## 1. Introduction

[2] Capillary pressure of a wetting fluid in a porous medium at a constant degree of saturation is a linearly decreasing function of temperature. The phenomenon appears to be universal, having been observed in porous-media samples fashioned from soils, rocks, monosized glass beads, quartz sand, and even granular glass. At 298 K, the relative decrease in capillary pressure is typically around −1% K^{−1}. The interfacial tension of water is also a decreasing linear function of temperature, but its relative decrease is much smaller, roughly −0.2% K^{−1}. The differences between the relative changes between capillary pressure and water's surface tension are too large to ignore, but formulating a quantative explanation has proven to be elusive. The problem has initially entranced, eventually preoccupied, and ultimately frustrated a long line of geophysicists.

[3] Here it is reported that a one-parameter model presented earlier by *Grant and Salehzadeh* [1996] can be fitted to most of the available water-air capillary pressure saturation relation (CPSR) data collected at more than one temperature. Also reported here is a two-parameter model, also based on the chemical thermodynamics of interfaces, which describes the effect of temperature on CPSRs for water-oil systems over wide ranges of temperature. Both the one- and two-parameter models are shown to be members of a class of possible linear models of interfacial tensions. These underlying linear models would be expected to sum regularly in heterogeneous porous media (Defined here as porous media in which the solid matrices are composed of mixtures of mineral and organic solids having different surface chemical properties.) and may explain the apparent universality of the one- and two-parameter models and their applicability to both homogeneous and heterogeneous porous media.

[4] Although predictive, neither the one-parameter model nor the two-parameter model can be reconciled with well-documented independently measured changes with temperature of surface tension and contact angles. The goals of this paper are to reexamine the limits of applicability of the Young-Laplace equation and the nature of interfacial tensions in porous media, and to determine the effects of temperature on CPSRs for wider temperature ranges, heterogeneous porous media, nonwetting phases other than air, and lower degrees of saturation.

[5] This paper begins with a discussion of the Young-Laplace equation and how the individual interfacial tensions should be modeled to describe the influence of temperature. Two candidate models are derived and tested by nonlinear regression analysis. The applicability of the models is then evaluated for heterogeneous porous media and porous media in which the nonwetting phase is a fluid other than air. The article concludes with a discussion of the effect of temperature on the capillary pressures in very dry soils.