Continuous Flow Stirred Cell Microfiltration of Ion Exchange Media to

ARTICLE pubs.acs.org/IECR

Continuous Flow Stirred Cell Microfiltration of Ion Exchange Media to Determine Mass Transfer Kinetics and Equilibrium Data Marijana M. Dragosavac, Richard G. Holdich,* and Goran T. Vladisavljevic Department of Chemical Engineering, Loughborough University, Leicestershire LE11 3TU, U.K. ABSTRACT: Sorption of copper ions from aqueous feed streams on to polystyrene divinylbenzene Dowex 50W-X8 resins was studied. The experimental work was performed in a continuous flow stirred cell that had a slotted (8 μm 400 μm) metal microfiltration membrane fitted to the bottom of the cell. The equilibrium parameters for a Langmuir isotherm (qm = 0.116 g g-1, b = 0.003 m3 g-1) were determined from both the batch and the continuous flow experiments, and good agreement between the two different approaches was obtained. Experiments were performed at constant pH (4.5) and ionic strength (0.2 M), using a background sodium nitrate matrix, at feed concentrations of copper up to 636 g m-3. The filtration flux was 582 L m-2 h-1. Increase of the NaNO3 decreased the amount of sorbed copper significantly. The effective diffusion coefficient of copper inside the resin was found to be 7 10-11 m2 s-1. The continuous flow stirred cell is shown to be an effective technique for both mass transfer kinetics as well as equilibrium data acquisition, combining both into a single step, and simplifying ion exchange analysis. Once determined, the design parameters can readily be used to model ion exchange contacting in well mixed and column operations.

’ INTRODUCTION Copper and other heavy metal ions are widely present in waste waters, and their disposal in the environment represents a threat since, if accumulated in humans or animals, it can induce severe health problems. The World Health Organization (WHO)1 recommends a maximal concentration of copper in drinking water of 1.5 g m-3. There are many conventional techniques for removal of metal ions from waste waters based on flotation,2 chemical precipitation,3 coprecipitation,4 reverse osmosis,5 nanofiltration,6 pertraction through liquid membranes,7 Donnan dialysis,8 electrodialysis,9 chemical sorption, biosorption,10 and ion exchange.1,11 However, the predominant techniques are precipitation and ion exchange/sorption. Conventional porous solids commonly used in sorption process, such as activated carbon, silica based materials, clay and fly ash have nonuniform pore structure and low sorption capacities with slow sorption kinetics and are difficult to regenerate. In addition, a wide range of biosorbents (peat,12 tea waste,13 orange peel,14 dehydrated wheat bran,15 soybean hulls,16 cotton boll,17 sawdust,18 marine red algae10) have recently been investigated as alternative sorbents for heavy metals, but they are usually not suitable for industrial applications because of low sorption capacities and slow kinetics. Ion exchange is particularly interesting for industrial applications because of the ability to tailor the ion exchange toward the specific requirement, which results in high selectivity. At the same time, the amount of waste sorbent for disposal is reduced, because the ion exchanger can be regenerated and reused. Ion exchange polymers, particularly ion exchange resins, are crosslinked polymers carrying fixed functional groups or sites.19 They are commonly prepared from styrene and different levels of the cross-linking agent divinylbenzene, but there are also phenolic and acrylic resins. The amount of cross-linking agent regulates the mechanical strength (higher amount of cross-linking agent leads to a higher mechanical strength), permeability, water r 2011 American Chemical Society

retention capacity (swelling), and total capacity of the resin. Various studies on removal of metal ions by ion exchange resins have been conducted. In many cases the Langmuir isotherm20 (eq 1) is successful in describing the sorption equilibrium capacity for copper sorption on different ion exchangers: qe ¼

qm bCeq 1 þ bCeq

ð1Þ

where qm is the maximum sorption capacity, which corresponds to the maximum amount of copper that can be sorbed and b is the Langmuir constant related to the energy of sorption which increases as the strength of sorption increases. Ion exchangers can be used in fixed bed columns,21 but they have to fulfill the requirement that pressure drop within the column is low so the beads used are usually large (greater than 100 μm). There is often a need for fine filtration before the column to ensure that solids from the feed stream will not deposit within the interstices of the resin particles which would lead to an increase in pressure drop. Holdich et al.22 reported that decreasing the ion exchanger bead size increased the ion exchanger utilization. However, if smaller particles are used in a column higher pressure occurs, and the use of columns results in high energy consumption and an increase in operating costs. On the other hand, fluidized bed columns23 allow operation with smaller beads and higher flow rates compared to fixed bed columns. Batch operation24 (ion exchanger and solution are simply mixed together and agitated) is rarely used in industrial processes, but is convenient for laboratory experiments because of the simplicity of the experimental apparatus. The main disadvantage of this batch process is that it cannot remove the ions completely and Received: August 12, 2010 Accepted: December 21, 2010 Revised: November 11, 2010 Published: January 18, 2011 2408

