Mathematics of multiphase multiphysics transport in porous media

Open Access
Khorsandi Kouhanestant, Saeid
Graduate Program:
Energy and Mineral Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
February 26, 2016
Committee Members:
  • Russell Taylor Johns, Dissertation Advisor
  • Russell Taylor Johns, Committee Chair
  • Turgay Ertekin, Committee Member
  • Luis F Ayala H, Committee Member
  • Wen Shen, Committee Member
  • Alberto Bressan, Committee Member
  • Enhanced oil recovery
  • MMP
  • Riemann problem
  • Hyperbolic equations
  • Method of Characteristics
Modeling complex interaction of flow and phase behavior is the key for modeling local displacement efficiency of many EOR processes. The interaction is more complex for EOR techniques that rely on mass transfer between phases such as those that occur during miscible gas floods. Accurate estimation of local displacement efficiency is important for successful design of enhanced oil recovery (EOR) processes. Displacement efficiency can be estimated by experimental and computational methods. The dispersion-free displacement efficiency is 100% at a pressure above the minimum miscibility pressure (MMP) for gas flooding processes. Slim-tube experiments are one of the most reliable experimental approaches for MMP calculation. Computational methods including simulation, mixing cell and method of characteristics (MOC) solutions rely on accurate EOS fluid characterization. MOC is the fastest and the only solution method which is not affected by dispersion. However, current MOC methods have significant limitations in converging to the correct solution. In addition, the assumptions made in MOC may not be correct for some fluids, which can cause errors as large as 5000 psia in calculated MMPs. Current MOC solutions are simplified by assuming that only shocks connect key tie lines. Likewise the velocity condition cannot be applied directly to the shock-jump approximate approach. These simplifications reduce the computation time but result in decreased reliability of “shock-jump” approximation methods as well. We examined the assumptions of MOC for the case where the two-phase region splits at a critical point. This is referred to hence as bifurcating phase behavior. In this case, the assumption that the non-tie-line eigenvalues change monotonically between two key tie lines is incorrect. The correct solution is constructed for ternary displacements with bifurcating phase behavior by honoring all constraints required for a unique solution – velocity, mass balance, entropy and solution continuity. The solution is further validated using simulation and the mixing cell method. The simulation results are highly affected by dispersion for some cases such that the results of simulation and analytical solutions match only after using a very large number of grid blocks. The construction of the entire composition route using conventional MOC solutions is very challenging as the number of components increases. The other option is to separate the phase behavior from flow and then solve the tie-lines independent of fractional flow. We examined and developed this approach in detail here. We developed a global Riemann solver for ternary displacements and later extended the splitting technique to multicomponent displacements. Our approach does not suffer from the singularities present in Pires et al. (2006) and Dutra et al. (2009). The solution in tie-line space is constructed for a variety of fluid models including pseudoternary displacements with bifurcating phase behavior, and real fluid displacements (Zick 1986, Metcalfe and Yarborough 1979). Finally the MMP is calculated for several multicomponent (>4) fluids using the analytical solution based solely on solving the continuous tie-line problem, where tie-line rarefactions and shocks can exist in tie-line space. Thus, we eliminate the need for the “shock jump” approximation assumption in determining the MMP. The splitting technique is used to construct analytical solutions for low salinity polymer flooding considering wettability alternation caused by cation exchange reactions. The solutions are validated using numerical simulation and experimental data. The solutions demonstrate that multiple salinity shocks form in low salinity injection and the fast moving salinity shock does not change the surface composition and wettability. In contrast, oil is recovered as a wettability front slowly moves in the reservoir and reduces the residual oil saturation. The wettability front creates an oil bank which will be gradually produced.