Compositional Multiscale Finite-Volume Formulation

The multiscale finite-volume (MSFV) method is extended to include compositional processes in heterogeneous porous media, which require accurate modeling of the mass transfer and associated phase behaviors. A sequential-implicit strategy is used to deal with the coupling of the flow (pressure) and transport (component overall concentration) problems. In this compositional formulation, the overall continuity equation is used to formulate the pressure equation. The resulting pressure equation conserves total mass by construction and depends weakly 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. The details of the MSFV strategy for the pressure equation are described. The only source of error in this MSFV framework is the localization assumption. No additional assumptions related to the complex physics are used. For 1D problems, the sequential strategy is validated against solutions obtained by a fully implicit simulator. The accuracy of the MSFV method for compositional simulations is then illustrated for different test cases.