Development of a Free Radical Kinetic Model for Industrial Oxidation of p -Xylene Based on Artificial Neural Network and Adaptive Immune Genetic Algorithm

Published: December 22, 2011

r 2011 American Chemical Society 3229 dx.doi.org/10.1021/ie200737x | Ind. Eng. Chem. Res. 2012, 51, 3229–3237

ARTICLE

pubs.acs.org/IECR

Development of a Free Radical Kinetic Model for Industrial Oxidationof p-Xylene Based on Artificial Neural Network and Adaptive ImmuneGenetic AlgorithmFeng Qian,*,† Lili Tao,† Weizhen Sun,‡ and Wenli Du*,†

†Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, and ‡State-Key Laboratory ofChemical Engineering, East China University of Science and Technology, Shanghai 200237, China

ABSTRACT: A novel kinetic model based on the free radical mechanism is used to simulate the oxidation of p-xylene (PX) in acontinuous stirred-tank reactor (CSTR) under industrial operating conditions. Because this kinetic model cannot provideappropriate prediction of the influence of the reaction factors, such as catalyst concentrations, water concentrations, andtemperatures, on the kinetic parameters for oxidation of PX in the laboratory semibatch reactor (SBR), the kinetic parametersthat are highly nonlinear of the reaction factors are estimated by a back-propagation neural network (BPNN). Furthermore,correction coefficients are introduced to accurately evaluate the kinetic parameters based on Adaptive Immune Genetic Algorithm(AIGA) due to the significant difference between the nature of PX oxidation conducted in the laboratory SBR and in the industrialCSTR. The model with the evaluated optimum kinetic parameters is obtained, and its efficiency is validated via comparison withindustrial data.

1. INTRODUCTION

Terephthalic acid (TPA) is one of the main rawmaterials usedto produce polyester, including polyester fiber, polyethyleneterephthalate (PET) bottle resin, and polyester film. Until2008, global TPA markets had been growing strongly at ratesof around 6�8%/year. The growth in TPA consumption hasbeen driven by strong polyester fiber demand, which accounts fornearly two-thirds of global polyester demand.

In industry, most TPA is produced by the liquid-phasecatalytic oxidation of p-xylene (PX) in the temperature rangeof 150�210 �C, with cobalt acetate, manganese acetate, andbromide as catalysts, acetic acid as solvent, and air as oxygensource (Kim et al.1). In general, there are four production tech-nologies for the PX oxidation process in terms of the difference oftheir reaction temperatures (i.e., BP-Amoco, Du pont-ICI, Mitsui,and Lurgi-Eastman). From both economic and control points ofview, an oxidation of PX to TPA model needs to be developed.Because the reactor of Mitsui process is more general than otherprocesses, the reactor model of Mitsui oxidation process wasinvestigated in our work.

The results of previous research demonstrated that the reac-tion mechanism was extremely complicated, involving lots ofcoupling effects, which made the model overparameterization(Sun et al.2). Although the reaction generates several intermedi-ates, for example, 4-methylbenzyl alcohol (TALC), p-tolualde-hyde (TALD), p-toluic acid (p-TA), and 4-carboxybenzaldehyde(4-CBA), it is unrealistic and unnecessary to take all intermedi-ates into account in the real industrial process. Among manyformer works (Cao et al.,3 Cincotti et al.,4 Yan et al.,5 Wanget al.6), most of the lumped reactions were assumed to be firstorder with respect to liquid reactants and zero order to oxygen. Itshould be mentioned a lumped kinetic model for oxidation of PXof the BP-Amoco process has been presented and validated withindustrial data (Yan et al.5). However, choosing the power-law

reaction kinetics for reaction behaviors is empirical and cannot beapplied at other conditions. On the basis of free radical chainreaction mechanisms, a simplified kinetic model was establishedand proved to bemore reliable than previous kinetic models (Sunet al.2). This model included only six rate constants with the mostimportant intermediates (as shown in Figure 1) and the final

product. Thus, this kinetic model is utilized to simulate theoxidation of PX in a continuous stirred-tank reactor (CSTR) ofMitsui PX oxidation process in this work.

