Evaluation of Pseudo Functions

Abstract To determine the range of validity of pseudo functions for upscaling of multiphase flow with gravity and capillary pressure, the performance of different kinds of pseudo functions is evaluated under different gravity numbers, capillary numbers and upscaling levels. The performance of pseudo functions can be measured as the percentage error between the results of fine grid simulation and the results of coarse grid simulation using pseudo functions. Furthermore, the performance can be shown as the bar graphs of percentage error for varying gravity number, capillary number and upscaling levels. A two-dimensional homogeneous water flooding case and a three-dimensional heterogeneous case have been studied using pseudo functions (Jacks et al.2, Kyte and Berry3, Pore Volume Weighted7, Flux Weighted Potential10, Modified Stone*4, Streamline5), and pseudo function performance has been evaluated under different conditions. Some guidelines for the use of pseudo functions are provided. The results show that (1) all of the pseudo functions have similar performance for the homogeneous case considered; (2) only the Jacks et al. pseudo function can be used in all cases; (3) using pseudo functions (except Jacks et al.) is unreliable, especially for the highly heterogeneous cases.