Temperature drop of feed liquid during pervaporation

Heat transfer during pervaporation through a membrane module of silicone-rubber microtubes was studied for ammonia/water and ethanol/water feeds. The temperature drops of the feed mixture were measured as a function of flow rate, concentration and permeate side pressure. A model calculation with a vapor-phase driving force was compared with the data. The vapor permeability of the permeate components needed in the model were independently measured using an original measurement method with a differential transformer. The present simple model for heat and mass transfer during pervaporation proved to be applicable to the theoretical calculation for a membrane module of pervaporation to be used as a heat-transfer unit.     

Effect of shell-side flows on the performance of hollow-fiber gas separation modules

A theoretical analysis of shell-side flow effects on the performance of hollow-fiber gas separation modules is presented. The theory uses Darcy’s law to relate fiber packing, pressure fields, and velocity fields within the shell. The resulting shell conservation equations are coupled to the lumen conservation equations through the permeation relationship. This two-dimensional (2-D) analysis quantifies the performance penalty associated with gas distribution across the fiber bundle at the shell inlet and outlet. Theoretical predictions for the production of nitrogen from air in a commercial shell-fed module are closer to experimental data than predictions obtained assuming one-dimensional (1-D) plug flow. Fluid flows primarily across fibers near the inlet and outlet ports, and along fibers between ports. Nitrogen composition increases along fluid streamlines, which leads to axial and radial concentration variations within the fiber bundle. Diffusional contributions to shell mass transfer are small for the modules considered here.     

Removal of volatile organic components (VOCs) from water by pervaporation: separation improvement by Dean vortices

Dense polydimethylsiloxane (PDMS) hollow-fibre membrane modules built in straight and coiled configurations were studied in pervaporation for volatile organic compounds (VOCs) removal. Two different aqueous organic mixtures, n-butanol–water and chloroform–water, were investigated to determine how the permeate fluxes are affected by the module geometry. Data with chloroform–water mixtures of 0.1 and 0.05 wt% chloroform revealed that, in the laminar regime, coiled modules show improved chloroform mass transfer compared to conventional modules where straight hollow-fibre membranes are aligned in parallel. The improvement factor increases with the Reynolds number to reach a value of 2.3 at N_Re=2000. In the conventional and helical designs, with a calculated diffusion coefficient, the results are lower than those given by the Lévêque equation and the mass transfer correlation previously found for water oxygenation respectively. With an apparent diffusion coefficient, these experimental values are consistent with these two equations.     

Numerical solution of nonlinear and non-isothermal general rate model of reactive liquid chromatography

Abstract

A nonlinear general rate model (GRM) of liquid chromatography is formulated to analyze the influence of temperature variations on the dynamics of multi-component mixtures in a thermally insulated liquid chromatographic reactor. The mathematical model is formed by a system of nonlinear convection–diffusion reaction partial differential equations (PDEs) coupled with nonlinear algebraic equations for reactions and isotherms. The model equations are solved numerically by applying a semi-discrete high-resolution finite volume scheme (HR-FVS). Several numerical case studies are conducted for two different types of reactions to demonstrate the influence of heat transfer on the retention time, separation, and reaction. It was found that the enthalpies of adsorption and reaction significantly influence the reactor performance. The ratio of density time heat capacity of solid and liquid phases significantly influences the magnitude and velocity of concentration and thermal waves. The results obtained could be very helpful for further developments in non-isothermal reactive chromatography and provide a deeper insight into the sensitivity of chromatographic reactor operating under non-isothermal conditions.     

