Dynamic adaptive and fully unstructured tetrahedral gridding: Application to CO2 sequestration with consideration of full fluid compressibility

Abstract

Numerical simulations of complex subsurface flow problems and geomechanics will advance enormously by dynamic adaptive gridding. Only a small part of a large domain where sharp changes occur may require fine gridding. In this work, we introduce a methodology to carry out dynamic adaptive gridding for large-scale flow problems. The algorithm allows 2D and 3D unstructured gridding with consideration of full fluid compressibility in single-phase, and two-phase compositional flow. We divide a triangular element into four and a tetrahedron element into eight which creates hanging nodes at each level of refinement. The handing nodes are eliminated by splitting extra elements. As a result, a transition region exists between the fine and coarse grid regions of the domain. We have applied the method to CO₂ sequestration in subsurface aquifers. The conditions are selected such that gravity fingers develop from density increase by the dissolution of CO₂ in the aqueous phase. The selected examples include large domains where neither systematic studies nor dynamic adaptive gridding have been reported in the past. Results from comparison with uniform gridding reveal a speedup of up to three orders of magnitude in 3D.