Purification of glycerol/water solutions from biodiesel synthesis by ion exchange: sodium removal...

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Research ArticleReceived: 21 July 2008 Revised: 8 October 2008 Accepted: 6 November 2008 Published online in Wiley Interscience: 30 December 2008

(www.interscience.wiley.com) DOI 10.1002/jctb.2106

Purification of glycerol/water solutions frombiodiesel synthesis by ion exchange: sodiumremoval Part IManuel Carmona,a Jose L. Valverde,a Angel Perez,a Jolanta Warcholb andJuan F. Rodrigueza∗

Abstract

BACKGROUND: In this study, equilibrium and kinetic data of the ion exchange of sodium from glycerol–water mixtures on thestrong acid resin Amberlite-252 were obtained. Basic parameters for the design of ion exchange units for the purification of thecrude glycerol phase from biodiesel production have been determined.

RESULTS: Equilibrium uptake of sodium ions with the strong acid ion exchanger Amberlite-252 was studied at threetemperatures. The Langmuir equation and the mass action law model were used to fit the experimental equilibrium data.Equilibrium constants and thermodynamic parameters were obtained at each temperature. Kinetic experiments were carriedout to evaluate the effective diffusion coefficients of sodium on the resin Amberlite-252 in glycerine–water media.

CONCLUSIONS: Equilibrium results indicate that this process is favourable and also that its selectivity decreases with temperatureincrease from 303 to 333 K. Both models were able to fit the experimental equilibrium data. Kinetic experiments showed thatthe rate of mass transfer in this binary system is high. An Arrhenius type equation allowed the correlation of effective diffusioncoefficients and temperature. The results indicate that the macroporous resin Amberlite-252 could be useful for removal ofsodium ions from glycerine/water solutions with a high salt concentration.c© 2008 Society of Chemical Industry

Keywords: glycerol; ion exchange; adsorption; biodiesel

INTRODUCTIONToday, the environmental impact of fossil fuels is receiving muchattention because their combustion releases millions of tonnes ofCO2 into the atmosphere each year, which is widely believed tobe contributing to global warming.1 In addition, the dependenceof humans on this kind of energy together with the continuouschanges in the price of petroleum has promoted research into lowcost alternative energy sources, which are environmental friendly.One of these alternative energies is obtained by the combustionof methyl esters of fatty acids, which are known as biodiesel.

Biodiesel is made from the transesterification of vegetable oilsand animal fats with methanol or another alcohol in the presenceof an acidic, alkali or enzymatic catalyst to produce alkyl esters(Equation (1)).

(1)

where R, R′ and R′′ are hydrocarbon chains with 12 to 22 carbonatoms.

The alkali NaOH and methanol, because of their low prices,are frequently used as catalyst and reactant, respectively, in thisprocess.2 As can be seen, in the forward reaction to producethe biodiesel fuel, glycerol is inevitably obtained as a by-product.Biodiesel manufacture yields 10 wt % of glycerol. The process isnormally carried out at 60 ◦C. At the end of biodiesel synthesisthe reaction product is separated into two phases, biodiesel andglycerol, which settles at the bottom of the reaction vessel.3

The glycerol stream containing 50 wt % glycerol leaving theseparator contains methanol, catalyst and soap. This stream is alow cost product, although its disposal is quite difficult.1 Refiningof glycerol started with an acid treatment to split the soaps intofree fatty acid and salts. Fatty acids are not soluble in glyceroland are separated from the top and recycled to the process; then,

∗ Correspondence to: Juan F. Rodriguez, Department of Chemical Engineering,University of Castilla – La Mancha, Avda. de Camilo Jose Cela s/n, 13004 CiudadReal, Spain. E-mail: [email protected]

a Department of Chemical Engineering, University of Castilla – La Mancha, Avda.de Camilo Jose Cela s/n, 13004 Ciudad Real, Spain

b Department of Water Purification and Protection, Rzeszow University ofTechnology, 6 Powstancow Warszawy Str., 35-959 Rzeszow, Poland

