End of linear flow time picking in long transient hydraulically fractured wells to correctly estimate the permeability, fracture half-length and original gas in place in liquid rich shales

Formation permeability (k) and fracture half-length (Xf) determination provides the ability to economically optimize well and fracture spacing. For wellbores completed in the gas-condensate and oil window (producing below saturation pressure) two-phase flow occurs from the fracture face increasing in distance until it reaches the no flow boundary from the adjacent fracture face along a horizontal wellbore. Thereafter the flow becomes boundary dominated. It becomes challenging to precisely pick the end of linear flow time and the start of boundary dominated flow regime due to long transient region in shales (low permeability nature). End of linear flow time is used to calculate both the permeability and original gas in place (OGIP) using production data. Existing practices in the literature suggest to pick the end of linear flow time implicitly from the plot of reciprocal rate vs cumulative production. The deviation on the line is termed as typically the time at which linear flow has ended. However, considering the lengthy transition regions in shales, this involves a great deal of error as the end of linear flow time is not calculated mathematically but picked on the analyst's eyeballing practices. Thus, a small mispick of end of linear flow time could result in substantially misleading permeability and OGIP. The primary work presented in this paper resolves the selection of end of linear flow time by proposing a technique which involves production data analysis equations and statistical methods along with graphical techniques to calculate and rightly pick the end of linear flow time. Since gas condensate ratio (GCR) remains constant during the linear flow regime, our methodology also involves reverification of the end of linear flow time. This is done by picking the increase in GCR which happens at the end of linear flow on the plot of cumulative production versus the GCR. While the procedure involved laboratory fluids, special core analysis, and numerical simulation, the methodology lends to a wide range of liquid-rich reservoirs where linear flow analysis is appropriate.