Upscaling Capillary Pressure–Saturation Functions Using Different Reference Pressure Elevations

Choice of reference pressure elevation (RPE) on average effective saturation- capillary pressure functions, <(S) over bar (e)> (psi), was investigated for monotonic drainage of homogeneous porous media. Nine columns of Flint sand with heights ranging from 4.3 to 55.0 cm were prepared. Measured <(S) over bar (e)> (psi) functions were determined gravimetrically using the hanging water column method. Predicted <(S) over bar (e)> (psi) functions were obtained by upscaling point function parameters determined by neutron radiographic imaging of a single drainage experiment. Bottom and midpoint RPEs resulted in the inaccurate parameterization of <(S) over bar (e)> (psi) functions for tall columns. A top RPE produced accurate upscaled functions for all column heights. To evaluate the overall performance of this RPE, observed effective saturations for the nine columns were linearly regressed against predicted values. The resulting best-fit model (slope = 0.98; intercept = 0.03; R-2 = 0.98) corresponded closely to a 1:1 line. The van Genuchten (vG) alpha and n parameters for the observed and predicted <(S) over bar (e)> (psi) functions decreased with increasing column height. A power model explained >95% of the variance in the predicted vG parameters and between 69 and 78% of the variance in the observed vG parameters. The lower R-2 values for the observed parameter models were attributed to experimental variation among the nine columns, whereas the predicted parameter models were upscaled from a single column. Despite these differences, the magnitudes and height dependencies of the observed and predicted average vG parameters were similar. For tall columns, the RPE should be established at the top for drainage experiments and at the bottom for wetting experiments.