RADIAL FLOW HOLLOW FIBERREVERSE OSMOSIS: EXPERIMENTS AND THEORY

The performance of a hollow fiber reverse osmosis system is studied both theoretically and experimentally. Experiments were carried out for applied pressure ranging from 200 to 400 psig, feed rates varying from 75 to 380 cc/sec and for feed concentrations up to 34,000 ppm of sodium chloride.

A mathematical model is proposed to predict productivity, ?, and product concentration, θ_p. The model involves solving membrane transport equations simultaneously with the hydrodynamic equations. The solubility-diffusion-imperfection, or pore diffusion model, is used to describe solute and solvent transport across the membrane. The axial gradients of shell side concentration, neglected in previous investigations, are taken into account. The differential equations are solved numerically by the 4th Order Runge-Kutta method.

Predicted values of ? and θ_p agree within 8% and 17% respectively, with experimental data over the entire range of operating conditions. However, membrane transport coefficients were found to be concentration dependent.

An approximate analysis shows that the concentration polarization is negligible in present day hollow fiber systems.     

Transport coefficients of asymmetric cellulose acetate membranes

Using the linear relations of thermodynamics of irreversible processes, the transport coefficients l_p,l_π,l_πp and σ were measured for an asymmetric cellulose acetate membrane with NaCl, Na₂SO₄, CaCl₂, NaF, and saccharose over the concentration range (0–0.5 mol/l or l mol/l) at 20°C or 25°C. The experimental findings manifest a strong dependence of the three transport coefficients l_p,l_π, and linπp on solute concentration. This strong dependence on concentration can be attributed to a concentration gradient within the porous sublayer of the asymmetric membrane. Thereby, it is shown that the transport coefficients of an asymmetric membrane depend on the solute concentration on both sides of the membrane instead of the mean concentration c?_s, as would be the case for a homogeneous membrane.     

RADIAL FLOW HOLLOW FIBERREVERSE OSMOSIS: EXPERIMENTS AND THEORY

The performance of a hollow fiber reverse osmosis system is studied both theoretically and experimentally. Experiments were carried out for applied pressure ranging from 200 to 400 psig, feed rates varying from 75 to 380 cc/sec and for feed concentrations up to 34,000 ppm of sodium chloride.

A mathematical model is proposed to predict productivity, ϕ, and product concentration, θ_p. The model involves solving membrane transport equations simultaneously with the hydrodynamic equations. The solubility-diffusion-imperfection, or pore diffusion model, is used to describe solute and solvent transport across the membrane. The axial gradients of shell side concentration, neglected in previous investigations, are taken into account. The differential equations are solved numerically by the 4th Order Runge-Kutta method.

Predicted values of ϕ and θ_p agree within 8% and 17% respectively, with experimental data over the entire range of operating conditions. However, membrane transport coefficients were found to be concentration dependent.

An approximate analysis shows that the concentration polarization is negligible in present day hollow fiber systems.     

Modeling of facilitated transport of Cr(III) using (RNH3+HSO4−) ionic liquid and pseudo-emulsion hollow fiber strip dispersion (PEHFSD) technology

The permeation of chromium (III) using PEHFSD technology and the ionic liquid (RNH₃⁺HSO₄^?), formed by reaction of the primary amine PRIMENE JMT and sulphuric acid, dissolved in n-decane as mobile carrier has been investigated. The alkaline feed solution containing Cr(III) was passed through the tube side, and pseudo-emulsions of the ionic liquid + n-decane + n-decanol and sulphuric acid were passed through the shell side in counter-current mode and using a single hollow fiber module for extraction and stripping. In this advanced membrane technology, the aqueous acidic strip solution is dispersed in the organic membrane solution in a tank with an impeller stirrer to form a strip dispersion. The pseudo-emulsion phase is circulated from the tank to the membrane module to provide a constant supply of the organic solution to the membrane micropores. Factors affecting chromium permeability, such as hydrodynamic conditions, carrier concentration in the organic phase, metal and NaOH concentrations in the feed phase, have been analyzed. A model is reported describing the transport mechanism, whereas the experimental data are quantitatively explained by mathematical equations describing the rate of transport. Different rate-controlling processes take place as long as the metal transport occurs.     

