ESTIMATING WATER RELATIVE PERMEABILITY FROM CAPILLARY PRESSURE CURVE AND ELECTRICAL RESISTIVITY

Water relative permeability, k_rw, is a key component for transport modeling in aquifers and production estimation in reservoirs. In the literature, various models were developed to estimate k_rw from other porous media characteristics, such as capillary pressure curve. Based on similarities between hydraulic and electrical flow in porous media, models were proposed to link water relative permeability to capillary pressure curve and electrical resistivity (see e.g., Wyllie and Spangler, 1952; Li, 2011). However, most of such models are either quasi-empirical or based upon a “bundle of capillary tubes” concept, that ignores interconnectivity among pores. In this study, we proposed a model using concepts from percolation theory and critical path analysis (Hunt et al., 2014). We theoretically related water relative permeability to pore-throat size distribution and electrical resistivity. Invoking a power-law probability density function for pore throats, we showed that our theoretical k_rw model reduces to the Burdine-Brooks-Corey (BBC) equation. We found that the empirical tortuosity-connectivity exponent in the BBC model is related to the critical scaling exponent of percolation that characterizes the power-law behavior of the saturation dependence of electrical resistivity. To evaluate the proposed theoretical approach, we compared our model estimations with experimentally measured k_rw values in four different porous media representing increasing pore structure complexity: (1) glass bead pack, (2) dune sand, (3) Bentheimer sandstone, and (4) Berea sandstone. Comparison with experiments indicated that our model estimated k_rw well over the entire range of water saturation and more accurately than the BBC model.

References

Hunt, A., Ewing, R., and Ghanbarian, B. (2014). Percolation theory for flow in porous media, Lecture Notes in Physics (Vol. 880, 3rd ed.). Berlin, Germany, Springer.

Li, K. (2011). Interrelationship between resistivity index, capillary pressure and relative permeability. Transport in Porous Media, 88(3), 385-398.

Wyllie, M. R. J., and Spangler, M. B. (1952). Application of electrical resistivity measurements to problem of fluid flow in porous media. AAPG Bulletin, 36(2), 359-403.