Vertical equilibrium with sub-scale analytical methods for geological CO₂ sequestration

Large-scale implementation of geological CO₂ sequestration requires quantification of risk and leakage potential. One potentially important leakage pathway for the injected CO₂ involves existing oil and gas wells. Wells are particularly important in North America, where more than a century of drilling has created millions of oil and gas wells. Models of CO ₂ injection and leakage will involve large uncertainties in parameters associated with wells, and therefore a probabilistic framework is required. These models must be able to capture both the large-scale CO ₂ plume associated with the injection and the small-scale leakage problem associated with localized flow along wells. Within a typical simulation domain, many hundreds of wells may exist. One effective modeling strategy combines both numerical and analytical models with a specific set of simplifying assumptions to produce an efficient numerical-analytical hybrid model. The model solves a set of governing equations derived by vertical averaging with assumptions of a macroscopic sharp interface and vertical equilibrium. These equations are solved numerically on a relatively coarse grid, with an analytical model embedded to solve for wellbore flow occurring at the sub-gridblock scale. This vertical equilibrium with sub-scale analytical method (VESA) combines the flexibility of a numerical method, allowing for heterogeneous and geologically complex systems, with the efficiency and accuracy of an analytical method, thereby eliminating expensive grid refinement for sub-scale features. Through a series of benchmark problems, we show that VESA compares well with traditional numerical simulations and to a semi-analytical model which applies to appropriately simple systems. We believe that the VESA model provides the necessary accuracy and efficiency for applications of risk analysis in many CO₂ sequestration problems.