Risk sharing in cooperative game models for CO$_2$ storage with uncertain geology and pressure competition
With an increasing number of prospective geological CO$_2$ storage projects and potential pressure communication between different projects, risk sharing under uncertain geological conditions are relevant to many project operators. In this work, the project operators are modeled as agents in a stochastic cooperative game. The agents can have different risk attitudes, here defined as being willing to accept more or less uncertainty in the predicted storage of CO$_2$. This uncertainty stems from lack of knowledge of geological parameters as well as unknown future actions of competing agents, and the corresponding probability distributions need to be estimated by numerical simulation. The agents can choose to share commercial risk if collaboration is preferable to a baseline scenario of individual injection. If their operations affect each other by means of, e.g., pressure communication, there may be no unique natural definition of a baseline scenario. As a remedy, we suggest belief distributions that combine uncertainty in physical data with maximum entropy prior distributions over the sets of viable injection actions. For a realistic storage site, exemplified by the Utsira Formation in the North Sea, we present numerical results for both cases of pressure competition, and no hydraulic connections between different project operations. It is shown that risk averse agents benefit from collaboration when there is no pressure communication or other interference between agents. It is also demonstrated that pressure communication leads to large variability in the feasible injection rates, but the resulting belief distributions are nevertheless informative and useful for decision making about collaboration.