Hydrocarbon Drainage along Corners of Noncircular Capillaries

An approximate solution for liquid flow along corners of noncircular capillaries is proposed that relates the flow resistance to the geometry of a capillary and to the contact angle of the interfaces. The theory predicts liquid flow rates for both two-phase (hydrocarbon/air) and three-phase (hydrocarbon/air/water) drainage. This solution is found to be superior to other expressions in the literature. Drainage rates of two different hydrocarbons along corners of square capillaries are measured with both air and water as stationary phases. The new solution was used to predict the measured hydrocarbon drainage rates successfully. Comparison of the measured and predicted drainage rates indicates that a free boundary is appropriate for the air/hydrocarbon interface and a no-flow boundary condition is valid for the water/hydrocarbon interface. The effect of spreading coefficient on drainage rates is also demonstrated by the measurements and is compared with the proposed solution. A brief discussion of three-phase relative permeabilities is offered based on the measured drainage rates and proposed solution.