Benchmarking a reduced order finite element method for multiphase carbon sequestration models

Carbon sequestration in deep saline aquifers has been proposed for long-term storage of CO₂ as an alternative to the release of CO₂ into the atmosphere. In this article, we present a computationally efficient numerical model based on a sequentially coupled Finite Element Method (FEM) and Streamline Upwind Finite Element Method (SU-FEM)-Finite Difference Method (FDM). An adaptive timestep strategy is implemented which allows computationally efficient and stable solutions as time progresses. The computational efficiency of the formulation is demonstrated by four examples that consider nonuniform permeability, multiple injection wells, an upsloping aquifer, and a dome-shaped aquifer. The adaptive timesteps reduce the computational cost by 75-82% compared to constant timesteps in the four examples considered. The proposed formulation is compared against a benchmark study where eleven different simulators were used to determine the arrival time of the CO₂ plume at a leaky well. The original benchmark study did not include an FEM-based discretization of the reduced order equations. To the authors’ best knowledge, the current work is the first FEM based implementation of reduced order (vertically averaged) multiphase flow equations evaluated against this benchmark. The proposed formulation is in good general agreement with the results from the various simulators studied in the benchmark, and excellent agreement with an FDM discretization of the vertically averaged governing equations.