Computational Studies of the Countercurrent Multistage Extraction-Coupled Esterification Process of Oleic Acid with Methanol Using Excess Methanol as Extractant

Computational Studies of the Countercurrent Multistage Extraction-Coupled Esterification Process of Oleic Acid with Methanol Using Excess Methanol as Extractant

0263–8762/04/$30.00+0.00 # 2004 Institution of Chemical Engineers Trans IChemE, Part A, May 2004 Chemical Engineering Research and Design, 82(A5): 599...

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0263–8762/04/$30.00+0.00 # 2004 Institution of Chemical Engineers Trans IChemE, Part A, May 2004 Chemical Engineering Research and Design, 82(A5): 599–604

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COMPUTATIONAL STUDIES OF THE COUNTERCURRENT MULTISTAGE EXTRACTION-COUPLED ESTERIFICATION PROCESS OF OLEIC ACID WITH METHANOL USING EXCESS METHANOL AS EXTRACTANT F. CHEN1*, J. KAWASAKI2 and Y. NAKA3 1

Research Institute of Tsinghua University in Shenzhen, Shenzhen, People’s Republic of China Department of Chemical Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan 3 Frontier Collaborative Research Center, Tokyo Institute of Technology, Yokohama 226, Japan 2

A

new process has been suggested for the esterification of oleic acid with methanol catalysed by a cation exchange resin, in which water is removed by simultaneous extraction with excess methanol as the extractant, and an algorithm for the simulation of countercurrent multistage extraction-coupled reaction processes has been proposed. The algorithm was applied to the new process and was proved to have good convergence. The calculated results showed that methyl oleate product with high yield and high purity could be obtained in the multistage countercurrent extraction-coupled esterification process. It was found that both yield and purity of methyl oleate product increase with the increase in the feed ratio of methanol=oleic acid as well as in the number of stages. A feed ratio more than six (in mole base) is required to obtain the purity and=or the yield higher than 95%. Purity of 99% and yield of 99% can be achieved in a four to nine stage process with a feed ratio of more than 8.5–16 when using 100% pure raw methanol. Keywords: extraction-coupled esterification; methyl oleate; excess methanol.

INTRODUCTION

dehydrating agent. The biggest advantage of using excess methanol as the extractant is that the composition of the product will be simple because no content other than the reactants are used. Furthermore, the operation of an extraction-coupled reaction process is considered to be easy in industry. However, multistage process must be considered in industry, because the yield in one stage of extraction-coupled reaction is not so high. The present paper will establish the algorithm for the simulation of COMER (countercurrent multistage extractioncoupled reaction process). The algorithm is applied to the esterification of oleic acid with methanol catalysed by a cation-exchange resin using excess methanol as the extractant and without using any dehydrating agent, to investigate the effects of the feed rate, the number of stages as well as the water content in the raw methanol on the methyl oleate product.

The esterification of fatty acids with alcohols is a kind of reversible reaction. Cation exchange resins can be used as the catalyst, which can be easily separated and reused and do not lead to environmental pollution or equipment corrosion compared with inorganic acids. Water produced has to be removed in order to obtain high yield of the product. Many methods such as esterification accompanied by membrane separation (Bagnell et al., 1993; Chemseddine and Audinos, 1996; Kita et al., 1987; Okamoto et al., 1994) have been studied for this purpose. Recently, the authors have reported an interesting result in the reaction system of long chain fatty acids with methanol (Chen et al., 2001). The system may split into two liquid phases, and forms an extraction-coupled reaction system when excess methanol is added. Water produced in the reaction is distributed between the two phases and can be removed by separating the polar phase from the reaction system. It is therefore considered that high yield of the ester may be obtained in an extraction-coupled reactor with excess methanol as the extractant and without any

BASIC EQUATIONS A diagram of the esterification process using COMER is shown in Figure 1. Figure 2 shows the scheme of COMER. It is composed of a series of reactors numbered as 1, 2, . . . , n from the top stage to the bottom stage. Each reactor consists of a mixer and a settler. Reactants are mixed

