The Unsteady-State Modeling Of Crossflow Microfiltration Of Particle Suspension Using Ceramic Membrane

Microfiltration, the most widely used and economical technology in membrane processing, is an increasingly important technique for the separation and purify of particulate suspensions in engineering areas. It's been the hot issue for the research on simulation of cross-flow microfiltratin process, but the most of simulations were for steady-state, few for unsteady-state. In cross-flow microfiltration process, it is a significant characteristic that membrane flux decreases with time, so in this paper, theory and experimental studies on the unsteady-state process of cross-flow microfiltration of CaCO₃ suspension have been done to acquire the unsteady-state mathematical model which can be used in wide operation conditions.As J_o is a membrane flux of pure water and related to all structure characters of membrane, the rate of membrane flux decline J/J_o introduced in this paper imparts the possibility to solely analyze the membrane surface area for markedly reducing process analysis. Starting with the force balance for one particle near the membrane surface, two novel characteristic parameters Re_m and Eu_m have been deduced out by using dimensional analysis method, which are similar to traditional Reynolds number and Euler number in forms, but have special meanings for cross-flow microfiltration. Based on the separation mechanism of cross-flow microfiltration, the unsteady-state mathematic model has been established:—dJ/dt= K₁C₀J-K₂Eu_m^a Re_m^βThe mathematic representation of membrane flux with time can be obtained by the integral of the above equation:J=(k₂Eu_m^a Re_m^β/K₁C₀)＋(J₀-k₂Eu_m^a Re_m^β/K₁C₀)exp(-K₁C₀t)Theα-Al₂O₃ ceramic membrane microfilter with 19 channels was used to acquire data of membrane flux under different operating conditions. The undetermined parameters K₁ , K₂ were regressed by using the Marquardt program of FORTRAN 90, and the results showed that operating conditions had no effects on K₁ , K₂.The prediction data of the mathematic model can give good correspondence with the experimental data in a broad range of operating conditions as following:Particle size: 2≤d_p/d_m≤9 (0.4μ＜d_p＜1.8μm in this paper),Transmembrane pressure: 0.1 MPa＜△P＜0.2MPa,Cross-flow velocity: 1.4 m. s^-1＜v＜3.5 m. s^-1,Feed concentration: 0.65 kg. m^-3＜c＜1.2 kg. m^-3。The average absolute relative error is 4. 4％。...