A model for the flow of gas mixtures in adsorption dominated dual porosity reservoirs incorporating multi-component matrix diffusion: Part I. Theoretical development

A matrix-fracture transfer function for multi-species gas flow with adsorption behavior is presented. This transfer function is developed from the extended Fick's law and therefore the coupling effect of mutual-diffusivity is included in the representation. The transfer function is formulated based on an exact formal solution of a set of linear partial differential equations for matrix blocks with regular geometry, and is expressed in the form of a series expansion with history-dependent integrals. This series, at first order, reduces to a simple algebraic expression that is of an equivalent computational efficiency in comparison with the extended Warren–Root model in which the mutual-diffusion effect is not present.The presented transfer function is compared with the Warren–Root relationship and it is shown that the Warren–Root model is a limiting case of the new model. It is also shown how the new model can be applied to reservoirs where gas is stored within the porosity rather than as an adsorbed phase.