Inmost of the previous works, how the catalysts influenced therate constants could not be well predicted due to the complexityof free radical chain reaction mechanisms. Therefore, an artificialneural network (ANN) is introduced to evaluate the value of therate constants in this work. As a typical artificial neural network,BPNN is chosen because it is a widely used algorithm associatedwith the training of a feed forward neural network (Mujtabaet al.7). In this work, the log-sigmoid function has been used asactivation functions in both the hidden and the output layers. Inaddition, due to the large difference between the performance of

Figure 1. Sequential reactions involved in PX oxidation.

Received: April 7, 2011Accepted: December 22, 2011Revised: October 20, 2011

3230 dx.doi.org/10.1021/ie200737x |Ind. Eng. Chem. Res. 2012, 51, 3229–3237

Industrial & Engineering Chemistry Research ARTICLE

PX oxidation in the laboratory semibatch reactor and that in theindustrial continuous stirred-tank reactor, correction coefficientsare introduced to modify the rate constants by using computa-tional intelligent method and industrial historical data in thisArticle. There have been many efforts to estimate the kineticparameters using intelligent methods (Mansoornejad et al.,8

Kadivar et al.9). Recently, the Adaptive Immune Genetic Algo-rithm (AIGA), one of the newly developed computationalintelligent algorithms based on the biological immune system,has been widely concerned by researchers (He et al.10). As aheuristic search technique, which has been successfully applied toa wide range of real-world complex problems, it can quickly con-verge to the global optimum and overcome the premature pro-blem in Simple Immune Genetic Algorithm (SIGA) (Quagliarellaet al.11). Therefore, AIGA is used to solve the optimization problemin this Article.

2. THE PX OXIDATION PROCESS CASE STUDY

2.1. Process Description. The Mitsui process consists of theproduction of TPA and the purification of crude TPA. The PXoxidation unit considered in this research, which is typically usedfor the production of TPA, is an essential part of a PTA (purifiedterephthalic acid) plant. Figure 2 shows the simplified flow-sheetof a Mitsui PX oxidation process in a PTA plant. The Mitsui PXoxidation process consists of the bubbling reactor followed byfour condensers and one reflux drum. At the top of the reactor,there is a dehydration section used for separating the acetic acidsolvent and water. The heat of reaction can be utilized to removethe water from the mixture of water and acetic acid to reduce theinvestment and operating costs. Also, the high-purity acetic acidwill return to the reactor to serve as the solvent. The reactionsection is followed by sequential purification units. The productPTA leaving the purification units is the final product, which canbe delivered to customers. In this work, we only consider the

operation of the PX oxidation process and neglect the purifica-tion process units.2.2. Kinetic Model. The theory and mechanism of PX

oxidation reaction process in the presence of cobalt acetate,manganese acetate, and bromide catalyst have been experimen-tally studied (Cao et al.,12 Zhou,13 Zhang14) because of the signi-ficant economic impacts. As a typical free radical chain reaction,the overall process of the oxidation reaction has been thoroughlydiscussed by Sun et al.2 and involves three steps: chain initia-tion, chain propagation, and chain termination.15,16 In summary,the whole progress is composed of the following reactions:Chain initiation:

MnIII þ Br� f MnII þ Br• ð1Þ

Br• þ RH f Br� þ R• þ Hþ ð2Þwhere RH represents those oxidizable components including PX,TALD, p-TA, and 4-CBA.Chain propagation:(1) Formation of aldehydes

R• þ O2 f ROO• ð3Þ

ROO• þ RH f ROOH þ R• ð4Þ

ROOH þ M2þ f R0CHO þ H2O þ M2þ ð5Þwhere M represents transition metals Co and Mn.(2) Formation of acids

ROO• þ R0CHO f ROOH þ R0CO• ð6Þ

R0CO• þ O2 f R0COOO• ð7Þ

R0COOO• þ R0CHO f R0COOOH þ R0CO• ð8Þ

Figure 2. Simplified flow-sheet of the PX oxidation process.



