Extension of Kozeny-Carman Model for Estimating Unsaturated Hydraulic Conductivity

We present a predictive model for unsaturated hydraulic conductivity (K) which makes use of the interrelationship among capillary pressure (P-c), wetting phase saturation (S-w), and nonwetting-wetting phase interfacial area. The newly developed model is general so that any closed form P-c-S-w equation can be incorporated. In particular, we formulate Kozeny-Carman-Brooks-Corey (KCBC) and Kozeny-Carman-van Genuchten (KCVG) models by including, respectively, the closed-form Brooks-Corey and van Genuchten P-c-S-w equations in the modified Kozeny-Carman (KC) model. For S-w approximate to S-e, S-e is effective saturation, the interfacial area based KCBC equation is identical to the geometrically (wetting phase hydraulic radius) based Brooks-Corey-Burdine (BCB) semi-empirical model. The capillary pressure thermodynamics are used to describe the KCBC/KCVG relative permeability integrals as well as a variable tortuosity connectivity, defined as the ratio of interfacial area for a soil sample to the interfacial area for the corresponding, idealized capillary bundle. The new model is tested for a database composed of 22 coarse-textured and 24 fine-textured samples. With the decoupling of the relative permeability integrals from the conventional P-c-S-w derived pore-size distribution models, both KCBC and KCVG formulations provide a good agreement between measured and predicted K for the fine- as well as coarse-textured sediments. The use of the conventional BCB and van Genuchten-Mualem (VGM) models results in large deviations between measured and predicted K, and considerable bias. To the contrary, for the entire moisture regime, the use of the KCBC and KCVG models produces very little bias and results in a comparable agreement for KCBC and KCVG model predictions with K(theta) measurements. Overall, the modified KC model, with interfacial areas derived from the thermodynamics of P-c, provide an improved description of K(theta) measurements, compared with standard B CB and VGM models.