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Purification of glycerol/water solutions from biodiesel synthesis www.soci.org

methanol is recovered by vacuum distillation. At this point, thesalts remain with the glycerol, which is in aqueous solution andits purity is about 85 wt %.1 – 4 Further glycerol refining is requiredbefore it can be used as a raw material for the manufacture ofother products. This purification process allows a product to beobtained with purity up to 99.5–99.7% using vacuum distillationto eliminate water, followed by ion exchange for salt removal.1 Therapid growth of biodiesel production motivated by governmentincentives is resulting in a worldwide surplus of glycerol thatdepresses its price. Although glycerol has more than 1000 uses,including many applications as an ingredient or processing aidin cosmetics, explosives, toiletries, personal care, drugs and foodproducts, it has become a low-value byproduct or a waste withan attached disposal cost. Additionally, the above applicationsrequired a highly purified product and crude glycerol is suitableonly for mixing with feed for animals.5

The valorization of the crude glycerol, while avoiding the ap-plication of expensive purification processes, will allow increasedprofitability of the biodiesel plants. One promising and econom-ical alternative is the transformation of glycerol into high valueproducts such as (mono- and di-fatty acids) by glycerolysis withmethyl esters at temperatures between 200 and 210 ◦C.6 Crudeglycerol may also be used as a source of renewable energy once adecrease in water and salts content is achieved.

Methods such as ion exchange,7 adsorption8 and membranetechnologies9,10 have been applied for the elimination of sodiumchloride from aqueous media. Regarding organic solutions, thereis a lack of information in the literature about the appropriatetechnology that should be applied. Ion exchange seems to be themost suitable method for small scale applications to treat liquidswith a very low salt content because of its simplicity, effectiveness,selectivity, recovery and relatively low cost.9 – 11

As discussed above, impurities contained in the glycerol arewater (about 10 wt %) and NaCl (concentration close to 1 mol L−1).A typical ion exchange process involves two steps: loading andregeneration. For sodium removal, the stream containing thesalt is passing through a fixed bed of resin filled with a strongacid cationic exchange resin. Sodium ions are exchanged withprotons initially on the resin until the resin exchange capacityis exhausted. Then, the spent resin is regenerated by usinga concentrated acid solution.12 – 14 Thus, it is clear that for anoptimized design of ion exchange fixed bed, one must be ableto predict both the loading and regeneration processes. Thus,modelling of the ion exchange equilibrium is an a priori step forsuccessful optimization of the design and operating conditions ofa fixed bed ion exchange column or for its scale-up. Nevertheless,there is a lack of fundamental information about basic parametersfor the design of such ion exchange systems, especially when anorganic media is considered.

The aim of this work is to obtain ion exchange equilibrium dataof sodium on the strong-acid cation resin Amberlite 252 in H+

form at different temperatures. The basic equilibrium parametersof the Na+/H+ system were obtained by applying the Langmuirequation and the mass action law. Also, the diffusion coefficientsof sodium in the resin were calculated at the same temperatures.

EXPERIMENTAL SECTIONChemicalsGlycerine (C3H8O3) with a water content of 2 wt % wassupplied by Sigma-Aldrich (Madrid, Spain) with a purity>97%. Sodium chloride, hydrochloric acid (37 wt %), and sodium

Table 1. Properties of Amberlite 25216

Activegroup

Particlesize,

D(m)

Resin capacityfor sodium,

n∞ (molkg−1 dry resin)

Surfacearea,

(m2 kg−1)

Voidfraction

(%)

Apparentdensity,

ρR(kg m−3)

Sulfonic 4.94 × 10−4 4.83 2.487 7.2 1.323

hydroxide PA grade quality were supplied by Panreac (Barcelona,Spain). Demineralized water with conductivity lower than 5 µS wasused to prepare the synthetic glycerol solutions with 10 wt % ofwater simulating the conventional solutions obtained in biodieselproduction processes.

Ion exchange resinAmberlite 252 (Rohm and Haas Co. (Barcelona, Spain)), amacroreticular sulfonated polystyrene-divinylbenzene resin, wasselected for sodium removal from glycerine/water mixturesbecause of its excellent behaviour in the uptake of alkali metalions, such as K and Cs, from non-aqueous media.15,16 The mainphysical properties are given in Table 1.

The resin was pre-treated and converted to the H+-form byrepeated treatment in a column with 1.0 mol L−1 NaOH and1.0 mol L−1 of HCl solutions. Then it was thoroughly rinsed withdemineralized water.17,18

Analytical methodsThe sodium content of solutions was analysed by atomic ab-sorption spectrophotometry with a Varian (Madrid, Spain) 220 ASspectrophotometer. The standard uncertainty and reproducibilityof measurements was found to be ±0.1%.

