Variable Exponential Decline: Modified Arps To Characterize Unconventional-Shale Production Performance

Abstract

Summary Different decline-curve-analysis (DCA) methods have been proposed to predict the production performance of both conventional and unconventional-shale reservoirs. These methods range from empirical to semiempirical and theoretical. The different methods were developed using specific data sets and have their own assumptions and limitations, and thus are not universally applicable. This study shows that a DCA method should be capable of simultaneously modeling the flow regime prevalent around the well and the changes in reservoir properties with time, to be able to successfully represent the production performance of the well and predict future performance. In shales, flow regimes can be linear, bilinear, multifracture linear, post-linear, stimulated-reservoir-volume (SRV) -dominated boundary flow, or compound linear. The change in fracture conductivity caused by fines migration, embedment, crushing, diagenesis, and change in stresses because of production is another important phenomenon for which a DCA method must account. This study critically analyzes various proposed historical DCA methods with respect to their capability to model fracture-flow regimes and changes in fracture conductivity with time. Upon close examination, it was found that both the linear-flow regimes and changes in fracture conductivity with time follow a power-law function. Thus, the reason for the successful application of the Arps (1944) hyperbolic, power-law-exponential (PLE), stretched-exponential-decline (SEPD), and Duong (2010) methods is that decline rates in these methods are a power-law function or can be closely approximated by a power-law function. A new simplified decline-curve equation is proposed by modifying the existing Arps exponential-decline equation, where the constant-decline rate is replaced by a power-law-function variable decline rate. The application of this method is shown using production data from Haynesville Formation and Eagle Ford Formation shales. The average error in cumulative-production prediction for 20 wells was found to be only 3% in Haynesville wells and 2% in Eagle Ford wells. This method is very robust and can account for different flow regimes and changes in fracture conductivity with time.