Ind. Eng. Chem. Res. 2008, 47, 5861–5870
5861
Isothermal Seeded Semicontinuous Reactive Crystallization of Crude Terephthalic Acid Crystals† Qinbo Wang,*,‡,§ Youwei Cheng,§ Lijun Wang,§ Haibo Xu,⊥ and Xi Li*,§ College of Chemistry and Chemical Engineering, Hunan UniVersity, Changsha, 418002 Hunan, P.R. China, Department of Chemical Engineering, Zhejiang UniVersity, Hangzhou, 310027 Zhejiang, P.R. China, and Zhejiang Hualian Sunshine Petrochemical Co., LTD., 312000 Zhejiang, P.R. China
In the reactive crystallization of terephthalic acid (TA) by liquid-phase oxidation of p-xylene (PX), four simultaneous physicochemical processes occurred, including the oxidation of PX to TA, the nucleation of TA from solution, the growth of TA crystals, and the incorporation of impurity 4-carboxybenzaldehyde (4CBA). In this work, by using the experimental technique of seeded semicontinuous reactive crystallization, the growth of TA crystals and the incorporation of impurity 4-CBA were studied. The effects of supersaturation and temperatures on the crystallization kinetics were experimentally examined. A detailed semicontinuous reactor model including chemical reactions, TA growth, and 4-CBA incorporation was developed. The model was solved numerically to optimize the model parameters for crystallization kinetics. The effect of temperatures on the growth rate and the incorporation rate was studied and correlated. The correlated results agreed with the experimental results satisfactory. The obtained crystallization kinetics can be used as essential data to predict the growth of TA crystals and the incorporation of impurity 4-CBA. Introduction Commercially, the majority of terephthalic acid (TA) is produced by the air oxidation of p-xylene (PX) in acetic acid (HAc) at 423.2-483.2 K. In the oxidation process, PX, aqueous HAc, and a solution of the cobalt-manganese catalyst and bromide promoter are fed continuously to one or more reactors, through which air is passed.1–3 Owing to the low solubility of product TA in aqueous acetic acid,4,5 most of it precipitates during the oxidation process. To gain a better insight into the crystallization process and identify the effects of different operation conditions on the progress of the crystallization process, it is essential to study the crystallization kinetics. Further, the rational design, optimization, control, and analysis of the crystallization and the subsequent slurry treating process require the knowledge of the kinetics.1–3 Saska examined the crystallization process by enclosing a small amount of a TA-water mixture in a glass capillary. These experiments were emphasized on the evolution of crystal structure and the results revealed rod-shaped, faceted crystals which had nucleated and grown on the original globular TA crystals.6–8 Similar work has also been done by Robinson.9 However, these experimental works were performed at temperatures lower than 373.2 K, which differed from the industrial operation conditions (423.2-483.2 K) greatly. The shortage directly constricted the applicability of their experimental results. Brown10,11 and Marquering12 studied the growth kinetics of TA in pure water and 90 wt % acetic acid solution, and the growth kinetics was measured by isothermal seeded desupersaturation crystallization. However, when the Arrehenius equation was used to correlate the effect of temperature on the growth rate, a negative activation energy was obtained. This meant the higher * To whom correspondence should be addressed. Fax: 86-57187951227. Tel.: 86-571-87952210. E-mail:
[email protected] (Q.W.),
[email protected] (X.L.). † This paper is partly abbreviated from the Ph.D. dissertation of Qinbo Wang. ‡ Hunan University. § Zhejiang University. ⊥ Zhejiang Hualian Sunshine Petrochemical Co., LTD.
the temperature was, the slower the growth rate would be. It was contrary to the common understanding on crystallization13 and need to be further proved. Furthermore, the experimental temperature adopted by Brown and Marquering ranged from 298.2 to 353.2 K, which also differed from the industrial operation condition greatly. Ding et al. had also studied the nucleation and growth kinetics for TA crystallization by the method of cooling crystallization in the reactive crystallized slurries.14–16 As described by Ding et al., the experiments consisted of three steps. At first, PX was oxidized into TA at 461-463 K in a reactor. The solubility of TA in aqueous acetic acid in the experimental temperature range was very low, and more than 95 wt % TA produced from the oxidation of PX precipitated in the reactor. Second, the slurry in the oxidation reactor was transferred into a preheated crystallizer, in which the initial temperature was controlled to be lower than the reaction temperature. Finally, the cooling program was started and the crystallization of TA began. During the course of crystallization, the solid and liquid phase were sampled at some time interval. From this experimental scheme, we could conclude that in the crystallizer less than 5 g TA might precipitate onto the surface of 95 g TA seeds in the crystallizer if the total mass of TA was 100 g. In such experiments the number of seeds was too much, and the growth kinetics was nearly impossible to be determined from the growth of 5 g TA onto the surface of 95 g TA seeds, let alone the nucleation kinetics. The growth and nucleation kinetics experimentally determined by Ding et al. were doubtful.1 It is a well established fact that crystallization in the presence of impurities can result in the incorporation of the impurity in the solid product. Besides the product TA and reactant PX, many other intermediates occur in the oxidation of PX. These intermediates will incorporate into the TA crystals to form crude TA, among which the intermediate 4-carboxybenzaldehyde (4CBA) is the most undesirable impurity. The difference between 4-CBA and TA is that 4-CBA has an aldehyde group rather than a carboxylic acid group para to the other carboxylic acid group on the benzene ring. 4-CBA is so chemically and physically similar to TA that it is one of the most difficult
10.1021/ie061595v CCC: $40.75 2008 American Chemical Society Published on Web 07/22/2008
5862 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008
