722
Ind. Eng. Chem. Res. 1991,30, 722-728
Precipitation of Salicylic Acid: Hydrotropy and Reaction Narayan S. Tavare* and Vilas G. Gaikart Department of Chemical Engineering, University of Manchester Institute of Science and Technology (UMZST), P.O.Box 88 Sackoille Street, Manchester M60 lQD, England
Precipitation kinetics of salicylic acid from its hydrotropic solution were investigated in a laboratory-scale agitated vessel using water or dilute sulfuric acid as a precipitant. Salicylic acid concentration and pH profiles were experimentally determined. The method of s-plane analysis was used to deduce simultaneody growth and nucleation rates from transient population density curves measured by a Coulter counter. Growth and nucleation kinetic expressions in terms of significant observable variables were correlated from the experimental results. The calculated time variation of salicylic acid concentration in the solution phase and population density c w e s using these kinetics correlations and a simulation algorithm compare favorably with experimentally observed profiles. Introduction Precipitation of solids resulting from a homogeneous chemical reaction between two reactants is frequently encountered in the chemical industry. Salicylic acid precipitates industrially from sodium salicylate by acid hydrolysis with sulfuric acid. The process provides an example of a reactive precipitation system. Salicylic acid is an important intermediary in the production of aspirin, and its derivatives are also used in the pharmaceutical and polymer industries for manufacture of disinfectants, antiseptics, and detergents. Only a few studies concerning reactive precipitations of this type have been reported in the literature. Precipitation of benzoic acid from its sodium salt by reaction with hydrochloric acid in an isothermal semibatch crystallizer was studied experimentally by Aslund and Rasmuson (1986) in order to find out optimal operating conditions with a view to obtain large particle size. An operating policy with feed flow rate increasing with time over a longer period of addition time was beneficial in achieving large product size. Franck et al. (1986,1988) studied the precipitation of salicylic acid by hydrolysis of sodium salicylate with stoichiometric amount of dilute sulfuric acid and monitored hydronium ion concentration by conductometry in order to deduce the concentration profiles of most other ionic species using conservation and equilibrium relationships. Optimal values of kinetic parameters in growth, nucleation, and agglomeration kinetics were determined to match the maximum crystallization rate and corresponding time and the final mass average crystal size. A simple model using these estimated kinetic parameters was used to describe the behavior of batch, continuous, and nonideal crystallizers. Al-Khayat (1988) employed pH measurement to calculate the concentration profiles of most species involved in salicylic acid precipitation from both batch and semibatch crystallizers. Generally smaller mean particle size was obtained in a batch crystallizer at higher stirrer speed and initial concentrations of reactants. Semibatch operation usually yielded large mean product crystal size compared to the batch crystallizer operation. Average product crystal size increased with a decrease in feed flow rate to the semibatch crystallizer. All these experimental studies were performed with dilute sodium salicylate solutions. Hydrotropic agents or hydrotropes are freely soluble organic compounds that, at a concentration sufficient to induce a solution structure of hydrotrope molecules or aggregate in a stacklike fashion, considerably increase the Permanent address: University Department Of Chemical Technology (UDCT),Matunga, Bombay 400 019, India.