Equilibrium experimentsThe experimental setup consisted of seven 250 cm3 Pyrex con-tainers hermetically sealed and mechanically agitated, submergedin a temperature-controlled thermostatic bath kept constant at303, 318 and 333 ± 0.1 K. Different known masses of resin, in theH+-form, were put in contact with 100 cm3 of glycerine/water(90/10 by weight) containing a total concentration of 1 mol L−1.The synthetic mixture was prepared by mixing different amountsof a 1 mol L−1 solution of NaCl with solutions containing HCl1 mol L−1 to vary the initial sodium content and therefore, theamount of ion exchanger required for the experiments. The ac-curacy of resin weighting was ±0.0001 g. The suspension formedby the resin and solution was vigorously agitated at 200 rpm bymeans of a multipoint magnetic stirrer. To ensure that equilibriumwas reached the experiments were left stirring overnight. At theend of this period, the mixtures were filtered to remove the ionexchange resin. Then, the filtrate was analysed for sodium contentas described above. The resin phase concentration in equilibriumwith the liquid phase was obtained by means of the followingmass balance equation:

q∗ = (C0 − C∗) · V

W· 103 (2)

where C0 and C∗ are the initial and equilibrium concentration ofsodium in the liquid phase (mol L−1), respectively; q∗ denotesthe resin phase equilibrium concentration of sodium (mmol g−1

of dry resin), V and W are the initial volume of the synthetic

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glycerine/water solutions (L) and the weight of dry ion exchangeresin (g), respectively.

Batch kinetics studiesEffective diffusion coefficients were studied by measuring the rateof sodium uptake from the liquid phase by the resin in a well-mixedtank. The reactor was hermetically sealed and equipped with fourbaffles, a standard turbine stirrer with six flat blades, a conductivitycell, and a heating system formed by a temperature-controlledthermostatic bath. The effective diffusion coefficient was evaluatedat 303, 318 and 333 K. A high agitation rate was applied toensure that the film mass transfer resistance was negligible. Inthis way, internal diffusion within the resin particle was the onlycontrolling step. In a typical experiment, pre-wetted resin (6 g)was placed in contact with a synthetic mixture of glycerine/water(90/10 w/w) (0.5 L) containing a total concentration 0.1 mol L−1 ofsodium chloride. The mixture was stirred for 2 h and the solutionconductivity was monitoring continuously and recorded.

RESULTS AND DISCUSSIONAlthough it seemed clear that ion exchange could be a suitabletechnique to remove sodium ions from a liquid phase, it wasimportant to know the available resin capacity of Amberlite 252when a glycerin phase is used, and the influence of temperatureon the ion exchange process equilibrium. To fit the experimentaldata, Langmuir and mass action law models were used, bothbeing widely used to describe the equilibrium of adsorption or ionexchange, respectively.

EquilibriumIt is well known that the Langmuir model describes satisfactorilyadsorption processes.19 Nevertheless, it can be applied empiricallyto predict ion exchange processes.20 The Langmuir isotherm(Equation (3)), contains the parameters qT and KLang, the totaluseful capacity of the ion exchanger and the Langmuir equilibriumconstant, respectively:

q∗ = KLangqT C∗

(1 + KLangC∗)(3)

Figure 1 shows the equilibrium isotherms at 303, 318, and 333 Kof sodium ions in glycerin/water solutions on Amberlite 252. Thecurves have been drawn using the parameters obtained by fittingthe experimental data to Equation (3).

As expected, sodium uptake is favoured at lower temperature.In spite of the high concentration and viscosity of this solution, andalso that this glycerol phase is formed at 333 K during the transes-terification process. This temperature is commonly used in the laststep of glycerol purification in the biodiesel production process.

The Langmuir parameters of the system Na+/H+ at eachtemperature are shown in Table 2. As can be seen, the Langmuirequilibrium constants are greater than 1.0, indicating that thesodium uptake is favourable at the temperatures studied.

This capacity is similar to the value reported by Sigma-Aldrich foraqueous solutions (Table 1). Nevertheless, this value is higher thanthat obtained by Perez-Collado et al.16 for caesium removal frompolyols and that obtained by de Lucas et al.15 for the potassiumremoval from the same liquid phase.

