Time-normalized conductivity concept for analytical characterization of dynamic-conductivity hydraulic fractures through pressure-transient analysis in tight gas reservoirs

Abstract

Abstract This paper presents a time-normalized conductivity concept to allow an analytical model for characterization of dynamically-closed fractures through pressure-transient analysis in tight gas reservoirs. Specifically, the fracture conductivity in our flow model is considered to be a function of time. With the definition of the time-dependent fracture conductivity in the model, calculation of variable-rate pressure-transient behavior (e.g., pressure buildup tests) can be still based on the solution of linear differential equations governing fluid flow in a gas reservoir. Therefore, the superposition principle can be legitimately utilized in our solution to model pressure buildup tests. We then introduce a modified exponential function to represent the decline behavior of the time-normalized fracture conductivity during the production stage, and the dynamic fracture conductivity is essentially handled in a stair-step manner to calculate bottom-hole pressures. The accuracy of the calculated transient pressures was validated by comparing with a commercial simulator. The pressure drawdowns at early-times, because of dynamically-closed fractures, clearly increase more than in the invariant-fracture-conductivity case. We examine the effects of fracture conductivity behavior and production history on the pressure-transient response extensively, and use them to help identify the presence of dynamically-closed fractures. Finally, we demonstrate the influence of dynamically-closed fractures in synthetic and field cases to show the utility of the methodology. Results indicate that integrating multiple pressure build-up data obtained in different production periods enable us to diagnose and then to understand the changes in fracture conductivity during reservoir depletion. Using the results from the multiple pressure-transient analyses, this method can further be used to forecast the trend of fracture conductivity changes.