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Journal of Crystal Growth 290 (2006) 213–219

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Growth kinetics of potassium chloride—I: Pure aqueous solutions

Ana Lopesa,�, Fatima Farelob

aDepartment of Chemistry, University of Beira Interior, R. Marques D’Avila e Bolama, 6201 001 Covilha, PortugalbInstituto Superior Tecnico, Technical University of Lisbon, 1049 001 Lisboa, Portugal

Received 8 October 2005; received in revised form 7 January 2006; accepted 11 January 2006

Available online 24 February 2006

Communicated by M. Uwaha

Abstract

Growth and dissolution rates of potassium chloride in pure aqueous solutions were measured in a fluidized bed crystallizer. Within the

experimental uncertainty, the growth rates are nearly first-order relatively to the thermodynamic driving force. The coefficient of the

overall kinetic equation was found to decrease with the residence time in the crystallizer, until a steady-state mode of growth is

reached.

The size of the seeds and the porosity of the fluidized bed have little influence on the steady growth of KCl crystals, but affect the

dissolution and, to a lesser extent, the initial stages of growth. The diffusive nature of dissolution is well illustrated by an activation

energy of 8.571.0 kJmol�1. The corresponding values pertaining to growth experiments with 5 and 20min of residence time were

(23.974.4 and 39.171.7) kJmol�1, respectively, thus indicating a significant role of the diffusional mass transfer step during the early

contact of the seeds with the solution. As the growth rates approach a constant value, the importance of this step decreases relatively to

the surface-reaction contribution. The linear correlation between growth rates and driving force suggests, therefore, a growth process

controlled by a direct integration mechanism.

r 2006 Elsevier B.V. All rights reserved.

PACS: 81.10. Dn

Keywords: A2. Growth from solutions; A2. Seed crystals; B1. Potassium compounds

1. Introduction

The first part of the present article deals with themeasurement of overall growth and dissolution rates ofpotassium chloride crystals in pure aqueous solutions,using a fluidized bed apparatus. This study will becompleted in a second paper concerning the influence ofethanol, a frequently used co-solvent in drowning-outcrystallization, on the crystallization kinetics of KCl,chosen as a model system.

The crystallization of potassium chloride from pureaqueous solutions has been studied by a number of authorsusing direct and indirect measurement techniques, e.g.,single-crystal [1–3], fluidized bed crystallizer [4–6], mixedsuspension mixed product removal (MSMPR) crystallizer

e front matter r 2006 Elsevier B.V. All rights reserved.

rysgro.2006.01.016

ing author. Tel.: +351 275 319 880; fax: +351 275 319 730.

ess: analopes@ubi.pt (A. Lopes).

[7], seeded controlled cooling batch crystallizer [8],unseeded desupersaturation runs [9–12], etc. Becausegrowth rates depend on supersaturation, as well as ontemperature and relative solid–liquid velocity, the use ofdifferent setups or operating conditions might, to a certainextent, explain the lack of agreement between the publishedresults. However, even for seeded experiments carried outin similar conditions of supersaturation, temperature andslip velocity, the reported linear growth rates of singlecrystals are about fivefold to tenfold higher than thosemeasured in fluidized beds or in batch crystallizers. Thesedisparate results represent a serious drawback whenevercrystallization data from the pure solutions are required asthe standard against which the modifications imparted bythe presence of organic admixtures are to be evaluated. Itwas, therefore, the objective of this study the measurementof the growth and dissolution rates of potassium chloridein pure aqueous solutions, for different seeds sizes,

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Nomenclature

Ed activation energy for dissolution (kJmol�1)Eg activation energy for growth (kJmol�1)F overall surface-volume shape factor (dimen-

sionless)kd dissolution rate coefficient (kgm�2 s�1)kD diffusional mass transfer coefficient

(kgm�2 s�1)kg overall growth rate coefficient (kgm�2 s�1)kr integration rate coefficient (kgm�2 s�1)Li

