Multiscale reconstruction of compositional transport

Abstract

A compositional formulation is a reliable option for understanding the complex subsurface processes and the associated physical changes. However, this type of model has a great computational cost, since the number of equations that needs to be solved in each grid block increases proportionally with the number of components employed, thereby making them computationally demanding. In an effort to enhance the solution strategy of the hyperbolic problem, we herewith propose a multiscale reconstruction of compositional transport problem. Until recently, multiscale techniques have been seldom implemented on transport equations. Here, the ideology consists of two stages, wherein two different sets of restriction and prolongation operators are defined based on the dynamics of compositional transport. In the first stage, an operator restricting the arbitrary number of components to single transport equation is implemented with the objective of reconstructing the leading and trailing shock positions in space. The prediction of front propagation is the most critical aspect of the approach, as they involve a lot of uncertainty. Once their positions are identified, the full solution lying in the regions outside the shocks can be conservatively reconstructed based on the prolongation interpolation operator. Subsequently, the solution for the multicomponent problem (full system) in the two-phase region is reconstructed by solving just two transport equations with the aid of restriction operator defined based on an invariant thermodynamic path (based on Compositional Space Parameterization technique). We demonstrate applicability of the approach for the idealistic 1D test cases involving various gas drives with different number of components. Further, the first stage reconstruction was tested successfully on more realistic problems based on implementation in recently developed Operator-Based Linearization (OBL) platform.