An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids

Abstract

Abstract Streamline-based methods can be used as effective post-processing tools for assessing flow patterns and well allocation factors in reservoir simulation. This type of diagnostic information can be useful for a number of applications including visualization, model ranking, upscaling validation and optimization of well placement or injection allocation. In this paper, we investigate finite volume methods as an alternative to streamlines for obtaining flow diagnostic information. Given a computed flux field, we solve the stationary transport equations for tracer and time of flight using either single-point upstream weighting or a truly multi-dimensional upstream weighting scheme. We use tracer solutions to partition the reservoir into volumes associated with injector-producer pairs and to calculate fluxes (well allocation factors) associated with each volume. The heterogeneity of the reservoir is assessed by using time of flight to construct flow capacity-storage capacity (F-Φ) diagrams which can be used to estimate sweep efficiency. We compare the results of our approach with streamline-based calculations for several numerical examples and we demonstrate that finite volume methods are a viable alternative. The primary advantages of finite volume methods are applicability to unstructured grids and ease of implementation for general purpose simulation formulations. The main disadvantage is numerical diffusion, but we show that a multidimensional upstream weighting scheme is able to reduce these errors.