Special relative permeability functions with analytical solutions for transient flow into unsaturated rock matrix

This paper presents a class of analytical solutions for transient flow into unsaturated rock matrix. These analytical solutions are derived using specially correlated, physically meaningful relative permeability and capillary functions. The transient flow processes in unsaturated rock matrix blocks are generally described by the Richardsʹ equation. The analytical solutions describe the full transient behavior of flow into unsaturated matrix blocks and have proven (through various examples) to be useful for verifying numerical model results.