contaminants to remove and, unfortunately, is probably one of the most deleterious. To gain a better insight into the incorporation process and identify the effects of operation conditions on the progress of the incorporation process, it is essential to study the impurity incorporation kinetics. Further, the rational design, optimization, control, and analysis of the incorporation and the subsequent purification process require the knowledge of the kinetics.1 Robinson studied the incorporation of 4-CBA into TA crystals by recrystallization experiments.9 The experimental results indicated that the degree of impurity incorporation was dependent on several variable parameters including the rate of mass transfer of impurity in solution and the rate of crystal growth from solution, and none of the existing theories on the distribution of impurities between the liquid and the solid phase provided an explanation for the observed experimental results. Later, Saska interpreted the observations of Robinson and simulated the binary crystal growth of TA and 4-CBA by Monte Carlo method.6–8 As mentioned above, the experimental conditions adopted by Robinson and Saska differed from the industrial operation condition greatly, which directly constricted the applicability of their experimental results. In a recent work, Cincotti simulated the cocrystallization of TA and 4-CBA theoretically, and the driving force for TA and 4-CBA crystallization was assumed to be the supersaturation existed in solution.17 It was reported that the solubility of 4-CBA in aqueous acetic acid was very high.18 We had checked the solubility of 4-CBA in the presence of TA at the industrial oxidation conditions by using the reported solubility data18,28 and found the predicted saturated 4-CBA concentration was still much large than the measured 4-CBA concentration in the reactor.1 It indicated that since the solubility of the cocrystal of TA and 4-CBA might be much lower than that of 4-CBA alone, the solution in the industrial reactor was still unsaturated with respect to 4-CBA.1 It was difficult for 4-CBA to crystallize into TA crystals if the driving force for 4-CBA cocrystallization was the supersaturation existed in solution as assumed by Cincotti. From the above brief literature survey, we can find that the available literature is not complete when one looks for the crystallization kinetics of TA and incorporation kinetics of impurity 4-CBA. There exists a scope and a necessity to study the kinetics of the two simultaneous processes, and it is just the purpose of this work. Reaction Scheme and Kinetics Kinetic Scheme. The liquid-phase catalytic oxidation of PX to TA belongs to the kind of classical free radical chain reaction. The mixture of cobaltic, manganic, and bromide salts are used as catalyst species. The formulation of detailed kinetic models of the complex process which describes all the involved radical chain reactions and all the intermediate products is not desirable in practice. This is mainly because the estimation of the kinetics parameters of the radical chain reactions by fitting of the experimental data is very difficult to be performed when the concentrations of the participating components (that is, the radical species in the liquid phase) are difficult to be measured. In order to low the computing efforts, the most common approach is to lump the detailed mechanism into a set of global reactions which involves only molecular species, whose concentration can be, in principle, easily monitored as a function of time.1–3,17,19–25 Without involving formal procedure of general validity but simply including the minimum number of reactions to describe the behavior of all the species of interest, various lumped kinetic schemes for the liquid-phase catalytic oxidation
Figure 1. Lumped kinetic scheme for the oxidation of p-xylene to terephthalic acid. Table 1. Reaction Kinetic Model Parameters in Equation 1 -10
10 ki0/(1/min) λi/(kgHAc/mol) ε Ea/(kJ/mol)
i)1
i)2
i)3
i)4
8.148 3.97
13.97 2.19
1.164 1.00
4.656 1.98
0.30 84.2
process of PX to TA have been developed in the literature.1–3,17,19–25 By accounting for the most important intermediates and final products of the process, i.e. p-tolualdehyde (TALD), p-toluic acid (PT), 4-CBA, and TA, Wang, Cheng, and Xu have recently proposed a lumped kinetic scheme shown in Figure 1 for the liquid-phase oxidation process1–3,22–25 where the reactions of PX to TALD and PT to 4-CBA involve the addition of 1 O2 and the removal of 1 H2O, and the reactions of TALD to PT and 4-CBA to TA involve the addition of 1/2 O2. Reaction Kinetics. By using specially designed experimental technique, the oxidation of PX oxidation to TA had been completely studied in our workgroup, and a great deal of experimental data was obtained.1–3,22–25 These studies disclosed the reaction mechanism and quantitatively determined the effects of various reaction conditions on the reaction rate, which was practically and theoretically valuable. Using several assumptions a simple fractional-like kinetic model as shown in eq 1 is derived from the assumed reaction mechanism.
( )
ri ) ki0 exp -
Ea ci RT λ1c1 + λ2c2 + λ3c3 + λ4c4 + ε
(1)
where ri and ki0 are the reaction rate and the reaction rate constant of ith step reaction shown in Figure 1, Ea is the activation energy, and ci is the concentration of the ith component in solution. Factors affecting ki0 are water content, catalyst concentration and ratio, etc. The meaning of other symbols is reported in the notation. The model parameters ki0, Ea, λi, and ε at the present experimental conditions have been reported in a previous paper and are listed in Table 1.22 Experimental Scheme and Procedure Experimental Scheme. Some coupled processes, including the oxidation of PX to TA, the nucleation of TA from solution, the growth of TA crystals, and the incorporation of impurity 4-CBA, simultaneously occurred in the reactive crystallization of crude TA. The simultaneous determination of the above four kinds of kinetics appears complicated and difficult. Alternatively, these simultaneous steps can be decoupled and studied in different specially designed experiments. Except the impurity incorporation of 4-CBA into TA crystals, the effect of crystallization on the reactions in liquid-phase is negligible, and the reaction kinetics have been determined in a previous work.22 By using the determined crystallization kinetics in the Ph.D. dissertation of Wang,1 the supersaturation of solute TA in solution for unseeded and seeded reactive crystallization process was simulated and qualitatively shown Figure 2.
Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5863
Figure 2. Supersaturation of solute TA vs time during reactive crystallization of TA.
In unseeded reactive crystallization, the concentration of solute TA would increase from zero to a critical value and the increasing rate was approximately equal to the generating rate of TA due to chemical reactions. At the critical supersaturation, there would be a burst of nucleation, and large amounts of crystal nucleus generated and grew into crystals at the expense of solute TA existing in solution, which would lead to a sharp decrease of TA concentration. The results showed in Figure 2 revealed it and indicated a primary nucleation, which made the whole crystallization process unpredictable and uncontrollable.1 Because of the nucleation, the experimental repeatability was affected. However, in the seeded reactive crystallization, the solution was initially saturated by solute TA and there were large amounts of seeds. The concentration of solute TA would also increase from saturation solution to a critical supersaturation, and the increasing rate was approximately equal to difference of the generating rate of TA due to chemical reactions and the consuming rate due to crystallization. In this sense, the supersaturation increasing rate for seeded crystallization would be much slower than that for unseeded crystallization before the supersaturation increased to the critical value, and the critical supersaturation for seeded crystallization was relatively lower than that for unseeded crystallization. By seeded crystallization, the primary nucleation can be neglected respecting to the number of seeds, and the growth kinetics can be determined. For the nucleation kinetics, by using the crystal growth kinetics determined in this work, we intend to regress it from the measured crystal size distribution (CSD) in industrial reactors, but not regress it from the experimental data.1 By this decoupling experimental technique, we can determine the coupled growth and impurity incorporation kinetics from seeded reactive crystallization. Apparatus and Procedure. The experimental apparatus, sampling apparatus and analytical methods used in this work was described in detail by Wang1,22 and Xu.23 Briefly, it consisted of a 2.0 L reactor maintained at the desired temperature through forced circulation of diathermic oil and wall electric heating shown in Figure 3. The 2.0 L reactor was constructed from titanium to resist corrosion and was designed for temperatures up to 533 K and pressures up to 60 atm. A paddle type agitator with a turbine impeller is used for agitation. The system was equipped with three condensers in order to ensure complete condensation and recycle of the evaporated compounds. The pressure was controlled by a back-pressure valve to be 18 atm. A Pt100 thermal resistance thermometer was inserted into the vessel for the measurement of temperature, and the thermometers had an uncertainty of (0.1 K. In each experiment, TA seeds, solvent acetic acid and water, and catalysts Co/Mn/Br were batch deposited into the reactor at room temperature. The temperature was maintained within (0.5 K of the desired
temperature by a proportional, integral, and derivative (PID) controlling system. The slurry in the vessel was heated at 10 K/min to the experimental temperature. When the slurry temperature was heated to the experimental point, the liquid reactant PX and the gaseous reactant air were continuously fed into the reactor, and the reactive crystallization began. Reactive crystallized slurry were sampled every 10 min. Each experiment lasted 90 min. To simultaneously determine the components content in the solution and solid, we separated the solution from the slurry at the experimental temperature by using the specially designed sampling system shown in Figure 3. When the sampling valve (valve 20) was open, the slurry was transferred from the reactor into a titanium pipe between the atmospheric valve (valve 21) and nitrogen sweeping valve (valve 19). The titanium pipe was electric heated around the wall and the wall temperature was controlled to be approximately equal to the slurry temperature. After this was done, the sampling valve was closed, and the atmospheric valve and the nitrogen sweeping valve were open. The slurry was then pressed toward a porous sintered metallic filter with an internal aperture size of 1 µm. The filtered solution was then collected and cooled in a liquid sample collector, and the components concentrations in the solution were determined by the chromatograph method. The cake in the solid-phase sample collector was taken out. About 10 mL saturated solution was sampled each time. The experimental runs’ reproducibility was verified by repeating each of them at least twice.1,22,23 The experimental conditions were listed in Table 2, while fixing the reaction pressure at 1.8 MPa, the oxygen volume fraction in the vent at 4%, the initial mass percent of water at 3%, the catalyst mass fraction at w(Co) ) 1.9 × 10-3, the catalyst ratio(molar) at Co/Mn/Br ) 26/1/18, and the mass of crude TA seeds at 50 g, in which the mass content of 4-CBA is 2500 ppm. Analytical Techniques. The liquid reactant PX, liquid intermediates TALD, PT, 4-CBA, and product TA in the solution were analyzed by high-performance liquid-phase chromatography (HPLC), and the solvent HAc was analyzed by gas chromatography (GC). The internal standard method was used in the analysis, and toluene was used as