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Two-dimensional subdiffusion in media separated by a partially communicating interface is considered. Starting with the appropriate Green’s functions, solutions are developed in terms of the Laplace transformation reflecting two circumstances at the interface: situations where there is perfect contact and situations where the interface offers a resistance. Asymptotic solutions are derived; limiting forms of the expressions reduce to known solutions for both classical diffusion and subdiffusion. Specifics are analyzed in depth with reference to flow in porous media with potential applications to the evaluation of the role of subsurface faults and flow in fractured rocks. Characteristics of the derivative responses are documented extensively as they are the linchpin for evaluation of pressure tests. Results given here may be used for evaluation at the Theis (1935;  Eos Trans. AGU   2 , 519–524) scale along with geological and geophysical properties, and production statistics. Yet a subdiffusive model does not imply a single value for properties. The method presented here may be extended to multiple contiguous media and to subdiffusive transport in many contexts (complex wellbores such as inclined, fractured and horizontal wells, situations such as sequestration, production of geothermal systems, etc.).

Subdiffusive flow in a composite medium with a communicating (absorbing) interface