_

mean size of seeds (m)m7 mean molality (mol kg�1)Mi initial mass of seeds (kg)Mf final mass of crystals (kg)N number of data points in an experimental seriesr order of the surface reaction step (dimension-

less)R ideal gas constant (Jmol�1K�1)

Rd mass dissolution rate (kgm�2 s�1)Rg overall mass growth rate (kgm�2 s�1)T absolute temperature (K)

Greek symbols

Dm thermodynamic driving force (Jmol�1)Dt time of growth/dissolution (s)e fluidized bed porosity (dimensionless)g7 activity coefficient in the molality scale (dimen-

sionless)mKC1,bulk chemical potential of KCl in the bulk mother

liquor (Jmol�1)mKC1,eq. chemical potential of KCl in the saturated

solution (Jmol�1)mKC10 (T) standard chemical potential (Jmol�1)

rc density (kgm�3), rc, KCl ¼ 1988 kgm�3

oi weight in Eq. (8)

A. Lopes, F. Farelo / Journal of Crystal Growth 290 (2006) 213–219214

fluidized bed porosities and temperatures, using a fluidizedbed crystallizer.

2. Experimental procedure

Growth and dissolution rates were experimentallyobtained, at constant temperature, in a fluidized bedcrystallizer similar to crystallization units described in theliterature [13,14]. Briefly, the 25L-capacity crystallizationplant used consists of a stirred stock vessel, a pump, acascade of three heat exchangers and a double-wallcrystallizer enabling the circulation of thermostated water.

The mother liquor circulates through the heat exchan-gers and the crystallization zone, where the fluidized bedcell is placed during the measurements, and returns tothe stock vessel through an outlet located at the upper partof the crystallizer. The storage vessel was kept attemperature higher than the saturation point (by about5–10K) in order to dissolve any entrained fines. The heatexchangers were connected to thermostated baths set atprogressively decreasing temperatures. Type K thermo-couples calibrated to the ITS-90 scale and coupled to aECD Model 50 Datalogger, allowed readings of thesolution temperature every 15 s, at the inlet and outletof the crystallizer and between the heat exchangers.The uncertainty of the temperature readings was betterthan 70.1K.

The 19 cm-long fluidized bed cell (1.5 cm i.d.), made ofPlexiglas, is equipped at both ends with sieves of 80 mm ofaperture to prevent the entrainment of solids by thecirculating liquid. For each experiment, the cell was loadedwith 570.0002 g of seed crystals, which were allowed togrow or to dissolve, at constant bed height, for a givenperiod of time. During the runs, the liquid flow rateentering the crystallizer was adjusted, through valves, to

guarantee a uniform suspension of the crystals. At theend of the growth or dissolution run, the crystalswere removed, filtered, washed with methanol saturatedwith KCl, air-dried and again weighed. Because thevariation in mass of the crystals was much smaller thanthe total mass of solute in the solution, the driving forcefor growth (or dissolution) was assumed constant duringeach run.Solutions were prepared by mass, using potassium

chloride (Riedel�de-Haen, p.a.) and deionized water. Themaximum content of lead ions, analyzed by graphitefurnace atomic absorption spectrometry on different sievecuts of the commercial potassium salt, was 2.5 ppm(maximum expanded uncertainty of 715%).Within each series of experiments, the supersaturation

was progressively reduced by adding small volumes ofsolvent to the mother liquor. After each addition, the liquidwas homogenized by circulation through the crystallizationunit, at maximum flow rate and without cooling, forseveral minutes. Two liquid samples (ffi3mL) werethen collected with a heated syringe, equipped with a0.45-mm filter, and transferred to capped vials. The sampleswere weighed and allowed to evaporate to dryness at375K. The salt concentration in the mother liquor wassubsequently calculated from the masses of anhydroussolid and solvent evaporated. This procedure was repeatedevery five or six experiments, carried out at identicalsupersaturation, to check the actual concentration of salt inthe solution.The seed crystals were obtained from sieve cuts of

450–500, 500–560 and 560–630 mm. Inspection of the seeds,by SEM, showed that the majority of crystals were tightlycemented aggregates of two crystals of nearly identical sizeand single cubic particles with much smaller cubes adheringto the faces, as shown in Fig. 1. To account for the

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Fig. 1. Photomicrographs of KCl seeds.