Thus, it is important to point out that this result agrees withprevious work indicating that the presence of water in anyconcentration in a mixture with an organic solvent exerts a strongerinfluence than that of the organic solvent on the overall behaviour

0.0 0.2 0.4 0.6 0.80

1

2

3

4

5

q* (m

mol

g-1

)

C*(mol L-1)

Experimental dataT = 303 KT = 318 KT = 333 K

Theoretical curvesT = 303 KT = 318 KT = 333 K

Figure 1. Ion exchange isotherms of sodium ions on Amberlite 252 inglycerine/water mixtures at 303, 318 and 333 K at a total concentration of1 mol L−1. Langmuir treatment.

Table 2. Equilibrium parameters of the system H+/Na+ for thesodium removal with Amberlite 252 by the Langmuir model

SystemT

(K)KLang

(L mol−1)qT (mmol g−1

dry resin) R2

303 8.49

H+/Na+ 318 6.47 4.87 0.987

333 5.68

R2 = 1 −

m∑i=1

(qexp

Obs − qTheorObs

)

m∑i=1

(qexp

Obs − qexpObs

) , where qexpObs and m are the average

experimental concentration in the solid phase and the total number ofexperimental data, respectively.

of the system. Water seems to be the only solvating agent for theion exchange sites and determines the behaviour of the system. Inthis system, as in other water/solvent mixtures, water is preferredby the resin over glycerol. Therefore, the solvent/water molecularratio inside the resin differs from that of the bulk solution, thusthe loaded and entering ions are not surrounded by the samemixture. It is clear that the hydrophilic interaction between theionic groups and the polar part of the solvent molecules is strongerthan the hydrophobic one, and not only determines the capacity ofthe resin but also its ion exchange equilibrium behaviour. Thus, thecapacity of the resin not fully accessible in pure organic solvents,in this case (mixtures glycerol–water) is completely available.21,22

Nevertheless, a more accurate interpretation of the physicalreality of the process can be achieved by using a model basedon the mass action law. An ion exchange reaction is defined asa reversible exchange of ions between a liquid phase containingcounter-ions, which are different from those initially in the solidphase. Let us consider the following ion exchange process for abinary system (Equation (4)) where the ion exchanger (r) is initiallyin the A-form and the counter-ion in solution is B. The counter-ionsexchange occurs, and the ion A in the ion exchanger is partiallyreplaced by B,

βAα+r + αBβ+

s ⇔ βAα+s + αBβ+

r (4)

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0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0y N

a+

xNa+

Experimental dataT = 303 KT = 318 KT = 333 K

Theoretical curvesT = 303 KT = 318 KT = 333 K

Figure 2. Ion exchange isotherms of sodium ions on Amberlite 252 inglycerine/water mixtures at 303, 318 and 333 K at a total concentration of1 mol L−1. Ideal Mass Action Law treatment.

where α and β are the valences of the ionic species A and B,respectively.

At equilibrium, the solid and liquid phases contain bothcompeting counter-ion species, A and B. Electroneutrality is nec-essarily maintained in this reaction whether in the ion exchangeror aqueous solution. This indicates that counter-ion exchangeoccurs in equivalent amounts and the ionic concentration for abinary system can be expressed as ionic fractions as follows:

xA = C∗A

N; xB = C∗

B

N(5)

yA = q∗A

q0; yB = q∗

B

q0(6)

where yB and xB represent the ionic fraction of the ion B in thesolid and liquid phases, respectively. N is the total concentrationof the co-ions in the solution phase (mol L−1); and q0 is the usefulcapacity of the resin in the system studied (mmol g−1 of dry resin).

An important factor that should be considered in a compre-hensive theory of ion exchange is the non-ideal behaviour ofions in the solid and liquid phases. This can be a consequence ofion–ion and ion–solid interactions, ionic charge, ionic radii andother molecular constants.23 Therefore, the equilibrium constantfor the exchange reaction (4) assuming real behaviour for bothphases could be expressed by the following equation:

KAB(T) = yαB

(1 − yB)β· (1 − xB)β

xαB

·(

γA

γ A

)β

·(

γ B

γB

)α

·( q0

N

)α−β

(7)

where γ and γ are the activity coefficients of each ion in the ionexchanger and in the solution, respectively.

Liquid phase activity coefficients in aqueous solutions weresuitably calculated from the Pitzer limiting law; the activitycoefficients in the solid phase can be calculated using the Wilsonequations that consider the combined effects of the differences inmolecular size and intermolecular forces.24 – 26

Figure 2 shows the equilibrium isotherms in dimensionless formfor the system Na+/H+ at 303, 318, and 333 K in glycerol/watersolutions on Amberlite 252.

