Computational Method for Relative Permeability Curves based on the Bernoulli Generalized Porous Media Equations

Obtaining the relperm curves as a result of multiphase flow calculation immediately in the porous media can be of current interest. Some researches have been carried out to date where relperms are derived by solving the Navier–Stokes equations for communicating pore channels. Those approaches have two significant drawbacks: (1) need to reconstruct the pore space based on the core CT scanning, and (2) intensive work for solving the Navier–Stokes equation system which requires supercomputers. The results of our work help to compute relperm curves using normal computers. We were able to do this due to several factors: (1) simplified pore space reconstruction based on capillary curve data, (2) using the flow-cluster notion as an element that averagely describe the pore space geometry, and (3) using the Bernoulli generalized two-phase flow equation. This approach helped to compute the relperm curves within plausible timing and compare them with actual test curves. We demonstrate that a material factor to affect the relperm curve shape is the pressure loss due to interfacial forces. We propose the empirical functions and parameters to simulate those effects. The computed relperm curves show a pretty good match with the actual test results.