Compositional multiscale finite-volume formulation

In this paper, the Multiscale Finite-Volume (MSFV) method is extended to include compositional displacements in heterogeneous porous media, in which accurate modeling of the mass transfer and associated phase behaviors is critical. A sequential-implicit strategy is employed to deal with the coupling of the flow (pressure) and transport (component overall concentration) problems. In this compositional formulation, the overall continuity equation (i.e., conservation of total mass) is used to formulate the pressure equation. The resulting pressure equation conserves total mass by construction and has weak dependencies on the distributions of the phase compositions. The transport equations are expressed in terms of the overall composition; hence, phase appearance and disappearance effects do not appear explicitly in these expressions. Given the discrete forms of the flow and transport problems, the details of the MSFV strategy are then described for the efficient solution of the pressure equation. The only source of error in this MSFV framework is due to the well-known localization assumptions. No additional assumption due to the complex physics is done in this framework. For one-dimensional problems, the proposed sequential strategy results are validated against those obtained by a fully implicit simulator. The accuracy and efficiency of the MSFV method for compositional simulations are then illustrated for different numerical test cases. It is shown that the MSFV results are identical to the fine-scale solutions for one-dimensional problems in transient- and steady- states.