As can be seen, all the points are above the diagonal andthe curve shapes allow the assumption that the system Na+/H+

exhibits ideal behaviour for both phases. Thus, the Equation (7) canbe simplified to:

KAB(T) = yB

(1 − yB)· (1 − xB)

xB(8)

The standard thermodynamic properties of each binary systemwere obtained using the following thermodynamic relations:27

�G◦AB = − RT

αβln KAB (9)

�G◦AB = �H◦

AB − T · �S◦AB (10)

where R is the ideal gas constant, �G◦, �H◦ and �S◦ are changesin free energy, enthalpy and entropy, respectively.

Combining Equations (9) and (10):

KAB(T) = 1

e

(αβR

)·[

�H◦AB

T− �S◦

AB

] (11)

The equilibrium experimental data at the three temperaturesstudied were simultaneously fitted to the model given byEquations (8) and (11). Thus the three unknown parameters ofthe model, the maximum capacity (q0) and the thermodynamicproperties �H◦ and �S◦ were calculated.

Predicted curves for each temperature are shown in Fig. 2.Thermodynamical properties and equilibrium parameter for thesystem Na+/H+ at each temperature applying the ideal massaction law model are given in Table 3.

As can be seen, the resin capacity is fully available for exchangein this mixed media. Besides, this model confirms the preferenceof this ion exchanger for sodium ions and that the selectivitydecreases with temperature. The equilibrium constant reported inthe literature for the same ionic system using Amberlite IR-120 at303 K is about 1.7. This value is almost five times lower than thatexhibited in this study for Amberlite 252.28 This result confirmsthat the equilibrium constant is strongly affected by the presenceof glycerine, favouring sodium uptake.29

The ion exchange selectivity is depending on the solvationof counter-ions and also on the solvation of ion exchange sites,which can be affected by the electrostatic field generated by bothcounter-ions and the extent of ion-pair formation between anion-exchange site and a counter-ion.30 Both Amberlite IR-120 andAmberlite 252 have the same type of ion exchange site with ahigh charge density (—SO−

3 ), which produces strong electrostaticfields without ion-pair formation. Thus, the higher selectivity ofthe system Na+/H+ for Amberlite 252 can be attributed to thelower solvation of the sodium by glycerol compared with water.

On the other hand, the negative value of �G◦ indicates thatthis ion exchange process is both feasible and spontaneous; thenegative value of �H◦ confirms that the ion exchange processesare exothermic and whereas, the negative value of �S◦ suggeststhat the randomness decreased in the liquid/solid interface whenthe protons are eluted from the solid by the sodium ions initiallypresent in the liquid phase.

Applying the Langmuir model to obtain the thermodynamicalproperties provides the following values of�H◦,−11.233 kJ mol−1

and �S◦ −19.455 J mol−1 K−1. These values allow the same


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Table 3. Equilibrium and thermodynamical properties of the system H+/Na+ on Amberlite 252 obtained by fitting the experimental data to theIdeal Mass Action Law

System T (K) KAB q0 (mmol g−1 dry resin) �H◦ (kJ mol−1) �S◦ (J mol−1 K−1) �G◦ (kJ mol−1) R2

303 9.88 −5.77

H+/Na+ 318 6.80 4.34 −19.93 −46.71 −5.07 0.988

333 4.85 −4.37

thermodynamical conclusions to be drawn. Finally, if one comparesthe coefficient of determination (R2) obtained with the two models,it can be concluded that the system under study is perfectlydescribed by either model.

KineticsA homogeneous model which assumes that a quasi-homogeneousphase exists inside the solid particle was employed in previouswork with satisfactory results to obtain the effective diffusioncoefficients.15,22 This is a useful way to obtain effective diffusioncoefficients even in the case of this macroporous resin (Amberlite252) with similar properties to those of a gell form resin.31,32

Intraparticle transport in ion exchange resins is generallycontrolled by the interdiffusion of counter-ions. The most generalsolution which supposes intraparticle controlled diffusion from awell-stirred solution of limited volume was given by Crank:33

F(t) = Mt

M∞= 1 −

∞∑n=1

6α(α + 1) exp(−p2nDeff t/R2

P)