the internal standard substance to correlate the data obtained from GC and HPLC analysis. The mass ratio of liquid component to toluene in the liquid was determined by HPLC. The mass ratio of solvent HAc to toluene in the liquid was determined by GC. The instrument information and detailed analytic technique has been given elsewhere.1,22,23 4-CBA concentration in TA crystals was determined by Agilent-1000 HPLC. The Hypersil SAX ion chromatographic column was used. The mobile phase consisted of water and acetonitrile. During the analytical process, the water content was maintained at 90 mass % and the content of acetonitrile was maintained at 10 mass %. The external reference method was used and each analysis took about 9 min. The size distribution of TA crystals was determined by the Malvern 2000S laser particle size analyzer. Ethanol saturated by TA crystals was used as the disperser. The typical reproducibility of volume-averaged crystal size between each size measurement was less than (1.5 µm. In this work, experimental run 2 was chosen as the reference experiments. In preliminary experiments, crystal sizing was carried out in duplicate for every sample. It was found that the sampling procedure was reproducible since the typical error of volume-averaged crystal size between each reading was less than (1.5 µm. The reported results thereafter corresponded to the average size of three
5864 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008
Figure 3. Experimental apparatus for the reactive crystallization of crude terephthalic acid. (1) nitrogen cylinder; (2) air cylinder; (3) mass flowmeter; (4) nitrogen/air switch valve 1; (5) air buffer vessel; (6) thermal resistance thermometer; (7) aging vessel; (8) vessel wall heating control circuit; (9) cooling coil; (10) cooling oil tank; (11) peristaltic pump; (12) agitator; (13) condenser; (14) back-pressure valve; (15) gas-liquid separator; (16) flowrator; (17) vent washing tank; (18) dewatering cotton; (19) nitrogen sweeping valve; (20) sampling valve; (21) atmospheric valve; (22) solid-phase sample collector; (23) sintered metallic filter; (24) liquid-phase sample collector; (25) plunger-type pump; (26) reactant tank. Table 2. Operating Conditions for the Experimental Runs run
1
2
3
4
5
6
T/(K) FPX/(g/min)
433.2 4.24
433.2 3.76
433.2 3.36
433.2 2.77
429.2 3.76
437.2 3.76
readings and the error bars were not included in any plot for clarity purposes since the error bars were very small. In our works, we designed a series of experiments to simultaneously determine the reaction kinetics and crystallization kinetics. The effect of gas-liquid mass transfer on the reaction must be eliminated. Experimental results showed the effect of stirring rate on the component concentration in solution was insignificant, and the influences of mass transfer and gas-liquid mixing on the oxidation process were negligible under the studied experimental conditions.1,22,23 The stirring rate for each experimental run could be chosen to be 750 rpm.
Figure 4. Measured CSD for crystallized TA at t ) 0, 50, and 90 min for experimental run 2. Table 3. Experimental Results for Run 2 at t ) 0 and 90 min mS/(gTA/kgHAc)
Laboratory Crystallizer Model Model Development. In this work, PX was continuously fed into the crystallizer and product TA was continuously produced, however, there was no TA crystals been removed from the crystallizer, which mean the operation manner was semicontinuous crystallization. Major equations describing semicontinuous crystallization include solute, solvent, energy and population balance. Simultaneous solution of these equations gives the crystal magma density, solution concentration, temperature, and population density. In this work the isothermal experiments were performed, which indicated that the energy balance was idle and could be removed from the set of equations. Before establishing the laboratory crystallizer model, the following two assumptions were made: (1) Nucleation could be neglected respected to the number of seeds. Taking experimental run 2 as example, according to the measured CSD as shown in Figure 4, the mass of seeds (t ) 0 min), the mass of solid when the reactive crystallization ended (t ) 90 min), and the crystal number N were calculated
t ) 0 min t ) 90 min
50.0 538.7
L43/(µm) 28.8 48.3
N/(no./kgHAc) 13
1.22×10 1.14×1013
CV 0.562 0.521
and shown in Table 3. Considering the number loss by sampling and caking on the cooling coil, the numbers of TA crystals at t ) 0 and 90 min were almost the same, which indicated that the nucleation could be neglected respect to the number of seeds. (2) Crystal shapes were uniform, and the increase of crystal size could be attributed to crystal growth. Figures 5 and 6 showed the scanning electron microscope (SEM) photographs for TA crystals at t ) 0 and 90 min, respectively. From the two photographs, we could clearly see that the crystal shapes can be regarded uniform, and the agglomeration of TA crystals could be neglected. From the CSD shown in Figure 6, we could see that the CSD was unimodal and no apparent crystal fragments are detected. From these results, we could assume that the increase of crystal size could be attributed to crystal growth. On the basis of the above two assumptions, the population balance for a seeded semicontinuous crystallizer in which
Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5865
NLS,5(t) )
Figure 5. SEM photography of seeds (×1000) for TA crystallization for experimental run 2.
