Modelling of cross‐flow microfiltration of dye‐loaded activated carbon in a ceramic tubular membrane module

Abstract

A hybrid process involving adsorption followed by microfiltration is a less energy-intensive alternative for treatment of textile effluent. Modelling of microfiltration of dye-loaded activated carbon in a tubular module is important for design and scale-up. In this work, a simple kinetic model for cake removal during microfiltration in a tubular module is derived from first principles.. Reactive black dye exhibits the highest flux decline rate among the four different dyes. Cake layer thickness is less than 1 % of the channel diameter for different operating conditions. The mathematical analysis is extended to predict the limiting pressure. Cake removal rate is in the range of 0.01–0.05 Pa^-1 · s^-1 for different dyes, lowest for reactive black and highest for reactive brown. The cake is thickest (14 μm) for reactive black, compared to other dyes at 104 kPa and 100 L/h cross-flow rate. Cake resistance of black dye is 1.5 times the membrane hydraulic resistance at a 50 L/h crossflow rate and 104 kPa, and it is the highest among all the dyes analyzed. Simulation shows that steady state permeate flux increases with Reynolds number at higher transmembrane pressure whereas it varies insignificantly at lower pressure. Attainment of steady state is delayed for a lower cake removal constant. For yellow dye, steady state is achieved at 15 min for k_r = 0.1 Pa^-1 · s^-1 and beyond 1 h for k_r = 0.1 Pa^-1 · s^-1. Cake compressibility has a stronger influence on limiting transmembrane pressure compared to cake removal rate at higher Reynolds numbers.