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20 th European Symposium on Computer Aided Process Engineering ESCAPE20S. Pierucci and G. Buzzi Ferraris (Editors) 2010 Elsevier B.V. All rights reserved.

Optimization of Batch Reactive DistillationProcess: Production of Lactic AcidElmahboub A. Edreder a, Iqbal M. Mujtaba a, Mansour Emtir ba School of Engineering, Design and Technology, University of Bradford, WestYorkshire, BD7 1DP,UK. Email: I.M.Mujtaba@bradford.ac.uk b National Oil Corporation, P.O. Box 2655, Tripoli, Libyan Arab Jamahiriya

AbstractLactic acid is widely used as a raw material for the production of biodegradablepolymers, food, chemical and pharmaceutical industries. The global market for lacticacid is set to reach 259 thousand metric tons by year 2012.

In this work, the performance of batch reactive distillation is evaluated to produce lacticacid by hydrolysis reaction of methyl lactate. Minimum time optimisation problem isdeveloped incorporating a process model within gPROMS software for range lactic acidpurity (from 80 % to 99 %) and the amount of product. For a given column theminimum operation time configuration is obtained by optimising the reflux ratio profile.The lactic acid being heaviest in the reaction mixture, reflux ratio policy plays animportant role in removing the light product methanol from the system while ensuringthe presence of both reactants in the reaction zone to maximise the conversion to lacticacid. Also unlike esterification reaction, total reflux operation is demanded at the end ofthe operation in the hydrolysis reaction to purify lactic acid to about 99 % by removingthe remaining reactants from the reboiler.

Keywords : Batch reactive distillation, Hydrolysis, Lactic acid, Methyl lactate,

Optimization.

1. IntroductionSeveral researchers in the past have proposed the esterification of lactic acid (impure)with methanol to obtain lactate ester which is then separated by distillation. Thedistilled lactate ester is then hydrolyzed into pure lactic acid (Fig. 1). Both continuous(Li et al. , 2005; Kumar et al., 2006 b and Rahman et al ., 2008) and batch (Choi andHong, 1999; Kim et al ., 2000; Kim et al. , 2002 and Kumar et al. , 2006 a) have beenemployed for the recovery of lactic acid.Li et al. (2005) studied purification of lactic acid based on the esterification of dilutedlactic acid with methanol in a reactor followed by hydrolysis of methyl lactate incontinuous column to achieve pure lactic acid. They observed the presence of methyllactate in the distillate due to incomplete hydrolysis to lactic acid. Kumar et al. (2006 a)considered both experiments and simulation of a continuous reactive distillation processcoupling esterification of lactic acid and hydrolysis of methyl lactate to obtain purelactic acid. They observed 100 % conversion in a column of 20 stages. Rahman et al .(2008) applied Differential Evolution (DE) algorithm for the optimisation of CSTRreactor followed by distillation column with hydrolysis of methyl lactate. The objectivewas to minimise the overall cost which gives the optimal variables such as:esterification reaction temperature, number of stages, feed location, reflux ratio, catalystweight, and number and position of reactive stages.

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Choi and Hong (1999) investigated an apparatus (two reactors and two batch distillationcolumns) to carry out the esterification and hydrolysis reactions and achieved relatively

pure lactic acid. Kim et al. (2000) considered a batch reactive distillation withesterfication and hydrolysis for the recovery of lactic acid using experiments and simplemodelling to obtain optimum design and effective operation. Kim et al. (2002) analyzedthe dynamic behaviour of batch reactive distillation of lactic acid in terms ofinstantaneous rate of esterification reaction. They observed that the rate increased bycontrolling of boil up rate and residence time during the operation by changing both themethanol recycle stream and feeding mode. They also compared semi-batch operationwith the batch mode. It was found that continuous feeding of methanol enhanced therecovery of lactic acid. Kumar et al . (2006 b) explored and investigated a novel reactivedistillation strategy involving experimental esterification and hydrolysis reaction forrecovery of lactic acid. They studied the effect of operating parameters such as feedconcentration, mole ratio, catalyst load, and boil up-rate on the recovery of lactic acid.As seen from the previous researches that the most of the work has been focused on

experiments to recover lactic acid. Optimisation problem in terms of minimum batchtime for hydrolysis of methyl lactate to lactic acid has not been considered in the past.Therefore, in this work, the performance of batch reactive distillation in terms ofminimum batch time is considered with the hydrolysis reaction of methyl lactate. Adynamic model for the process (Edreder et al., 2009) is used which is incorporated intothe optimization framework. Product amount and purity are used as constraints. Refluxratio is used as control variable which is discretised using Control VectorParameterization technique. This results in a Non Linear Programming (NLP) problem,which is solved using an SQP-based optimization technique available within gPROMS(2004).

