Effective fracture properties that contribute to the flow in the tight formations are very important in stimulation job evaluation, productivity estimation, and production forecast. However, there are no direct measurements on the volume of stimulated region or the effective permeability of fracture because hydraulic fractures not only stimulate local matrix, but also connect natural fractures. Therefore, the effective drainage volume contributing to production can be much bigger than the extension of hydraulic fractures.

After a high initial rate, production data for stimulated tight formation has an extended transient flow period in which the matrix functions as a source and behaves in a transient fashion. This behavior can be captured by a dual-porosity model with transient matrix performance under a constant bottom-hole pressure.

This paper studies the problem from an inverse perspective and couples the production data with an interporosity flow model to estimate the effective drainage volume that a well controls as well as the effective permeability that can be used for production rate forecast. The problem is solved in Laplace domain. The proposed model is validated with the numerical simulation and the field production data from Mississippian Lime. Furthermore, the interporosity model is sufficient to forecast the production trend from the given examples.

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