dx.doi.org/10.1021/ie101710e | Ind. Eng. Chem. Res. 2011, 50, 2408–2417

Industrial & Engineering Chemistry Research that the process itself is discontinuous and requires a phase separation process at the end of the process. In the laboratory, batch operation is used to determine the sorption isotherm, and in this work it is compared to a new technique to determine the isotherm based on continuous flow through a stirred cell. The new technique is scalable to process operation, where the stirred cell would, most likely, be replaced by a crossflow microfiltration flow loop with resin added. Ion exchange can also be performed in a continuous stirred tank reactor (CSTR). CSTRs are not often used in ion exchange processes because of potential problems caused by mixing and short circuiting. Nevertheless, their capability of continuous operation makes them interesting for studies especially when working with hazardous and nuclear wastes. To prevent ion exchanger from leaving the system, CSTR sorption has to be combined with particle separation. Ion-exchange particles can be either settled in settling tanks or filtered using membranes. Crossflow microfiltration-sorption (external loop) hybrid systems demand higher energy for operation, while the submerged membrane sorption hybrid system requires only a low suction pressure for filtrate removal, thus requiring lower energy for its operation. Microfiltration with conventional membranes25 has a potential problem that since the pore openings of conventional membranes are often an order of magnitude bigger than the filter rating, the pores can become blocked resulting in permeate flux decay. Slotted membranes do not rely on depth filtration mechanisms as is case with conventional membranes,26 and the membranes are less susceptible to surface fouling than track-etched membrane filters with circular pores.27 Submerged membranes have also been investigated because of their lower operation energy.28 Holdich et al.22 have previously investigated a submerged microfiltration membrane process in a continuous flow stirred cell for boron removal (“seeded microfiltration”), but operating at very low feed concentration. For ion exchange, several studies11,29,30 reported kinetic analyses of contact time results based on the application of kinetic, or pseudo-kinetic, modeling. However, such models require equilibrium constants and activity coefficients for metal ion, or yield pseudo-rate constants, specific to a single experiment. Rate parameters obtained from each experiment were different and therefore, the application of these kinetic models to generate designs is limited. More applicable models are based on a mass balance combined with diffusion controlled mass transfer. Film and pore diffusion are the two main mass transfer mechanisms.31 For systems with high feed concentration film diffusion is normally neglected and pore diffusion is the limiting mechanism. Often, in the literature pore diffusion models are based on a single effective diffusion coefficient in the solid phase,22 or different solid phase diffusivities such as the diffusion within the pores of the resin and the surface diffusion within the resin.32 However, it is not easy to separate the effects of the different solid phase diffusional resistances (pore and surface), and for all practical purposes a single effective diffusion coefficient in the solid phase may be sufficient for design. Previous work22 in a continuous flow stirred cell with submerged membrane involved removal of boron with the ion exchanger Purolite S-108 (N-glucamine type resin). Boron concentration in the experiments was low, and high flow rates were used. In this work Dowex 50W-X8 resin is investigated as a sorbent material for continuous copper removal in a continuous flow stirred cell with a submerged slotted pore MF membrane

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(“seeded MF”). This research aims at determining the equilibrium constants beside the mass transport properties (aqueous film coefficient and internal diffusion coefficient) just by using a continuous flow stirred cell; introducing a new technique to determine the isotherm data without the need for separate batch tests. The flow rate used was calculated to provide sufficient residence time to establish the equilibrium. The effect of initial solute concentration and concentration of sodium nitrate on copper removal was also investigated. To predict the behavior of the seeded MF process, a conventional mass transfer model was applied based on mass transfer resistance within the aqueous film surrounding the particles together with diffusional resistance within the particle. However, the analysis was coupled with a material balance to account for the continuous nature of the process. Kinetic Modeling of Copper Transfer. Mass transfer in seeded microfiltration is much faster compared with that obtained in fixed bed ion exchange columns,22 which makes it useful in laboratory experiments for estimating the mass transfer coefficient and intraparticle diffusivity. The following assumptions are made in modeling: isothermal operation, rapid chemical reaction of binding the copper to ion exchanger, sorption equilibrium described by the Langmuir isotherm, ideal mixing in the system with continuous flow, mass transfer of copper through external aqueous phase film by film diffusion and through pores represented by a single internal diffusion coefficient. The mass balance of copper for sorption in a well-mixed continuous flow stirred cell can be expressed as follows: V