Table 1

Operating conditions and overall growth rate coefficients

e T (K) Li ðmmÞ Dt (min) kg� 102 ( kgm�2 s�1) N % Sra

0.93 303 468 3 0.430 11 12.5

12.5 0.120 10 7.8

519 3 0.479 8 9.8

5 0.297 12 22.7

12.5 0.131 14 16.2

20 0.130 12 13.3

580 12.5 0.136 9 23.1

308 519 5 0.369 13 11.3

20 0.168 13 16.3

313 519 5 0.415 11 14.5

20 0.220 12 14.8

0.80 303 519 3 0.463 14 22.2

12.5 0.118 8 11.6

a.%Sr ¼ 100PNj¼1

½ðRcalc � RexpÞ=Rexp�2

!=ðN � 2Þ

" #1=2.

Table 2

Operating conditions and dissolution rate coefficients

e T (K) Li ðmmÞ Kd� 102 (kgm�2 s�1) N % Sr

0.93 303 468 1.46 15 15.6

519 2.86 12 18.5

580 4.13 10 16.0

308 519 3.04 11 17.9

313 519 3.29 14 15.3

0.80 303 519 2.12 14 26.5

A. Lopes, F. Farelo / Journal of Crystal Growth 290 (2006) 213–219 215

breakage of loose aggregates in the solution, samples of thethree types of seeds were gently stirred in KCl-saturatedethanol for about 20min at room temperature, and sizedafter drying. From the size distributions of the washedparticles, weighed mean sizes of 468, 519 and 580 mm werecalculated.

Growth and dissolution rates of KCl were measured at303, 308 and 313K and E93% of bed-porosity. Experi-ments with residence times of 3, 5, 12.5 and 20min werecarried out, at constant driving force. The influence of asmall variation of the fluidized bed porosity on the growth/dissolution kinetics of KCl was also analyzed. A summaryof the operating conditions of the crystallization experi-ments is presented in Tables 1 and 2.

3. Thermodynamic driving force

The measured growth and dissolution rates werecorrelated with the thermodynamic driving force, definedat the temperature of the experiment, as

DmðTÞ ¼ mKCl;bulkðTÞ � mKCl;eq:ðTÞ. (1)

For KCl, a 1–1 type salt, the chemical potential in theliquid phase is

mKClðTÞ ¼ m0KClðTÞ þ 2RT lnðg�m�Þ, (2)

where m0KClðTÞ, the reference chemical potential, at anarbitrarily standard state, is chosen so that the salt activitycoefficient becomes unity at infinite dilution. Therefore, by

ARTICLE IN PRESSA. Lopes, F. Farelo / Journal of Crystal Growth 290 (2006) 213–219216

appropriately substituting Eq. (2) into Eq. (1), thedimensionless thermodynamic driving force was expressedas

Dm=ð2RTÞ ¼ ln ðg�m�Þbulk=ðg�m�Þeq� �

: (3)

The solubility of KCl was obtained from literature, as afunction of temperature [15], whilst the activity coefficientswere calculated by means of the ion-interaction modelproposed by Pitzer [16] and parameterized by Holmes andMesmer [17].

