Evaluation of Dynamic Pseudofunctions for Reservoir Simulation

Abstract

Summary We present a detailed investigation on the reliability of some of the dynamic pseudofunctions used to upscale flow properties in reservoir simulation. A one-dimensional example (1D) and a real field application are used to evaluate methods developed by Kyte and Berry and Stone, and a new flux weighted potential (FWP) method. A derivation of Stone's method (based on the description given by Stone above) is presented, which is found to give an inconsistent set of equations. Stone's analytical example was used to illustrate how pseudorelative permeabilities that exhibit non-physical behavior may still give acceptable results, but this success can disappear with changes in boundary conditions. The pseudofunctions from a field application were not able to match the 2D simulations from which they were calculated, even when a different pseudofunction was used for each coarse grid block. Improvements were obtained when directional pseudofunctions were used, but still the results were not satisfactory. Similar results were found when comparing fine and coarse grid 3D simulations for a quarter of a five-spot pattern in this field. The results presented in this article suggest that dynamic pseudofunctions, as applied here and as commonly used in industry, may not be an adequate approach to up-scaling. The possibility of large errors and the difficulty in predicting when they may occur make the use of pseudofunctions examined in this paper unreliable.