Research On Random Grid-based Percolation Model And Its Application In The Deep Bed Filtration

Filtration is a dynamic and complex process. Each kind of mathematical modelestablished so far has some defect. As a result, it is necessary to introduce some newideas into the establishment of the mathematical model of deep bed filtration.Percolation theory and its model have a unique advantage in the research field of porousmedia. The process of suspended particles in the suspension liquid plugging hole issimilar to the process of the group formation in the percolation theory. What’s more, thestructure of random grid is rather close to the structure of deep bed filtration mediummade by particle accumulation. Consequently, the idea of percolation was introducedinto the research.Percolation theory was perfected before the establishment of mathematical model.The expression of group distribution function was obtained by studying the groupdistribution characteristics. The expression was log(n s(p))=a×s-b×log s+c. Thecoefficients of the formula were also calculated. And the influence of grid scale on thepercolation parameters was analyzed. The dynamic process of direct percolation in thediagonal square grid was described. Then the law of particle walking in thetwo-dimensional and three-dimensional grid based on direct percolation could beobtained.Stacking structure formed by particles under gravity was simulated by PFC3Dsoftware. The center coordinates of the medium particles (glass beads) could beobtained according to the glass bead size distribution. Then pore size distributionfunction was gotten. The relation between filtration coefficient and the average captureprobability obtained by percolation theory was lμ (1-f*l)b（f*l> f*c）. Particlesfollowed the maximum or minimum capture mechanism when they walked in thechannel. The process of deep bed filtration was simulated using three kinds of grid thatwere the diagonal square grid, BCC grid and three-dimensional Voronoi grid in thechannel established above under gravity. Then percolation-filtration model wasestablished. The change of filtration coefficient and particles walking in the channelwere studied. The results showed that β (BCC grid, about1.9)> β (the diagonal squaregrid, about1.5)> β (three-dimensional Voronoi grid, about0.75)(based on the minimumcapture mechanism).Deep bed filtration experiment was done using filtration column. The change of filtration coefficient and particles walking in the channel were also studied. The bestpercolation-filtration model was chosen by comparing the result from experiment andsimulation.The study result showed that percolation-filtration model under three-dimensionalVoronoi grid was the best. In the actual filtration unit operation, this model could beused to guide the practice. People could choose the medium with better effect for onekind wastewater in order to gain the effluent water with better quality.