The Study Of Deep Bed Filtration Process Based On Percolation Theory

Deep bed filtration(DBF) represented by sand filtration is a traditional filtering operation in industry. Because of its simple structure, good filtering effect, low operating costs, it has widely application in drinking water treatment, wastewater treatment etc. In order to understand the filtration mechanism of DBF, thereby guiding the design and operation of DBF process, people have developed many DBF theories. They are mainly based on the research of the deposition for suspended particles in pore space of the filter media to establish macro empirical formula of the effluent turbidity, which has not revealed the microscopic process and essence of DBF.In the current study, aiming at the structure similarity between network and deep bed filter media and process similarity between cluster growth in percolation model and pore blockage of the filter media in DBF by suspended particles, a straining-dominant DBF model based on percolation theory was established. Subsequently, this model was conducted to validate and analysis with laboratory experiment, percolation theory, and numerical network simulation for DBF. Finally, two actual engineering application cases of this model have been proposed.As the current theories were flawed in the interpretation of the experimental data, and the percolation model was very similar to the DBF process. For staining-dominate DBF process, an equation described filtration coefficient(λ) related to pore size distribution(PSD) of filter media, colloidal particle size(rs) and finite cluster size distribution ns(p) was established based on percolation theory analysis. In consideration of the cluster size distribution ns(p) is unknown for large cluster, the statistical behavior of ns(p) for site percolation and bond percolation at different lattices and dimensions was investigated. An equation to approximate ns(p) was established: log[ns(p)]=a(p)·s+b(p,d) ·logs+c(p,d,z). Moreover, using finite-size scaling method with nonuniversal metric factor, the relationship about the coefficients of the equation related to occupied ratio p, lattice dimension and coordination number was investigated, and some interesting scaling behavior were found. With the substitution of ns(p) to the equation about filtration coefficient, the percolation filtration model described filtration coefficient related to PSD and rs was obtain, λ=K?(1-fl*)β. Based on attentively analyzing the structure filtration cluster, another equation(filtration cluster equation) for the normalized effluent concentration(Ce/C0) calculation was obtained. For PSD is a key microscopic parameter, the sensitivity studies of two equations indicated that the two parameters μ and σ in PSD significantly influence the power law exponent fitting and Ce/C0 calculation. For the power law formula, increasing PSD parameter μ will decreases exponent β whereas the increase in PSD parameter σ will increased exponent β.For the filtration cluster equation, An increasing μ results in increased Ce/C0 for same rs, whereas an increasing σ leads to reduced Ce/C0 for same rs.For model validation, a staining-dominate deep bed filtration small scale experiment was established with injection of various monodisperse colloidal particle suspensions into porous media consisted of packing glass bead with monitored inlet and breakthrough particle concentrations. Three methods were used to estimate the PSD from packing glass granules; the methods were, Monte Carlo procedure with Latin-Hypercube Sampling based on Descartes ’theorem, closed packing circle method, and parallel tube model. The obtain PSD and current DBF theory such as the classical filtration theory, parallel tube model(PTM) theory were applied in analyzing the experimental data, the results showed that the normalized effluent particle concentration predicted with these theory were consistent with the experimental values, but the average distance between two chambers is much larger than the average pore size and packed particles size, which was inconsistent with the actual situation. By the way, the normalized effluent particle concentration predicted with network simulation was also not agreed with the experimental data. The experimental data and the reference data are used for power law formula and filtration cluster equation validation, the results showed that Ce/C0 predicted from equations were consistent with the experimental data and the reference data.To further verify the percolation filtration model, and investigate the role and mechanism of microscopic parameters played in DBF, The numerical simulation model of staining-dominate DBF process was established to study the effects of simulation parameters such as lattice type, lattice coordination number z, PSD and particle capture scheme to seek the optimal simulation conditions. It was found that the simulation Ce/C0 for various rs was agreed the power law formula. The exponent and Ce/C0 of the minimum capture scheme should be larger than that of maximum capture scheme on the same lattice with same PSD. With the same PSD parameters, Ce/C0 and exponents increase as the coordination number z increases; this trend is particularly more significant in minimum capture scheme. The change of PSD parameters results in the change of flux and weight of path type linked to node, thereby affecting the numerical simulation results of staining-dominate DBF process on networks. Through estimation the particle total capture probability for different 2D and 3D networks with same PSD, it’s found that if different networks have the same total capture probability, then the simulated Ce/C0 of them are basically the same; on the contrary, the very different total capture probabilit ies leads simulated Ce/C0 varies greatly on different lattices. The simulation results agree with the experimental data if proper simulated conditions are used. For the experimental conditions of this paper, a variety of 2D and 3D network simulation are investigated. It was found the simulated Ce/C0 and exponents were consistent with the experimental data when the simulation was performed under maximum capture scheme, BCC lattice(z=8), and the PSD estimated by PTM methods. The exponents for the simulation(0.878±0.031) was consistent with the experimental value(0.872±0.2780) in the range of permitted errors.Finally, the percolation filtration model is used to predict the effect of filter media in the actual process for filter media choosing. For a given filter media and suspended particle size distribution, a method for estimation the PSD of porous media based on the percolation filtration model and experimental data. Moreover, the result also compared with PSD parameters estimated by other methods and other data in the literature. In order to validate this method, the obtained PSD parameters were applied in the simulation of straining-dominant filtration, the simulation result was consistent with the experimental data. It’s indicated that this method was relatively accurate and effect ive. The particle size distribution function for the effluent polydisperse particle in staining-dominate DBF process can be estimated from power law formula. This method was validated with numerical simulation of staining-dominate DBF. Therefore, exclusion size and efficiency of the suspended particle for filter media can be obtained to determine whether the grading of filter media is reasonable.In this paper, aiming at the defects of current theories, finite cluster size distribution ns(p) was described and applied to the study of DBF process. A staining-dominate DBF model based on percolation was established and verified with experiment and numerical simulation, and the role and mechanism of microscopic parameters played in DBF was also investigated. This study reveals the microscopic process of deep bed filtration and results can be applied in the actual filtration. It also has great theoretical and practical significance for understanding essence of filtration and guiding optimization of DBF operation.