*Correspondence to: Dr F. Chen, Research Institute of Tsinghua University in Shenzhen, Shenzhen 518057, People’s Republic of China. E-mail: [email protected]

599

600

CHEN et al. It is assumed that both reaction equilibrium and liquid– liquid equilibrium are reached in each stage. The equilibrium constant of reaction, K, is represented as K¼

N Y

Figure 1. The diagram of esterification process using COMER.

equably in the mixers. Each stage has two inlets and two outlets. Light phase is fed from the bottom stage (stage n) and heavy phase from the top (stage 1). Both phases contain N components. For a given stage, such as stage j, the compositions and the flow rates of the two inlets are represented as x0i, jþ1 (i ¼ 1, 2, . . . , N ), L0jþ1 and x00i, j1 (i ¼ 1, 2, . . . , N ), L00j1 , respectively, and those of the two outlets are represented as x0i, j (i ¼ 1, 2, . . . , N ), L0j and x00i, j (i ¼ 1, 2, . . . , N ), L00j , respectively. The overall composition of the feed to stage j before the reaction on the same stage is wi, j ¼

L0jþ1 x0i, jþ1 þ L00j1 x00i, j1 L0jþ1 þ L00j1 (i ¼ 1, 2, . . . , N ; j ¼ 1, 2, . . . , n)

( j ¼ 1, 2, . . . , n)

(3)

where ai, j is the activity of component i on stage j. The activities of each component in both liquid phases on a given stage are the same: g0i, j x0i, j ¼ g00i, j x00i, j ¼ ai, j (i ¼ 1, 2, . . . , N ; j ¼ 1, 2, . . . , n)

(4)

where g0i, j and g00i, j are the activity coefficients of component i in liquid phase I and liquid phase II, respectively, on stage j. For non-electrolyte systems, the activity coefficients of each component in both phases can be estimated using any activity estimation method, such as UNIQUAC, UNIFAC, etc. The overall composition of the reaction mixture including the two liquid phases on stage j in reaction equilibrium is

(1)

The reaction equilibria in all stages are the same as described as m1 C1 þ m2 C2 þ    mi Ci þ    þ mN CN ¼ 0

ai, j mi

i¼1

zi, j ¼ PN

wi, j þ mi qj

l¼1 (wl, j

þ ml, j qj )

(i ¼ 1, 2, . . . , N ; j ¼ 1, 2, . . . , n)

(5)

(2)

where Ci represents component i in the reaction system, mi the stoichiometric coefficient of Ci. mi < 0 if Ci is a reactant or mi > 0 if Ci is a product or mi ¼ 0 if Ci does not participate in the reaction.

where qj is the reacted amount of any reactant for which mi ¼ 1. From material balance the following two equations are obtained: L0j þ L00j ¼ (L0jþ1 þ L00j1 )

N X

(wi, j þ mi qj )

i¼1

( j ¼ 1, 2, . . . , n) (L0j

þ

L00j )zi, j

¼

L0j x0i, j

þ

(6)

L00j x00i, j

(i ¼ 1, 2, . . . , N ; j ¼ 1, 2, . . . , n)

(7)

Equation (7) can be rewritten as zi, j ¼ sj x0i, j þ (1  sj )x00i, j (i ¼ 1, 2, . . . , N ; j ¼ 1, 2, . . . , n)

(8)

where sj, the phase separation ratio on stage j, is represented as sj ¼

L0j L0j þ L00j

( j ¼ 1, 2, . . . , n)

(9)

Because zi, j  0, we have (wi, j þ mi qj)  0 or qj  wi, j=mi for all mi < 0 (i ¼ 1, 2, . . . , N). Note that qj  0 and qj is always less than qj,max which is defined as  Figure 2. The scheme of COMER.

qj, max ¼ min

mi <0

wi, j mi

 (10)