aqueous solubility of organic substances which are otherwise practically insoluble under normal conditions, by probably similar associative mechanisms. Sodium salicylate is a known anionic hydrotrope (McKee, 1946; Saleh et al., 1983a,b; Balasubramanian et al., 1989) and should increase the solubility of salicylic acid. As hydrotropy appears operative at high aqueous hydrotrope concentrations, the solute (i.e., salicylic acid) will precipitate out on dilution with water. Thus the process of precipitating salicylic acid out by diluting with water sodium salicylate solution, saturated with respect to salicylic acid, was investigated in this study. Instead of water dilute sulfuric acid if added will react with sodium salicylate to produce more salicylic acid in the solution. Therefore salicylic acid will then be precipitated due to both these effects, viz., hydrotropy and reaction. The purpose of this paper is to study the precipitation of salicylic acid from its hydrotropic aqueous solution by diluting with water alone or reacting with dilute sulfuric acid, sodium salicylate being used as a hydrotrope. This study is aimed at developing crystallization kinetic expressions from the experimental responses and using them in subsequent simulation of the process. Such analysis is useful in gaining an understanding of the interplay among the rate processes involved and identifying improvements that may be obtained in operation and product quality. Physical Visualization Hydrotrope molecules are assumed to aggregate in a stacklike fashion in solution and solubilize the solute (or solubilizate) by similar associative mechanisms perhaps involving cooperative intermolecular interactions in the solubilization process. Hydrotropy does seem operative above a particular concentration termed critical or minimum hydrotrope concentration. Above this critical concentration the solubilization Irises markedly and may level off to a plateau thus leading to a sigmoidal solubility profie with hydrotrope concentration. The critical hydrotrope concentration being the same for many solubilizates appears to be the characteristic of a hydrotrope and is 0.67 mol/L for sodium salicylate. The surface tension decreases gradually from 72 mN/m for water to a limiting value of 50 mN/m with hydrotrope Concentration (Balasubramanian et al., 1989). As the hydrotropes are believed to form molecular aggregates incorporating solubilizate by intermolecular interactions, it may be visualized to form a pseudophase. Thus both the hydrotrope and solubilizate, in the present case sodium salicylate (NaS) and salicylic acid (SH), are partitioned between the aqueous phase and the aggregative pseudophase. The molecular species of salicylic acid (SH) is assumed bound in the aggregative pseudophase of bound N
0888-5885/91/2630-0722$02.50/00 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991 723 molecular species of sodium salicylate (NaS). All sodium salicylate above the critical hydrotrope concentration is in bound molecular form constituting an aggregate pseudophase and up to the critical hydrotrope concentration dissociated completely in ionic species. Thus if [NaS], is total concentration of sodium salicylate in solution (kmol/kg), ita concentration in aggregate pseudophase is [NaSIb = [NaSl, - [NaS], [NaSI, > [NaSl, =0 [NaS], C [NaS], (1) Above the critical hydrotrope concentration, salicylic acid concentration (kmol/kg) in bound form can be expressed
represented by a circumflex (*) over the corresponding symbol. The total amount of sulfuric acid present within the precipitator at any time due to addition of dilute sulfuric acid as a precipitant can be described by dc^A/dt Q c ~ (11) This also reflects the measure of the total amount of sulfate radical present in the crystallizer as [H+]will be consumed. As only total concentration of salicylic acid (bound, free, and ionic) in the solution phase is empirically observable, ita variation can be expressed
as [SH]b = [[NaSIb + (2) where [ and ( are constants determined from the experimental solubility data. The remaining salicylic acid will exist as molecular and ionic species in aqueous phase being in equilibrium with each other at any time. The proposed scheme of salicylic acid precipitation with chemical reaction from its hydrotropic solution may be written as NaSb Na+ + s(3) SHb
+
-* + - ++ -
H2S04
SHf
H+
HS04-
S-
The first term on the right-hand side of eq 12 represents the total rate of salicylic acid generation due to chemical reaction between sodium salicylate and sulfuric acid and is equal to
(4)
(5)
H+
HS04- S042- H+ (6) SHf SH, (7) The two equilibrium relations in the solution phase are [H+][S-] = KSH[SH]
where
'
[H+1[S042-I ='KHS04[HS04-l
(8) (9)