F5 2M5
∫
∞
0
kaL2n(L, t)G(L, t) dL
(5)
During the course of TA crystallization, the major impurity 4-CBA will simultaneously incorporate into the TA crystals. It was difficult for 4-CBA to crystallize into TA crystals if the driving force for 4-CBA cocrystallization was the supersaturation existed in solution, since 4-CBA is unsaturated in the solution. The difference between impurity 4-CBA and product TA is that 4-CBA has an aldehyde group rather than a carboxylic acid group para to the other carboxylic acid group on the benzene ring. On the basis of the adsorption layer theories for crystal growth, when TA molecular arrives at the crystal face, it will link into the crystal lattice in positions where the attractive forces are greatest, and under ideal conditions this stepwise build-up will continue until the whole plane face is completed. 4-CBA is so chemically and physically similar to TA that it can be adsorbed selectively on to the TA crystal faces to form cocrystals. The adsorption rate depends on temperature, impurity content in solution, and the precipitation rate of TA. The adsorption mechanism may be one of the reasons for the incorporation of impurity 4-CBA.The other incorporation mechanism might be due to the inclusion of mother liquor. For this mechanism, the rate also depends on temperature, impurity content in solution, and the precipitation rate of TA. Experimental results show that the higher the crystallization rate or the concentration of 4-CBA in solution is, the faster the incorporation rate will be.2 On the basis of these qualitative results and supposed impurity incorporation mechanism, the following incorporation rate relation for impurity 4-CBA can be obtained NLS,4 ) βc4NLS,5
(6)
where β is the incorporation rate constant and is affected by temperature. For the impurity 4-CBA in solid phase, the mass balance can be expressed as c4,S(t)F5kV
∫
∞
0
L3n(L, t) dL ) c4,S(0)kVF5
∫
∞
0
L3n(L, 0) dL +
∫N t
0
LS,4(t)
dt
(7)
For the impurity 4-CBA in solution, the mass balance can be expressed as dc4 ) r3(c1, c2, c3, c4) - r4(c1, c2, c3, c4) - NLS,4(t) (8) dt For the other concerned reactant and intermediates, the mass balance can be expressed as Figure 6. SEM photography of reactive crystallized TA crystals (×1000) at t ) 90 min for experimental run 2.
nucleation is neglected, crystal agglomeration and breakage are absent, and crystal shapes are uniform is ∂n(L, t) ∂(G(L, t)n(L, t)) + )0 (2) ∂t ∂L The initial condition for eq 2 is the population density of seeded crystals. The boundary condition is n(0, t) ) 0 The solute balance for TA in solution is
(3)
dc5 ) r4(c1, c2, c3, c4) - NLS,5(t) (4) dt where NLS,5 is precipitation rate of TA due to crystallization and can be expressed as
dc1 ) -r1(c1, c2, c3, c4) + F/M1 dt
(9)
dc2 ) r1(c1, c2, c3, c4) - r2(c1, c2, c3, c4) (10) dt dc3 ) r2(c1, c2, c3, c4) - r3(c1, c2, c3, c4) (11) dt Assuming the solution was saturated at the beginning of the reactive crystallization, the initial condition for eq 4 would be the saturation concentration. The initial conditions for eqs 8–11 are cj(0) ) cj0 j ) 1 ∼ 4
(12)
The description of the diffusion and reaction processes at the gas-liquid interface is neglected because of the elimination of mass transfer influence.1,22 The meaning of other symbols has
5866 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008
been reported in the notation. At the experimental oxygen partial pressure, no obvious effect of oxygen partial pressure on the reaction was found. The oxygen mass balance is not considered here.1,22 Model Solving Algorithm. Equation 2 falls in the general class of hyperbolic partial differential equations (PDEs) know as flux conservation equations. An analytical solution for these equations does not exist. Several solution schemes for the solution of this class of equations are available, among which the moment method defined by eq 13 perhaps is the most widely adopted26 µj(t) )
∫
∞
0
Ljn(L, t) dL
(13)
Assuming the growth rate G(L,t) is independent of crystal size L and neglecting the effect of nucleation, the moment method converts the above crystallizer model consisted of PDEODEs into the following ordinary differential equations (ODEs) dc1(t) ) -r1(c1, c2, c3, c4) + F/M1 dt dc2(t) ) r1(c1, c2, c3, c4) - r2(c1, c2, c3, c4) dt dc3(t) ) r2(c1, c2, c3, c4) - r3(c1, c2, c3, c4) dt dc4(t) kaF5 ) r3(c1, c2, c3, c4) - r4(c1, c2, c3, c4) - β c (t)G(t)µ2(t) dt 2M5 4 kaF5 dc5(t) ) r4(c1, c2, c3, c4) G(t)µ2(t) dt 2M5 dµj(t) ) jG(t)µj-1(t) (14) dt along with the following initial condition µj(0) ) µj0,
cj(0) ) cj0
( )
Eg (c (t) - csat)g (16) G(t) ) kg exp RT 5 For the impurity 4-CBA in solid phase, the mass balance can be transferred into βka µ3(0) + µ3(t) 2kvM5µ3(t)
∫ c (t)G(t)µ (t) dt t
0
We are concerned with the volume-averaged crystal size L43 and the uniformity of the CSD. L43 is defined by the following equation L43 )
4
2
(17) From model eqs 14–17, the concentration of component i in solution, the concentration of impurity 4-CBA in solid, and the zeroth to fifth moment can be calculated. The concentration of component PX, TALD, PT, and 4-CBA in solution calculated were used to optimize the model parameters in reaction kinetics, by minimizing the difference between the calculated and experimental determined concentrations. The optimal model parameters had been reported in a previous paper.22 The concentration of component TA in solution and the moments µ0∼µ5 were used to optimize the model parameters for crystallization kinetics of TA, and the calculated concentration of 4-CBA in solid were used to optimize the model parameters for the incorporation kinetics of 4-CBA. Analytic instrument used for particle size determination in this work reported crystal size distribution as percent volume of crystals in certain size intervals, from which the moments µ0∼µ5 can be determined.