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A5): 599–604

COUNTERCURRENT MULTISTAGE EXTRACTION-COUPLED ESTERIFICATION In addition, the following unity equations must be satisfied: N X

x0i, j ¼ 1 or

i¼1

N X

x00i, j ¼ 1

( j ¼ 1, 2, . . . , n)

(11)

i¼1

N X

x0i,nþ1 ¼ 1

(12)

x00i,0 ¼ 1

(13)

i¼1 N X i¼1

From equations (4) and (8), we have x0i, j ¼

x00i, j

Di, j zi, j sj Di, j þ (1  sj )

(i ¼ 1, 2, . . . , N ; j ¼ 1, 2, . . . , n) zi, j ¼ sj Di, j þ (1  sj )

(14)

(i ¼ 1, 2, . . . , N ; j ¼ 1, 2, . . . , n)

(15)

for the algorithm for single stage process (Chen et al., 2001).  Step 2 (initialization) Action: To calculate x0N ,nþ1 and x00N ,0 with equations (12) and (13), respectively; let x0i, j ¼ x0i,nþ1 , x00i, j ¼ x00i,0 , L0j ¼ L0nþ1 , and L00j ¼ L000 for i ¼ 1 to N and j ¼ 1 to n.  Step 3 (exchange) ¼ x0i, j , x00(old) ¼ x00i, j , L0(old) ¼ L0j , Action: to put x0(old) i, j i, j j 00(old) 00 ¼ Lj for i ¼ 1 to N and j ¼ 1 to n. and Lj Explanation: the variables assigned with superscript (old) are used for the modifications at step 4 and for the comparison to judge the convergence of calculation at step 5.  Step 4 (calculation) Action: to calculate wi,j, zi,j, x0i, j , x00i, j , Di,j, sj, qj, L0j and L00j for i ¼ 1 to N and j ¼ 1 to n by solving the simultaneous equations of equations (1), (3), (5), (11), (14)–(18) with the algorithm for single-stage process (Chen et al., 2001). Explanation: this calculation proceeds stage by stage from stage 1 to stage n. The compositions and flow rates are modified simultaneously as

where Di, j ¼

g00i, j g0i, j

601

x0i, j ¼ ax0i, j þ (1  a)x0(old) i, j (i ¼ 1, 2, . . . , N ; j ¼ 1, 2, . . . , n)

Di, j is the distribution ratio of component i between the two liquid phases on stage j. From equations (6) and (9), we can obtain L0j ¼ sj (L0jþ1 þ L00j1 )

x00i, j ¼ ax00i, j þ (1  a)x00(old) i, j

(16)

L0j ¼ bL0j þ (1  b)L0(old) j and L00j ¼ bL00j þ (1  b)L00(old) j

N X

(for i ¼ 1 to N and j ¼ 1 to n)

(wi, j þ mi qj ) ( j ¼ 1, 2, . . . , n)

i¼1

(17) and L00j ¼ (1  sj )(L0jþ1 þ L00j1 )

N X

(wi, j þ mi qj )

i¼1

( j ¼ 1, 2, . . . , n)

(18)

If n, N and temperature are given, there are 5nN þ 2N þ 4n þ 2 unknown variables including x0i, j and x00i, j1 (i ¼ 1 to N and j ¼ 1 to n þ 1), wi, j, zi, j and Di, j (i ¼ 1 to N and j ¼ 1 to n), L0j and L00j1 ( j ¼ 1 to n þ 1), and qj and sj ( j ¼ 1 to n), while there are 5nN þ 4n þ 2 independent equations including equations (1), (3), (5) and (11)–(18). The number of variables is 2N more than that of equations. Therefore, 2N variables must have their own values before calculation. ALGORITHM We propose an algorithm to calculate the equilibrium compositions and the flow rate of each phase on all stages with a given value set of N, n, temperature, L000 , L0nþ1 , x0i,nþ1 and x00i,0 for i ¼ 1 to N 7 1. From the above analysis, an algorithm for the simulation of COMER can be established as follows:  Step 1 (input data) Action: to input N, n, temperature, K, L000 , L0nþ1 , key1, key2, mi for i ¼ 1 to N, x0i,nþ1 and x00i,0 for i ¼ 1 to N 7 1, and data for the calculation of activity by UNIQUAC or another method. Explanation: key1 and key2 indicate the ‘key’ component in phase I and phase II, respectively, which is necessary

where 0
and

0 < b  1:

The new compositions and flow rates obtained of any stage are used at this moment in the calculation for the next stage. Both a and b are the weight factors the values of which are given by the simulator. If one gives large values to both, the simulation will be completed fast, but it may not converge in some cases. Therefore, it should be better to choose their values with care. The authors recommend to give a small value, for example, 0.5 to a and b. It should be noted that there maybe only one phase on some stages due to the improper initial condition or intermediate values during the calculation. In this case, the different values of x0i, j and x00i, j cannot be obtained by equations (14)–(15) because Di, j ¼ 1 and sj ¼ 0 or sj ¼ 1. An appropriate strategy to overcome this barrier is (taking stage k as an example): Let x0i,k ¼x0i,kþ1 , x00i,k ¼ x00i,k1 and sk ¼L0kþ1 =(L0kþ1 þ L00k1 ):  Step 5 (convergence judgment) Action: to go step 6 if all the following conditions are satisfied: jx0(old)  x0i, j j < 0:001, jx00(old)  x00i, j j < 0:001, i, j i, j    0(old)  00(old) L L  L0j   L00j   j  j  < 0:0001, and  00  < 0:0001  00  L0 þ L0nþ1   L0 þ L0nþ1  (for i ¼ 1 to N and j ¼ 1 to n) Otherwise go step 3.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A5): 599–604

602

CHEN et al.

 Step 6 (output) Action: output all results obtained. Because of high non-linearity, the calculation may not converge sometimes. It should be better to take a count limitation of iterations in the calculation and make adjustments to a and b according to circumstances. CALCULATED RESULTS The reaction equilibrium of oleic acid with methanol is as C17 H34 COOH þ CH3 OH Ð C17 H34 COOCH3 þ H2 O (19) The stoichiometric coefficients (m) are 1 for oleic acid and methanol, and 1 for methyl oleate and water. The constant of the reaction equilibrium, K, was estimated (Chen et al., 2001) as 2.19 at 346.15 K. Since the oleic acid–methanol–methyl oleate–water system is composed of non-electrolyte components, the activity coefficients of all the components can be calculated by using UNIQUAC (Prausnitz et al., 1980). The interaction parameters for UNIQUAC are listed in Table 1. Now, we try to make some calculations of the COMER for the esterification of oleic acid with methanol catalysed by an acidic ion exchange resin. The conditions for calculation are: (1) the feed of light phase contains methanol and some water, and the feed of heavy phase contains only oleic acid; (2) the amount of methanol feed is in excess to allow the formation of two liquid phases in each stage; (3) the residence time at each stage is enough to allow the reaction and liquid–liquid distribution equilibria; and (4) the temperature of esterification is 346.15 K

Table 1. The interaction parameters, Ai, j, of UNIQUAC estimated for the reaction and liquid–liquid distribution equilibria of oleic acid (1)–methanol (2)–methyl oleate (3)–water (4) system (Chen et al., 2001). j i

1

2

3

4

1 2 3 4

0.0 13920 159.4 140.1

170.5 0.0 214.5 56.58

306.8 889.9 0.0 220.7

9805 415.5 366.6 0.0

Figure 3. The purity of methyl oleate product vs the feed ratio (pure methanol).

Figure 4. The yield of methyl oleate product vs the feed ratio (pure methanol).

Figure 5. Water concentration in methanol-rich phase vs the feed ratio (pure methanol).