where K S Hand KHso,are the equilibrium constants for salicylic acid and bisulfate ion, respectively. These can be determined from the literature values (Landolt-Bornstein, 1960; Robinson and Stokes, 1955) by correcting for average activity coefficients according to the method of Guntelberg (Guggenheim, 1965) from the ionic strength of the mixture during the precipitation (see also Franck et d. (1988)). There are eight species in the solution ( N d b , SHb, SHf, H+, S-,HS04-, S042-, Na+) and the solid precipitate. For the case of precipitation without chemical reaction eqs 5,6, and 8 are not required and species HS04and SO4* are absent. It is possible to set up an algorithm to calculate concentrations of the species in terms of measured quantities using the principle of electroneutrality and species balance equations. The process description evolved in the following section is based on empirical observations and uses only observables in its characterization. Mathematical Representation Salicylic acid is precipitated as a result of both fast chemical reaction between sodium salicylate and dilute sulfuric acid and changes in solubility due to decrease in sodium salicylate concentration. Solvent Capacity and Concentration Variations. The variation of solvent capacity, Le., the amount of water, starting from an initial solvent capacity Vo may be represented as dV/dt = Q (10) As the total solvent capacity of the precipitator is time varying, the specific quantities like concentration and population density need to be defined on the basis of total solvent capacity at any time. These quantities will be
The initial conditions are v = VO, 2 A = 0, C*SA = c@vO, 2 ~ =~ C 9N ~ ~ V Oat t = 0 (15)
If however water is used as precipitant, salicylic acid will not be produced by a virtue of chemical reaction and consequently eqs '11 and 14 will not be applicable. Equation 12 without the first term on the right (Le., generation due to chemical reaction) will represent the overall salicylic acid mass balance for this system. Addition of water as a diluent to the precipitator will reduce the concentration of hydrotrope &e., sodium salicylate), resulting in lower solubility of salicylic acid and subsequent precipitation due to generation of supersaturation. Population Balance and Moment Equations. With negligible agglomeration and breakage of crystals the population balance equations for a semibatch'precipitator is afi I aii -+G-=O at aL where G is the size-independent overall linear growth rate. For an unseeded semibatch crystallizer the relevant boundary conditions to the population balance equation (eq 16) are fi(O&) = 0 (17) and ii(t,O) = B/C (18) where B is the nucleation rate at near zero size. Moment transformation of the population balance equation (eq 16) with respect to size yields dpo/dt = B (19) dfi,/dt = DOG
(20)
d&/dt
(21)
2ji1G
dfi,/dt = 3&G with boundary conditions
(22)
724 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991
iij = 0 at. t = 0
j = 0, 1, 2, 3
(23) P"trddllbndt 1. waterbath 2. preolpltant stock solutlon 3. perlataltlo pump 4. constant head tank 6.needle MIW 6.rotemeter 7. caplllary tube h.olDlt.l# unlt 8. preolpltetor 9. eleotrlc motor 10. dlgltal rpm meter 11. thermmter 12. aampllng tube 13. pH probe 14. waterbath
The variation of crystal size in a semibatch crystallizer starting from L = 0 at t = 0 as the initial condition may be represented as &/dt = G (24) The population balance equation (eq 16) coupled with concentration profiles (eqs 10-14) through the set of moment equations (eqs 19-22) with appropriate boundary conditions represents mathematically the semibatch reactive precipitation of salicylic acid. Process Identification. In order to characterize the rate processes in a precipitator, experimental responses obtained from a laboratory-scale crystallizer can be used. Chemical reaction between sodium salicylate and sulfuric acid is fast and chemical equilibria between ionic and molecular species prevail a t any time. The total rate of disappearance of sodium salicylate (kg/s) due to chemical reaction from simplified species mass balance can be written as
The total amount of sulfuric acid (i.e., sulfate radical) in the precipitator (eq 11)and [H+]from the measured pHtime variation are known. Using eq 9 with the equilibrium constant, &so,, corrected for average activity coefficients of ionic species, it is possible to determine the concentration of sulfate and bisulfate ions and hence the rate of disappearance of sodium salicylate due to chemical reaction (eq 25), which is the same as the rate of generation of salicylic acid (eq 14) because of chemical reaction at any time. When water is used as a precipitant no chemical reaction occurs. The method of s-plane analyis can be used to determine both the growth and nucleation rate from a pair of experimental transient population density curves obtained from a solvent capacity varying and perfectly mixed precipitator (Tavare and Garside, 1986,1987). By taking the Laplace transform of population balance equation (eq 16) with respect to size and assuming G and n(t,O) constant over a small time interval between t and t + At, the following working equation results on further simplification: Afi(s,t) -= -Cs(fi(s,t)) + B At where A;(s,t) is the difference between the Laplace transformed population densities at any time t and t + At and ( f i ( s , t ) ) is the average of these quantities. In this method a plot of the time rate of change of the Laplace transformed population density against the product of the Laplace transform variable and the average Laplace transformed population density over the optimal ra_nge of the Laplace transform variable constrained by sfLz yields a straight line with slope = -G and intercept = B. The nucleation and growth rates represent the average value over the time interval, and so all other state variables incorporated in the kinetic correlations should correspond to an average time.
