Extension of a temperature effects model for capillary pressure saturation relations

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Abstract

[1] A series expression describing the effect of temperature on capillary pressure saturation relations was derived from the chemical thermodynamics of interfaces. Most systems studied could be described well by truncations of the series expression that retained one or two parameters. The one-parameter expression was appropriate for describing capillary pressures of soils experiencing modest changes in temperature. Thevan Genuchten [1980] equation modified with the one-parameter expression could be fitted precisely to 36 of 41 water-air capillary pressure saturation relations determined at more than one temperature. The residuals of the fitted equation were unaffected by degree of saturation. The one-parameter expression could describe equally well the effect of temperature on capillary pressures of homogeneous synthetic and natural heterogeneous porous media, for which a theoretical explanation was proposed. Asymptotic standard errors of the estimates for nonlinear regression analysis for the one-parameter expression fitted to water-oil and water-NAPL systems were of the order of the parameters themselves. This lack of fit may be more due to the wide temperature ranges studied for many of the water-oil and water-NAPL systems than the nature of the nonwetting phase. The two-parameter expression was appropriate for systems, such as petroleum reservoirs, subjected to pronounced changes in temperature. When compared to nonlinear regression fits to the one-parameter model, fits of van Genuchten's equation modified with the two-parameter expression generally reduced the errors of the parameter estimates but yielded only slight improvement in the mean square errors of the predicted values. A theoretical derivation indicates that the one-parameter expression should be appropriate also to describe the effect of temperature on the capillary pressures in very dry soils.

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