∫
∞
0
L4n(L, t) dL/
∫
∞
0
L3n(L, t) dL ) µ4/µ3
(18)
From the CSD and the calculated coefficient of variance (CV) for experimental runs 1-6, we can find that the shapes of CSD curves all vary slightly from the same initial distribution to approximately Gaussian distribution, which can be seen as an example in Figure 4. The CSD can be approximately determined by the initial CSD and the time evolution of L43. This means that L43 can be used as a characteristic parameter to represent the CSD, if the initial CSD is determined in nucleation neglected crystallization. The following objective function is selected in the parameter optimization
(15)
These equations can be easily solved by fourth-order Runge-Kutta method accompanied with the linear growth rate of crystals in eq 14 expressed in the following relation
c4,S(t) ) c4,S(0)
Figure 7. Supersaturation of solute TA at different feed rates of PX: (0) FPX ) 4.24 g/min; (2) FPX ) 3.76 g/min; (O) FPX ) 3.36 g/min; ([) FPX ) 2.77 g/min; (line) model calculated results; (scatter) experimental results.
jmax imax
min(F) )
∑∑ j)1 i)1
(((
w1
((
) ) ) ))
2 L43,cal(tij) - L43,exp(tij) × 100 + L43,exp(tij)
w2
c4,S,cal(tij) - c4,S,exp(tij) × 100 c4,S,exp(tij)
2
(19)
where tij is the ith time point in the jth experiment, jmax represents the number of batch experiments, and imax represents the number of samples in every experiment. w1∼w2 are the weight of averaged crystal size, and concentration of impurity 4-CBA in solid phase, respectively. The Nelder-Mead Simplex approach was used for the minimization of the objective function.27 Any commercially available software may be used for this purpose. Function fminsearch in the optimization toolbox of Matlab (Mathwork, MA) uses the Nelder-Mead Simplex approach and can be employed for the minimization of the objective function. Results and Discussion Growth Kinetics Determination. The purpose for growth kinetics determination is to determine the effect of supersaturation of TA on the crystal growth rate, as shown in eq 16. Figures 7 and 8 showed the time evolution of TA supersaturation and the volume-averaged size of TA crystals at different PX feed rate, respectively. As can be seen in Figure 7, the supersaturation increases with time quickly to a maximum value and then asymptotically decreases to a constant value. Both the maximum supersaturation and the constant supersaturation increase with the increasing of PX feed rate. The maximum
Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5867 Table 4. Available Useful Growth Kinetics for TA Crystals workgroup
method
Myerson, A. S.10–12
isothermal seeded desupersaturation crystallization seeded batch cooling crystallization isothermal seeded semicontinuous reactive crystallization
Ding, H. B.14–16 Wang, Q. B.; Li, X.
solvent 10 wt % H2O +90 wt % HAc 100 wt % H2O 8.7 wt % H2O +91.3 wt % HAc aqueous HAc solution with water content range from 3 to 12 wt %
supersaturation indicates that some nucleation occurs. However, by seeded crystallization technique, the nucleation can be neglected respected to the number of seeds, which can also be indicated from the little difference between the maximum and the constant supersaturation. As can also be seen in Figure 7, the higher the feed rate of PX is, at the same experimental time the higher the supersaturation will be. A higher supersaturation means a faster growth rate of TA crystals, which will results in a bigger averaged crystal size at the same experimental time. The experimental results shown in Figure 8 prove it. Accompanied the solubility data determined in previous works4,5 with the experimental data shown in Figures 7 and 8, the optimization algorithm gives the following kinetic correlation for linear growth rate of TA crystals
model parameters
temperature range/(K)
crystallizer volume/(mL)
Eg/(kJ/mol)
313.2-353.2
500
-23.5
1.1
298.2-343.2 383.2-423.2
500 5000
-22.4 12.9
1.1 1.83
429.2-437.2
2000
47.3
g
1.00 ( 0.06
crystallization of TA. Figure 9 shows the time evolution of c4,S, the content of impurity 4-CBA in TA crystals, at different PX feed rate. As it can be seen, c4,S first decreased to a minimum content and then increased. This experimental results coan be interpreted beginning with eq 17, which can be transferred into the following expression c4,S(t) )
1 (k F c (0)µ3(0) + kVF5µ3(t) V 5 4,S
∫N t
0
LS,4
dt) )
m4(t)/M4 m5(t) (21)
The lines in Figures 7 and 8 depict the experimental and simulated supersaturation and volume-averaged crystal size vs time at different PX feed rate using the above kinetics. The difference between associated plots could be due to the measurement error including experimental and random errors and the simulation assumptions such as the absence of breakage, agglomeration, and nucleation. The averaged 6% relative deviation in the prediction of supersaturation and volumeaveraged crystal size proves that the above model is accurate enough for the prediction of TA crystals growth. Crystal growth rate of TA had also been measured by another two workgroups because of the importance of such measurement. The available useful works for the crystal growth kinetics, including the kinetics obtained in this project are given in Table 4. An overall order of 1.00 ( 0.06 for the crystallization kinetic model eq 16 agreed with the overall order of 1.1 obtained by the workgroup of Myerson10–12 but greatly differed from the overall order obtained by Ding et al. Incorporation Kinetics of Impurity 4-CBA. Impurity 4-CBA will incorporate into TA crystals along with the
where the numerator represents the mole number of impurity 4-CBA in TA crystals and the denominator represents the mass of TA crystals. The terms m4(t) and m5(t) both increase with time. However, at the earlier stage of reactive crystallization, because of the relatively lower concentration of 4-CBA in solution, the impurity incorporation rate is lower, which results in the increasing rate of m4(t) is smaller than that of m5(t). In this circumstance, according to eq 21, c4,S will decrease with time. As the reaction goes on, the concentration of 4-CBA in solution become higher and higher, which will also make the incorporation rate become higher and higher. Once the incorporation rate becomes so high that the increasing rate of m4(t) is bigger than that of m5(t), c4,S will increase with time. As it can also be seen in Figure 9 that c4,S increases with the increasing of PX feed rate at the same experimental time. This is because the concentration of 4-CBA in solution increases with the increasing of PX feed rate at the same experimental time, which will result in a higher incorporation rate according to eq 6. According to the above models and experimental results, the optimization algorithm gives the incorporation rate constant for 4-CBA incorporation kinetics to be β ) 0.256 ( 0.022. The lines in Figure 9 depicts the experimental and simulated c4,S vs time at different PX feed rate using the above kinetics. An averaged 7% relative deviation in the prediction of c4,S proves that the above model is accurate enough for the prediction of incorporation of impurity 4-CBA.