Fig. 1 Batch reactive distillation process for lactic acid synthesis

Methyl lactate (ML) + Water (H 2O) Lactic acid (LA) + Methanol (MeOH )

Esterification

Hydrolysis

MeOH(Unreacted)

H2O ML

LA +MeOH

LA (Final product)

MeOH H2O

Make up H 2O

Esterfication Hydrolysis

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2. Hydrolysis Reaction

2.1. Chemical Reaction and KineticsThe hydrolysis reaction of methyl lactate can be expressed as follows

Methyl lactate (1) + Water (2) Lactic acid (3) + Methanol (4) (1)

B.P (K) 417.15 373.15 490.15 337.15 A quasi-homogeneneous (QH) activity ( a i = i xi) based kinetic model is used (takenfrom Sanz et al ., 2004) and can be written as:

436

215 aa)

RT52.48

exp(1016.1aa)RT

91.50exp(1065.1r

= (2)

2.2. Vapor-Liquid Equilibrium (VLE)K-values (VLE constants) are computed from (Eq. 3) where i is computed fromUNIQUAC equation , the vapor pressure (P sat) of pure components has been obtained byusing Antoines equation. The UNIQUAC binary interaction parameters and Antoineparameters were taken from Sanz et al. (2003). Vapor phase enthalpies are calculatedusing empirical equations from formulation Holland (1981) and the liquid phaseenthalpies were calculated by subtracting heat of vaporization from the vapor enthalpies

Psat iPiK / = (3)

3. Optimization ProblemThe performance of batch reactive distillation column is evaluated in terms ofminimizing the operating time. Single and multiple reflux ratio strategies are used,yielding an optimal reflux ratio policy. For multiple reflux ratio policy, within each

interval the reflux ratio (assumed piecewise) together with the switching time from oneto other interval is optimized. Values of profile over time intervals concerned areassumed. The amount of bottom product (lactic acid) and product purity are specified asconstraints bounds in the optimization problem. In addition to the constraints mentionedthe differential algebraic equations (DAE) process model act as equality constraints tothe optimization problem.

given: the column configuration, the feed mixture, vapour boilup rate,product purity, amount of bottom product.

determine: optimal reflux ratio which governs the operationso as to minimise: the operation time.subject to: equality and inequality constraints (e.g. model equations).

Mathematically, the Optimisation Problem (OP) can be represented as:

)constrainty(inequalitxx)constrainty(inequalit*BB

s)constriant(equalityEquationModelocessPrt.s

)t(RtMin

*33

f

+=

(4)

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Where B, x 3 are the amount of bottom product and composition at the final time t f ,(denotes that the B and x 3 are specified) , R(t) is the reflux ratio profile which is

optimized. is the small positive number of the order of 10-3

.

4. Case Study

4.1. SpecificationsThe case study is carried out in a 10 stages column (including condenser and reboiler)with condenser vapour load of 2.5 (kmol/hr). The total column holdup is 4 % of theinitial feed (50 % is taken as the condenser hold up and the rest is equally divided in theplates) and the reboiler capacity is 5 kmol. The feed composition is : .

4.2. Results and DiscussionsHere, four cases are studied. In Case 1, single time interval (NCI = 1) is used while inthe other three cases, time dependent reflux polices (discretised into two (NCI = 2),three (NCI = 3) and four (NCI= 4) time intervals) are considered. For each case, Table 1summarises the optimisation results in terms of optimal reflux ratios, conversion ofmethyl lactate to lactic acid and minimum operating time for different product purity byusing single and time dependent reflux policies.

Table 1 Summary of the results using single and multiple reflux ratio strategies

Note: * means Not possible to achieve the product at the desired purity

It is noticed from the optimization results that, the column operated with single timeinterval for reflux ratio was not sufficient to produce the main product at high purityspecifications (> 0.925 mole fraction a lactic and in the bottom product). The multi-

Case 1: NCI=1 interval Case 2: NCI= 2 intervalsx purity R t f (hr) Conv.% x purity t1,R1 R2, tf Conv. %0.80 0.933 14.88 77.7 0.80 9.54, 0.914 0.957, 13.72 77.70.85 0.957 23.28 82.5 0.85 9.43, 0.937 0.957, 19.04 82.70.90 0.973 46.04 86.9 0.90 8.66, 0.922 0.979, 23.95 87.9

0.925 0.993 135.4 89.2 0.925 12.50, 0.950 0.983, 31.41 90.10.950 * * * 0.950 10.55, 0.935 0.990, 44.73 92.5

Case 3: NCI= 3 intervalsx purity t1,R1 t2,R2 R3, t f Conv. %0.800 2.33, 0.813 2.00, 0.907 0.945, 11.27 77.80.850 7.49, 0.907 3.99, 0.971 0.964, 16.72 82.90.900 4.86, 0.886 3.74, 0.950 0.980, 21.90 88.10.925 5.75, 0.899 12.08, 0.975 0.989, 28.88 90.50.950 6.24, 0.909 11.09, 0.975 0.992, 37.82 92.90.975 16.31, 0.956 17.70, 0.988 0.996, 55.07 94.80.990 * * * *Case 4: NCI= 4 intervalsx purity t1,R1 t2,R2 t3,R3 R4, t f Conv. %0.800 0.500, 1.00 2.11, 0.800 2.63, 0.918 0.935, 10.80 77.90.850 1.280, 0.921 5.49, 0.908 5.10, 0.962 0.957, 16.55 82.90.900 0.420, 1.00 2.70, 0.835 3.88, 0.937 0.976, 20.09 88.30.925 0.500, 1.00 1.26, 0.779 4.61, 0.924 0.982, 27.26 90.70.950 0.540, 1.00 2.93, 0.848 8.79, 0.964 0.989, 34.17 93.30.975 6.03, 0.962 10.95, 0.955 17.43, 0.988 0.996, 54.88 94.70.990 15.34, 0.954 20.72, 0.994 51.10, 0.996 1.00, 142.08 96.0

