We have completed all components of a semi-analytical model for leakage along multiple wells, over field-scale systems with multiple geological layers, and we are now publishing these new solutions in a variety of scientific journals. We have also begun to demonstrate the use of these solutions in the context of Monte Carlo simulations, where we will relate different well statistics (for example, the statistics of effective permeabilities along leaky wells) to leakage probabilities. To do this, we will use a test site that we have identified in Alberta, Canada, in conjunction with our collaborator Stefan Bachu. We will complete the initial computational analysis of this field site in the first year, and then extend the analysis over the next year to identify threshold statistics for the well field in order to remain below target leakage values. We will also seek out additional field sites to apply our new models. For example, we may be able to use the data set on wells that has been compiled during the first phase of the Weyburn project.
As results from detailed, local-scale geochemical analysis of cement degradation become available, we will incorporate these results into our field-scale models. This will be done by modifying the properties of leaky wells as a function of local conditions and time, based on the results described in the previous section.
While these semi-analytical models have been shown to compare well to full numerical solutions, they are still restricted by simplifying assumptions about system geometry, material homogeneity, and other aspects of the system. We will systematically evaluate the limits of these assumptions, with a focus on sloping layers, material heterogeneity, and the need to include capillary pressure (note that we already include residual saturations, but not a full capillary pressure function). To model conditions for which the analytical solutions are found not to apply, we will develop a hybrid numerical-analytical model where the injection formation is modeled with a numerical simulator, capable of including sloping layers and heterogeneity, while leakage along wells and into layers above the injection formation will be modeled analytically. As with our other developments, the objective is to create a model that is as simple as possible, while capturing the essential physics of the problem. Development and application of this hybrid numerical-analytical model will form the basis of a PhD dissertation for a new graduate student (to be admitted this year).
Over the entire five-year period, we will continue to develop ties with outside collaborators while maintaining the important connections we already have. For example, we will continue our very productive collaborations with Stefan Bachu in Alberta, and with Jan Nordbotten and the applied mathematics group in Bergen. In addition, we have been invited by colleagues at Los Alamos National Laboratory to incorporate our semi-analytical models into the systems model they are constructing for CO2 injection and associated risk analysis. We will also attempt to coordinate an effort to develop a community model for CO2 injection, migration, and leakage. This is something we initiated a few months ago at a workshop we organized and held at Princeton. Finally, we plan to use our models to propose designs for specific field experiments, and to work with partners at BP and elsewhere to try to implement these field experiments.