The feed ratio of methanol=oleic acid is represented as r (r ¼ L0nþ1 x0methanol,nþ1 =L000 x00oleic acid,0 ). The system contains one solid phase (the cation-exchange resin) and two liquid phases. Since the solid phase does not have any influence on the equilibria, it is not taken into account in the calculation. Both liquid phases are composed of four components: oleic acid, methanol, methyl oleate and water. Thus N ¼ 4. In the present calculation, methanol and methyl oleate are designated as key1 and key2, respectively. Calculations were done for r ¼ 4–20 and n ¼ 1–9. The results for pure methanol feed are shown in Figures 3–5 where YE is the yield of methyl oleate, PE is the purity of methyl oleate product, and cW is the concentration of water

Figure 6. The purity of methyl oleate product vs the feed ratio (methanol contains 0.5 wt% water).

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A5): 599–604

COUNTERCURRENT MULTISTAGE EXTRACTION-COUPLED ESTERIFICATION

603

Table 2. Conditions of COMER to obtain the methyl oleate product with >99 wt% purity when using pure methanol. Number of stages (n) Feed ratio (r)

Figure 7. The yield of methyl oleate product vs the feed ratio (methanol contains 0.5 wt% water).

Figure 8. Water concentration in methanol-rich phase vs the feed ratio (methanol contains 0.5 wt% water).

in methanol-rich phase leaving the top stage. YE and PE are defined respectively as methyl oleate in product oleic acid feed  100% (in mole base) methyl oleate in product PE ¼ (methyl oleate þ oleic acid) in product  100% (in weight base) YE ¼

(20)

(21)

In practice, raw methanol may not be pure and it generally contains water. It is thought that the yield of methyl oleate is affected also by the purity of the raw methanol. Therefore, the calculation for the feed of methanol with 0.5 wt% water was also made and the results are given in Figures 6–8. The values of both a and b were given as 0.3, 0.5, 0.75 or 1.0 in these calculations. The convergence of the algorithm was proved to be good. In general, the number of iterations needed was 8–60 according to circumstances, such as the concentration of water in the raw methanol, the feed ratio, and the number of stages, etc.

4 16

5 13

7 10

9 8.5

unreacted oleic acid. PE increases with the increase in both n and r (Figure 3). Though the purity is no more than 85 wt% in a single stage process (n ¼ 1) with r < 20, it becomes higher in multistage process and even 99% purity can be obtained. Listed in Table 2, for example, are the conditions to obtain a product with the purity higher than 99 wt% in COMER. It requires a large number of stages while r is less than 9, or needs a large feed ratio when n is less than 4, to obtain 99% purity. The yield of methyl oleate is another important factor in industry. As shown in Figure 4, it increases with the increase of n and r. YE in the COMER is much higher than that in the single stage process. The concentration of water in methanol-rich phase leaving the top stage, cW, is also considered to be important in COMER, because this phase must be treated to recovery methanol. Since the phase mainly contains water and methanol, it is easy to recover methanol by distillation. To decrease the load of distillation, less amount of methanol is desired. In other words, high cW is desirable. The calculated results showed that cW decreases with the increase of r, while it increases with the increase of n (Figure 5). It can be as high as about 16 wt% in the process with more than 4 stages and with r ¼ 4. However, when r > 13, cW may be less than 5 wt%. As shown in Figures 6–8, PE and YE becomes low when the raw methanol contains 0.5 wt% water, although the other conditions are the same as the case when 100% raw methanol is used. Both PE and YE are no more than about 96% even with a large number of stages or a large feed ratio. However, the pattern of variations of PE, YE and cW vs r or n are almost the same as the case when 100% raw methanol is used. The dependence of PE, YE and cW on the water content are given in Figure 9 for a seven-stage process with r ¼ 15 as an example. As the water content increases, both PE and YE decrease almost linearly while cW increases almost linearly. The concentration profile on each stage is also interesting in the process design. As an example, Figure 10 shows the

DISCUSSION The product phase from this process is rich in methyl oleate and it can be easily purified by separating water and methanol by means of vacuum evaporation. The final product after purification will contain little amount of