9 + 9α + p2nα

2 (12)

where Mt and M∞ are the amounts of sodium ions in the particlesat time t and at infinitity, respectively; t is the kinetic time (s); RP

is the average radii of the particle size (m); and, pn are non-zeroroots defined by the following equation.

tan(pn) = 3pn

3 + α · p2n

(13)

Taking into account that the kinetic process ends whenequilibrium is achieved, the dimensionless ratio of the volumes ofsolution and sphere (α) is dependant upon the partition factor K :

α = V

W · K(14)

If the initial bulk solution is free of the ions present initially onthe resin, a mass balance between the both phases leads to thefollowing relationship:

F(t) = Mt

M∞= qB

q∗B

= CA · V/

W

C∗A · V

/W

= CA

C∗A

(15)

The partition coefficient was found using Equations (2) and(8) and solving for C∗

B . This procedure was carried out at eachtemperature studied. Thus, the equation for α as a function oftemperature becomes:

α = V

W · q∗A

C∗A

∣∣∣∣T

· 103 (16)

Intraparticle effective diffusivity values (Deff (m2 s−1)) weredetermined by fitting the experimental data to Equation (12) by

0 1000 2000 3000 4000 5000 6000 70000.0

0.2

0.4

0.6

0.8

1.0

F(t

)Time (s)

Experimental DataT = 303 KT = 318 KT = 333 K

Theoretical CurvesT = 303 KT = 318 KT = 333 K

Figure 3. Kinetics of ion exchange of sodium ions on Amberlite 252 inglycerine/water mixtures at 303, 318 and 333 K and a total concentrationof 0.1 mol L−1.

means of the solver tool in an in-house spreadsheet in Excel usinga non-linear fitting method. This iterative method is solved usingan objective and a constrained cell. The objective cell was the sumof each squared absolute difference between experimental andcalculated values of F. The constrained cell was obtained as thesum of each relative error between the experimental value andthe calculated value divided by the experimental F value.

To test the effect of the temperature on sodium uptake, aset of experiments were carried out using a synthetic mixtureof glycerol/water (90/10 w/w) containing a total concentration0.1 mol L−1 of sodium chloride. Figure 3 shows the kinetics of thesodium uptake with temperature.

As can be seen, the higher the temperature, the faster the kineticprocess. That is, while equilibrium is attained in 1 h at the highesttemperature, the system needs more than 2 h to reach equilibriumat the lowest temperature. The model proposed was able to fitproperly the experimental data (Table 4).

According to previous work,15 effective diffusion coefficients ofsodium uptake from mixtures of glycerol/water (90/10 w/w) are inthe order of magnitude of those obtained for potassium removalfrom crude polyols with this same resin at higher temperatures.This result confirms that the macroporous resin performance isalso good in this mixed solvent.16,34 – 37 The effective intraparticlediffusivities obtained are in the range found in the literatureDeff = 1 × 10−12 m2 s−1 for small size ions present in organicmedia, and also for the uptake of high molecular weight moleculesfrom aqueous media.38 – 40

The increase of the ion mobility and the decrease in the retardingforces acting on the diffusion ions results in an increase of Deff

with temperature.41


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Table 4. Effective and pore diffusion coefficients of sodium uptakeby Amberlite 252 in H+ form at different temperatures. The averagedeviation between the theoretical values of the fitting and theexperimental data using the homogeneous model are also included

Temperature(K)

Deff ·1012

(m2 s−1)Ave. Dev.

(%)Dp 1011

(m2 s−1)

303 1.59 3.91 1.57

318 3.90 2.23 8.23

333 5.11 3.85 8.84

Av.Dev.(%) =m∑

i=1ABS

(FObsi

exp − FObsitheor

/FObsi

theor)

× 100/

m; m:

total number of experimental data

The dependence of the effective diffusion coefficient ontemperature is often represented by an Arrhenius equation:41,42

Deff = D0 exp

[−Ea

RT

](17)

where D0 is the frequency factor (m2 s−1), Ea is the activation energy(J mol−1), R the universal gas constant and T the experimentalabsolute temperature (K).

