The effect of heterogeneity on the drainage capillary pressure‐saturation relation

Proper mathematical description of multiphase fluid displacement in porous media requires specification of appropriate constitutive relations, including the relationship between capillary pressure and saturation. This pressure‐saturation relationship may be measured at the laboratory core scale, but extension to larger scales is difficult in heterogeneous materials. To date, stochastic and volume averaging methods have been used to estimate the “effective” pressure‐saturation relation in heterogeneous media. A third method, based on network percolation models, may be developed and used to define effective relationships. This last method is appealing in that pore scale physics are directly incorporated into the model, assumptions are clear, and numerical tests are most similar to those performed in the laboratory. Numerical results based on network models indicate that heterogeneities have a significant impact on the effective relationship. In addition, these results indicate that application of any sort of linear averaging of the individual small‐scale relationships to define an effective relationship may provide incorrect results.