R0COOOH þ 2Co2þ þ 2Hþ f R0COOHþ 2Co3þ þ H2O ð9Þ

R0COOO• þ RH f R0COOOH þ R• ð10ÞChain termination:

i�OO• þ j�OO• f i�O4�j ð11Þwhere i and j represent alkyl or acyl.Worthy of notice, PX oxidation reaction involves many side

reactions, among which acetic acid combustion and PX combus-tion are the most important. The mechanism of acetic acid com-bustion reaction has been detailed as described by Kenigsberget al.17

Cao et al.3 investigated the kinetics of PX oxidation at lowtemperatures (80�130 �C). They proposed a reaction kineticsmechanism assuming that all of the reactions were first-orderwith respect to liquid reactants and zero-order to oxygen. Thisempirical mechanism has been improved by Yan et al.5 Theyproposed that all of the reactions are 0.65th-order to PX and first-order to the other liquid reactants. On the basis of the free radicalchain reaction mechanisms, Wang et al.6 proposed a fractional

kinetic model, which involved 13 kinetic parameters. However,Sun et al.2 suggested the number of parameters should bereduced for the reliability of the kinetic model. Therefore, theydeveloped a simplified free-radical kinetic model including sixparameters based on the reaction kinetics mechanism asdiscussed earlier. In addition, some key indexes of the modelsuch as residual analysis, statistical analysis, were compared bySun et al.2 The results showed that the simplified free-radicalkinetic model is better than the other three models in statisticalanalysis and the width of the confidence interval. Therefore,the simplified free-radical kinetic model is used in this work tosimulate the oxidation of PX process. The kinetic expressionsmentioned above are listed in Table 1. It should be noted thatonly main reactions are considered in the models shown inTable 1, where Ci (i = 1�5) is the concentration of the ithliquid components (i.e., PX, TALD, p-TA, 4-CBA, and TPA);Co2 represents the concentration of the oxygen in the liquidphase; ki (i = 1�4) is the rate constant of the ith lumped reaction;ri (i = 1�5) is the production rate of the ith liquid components;ni (i = 1�4) and mi (i = 1�4) are reaction orders of two reac-tants of the ith lumped reaction; and di and ε are the modelparameters.

Table 1. Kinetic Models for the Reactions

kinetic model reference

r1 ¼ � k1Cn11 C

m1O2

r2 ¼ k1Cn11 C

m1O2

� k2Cn22 C

m2O2

r3 ¼ k2Cn22 C

m2O2

� k3Cn33 C

m3O2

r4 ¼ k3Cn33 C

m3O2

� k4Cn44 C

m4O2

r5 ¼ k4Cn44 C

m4O2

8>>>>>>>><>>>>>>>>:

Cao et al.3

r1 ¼ � k1Cn11 C

m1O2

r2 ¼ k1Cn11 C

m1O2

� k2Cn22 C

m2O2

r3 ¼ k2Cn22 C

m2O2

� k3Cn33 C

m3O2

r4 ¼ k3Cn33 C

m3O2

� k4Cn44 C

m4O2

r5 ¼ k4Cn44 C

m4O2

8>>>>>>>><>>>>>>>>:

Yan et al.5

rj ¼kj

ð ∑5i¼ 1

diCi þ εÞβjCj

Wang et al.6

rPX ¼ � k1CPX � k2C½O�CPX Sun et al.2

r½O�PX ¼ k1CPX þ k2C½O�CPX � BC½O�PX � k6C½O�PXC½O�

rTALD ¼ BC½O�PX � k1CTALD � k3C½O�CTALD

r½O�TALD ¼ k1CTALD þ k3C½O�CTALD � BC½O�TALD � k6C½O�TALDC½O�

rp �TA ¼ BC½O�TALD � k1Cp �TA � k4C½O�Cp �TA

r½O�p �TA¼ k1Cp �TA þ k4C½O�Cp �TA � BC½Op �TA

� k6C½O�p �TAC½O�

r4 �CBA ¼ BC½O�p �TA� k1C4 �CBA � k5C½O�C4 �CBA

r½O�4 �CBA¼ k1C4 �CBA þ k5C½O�C4 �CBA � BC½O�4 �CBA

� k6C½O�4 �CBAC½O�

rTPA ¼ BC½O�4 �CBA

whereC½O� ¼ C½O�PX þ C½O�TALD þ C½O�p �TA

þ C½O�4 �CBA

B ¼ k2CPX þ k3CTALD þ k4Cp �TA þ k5C4 �CBA



3. MODELING OF THE PX OXIDATION PROCESS

3.1. Mass and Energy Balance Equations. The oxidationreactor of theMitsui process can be generally assumed as an idealcontinuous stirred-tank reactor including a reaction part and adehydration part. Traditionally, the oxidation reactor is modeledby writing the mass balance of the components involved in thereaction. Thus, the mass balance equations based on the freeradical mechanism can be given as:

FinCin, PX � FoutCPX þ Mr1 ¼ 0 ð12Þ

FinCin, TALD � FoutCTALD þ Mr2 ¼ 0 ð13Þ

FinCin, p �TA � FoutCp �TA þ Mr3 ¼ 0 ð14Þ

FinCin, 4 �CBA � FoutC4 �CBA þ Mr4 ¼ 0 ð15Þ

� FoutCTPA þ Mr5 ¼ 0 ð16Þwhere rj (j = 1�5) represents the production rate of jth liquidcomponents (i.e., PX, TALD, p-TA, 4CBA, TPA); Fin is the inletmass flow rate of acetic acid (HAc); Fout is the outlet mass flowrate of acetic acid; andM is the total mass of the acetic acid in thereactor and can be calculated as:

M ¼ VtotalFmixεL 1 þ ∑Ciwi

1000

� ��1

ð17Þ

whereVtotal is the reaction volume; εL is the liquid phase fraction;Ci represents the concentration of the ith component in liquidphase except acetic acid; wi represents the molecular weight ofthe ith component in liquid phase except acetic acid; Fmix is thedensity of the mixture of water and acetic acid, which can becalculated as:

1Fmix

¼ xH2O

FH2Oþ xHAC

FHACð18Þ

where xH2O and xHAC represent the molar fractions of water andacetic acid, respectively; FH2O and FHAC represent the densities ofwater and acetic acid, respectively.With respect to the energy balance, this reaction is a very

typical exothermic reaction, which involves three types of heatexchange and release: sensible heat of gaseous and liquidcomponents, latent heat produced from the solvent evaporation,and reaction heat. Assuming that the reaction is in phaseequilibrium, the energy balance consists of five equations.The thermal power for liquid reactants to heat from the inlet

temperature to the reaction temperature can be expressed by:

Q1 ¼ ð∑jFinCin, jÞCP, inðT � TinÞ ð19Þ

where Cin,j (mol/kg HAc) is the concentration of the jthcomponent in the liquid phase; CP,in is the average heat capacityat constant pressure of the inlet flow rate; andTin andT representthe inlet temperature and reaction temperature, respectively.The thermal power for air heating from the inlet temperature

to the reaction temperature can be expressed by:

Q2 ¼ FairCP, airðT � TairÞ ð20Þwhere Fair is the mass flow rate of air; CP,air is the average heat

capacity at constant pressure of air; and Tair and T represent theinlet temperature and reaction temperature of air, respectively.The thermal power for liquid components that recycle back to

the reactor from the distillation column heating from refluxtemperature to the reaction temperature can be expressed by:

