Pattern Structure of Deterministic Displacement in Random Porous Media with Dispersion Effect

A new model — model of random porous media degradation via several fluid displacing, freezing, and thawing cycles is introduced and investigated in this paper. The fluid transport is based on the deterministic method with dispersion effect. The result shows that the topology and the geometry of the porous media have a strong effect on displacement processes. The cluster size of viscous fingering (VF) pattern in percolation cluster increases with the increase of iteration parameter n. When iteration parameter , VF pattern does not change with n. We find that the displacement fluid forms trapping regions in random porous media with dispersion effect. And the trapping regions will expand with the increasing of the iteration parameter n. When r (throat size) and , the peak value of the distribution increases as n increases, where is the normalized distribution of throat sizes after different displacement-damages but before freezing. The peak value of the distribution reaches a maximum when and , where is the normalized distribution of the size of invaded throat. This result is different from invasion percolation. It is found that the sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L, and E has a minimum as L increases to the maximum size of lattice. The VF pattern in percolation cluster has one frozen zone and one active zone.

Adaptive Stroud Stochastic Collocation Method for Flow in Random Porous Media via Karhunen-Loeve Expansion

In this paper we develop a Stochastic Collocation Method(SCM)for flow in randomly heterogeneous porous media.At first,the Karhunen-Lo`eve expansion is taken to decompose the log transformed hydraulic conductivity field,which leads to a stochastic PDE that only depends on a finite number of i.i.d.Gaussian random variables.Based on the eigenvalue decay property and a rough error estimate of Stroud cubature in SCM,we propose to subdivide the leading dimensions in the integration space for random variables to increase the accuracy.We refer to this approach as adaptive Stroud SCM.One-and two-dimensional steady-state single phase flow examples are simulated with the new method,and comparisons are made with other stochastic methods,namely,the Monte Carlo method,the tensor product SCM,and the quasiMonte Carlo SCM.The results indicate that the adaptive Stroud SCM is more efficient and the statistical moments of the hydraulic head can be more accurately estimated.

Statistical second-order two-scale analysis and computation for heat conduction problem with radiation boundary condition in porous materials

This paper discusses a statistical second-order two-scale（SSOTS） analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation.