillary. It is shown that this approach results in a more accurate prediction of quantities such as total oil recovery and fluid production ratio in coarse grid models. Here, we explore the relationship between the sub-grid properties described above, and coarse scale numerical simulations for several synthetic model problems. To do this, we first introduce capillary terms into the volume averaging equations3 to allow us to assess the coarse scale simulations when capillary pressure is important in the fine grid models. Then we proceed to the two-stage testing of the proposed technique to study the relationship of sub-grid variability to the error in the coarse scale simulation results. In the first stage testing, we consider many different aggregations of 2D, 20-layer fine grid systems to equivalent 2-layer coarse grid systems and in the second stage testing, we then apply our findings to more heterogeneous interbedded sand cases where capillary forces are more important and consider coarsening the fine grid model to more than 2 layers.