  We propose a novel framework for optimizing injection strategies in
large-scale CO$_2$ storage combining multi-agent models with multi-objective
optimization, and reservoir simulation. We investigate whether agents should
form coalitions for collaboration to maximize the outcome of their storage
activities. In multi-agent systems, it is typically assumed that the optimal
strategy for any given coalition structure is already known, and it remains to
identify which coalition structure is optimal according to some predefined
criterion. For any coalition structure in this work, the optimal CO$_2$
injection strategy is not a priori known, and needs to be found by a
combination of reservoir simulation and a multi-objective optimization problem.
The multi-objective optimization problems all come with the numerical
challenges of repeated evaluations of complex-physics models. We use versatile
evolutionary algorithms to solve the multi-objective optimization problems,
where the solution is a set of values, e.g., a Pareto front. The Pareto fronts
are first computed using the so-called weighted sum method that transforms the
multi-objective optimization problem into a set of single-objective
optimization problems. Results based on two different Pareto front selection
criteria are presented. Then a truly multi-objective optimization method is
used to obtain the Pareto fronts, and compared to the previous weighted sum
method. We demonstrate the proposed framework on the Bjarmeland formation, a
pressure-limited prospective storage site in the Barents Sea. The problem is
constrained by the maximum sustainable pressure buildup and a supply of CO$_2$
that can vary over time. In addition to identifying the optimal coalitions, the
methodology shows how distinct suboptimal coalitions perform in comparison to
the optimum.
