Simulation Of The Separation Process Of Polymeric Ultrafiltration And Nanofiltration Membrane

The lack of freshwater resources has become a worldwide problem. Membrane separation technology has drawn universal attention because of its outstanding advantages of no-phase transformation, no secondary pollution and high separation efficiency. However, during the process of membrane separation, many drawbacks including the adsorption, pores blocking, concentration polarization and cake layer formation of colloids, particles or solute macromolecules lead to the decline of the flow flux and separation efficiency, which severely restricts the wide application of membrane technology. In this paper, a mathematical model of fouling during the process of ultrafiltration is established and the quantitative analysis of the fouling process is carried out. Then the ion rejection of the nanofiltration process is studied and some regularities of the membrane separation process are proposed.Based on the membrane fouling mechanism and the continuity equation, the mathematical model of the membrane fouling process of the surface active layer is constructed according to Darcy’s law, convection-diffusion equation and dynamic adsorption equation. Then the relationship among permeability and particle diameter, concentration, cake layer porosity, deposition, membrane initial porosity is obtained. The evolution characteristics of the flow flux in the membrane thickness direction are obtained by means of finite element simulation, and the reason why the flow flux decreases is analyzed, then the influences of the properties of feeding solution and ultrafiltration membrane on the flow flux are revealed. The conclusions are as follows: The increase of deposition and the decrease of cake layer porosity are essential reasons for the flow flux decrease. The fouling is more serious at the upper part than the lower part, which results in the permeability changing along the thickness direction of the membrane. The pressure gradient increases at the upper part of the membrane, but decreases at the lower part of the membrane with the increase of filtration time. The higher the concentration of solution and smaller of particle size are, the more serious the membrane fouling is. The greater the adsorption rate and smaller desorption rate are, the more serious the membrane fouling is.Due to fluid shear stress on the membrane surface, the permeability changes in the channel length direction for cross-flow ultrafiltration, so the analysis is more complex than dead-end ultrafiltration. In the upper layer of the membrane, the free fluid space is introduced and described by the Navier-Stokes equations. The interface between the free space and the membrane is coupled using the continuity of the fluid flow field. Based on dead-end ultrafiltration fouling model, membrane fouling description is built up. Combined with the data from the literature, the calculation expression is established for the adsorption rate coefficient and the desorption rate coefficient which are difficult to measure by experiments. Then a complete model is established and verified. The transmembrane pressure, adsorption deposition and permeating flux under different inlet velocities along the channel are analyzed by means of finite element simulation. The regularities of permeability, pressure gradient and deposition along the thickness of the membrane are analyzed, and the following conclusions are obtained:The greater the inlet velocity of the fluid is, the greater the transmembrane pressure and the shear stress are, which lead to the smaller deposition and greater permeate flux. However, greater inlet velocity consumes more energy. In the actual production, appropriate inlet velocity should be selected according to the required treatment efficiency and cost requirements. The regularities of permeability, pressure gradient and deposition along the thickness of the membrane of cross-flow filtration are similar with dead-end filtration.Nanofiltration membrane is a kind of charged pressure-driven membrane. The separation of the inorganic salts is governed by not only the chemical potential, but also electric potential, so the separation mechanism is more complex. Nernst-Planck equation is adopted to describe ions migration in the membrane caused by diffusion, convection and electric field, and the differential equation of ions concentration gradient along the membrane pore axis is obtained. Membrane volumetric charge density is obtained by the Gouy-Chapman theory. Combining the electroneutral conditions inside the membrane and in the bulk solution, Donnan equilibrium model and steric effects, the boundary conditions of both the inlet and outlet of the membrane pores are solved. Then the distribution of ions in the membrane pore axis can be obtained by the differential equation and the boundary conditions. Since the filtrate concentration affects the solution of the differential equation, it is a coupled relationship between the filtrate concentration and differential equation which needs to seek re-iteration, until a converged solution is got. The coupling is realized using COMSOL Multiphysics software platform. The ion retentions of KC1solution and MgSO4solution are solved using NF-45membrane by finite element method, and the results are compared with experimental results from the literature to verify the reliability of the mathematical model and calculation method. With in-depth analysis of the simulation results, the following conclusions are obtained:The ion rejection increases with the increase of the permeate flux. For the electrolyte with low concentration solution, the ion rejection increases faster. Meanwhile, with the increase of electrolyte solution concentration, the ion rejection decreases. For different types of electrolyte solutions, the ion rejections decrease with the increase of cations diffusion coefficient and increase with the increase of ion hydration radius for the same anions of inorganic salts. The quantity of the volumetric charge density and polarity will affect the ion retention. For MgSO4solution, within a certain range of the volumetric charge density quantity, the average ion retention of electronegative membrane is greater than electropositive membrane and the minimum ion retention is observed for a negative near-30mol/m3and this result can be useful to design suitable membrane for a specific solution.