FLOW AND TRANSPORT IN CHAOTIC MEDIA: FOUR CASE STUDIES (POROUS, DISPERSION, ELASTICITY, FINGERING).

摘要

The thesis comprises four case studies of the modeling of flow and transport in chaotic porous media. The first is a comparison between the percolation and percolation-conduction properties of the Voronoi network and regular networks. Percolation and conduction properties are estimated from Monte Carlo simulation and critical exponents are estimated from finite-size scaling theory. The results show that the effect of random topology as provided by the Voronoi network is negligible.; The second study is of the effective elastic constants of network models of the elastic properties of porous media generated from finite element (FEM) and finite difference approximations of the equations of linear elasticity. Effective medium approximation (EMA) agrees well with Monte Carlo simulation and shows that the models reduce to scalar transport and their effective Poisson ratio becomes negative as the percolation threshold is approached. EMA of the effective spring constant of networks of central force springs is particularly simple and agrees well with Monte Carlo simulation.; The third is of the Peclet number dependence of the virtually convection-dominated dispersion in flow in porous media. Dispersion coefficients are estimated from the statistics of the displacements of a population of Brownian tracer particles. The velocity distribution within pores is found by FEM solution of the equations of creeping flow. A network reduction and EMA yield estimates of the flow in clusters of pores in an unbounded medium. Rough results exhibit a mildly nonlinear Peclet number dependence and indicate that dispersion coefficients become time-independent and the distribution of displacements of tracer particles approaches a Gaussian as time proceeds.; The fourth is of the stability to fingering of a wave of permanent form solution to the convective-diffusion equation for two-phase flow through porous media with significant capillary effect. Stability of the front is found by solving the eigenproblem to which linear stability theory leads using the FEM and a small-wavenumber expansion. A generalized mobility ratio, gravity acting on density contrast, the length of disturbances in the flow direction and the width of fingers are found to determine stability.