Estimation of relative permeability and capillary pressure from mass imbibition experiments

We perform spontaneous imbibition experiments on three carbonates - Estaillades, Ketton, and Portland - which are three quarry limestones that have very different pore structures and span wide range of permeability. We measure the mass of water imbibed in air saturated cores as a function of time under strongly water-wet conditions. Specifically, we perform co-current spontaneous experiments using a highly sensitive balance to measure the mass imbibed as a function of time for the three rocks. We use cores measuring 37 mm in diameter and three lengths of approximately 76 mm, 204 mm, and 290 mm. We show that the amount imbibed scales as the square root of time and find the parameter C, where the volume imbibed per unit cross-sectional area at time t is Ct1/2. We find higher C values for higher permeability rocks. Employing semi-analytical solutions for one-dimensional flow and using reasonable estimates of relative permeability and capillary pressure, we can match the experimental data. We finally discuss how, in combination with conventional measurements, we can use theoretical solutions and imbibition measurements to find or constrain relative permeability and capillary pressure.