Kinetics of catalytic esterification of terephthalic acid with methanol vapour

Kinetics of catalytic esterification of terephthalic acid with methanol vapour

Chemical Engineering Science, 1973, Vol. 28, pp. 337-344. PCWIIIO~ Press. &ted in Great Brit& Kinetics of catalytic esterikation of terephthali...

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1973, Vol. 28, pp. 337-344.



in Great Brit&

Kinetics of catalytic esterikation of terephthalic acid with methanol vapour J. BHATIA and S. Z. HUSSAIN Department of Chemical Engineering, Indian Institute of Technology, Bombay, India (First Received23 Novenber 1971, in revisedform 14 March 1972) Abstract-This paper describes the investigations carried out on the kinetics of the solid-gas reaction between terephthalic acid and methyl alcohol in presence of phosphoric acid as the catalyst. As phosphoric acid itself reacts with the alcohol forming methyl phosphates, the kinetic data obtained have been analysed takii this reaction into account. The rate of formation of monomethyl phosphate has been found to be. proportional to the square of the mole fraction of the acid present at any instant. The activation energy involved in this reaction is 11.3 kcal/g mole. The data obtained on terephthalic acid esterification show that; (i) the conversion sharply increases with an increase in the catalyst concentration between 30-35 per cent (w/w), (ii) the ‘shrinking particle’ model, proposed by Levenspiel for solid-gas reactions, can be conveniently adapted to represent the reaction, and (iii) the temperature dependency of the reaction follows the Arrhenius law, with activation energy being 11.5 k&/g mole.


THE LIQUIDphase esterification of terephthalic acid with methanol under pressure is an established commercial process. The reaction is often conducted in batch autoclaves in presence of sulphuric acid as the catalyst [l]. A continuous high pressure esterification process[21 has been recently developed and is presently exploited on industrial scale. Esterification in vapour-solid systems at normal pressures, wherein either one or both of the reactants are in the gaseous state and the catalysts used are solids such as, silica gel, alumina, oxides of thorium, zinc, antimony, etc. is a subject of the most recent studies. Almost all the available information on these investigations is in patent literature. A process, in which the vapours of the acid and alcohol are allowed to react in a tubular reactor packed with silica gel, has been patented by Chemische Werke Huels [3,4]. The method described is as follows: Super-heated methanol vapour at about 400” is passed through a sublimer containing briquettes of terephthalic acid. The flow of methanol is kept at such a rate that the methanol to acid ratio is maintained at 1: 50.

This vapour mixture is passed through a bed of granular silica gel at 300” to obtain dimethyl terephthalate in good yields. Reaction between methanol vapour and solid terephthalic acid mixed with silica gel has also been reported. Novotony[5] has described a process which employs a fluidized bed reactor. The bed, consisting of terephthalic acid and silica gel, is fluidized by methanol vapour. In the process patented by Chemische Werke Huels[6,7], a rotary kiln has been used for the solid-vapour esterification. Methanol vapour is admitted to the kiln containing solid terephthalic acid and silica gel at about 300°C. Since the sublimation point [l] of terephthalic acid is about 402”, the heat requirement of the process in which both the acid and methanol are vapourised is greater than that where only methanol is vapourised. Hence the latter appears to be relatively more attractive than the former. These systems will be referred as, vapour-solid catalyst (VSC) and solid-methanol vapour (SMV) systems respectively. The purpose of this paper is to present; (i) results of the relative performance of the selected catalysts in VSC and SMV systems and (ii)

337 CESVoL28,Na2-A



the kinetic analysis of the reaction conducted in an SMV system with phosphoric acid as the catalyst. EXPERIMENTAL

experiments were conducted in an allglass (Pyrex) assembly, shown in Fig. 1. The vertical limb (2.2 cm dia., 24 cm height) of the ‘L’ shaped portion of the assembly was used as the reactor proper and the horizontal limb (3 cm dia., 27 cm length) as the preheater. For the VSC system, the latter also served as the acid sublimer. In order to carry out the reaction in the SMV system, the mixture of terephthalic acid and catalyst (phosphoric acid, 87.5 per cent cont.) was taken in a cylindrical crucible (2.0 cm dia., 4 cm height), made out of a stainless steel wire gauze (60 mesh), which was hung in the reactor by the hook provided at the tip of the thermocouple well. Experiments for the kinetic study were carried out by placing the crucible containing terephthalic acid-catalyst mixture in the reactor, when it had almost attained the desired temperature. The reactor was then allowed to attain constant temperature and methanol vapour was admitted through the preheater. The appearance of a very thin layer of dimethyl terephthalate bulb was marked as zero time. To quench the reaction the methanol supply was cut-off (by The

