Comprehensive application of semi-analytical PTA and RTA to quantitatively determine abandonment pressure for CO2 storage in depleted shale gas reservoirs

Abstract

Recent studies suggest the possibility of CO2 sequestration in depleted shale gas reservoirs, motivated by large storage capacity estimates in these formations. Although various approaches have been proposed to evaluate and estimate CO2 storage capacity and even almost all of researches mainly focus on the calculation of storage capacity at the present time, questions remain regarding the quantitative determination of abandonment pressure for a depleted shale gas reservoir, which is a key joint between shale gas recovery and CO2 storage operation. Also the determination of abandonment pressure is the inversion problems of estimation of CO2 capacity. Therefore, in this paper, to quantitatively determine the abandonment pressure and mathematically analyze related impacts of dynamic parameters on it, two semi-analytical models of pressure and rate transient analysis are simultaneously proposed for the closed outer boundary condition, without the assumption of sequential flow between the three contiguous media. Adsorption, desorption, diffusion flow, stress sensitivity and non-Darcy flow effects are simultaneously considered. Besides, a new modified Langmuir isotherm equation of CO2 is initially established to consider the impacts of residual adsorption shale gas. Laplace transformation, source function, perturbation transformation method, superposition principle and numerical discretion method are employed to effectively solve these new models. Laplace solutions are inverted into real time space with stehfest numerical inversion algorithm. Numerical simulation and existing models are also simultaneously conducted to validate this proposed mathematical models. Based on this new solution, some crucial dynamic engineering parameters, including abandonment pressure and non-Darcy flow, are creatively analyzed combining pressure transient analysis (PTA) and rate transient analysis (RTA) For two kinds of CO2 injection control: constant injection pressure and constant injection rate, it is the essence of this paper that typical chart referring quantitative determination of abandonment pressure is originally established via pressure transient analysis (PTA) and rate transient analysis (RTA). Via regression method using synthetic and real data, results mathematically show that for PTA method, the abandonment pressure has exponent relationship with the injection pressure, however, for RTA method, the abandonment pressure has logarithm relationship with CO2 injection volume. Finally, well testing of gas production data, micro seismic date and core analysis allow for formation parameter estimation, two real shale gas wells from Sichuan Basin in China are selected to show the promising application prosperity of the new performance analysis and quantitatively determination of abandonment pressure for CO2 storage in depleted shale gas reservoirs.