Prediction of permeate flux during osmotic pressure-controlled electric field-enhanced cross-flow ultrafiltration

Electric field-enhanced cross-flow ultrafiltration has been carried out to separate protein, bovine serum albumin, from aqueous solution using a 30,000 molecular weight cutoff membrane. A theoretical model is developed to predict permeate flux under a laminar flow regime including the effects of external d.c. electric field and suction through the membrane for osmotic pressure-controlled ultrafiltration. The governing equations of the concentration profile in the developing mass transfer boundary layer in a rectangular channel are solved using a similarity solution method. The effect of d.c. electric field on the variation of membrane surface concentration and permeate flux along the length of the channel is quantified using this model. The expression of Sherwood number relation for estimation of mass transfer coefficient is derived. The analysis revealed that there is a significant effect of electric field on the mass transfer coefficient. A detailed parametric study has been carried out to observe the effect of feed concentration, electric field, cross-flow velocity, and pressure on the permeate flux. For 1 kg/m3 BSA solution, by applying a d.c. electric field of 1000 V/m, the permeate flux increases from 42 to 98 L/m2 h compared to that with zero electric field. The experimental results are successfully compared with the model predicted results.     

Pervaporation dehydration of ethanol–water mixtures with chitosan/hydroxyethylcellulose (CS/HEC) composite membranes: I. Effect of operating conditions

Composite hydrophilic pervaporation membranes were prepared from chitosan blended with hydroxyethylcellulose using cellulose acetate as a porous support. The membranes were tested for dehydration performance of ethanol–water mixtures of ethanol concentrations 70–95 wt.% in the laminar flow region, at temperatures 50–70°C and at permeate pressures of 3–30 mmHg. The composite membrane showed an improved dehydration performance compared with dense CS/HEC membrane developed earlier. The effects of operating conditions also revealed that pervaporation of low water content feed carried out at high feed flow rate and at low temperature and permeate pressure was an advantage.     

Reduction of concentration polarization in pervaporation using vibrating membrane module

A vibrating membrane module currently marketed for filtration applications was evaluated for the separation of volatile organic compounds (VOCs) from aqueous solutions by pervaporation. Preliminary screening experiments with three VOCs, three silicone membranes, and in the presence and absence of a surfactant were performed to determine if further consideration of the vibrating module for a field demonstration project was warranted. The primary process variables studied were vibrational amplitude and liquid flow rate. The vibrations greatly reduced concentration polarization in the system as inferred from an order of magnitude increase in the overall mass transport coefficient. Mass transfer coefficients for the vibrating module compared favorably with those for traditional spiral wound modules.     

Coupled pervaporation/mass spectrometry for investigating membrane mass transport phenomena

The integration of organophilic pervaporation into processes of varying feed concentration, such as bioconversions, chemical reactions, or analytical sample preparation, requires not only the understanding of mass transport phenomena across the membrane under steady-state conditions, but also the insight into the transient response of the pervaporation membrane to changes as they occur in practice. For this purpose, a laboratory-scale pervaporation unit was coupled to a mass spectrometer for on-line permeate analysis, maintaining the overall pervaporation operating conditions controllable independently, and without introducing any inert gases for sample transfer.The experimental set-up was employed for investigating the transport of aroma compounds across a POMS–PEI composite membrane, focusing in particular on the so-called “membrane conditioning”; the possible synergetic effect of ethanol on the flux of one model aroma compound, ethyl hexanoate; the application of the system proposed to the rapid screening of the effect of the hydrodynamic upstream conditions on the degree of concentration polarisation.The method proposed proved to be robust and flexible, not only allowing insights into transient mass transport phenomena otherwise not attainable, but also reducing experimental workload significantly when characterising the effect of varying operating conditions on the pervaporation performance.     