Wire mesh crwzible

operating the two-way stop cock to channel the vapour to the side condenser), the reactor was allowed to cool down and methanol vapour in the preheater-reactor system was flushed off by nitrogen. The progress of the reaction was followed by the loss in weight of terephthalic acid during a specified interval. Since phosphoric acid also reacts with methanol to form mono-, di-, and trimethyl phosphates, the reactions envisaged in this system are: C,H,(COOH), (A) + 2CH,OH (B) 5 CJ-IKOOCH,), + 2H,O H,PO,(P) + CH,OH (B) a

(1) CH,H,PO, + H,O (2)



(CHJ2HP04 + CH,OH (CH,XPO,(s) + H,O.


In order to determine the amount of phosphoric acid converted to its esters, the catalyst retained by the unreacted terephthalic acid was extracted with water (solubility of terephthalic acid in water at 25”[1] being ONl19 per cent by wt). The loss in weight of terephthalic acid obtained by total weight loss minus the weight loss of phosphoric acid compared very well with the difference in weight of terephthalic acid originally taken and that recovered after the reaction (within 4 per cent). Fresh samples were used for each reading and several readings were repeated to test the consistency of the data. The average deviation in the fractional conversion of terephthalic acid at any specified interval was about &3 per cent. In several runs dimethyl terephthalate formed was recovered and the amount obtained was found to agree within 5 per cent with the value determined by the weight loss. RESULTS



Pet$ormance of various catalysts The results of a detailed study on the catalyst Fig. 1. Experimental set-up.

evaluation in a VSC system have been presented 338

Kinetics of catalytic estetihcation

elsewhere [8]. The relative performance of a few catalysts in the VSC and SMV systems are presented in Table 1. The relatively low conversions with the solid catalysts in the latter system are mainly due to the lower operating temperature (200°C) and incomplete contact between the reactants and the catalyst. Higher conversion can be achieved if the reaction temperature is raised above 300°C. It may be observed that, under these conditions, phosphoric acid showed better catalytic activity than the others. Table 1. Catalyst evaluation Conditions VSC system: Space velocity Catalyst volume Catalyst particle size Reaction temperature Sublimation temperature

= = = = =

360 hr-’ 75 cm3 0203 cm 300°C 300°C

SMV system: Methanol distillation rate = 268 cms/min = 200°C Reaction temperature =lhr Reaction period VSC system


wt% cat.

Silica gel U,O, on silica gel 25 Thq on silica gel 25 ZnO on silica gel 25 Phosphoricacid (87.5% con.) (Mixed with terephthalic acid)

Conversion % 19.7 74.9 41.9 29.8 -

SMV system wt % cat. loo loo loo 100 30

Conversion % 4.7 4.2 4.3 5.5 27.8

Reactions l-4 produce water as one of the reaction products, complete dehydration leading to pyrophosphoric or meta phosphoric acid is unlikely [lo]. Formation of monomethyl phosphate, according to Reaction 2, is the slowest step and can only be effected[ 111 at ‘high temperatures and reduced pressures’. Consequently, a fraction of phosphoric acid taken is retained by terephthalic acid and its presence catalyses Reaction 1. Under the experimental conditions Reaction 3 is very fast, since diester can be prepared by warming methanol and monomethyl phosphate at 50-65°C [ 121. The analysis of the product mixture collected in the bulb and the receiver distinctly showed the presence of only monobasic acid. It can therefore be assumed that monomethyl phosphate is completely converted to di- and &i-methyl phosphate while leaving the reactor. Because of the limitations of the analytical method it was not possible to distinguish between dibasic monoester and phosphoric acid retained by the contents of the crucible. However, as the monoester seems to decompose [ 131 at 17O”C, tihen heated under ordinary conditions, it is highly improbable that the monoester is retained by the unreacted phosphoric acid in the temperature range 190-220°C. The data, pertaining to the change in mole fraction of phosphoric acid (based on moles of the acid initially taken) with respect to the reaction period, were analysed and the rate of disappearance of phosphoric acid could be expressed by the equation,