=a
Experimental Section A series of experiments was performed to study the precipitation of salicylic acid from its hydrotropic solution in a 1.3-Ljacketed and agitated glass vessel provided with a flat lid. The schematic diagram of the experimental setup is shown in Figure 1. A 4-cm-diameter stainless steel six-blade turbine impeller was mounted at the central axis
Figure 1. Experimental setup.
with a clearance of 1.3 cm from the bottom. The temperature within the crystallizer was maintained at a constant value of 30 "C by circulating constant-temperature water from the water bath through the jacket. The precipitant (either water or dilute sulfuric acid solution having concentration 2.8 X lob kmol/kg) maintained at the same constant temperature of 30 "C in a water bath was pumped via a peristaltic pump to a constant head tank and then added continuously at a predecided rate into the crystallizer via a rotameter from the constant head tank. In a typical experiment -200 g of concentrated solution of sodium salicylate (-0.8 kg of NSA/kg of water) nearly saturated with respect to salicylic acid was charged into the crystallizer. When the working temperature was reached and the stirrer speed adjusted to a desired value, the precipitant addition a t a desired rate was started to begin the run. The pH meter electrode was inserted into the crystallizer to monitor the pH profile during the run. Several samples (-5 g) of clear solutions were withdrawn at different time intervals for solution concentration analysis. Small suspension samples of known volume (1-5 mL) were taken from the crystallizer for crystal size analysis, eight or nine such samples being taken at approximately 10-min intervals. After running the crystallizer for about 90 min the entire contents were removed and filtered and the product crystal was air-dried. Scanning electron micrographs of the final product crystals were taken to observe the crystal habit. The concentration of solution samples was determined volumetrically by titrating against standard sodium hydroxide solution (0.02 mol/L) and reflecta the total aalicylic acid (bound, free, and ionic) in the solution phase. The transient batch population density was measured by using a multichannel Coulter counter (Model TAII with population count accessory) fitted with a 280-pm-diameter orifice tube, measurements being made in the range 6.5-130 pm. The electrolyte used was Isoton supplied by Coulter Electronics and saturated with salicylic acid and small amount of Teepol as a dispersant was added. The solubility of salicylic acid in aqueous solution of sodium salicylate was determined by equilibrating an excess of solid salicylic acid with the solution of known sodium salicylate Concentration. The equilibration was carried out in a 50-mL magnetically stirred flask for several hours at a constant temperature of 30 "C and with the flask kept overnight without agitation. The salicylic acid concentration in this solution phase was determined volumetrically by titrating against standard sodium hydroxide solution (0.02 mol/L). Results and Discussion The solubility expressed in kg of SA/kg of water was
Ind. Eng. Chem. Res., Vol. 30,No. 4, 1991 725 0. I O
-
C r I t I ca I h y d r o t rope concent r a t I on cNc = , 108 kg NSA/kg water
L
-----.
-
x 07
C a l c u l a t e d from e q ( 2 7 )
v Run 2 Run
3
o Run 8
from Eq 127)
Y
m
cmloulmtmd emmntrmt ion
.qui librim cmmntrmt ion
B
\
< cn 07
Y
30.05 x
Y
-
A
n A
0
cn
0.00 0.5
0.0
1.0
0
Tim.,
6ooo
t (a)
Figure 4. Salicylic acid concentration profiles: effect of stirrer speed and reaction.
Figure 2. Solubility relation. 5.5
bo00
ZMK)
Concentrat Ion, c, ( k g NSA/kg water)
-.
