  Imbibition is a commonly encountered multiphase problem in various fields,
and exact prediction of imbibition processes is a key issue for better
understanding capillary flow in heterogeneous porous media. In this work, a
numerical framework for describing imbibition processes in porous media with
material heterogeneity is proposed to track the moving wetting front with the
help of a partially saturated region at the front vicinity. A new interface
treatment, named the interface integral method, is developed here, combined
with which the proposed numerical model provides a complete framework for
imbibition problems. After validation of the current model with existing
experimental results of one-dimensional imbibition, simulations on a series of
two-dimensional cases are analysed with the presences of multiple porous
phases. The simulations presented here not only demonstrate the suitability of
the numerical framework on complex domains but also present its feasibility and
potential for further engineering applications involving imbibition in
heterogeneous media.
