CMOR Technical Reports

Permanent URI for this collection

https://hdl.handle.net/1911/101542
Computational Applied Mathematics and Operations Research (CMOR) technical reports 1981-present. Use the "Browse" bar to filter by date, author, etc.

Browse

Browsing CMOR Technical Reports by Author "Arbogast, T."

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Gravitational Forces in Dual-Porosity Systems I. Model Derivation by Homogenization
    (1992-03) Arbogast, T.
    We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.
  • Thumbnail Image
    Item
    Gravitational Forces in Dual-Porosity Systems II: Computational Validation of the Homogonized Model
    (1992-03) Arbogast, T.
    Three models are considered for single component, single phase flow in naturally fractured porous media. The microscopic model holds on the Darcy scale, and it is considered to govern the system. The macroscopic, dual-porosity model was derived in Part I of their work from the microscopic model by two-scale mathematical homogenization. In this paper, we show that the dual-porosity model predicts well the behavior of the microscopic model by comparing their computed solutions in certain reasonable test cases. Homogenization gives a complex formula for a key parameter in the dual-porosity model; herein a simple approximation to this formula is presented. The third model considered is a single-porosity model with averaged parameters. It is shown that this type of model cannot predict the behavior of the microscopic flow.