4. Results and discussion

Overall mass growth and dissolution rates were calcu-lated as [18]

Rg;d ¼3LircFDt

M f

M i

� �1=3

� 1

���������� (4)

on the assumption that breakage and agglomeration of thecrystals was negligible. The overall surface-volume shapefactor included in Eq. (4) was obtained from literature as6.6, 6.7 and 6.1, respectively, for particles belonging to thesieve cuts 450–500, 500–560 and 560–630 mm [19]. Themaximum uncertainties of the experimental data, namelycrystals mass, residence time and seeds size, were estimated,respectively, as 70.0002 g, 715 s and 72.5%. The relativeuncertainty of the measured growth and dissolution rates,evaluated as

DRg;d

Rg;d¼

DLi

Li

þDðDtÞ

Dtþ

1

3

DMf

M fþ

DM i

M i

� �

þrcLi

FDtjRg;dj

DM f

Mfþ

DM i

M i

� �ð5Þ

was, therefore, estimated for the most unfavorable experi-mental conditions, e.g., low driving forces and 3min runs,as 718%. The relative uncertainty of the driving force wascalculated as

DðDmÞDmffi

DT

Tþ

2RT

jDmjDm

mþ

Dg�g�

� �(6)

with DT ¼70.1K, Dm ¼71.3� 10�4mol kg�1 andDg7 ¼ 10�4.

Fig. 2. KCl growth and dissolution rates vs. thermodynamic driving

The experimental growth and dissolution rates of KCl inpure aqueous solutions at 303K, Li

_

¼ 519 mm; Dt ¼

12:5 min and effi 93% are plotted, against the thermo-dynamic driving force, in Fig. 2. Some literature data,calculated from correlations developed for similar experi-mental conditions, were also included in the same plot afterbeing converted to the thermodynamic scale. The trend ofthe overall growth data was nearly first-order with respectto the driving force, in accordance with the findings of thelarge majority of authors [1–3, 7–11].The measured growth rates are well correlated by the

kinetic equation of Nyvlt [8], and are about 30% higherand 60% lower than those calculated from the equationsproposed, respectively, by Konig and Konig [10] and bySayed et al. [5]. It is also evident, from Fig. 2, that thedissolution of KCl is much faster than growth. Theexperimental dissolution data are in excellent conformitywith the values given by Tengler and Mersmann [2], albeitthe total lack of agreement in what concerns the growthrates (not shown).The growth kinetics of KCl were first described by the

usual power law correlation:

Rgðkgm�2 s�1Þ ¼ kg½Dm=ð2RTÞ�g (7)

and the overall rate parameters calculated from a weighedleast-squares fit of Eq. (7) to the experimental data, usingas the minimization criterion:

C ¼ minXN

j¼1

oiðRcalc � RexpÞ2

" #. (8)

The weights accounting for the varying quality ofexperimental data, which depends on the working drivingforce, were arbitrarily set from 1 to 6 according to aninverse relation with the driving force uncertainty. Becausethe fitted exponents of the power law equation varied from0.88 to 1.10 in a random manner, the overall ratecoefficients kg were subsequently recalculated takingg ¼ 1, as listed in Table 1. For the dissolution rates alinear dependence with the thermodynamic driving forcewas assumed, thus producing the kd constants tabulated inTable 2.The seeds’ residence time in the crystallizer is a variable

of importance for the study of the crystallization of KCl, as

force in pure aqueous solutions: (a) growth and (b) dissolution.

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Fig. 3. Influence of residence time on the growth rates of KCl in pure

aqueous solutions at 303K, Li

_

¼ 519 mm and effi 93%.

A. Lopes, F. Farelo / Journal of Crystal Growth 290 (2006) 213–219 217

illustrated in Fig. 3. The overall growth rates decreasedcontinuously with time, by as much as 80% when datapertaining to 3 and 12.5min runs are compared. Thedifferences between the measured data in 12.5 and 20minruns are already within the experimental uncertainty, thusindicating that after a given period of contact with thesupersaturated solution the crystals grow at constant rate.This phenomenon, which may help explain the diversity ofresults found in the literature for the KCl kinetics, parallelsthe time-dependent growth rates reported for other salts,such as ADP or KDP [20], although without thepeculiarities of the fast growth mode of these salts.Oppositely, the duration of the runs, in the time rangefrom 3 to 12.5min, had no noticeable effect on thedissolution rates.

