How simple can we make models for CO₂ injection, migration, and leakage?

Analysis of geological storage of CO₂ almost always involves some set of computational models that provide a mathematical description of the problem. These models can have many purposes, but ultimately they should be able to answer practical questions about the system. These questions usual involve the spatial extent of the CO₂ plume, the spatial extent of pressure perturbations, the spatial and temporal dynamics of leakage out of the injection formation, and the spatial and temporal evolution of different trapping mechanisms. Answers to these questions require models that apply to large spatial and temporal scales while including certain small-scale features like leakage pathways. Development of computationally efficient models that can span the appropriate scales may be achieved by analyzing the length and time scales associated with the important processes in the system, and incorporating those scales into a systematic model development. Such a procedure can be described as multi- scale modelling. Beginning with the most complex models, a sequence of simplifying assumptions may be proposed, based in part on scaling arguments for the physical processes involved, to produce a sequence of successively simpler models. Through this approach, the assumptions in all of the simplified models are made transparent, and the length and time scales appropriate for different models can be identified. In addition, by associating length and time scales to the questions being asked, models can be developed that are consistent with those scales and therefore are appropriate to answer the questions.