Improved Darcy and non-Darcy flow formulations around hydraulically fractured wells

Fracturing is one of the most common well stimulation techniques especially for tight gas reservoirs. Hence, considerable amount of efforts have been devoted to study the performance of hydraulically fractured wells (HFWs). However, there are uncertainties regarding the impact of some of the pertinent parameters, especially the non-Darcy effect.In this work, a number of simulators have been developed to study and compare the productivity of a HFW at both steady and pseudo steady states conditions.Description of HFWs in gas reservoirs using such numerical simulators requires the use of very fine grids to capture the significant changes of flow properties occurring in and around the fracture. This task is very cumbersome, time consuming and impractical. Therefore, the results of the in-house simulators have been used to develop more generalized formulae for calculation of Darcy flow fracture skin and effective wellbore radius. These formulae can be used in an equivalent open-hole system that replicates flow around HFW with no need for the fine grid exercise.Considering that inertial effect can significantly reduce the effective fracture conductivity, we have extended the application of these developed formulae to non-Darcy flow systems by replacing absolute fracture conductivity with the effective fracture conductivity. Here we have also addressed the conflicting reports on the extent of negative impact of inertia on the flow performance of HFWs and have identified the most reliable formula.

► A new formula was developed for estimation of effective wellbore radius of an hydraulic fracture well.
► The formula is applicable to steady-state and pseudo steady-state conditions and Darcy and non-Dracy flow systems.
► The most reliable formulation expressing the extent of negative impact of inertia on the flow performance of a hydraulic fracture well was identified.
► It was shown that if the equation developed for pseudo steady-state is used for steady-state conditions or vice-versa, highly erroneous results were obtained.