Microstructure modeling of fluid flow in a layered medium
Fluid flow through a fissured medium in which the fissures occur in a layered structure is modeled as a double porosity microstructure model. The model consists of a matrix of fissures and cells with the cells distributed continuously throughout the fissure system, so that at each point in the matrix two sets of values are used to describe the fluid and the medium through which it flows. One set reflects conditions at the point in the fissure itself, and one gives the values for the cell associated with that point. Flow in the fissure system and in each cell is described by diffusion equations over the corresponding spaces, with the effects of the cells manifested as point sources on the global (fissure) scale and with the fissures affecting each cell through the boundary conditions associated with that cell. The main interest is in the effects of the layered structure which is modeled by the geometry of the cells and in the effects of the flow normal to the layers of cells. In the general case this model is described as a Cauchy-Dirichlet problem for a parabolic system of the form: d/dt a(u(x,t)) - [rvec [del]] [center dot] A([rvec [del]]u(x,t)) + q(U(x,y,t)) = f(x,t); d/dt b(U(x,y,t)) - [rvec [del]][sub y] [center dot] B([rvec [del]][sub y]U(x,y,t)) = F(x,y,t) with appropriate boundary conditions. u(x,t) represents the value of the fluid density in the fissure at the point x. The density at y, within the cell located at x, is given by U(x,y,t). The operators A and B are monotone and (possibly) nonlinear, q is the point source associated with the individual cell, and f and F represent any outside sources. By writing the above in variational form, the problem can be formulated as a single Cauchy problem on a continuous direct sum of Banach spaces of Sobolev type. In this form the stationary operator is shown to be type-M, bounded and coercive under conditions prescribed on A and B, and existence and uniqueness of a (weak) solution of the system are obtained.
- Research Organization:
- Texas Univ., Austin, TX (United States)
- OSTI ID:
- 7301231
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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