Fully Coupled Air-Water Flow Model in Unsaturated Porous Media

by
Myeong Hwan Noh, MSE

University of Texas at Austin, 1999
Supervisor: Mary F. Wheeler

In this thesis, we have formulated and implemented a fully coupled, three-dimensional air-water flow model for distributed parallel computing environments. The model involves a non-reactive gas phase based on the real gas law coupled with a slightly compressible aqueous phase. The mathematical model is described by a system of nonlinear partial differential equations for the conservation of mass of each phase and a Darcy's law constitutive relation. In the numerical discretization, we employ a fully implicit mixed finite element method or cell centered finite difference method with upwinding. General Dirichlet and/or no-flow boundary conditions can be imposed in the model. Pressure or mass flow rate specified wells, which are fully or partially penetrating, can be placed arbitrarily in the porous media. General but physically meaningful functionality is imposed through the use of spline approximation of fluid and rock properties. A Newtonian iteration with a multistage preconditioned GMRES linear solver is used to solve the resulting nonlinear algebraic system of equations.

This two-phase model is one of eight physical models, which have been implemented in a framework known as the Integrated Parallel Accurate Reservoir Simulator (IPARS). The general functionality of IPARS , which can be viewed as a problem solving environment, allows the user to implement a parallel physical model without having to write message passing statements, spline routines and lookup tables, well models, solvers, visualization, and input/output statements.

In this thesis we present validation of the model by comparison with known one-dimensional single-phase flow solutions. In addition, we discuss test cases, which include studies of modeling injection and production wells in a confined reservoir, and flooding over dry land from nearby lakes or rivers. Finally, it is noted that this model is more general than the air-water Richards' equation formulation, which one frequently encounters in environmental modeling and that our approach allow for flexible couplings with wetlands and/or surface water models.

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