In stirred crystallizers, the decrease of KCl growth rateswith time has been interpreted in terms of breakage of ill-fitted aggregates and of attrition, given the rounded shapeof the particles grown for long periods [11]. The sameinterpretation does not hold, however, when the growthrates are evaluated from the mass deposited upon the seeds,unless a significant loss of crystalline matter, increasingdirectly with time, occurs during the runs. In the presentstudy, the SEM observations showed that particles grownfor 20min were not significantly more abraded than thosegrown for smaller periods. On the other hand, the loss offines during the experiments was largely prevented by the80 mm-traps located at both ends of the crystallization cell.

Because no particular mode of growth of KCl crystals isassociated with the initial decay of the rates, the observedbehavior may stem from a slowdown of the growthprocess, due to the ‘‘healing’’ of the seeds in contact withthe supersaturated solution, accompanied or not by areversal of the relative importance of the rate controllingmechanisms.

The issue of the growth rate controlling mechanism ofpotassium chloride is still to date an unresolved one, a factthat is clearly illustrated in the literature by the identical

number of opinions defending the diffusional mass transfer[1,2,5] or a first-order surface-reaction [3,8,9] as thepreponderant mechanism. The assessment of the relativeimportance of these two steps based on the usual linearizedform of the equation that combines both contribu-tions [18]:

½Dm=ð2RTÞ�R�1g ¼ k�1D þ k�1r R1=r�1g (9)

is inconclusive when the dependence of the overall growthrate is first order to supersaturation. When the previousequation is fitted to the smoothed growth data theintegration step’s order must necessarily be 1, if it isassumed that kr does not depend on the driving force.Hence, provided that kr and kD are larger than kg, anycombination of those rate constants satisfying the exactrelationship:

k�1g ¼ k�1D þ k�1r (10)

has physical meaning and, as such, the fitting proceduredoes not allow the evaluation of the prevalent mechanism.On the other hand, when Eq. (9) is fitted to the raw growthdata, different sets of constants satisfy the minimizationcriterion used for the regression, albeit pointing to contra-dictory conclusions as shown by Konig and Emons [3].The analysis of the influence of temperature and of

relative solid–liquid velocity can, however, shed some lighton the relative importance of the rate controlling mechan-isms. The mother liquor’s velocity past the crystallinesurfaces is directly related to the expansion of the fluidizedbed, as well as to the size of the suspended crystals as thesettling velocity increases with the particle diameter.Therefore, to investigate in more detail the growth processof KCl, the influence of the seeds’ size, fluidized bedporosity and temperature on the salt growth and dissolu-tion rates was here assessed. These experiments werecarried out at operating conditions slightly different fromthose used in the reference runs (303K, effi 93%,Li

_

¼ 519 mm), by changing one variable at a time, e.g.: at303K, effi 93%, with seeds of 468 and 580 mm of meandiameter; at 303K, Li

_

¼ 519 mm and bed porosity of 80%;at 308 and 313K, effi 93%, using particles of 519 mm ofinitial mean size.The apparent effect of the initial seeds’ size on the

growth of KCl crystals is shown in Fig. 4(a), using datafrom 3 and 12.5min runs. The deviations between thereference and the modified sets of data are almostnegligible when compared with the influence of theresidence time. For the shorter runs the growth ratesincrease, although slightly, with the particle size, whereasfor the 12.5min experiments this influence becomes onlybarely detectable for driving forces larger than E0.008.The apparent effect of particle size on the dissolution ratesof KCl (Dt ¼ 3212:5 min) is illustrated in Fig. 4(b). Avariation of about 710% in particle mean size around519 mm led to changes of 750% in the overall masstransfer coefficients, thus indicating that the particles’ size

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Fig. 5. Growth rates of 519mm seeds of KCl: (a) influence of fluidized bed porosity, at 303K and (b) influence of temperature, at effi 93%.

