A multi-layer vertically integrated model with vertical dynamics and heterogeneity for CO2 sequestration

Abstract:

Mathematical models with different level of complexity are needed to address a range of engineering questions on security issues of CO₂ sequestration, which has been proposed as a promising strategy for carbon mitigation. Among this wide range of mathematical models, a family of vertically integrated models has been developed. These models are usually based on a vertical equilibrium (VE) assumption, which states that due to strong buoyancy, CO₂ and brine segregate instantaneously and reach a hydrostatic pressure distribution in the vertical dimension. Such VE models are accurate and computationally efficient as long as the VE assumption is valid. By comparing VE models with a full three-dimensional model for a series of practical problems, Court et al. (2012) found that there are a number of cases for which the VE model is not applicable, especially when the geological formations have relatively low vertical permeability, on the order of 10 milliDarcy or lower. To overcome the VE limitation, Guo et al. (2014) have developed a vertically integrated model for homogeneous formations that relaxes the VE assumption and accounts for vertical dynamics of CO₂ and brine. Though, limited to homogeneous formations, this model has a much wider applicability compared to VE models while maintains much of the VE model’s computational efficiency.

In this contribution, we extend the vertically integrated model of Guo et al. (2014) to deal with the horizontally layered systems to include vertical heterogeneities. Each layer of the system can have different material properties but is assumed to be homogeneous within the layer. Such horizontally layered systems are of high practical relevance because of the depositional history of the geological formations. We develop coupling conditions between the layers and use a similar algorithm of Guo et al. (2014) to solve the individual layers. The end result is a model capable of dealing with vertical geological heterogeneities while still maintaining much of the computational advantages of VE models. Comparison of results with a VE model and a full three-dimensional model will be presented to demonstrate the applicability of the new model.