Modeling of the variations of permeate flux,concentration polarization,and solute rejection in nanofiltration system

A numerical model is presented and experimentally validated for predicting the local concentration polarization and the related separation performance of nanofiltration (NF) system. The model combines computational fluid dynamics for describing the transport phenomena in NF channel, with Spiegler-Kedem-Katchalsky model for considering the permeation properties through NF membrane. Particular attention is given to the modeling of spatially varied solute rejection and solute transport through membrane, representing essential distinctions from the modeling of reverse osmosis (RO) membrane. Also, an experimental-numerical framework is proposed to determine model parameters related to solute transport, including reflection coefficient and solute permeability as functions of feed solute concentration. The usefulness of this model is highlighted by predicting concentration polarization under different conditions related to operations, membrane systems (NF vs. RO), and solute types (NaCl vs. MgSO₄). Also, the contributions by convection and diffusion to solute transport are clarified, benefiting by the modeling of solute transport. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1076–1087, 2019     

Dependence of extraction equilibrium of monocarboxylic acid from aqueous solutions on the relative basicity of extractant

This paper describes monocarboxylic acid extraction from aqueous solution experiments, using five types of mixed solvents and 12 monocarboxylic acids. From the results of these experiments, a new mathematical model, including a new definition of extractant's basicity (pK_a,BS), was developed and validated. Trioctylamine (TOA)/1-octanol, TOA/methyl iso-butyl ketone (MIBK), TOA/tetrachloromethane (CCl₄), trialkylphosphine oxide (TRPO) /1-octanol and TRPO/ kerosene, were used as the extractant, and formic, acetic, propionic, butyric, valeric, caproic, monochloroacetic, dichloroacetic, trichloroacetic, glycolic, glyoxylic, and lactic acids, were used as the solutes extracted. The relative basicity of the extractant to the solute extracted (pK_a,BS) was measured in different extractant concentrations. The experimental result confirms the mathematic model to predict the extraction equilibrium more accurately. pK_a,BS can represent the complicated solvating power of the dilute to the association compound, and depends on the extractant concentration and the type of extractant, diluent and solute.     

Simulation of micro- and macro-transport in a packed bed of porous adsorbents by lattice Boltzmann methods

In this study we report 3D simulation of concentration profiles in a fixed bed packed with spherical porous adsorbents using lattice Boltzmann methods (LBMs). The lattice models have been developed to investigate evolution of concentration profiles due to inter- and intra-particle mass transport in an adsorber having small tube-to-sphere diameter (d_t/d_p) ratios. The multi-scaling feature of LBMs permits full 3D simulation of concentration profiles both in the bed voids and within the pores of the adsorbents without using any empirical correlations or without making 1D or 2D approximations that are usually made in traditional numerical methods. The model simulation is carried out for varying packing arrangements and small to large pore diffusivities. The simulation results show significant concentration gradients for small pore diffusivities and large particle size, which must be considered in predicting breakthrough and adsorption times for a tubular adsorber having d_t/d_p<10. The model predicted breakthrough curves are validated with the experimental data obtained by tomography technique in a tubular adsorber packed with zeolite particles.     

Selective enantioseparation of levocetirizine via a hollow fiber supported liquid membrane and mass transfer prediction

The enantioselective separation of levocetirizine via a hollow fiber supported liquid membrane was examined. O,O′-dibenzoyl-(2R,3R)-tartaric acid ((?)-DBTA) diluted in 1-decanol was used as a chiral selector extractant. The influence of concentrations of feed and stripping phases, and extractant concentration in the membrane phase, was also investigated. A mathematical model focusing on the extraction side of the liquid membrane system was presented to predict the concentration of levocetirizine at different times. The extraction and recovery of levocetirizine from feed phase were 75.00% and 72.00%, respectively. The mass transfer coefficients at aqueous feed boundary layer (k _f ) and the organic liquid membrane phase (k _m ) were calculated as 2.41×10² and 1.89×10² cm/s, respectively. The validity of the developed model was evaluated through a comparison with experimental data, and good agreement was obtained.     