Table 3

Activation energy for growth and for dissolution of KCl

Dt (min) Eg (kJmol�1) Ed (kJmol�1)

5 23.974.4 8.571.0

20 39.171.7

Fig. 4. Influence of seeds size on KCl growth and dissolution rates in pure aqueous solutions at 303K and effi 93%.

A. Lopes, F. Farelo / Journal of Crystal Growth 290 (2006) 213–219218

(or indirectly, the solution velocity required to maintain auniform suspension with constant bed porosity) has amore pronounced influence on the dissolution than ongrowth. The same plot shows the excellent agreementbetween the results obtained for the 468 mm seeds andpublished data concerning the dissolution of crystals ofsimilar size [5].

Fig. 5 shows the influence of bed porosity and ofcrystallization temperature on the measured growth data.The enhancement of the mass transfer step due to theincrease of the relative velocity between the fluidizedcrystals and the mother liquor is small and nearlyindependent of the residence time in the crystallizer(Fig. 5(a)). Despite the larger scatter of the data measuredat the lower bed porosity, the effect of this variable on thegrowth rates of KCl is analogue to the one induced bychanging the particles size. Dissolution was significantlymore influenced by the variation of the bed height thangrowth. Hence, at constant undersaturation, expanding thefluidized bed from a porosity of 80–93% led to an increase ofabout 35% in the kinetic constant for dissolution (Table 2).

In what concerns the influence of temperature (Fig.5(b)), it was observed that raising the temperature by asmuch as 10K translates into increases of 56% and 68% ofthe overall mass transfer coefficients for growth pertainingto 5 and 20min runs, respectively. In the narrow range oftemperatures studied, the dissolution of KCl is littleinfluenced by this variable and the increase of kd from303 to 313K is less than 15%.

The activation energies for the growth and dissolutionprocesses, listed in Table 3, were estimated from the datameasured at 303, 308 and 313K. Because of the reducednumber of data points available for the correlation, thecalculated parameters give only qualitative indications. Thesmall activation energy for the dissolution of KClindicates, as expected, a diffusion mechanism of masstransfer. The calculated values of Eg are about three tofivefold the activation energy for dissolution, depending onthe time allowed for growth. For steady-state the activationenergy is close to the range of values pertaining to thekinetic mode of growth [18], whereas for the shorter runsthe calculated value points to a significant contribution ofthe diffusional mass transfer step. Unfortunately, the widedispersion of the activation energy values given in theliterature: 1.38 kJmol�1 for KCl crystals growing from asolution co-saturated in NaCl [21] and 35.7 kJmol�1 inpure aqueous solutions [22] (or 65.2 kJmol�1 as laterclaimed [9]), do not allow a meaningful comparison withthe calculated data.

ARTICLE IN PRESSA. Lopes, F. Farelo / Journal of Crystal Growth 290 (2006) 213–219 219

5. Conclusions

Potassium chloride crystals exhibit time-dependent growthrates, a phenomenon that may help explain the diversity ofresults found in the literature for the KCl kinetics. The decayof the growth rates with the contact time of crystals andsupersaturated solution was interpreted in terms of thedecrease of the surfaces’ roughness, at molecular level, as thecrystalline matter deposits onto the seeds.

The growth rates of KCl were found nearly first-orderwith respect to the thermodynamic driving force, inaccordance with literature. The results obtained, namelythe large differences in the growth and dissolution ratesand the negligible influence of the crystal size and fluidizedbed height on the steady-state growth of KCl seeds,qualitatively support the dominance of surface integration,as the growth controlling mechanism. The magnitude ofthe activation energy of growth, somewhat lower than itwould be expected for a surface-reaction controlledprocess, may be ascribed to the contribution of thediffusional mass transfer, which plays a not negligible roleduring a significant part of the time allowed for growth.The linear correlation between growth rates and super-saturation suggests, therefore, a growth process controlledby a direct integration mechanism.

Acknowledgment

This work was supported by Fundac- ao para a Ciencia ea Tecnologia, Portugal.

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