Summary

In this paper, a mathematical model has been developed and successfully applied to accurately determine the fracture conductivity in tight formations with non-Darcy flow behavior. A new non-Darcy flow number is first defined to account for the effect of characteristic length in a hydraulic fracture. A semianalytical method is then applied to solve the newly formulated mathematical model by discretizing the fracture into small segments, assuming that there exists unsteady flow between the adjacent segments. The newly developed model has been validated by simplifying it to the traditional Forchheimer (i.e., non-Darcy) model and by performing numerical simulation with a reservoir simulator as well. The pressure response and its corresponding derivative type curves have been reproduced to examine non-Darcy flow behavior under different fracture conductivities. Both relative minimum permeability and characteristic length are found to impose a negative effect on the fracture conductivity. Compared with relative minimum permeability, characteristic length is a strong function dominating the non-Darcy flow behavior in the fractures. It is obvious that the fracture conductivity can be accurately determined when non-Darcy flow behavior in the fracture network is taken into account.

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