Analytical solution for clay plug swelling experiments

Clay swelling experiments frequently involve monitoring the one-dimensional displacement with time of an initially dry clay plug as it imbibes water from a supply at its base. This article presents a new analytical solution for interpreting such experiments based on Richards' equation for flow in a partially saturated porous medium combined with a linear empirical function relating moisture ratio with void ratio. The analytical solution is described by just two parameter groups. The first parameter group describes the swelling potential of the clay. The second parameter group describes the rate at which the swelling plug reaches equilibrium, which is controlled by permeability and capillary pressure. Application of the analytical solution is demonstrated by calibration to one-dimensional displacement data from clay swelling experiments for an illite and bentonite clay.