Esterification of terephthalic acid was therefore carried out in presence of phosphoric acid, with a view to determine the influence of the flow rate of methanol vapour, catalyst to terephthalic acid ratio (per cent w/w) and the operating temperature on the rate of the reaction. Reaction between phosphoric acid and methanol

Phosphoric acid (87.5 per cent cont.) loses its free as well as combined water[9] when heated between 180-2 10°C. However, since 339






where mp = nplnp, Equation (l), when integrated between the usual limits and rearranged, takes the form

J-= m



where s = k’lnp,. Figure 2 contirms the relationship given by Eq. (2). Under the experimental conditions,



EsteriJication of terephthalic acid

Reaction 1 represents the overall reaction between the acid and methanol in presence of phosphoric acid. Since the product obtained was dimethyl tere thalate and the content of the e removal of the catalyst) was to be only the unreacted acid, it appears that the intermediate formed (viz., monomethyl terephthalate) readily converts to the diester. Hence, under the conditions employed, the formation of monoester may be regarded as the rate controlling step of the overall process. The injluence of thefiow rate of methanol vapour I.0

It may be observed that the conversion of terephthalic acid attains a maximum value when the rate of methanol distillation is about 268 cm3/ min (Fig. 4). Hence it may be concluded that the external diffusional resistance due to the stagnant vapour film is reduced to a minimum at this flow rate. The slight decrease in conversion with the increase in flow rate may be attributed to channelling and slight reduction in contact time of the vapour at higher flow rates. Conversion of phosphoric acid followed a similar pattern with the variation in the flow rate. Thus, in order to eliminate the external diffusional resistance, subsequent experiments were conducted with 268 cm3/min distillation rate.

0123456769 Time,


Fig. 2. Relationship between mole ratio of unreacted H,PO, and reaction period (Eq. 2) for reaction 2.

namely, 200°C and initial moles of H,PO, ranging between O-87-1-53, the values of k’ were found to be almost constant, with an average value of about 4.0 x lo+ g molelsec. Thus Eq. (1) accurately represents the data obtained on the rate of disappearance of H,PO,. The influence of temperature

The effect of temperature on the apparent rate constant for the disappearance of H,PO, (Reaction 2) is given by the Arrhenius plot (Fig. 3), with apparent activation energy being 11.3 kcal/ g mole and frequency factor O-7154g molelsec.

20 15 IO 5




mte. cm3/min

Fig. 4. Influence of flow rate of methanol vapour on the conversion of terepthalic acid.

Uncatalysed reaction 2.00






Fig. 3. Influence of temperature on the apparent rate constant for disappearanceof H,PO,, reaction 2.

Esterification of terephthalic acid with methanol was not found feasible in absence of the catalyst in the temperature range studied, viz. 190-200°C. However, the blank mns 340

Kinetics of catalytic esteriikation

conducted showed that the total amount of terephthalic acid sublimed during 25 hr was Within l-5 per cent at 200°C (Fig. 5). There was a sharp rise in sublimation at 220°C. Hence the conversions obtained in presence of the catalyst at reaction temperatures 210 and 220°C were corrected for the loss of the acid due to sublimation. I A2200

the extent of the reaction, takes the form -1 dn,_ zzdt-

the rate expression

Zdn, = c&m&,. 4nr’ dt


Now, the moles of terephthalic acid in a particle (assumed spherical) can be related to its density and volume by the expression

I n



PV _ M

4mr3p 3M ’


Differentiating Eq. (4) and substituting the result in Eq. (3), gives o



3 Time,








tx ID3sec

Fig. 5. Influence of temperature on terephthalic limation.

acid sub-

(6 1f =


Substituting Eq. (2) in (5) and rearranging gives The reaction model The main reaction (Reaction l), being heterogeneous, occurs on the surface of the solid particles. Since the catalyst is absorbed by the particles, both terephthalic acid and phosphoric acid (as H,PO,) compete with each other for methanol vapour. Dimethyl terephthalate, thus formed, sublimes at the reaction temperature and, consequently, the product layer is not retained by the particles. Hence the reaction appears to bear a close similarity with the ‘shrinking particle’ model [ 141 postulated for solid-gas non-catalytic reactions. For the reaction to occur at the surface, methanol has to diffuse through a stagnant vapour film surrounding the particles. In view of the fact that the external diffusional resistance has been reduced to a minimum (Fig. 4) by increasing the fhrx of methanol vapour, the chemical reaction at the surface should only be the controlling step. In general, the rate of solid-gas reactions, expressed as change in moles of the solid per unit time per unit surface area, is found to be proportional to the concentration of the reactant in the fluid phase[l5]. For the system under consideration, since the amount of phosphoric acid present at any instant directly intluences


= (y)(&d.