dC dq ¼ FðCo - CÞ - m dt dt

ð2Þ

where V is the liquid volume in the cell, C is the copper concentration in the bulk solution at time t (both in the cell and at the exit), Co is the copper concentration in the feed stream, F is the volume flow rate of the feed solution, m is the total mass of resin in the cell, and is the average mass of adsorbed copper per unit mass of resin. can be obtained by integrating the local mass throughout the resin from r = 0 to r = R Z 3 R qðtÞ ¼ 3 qðr, tÞr 2 dr ð3Þ R 0 where R is the Sauter mean radius of the resin particles and r is the radial distance from the center of particle. Fick’s second law for diffusion of copper inside a spherical particle is given by: Dq 1 D Dq ¼ 2 Deff r 2 ð4Þ Dt r Dr Dr where Deff is the effective diffusion coefficient of copper inside the particle. The total mass of copper entering the solid phase per unit time is m

dq ¼ kAðC - Ce Þ dt

ð5Þ

where A is the total surface area of the resin particles, Ce is the equilibrium concentration of copper in the liquid phase at the interface, and k is the mass transfer coefficient in the liquid phase. According to the film theory31 k ¼ 2409

Dliq δ

ð6Þ

dx.doi.org/10.1021/ie101710e |Ind. Eng. Chem. Res. 2011, 50, 2408–2417

Industrial & Engineering Chemistry Research

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where Dliq is the diffusion coefficient of copper in the liquid phase and δ is the film thickness (distance over which liquid phase diffusion takes place). The Fr€ossling equation33 can be used to evaluate k, using Sherwood, Particle Reynolds and Schmidt dimensionless numbers: 0:33 Sh ¼ 2 þ 0:6Re0:5 slip Sc

Sh ¼

ð7Þ

νslip 2RF k2R μ Reslip ¼ Sc ¼ Dliq Dliq F μ

ð8Þ

where μ is the liquid dynamic viscosity, F is the liquid density, and vslip is the relative particle-liquid velocity (slip velocity). Harriott34 suggested that at the just suspended conditions, for example, at the minimum agitation conditions at which all particles attain complete suspension, the slip velocity is of the order of the terminal velocity.35 We have assumed in our modeling that vslip was equal to the terminal particle velocity, because of relatively low agitation speed in the cell. The concentration of copper in the liquid phase at the interface can be found from eq 1 by assuming that at the interface the liquid phase is in equilibrium with the surface layer of the solid phase: Ce ¼

qjr ¼ R bðqm - qjr ¼ R Þ

ð9Þ

The total surface area of the resin particles, A, can be expressed in the terms of the Sauter mean radius: A ¼

3m R Fs

ð10Þ

Therefore, the mass rate of copper entering the particle is given by: dq Dq 3 Dq ¼ AFs Deff ¼ mDeff m dt Dr R Dr r¼R

r¼R

and hence, eq 2 can be rewritten as:

dC 3 Dq ¼ FðCo - CÞ - mDeff V dt R Dr

ð11Þ r¼R

For solving the differential eq 11 the boundary conditions have to be specified. At the beginning of the process, there is no copper in the liquid phase inside the cell: qðt ¼ 0, 0 e r e RÞ ¼ 0

Cðt ¼ 0Þ ¼ 0

ð12Þ

The concentration gradient is zero in the center of the bead (r = 0): Dqðt g 0Þ ¼ 0 ð13Þ Dr r¼0

and for the full radius of the beads (r = R) the boundary condition is Dqðt g 0Þ k ¼ ðC - Ce Þ ð14Þ Dr Deff Fs r¼R

The system of eqs 4 and 11 subject to boundary conditions 12, 13, and 14 must be solved simultaneously in an equation solver capable of solving partial differential equations.

Figure 1. (a) Particle size distribution of Dowex 50W-X8 resin used in this work with different particle size (100-200 and 200-400 mesh). (b) Microscopic photographs of dry resins.

For this purpose, PDESOL (Numerica, Dallas, U.S.A.) was used in this work. Constants used in modeling are qm = 0.116 kg kg-1, b = 3 m3 kg-1, m = 10-3 kg, F = 1.3 10-7 m3 s-1, V = 0.14 10-3 m3, μ = 0.001 Pa s, Fs = 1443 kg m-3, F = 1000 kg m-3, and Dliq = 1.2 10-9 m2 s-1 (calculated using the Nernst equation).

