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

This thesis presents the development of 2-D and 3-D multiphase flow simulators named 2DMPS(2-D Multifluid Phase Simulator) and 3DMPS (3&barbelow;-D&barbelow; M&barbelow;ultifluid P&barbelow;hase S&barbelow;imulator) 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 L&barbelow;agrangian-E&barbelow;ulerian decoupling method with an adaptive ZOOMing and P&barbelow;eak/valley C&barbelow;apture 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 are 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 multidimensional a 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. Besides the fractional flow based approach adopts primary variables such as water and total liquid saturation, which can be always defined no matter how a set of phase is changed in both time and space.; In this study, 2DMPS and 3DMPS are developed and verified with an analytical solution and other numerical models (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 the field problem. Also algorithm of multidimensional particle tracking technique accounting for transient state flow is presented and verified with analytical solution for both accuracy and efficiency. (Abstract shortened by UMI.)...