Integrated approach for non-Darcy flow in hydraulic fractures considering different fracture geometries and reservoir characteristics

The motivation is eliminating the uncertainties in predicting reservoir performance, and reducing the errors in the reservoir characterization resulted by neglecting the impact of non-Darcy flow. In this study, an analytical multi-linear flow regimes model has been developed for pressure distribution in hydraulically fractured reservoirs and modified for the existence of non-Darcy flow by introducing the rate-dependent skin factor to the flow equations. This model is solved for different impacts of non-Darcy flow by assuming a constant flow rate and different non-Darcy flow coefficients. The effects of different cross-section areas of flow inside hydraulic fractures on the non-Darcy flow coefficient are considered in this study as well as different fracture conductivities. Reservoir configurations and petrophysical properties are also considered in calculating pressure distributions. Analytical models for hydraulic fracture linear flow regime, bi-linear flow regime, and boundary-dominated flow regime are developed based on pressure responses for different non-Darcy flow impact. Analytical models for transient and pseudo-steady state productivity indices are presented in this paper to demonstrate the impact of non-Darcy flow on these indices. The results of this study showed there are considerable effects of non-Darcy flow on reservoir performance and developed analytical mathematical models for recognized flow regimes which observed during reservoir production period. Additionally, results illustrated the reservoir configurations and petrophysical properties may not have significant contribution in developing non-Darcy flow. Finally, the productivity index has been sharply declined for later production time. Meanwhile, it is constant for high rate-dependent skin factors at the early time of production.