Reverse osmosis separation of amino acids in aqueous solutions using porous cellulose acetate membranes

Polar and steric effects together govern the reverse osmosis separation of amino acids in single-solute aqueous solution systems. The solute transport parameter for the completely ionized aliphatic amino acids (with no additional polar groups other than one ? NH₂ and one ? COOH) in the pK₁ range of 4.03 to 1.71 can be represented as a function of pK₁ and the steric parameter ΣE_s. The latter parameter has a relatively greater influence with respect to the separation of zwitter ions. The effect of the polar parameter pK₁ on solute separation increases with increase in the concentration of the ionic species R⁺ (or decrease in the concentration of the ionic species R^?) in the feed solution. The effect of the presence of additional polar groups in the amino acid molecule is to increase its basicity. Experiments with p-aminobenzoic acid solutions indicate that the undissociated acid is preferentially sorbed at the membrane–solution interface. With respect to both aliphatic and aromatic amino acid ions, solute separation is in the order R^? > R^± > R⁺ for the cellulose acetate membrane material studied.     

Modeling and Simulation of Rotating Disk-Membrane Module in Ultrafiltration of Bovine Serum Albumin

A dynamic mass transfer model, coupled with transient back transport flux for a Rotating Disk-Membrane (RDM) module has been developed in the present study. The simulation algorithm is capable of predicting the permeate flux (J), membrane surface concentration (c _m ), and permeate concentration (c _p ) under different parametric conditions of transmembrane pressure (TMP), feed concentration (c ₀), stirrer speed (Ω₂), and membrane speed of rotation (Ω₁). The key feature of the proposed model is the analytical solution of the governing component balance equation. Additionally, the well-known osmotic pressure model and the Spiengler-Kedem black box model were used to describe the solvent transport through membrane. The proposed model was validated with the experimental results obtained in ultrafiltration of bovine serum albumin (BSA)/water solution conducted in a standard RDM module, fitted with polyethersulphone (PES) membrane of 30 kDa molecular weight cut-off (MWCO). The maximum absolute deviation of the model predictions with respect to the experimental results was observed to be well within 5%.     

Modeling of CO2 mass transport across a hollow fiber membrane reactor filled with immobilized enzyme

The enzyme‐based contained liquid membrane reactor to capture CO₂ from the closed spaces is a very complicated process with large numbers of interdependent variables. A theoretical and experimental analysis of facilitated transport of CO₂ across a hollow fiber membrane reactor filled with immobilized carbonic anhydrase (CA) by nanocomposite hydrogel was presented. CO₂ concentration profiles in the feed gas phase and the membrane wall were achieved by numeric simulation. The effects of CO₂ concentration, CA concentration, and flow rate of feed gas on CO₂ removal performance were studied in detail, and the model solution agrees with the experimental data with a maximum deviation of up to 18.7%. Moreover, the effect of CO₂ concentration on the required membrane areas for the same CO₂ removal target (1 kg/day) was also investigated. This could provide real‐world data and scientific basis for future development toward a final efficient CO₂ removal device. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Kinetics of the recovery of Cd from highly concentrated aqueous solutions by non-dispersive solvent extraction

In this paper, the kinetics of the non-dispersive extraction and back-extraction of cadmium from high concentration aqueous solutions using D2EHPA as selective extractant are reported. Batch experiments were performed in order to analyse the influence of the initial Cd concentration in the feed, organic and back-extraction phases. The proposed kinetic model consists of a system of partial differential and algebraic equations describing the mass balances of Cd in the fluid phases of the hollow-fibre contactors and homogenisation tanks. The main hypothesis is that membrane mass transport controls the extraction kinetics. Two design parameters K_m, membrane mass transport coefficient, and K_eq, equilibrium parameter of the extraction reaction have been calculated from the correlation of the experimental results by the reported model. The comparison of experimental and simulated data confirmed the validity of the kinetic analysis.     