Impact of homogeneous–heterogeneous reactions on heat and mass transfer flow of Au–Eg and Ag–Eg Maxwell nanofluid past a horizontal stretched cylinder

The object of this study is to analyze the impact of heterogeneous and homogeneous reactions on the flow, heat and mass transfer analysis of Maxwell nanofluid of Tiwari–Das kind over a stretched cylinder by considering convective boundary condition and velocity slip. Ethylene glycol (Eg) is used as base fluid; while gold (Au) and silver (Ag) are taken as nanoparticles. The governing equations represent nanofluid momentum, and energy and mass are reduced to system of nonlinear ordinary differential equations by utilizing similarity transformation procedure and are numerically evaluated by using finite element method. The sway of several pertinent parameters on the sketches of velocity, temperature and concentration is plotted through graphs. In addition to that the values of rate of heat transfer and skin-friction coefficient are calculated and presented through tables. The values of skin-friction coefficient are intensified as the values of homogeneous–heterogeneous reaction parameters rises. The velocity and concentration scatterings are both declines as the strength of Maxwell parameter raises.

     

Mass transfer examination in electrodialysis using limiting current measurements

The impact of electrodialysis module characteristics on mass transfer was examined using the limiting current method. The current-voltage curves of different electrodialysis modules were measured and limiting currents were determined using the derivative method. The mass transfer coefficients were calculated and the parameters of their dependence on linear flow velocity were estimated. From these the impact of spacer thickness, spacer net type, membrane type, and module geometry were evaluated. It was found that the impact of spacer thickness was almost negligible within the examined range, but a decrease in the mass transfer coefficient could be expected in the case of thicker spacers. By contrast, the spacer net type and type of membrane were found to be very important parameters able to significantly influence the mass transfer. By modifying the module geometry, the mass transfer coefficient could also be altered and, only in this case, the exponential parameter of the dependence was changing. The parameters thus determined may be used to calculate the limiting current in a wide range of operational conditions and may help predict the performance of different electrodialysis module types.     

Modelling the effect of operating conditions on hydrodynamics and mass transfer in a Pd–Ag membrane module for H2 purification

In this work a novel modelling approach based on Computational Fluid Dynamics (CFD) for the prediction of the gas separation process in a Pd–Ag membrane module for H₂ purification is presented. With this approach, the pressure and velocity flow fields of the gas mixture and the species concentration distribution in the selected three-dimensional domain are simultaneously and numerically computed by solving the continuity, momentum and species transport equations, including a gas-through-gas diffusion term derived from the Stefan–Maxwell formulation. As a result, the H₂ permeation calculations depend on the local determination of the mass transfer resistances offered by the gas phase and by the membrane, which is modelled as a permeable surface of known characteristics. The applicability of the model to properly predict the separation process under a wide range of pressure, feed flow rate, temperature and gas mixtures composition is assessed through a strict comparison with experimental data. The influence of inhibitor species on the module performance, that is obtained by implementing in the CFD model a suitable literature correlation, is also discussed.     

Gas dynamics in channels of a gas-feed direct methanol fuel cell: exact solutions

The gas dynamics in channels on both sides of a gas-feed direct methanol fuel cell (DFMC) are considered. The basic equations for the flow velocity and density are derived, taking into account the mass and momentum transfer through the channel/backing layer interface. For the practical case of small inlet velocities the analog of the Bernoulli equation is formulated and the exact solution of nonlinear gas dynamics equations is obtained. It is shown that the flow in both the cathode and anode channels is incompressible (its density is constant) and electrochemical reactions affect only the flow velocity v. Simple formulae for v as a function of local current density and effective water drag coefficient are derived.     

Finite element analysis as a tool for crossflow membrane filter simulation

Finite element analysis (FEA) is a very powerful tool in analyzing many engineering problems. In this study, FEA was used to simulate the development of concentration polarization in ultrafiltration of protein solutions. A miniature crossflow membrane filter was developed to verify the FEA models. Polysulfone membrane disks (47 mm) were used in this study. Bovine serum albumin (BSA) solutions of different concentrations were pumped across the membrane flow channel. The crossflow velocity of the feed solution was carefully controlled at the laminar region. With the flow velocities within the flow channel estimated by a perturbation solution, the protein concentration on the membrane surface and the mass transfer coefficient were accurately predicted by FEA. This simulation method may provide a useful tool in engineering analysis and design of a membrane filtration process.     