Although the resin has been considered for modelling purposesas in quasi-gel form, it is defined by the manufacturer asmacroporous. Thus it seems appropriate to give a value of thepore diffusion coefficient from the values of Deff , Table 4:43,44

Deff = DP

/ dqB

dCB

∣∣∣∣T

(18)

where DP is the porosity diffusion coefficient (m2 s−1) anddqB

/dCB

∣∣T is the derivative of the equilibrium equation at each

temperature.The derivative of Equation (8) gives:

dqB

dCB

∣∣∣∣T

= Nq0KAB

[N + (KAB − 1)CB]2 (19)

Porosity diffusion coefficients were obtained by combiningEquations (17) and (18). These values are reported in Table 4.Nevertheless, the above expression has been simplified in theliterature to the equilibrium constant when the isotherm isconsidered as linear.44 Thus:

dqB

dCB

∣∣∣∣T

∼= KAB|T (20)

Using this simplification and combining Equations (11), (17)and (18), the following relationship between the pore diffusioncoefficient and the thermodynamical standard properties is found:

LnDP = − 1

T

[Ea + �H

R

]+ �S

R+ LnDo (21)

As seen in Fig. 4, the Arrhenius equation allows adequatecorrelation of the temperature with the pore diffusion coefficients.The following values of D0, 1.089 m2 s−1 and Ea 68.435 kJ mol−1,were obtained with a coefficient of determination (R2) of 0.962. Thevalue of the activation energy is in the range found in literature,

2.9 3.0 3.1 3.2 3.3 3.4-26

-25

-24

-23

-22

Ln(D

P)

1/T·103

Figure 4. Correlation between temperature and pore diffusion coefficients.

i.e. 3–11 kJ mol−1 for trivalent chromium diffusion into activatedcarbon, and 8–23 kJ mol−1 for water diffusion on mango slices atdifferent stages of maturity during air drying.41,42

As shown in the equilibrium section, the number of resin activesites exchanged decreased with temperature, indicating the higherselectivity of this material for the entering ion at lower operatingtemperature, despite the maximum usable capacity seeming tobe fixed. Thus, it is possible that this selectivity has an importanteffect on the effective diffusion coefficients. In a previous paper15

an empirical correlation between the effective diffusion coefficient

and the final conversion of the solid active sites (yB = q∗B

q0

∣∣∣∣T

),

was employed, where q∗B is the equilibrium concentration of the

entering ion in the solid phase at the equilibrium state (mmol g−1

of dry resin); and q0 is the useful capacity of the resin in the systemstudied (mmol g−1 of dry resin).

Deff |T = D∞[

q∗B

q0

∣∣∣∣T

]s

(22)

where D∞ and s are constants not dependent on the temperature.Fitting the theoretical effective diffusion coefficients and the

conversions obtained at each kinetic experiment to the aboveequation, the following values of D∞ 2.848 × 10−14 m2 s−1 ands −23.864 were obtained with the determination coefficient R2

equal to 0.99.The negative value of s indicates that this ion exchange process

is favoured at lower temperatures as discussed in the equilibriumsection. Thus, if kinetics with the same external concentrationwere carried out at different temperatures, the highest conversionwould be achieved at the lowest temperature. In this case, theprocess would be logically the slowest.

CONCLUSIONSEquilibria for the sodium uptake from solution of glycerine/water90/10 w/w using Amberlite 252 in H+-form was favourable over thetemperature range studied (303–333 K). As expected, the selec-tivity decreased with temperature. Both, empirical and theoreticalmodels based on the Langmuir or mass action laws were able to fitthe experimental equilibrium data. The ideal behaviour exhibitedby this ionic system allowed the observation that both equilibriummodels led to similar equilibrium parameters. Finally, the stan-


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dard thermodynamical properties indicated that this process wasexothermic, spontaneous and feasible.

Kinetic experiments carried out at different temperaturesshowed that this ion exchange process was faster at highertemperatures. In addition, a kinetic homogeneous model allowedeffective diffusion coefficients to be obtained at each studiedtemperature with satisfactory results. An Arrhenius type equationallowed the correlation of effective diffusion coefficients with thetemperature of the kinetic studies. The activation energy was ofthe same order of magnitude as those reported in the literature. Anempirical equation based on the final conversion of the solid activesites allowed reproduction of the effective diffusion coefficients.

The results confirmed that the macroporous resin Amberlite 252could be a good choice to remove sodium ions from glycerol/watersolutions with a high salt concentration.

ACKNOWLEDGEMENTAn introduction to this work was presented at the IEX-2008 andincluded in IEX 2008 Proceedings.

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Purification of glycerol/water solutions from biodiesel synthesis by ion exchange: sodium removal...

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