In this work we present the “Transient Hyperbolic” relation for the analysis and interpretation of time-rate performance data from wells in shale gas/liquids-rich shale plays. This model assumes a transient “b(t)” function which has constant early-time and constant late-time values, with an exponentially decaying transition function. This “b(t)” function is derived from the Gompertz logistic function.
Our goal in developing this formulation is to represent the early-time (or clean-up) portion of the production profile (often a hyperbolic function), the transition to the terminal hyperbolic behavior, and finally, the terminal hyperbolic behavior — where the terminal hyperbolic is usually representative of the “non-interfering” vertical fractures in a multi-fractured horizontal well (MFHW). We could further modify this relation to have a terminal exponential decline (thought to represent the performance of the stimulated-reservoir-volume (or SRV)), but that is not a primary purpose of this work — our primary purpose is to demonstrate the “Transient Hyperbolic” nature of the flow behavior from a multi-fractured horizontal well in a shale gas/liquids-rich shale play.
The technical contributions of this work are:
Development of the “Transient Hyperbolic” time-rate relation — this relation includes an early AND a late-time hyperbolic behavior, as well as a logistic transition function.
Application of the “Transient Hyperbolic” time-rate relation to modeling completion heterogeneity in a MFHW by a superposition of divisions that have differing durations of linear flow.
Application of the “Transient Hyperbolic” time-rate relation to several field cases — specifically: tight gas, shale gas, and “liquids-rich” shale cases.