To reduce CO2 emissions in response to global climate change, depleted shale reservoirs are ideal for long-term carbon storage. However, hydraulic fracturing measures and large injections of carbon dioxide can cause faults and fractures to reactivate, causing gas migration and leakage. In this paper, a partially permeable boundary is introduced to characterize the region where CO2 leakage occurs. This study proposes a model for predicting CO2 sequestration potential in novel depleted shale gas reservoirs considering gas adsorption, diffusion, and gas leakage. Furthermore, the multi-scale transport model is solved using Laplace transformation and potential energy superposition and is verified using numerical simulations based on the field data from the Marcellus Shale. The results show that the analytical solutions of the proposed model are in good agreement with the results of conventional numerical simulations. Moreover, shale reservoirs with high Langmuir volume and low Langmuir pressure are ideal for CO2 storage, with larger CO2 storage capacity and minor gas leakage. The findings have tremendous significance for the potential utilization of depleted shale gas reservoirs, considering the leakage of CO2.