A study of heat and mass transfer of Non-Newtonian fluid with surface chemical reaction

Considering the significance of non-Newtonian fluid usage in manufacturing such as molten plastics, polymeric materials, pulps, and so on, significant efforts have been made to investigate the phenomenon of non-Newtonian fluids. In this article the influences of heat and mass transfer on non-Newtonian Walter's B fluid flow over uppermost catalytic surface of a paraboloid is encountered. An elasticity of the fluid layer is considered in the freestream together with heat source/sink and has the tendency to cause heat flow in the fluid saturated domain. The flow problem of two-dimensional Walter's B fluid is represented using Law of conservation of mass, momentum, heat, and concentration along with thermal and solutal chemical reactive boundary conditions. The governing equations are non-linear partial differential equation and are non-dimensionalized by employing stream function and similarity transformation. The final dimensionless equations yielded are coupled non-linear ordinary differential equations. Furthermore, shooting technique along with RK-4th order method is used to get the numerical results. Graphs and tables are modeled by using MATLAB software to check the effects of Walter's B parameter, Chemical reaction parameter and Thickness parameter on temperature, velocity, and concentration profiles. Tabular analysis shows the results of some physical parameters like skin friction coefficient, Nusselt number and Sherwood number due to the variation of Walter's B parameter, thickness parameter and chemical reactive parameter.     

On the mechanism of separation of ethanol/water mixtures by pervaporation II. Experimental concentration profiles

Ethanol—water concentration profiles in cellulose acetate membranes were measured under steady-state pervaporation conditions. Knowledge of these profiles leads to a better understanding of the diffusion process during pervaporation. The concentration profiles were determined by a film-stack method, using three to six layers. It is shown that permeation of ethanol—water mixtures proceeds in a coupled way and that crossterm diffusion coefficients need to be considered. Furthermore, the occurrence of sorption resistances at the feed/membrane interface can be established from these experiments.     

Numerical approximation of a nonisothermal two-dimensional general rate model of reactive liquid chromatography

A nonlinear and nonisothermal two-dimensional general rate model is formulated and approximated numerically to allow quantitatively analyzing the effects of temperature variations on the separations and reactions in liquid chromatographic reactors of cylindrical geometry. The model equations form a nonlinear system of convection-diffusion-reaction partial differential equations coupled with algebraic equations for isotherms and reactions. A semidiscrete high-resolution finite volume method is modified to approximate the system of partial differential equations. The coupling between the thermal waves and concentration fronts is demonstrated through numerical simulations, and important parameters are pointed out that influence the reactor performance. To evaluate the precision of the model predictions, consistency checks are successfully carried out proving the accuracy of the predictions. The results allow to quantify the influence of thermal effects on the performance of the fixed beds for different typical values of enthalpies of adsorption and reaction and axial and radial Peclet numbers for mass and heat transfer. Furthermore, they provide useful insight into the sensitivity of nonisothermal chromatographic reactor operation.     

The effect of shell side hydrodynamics on the performance of axial flow hollow fibre modules

Fluid flow and mass transfer experiments have been performed on axial flow hollow fibre modules of varying packing density (32 to 76%). Shell-side pressure drop was found to be proportional to (flowrate)ⁿ, where n varied from about 1.1 at high packing density to 1.5 at low packing density, for shellside Reynolds numbers < 350. Assuming an Ergun-type pressure drop relationship it was found that for packing densities < about 50% the inertial (turbulent) losses exceeded the viscous (laminar) losses. Inspection of cross-sections taken from the middle of modules revealed non-uniform fibre packing with regions of high and low packing density. The cross-sections also change along the length of the module. It is inferred that, in addition to axial flow along fibres, there is also a degree of stream splitting which provides transverse flow across fibres as fluid continuously seeks preferential paths through regions of lower packing density. The presence of transverse flow would explain the higher than expected velocity exponent. Mass transfer experiments involving the removal of oxygen from water flowing through the shell to a sweep gas in the fibre lumens produced higher than expected shell-side mass transfer coefficients. The results are correlated within ± 15% by Sh = (0.53 − 0.58φ)Re^0.53Sc^0.33. The exponent on Re is consistent with entry region conditions, caused by repeated stream splitting and transverse flow. Compared with mass transfer predicted for axial flow through a uniformly packed shell the experimental results are up to 2× higher, with the most significant enhancement at the lower packing densities. The implication of this work is that module design requires a more sophisticated approach than the traditional assumption of laminar flow through parallel axial ducts.     