’ MATERIALS AND METHODS Liquid Phase. All the chemicals used were of analytical grade, supplied by Sigma Aldrich, U.K. The solutions of copper ions were prepared by dissolving appropriate amounts of CuNO3)2 3 6H2O in deionized water. The copper concentration used in the feed solution was in the range between 19 and 636 g m-3. The ionic strength in the liquid phase was adjusted by NaNO3 and kept at 0.2 M, unless stated differently. The pH was kept constant at 4.5 ( 0.1 by adjustment using 0.4 M NaOH and was measured directly in the cell using a pH meter (PW9420 Philips, U.K.). The pH adjustment was needed only at the very beginning of the experiment, when the resin swapped from the hydrogen form to the sodium form because of the concentration of sodium nitrate used. This is a rapid process,36 and the time taken was neglected from subsequent kinetic modeling. Ion Exchange Resin. Two different sizes of ion-exchange resin beads Dowex 50W-X8 (100-200 and 200-400 mesh) were obtained from Sigma Aldrich. Dowex 50W-X8 is a strong acid cation polystyrene resin containing 8% divinylbenzene. The size distribution of Dowex resin particles was determined by a laser diffraction particle size analyzer (Malvern Mastersizer S, U.K.). The cumulative size distribution curves for both sizes of Dowex 50W-X8 particles are presented in Figure 1a while microscopic photographs of the resin particles are shown in Figure 1b. The particle size range of Dowex 50W-X8 particles with 100200 and 200-400 mesh was 101-679 and 34-517 μm, 2410



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Table 1. Content of Each Flask for Batch Experiments flask

V / m3

m / kg

Co / g m-3

Co,Na / g m-3

1

0.05

0.001

11300

3790

2

0.08

0.005

870

3760

3

0.08

0.005

430

3680

4

0.08

0.005

230

3670

5

0.08

0.005

120

3780

6

0.08

0.005

70

3680

7

0.08

0.005

35

3800

8 9

0.08 0.08

0.005 0.005

20 10

3650 3770

respectively. Probably, the diameters larger than those stated by the manufacturer are a consequence of the resin swelling. The Sauter mean radius of Dowex 50W-X8 particles with 100-200 and 200-400 mesh was 87 and 42 μm, respectively (3 independent samples were analyzed and a mean value is calculated). These Sauter mean radii were used in eqs 3, 8, 10, and 11 for the prediction of copper concentration in the effluent. Prior to each use the ion exchanger was soaked for about 1 h in deionized water to swell. Most of the water was then removed from the resin by decanting, and the resin was washed several times with 1 M HNO3 followed by washing with deionized water. The remaining amount of water was removed by placing the ion exchanger in a vacuum drier at 50 °C overnight and kept in a desiccator before use. In all experiments 1 g of resin (dry mass) was used. Analytical Procedure. The copper and sodium concentrations in the samples were determined using an Atomic Absorbance Spectrophotometer (AAS) (Spectra AA-200 Varian, U.K.) operating at a wavelength of 244.2 nm for copper and 330.2 nm for sodium. Calibration was performed before each experiment. The samples were analyzed automatically based on the calibration curve, and the mean value of 3 independent samples was used. Batch Sorption Experiments. The batch sorption experiments were carried out in a series of flasks containing different initial Cu (II) concentration in the liquid phase. In Table 1 the content of each flask is presented. In all the solutions the pH and ionic strength were kept constant. After equilibration (the flasks were left to shake for one month at the room temperature), the liquid phase was separated from the solid phase and analyzed. This represents the conventional approach to the determination of the sorption equilibrium isotherm. The equilibrium sorption capacity was calculated using the following mass balance equation: qe ¼

ðCoi - Ceq ÞV m

ð15Þ

where qe is the equilibrium sorption capacity, Coi and Ceq are the initial and final concentration of copper(II) in the liquid phase, respectively, V is the volume of the liquid phase, and m is the mass of dry resin used. A control experiment with copper(II) solution in the absence of any resin confirmed that there was no copper sorption onto the walls of a flask. Continuous Flow Experiments (Combined MF and Sorption or “seeded MF”). All continuous flow experiments were carried out at room temperature in a microfiltration cell (Figure 2) provided by Micropore Technologies Ltd., Loughborough, U.K. Fresh copper solution was continuously delivered to the cell from a feed tank by a peristaltic pump (Watson-Marlow Ltd., U.K.).

Figure 2. (a) Schematic diagram and geometry of seeded microfiltration system; (b) micrograph of the slotted pore membrane used in this work.

