Purpose: This paper aims to numerically study the compositional flow of two- and three-phase fluids in one-dimensional porous media and to make a comparison between several upwind and central numerical schemes. Design/methodology/approach: Implicit pressure explicit composition (IMPEC) procedure is used for discretization of governing equations. The pressure equation is solved implicitly, whereas the mass conservation equations are solved explicitly using different upwind (UPW) and central (CEN) numerical schemes. These include classical upwind (UPW-CLS), flux-based decomposition upwind (UPW-FLX), variable-based decomposition upwind (UPW-VAR), Roe’s upwind (UPW-ROE), local Lax–Friedrichs (CEN-LLF), dominant wave (CEN-DW), Harten–Lax–van Leer (HLL) and newly proposed modified dominant wave (CEN-MDW) schemes. To achieve higher resolution, high-order data generated by either monotone upstream-centered schemes for conservation laws (MUSCL) or weighted essentially non-oscillatory (WENO) reconstructions are used. Findings: It was found that the new CEN-MDW scheme can accurately solve multiphase compositional flow equations. This scheme uses most of the information in flux function while it has a moderate computational cost as a consequence of using simple algebraic formula for the wave speed approximation. Moreover, numerically calculated wave structure is shown to be used as a tool for a priori estimation of problematic regions, i.e. degenerate, umbilic and elliptic points, which require applying correction procedures to produce physically acceptable (entropy) solutions. Research limitations/implications: This paper is concerned with one-dimensional study of compositional two- and three-phase flows in porous media. Temperature is assumed constant and the physical model accounts for miscibility and compressibility of fluids, whereas gravity and capillary effects are neglected. Practical implications: The proposed numerical scheme can be efficiently used for solving two- and three-phase compositional flows in porous media with a low computational cost which is especially useful when the number of chemical species increases. Originality/value: A new central scheme is proposed that leads to improved accuracy and computational efficiency. Moreover, to the best of authors knowledge, this is the first time that the wave structure of compositional model is investigated numerically to determine the problematic situations during numerical solution and adopt appropriate correction techniques.
Moshiri, M., & Manzari, M. T. (2019). A comparative study of explicit high-resolution schemes for compositional simulations. International Journal of Numerical Methods for Heat and Fluid Flow, 29(1), 94–131. https://doi.org/10.1108/HFF-08-2017-0333