Q3 ¼ ∑jLxjCP, LðT � TBÞ ð21Þ

where Lxj is the recycle molar flow rate of the jth component inthe liquid phase; CP,L is the average heat capacity at constantpressure of the liquid recycle flow rate; and TB and T representthe recycle temperature and reaction temperature of air,respectively.In the above equations, the average value of heat capacity at

constant pressure CP is calculated according to the followingequation:

CP ¼ ∑j

Cj

∑iCi þ 1000

wHAC

Cp, j ð22Þ

where Cj (mol/kg HAc) and Cp,j represent the jth concentrationand molar heat capacity of the components in the liquid phase,respectively; Ci is the ith concentration of the components in theliquid phase except acetic acid; and wHAC is the molecular weightof acetic acid.The latent heat of solvent evaporation can be expressed by:

Q4 ¼ VyHACHvHAC þ VyH2OH

VH2O ð23Þ

where VyHAC and VyH2O represent the vapor evaporation flowrates of acetic acid and water, respectively; and HHAC

v andHH2OV represent the latent heat of acetic acid andwater, respectively.The total reaction heat, which can be simply considered the

reaction heat of the reactant PX transformed into the finalproduct TPA due to the high yield of the reaction, can be givenby:

Q5 ¼ ðFinCin, PX � Fout ∑4

1CjÞð �ΔHr,mÞ ð24Þ

whereCin,PX is the concentration of PX in the inlet stream;Cj (j =1�4) represents the jth concentration of liquid reactants (i.e.,PX, TALD, p-TA, 4CBA), respectively; Fin and Fout represent theinlet and outlet mass flow rate of the acetic acid; andΔHr,m is thereaction enthalpy of PX transforming into TPA.Therefore, the overall energy balance equation can be for-

mulated as:

Q1 þ Q2 þ Q3 þ Q4 þ Q5 ¼ 0 ð25Þ

3.2. Method of Solution. The mass and energy balanceequations can be solved only after parameters associated withthem are obtained. Briefly, the solution procedure is as follows:(1) By using the experimental data provided by Sun et al.,2 a

BPNNmodel is used to estimate the rate constants of theexperimental process.

(2) An adaptive immune algorithm is applied to correct therate constants due to the large difference between the natureof PX oxidation in the laboratory and in the industry. Theestimated rate constants by the BPNN model are used asinitial conditions for the algorithm.



(3) The concentrations of the reactants and products can beobtained from step (2) and compared to industrial data.The procedure is repeated from step (2) until a certaintermination criterion is reached.

3.3. Parameter Estimation and Correction. Among theparameters of the model discussed above, the rate constantsare the most important and can be influenced by many reactionfactors, such as catalyst concentrations, water concentrations,and temperatures. However, it is difficult to estimate values of therate constants on the basis of limited data provided by previousworks. Thereby, one of the most important problems encoun-tered is how to estimate values of the rate constants. Besides, thedifference between the nature of PX oxidation in the laboratorysemibatch reactor and that in the industrial continuous stirred-tank reactor is quite large. Therefore, a BPNN is introduced toobtain the estimated values of the rate constants. Furthermore,an adaptive immune algorithm is applied to revise it.On the basis of the free radical mechanism, temperature and

catalyst concentrations only affect the rate constants in the chaininitiation stage. This indicates that only k1 changes while k2, k3,k4, k5, and k6 almost remain constant at different reactionconditions (Sun et al.2). k1 is found to be changed by the catalystconcentrations, temperature, and water concentration. So, thestructure of the BPNNmodel is shown in Figure 3. As expressedabove, the rate constants obtained by experimental data do not fitthe industrial process well, and thus need to be revised. Correc-tion coefficients σi1 and σi2 (i = 1, 2, 3, 4, 5, 6) are introduced toaccurately modify the values of ki. Thus, ki is defined as:

k1 ¼ σ11f1ðx1, x2, x3, x4, x5Þ þ σ12

k2 ¼ σ21k02 þ σ22

k3 ¼ σ31k03 þ σ32

k4 ¼ σ41k04 þ σ42

k5 ¼ σ51k05 þ σ52

k6 ¼ σ61k06 þ σ62

8>>>>>>>>><>>>>>>>>>:

ð26Þ

where x1 (ppmw) is the concentration of cobalt catalyst in thefeed, x2 (ppmw) is the concentration of manganese catalyst inthe feed, x3 (ppmw) is the concentration of bromide catalyst inthe feed, x4 (�C) is the reaction temperature, and x5 (%) is thewater concentration. f1 is the BPNN model of the rate constantk1; kj0 (j = 2, 3, 4, 5, 6) (mol kg�1 min�1) are the constants’ ratesevaluated by BPNN.Thus, a minimization problem is formulated, where the

objective is to minimize the deviation of the calculated concen-trations and the industrial concentrations of reactants andproducts, that is, PX, TALD, p-TA, 4CBA, and TPA. Twelvevariables for optimization are the correction coefficients σi1 andσi2 (i = 1, 2, 3, 4, 5, 6). Accordingly, optimization vector X can be

formulated as:

X ¼ f ðσ11, σ12, σ21, σ22, σ31, σ32, σ41, σ42, σ51, σ52, σ61, σ62Þð27Þ

Also, the deviation is defined as follows:

Fj ¼ ∑5

i¼ 1

CðjÞi � CðjÞ

i

CðjÞi

!2

ð28Þ

where Ci(j) (i = 1, 2, 3, 4, 5) and Ci

(j) (i = 1, 2, 3, 4, 5) are the jthcalculated concentrations and industrial concentrations of PX,TALD, p-TA, 4CBA, and TPA, respectively.Mathematically, the optimization problem can be written as:

min E ¼ ∑n2

j¼ 1Ej ¼ ∑

n2

j¼ 1∑5

i¼ 1

CðjÞi � CðjÞ

i

CðjÞi

!2

ð29Þ

where the objective function E denotes the total deviation; n2 isthe number of the total sample.In this Article, the Adaptive Immune Genetic Algorithm

(AIGA) is applied to solve the optimization problem. The maincomponents of AIGA are calculation of affinity values, clonalselection, crossover, and adaptive mutation.For calculation of affinity values, AIGA uses affinity as a

discriminator of the quality of solutions, and the antibody withhigher affinity is more likely to be selected and survives to thenext generation at higher probability. In this Article, affinity isdefined as:

af f inityi, t ¼ r � ð1� rÞi � 1 ð30Þwhere r∈ [0,0.5], and i is the numerical order of each antibody inthe population by arranging them according to their func-tion value.For clonal selection, the definition of thickness of antibody is

the same as SIGA as follows:

coni, t ¼ 1popsize ∑

popsize

j¼ 1KAbij ð31Þ

where

KAbij ¼1, Abi, t � Abj, t�� < l

0, otherwise

(ð32Þ

Selection probability is then given by:

Pri, t ¼af f inityi, tconi, t

∑popsize

i¼ 1

af f inityi, tconi, t

ð33Þ

Crossover and adaptive mutation (Lopez Cruz et al.18):

Ab0i, t ¼ b1 � Abm, t þ b2 � Abn, tAb0j, t ¼ b2 � Abm, t þ b1 � Abn, t

(ð34Þ

where b1 = 0.5 + b, b2 = 0.5 � b, b ∈ [0,1]:

Ab0i, t ¼ Abi, t þ F0 � 2e1 � ðT=T � t þ 1Þ

� ðAbm, t � Abn, tÞ ð35Þ

Figure 3. BNPP model.



where T is the number of maximum iteration; t is the currentgeneration; and F0 is the mutation parameter.Therefore, the main loop of AIGA can be described in

Figure 4.With respect to the side reactions, we are only concerned

about the acetic acid combustion loss and PX combustion loss ofthe reactor. Because the main products of side reactions are COand CO2, which can be analyzed from the reactor off-gas, a modelof the combustion loss can be established by BNPP. The detailed

discussion about modeling of acetic acid combustion loss and PXcombustion loss can be found in Du.19