In all experiments the liquid phase flow rate was constant at 7.8 mL min-1 (1.3 10-7 m3 s-1). A two blade paddle stirrer attached to the laboratory power supply (Instek Laboratory DC, U.K.) provided agitation in the cell at a constant speed of 270 rpm. In all experiments the volume of the liquid phase in the cell was 140 mL. A slotted-pore metal membrane with an effective diameter of 3.2 cm was fitted to the bottom of the cell. The pore width and length were 8 and 400 μm, respectively. This pore width was fine enough to keep even the smallest resin particles in the cell. As shown in Figure 1, the smallest particle size for Dowex 50W-X8 200-400 was 34 μm. For the tests, the cell was filled with a pure buffer solution (0.2 M NaNO3) and fresh wetted resin was added to the cell. Before immersion in the buffer solution the tube from the feed tank was filled with the feed copper solution and clamped. The clamp on the tubing was released after starting the pump. At predetermined times 10 mL of effluent samples were collected and at the end of the experiment all samples were analyzed as previously described. In all experiments the pH of the liquid phase was maintained constant at 4.5, but this was needed only at the very beginning of the experiment. Figure 3 shows the copper concentrations in the effluent when the tube immersion depth was 10 mm in the absence of any resin in the cell and a CST model of mixing in the cell, showing that the system was well mixed and predictable.

’ RESULTS AND DISCUSSION Determination of the Equilibrium Parameters-Batch Experiments. Figure 4 shows the experimental results of the sorp-

tion of copper onto fresh resin at different concentrations of copper. The concentration of NaNO3 in all flasks was 0.2 M which ensured that the resin was converted into Naþ form and at the same time provided the ionic strength of ∼0.2 M during the experiment. The Langmuir isotherm (eq 1) was used to fit the experimental data. The equilibrium parameters obtained by fitting 2411



Figure 3. No ion-exchange resin in the cell. Inlet copper concentration Co = 78 g m-3, Flow rate F = 1.3 10-7 m3 s-1 and inlet tube is 10 mm from the liquid level in the cell.

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Figure 5. Graphical explanation for calculating the amount of adsorbed copper qe on the resin.

continuous flow stirred cell if resin is not present can be expressed as follows: Co F dt - CF dt ¼ V dC

ð16Þ

where CoF dt represents the mass of copper that enters the cell, CF dt is the mass of copper that leaves the cell, and V dC is the mass of copper accumulated in the cell (Co is inlet concentration, F is flow rate, and dt is time interval). If the resin is present in the cell (CST þ resin), then the mass balance for the continuous flow stirred cell is Co F dt - CIX F dt ¼ V dC þ AccIX

ð17Þ

CIXF dt is the mass of copper that leaves the cell and AccIX (= m(d)/(dt) see eq 2) is the mass of copper that enters the resin. Combining the eqs 16 and 17 the mass of copper that enters the resin is Figure 4. Langmuir isotherm for copper sorption on Dowex 50W-X8 determined by batch experiments. The inset represents the Langmuir isotherm at copper concentrations in the liquid phase below 100 g m-3.

are qm = 0.116 g g-1 and b = 0.003 m3 g-1. The maximal sorption capacity qm obtained in this work compares with the qm value stated by the manufacturer (0.154 g g-1) and reported by Awang37 (0.116 g g-1) and Sing37 (0.104 g g-1). The Langmuir constant b is very low as compared to 0.13 m3 g-1 reported by Awang37 and 0.245 m3 g-1 reported by Sing,38 but they used the resin in Hþ form at very low ionic strength (∼0 M), and this strongly influences the isotherm, as discussed later. A lower value indicates a lower affinity of copper for sorption. Determination of Equilibrium Constants-Continuous Flow Stirred Cell. The sorption equilibrium parameters can be also estimated from the experiments in the stirred cell with continuous flow of the liquid phase. Comparing two experiments, one with and one without ion exchanger, in the stirred cell it is possible to determine the amount of copper sorbed providing that the experimental time is long enough to ensure that equilibrium is reached. In the absence of the ion-exchange resin the concentration of copper in the effluent will be equal to that predicted by a continuous flow stirred tank model, validated in Figure 3. However, with ion exchange, or sorption, present in the cell the outlet concentration will be below that of the continuous flow stirred tank model. A mass balance for the