Figure 9. The influence of water content in methanol feed on the product for the case of the seven-stage process with r ¼ 15.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A5): 599–604

604

CHEN et al. NOMENCLATURE a C cW

Figure 10. Concentration profile of product phase for the case of the sevenstage process with r ¼ 15 and methanol feed containing 0.5 wt% water.

results for a seven-stage process with r ¼ 15. The mole fraction of water in the product phase remains at a very low level from the top to the bottom stages. This indicates that the extraction of water by methanol is very effective. The mole fractions of oleic acid, methanol and water decrease, while that of methyl oleate increases from the top to the bottom stages. Therefore, the product from the bottom stage contains very few amounts of oleic acid and water. This makes the final product having a very high yield and purity. In addition, the variations of the concentrations for all of the four components are very small from stage 4 to stage 7 (the bottom stage). The major part of reaction seems to occur on stages 1–4.

D K L m N n PE q r s w x YE z

activity component concentration of water in methanol-rich phase of the top stage, wt% distribution ratio equilibrium constant of reaction flow rates of a liquid phase, mol h1 stoichiometric coefficient number of components in the reaction system number of stages purity of methyl oleate product, wt% reacted amount of any reactant with m ¼ 1, mol feed ratio of methanol=oleic acid, (mol h1)=(mol h1) phase separation ratio overall composition of feed before reaction (mole fraction) composition in a liquid phase (mole fraction) yield of methyl oleate, mol% overall composition of the reaction mixture including the two liquid phases (mole fraction)

Greek symbols a, b weight factors for the modification of composition and flow rate, respectively g activity coefficients Superscripts liquid phase I liquid phase II

0

00

Subscripts i sequence number of component j sequence number of stage

REFERENCES CONCLUSION For the esterification of oleic acid with methanol catalysed by cation exchange resin, the simulation results showed that high yield and high purity of methyl oleate product could be obtained in countercurrent multistage extraction-coupled reaction process (COMER) with excess methanol as the extractant and without any dehydrating agent. The yield and the purity of methyl oleate product increase with increasing both the number of stages and the feed ratio of methanol–oleic acid. However, they decrease almost linearly with the increase of water content in the raw methanol. The results indicated that the yield and the purity of methyl oleate product could be as high as about 99% in a COMER with four or more stages and with an appropriate feed ratio when using pure raw methanol. In addition, the proposed algorithm for the simulation of COMER has good convergence for the present system.

Bagnell, L., Cavell, K., Hodges, A.M., Mau, A.W.-H. and Seen, A.J., 1993, The use of catalytically active pervaporation membranes in esterification reactions to simultaneously increase product yield, membrane permselectivity and flux, J Membrane Sci, 85: 291–299. Chemseddine, B. and Audinos, R., 1996, Use of ion-exchange membrane in a reactor for esterification of oleic acid and methanol at room temperature, J Membrane Sci, 115: 77–84. Chen, F., Sun, H., Naka, Y. and Kawasaki, J., 2001, Reaction and liquid– liquid equilibria in oleic acid=methanol=methyl oleate=water system at 73 C, J Chem Eng Japan, 34: 1479–1485. Kita, H., Tanaka, K., Okamoto, K. and Yamamoto, M., 1987, The esterification of oleic acid with ethanol accompanied by membrane separation, Chem Lett, 2053–2056. Okamoto, K., Yamamoto, M., Noda, S., Semoto, T., Otoshi, Y., Tanaka, K. and Kita, H., 1994, Vapor-permeation-aided esterification of oleic acid, Ind Eng Chem Res, 33: 849–853. Prausnitz, J., Anderson, T.F., Grens, E.A., Eckert, C.A., Hsieh, R. and O’Connell, J.P., 1980, Computer Calculations for Multicomponent Vapor–Liquid and Liquid–Liquid Equilibria (Prentice-Hall, Englewood Cliffs, NJ, USA), pp 40–44. The manuscript was received 25 July 2002 and accepted for publication after revision 15 December 2003.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A5): 599–604