-
cmlculmtmd pH from mmcond ordmr polynontml Run
3
I Run
Run o Run
3 4 8
-
-----.
3
cmlculmtmd ooncmntrmt ion
mqui l i b r i u concmntrmtlon
Run 4 o Run 5
from Eq 127)
:
v Run 1
PO
ra b. 5
3 L 0
5.158 5.123 5.050
-0.312 -0.2bS -0.277
0.248 0.16b 0.277
1.0
bo00
zoo0
0
Time,
6000 0
t (61
Figure 3. pH-time variations.
correlated empirically into a second-order polynomial at 30 "C as C& = -0.026 0.13~~ - 0 . 0 3 ~ ~ CN ~ 2 0.4
+
0.0036 - OmOllcN + 0 . 1 3 ~ ~CN ~ < 0.4 (27) where cN is the concentration of sodium salicylate (kg of NSA/kg of water). Figure 2 shows this correlation which indicates that the solubility of salicylic acid increases rapidly above the critical hydrotrope concentration (cN, = 0.108 kg of NSA/kg of water 0.67 mol/L solution) and -20-fold increase in solubility can be realized. An exploratory experimental work suggested that sodium sulfate had little influence on solubility (change in solubility -0.003 kg of SA/kg of water). Eight successful runs were performed. During the first three runs (runs 1-3) with hydrotropy and the last three (runs 6-8) with hydrotropy and reaction, the precipitant flow rate was kept constant (-0.15 g/s) and stirrer speed varied from -5 to -10.4 rev/s. For run 4 the precipitant (water) was added a t low flow rate initially (-0.095 g/s until 2700 8) and then a t high flow rate (-0.28 g/s) till
boo0
ZMK)
6Ooo
Tlne, t (SI
Figure 5. Salicylic acid concentration profiles: effect of precipitant addition rate.
the end while for run 5 the initial flow rate was high (-0.28 g/s until 1800 s) and then low (-0.095 g/s) till the end. Experimentally observed pH-time variations along with their second-order-polynomial fits for three runs are depicted in Figure 3. The variations of salicylic acid concentrations as determined by volumetric analysis and solubility relation (eq 27) for six runs are shown in Figures 4 and 5 while the calculated time variations of concentration of sodium salicylate and added sulfuric acid along with solvent capacity are delineated in Figure 6. In all these runs pH decreases from about 5.2 to 4.3. These variations reflect the precipitant addition profiles with and without reaction. In general with the high precipitant addition rate pH decreases rapidly thus increasing [H+]. With reaction usually pH is maintained at slightly higher value than those without reaction. The pH of concentrated solution of sodium salicylate (-0.8 kg of NSA/kg of water) is about 2.4. With stoichiometric proportion of dilute reactants in water, pH increases slightly to about 2.5 in a batch experiment and decreases from -4
726 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991 1 XIO"
r (P
2 0
V 0
n
1 XlO'
RO
0
4000
t
11
___-------------- I .?om
I 50
0
6ooo
to -2.5 in a semibatch mode with sulfuric acid addition (Franck et al., 1988; Al-Khayat, 1988). In all the runs measured and equilibrium concentration of salicylic acid in the solution phase decreases with time as a result of decrease in concentration of sodium salicylate (Figure 6) by virtue of dilution with water and reaction with sulfuric acid if present. In Figure 4 runs 2 and 3 were performed at high (-10.4 rev/s) and low ( - 5 rev/$ stirrer speeds, respectively, and run 8 was performed at the same stirrer speed as run 3. Both the stirrer speed and reaction appear to have slight effect on concentration profiles of salicylic acid. Precipitant addition rate can influence significantly salicylic acid concentration profile as shown in Figure 5 and subsequent product characteristics. This is consistent with the previous studies (Tavare and Garside, 1987,1990). Concentration profiles of sodium salicylate and added sulfuric acid and solvent capacity variation in Figure 6 reflect the precipitant addition rates. Mass balance on salicylic acid appears to give a reasonable closure in these runs; i.e., the difference between weight of product solid salicylic acid produced and that calculated from concentration analysis is small. Solid precipitate obtained in runs with reaction (runs 6-8) is just over 6 g and without reaction (runs 1-5) is around 2.5 g. Scanning electron micrographs of the product salicylic crystals indicated that they were rod-shaped crystals and had exactly the same crystal habit as those precipitated from dilute sodium salicylate solution in both batch and semibatch modes of operation (Al-Khayat, 1988). Both scanning electron micrographs of the product crystals and the crystal size distribution measurements by the Coulter counter tended to suggest that high stirrer speed, high initial addition of precipitant, and chemical reaction yielded a large number of small particles and slow stirrer speed and initial slow precipitant addition produced a small number of large particles. Both supersaturation and hydrodynamics appeared to influence nucleation and growth processes. Size distribution data obtained from the Codter counter measurements, some results from run 3 being shown in Figure 7, were used to calculate the growth and nucleation rates by the method of s-plane analysis. Growth and nucleation rates obtained from all the experimental runs (32 observations from 8 runs) using the successive pairs of population density curves were correlated by power law
IO0
I50
C r y s t a l size, L
Tlme, t ( 8 )
Figure 6. Variations of sodium salicylate and sulfuric acid concentrations and solvent capacity.
