Stochastic simulation of flows and particle transport in porous tubes

Abstract

A Monte Carlo method is developed for stochastic simulation of flows and particle transport in tubes filled with a porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modelled in a tube with prescribed boundary conditions. Numerical experiments are carried out by solving the random Darcy equation for each sample of the hydraulic conductivity by a SOR iteration method, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, diffusion coefficients, the mean and variance of Lagrangian trajectories, and discuss a ''stagnation" effect which was found in our simulations.