It has been found experimentally that the relationship between the imbibition rate and the reciprocal of recovery by spontaneous water imbibition has two linear parts in rocks with fractures but has only one linear part in rocks without fractures. One of the two linear parts may represent the fracture property and the other may represent the matrix or the set of smaller fractures. A method to infer the effective fracture aperture (or permeability) and the matrix permeability simultaneously has been developed using the experimental data of spontaneous water imbibition in gas-saturated (dried) rocks. The mathematical model has been derived theoretically based on the fundamental laws of fluid flow in porous media. These include Darcy's law, material balance, and continuum equation. The theoretical model characterizes the relationship between imbibition rate and the reciprocal of recovery in both fractures and matrix. Several spontaneous water imbibition experiments have been conducted in rocks with different permeability, with and without fractures. Experiments have also been conducted in coal samples with fractures because of the importance in the production of coal bed methane. The values of the effective fracture aperture and matrix permeability of the core samples were inferred using the mathematical model derived in this study.

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