Modeling of Spontaneous–Imbibition Experiments With Porous Disk—On the Validity of Exponential Prediction

Abstract

Summary Imbibition experiments with porous disk can be used to derive accurate capillary pressure curves for porous media. An experimental setup is considered in which brine spontaneously imbibes cocurrently through a water-wet porous disk and into a mixed-wet core. Oil is produced from the core's top surface, which is exposed to oil. The capillary pressure is reduced in steps to determine points on the capillary pressure curve. A mathematical model is presented to interpret and design such experiments. The model was used to history match experimental data from Ahsan et al. (2012). An analytical model was then derived from a simplification of the general model, and validated by comparing the two by use of parameters from history matching. The main assumption of the analytical model is that the imbibition rate is sufficiently low, allowing fluids to redistribute inside the core, leading to a negligible capillary pressure gradient. This results in an exponential imbibition time profile with a time scale τ. Exponential matching has been applied earlier in the literature, but, for the first time, we derive this expression theoretically and provide an explicit formulation for the time scale. The numerical simulations show that, at low saturations, there can be a significant flow resistance in the core. A capillary-pressure gradient then forms, and the analytical solution overestimates the rate of recovery. At higher saturations, the fluids are more mobile, and imbibition rate is restricted by the disk. Under such conditions, the exponential solution is a good approximation. The demonstrated ability to predict the time scale in the late stage of the experiment is of significant benefit, because this part of the test is also the most time-consuming and most important to estimate. A method is presented to derive capillary pressure data point by point from measured imbibition data. It provides reliable data between the equilibrium points, and demonstrates consistent variations in flow resistance during the imbibition tests. Gravity had minor influence on the considered experimental data, but generally implies that equilibrium points have higher capillary pressure than the phase pressure difference defined by the boundary conditions.