Summary
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 by use of either single-point upstream (SPU) weighting or a truly multidimensional upstream (MDU) 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 with time of flight to construct flow-capacity/storage-capacity (F-vs.-Φ) diagrams that 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 the applicability to unstructured grids and the ease of implementation for general-purpose simulation formulations. The main disadvantage is numerical diffusion, but we show that a MDU weighting scheme is able to reduce these errors.
A unified treatment of boundary conditions in least-square based finite-volume methods
