Development of 2- and 3- simulator for three-phase flow with general initial and boundary conditions on the fractional flow approach

Open Access
Suk, Heejun
Graduate Program:
Civil Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
November 25, 2002
Committee Members:
  • Peggy Ann Johnson, Committee Member
  • Christopher J Duffy, Committee Chair
  • Derek Elsworth, Committee Member
  • Gour Tsyh Yeh, Committee Chair
  • Phase Configuration change
  • Fractional flow formulation
  • Multiple phase flow
  • Particle tracking
  • analytical method
  • linear spatial and temporal velocity variation
  • semi-analytical method
  • General boundary conditions
  • Fractional flow approach
  • three dimensional multiphase flow
ABSTRACT This thesis presents the development of 2-D and 3-D multiphase flow simulators as named 2DMPS(2-D Multifluid Phase Simulator) and 3DMPS (3-D Multifluid Phase Simulator) for three-phase flow (Water, NAPL, and Gas) in the subsurface, respectively. The 2DMPS and 3DMPS are developed using hybrid the Lagrangian and Eulerian approach (e.g. LEZOOMPC, The Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture scheme) and the Eulerian approach (e.g. Galerkin upstream finite element method). The governing equations of the fractional flow based approach consists of two saturation equations having an advection-diffusion form with advection dominated term, and a global pressure equation having an elliptic form. The former set of equations is well suited for numerical solution with the method of characteristics while the latter can be solved with conventional finite element method (e.g. Galerkin finite element method). Accordingly, a mixed Lagrangian-Eulerian approach (LEZOOMPC) is used for solving simultaneously two coupled nonlinear saturation equations, in which advection term can be effectively and accurately dealt with LEZOOMPC algorithm. Specifically, the accuracy in determining the Lagrangian saturation in most Lagrangian-Eulerian methods including LEZOOMPC depends on both the particle tracking algorithm and interpolation scheme. Most particle tracking methods are limited for the steady state flow case. However, in this research a multidimensional particle tracking algorithm has been developed to account for both temporal and spatial variations of velocity fields during the time step and incorporated into the LEZOOMPC algorithm. In addition to the aforementioned ablity of effectively and accurately solving the fractional flow approach equations with the LEZOOMPC scheme, fractional flow appraoch has its own inherent advantages. Since primary variables such as water and total liquid saturations are adopted in the fractional flow approach, 2DMPS and 3DMPS have the capability of automatically handling phase change configuration during the simulation time without any assumption or variable switching technique. The primary variables can be always defined no matter how a set of phase is changed in both time and space. Even though the fractional flow based approach has the several advantages over the pressure-based approach, it also has a difficulty in dealing with boundary conditions that are very often encountered in groundwater literature. However, in this research, general initial and boundary conditions are incorporated into 2DMPS and 3DMPS. The general boundary condition consists of ten types. Eight of these are combinations of the flux type or Dirichlet-pressure type of each individual phase and the last two, defined as variable boundary conditions, are the combination of gradient of capillary pressure or flux type of each individual phase depending on the velocity direction of each phase on the boundary. The general initial condition consists of eight types, which are the combinations of initial pressure and saturation of three individual phases. Any type of aforementioned initial and boundary conditions have been transformed and incorporated in terms of the primary variables, a global pressure and two saturations. In this study, 2DMPS and 3DMPS are developed and verified with an analytical solution and other numerical software (e.g. 2DTATMIC). Also several examples are presented to represent the treatment of general boundary and initial conditions and automatic adaptation of phase appearance and disappearance without any variable switching technique, and to show the applicability of real or field problems. Also an algorithm of multidimensional particle tracking technique accounting for transient state flow is presented and verified with analytical solution for both accuracy and efficiency.