4. RESULTS AND DISCUSSION

We write an Aspen Plus user model in Fortran to extend thecapabilities of Aspen Plus, because the PX oxidation model isbased on the free radical mechanism, which cannot be written bybuilt-in models provided by Aspen Plus software. Figure 5 showsthe flowsheet of PX oxidation plant in China designed accordingto Mitsui technology. The overall PX oxidation reaction involvestwo stages. At first, PX (10A), a mixture (13A) including aceticacid solvent and catalysts and air (16A), is continuously fedinto the reactor (unit YR1-201), which consists of severalFortran subroutines to implement models of radical reactionand the BPNN; second, unreacted PX, partially oxidized pro-ducts, and catalyst are refluxed to the reactor (unit YR1-201) andrecycled. Simultaneously, exothermic heat of reaction is removedby condensing the boiling reaction solvent and water (unitTT201). The unit B2 is a flash built to simulate the vapor�liquidequilibrium process. The operating conditions used in thesimulation are taken from an operational PTA plant as listed inTable 2.

Considering the correction of the rate constants achieved byAIGA, the population size of AIGA N = 50, the size of memorybase CM = 20, initial crossover rate Pc = 0.7, initial mutation rateα = 0.2, and the maximum iteration number T = 100. Theobjective function curve in optimization process is recorded inFigure 6. The optimum parameters of the free radical kineticmodel calculated by the AIGA technique are listed in Tables 3and 4.

The new kinetic parameters are then applied to simulate thePX oxidation reactor of the Mitsui process, and the outputFigure 4. The flowchart of AIGA.

Figure 5. PX oxidation process. 10A, PX; 13A, acetic acid solvent and catalysts; 16A, air; WG, off-gas from the reactor; 26A, water and acetic acid fromthe distillation column; OUTFLOW, product from the reactor.



component concentrations are obtained. The distributions of thecalculated component concentrations of the liquid reactantsbased on the optimum kinetic parameters versus the historicaldata of an actual industrial Mitsui process are shown in Figures 7and 8.

Figure 6 shows that the application of AIGA in the oxidationreaction process can quickly converge to the global optimum andperform very well in the rate constants correction. Figure 7 showsthe distributions of p-TA, in which Cp‑TA

1 denotes the calculatedconcentration of p-TA based on the optimum kinetic parametersand Cp‑TA

2 denotes the concentration of p-TA without optimumcorrection coefficients. Figure 8 shows the distributions of

4-CBA, one of the key index to the quality of TPA (Yan et al.5),in which C4‑CBA

1 denotes the calculated concentration of 4-CBAbased on the optimum kinetic parameters and C4‑CBA

2 denotesthe concentration of 4-CBA without optimum correction coeffi-cients. The diagonals in Figures 7 and 8 represent the values ofthe practical data in an actual industrial Mitsui process. It isobvious in Figure 7 that the model without the optimum correc-tion coefficients overpredicts the concentrations of the reactants,and the differences between calculated data and industrial dataare relatively high. The maximum relative error of p-TA con-centrations calculated from the model with optimum kineticparameters with respect to the industrial data is 9.87%. Also, asseen in Figure 8, the performance of the PX oxidation processmodel with the optimum correction coefficients fits better to theindustrial data than that of the model without the correctioncoefficients. The maximum relative error of 4-CBA concentra-tions with respect to the industrial values is 3.86%. Therefore,comparison of the results confirms that the model with theoptimum kinetic parameters can accurately predict the industrialPX oxidation reaction process.