AccIX ¼ CF dt - CIX F dt

ð18Þ

On Figure 5 CF dt is the surface under the square marker curve and CIXF dt is the surface under the triangle marker curve. The difference in mass of copper that leaves the cell with and without the resin represents the amount of copper that is adsorbed on the resin (qe) at the equilibrium concentration Ce (i.e., the inlet concentration Co). On Figure 6 the amount of copper sorbed on the ion exchanger deduced by this method is compared with the conventional batch experiments for isotherm determination. The equilibrium values obtained in the continuous experiments give the same isotherm as the batch experiments, for both sizes of beads used. The only data point off the single isotherm curve is one obtained when the resin was in Hþ form (NaNO3 was not used, therefore the resin maintained the Hþ form) and the background ionic strength was much lower (∼0), which is consistent with the earlier discussion on literature values of the isotherm in Hþ form at low ionic strength, and the effect of this on mass transfer modeling will be investigated further later in the paper. Effect of Initial Copper Concentration. To study the effect of the initial copper concentration on Dowex 50W-X8 solutions were prepared in the range from 19 to 636 g m-3. Concentration of NaNO3 in all experiments was 0.2 M. The pH of the solutions was adjusted by adding a 0.4 M solution of NaOH, providing a constant pH of 4.5. The liquid flow rate was 7.8 mL min-1. 2412



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Figure 6. Comparison of the Langmuir isotherm obtained from the batch and the continuous experiments.

Figure 8. (a) Influence of the inlet copper concentration (20-89 g m-3) on the copper concentration in effluent - Big beads. (R = 87 μm) and mass transfer model eqs 2 to 14 (solid curves on figure). Flow rate F = 1.3 10-7 m3 s-1. (b) Influence of inlet copper concentration (180-636 g m-3) on copper concentration in effluent - Big beads (R = 87 μm) and mass transfer model eqs 2 to 14 (solid curves on figure). Flow rate F = 1.3 10-7 m3 s-1.

Figure 7. (a) Influence of the inlet copper concentration (21.3-98 g m-3) on the copper concentration in effluent - Small beads (R = 42 μm) and mass transfer model eqs 2 to 14 (solid curves on figure). Flow rate F = 1.3 10-7 m3 s-1. (b) Influence of the inlet copper concentration (180-625 g m-3) on the copper concentration in effluent Small beads (R = 42 μm) and mass transfer model eqs 2 to 14 (solid curves on figure). Flow rate F = 1.3 10-7 m3 s-1.

Copper concentration in all feed solutions was high; hence, particle diffusion was the limiting step in the mass transfer. Resistance in the fluid phase (1/k) for both sizes of the used resins is

not more than 5% of total resistance (1/k þ R/Deff) (for the smaller beads k = 3.6 10-5 m s-1 and for the larger beads k = 3.74 10-5 m s-1). As the resistance in the particle R/Deff is more than 95% the simplification used in the calculation of k (the slip velocity is equal to the terminal velocity) did not adversely influence the model accuracy. Figures 7 and 8 represent the experimental results for Dowex 50W-X8 together with model curves (eqs 2-14). Comparing the model and experimental data, the initial part of the experimental curves the system showed a better mass transfer than the model predicted meaning that copper removal was more efficient. This type of behavior of ion exchange beads can be due to the nature of the system: where the resin is converting between the hydrogen and sodium forms. The model assumes a uniform distribution of ion exchange sites within the bead; whereas it is most likely that the outer part of the bead has a higher number of sites than the inner part of the bead, a likely consequence of bead production, and contributing to the initial more efficient copper removal. The effective diffusion coefficient of copper inside the particle, Deff, that gave the best fit of experimental results was 7 10-11 m2 s-1, used for both bead sizes and at all the copper concentrations used in this work. When trying to minimize the number of experiments to determine the mass transfer parameters (effective diffusivity in 2413



Figure 9. Influence of effective diffusivity on the shape of the mass transfer model curves (eqs 2-14, curves on the figure). Inlet copper concentration (100 g m-3) - Small beads (R = 42 μm). Flow rate F = 7.7 10-7 m3 s-1.

Figure 10. Influence of effective diffusivity on the shape of the mass transfer model curves (eqs 2-14, curves on the figure). Inlet boron inlet concentration (1 g m-3) - Purolite S-108 resin beads (R = 95 μm). Flow rate F = 7 10-7 m3 s-1.

