A novel semi-analytical model for horizontal fractures with non-Darcy flow

Based on Darcy law in matrix and non-Darcy law in horizontal fractures, a novel semi-analytical model is presented to investigate effects of non-Darcy on flow behavior. The proposed semi-analytical model convergences rapidly and it is convenient to add wellbore storage and skin effect in this model. The effects of the parameters on dimensionless pressure curves and their derivative curves are discussed in detail, including Forchheimer number, dimensionless formation thickness, fracture conductivity, and fracture diffusivity factor. Calculative results show that a big Forchheimer number, a big dimensionless formation thickness and a low conductivity will lead to big pressure depletion at early time. However, flow characteristics in entire flow regime cannot be determined by diffusivity factor. Then effects of the Forchheimer on the flow rate profiles are also discussed, indicating that as the time increases the effect of non-Darcy on flow behavior becomes weak. The proposed model could be well applied to make well test data analysis for a finite conductivity horizontal fracture with non-Darcy flow.