Semi-Analytical Analysis of Peak Production Rates in Unconventional, Boundary-Dominated Gas Reservoirs with Adsorptive Storage

Abstract

The objective of this study was to develop tools to analyze the production profile of unconventional gas reservoirs where adsorption is a dominant storage mechanism. Specifically, the research is focused on analyzing the conditions that affect the time needed to achieve peak gas production rate. To this end, we have successfully derived the analytical expressions for the reservoir pressures at which peak gas production occurs under various operating scenarios. The methodology involves the development of a system of generalized two-phase material balance equations for boundary dominated flow in unconventional gas reservoirs where adsorption is a dominant storage mechanism. The resulting analytical ODEs are then solved numerically (Runge-Kutta) which yields a semi-analytical solution for pressure and saturation versus time. Once the pressure and saturations are determined numerically, gas and water production rates, along with their derivatives, are determined analytically and used to analyze the production profiles. Through the analytical derivatives, reservoir and fluid parameters can be modified to observe their effects on the time to peak gas rate. In this study, three different well specifications were investigated (constant flowing well pressure, constant well drawdown, and constant water production rate) with only two of the three well specifications resulting in a peak gas production rate - no peak gas production rate was observed for the water rate specified wells. Furthermore, the developed semi-analytical model, under appropriate conditions, gives results comparable to numerical reservoir simulator. The paper will discuss conditions at which the material balance results are comparable to full reservoir simulation. Through this research, a new material balance method has been developed that can be presented in different domains (pressure, time, and cumulative produced fluids domains). Also, the novel use of derivatives from the generalized material balance equations was applied in this research to analytically and graphically analyze the production profile. Furthermore, in addition to the peak gas production rate, additional inflection points were observed that have not been reported in the current literature.