the particle), care has to be exercised over the experimental conditions selected. For example, Figure 9 illustrates the mass transfer from 100 g m-3copper solution into Dowex modeled by four different diffusion coefficients. Using the experimental data, a diffusivity of 10-13 is clearly incorrect, but under the experimental conditions selected there is little difference in the model result for diffusivities from 10-12 upward. The reported effective diffusivity of 7 10-11 m2 s-1 has been deduced by modeling the wide range of experimental conditions tested. High sensitivity for the correct assignment of the effective diffusivity is achieved under appropriate operating conditions, and is favored when the internal particle diffusivity is low. An example is illustrated in Figure 10, where data for boron (B[OH]4-) extraction onto Purolite S-108 is reproduced.22 Hence, it is appropriate to plan the experimental tests to be performed to determine the effective diffusivity, investigating operating conditions using the mathematical model, so that the number of tests can be minimized but the data achieved may be comprehensive. It may be that tests at high concentration are required for isotherm determination

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Figure 11. Breakthrough curve together with the different models predictions. Inlet copper concentration (380 g m-3) - 3 g of big beads (R = 87 μm). Flow rate F = 1.2 10-7 m3 s-1; Ph 4.5; ionic strength 0.2M. Column ID L = 1 10 cm.

and other tests are more appropriate for mass transfer analysis. However, model testing and verification should be achieved with all the tests. Equilibrium parameters (qm and b) as well as effective diffusivity (Deff) obtained with the continuous stirred cell were used to model the sorption of copper in the fixed bed 10 cm high column (Sigma Aldrich, U.K.). The breakthrough curve for copper/Dowex system in a fixed bed column together with several model predictions is presented in Figure 11. Prediction of the concentration in the effluent used the fixed bed shock and saturation model, Glueckauf’s model31 and a model that treated the fixed bed as a series of stirred tanks. As seen in the Figure 11, the shock and saturation models did not predict the breakthrough curve, but did the starting and the end points of the curve. Such prediction is expected since the models do not take into consideration film or particle diffusion, only equilibrium data obtained from the isotherm. Glueckauf’s model is based on the concept of “effective plates”. The plate height is calculated from the fundamental data, and the model takes into consideration film and particle diffusion. The model gave quite good prediction of the lower part of the breakthrough curve but failed to predict closer to saturation. Another model used was based on a series of identical continuous stirred cells. For the purposes of the modeling the bed was split into sections and each section was modeled as a stirred cell using the eqs 2-14. eq 2 had to be modified: εb Vbed dCi m dqi ¼ FðCi - 1 - Ci Þ N dt N dt

ð19Þ

εb is bed porosity (εb = 0.5), Vb is bed volume, N is number of column sections (identical stirred cells) used in the model (N = 11), and i is bed section (i = 1, 2, ..., N). As it can be seen from the Figure 11, the model gave a good prediction of the start and the end of the breakthrough curve using the mass transfer and equilibrium parameters obtained from the experiments in the stirred cell. Effect of NaNO3. The influence of NaNO3 on copper sorption was also investigated. As a background for adjusting the ionic strength NaNO3 was used coupled with adjusting the pH inside of the cell. In all experiments the buffer ionic strength of 0.2 M was maintained, so that during all experiments the variation in 2414



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Figure 12. Influence of NaNO3 on copper sorption on to Dowex 50W-X8. Inlet copper concentration in all experiments was 20 g m-3.

Table 2. Copper and Sodium Concentrations in the Flasks during the Batch Experiments equilibrium copper concentration

sodium concentration (g m-3)

qe (g m-3)

before sorption

after sorption

10

3770

3980

230 430

3670 3680

3990 3870

870

3760

3990

ionic strength due to ion exchange was less that 5%. A set of experiments in the stirred cell were performed to monitor the influence of sodium on the sorption of copper ions on the ion exchange (Figure 12). Inlet solutions contained different amounts of NaNO3. A significant reduction in the sorption of copper was observed with an increase of NaNO3 content in the inlet solution. The influence of NaNO3 on copper sorption on the resin can also be seen on the Figure 6, where one experiment in the continuous stirred cell was done without NaNO3 in solution. When NaNO3 was not present in the solution a much higher amount of copper was sorbed onto the resin. To determine if there is a competitive sorption of sodium ions on the surface of the ion exchanger at equilibrium the sorption of sodium ions was monitored. For this purpose the same samples from batch experiments used for determining the Langmuir isotherm were investigated. The samples were analyzed before and after the sorption, and a few results are presented in the Table 2. In all cases reported in Table 2 the sodium concentration is higher after the batch isotherm experiment compared to before, because of the addition of sodium hydroxide to maintain the pH at 4.5. The amount of extra sodium matches that added. Hence, it can be concluded that sodium did not exchange onto the resin under the experimental conditions, and any influence of the sodium nitrate concentration on the copper extraction is probably due to decreasing copper ion activity with increasing ionic strength.