Use of axial membrane vibrations to enhance mass transfer in a hollow tube oxygenator

Membrane-oxygenator performance is limited by the mass-transfer resistance on the blood side. The most successful techniques thus far for enhancing oxygenator performance have employed liquid-side pressure pulsations. However, this technique is limited since it causes the least relative motion near the membrane. In this study we explore the use of axial vibrations of a membrane tube bundle to increase oxygen transfer to the intralumenal liquid flow. An analytical solution is first developed for the hydrodynamics of laminar flow through a sinusoidally vibrated straight cylindrical tube. This indicates that the effect of the tube vibrations is characterized by a dimensionless velocity and frequency. A novel oxygenator is designed that permits vibrating a parallel membrane hollow tube bundle without directly pulsing the intralumenal liquid flow. An embodiment of this design employing 41 silicone rubber tubes is used to study the oxygenation of water. A tuned response is observed in that the maximum enhancement in mass transfer for a fixed dimensionless vibration velocity occurs at a specific dimensionless frequency. These experiments demonstrate that axial membrane vibrations can increase the mass-transfer coefficient by at least a factor of 2.65. Even greater enhancement may be possible for systems characterized by larger Schmidt or Graetz numbers for which diffusive mass transfer is more limiting. Employing membrane vibrations may offer the additional advantage of minimizing fouling in blood oxygenator as well as other applications.     

The effect of ion-conducting spacers on mass transfer — numerical analysis and concentration field visualization by means of laser interferometry

Mathematical model is developed for the study of mass transfer processes under the laminar stationary flow in the channels of electromembrane system formed by alternating cation- and anion-exchange membranes at whose surfaces the ion-conducting spacers are fixed. The results of calculations are given of velocity and concentration fields, of current density distribution along the channel length for some values of Reynolds number and the values of the applied voltage. The comparison is made between the calculated mass transfer characteristics and the experimental data obtained by means of laser interferometry.     

Response surface modelling and optimization in pervaporation

Both the conventional method of experimentation, in which one of factors is varied maintaining the other factors fixed at constant levels and the statistically designed experimental method, in which all factors are varied simultaneously are carried out for organic removal from water by pervaporation. Binary acetonitrile–water mixtures are considered. The effects of the operating parameters on the pervaporation performance of the membrane system have been investigated. The overall mass transfer coefficients have been determined for different conditions of feed temperature and initial organic concentration. In addition, the activation energy associated to the permeation process has been determined and discussed for each feed organic mixture. Statistical experimental design and response surface methodology, RSM, have been applied to optimize the operational conditions of pervaporation process in order to maximize the output responses, which are permeate flux ratio and concentration of organic in permeate. The input variables employed for experimental design were the feed temperature, initial concentration of organic in feed and operational downstream pressure. Based on the design of experiment the quadratic response surface models have been developed to link the output responses with the input variables via mathematical relationships. The constructed response models have been tested using the analysis of variance and the canonical analysis. The obtained optimal point by means of Monte Carlo simulation method and desirability function corresponds to a feed temperature of 57.69 °C, a feed acetonitrile concentration of 6.96 wt% and a downstream pressure of 28.95 kPa. The maximal values of the permeate flux ratio and the concentration of organic in permeate obtained under optimal process conditions have been confirmed experimentally.