Imbibition into Capillaries with Irregular Cross Sections: A Modified Imbibition Equation for Both Liquid-Gas and Liquid-Liquid Systems

Due to discrepancies observed between many experimental results and predictions from the Bell-Cameron-Lucas-Washburn (BCLW) imbibition equation, the BCLW equation was often modified by considering the effects of pore/throat characteristics. As previous works mainly focused on liquid-gas systems, the effects of the viscosity ratios are neglected. In this study, the nonwetting-/wetting-phase-viscosity ratio (psi) is varied by four orders of magnitude (0.018 to 8), which covers the common fluid viscosity in waterflooded tight reservoirs. Capillaries with irregular cross sections (namely, complex capillaries), which are recognized to more representative for porous media, are used to theoretically study imbibition kinetics in both the liquid-gas and liquid-liquid system. To considering the effects of viscosity ratio, we propose a modified imbibition equation based on the Poiseuille law and a piecewise method to calculate the equivalent radius for complex capillaries. The predictivity of the new imbibition equation is mathematically validated in varying viscosity ratios and geometries characteristics (such as the radius levels and the numbers/length ratios of radius levels). The study proves that an equivalent straight capillary can globally predict imbibition behaviors in complex capillaries. Except for a few scenarios, the equivalent radius of the straight capillary is affected by capillary geometries and viscosity ratios. Only in the early stage of imbibition (l(x)/l <= 0.12 psi/(psi- 1)), the modified imbibition equation can be expressed as a power-law relation (i.e., l(x)/l proportional to 1/psi t(alpha)) as psi is higher than 1. In general, it is more suitable to express the imbibition equations in a quadratic form, especially for liquid-liquid imbibition systems.