Imbibition experiments with porous plate can be used to derive accurate capillary pressure curves for porous media flow. A setup is considered where a brine spontaneously imbibes cocurrently through a water-wet porous disc and into a mixed-wet core. The capillary pressure is reduced in steps to allow for imbibition of more brine and determine distinct points on the capillary pressure curve. The aim of this work is to present a mathematical model which can be used for the interpretation or design of such experiments. A numerical discretization of the proposed model approach is used to historymatch experimental data (Ahsan et al, 2012) and evaluate the role of mechanisms controlling the process. An analytical solution of the model is then derived. It is validated against the full numerical solution. The simplest analytical solution for the imbibition time profile is of an exponential form with a time scale $tau$. Such a model has been applied earlier in the literature, however we show that it is an appropriate formulation and provide an explicit expression for the time scale.


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