5. CONCLUSIONS

A novel kinetic model based on free radical mechanism isused to simulate the oxidation of PX in continuous stirred-tank reactor. Because primary kinetic parameters, tightly asso-ciated with the reaction, can be influenced by many operatingconditions, a back-propagation neural network was intro-duced to predict the rate constants. Although this novel kineticmodel was proved to be more reliable than previous kineticmodels, however, due to the difference between the experimentaland industrial conditions, an Adaptive Immune Genetic Algo-rithm was carried out to modify the rate constants. The modelwith the optimum kinetic parameters has been successfullyapplied into a PTA project in China to predict the key index ofthe process with relative error less than (10%. The approach

Figure 6. Objective function curve in optimization process.

Table 3. Calculated Kinetic Parameters

parameter model

optimizedvalue byAIGA

95%confidence

limit

k1 (min�1) f bpnn

(x1,x2,x3,x4,x5)

f bpnn

(x1,x2,x3,x4,x5)0.0278 + 0.1053

k2 (mol kg�1 min�1) 15 879.45 6569.29 256k3 (mol kg�1 min�1) 17 088.896 633.699 19.64k4 (mol kg�1 min�1) 3275.478 528.167 20.94k5 (mol kg�1 min�1) 9814.47 111.112 3.18k6 (mol kg�1 min�1) 0.5436 0.286 0.0093

Table 2. Operating Conditions of the Industrial PXOxidation Reactor

operation conditions initial values

concentration of cobalt catalyst (ppm) 425

concentration of manganese catalyst (ppm) 222

concentration of bromine promoter (ppm) 906

temperature of the reactor (�C) 187.14

water concentrations (%) 8

inlet mass flow rate of PX (t/h) 27.459

inlet mass flow rate of HAc (t/h) 132.395

residence time of the first reactor (min) 56.8

Table 4. Calculated Kinetic Parameter k1 for Different Op-erating Conditions

[Co]

ppm

[Mn]

ppm

[Br]

ppm

temperature

(�C)

mass

concentration

of water

k1 �10�6

(min�1)

425 222 906 187.13 8% 2.571

425 222 906 187.03 8% 2.567

430 233 966 187.55 8% 2.653

522 289 1044 187.37 8% 2.771

443 256 972 188.11 8% 2.697

443 256 973 188.57 8% 2.711

492 285 1000 188.50 8% 2.762

492 285 1002 188.49 8% 2.763

479 274 999 188.40 8% 2.753

492 285 999 188.42 8% 2.759

505 279 932 188.15 8% 2.694

528 297 910 188.03 8% 2.669

530 299 962 187.66 8% 2.709

651 364 981 187.62 8% 2.615

651 364 981 187.77 8% 2.620

668 374 962 187.76 8% 2.569



presented in this Article has proven its importance in con-junction with a real-life industrial process. The comparisonbetween model prediction and industrial historical data is alsopresented, and the agreement is quite satisfactory. The obtainedresults show that the model with the evaluated optimum kineticparameters is able to predict the reactor behavior very well.The model combined with intelligent methods in this work notonly provides technical support for industrial PX oxidation processbut serves as a foundation of dynamicmodeling in our future work.

’AUTHOR INFORMATION

Corresponding Author*(F.Q.) E-mail: [email protected]. (W.D.) Email: [email protected].

’ACKNOWLEDGMENT

This research was supported by Major State Basic ResearchDevelopment Program of China (973 Program: 2012CB720500),National Natural Science Foundation of China (Key Program:U1162202), National Natural Science Foundation of China(General Program: 20876044), Shanghai Key TechnologiesR&D Program (10dz1121900), the 111 Project (B08021),Shanghai Leading Academic Discipline Project (B504).

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Figure 7. Comparison of industrial concentrations of p-TA with predicted concentrations.

Figure 8. Comparison of industrial concentrations of 4-CBA with predicted concentrations.



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’NOTE ADDED AFTER ASAP PUBLICATION

This paper was published on the Web on January 20, 2012.Additional information was added to the Acknowledgmentparagraph and the corrected version was reposted on February8, 2012.

Documents

Development of a Free Radical Kinetic Model for Industrial Oxidation of p -Xylene Based on Artificial Neural Network and Adaptive Immune Genetic Algorithm