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reflux interval strategies (Case 2-4) were found to be better to produce products withhigher purity specifications with shorter batch time. Fig. 2 proves this fact in terms of

minimum operating time as a function of bottom product purity specifications andreflux ratio policy. For example the operation time using two time intervals (in case ofproduct purity 0.925) is reduced by 76.8 % compared to that obtained by using singleinterval. This is due to the fact that the column initially operated at lower reflux ratio(R1) to remove the light component (methanol) and then at higher reflux (R 2) to meetthe product specification in a shorter time. Note, it was not possible to achieve thebottom product at (0.975 purity) with two reflux intervals.Observation also shows that the operating time for some cases can be saved by 79 %when the column operated using 3 reflux ratio intervals compared to the operation timesobtained using single interval. Moreover the operating time has been saved by anaverage of 37 %, 46 % and 48 % using 2, 3 and 4 time intervals respectively for thepurity range from 0.8 to 0.925. This clearly shows the benefit of using multi refluxintervals. It can be observed also that at product purity 0.975 no significant

improvement is noticed in terms of operating time when the column operates with 3 or 4reflux ratio level intervals.The lactic acid product with purity of 0.99 molefraction was not possible to achievewith 3 reflux intervals but was possible to achieve with 4 reflux intervals. Note, in thelast time interval (R 4, t f ) for Case 4, the column operates at total reflux for a long period(~ 91 hrs). Although there was no distillate withdrawn during that period, compositionprofiles in the condenser holdup tank, internal stages and in the reboiler took place topurify the bottom product to the desired purity. Finally, note for each product purity, theamount of bottom product could be further improved by multi-reflux policy. Unlikeesterification reaction in conventional batch reactive distillation where the reactionproduct (ester) is the lightest, the hydrolysis reaction considered here produces theproduct (lactic acid) which is the heaviest in the mixture. The column has to alwaysoperate at high reflux ratio so that both the reactants are available in the reaction zone(reboiler and stages). Low reflux ratio operation will separate the reactants from thesystem and will thus lower the conversion (as can be seen in Case 1). Multi-refluxoperation enjoys more freedom to balance between the conversion and product purity(as can be seen in Cases 2-4)

Fig.2. Minimum batch time as a function of lactic acid purity specification

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5. ConclusionsThe performance of batch reactive distillation process in terms of minimum batch timeis studied here with hydrolysis reaction of methyl lactate to produce lactic acid andmethanol. A dynamic optimization problem incorporating a process model is formulatedto minimize the batch time subject to constraints on the amount and purity of lactic acid.Piecewise constant reflux ratio profile (with single and multiple time intervals) isconsidered as a control variable. A series of minimum time problems was solved atdifferent values of product purity ranging from 0.8 to 0.99 molefraction and the impactof time dependant reflux ratio policy on the product quality and batch time are analyzed.For a given column configuration, it is noticed that, the column operated with singlereflux ratio interval was not sufficient to produce high purity lactic acid. The saving inoperating time and improvements in product purity shows the benefit of using multi-reflux intervals strategy rather than single reflux ratio policy. Multi-reflux operationenjoys additional freedom to have the balance between the conversion and the productpurity.

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distillation using ion-exchange resins, Chinese J. Chem. Eng., 13, 24- 31.Kumar, R., Nanavati, H., Noronha, S.B., Mahajani, S.M. (2006 a). A continuous process for therecovery of lactic acid by reactive distillation, J. Chem. Technol. Biotechnol., 81, 1767-1777.Kumar, R., Mahajani, S.M., Nanavati, H., Noronha, S.B. (2006 b). Recovery of lactic acid bybatch reactive distillation. J. Chem. Technol. Biotechnol., 81, 1141-1150.Rahman, I., Ahmed, A., Kumar, P. and Kulkarni, B. (2008). Optimization of a continuous processfor recovery of lactic acid using differential evolution algorithm, Chemical Product and ProcessModeling , vol.3 , Iss.1, Article 6.Sanz, M.T., Beltran, S., Calvo, B., Cabezas, J.L. (2003). Vapor Liquid Equilibria of the Mixturesinvolved in the esterification of lactic acid with methanol, J. Chem. Eng. Data, 48, 1446-1452.Sanz, M.T., Murga, R., Beltran, S. Cabezas, J.L. and Coca J. (2004). Kinetic study for the reactivesystem of Lactic Acid esterification with methanol: Methyl lactate hydrolysis, Ind. Eng. Chem.Res., 43, 3, 2049-2053.