i
1 XlO'
(pm)
Figure 7. Population density data.
I
.w.
b
8
6
? # * I
I
Growth r a t e , G,
8
.le
4
I
a r D * i
(m/d
Figure 8. Growth rate correlation.
kinetic expressions in terms of observables as density curves were correlated by power law kinetic expressions in terms of observables as
G = (9.7 x 1 0 ~ ) ~ ~ p ~ ~ 4 " 0 ~(28) 7 and B (1.6 X 10")GW9 (29) During the experimental program precise estimation of supersaturation driving force was not possible, and hence it was not incorporated in these correlations. The other conventional and observable variables were less significant over the range of variables encountered. Graphical presentation of these correlations are depicted in Figures 8 and 9, showing reasonable quality for precipitation kinetics (multiple regression coefficient r = 0.4 for the growth rate correlation (eq 28) and 0.7 for the nucleation rate correlation (eq 29)), the scatter in the growth rate correlation being usually large with this method. The relative root mean square errors based on the observed value in log and
Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991 727
@
\
-
P
----
u Run 4
--
o Run 0
Run
3
0 C Y
-... (p' L,
0
I
8
' 4
f
0
Nucl-tvon
rrte, #& (no/s kg water)
Figure 9. Nucleation rate correlation.
the actual variables in the growth rate correlation (eq 28) were 4 and 11270,and those in the nucleation rate correlation (eq 29) were 13 and 306%, respectively. All the exponents in these kinetic correlations in terms of observables appeared reasonable. Variances of the parameter estimates for exponents of measured total salicylic acid (bound, free, and molecular) concentration, hydrotrope (i.e., sodium salicylate) concentration (as determined from the mass balance relationship), and stirrer speed in the growth rate correlation (eq 28) were 0.4,0.8, and 0.3 and for exponents of growth rate &e., relative kinetic order) and stirrer speed in the nucleation rate correlation (eq 29) were 0.05 and 0.6, respectively. It was rather difficult to attribute any mechanistic implication to these exponents. Concentrations of salicylic acid and sodium salicylate and stirrer speed appeared to influence both these rates. In order to demonstrate the consistency of these parameter estimates, the time evolution of population density curves and the salicylic acid depletion curves were calculated in all these runs by solving simultaneously the set of equations set out in the section Mathematical Representation using the kinetic correlations and appropriate initial conditions. In the numerical algorithm once the precipitate was produced a provision of constraining the calculated salicylic acid concentration to equilibrium value (as determined by eq 27) in order to calculate the kinetic rates (eqs 28 and 29) was incorporated. Calculated salicylic acid variations along with the corresponding equilibrium concentration profiles (determined from eq 27 using calculated concentration of sodium salicylate from mass balance relation) are included in Figures 4 and 5. A comparison between the measured size distribution of the final sample by the Coulter counter and that calculated from the numerical algorithm is shown in Figure 10. Both the calculated depletion of salicylic acid and the corresponding final size distribution are in reasonable agreement with the experimental curves. Measured population density curves show substantially higher changes than the calculated population density curves. Uncertainties associated with the estimated kinetic rates are usually large. It is important to note that the maximum size in the calculated population density curve is determined by the average growth rate (eq 24). Comparison between the observed and calculated size distri-
U P
0
50
100
150
Cry8t.l 8120, L P m ) Figure 10. Comparison between observed and calculated final population density curves.
