Abstract

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 behaviour. A new non-Darcy flow number is first defined to account for effect of characteristic length in a hydraulic fracture. A semi-analytical 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. The pressure response together with its corresponding derivative type curves has been reproduced to examine non-Darcy flow behaviour under different fracture conductivities. Both relative minimum permeability and characteristic length are found to impose a negative impact on fracture conductivity. Compared to relative minimum permeability, characteristic length is a strong function dominating the non-Darcy flow behaviour in the fractures. It is obvious that the fracture conductivity can be accurately determined when non-Darcy flow behaviour in the fracture network is taken into account.

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