New liquid membrane technology for simultaneous extraction and stripping of copper(II) from wastewater

In this paper, a new liquid membrane technique, hollow fiber renewal liquid membrane (HFRLM), is presented, which is based on the surface renewal theory, and integrates the advantages of fiber membrane extraction, liquid film permeation and other liquid membrane processes. The results from the system of CuSO₄+D2EHPA in kerosene+HCl show that the HFRLM process is very stable. The liquid membrane is renewed constantly during the process, the direct contact of organic droplets and aqueous phase provides large mass transfer area. These effects can significantly reduce the mass transfer resistance in the lumen side. Then the mixture of feed phase and organic phase flowing through the lumen side gives a higher mass transfer rate than that of stripping phase and organic phase, because the aqueous layer diffusion of feed phase is the rate-controlling step. The overall mass transfer coefficient increases with increasing flow rates and D2EHPA concentration in the organic phase, and with decreasing initial copper concentration in the feed phase. The overall mass transfer coefficient also increases with increasing pH in the feed phase, and reaches a maximum value at pH of 4.44, then decreases. Also, there is a favorable w/o volume ratio of 20:1 to 30:1 for this process. Compared with hollow fiber supported liquid membrane and hollow fiber membrane extraction processes, HFRLM process has a high mass transfer rate. Mathematical model for the HFRLM process based on the surface renewal theory is developed. The calculated results are in good agreement with experimental results under the conditions studied.     

Some transport characteristics of aromatic polyamide membranes in reverse osmosis

The effects of solute concentration in the range of 0.0013 to 1.051 molality in the feed solution and operating pressure in the range of 100 to 900 psig on solute transport parameter D_AM/Kδ in reverse osmosis have been studied for a class of laboratory-made aromatic polyamide membranes and aqueous sodium chloride feed solutions. The results showed that D_AM/Kδ for NaCl increased both with increase in operating pressure and solute concentration in the concentrated boundary solution on the high-pressure side of the membrane. A general expression for D_AM/Kδ for NaCl including the effects of both the above operating variables is given. These results are different from the corresponding results obtained for cellulose acetate membranes.     

Ultrafiltration modeling of multiple solutes system for continuous cross-flow process

A mathematical model suitable for the multiple solutes system in continuous cross-flow ultrafiltration is developed. This model is based on mass balance analysis coupled with the filtration theory (osmotic pressure model, Kozeny-Carman equation), resistance-in-series model and gel polarization model. This model is characterized by the parameters R_m, P_m, K_b,K_bi and k_i. These parameters are estimated by using the Levenberg-Marquardt method coupled with the Gauss-Newton algorithm based on the experimental data obtained from the treatment of pretreated palm oil mill effluent (POME) as a feed in the pilot plant scale ultrafiltration system. The pretreated POME is composed of a ternary system with the solutes of carbohydrate constituents, crude protein and ammoniacal nitrogen. The simulation results show a good agreement with the experimental data. The proposed model is suitable for predicting the performance of multiple solutes in an ultrafiltration process. The concentration of each solute present is correlated with the COD value of the permeate stream.     

LIX984N为载体的中空纤维更新液膜中铜的传递过程

以LIX984N为载体,煤油为稀释剂,H2SO4为反萃剂,研究了中空纤维更新液膜过程中铜的传递行为。考察了两相压差、铜离子浓度、两相流速、操作方式以及膜丝有效长度等对传质过程的影响。结果表明:膜丝两侧的操作压差对传质过程几乎没有影响;随着料液相中溶质Cu(Ⅱ)浓度的增大传质通量增大,而反萃相中的Cu(Ⅱ)浓度对传质过程几乎没有影响;传质通量会随着壳程料液流速的增大而增大,但管程侧反萃相的流速对传质过程影响很小;逆流和并流两种操作方式对传质过程的影响可以忽略,而膜丝有效长度的增加会导致单位面积平均传质通量的下降。     

