Modeling of volatile organic compounds removal from water by pervaporation process

Pervaporation is a membrane technology utilizing a dense non-porous homogeneous polymeric film as a selective separation barrier. In recent years, pervaporation using dense membranes has emerged as a promising remediation method for trace organic removal from dilute aqueous solutions. The mathematical model commonly used to determine liquid and polymer phase resistances is the resistance-in-series model. In most studies the concentration or pressure gradient is considered as the driving force. In the present study a model was developed based on resistance-in-series model considering the chemical potential gradient as the true driving force in which the total resistance to mass transfer is defined as the sum of the liquid, membrane and vapor resistance. The model was validated by the experimental data available in the literature for various organic solutions and different membranes including PDMS and composite membranes. The results obtained show that the liquid phase boundary layer plays a significant rule in overall mass transport for all cases under study and ignoring this contribution could lead to a significant error in design and scale-up applications. It was also shown that the flux of permeating component is unaffected by the downstream pressure at low pressures up to 10 mmHg which indicates that for such systems the operating condition can be economically designed based on a moderate vacuum at downstream side instead of using a full expensive vacuum system.

In this study a mathematical model was developed based on resistance-in-series using chemical potential as true driving force which takes into account the membrane phase as well as adjacent liquid boundary layer resistance. A simple expression was derived for overall driving force based on easily accessible bulk phase properties. The method of model parameter estimation was explained. The experimental data available in the literature for various organic solutions and different membranes including PDMS and a kind of composite membrane were used to identify rate controlling step in overall transport. The results obtained reveal that the liquid phase boundary layer plays a significant rule in overall mass transport for all cases under study and ignoring this contribution could lead to a significant error in design and scale-up applications. The interfacial concentrations at both sides of membrane interface were found using a thermodynamic model which justifies a faster permeation of some solutes such as toluene across the membrane is due to their higher solubilities. It was also shown that the flux of permeating component is unaffected by the downstream pressure at low pressures up to 10 mmHg which indicates for such systems the operating condition can be economically designed based on a moderate vacuum at downstream side instead of using a full expensive vacuum system. Nomenclature ai Ci kl kv K0 Lm Ni Rliq Rvap Rvmem Rt P activity of i in liquid (–) molar concentration of i in liquid (mol/m3) liquid phase mass transfer coefficient (mol2/h m2 J) vapor phase mass transfer coefficient (mol2/h m2 J) overall mass transfer coefficient (mol2/ h m 2 J) phase mass transfer coefficient (mol2/h m J) molar flux of i (mol/m2 h) liquid phase resistance (h m2 J/mol2) vapor phase resistance (h m J/mol2) membrane phase resistance (h m J/mol2) overall resistance (h m2 J/mol2) pressure (mmHg) pisat T xi xi* yi saturation pressure (mmHg) temperature (K) mole fraction of i in bulk liquid (–) mole fraction of i in liquid at membrane interface (–) mole fraction of i in vapor (–) Greek symbols mi,l mi,m mi,v gi fi chemical potential of i in liquid phase (J/mol) chemical potential of i in membrane phase (J/mol) chemical potential of i in vapor phase (J/mol) activity coefficient in liquid (–) volume fraction of i in membrane (–)