Figure 8. Volume-averaged size of TA crystals at different feed rates of PX: (0) FPX ) 4.24 g/min; (2) FPX ) 3.76 g/min; (O) FPX ) 3.36 g/min; ([) FPX ) 2.77 g/min; (line) model calculated results; (scatter) experimental results.
Figure 9. Content of impurity 4-CBA in TA crystals at different feed rates of PX: (0) FPX ) 4.24 g/min; (2) FPX ) 3.76 g/min; (O) FPX ) 3.36 g/min; ([) FPX ) 2.77 g/min; (line) model calculated results; (scatter) experimental results.
G ) (1.802 ( 0.116) × 10-6(c5 - csat)1.00(0.06
(20)
5868 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008
Figure 10. Supersaturation of solute TA at different temperatures: (0) T ) 429.2; (2) 433.2; (O) 437.2 K; (line) model calculated results; (scatter) experimental results.
Figure 12. Content of impurity 4-CBA in TA crystals at different temperatures: (0) T ) 429.2; (2) 433.2; (O) 437.2 K; (line) model calculated results; (scatter) experimental results.
temperature. According to the above models and experimental results, the optimization algorithm gives the following correlation for the linear growth rate of TA
(
G(t) ) (0.9118 ( 0.0664) exp -
Figure 11. Volume-averaged size of TA crystals at different temperatures: (0) T ) 429.2; (2) 433.2; (O) 437.2 K; (line) model calculated results; (scatter) experimental results.
Effect of Temperature on Crystal Growth. Figures 10 and 11 show the time evolution of TA supersaturation and the volume-averaged size of TA crystals at different temperature. As can be seen in Figure 10, similar to the evolution at different PX feed rate, the supersaturation increases with time to a maximum value at the initial period and then asymptotically decreases to a constant value. Both the maximum supersaturation and the constant supersaturation decrease with the increasing of temperature. The chemical reaction rate varied with temperature. The higher the temperature is, the faster the chemical reactions will be. It results in lower reactant concentrations and higher TA supersaturation at higher temperature. On the other hand, the crystal growth rate constant increases with the increasing of temperature. More TA will precipitate at higher temperature, which will lead to a lower TA supersaturation at higher temperature at the same PX feed rate. Considering both the supersaturation and the temperature on the crystal growth, the precipitation rate varies with temperature only for initial period of time and then is almost constant, and the precipitation rate approximately be equal to the generating rate of TA due to chemical reactions. As it can be seen, for the same kind and amount of seeds, the initial L43 at different temperatures is different. The higher the temperature is, the smaller L43 is at t ) 0. This is because the solubility of TA increases with the increasing of temperature.4,5 For the same kind and amount of TA seeds, the higher the temperature is, the more seeds will be dissolved into solution, which makes L43 smaller. As it can also been seen in Figure 11, although smaller at t ) 0, L43 increases with the increasing of crystallization temperature at the same experimental time, which indicates that the crystallization rate increases with
47300 ( 2160 × RT (c5(t) - csat)1(0.06
)
(22)
The lines in Figure 11 depict the experimental and simulated L43 vs time at different temperature, and the averaged deviation is 9.4%., which means a satisfactory agreement between the model calculated and experimental results. The available activation energies for the growth of TA crystals are listed in Table 4.10–16 The activation energy reported by the workgroup of Myerson was negative.10–12 It means the higher the temperature was, the slower the growth rate would be. It was contrary to our common understanding13 on crystallization and was also inconsistent with the experimental results shown in Figure 11. The activation energy reported by the workgroup of Ding et al. was positive, 14–16 but much smaller than that obtained in this work. Just as mentioned above, the experimental scheme adopted by Ding et al. was debatable. Their reported results were qualitatively acceptable.14–16 Effect of Temperature on Impurity Incorporation. The time evolution of experimentally determined c4,S at different temperature are scattered in Figure 12. As it also can be seen as that in Figure 12, c4,S first decreases to a minimum content and then increase. The higher the temperature is, the lower c4,S will be at the same experimental time. This can be interpreted in two aspects. One is the effect of temperature on the incorporation rate constant, and the other is the effect of temperature on the 4-CBA concentration in solution and the precipitation rate of TA. For the same PX feed rate, the precipitation rate of TA various slightly, however, the concentration of 4-CBA in solution decreases remarkably with the increasing of temperature at the same experimental time. This will result that the incorporation rate of impurity 4-CBA into TA crystals decreases remarkably according to eq 6. However, when this effect is considered to predict c4,S at different temperature, we find a 20-30% deviations between the predicted results and the experimental results. This is mainly because of neglecting the effect of temperature on the incorporation rate constant β. Wang points out that the higher the temperature is, the more soluble 4-CBA will be, which results that 4-CBA is more prone to exist in solution.1,28 When the Arrehenius equation is used to represent the effect of temperature on the incorporation rate constant β, the following equation was obtained from the optimization algorithm
Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5869
( 16528RT( 542 )
β ) (0.0026 ( 0.0003) exp
(23)
A comparison of the calculated and experimental c4,S at different temperature is shown in Figure 12. An averaged 5.9% relative deviation in the prediction of c4,S proves that the above model is accurate enough for the prediction of temperature effect on the incorporation of impurity 4-CBA. Equation 22 reveals that temperature has a negative effect on the impurity incorporation, and 4-CBA is more prone to stay in the solution than TA at higher temperature. This might because the solubility of 4-CBA is much larger than that of TA at higher temperature. From eq 22, we can find the incorporation rate constant decreases with the increasing of temperature. If we want to control the impurity 4-CBA content in TA crystals within a relative low value, the increasing of temperature is a preferred choice. This conclusion provides an important engineering method to improve the operation condition. Disadvantage of the Optimization Method. The simplex method is used to optimize the model parameters. A disadvantage of the simplex method is that no information about the confidence intervals of the parameters is obtained. Several optimizations were carried out starting from different initial parameter values. The experimental results of run 1-6 were put together to regress the model parameters. The results given in this work showed the obtained averaged parameter values and the deviations of parameters from different initial parameter values, weight of averaged crystal size, and weight of concentration of impurity 4-CBA in solid phase. Conclusions In the reactive crystallization of terephthalic acid (TA) by liquid-phase oxidation of p-xylene (PX), four simultaneous processes occurred in liquid and solid phase, including the oxidation of PX to TA, the nucleation of TA from solution, the growth of TA crystals, and the incorporation of impurity 4-CBA. In a previous paper, the reaction mechanism and kinetics of PX to TA was discussed in detail.22 In this work, by using the experimental technique of seeded semicontinuous reactive crystallization, the growth of TA crystals and incorporation of impurity 4-CBA were studied, while neglecting the effect of nucleation. The effects of supersaturation and temperature on the growth and incorporation kinetics were experimentally examined. The following results are obtained: (1) A detailed semicontinuous reactor model including the chemical reactions, TA growth, and 4-CBA incorporation was developed. The model was solved numerically to optimize the model parameters for TA growth and 4-CBA incorporation kinetics. (2) The effects of temperature and supersaturation on the crystal growth were studied and the linear crystal rate could be correlated by the following equation G(t) )
47300 ( 2160 dL ) (0.9118 ( 0.0664) exp × dt RT 1(0.06 (c5(t) - csat) (24)
(
)
(3) The incorporation rate of 4-CBA into TA crystals was proportional to both the precipitation rate of solute TA and the concentration of 4-CBA in solution. The effect of temperature on the incorporation rate constant could be correlated by the Arrehenius equation as
( 16528RT( 542 )
β ) (0.0026 ( 0.0003) exp
(25)
which revealed that the incorporation rate constant decreased with the increasing of temperature. The correlated results agreed with the experimental results satisfactory. The obtained crystallization and impurity incorporation kinetics can be used as essential data in engineering aspects. Acknowledgment This project was granted financial support from China Postdoctoral Science Foundation (20060101044) and Key International S&T Cooperation Project of Zhejiang Province (2006C14013). Notation ci ) concentration of ith component in solution, mol/kgHAc ci,S ) concentration of ith component in solid, mol/kgsolid ci0 ) initial concentration of ith component, mol/kgHAc csat ) saturation concentration of TA in solution, mol/kgHAc CV ) coefficient of variation for TA CSD Ea ) activation energy for chemical reaction rate, kJ/mol Eg ) activation energy for crystal growth rate, kJ/mol Fi ) feed rate of ith component, g/min g ) particle growth exponent in the eq 16 G ) particle growth rate, m/min ka ) area shape factor of TA crystal kg ) crystal growth rate constant, m/min(mol/kgHAc)-g ki0 ) reaction rate constant of the ith step reaction, 1/min kv ) volume shape factor of TA crystal L ) particle size, m L43 ) volume-averaged particle size, m mi ) mass of ith component, g Mi ) molar weight of ith component, g/mol n ) crystal number density function, no./(kgHAc m) N ) number of TA crystals, no./kgHAc NLS,i ) the transfer rate of component i from solution to solid, mol/ (kgHAc min) ri ) rate of the ith step reaction, mol/(kgHAc min) t ) time, min T ) absolute temperature, K V(Li) ) percent volume of crystals in size intervals Li∼Li +∆Li, % wi ) weight of parameter i in the objective function of eq 18 Greek Letters β ) 4-CBA incorporation rate constant, defined in eq 6, kgHAc/ mol Fi ) density of component i in solid, kg/m3 µi ) jth moment defined by eq 12 AbbreViations 4-CBA ) 4-carboxybenezaldehyde CSD ) crystal size distribution GC ) gas chromatography HPLC ) high pressure liquid chromatograph ODEs ) ordinary differential equation PDEs ) partial differential equations PT ) p-toluic acid PX ) p-xylene SEM ) scanning electron microscope TA ) terephthalic acid TALD ) p-tolualdehyde
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ReceiVed for reView December 12, 2006 ReVised manuscript receiVed April 30, 2008 Accepted May 27, 2008 IE061595V
