Correspondence of the Gardner and van Genuchten/Mualem relative permeability function
The Gardner and van Genuchten models of relative permeability are widely used in analytical and numerical solutions to flow problems. However, the applicab ility of the Gardner model to real problems is usually limited, because empirical relative permeability data to calibrate the model are not routinely available. In contrast, van Genuchten parameters can be estimated using more routinely available matric potential and saturation data. However, the van Genuchten model is not amenable to analytical solutions. In this paper, we introduce generalized conversion formulae that reconcile these two models. In general, we find that the Gardner parameter alpha G is related to the van Genuchten parameters alpha vG and n by alpha G=alpha vG ~; 1:3 n. This conversion rule will allow direct recasting of Gardner-based analytical solutions in the van Genuchten parameter space. The validity of the proposed formulae was tested by comparing the predicted relative permeability of various porous media with measured values.