Development of a Trilinear-Flow Model for Carbon Sequestration in Depleted Shale

Many researchers are currently seeking conventional geological sequestrations for carbon dioxide (CO2) storage, including saline aquifers, depleted conventional hydrocarbon reservoirs, and unminable coal seams. Only a few researchers have looked into depleted-shale formations for possible CO2 sequestration because of safety and economic reasons. To improve this situation, many measures should be taken. First and foremost, it is of great significance to find a method to estimate the CO2-storage capacity in depleted shale. In this paper, a new analytical method to estimate CO2-storage capacity in shale was developed. First, a trilinear-flow model proposed for the depleted-shale reservoir had a horizontal injection well-namely, a multiple-fractured horizontal well (MFHW)-at a constant injection rate. The model incorporated multiple mechanisms such as Knudson diffusion, gas adsorption, and effect of stress sensitivity. Then, the transient-pressure solution of the injection well was solved by applying mathematical methods of the Pedrosa (1986) substitution and Laplace transform. Subsequently, CO2-storage capacity was evaluated according to the transient-pressure performance of the injection well. After that, model verification and sensitivity analysis were conducted. Finally, we applied the proposed method in a case derived from the New Albany Shale, which had been proved to be a promising candidate for CO2 storage. The results show that good agreements exist between our analytical results and these numerical solutions. The average difference is approximately 3.03%, which shows our methodology is reasonable. Further, it only takes approximately 10 seconds of central-processing-unit (CPU) time with 100 timesteps by use of the proposed approach to estimate the CO2-storage capacity of the study area in the New Albany Shale, which indicates the new approach is rapid. In addition, results of sensitive analysis show that as stress-sensitivity coefficient, adsorption index, and Knudsen diffusion coefficient increase, CO2-storage capacity increases. As storage ratio increases, CO2-storage capacity decreases. This work provides a new approach to the estimation of CO2-storage capacity, which is beneficial to exploit the residual depleted-shale reservoirs as well as decrease CO2 emissions.