A New Upscaling Approach for Highly Heterogeneous Reservoirs

Abstract

Abstract Upscaling in highly heterogeneous reservoir models is a very challenging procedure, despite much research having been carried out over the past few decades. The fluid flow depends on the well locations, and crossflow may be significant. Traditional upscaling approaches such as the pressure solution method with locally applied boundary conditions, may be highly inaccurate. In two-phase systems, such as waterfloods, accurate reproduction of the flood front is also problematic. Two-phase upscaling is often impractical, but using only traditional single-phase upscaling may lead to large errors. In this paper we demonstrate how conventional upscaling approaches may produce erroneous results and suggest a simple alternative. The new method uses boundary conditions based on the actual well pressures and solves the single-phase pressure equation over the global fine scale geological model. Inter-block transmissibilities and upscaled well connection factors are then computed. By using the appropriate boundary conditions, single-phase flow is accurately reproduced, and therefore the accuracy of two-phase flow at the coarse-scale is greatly increased. We have verified that the new method may be applied to two-phase, highly heterogeneous reservoir models, including models with multiple relative permeability curves and significant gravity effects. We have also applied the method to the benchmark model of the SPE 10th Comparative Solution Project (1.1 million cells, unstable flood). The results show good agreement with the fine grid solution provided by Landmark using a parallel simulator. As models of tens of millions of grid cells are now solvable on a PC in an hour, this method is a feasible approach for achieving highly accurate upscaled models. This method is particularly appropriate for later stages of field development, when models are large and accurate flow simulation is required. Introduction During the last decade, 3D object-based geological modelling has become common practice for modelling reservoirs. Numerous discontinuous "geo-units" (channels, shales, sedimentological or diagenetic bodies etc.) are derived from geophysical and geological data and are usually modelled by placing them within a background facies. (See, for example, references [1] and [2]). The models generated through this approach usually contain a high level of heterogeneity: on one hand, the variations of the properties between the objects are large and, on the other hand, there is variation within the objects themselves. In addition to differences in porosities and permeabilities, often the geological objects possess different relative permeabilities. Since fine-scale geological models usually contain too many grid cells for flow simulation, they need to be upscaled, and it is important that the upscaling process preserves the salient flow features of the fine-scale model. Many upscaling approaches have been developed in the past few decades. These are described in several reviews of upscaling[3][4], so a complete review of upscaling methods will not be presented here. However, we outline one of the conventional methods: the pressure solution method for upscaling single-phase flow. In this method, a single-phase pressure solve is carried out in each coarse cell in turn, and Darcy's law is used to calculate the effective permeability tensor[5]. In order to solve the pressure equation, boundary conditions must be applied to each cell. (This is referred to as a local upscaling method.) The most common of these is the no-flow, or constant pressure boundary condition, where the pressure is fixed at either end of the model, and no flow is allowed through the sides. Other boundary conditions include linear pressure[3] and periodic boundary conditions[6]. Such boundary conditions, however, may differ significantly from the actual boundary conditions within the fine-scale model.