butions illustrates a generd feature of calculation technique, and similar observations have been reported previously in batch potash alum crystallization and semibatch silica precipitation studies (Tavare and Garside, 1986, 1987). Moments analysis can conveniently be used to characterize the model parameters. It is rather difficult to recover the original experimental responses from known moments. Nevertheless the study does provide valuable information regarding precipitation kinetics of salicylic acid from ita hydrotropic solution and an example of superimposition of chemical reaction on precipitation process. Conclusions Precipitation of salicylic acid from concentrated sodium salicylate solution using water or dilute sulfuric acid as a precipitant was studied in a 1.3-L laboratory-scale agitated and jacketed glass vessel used in a semibatch mode. Sulfuric acid reacts with sodium salicylate to produce salicylic acid. When concentrated sodium salicylate solution is diluted with the precipitant, the solubility of salicylic acid decreases substantially resulting in precipitation of salicylic acid. Thus supersaturation of salicylic acid can be generated by both chemical reaction and solubility changes on dilution due to hydrotropy. In a series of experiments, profiles of solution concentration of salicylic acid and pH and transient population density curves were determined. Kinetic correlations for crystal growth and nucleation rates were developed from these experimental results, viz., crystal size distribution data and concentration and pH profiles. An algorithm to evaluate the salicylic acid concentration profiles and the crystal size distributions of the product precipitate resulting from a homogeneous chemical reaction and hydrotropy in a semibatch precipitator was developed. Results of both the salicylic acid concentration profiles and crystal size distributions of product precipitate compare favorably with the experimental observations. Acknowledgment We thank Mr. A. Al-Khayat for his help during this work. Nomenclature ai = constants in second-order polynomial for p H (Figure 3) B = nucleation rate (no./(kg of water s))
728
Znd. Eng. Chem. Res. 1991,30, 728-733
c = concentration of
solute (kg of SA/kg of water)
Ac = concentration driving force, c - c* (kg of SA/kg of water)
G = overall linear growth rate (m/s) i = relative kinetic order, i.e., exponent of G in eq 29 k, = surface shape factor k, = volume shape factor K = equilibrium constant (kmol/kg) L = crystal size (m, pm) t 2= population average size at time t + At (m) AL = difference between successive sizes (m, rm) M N =~molecular weight of sodium salicylate (kg/kmol) n = population density (no./(m kg of water)) no = nuclei population density (no./(m kg of water)) N = stirrer speed (rev/s) Q = precipitant (water or sulfuric acid) addition rate (kg/s) s = Laplace transform variable (m-*) t = time (s) T = temperature ("C,K) V = solvent capacity of the crystallizer (kg) Greek Symbols a = solid salicylic acid deposition rate (kg of SA/(kg of water 8))
A = difference
t = constant in eq 2 (kmol/kg)
= jth moment of crystal size distribution (no. of crystals mj/kg of water) [ = constant in eq 2 p = density (kg/m3) Subscripts
A = sulfuric acid b = bound c = critical, crystal f = final, free L = at size L N = hydrotrope NaS = sodium salicylate (total or ionic) NSA = sodium salicylate (total) 0 = initial value r = reaction s = solute, solution, solid SA = salicylic acid (total) SH = salicylic acid (molecular) t = total Superscripts
= based on total capacity at any time Registry No. SH, 69-72-7;NaS, 54-21-7;HfiO,, 7664-93-9; HZO, 7739-18-5.
