An evaluation of Stones method to determine pseudo-relative permeability

Abstract

Determination of pseudo-relative permeability and capillary pressure functions or simply pseudofunctions is an important problem in reservoir simulation studies. Modeling the reservoir as simply as possible is quite often desirable to reduce computing costs and complexities. Such modeling, however, often requires special saturation-dependent functions since use of rock functions will, in most cases, produce incorrect results. These so-called pseudofunctions must be defined so that they will produce the same initial fluid distribution, fluid movement, and pressure, distribution as the model with fine grids if they are applied to a coarsely-gridded model. Numerous methods for generating the pseudofunctions by averaging flow properties and fluid saturations in the vertical direction have been published. However, at present, the most common method is either the method proposed by Jacks et al. or Kyte and BeiTy. Both methods use fine-grid reservoir simulation results. Stone developed a new method based on fractional flow principles rather than on Darcy's Law. Stone's method also uses fine-grid reservoir simulation results. The method has been reported to be applicable for cases for which the previous methods lead to poor results. However, no verification of this claim has been presented in the literature. This study evaluates and validates the use of Stone's method based on both numerical simulation and mathematical analyses. Stone's pseudos are applied to a I-D linear model to duplicate the performance of the 2-D cross-sectional model from which the pseudos are generated. The simulated results are then discussed to determine the validity and applicability of Stone's pseudofunctions and the advantages of these pseudofunctions over those published previously. An analysis on the development of the equations used by the method is also performed. In addition, a comparison to Jacks et al. method is studied numerically and analytically. The results of this study will be valuable since their, is almost no other technique for reducing the number of grid blocks better than using pseudofunctions. In addition, the results of this study can lead to a modification of the method or even a development of a better method. More specifically, evaluation of Stone's method may provide an answer to the problems resulting from the use of previous methods.