Hydraulic fracture conductivity (wfkf) is a critical parameter in completion design of horizontal shale wells. Field evidence and laboratory investigations suggest that these fractures could have finite conductivity values that are influenced by the fracture closure stresses developing during production. Consequently, the fracture conductivity decreases as a function of production time. Currently no field test exists that can capture the dynamic behavior of the conductivity. Bilinear flow analysis (¼-slope flow regime) is a common rate-transient-analysis (RTA) technique that uses the first few days of production data to obtain a conductivity value averaged over time for all the fractures of the well. But it does not consider the stress-sensitivity of the production. In this paper, using forward simulation of flow and production from a hydraulically fractured shale gas well with a stress-sensitive (dynamic) permeability field, we show that the error associated with the averaging of the dynamic behavior of the fracture conductivity could be large. We re-visit bilinear flow theory and modify the RTA method for the presence of stress-sensitive hydraulic fracture conductivity. Now the ¼-slope analysis gives an average of the dynamic fracture conductivity, which could be lower than the initial conductivity. The work shows the need to extend the analysis to formation linear-flow and boundary dominated flow regimes.
Bilinear flow occurs in shale gas wells, as a manifestation of linear flow in both matrix and fracture simultaneously. The duration of this flow regime spans the first few days of production, typically after the fracture linear flow regime, when flowback of the injected fracturing fluid occurs, preceding the widely-observed half-slope formation linear flow regime. Its signature on a log-log diagnostic plot is ¼ slope on pressure and radial derivative plots and zero-slope on the linear derivative plot (Clarkson and Beierle 2010) The interpretation of fracture linear and bilinear flows can aid us in obtaining a fracture conductivity averaged for all the fractures of the well.