A Reaction Flux Model for Extraction of Cu(II) with LIX84I in HFSLM

Hollow fiber supported liquid membrane (HFSLM) is a favorable method to extract both valuable compounds and heavy metal pollutants such as chromium, copper, and nickel at a very low concentration. In this work, the extraction of Cu(II) by LIX84I dissolved in kerosene was theoretically and experimentally investigated. A model to estimate the percentage of extraction of copper ions from synthetic water considering the effect of reaction flux in membrane phase of the HFSLM system was studied. H₂SO₄ solution was used as the stripping solution. The facilitated transport mechanism of the chemical reaction at the feed-membrane interface was taken into account in the model equations. The percentage of copper ion extraction was plotted against its initial concentration in feed and also feed flow rate. Subsequently, the separation time and separation cycle were determined in accordance with the simulated values of copper ion concentration and the feed flow rate from the model. The modeled results were in good agreement with the experimental data at the average percentage of deviation about 2%.     

Separation of Liquid Solutions by Contained Liquid Membranes

Abstract

The technique of contained liquid membranes (CLM) for liquid solution separation is discussed. The CLM is obtained by confining the membrane liquid between two sets of microporous hollow fibers (MHF). The lumen of the hollow fiber carries the feed or the strip solution under proper phase pressure condition vis-a-vis the membrane phase. Various possible structural configurations of the CLM are illustrated with respect to the nature of microporous hollow fiber substrate, the feed solution and the liquid membrane. The contributions of different resistances to the solute transport rate are identified. Some basic experimental data obtained in small CLM permeators are presented for two systems with organic liquid membranes to illustrate how steady state separation is achieved after an initial unsteady period. The considerable advantages of the CLM structure over more traditional liquid membrane techniques such as supported liquid membrane (SLM) with respect to membrane stability, membrane regeneration and feed equilibration are pointed out.     

Transport of cobalt(II) through a hollow fiber supported liquid membrane containing di-(2-ethylhexyl) phosphoric acid (D2EHPA) as the carrier

This work presents experimental, modeling and simulation studies for Co²⁺ ion extraction using hollow fiber supported liquid membrane (HFSLM) operated in a recycling mode. Extractant di-(2-ethylhexyl) phosphoric acid (D2EHPA) diluted with kerosene has been used as the membrane phase. The Co²⁺ ion concentration in the aqueous feed phase was varied in the range of 1–3 mM. Also, D2EHPA concentration was varied in the range of 10–30% (v/v). A mass transfer model has been developed considering the complexation and de-complexation reactions to be fast and at equilibrium. Equations for extractant mass balance and counter-ion (H⁺) transport have also been incorporated in the model. Extraction equilibrium constant (K_ex) for cobalt–D2EHPA system has been estimated from equilibration experiments and found to be 3.48 × 10⁻⁶. It was observed that the model results are in good agreement with the experimental data when diffusivity of metal-complex (D_m) through the membrane phase is 1.5 × 10⁻¹⁰ m²/s. Feed phase pH and strip phase acidity had negligible effect on the extraction profiles of Co²⁺ ions. An increase in D2EHPA concentration increased extraction rates of Co²⁺ ions. The membrane phase diffusion step was found to be the controlling resistance to mass transfer.     

Specification of commercial reverse osmosis modules and predictability of their performance for water treatment applications

Techniques for specifying membranes in commercial modules and reverse osmosis systems involving such modules, and for predicting data on performance of the modules so specified are illustrated with particular reference to water treatment applications. Four commercial modules (Roga-4000, Westinghouse, Raypak and Du Pont-B9) were studied in. this work for such specification and prediction. Experimental reverse osmosis data using NaCl-H₂O feed solutions were used for obtaining data on membrane specifications. Equations of system analysis were used for prediction of data on module performance. Three sets of calculated data are reported for the operating pressure of 2758 kPa gauge (400 psig). The first set of data shows good agreement between calculated and experimental results on the performance of the modules with aqueous sucrose feed solutions. The second set of data shows the variations in solute separation and membrane productivity for each of the four- modules studied as functions of volumetric fraction product water recovery and membrane compaction for a 3000 ppm NaCl-H₂O feed solution. The third set of data shows the variations in solute separation as a function of solute transport parameter at different levels of mass transfer coefficient on the high pressure side of the membrane for very dilute aqueous feed solutions.