Constant-pressure well test analysis of finite-conductivity hydraulically fractured gas wells influenced by non-Darcy flow effects

Non-Darcy flow effects have long been recognized to have serious adverse impact on the performance of high flow rate gas wells. These effects may mask the presence of fractures around the wellbores of naturally fractured reservoirs and may render the effective fracture conductivity and fracture half-length of hydraulically fractured wells much less than the designed parameters.Even though the effects of non-Darcy flow have been identified in the field and properly acknowledged in the well testing literature, little has been done to improve the well test analysis results. This paper presents a new technique that accurately determines the fracture conductivity of hydraulically fractured gas wells producing at constant-bottomhole pressure and provides direct means to calculate the magnitude of turbulence in the fracture around the wellbore from a single well test.A semi-analytical equation that incorporates the effects of non-Darcy flow in the fracture is presented for the first time. A detailed investigation of the various parameters that influence the flow behavior of real gas in the fracture nearby the wellbore is also illustrated. Furthermore, a systematic method for calculating the fracture conductivity and non-Darcy flow coefficient from a single well test is outlined. The final working equations are presented in such a way that permits a straightforward, simple, yet accurate analysis of the variable flow rate with time. No type-curve matching, multirate tests or correlations are required. The methodology of the proposed technique is illustrated using several synthetic examples.