Several techniques were developed to analyze the after-closure fracture data of a DFIT/MiniFrac test. The majority of these techniques assume the reservoir is homogeneous. However, this assumption is not always satisfied: a formation may be heterogeneous and naturally fractured, making the published techniques not applicable in this case.

A most recent technique developed by Soliman et al. (2010) presented an analytical solution for an injection-falloff test for a naturally fractured formation. The solution was found to be effective, especially in the analysis of MiniFrac tests. However, the solution was applicable only in the absence of residual fracture conductivity.

A solution for an injection-falloff test for a naturally fractured and hydraulically fractured formation has been developed. The solution was established by inference using numerical simulation. MiniFrac tests are simulated and analyzed for naturally and hydraulically fractured formations. The study includes infinitely conductive fractures, finite conductivity fractures and radial flow regime.

Furthermore, the developed solution was employed successfully to analyze field data of a shale formation that is known to be naturally fractured. A naturally fractured formation that was hydraulically fractured is examined and presented.

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