Literature Cited Al-Khayat, A. Reaction Crystallization of Salicylic Acid. M.Sc. Thesis, Victoria University of Manchester, Manchester, 1988. Aslund, A.; Rasmuson, E. A. Reactiue Crystallization of Benzoic Acid. Report submitted to Royal Institute of Technology, Stockholm, 1986. Balasubramanian, D. J.; Srinivas, V.; Gaikar, V. G.; Sharma, M. M. Aggregation Behavior of Hydrotrope Compounds in Aqueous Solution. J. Phys. Chem. 1989,93,3865-3871. Franck, R.; David, R.; Klein, J. P.; Villermaux, J. A Chemical Reaction Engineering Approach to Salicylic Acid Precipitation: Modelling of Batch Kinetics and Application to Continuous Op eration. In World Congress 111 of Chemical Engineering; The Society of Chemical Engineers: Tokyo, 1986;Vol. 11, paper no. 8g-216,pp 992-995. Franck, R.; David, R.; Viermaux, J.; Klein, J. P. Crystallization and Precipitation Engineering-I1 h Chemical Reaction Engineering Approach to Salicylic Acid Precipitation: Modelling of Batch Kinetics and Application to Continuous Operation. Chem. Eng. Sci. 1988,43,69-77. Guggenheim, E. A. Thermodynamique; Dun& Paria, France, 1965; p 337. Landolt-Bornstein. Zahlenwerte und Funktionen aus Physik, Chemie Astronomie, Ceophysik und Technik, 6 sufl, Band 11, Teill 7,Flektnsche Eigenhaften 11; Springer: Berlin, 1960; p 867. McKee, R. H. Use of Hydrotrope Solutions in Industry. Ind. Eng. Chem. 1946,38,382-384. Robinson, R. A.; Stokes, R. H. Electrolytic SoZutiom; Butterworth London, 1955; p 376. Saleh, A. M.; Badwan, A. A.; El-Khordagui, L. K.; Khalil, S. A. The Solubility of Benzodiazepines in Sodium Salicylate Solution and a Proposed Mechanism for Hydrotropic Solubilization. Int. J. Pharm. 1983a,13,67-74. Saleh, A. M.; Badwan, A. A.; El-Khordagui, L. K. A Study of Hydrotropic Salts, Cyclohexanoland Water Systems. Int. J. Phurm. 1983b, 17, 115-119. Tavare, N. S.; Garside, J. Simultaneous Estimation of Crystal Nucleation and Growth Kinetics from Batch Experiments. Chem. Eng. Res. Des. 1986,64,109-118. Tavare, N. S.; Garside, J. Reactive Precipitation in a Semi-batch Crystallizer. In Recent Trends in Chemical Reaction Engineering; Kulkarni, B. D., Mashelkar, R. A,, Sharma, M. M., Eds.; Wiley Eastern: New Delhi, 1987;Vol. 11, pp 272-281. Tavare, N. S.; Garside, J. Simulation of Reactive Precipitation in a Semi-batch Crystallizer. Trans. Inst. Chem. E. 1990, 68A, 115-122.
- = average quantity * = equilibrium
Receiued for review June 16,1990 Revised manuscript receiued October 10, 1990 Accepted October 23, 1990
= derivative
Moment Analysis of Transient Membrane Permeation with an Immobilizing Chemical Reaction B a r r y P.Vant-Hull and Richard D.Noble* Chemical Engineering Department, University of Colorado, P.O.Box 424, Boulder, Colorado 80309
The use of moment analysis to analyze the transient response of membranes containing an immobilizing chemical reaction is presented. Moment analysis has the advantage that the analysis can be done in the Laplace domain so that inversion of the Laplace domain solution is unneceseary. The analysis can be used for any transient input function. Examples are presented to illustrate the technique. Introduction As reactive membranes grow in importance as a method of gas separation, it becomes increasingly important to develop means for analysis of their physical properties and
kinetic characteristics. Moment analysis is a method that has been of great value in the analysis of chromatography columns and catalytic packed columns and shows promise in membrane science as well. It is applied here to the
0888-5885/91/2630-0728$02.50/00 1991 American Chemical Society
