Geological storage of carbon dioxide (CO2) is likely to be an integral component of any realistic plan to reduce anthropogenic greenhouse gas emissions. In conjunction with large-scale deployment of carbon storage as a technology, there is an urgent need for tools which provide reliable and quick assessments of aquifer storage performance. Previously, abandoned wells from over a century of oil and gas exploration and production have been identified as critical potential leakage paths. The practical importance of abandoned wells is emphasized by the correlation of heavy CO2 emitters (typically associated with industrialized areas) to oil and gas producing regions in North America. Herein, we describe a novel framework for predicting the leakage from large numbers of abandoned wells, forming leakage paths connecting multiple subsurface permeable formations. The framework is designed to exploit analytical solutions to various components of the problem and, ultimately, leads to a grid-free approximation to CO2 and brine leakage rates, as well as fluid distributions. We apply our model in a comparison to an established numerical solverforthe underlying governing equations. Thereafter, we demonstrate the capabilities of the model on typical field data taken from the vicinity of Edmonton, Alberta. This data set consists of over 500 wells and 7 permeable formations. Results show the flexibility and utility of the solution methods, and highlight the role that analytical and semianalytical solutions can play in this important problem.