Published techniques for after-closure analysis of fracturing data usually assume the presence of a vertical fracture intersecting a vertical well. In addition, these published techniques usually assume that the formation is homogeneous. When the formation is naturally fractured or the well is horizontally intersecting a transverse vertical fracture, those assumptions are obviously violated and the published analysis techniques might not be applicable. Through the use of analytical and numerical solutions and application to actual field data, this paper investigates the analysis of after-closure data for heterogeneous formations, a naturally fractured formation, a CBM, and a fractured horizontal well.

This paper briefly reviews the various available techniques for after-closure analysis, pointing out the strengths and weaknesses of each. An analytical solution for an injection-falloff test for a naturally fractured formation has been developed and is presented. This solution might be used to analyze data for a minifrac test in a naturally fractured formation where the fracture has healed. Numerical simulation validated the developed solution for a fracture that has healed. The same numerical simulator was used to expand the solution to a situation where the fracture maintains residual conductivity.

The solution for a minifrac test in the case of a transverse fracture is also presented and discussed. Using a numerical simulator, minifrac tests are simulated and analyzed for both heterogeneous formations and fractured horizontal wells. Guidelines for the analysis of such data have been developed and presented.

Field data are also presented. One case presents a minifrac test for a heterogeneous formation. A case for a transverse fracture intersecting a horizontal well is also presented and analyzed. A third case for CBM is discussed.

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