Parameter estimation of two-fluid capillary pressure-saturation and permeability functions

Accurate characterization and modeling of subsurface how in multi-fluid soil systems require development of a rapid, reproducible experimental method that yields the information necessary to determine the parameters of the capillary pressure-saturation and permeability functions. Previous work has demonstrated that parameter optimization using inverse modeling is a powerful approach to indirectly determine these constitutive relationships for air-water systems. We consider extension of the inverse parameter estimation method to the modified multi-step outflow method for two-fluid (air-water, air-oil and oil-water) flow systems. The wellposedness of the proposed parameter estimation problem is evaluated by its accuracy, uniqueness and parameter uncertainty. Seven different parametric models for the capillary pressure-saturation and permeability functions were tested in their ability to fit the multi-step outflow experimental data; these included the van Genuchten-Mualem (VGM) model, van Genuchten-Burdine (VGB), Brooks-Corey-Mualem (BCM), Brooks-Corey-Burdine (BCB), Brutsaert-Burdine (BRB), Gardner-Mualem (GDM) and Lognormal Distribution-Mualem (LNM) models. The VGB, BCM and BCB models fitted the multi-step outflow data poorly, and resulted in relatively large values for the root-mean-squared residuals. It was concluded that the remaining VGM, LNM, BRB and GDM models successfully characterized the multi-step experimental data for two-fluid flow systems. Although having one parameter less than the other models, the GDM model's performance was excellent. Finally, we conclude that optimized capillary pressure-saturation functions for the oil-water and air-oil could be predicted from the respective air-water function using interfacial tension ratios. (C) 1999 Elsevier Science Ltd. All rights reserved.