Since the concentration of methanol in the bulkphase, C,, remains substantially constant, Eq. (6) on integration becomes (rO-r) =Tln



or In (l+st)


Radius of the particle can be expressed in terms of fractional conversion of terephthalic acid



3 .


The relationship between time and conversion can be obtained by combining Eqs. (8) and (9) h(l+~t)=~[l-(l-Xd)1’3].

The conversion-time 341



data obtained for various



catalyst concentrations and reaction temperatures are presented in Fig. 6. These data, along with those presented in Table 2, were used to evaluate the values of the rate constant k employing Eq. ( 10). The values of k for any given set of conditions were found constant showing that the proposed model represents the reaction very well.





s 6 1

4 0 2

0 0’



L!!_! 0 01




Catalyst fraction Fig. 7. Influence




3 4 Time,

5 6 t x l0%ec








on the rate


x IO3

Fig. 8. Influence of temperature on the rate constant k for reaction 1.

The activation energy and frequency factor determined by the Arrhenius plot, Fig. 8, and the equation

Table 2. Properties of the system

Stoichiometric coeflicient, a Molecular weight of TPA, M Density of TPA, p Average Initial radius of TPA particle, r, Concentration of methanol vapour at 190°C 200°C 210°C 220°C

2.04 I/T

Fig. 6. Conversion-time data for reaction 1, at various catalyst concentrations and temperatures.


of catalyst concentration constant k for reaction 1.

Value O-5

kl = Ale-E/RT

165 1.5 g/cm3


were found to be 15.5 kcal/g mole and 6.8 x 103 cmlsec. respectively. Since the influence of temperature on the reaction rate has been studied with 30 per cent catalyst concentration, a generalised equation that may be applicable to all conditions of catalyst concentration and temperature, that is,

0.015 cm 2.63 X 10es g mole/ems 2.58 X lo+ g mole/ems 2-52 X 10es g moIe/cms 2.47 X 10” g mole/cmS

The influence of the catalyst and the temperature The effect of the catalyst concentration and temperature are presented in Figs. 7 and 8 respectively. Figure 7 shows that the rate of esterification of terephthalic acid increases sharply with an increase in catalyst concentration between 30 and 35 per cent (w/w).

kT = Ae--EIRT


involve a frequency factor A, which varies with the catalyst concentration. Thus, in Eq. ( 12), A can be expressed as will


A = WkdA,


Kinetics of catalytic esterification

where k and k, represent the numerical values of rate constants obtained at any catalyst concentration and 2OO”C, and catalyst concentration 30 per cent (w/w) and 2OO”C,respectively. Thus the values of the frequency factor A for catalyst concentrations 20, 25 and 35 per cent (w/w) were found to be 4.02 X 103, 4.33 X lo3 and l-39 X lo4 respectively. As frequency factor is a measure of the probability or extent of reaction, it may be concluded that the reaction rate is doubled when the catalyst concentration changes from 30 to 35 per cent (w/w). A comparison of activation energies of Reactions 1 and 2, shows that the former is more temperature sensitive than the latter. Furthermore, the values of the frequency factors suggest that the extent of the reaction in case of terephthalic acid esterification is comparatively far greater than that in phosphoric acid esterification. The fact that a significant fraction of phosphoric acid is retained by the mixture, confhms this conclusion. Using proper values of A, rate constants were calculated by Eq. (12). A comparison of the calculated and experimental values of rate constant, presented in Fig. 9, shows good agreement. IO


0 0 x

5 : .E








Fig. 9. Comparison of calculated values of rate constant’with the experimental values.

