Applicability of vertical-equilibrium and sharp-interface assumptions in CO₂ sequestration modeling

Analysis of geological sequestration of carbon dioxide (CO₂) requires mathematical models of different complexity to answer a range of practical questions. A family of vertically-integrated models of intermediate complexity can be derived by assuming that the strong buoyant drive in the system leads to vertical segregation of the injected CO₂ and resident brine on a time scale that is fast enough to model the system as being stratified and in vertical-equilibrium. These models range from vertically-integrated numerical models which include capillary forces via mathematical reconstruction, to analytical models assuming a sharp-interface and homogeneous formation parameters. This paper investigates the limits of numerical vertical-equilibrium models and the more restricted vertical-equilibrium sharp-interface models via direct comparisons with a homogeneous three-dimensional model, exploring the impacts of injection rate, injection time, and formation characteristics. We use the commercial simulator ECLIPSE for the three-dimensional model. Our results demonstrate that the applicability of a vertically-integrated modeling approach to CO₂ sequestration depends on the time scale of the vertical brine drainage within the plume, relative to the time scale of the simulation. The validity of the sharp-interface assumption is shown to depend on the spatial scale of the capillary forces, which drive the thickness of the capillary transition zone. A finite-capillary-transition-zone vertically-integrated numerical model with saturation reconstruction closely matches results from the three-dimensional model (ECLIPSE) including capillary pressure as long as the segregation time scales are respected. Overall, our results demonstrate that vertically-integrated and sharp-interface models are useful and accurate when applied within the appropriate length and time scales.