A Thermodynamic Analysis of the Impact of Temperature on the Capillary Pressure in Porous Media

Abstract

AbstractA thermodynamic analysis of the capillary drainage, imbibition and hysteresis pressure in two‐phase porous media systems at different temperatures has been performed. Expressions for the work required or gained when the fluid saturations change, proportional to the capillary pressures, are presented. The expressions are determined using the criterion that changes in Helmholtz free energy equals zero at equilibrium. From these expressions, the variation of capillary drainage, imbibition and hysteresis pressures for increasing temperature are determined without calculating the actual capillary pressure values. The temperature dependency results show that the capillary drainage pressure declines with a fractional rate for increasing temperature with contribution from two terms, the air‐water interfacial tension and the entropy term, which give a total fractional reduction of −0.0082 K−1, close to the value −0.0084 K−1 found experimentally. The capillary imbibition pressure increases with a total fractional rate versus temperature equal +0.004 K−1 in line with the observation that water tables in soils are lifted upon day‐time heating. The total fractional temperature variation of the hysteresis capillary pressure term declines with a rate of −0.0143 K−1 for increasing temperature in qualitative agreement with experimental data. The results support the hypothesis that the thermodynamic approach applied under given assumptions can account for the major effects determining the temperature dependency of two‐phase capillary pressure in porous media. Furthermore, the entropy term adds an additional hysteresis term to the conventional term, even under isothermal conditions. The capillary pressure hysteresis phenomenon is therefore caused by two effects: Differences in interfacial areas including contact angle hysteresis plus the entropic contribution.