’ CONCLUSIONS Equilibrium parameters (qm = 0.116 g g-1 and b = 0.003 m3 -1 g ) for a Langmuir isotherm of Dowex 50W-X8 resins (Sauter mean radii of 87 and 42 μm) were obtained from conventional

batch experiments for the isotherm, and by tests in a continuous flow stirred cell. Good agreement using the two different methods was achieved. The pH and ionic strength during the experiments were kept constant. The Langmuir constant b was found to be quite low, compared to previously published values, attributed to the lower affinity of copper sorption when the sodium nitrate concentration is high. Conventional batch experiments for determining the sorption equilibrium require several days while the length of the experiments in the continuous flow stirred cell can be controlled by selecting the mass of the resin to use and inlet concentrations of the solution. Hence, the experimental time in the continuous flow stirred cell can be much shorter, and it is possible to use the continuous flow stirred cell experiments to replace the conventional batch equilibrium tests. Thus, both mass transfer and equilibrium data can be accrued in the same experiments. The experiments were performed using high copper concentrations, in the range between 19 and 636 g m-3. The experimental results were compared with a mass transfer model which was based on a well mixed stirred system with continuous flow, aqueous film diffusion, constant internal effective particle diffusion, and a Langmuir type isotherm for the equilibrium conditions. In the initial part of the experimental curves the system showed a slightly better mass transfer than the model predicted, meaning that copper removal was more efficient. The effective diffusion coefficient of copper inside the particle, Deff, that gave the best fit of experimental results was 7 10-11 m2 s-1, used for all the tests performed with different size beads, flow rates, and copper concentrations. By using the equilibrium and mass transfer parameters obtained from the experiments with the continuous laboratory stirred cell it was then shown that conventional column operation could also be predicted. Hence, the stirred cell laboratory technique has utility for ion exchange design based on different contactors. Overall, it is shown that the continuous stirred cell represents an effective laboratory technique for determining both equilibrium and mass transfer parameters. After having achieved the mass transfer and equilibrium data, it is possible to use the same mathematical model to predict the performance of a seeded microfiltration process using larger volumes of liquid, filter area, and so forth to enable the design of a combined ion exchange and microfiltration process, or other types of contactors, such as columns. It will be particularly relevant to instances when the mass of ion exchange particles available for testing is low, less than 1 g, and when dealing with hazardous or expensive materials.

’ AUTHOR INFORMATION Corresponding Author

*Phone: þ44 1509 222519. Fax: þ44 1509 223923. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors wish to acknowledge the financial support of the U.K. Engineering and Physical Sciences Research Council. The work was undertaken as part of the DIAMOND project into Decommissioning, Immobilisation And Management Of Nuclear wastes for Disposal. List of Symbols A = total surface area of the resin particles, m2 2415


Industrial & Engineering Chemistry Research AccIX = mass of copper that enters the resin, g b = Langmuir constant related to the energy of sorption, m3 g-1 C = copper concentration in the bulk solution, g m-3 Ce = equilibrium concentration of copper in the liquid phase at the interface, g m-3 Ceq = equilibrium copper concentration in the liquid phase, g m-3 Ci = molar concentration of the ion i, g m-3 CIX = copper concentration in the effluent, g m-3 Co = copper concentration in the feed stream, g m-3 Coi = copper concentration in the liquid at the start, g m-3 Co,Na = sodium concentration in the liquid at the start, g m-3 Deff = effective diffusion coefficient of copper inside the particle, m2 s-1 Dliq = diffusion coefficient of copper in the liquid phase, m2 s-1 F = volume flow rate of the feed solution, m3 s-1 g = gravitational acceleration, m s-2 I = ionic strength, mol L-1 k = mass transfer coefficient in liquid phase, m s-1 m = total mass of the resin in the cell, kg N = number of identical stirred tanks = average mass of copper per unit mass of resin, g g-1 q = copper concentration on the particle, g g-1 qe = copper concentration on the resin particle, g g-1 qm = maximal amount of copper that can be adsorbed on the resin, g g-1 r = radial distance from the center of particle, m R = Sauter mean radius, m Reslip = Reynolds number at v = vslip Sc = Schmidt number Sh = Sherwood number t = time, s V = liquid volume in the cell, m3 Vb = bed volume, m3 vslip = relative particle-liquid velocity (slip velocity), m s-1 Greek symbols

δ = film thickness, m μ = liquid dynamic viscosity, kg m-1 s-1 F = liquid density, kg m-3 Fs = density of the swollen particle, kg m-3 εb = bed porosity, -

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Continuous Flow Stirred Cell Microfiltration of Ion Exchange Media to

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