Reactors for SMV system

Three types of reactors can be proposed for the esterification of solid terephthalic acid (blended with phosphoric acid) with methanol vapour. These are: (i) A horizontal tubular reactor provided with a screw conveyor, wherein methanol vapour can be admitted to the reactor through the shaft of the screw conveyor, made out of a perforated tube. (ii) A fluidized bed reactor where methanol vapour and terephthalic acid (mixed with the catalyst) constitute the continuous and discontinuous phases respectively. (iii) A rotary-mill type reactor to bring the solid in close contact with the vapour. CONCLUSIONS

As against the conventional high pressure process, a simple and normal pressure method has been developed for the production of dimethyl terephthalate using phosphoric acid as the catalyst. It has been observed that the catalyst (875 per cent phosphoric acid) concentrations greater than 35 per cent lead to agglomeration of the terephthalic acid particles, thereby reducing the contact area between the particles and methanol vapour. Moreover, the consumption of methanol due to the formation of methyl phosphates also increases at higher catalyst concentrations. It can therefore be concluded that the most suitable catalyst concentration lies in the range 30-35 per cent. In view of the fact that at about 210°C appreciable amount of terephthalic acid sublimes and escapes the reaction, the product obtained at higher temperatures needs purification. Hence, in order to avoid the purification step, the most desirable operating temperature appears to be 200°C. Acknowledgements-The authors are grateful to Prof. N. R. Kamath for his keen interest and valuable suggestions during this work. Thanks are also due to Mr. M. Ghouse for his cooperation and assistance in the analytical work. One of the authors (J. Bhatia) wishes to express his sincere




gratitude to the authorities of the Institute for the grant of the scholarship which enabled him to participate in this project. NOTATION


c E k k M m n r

frequency factor for esterification of TPA, cmlsec concentration, g mole/cm3 activation energy for esterification of terephthalic acid, k&/g mole reaction rate constant for esterification of terephthalic acid, cm/set apparent rate constant for I&PO, esterification, g molelsec molecular weight of terephthalic acid mole ratio of a component to its initial moles gram moles of a component, g mole mean radius of terephthalic acid particles at any instant, cm


slope of the lines of Fig. 2, Eq. (2) . reaction period, set x conversion defined as the ratio of change in moles of a component to that taken init$lly OL stoichiometric coefficient p density of terephthalic acid, g/cm3 t

Subscripts A B P T

terephthalic acid methanol phosphoric acid any temperature within the range of experimental study 0 initial value of a quantity 1 reaction conditions: 30 per cent catalyst cont. and 200°C

REFERENCES 111 KIRK R. E. and OTHMER D. F., Encyclopedia ofchemical Technology, Vol. 15,2nd Edn. Interscience N.Y. [2] Anon, Petrochem. Handbook, 1969 48 172. [3] Chemische Werke Huels, French Patent No. 1,388,467 1965. [4] STRAUSS G. et af., German Patent No. 1,188,580 to Chemische Werke Huels, (1965). [5] NOVOTONY R., E&l Kohle- Erd. Petrochem. 1962 15 707. [6] Chemische Werke Huels, French Patent No. 1,367,278 1964. [7] VON FERDINEND L., Erdol Kohle- Erd. Petrochem. 1969 22 197. [8] BHATIA J. and HUSSAIN S. Z., Znd. Chem. Jll9716 34. PI MELLOR J. W., A Comprehensive Treatise on Inorganic and Theoretical Chemistry. Vol. 8, p. 961. Longmans-Green, London, 1953. [lo] ADLER H. and WOODSTOCK H. W., Chem. Ind. 1942 515 17. [l 11 VAN WAZER J. R., Phosphorus and its Compounds, Vol. 1, p. 57. Interscience, N.Y., 1958.1,570. [12] BEILSTEIN, Beilstein Handbuch der Organ&hen Chemie, Vol. 6, p. 1205, (System No. 16-70). Edward Bros., Berlin 1942. [13] WAGGAMAN H. W., Phosphoric Acid, Phosphates and Phosphatic Fertilisers, p. 488. Reinhold, N.Y. 1960. [14] LEVENSPIEL O., Chemical Reaction Engineering, p. 350. Wiley Eastern, New Delhi 1969. [IS] SMITH J. M., Chemical Engineering Kinetics, 2nd Edn., p. 573. McGraw-Hill 1970.