ARTICLE pubs.acs.org/IECR
Computer Simulation of Fatty Acid Esterification in Reactive Distillation Columns Guilherme Duenhas Machado,† Donato A. G. Aranda,‡ Marcelo Castier,§,|| Vladimir Ferreira Cabral,*,† and Lucio Cardozo-Filho† †
Departamento de Engenharia Química, Universidade Estadual de Maringa, Av. Colombo 5790, Maringa, PR, 87020-900, Brazil Departamento de Engenharia Química, Escola de Química Universidade Federal do Rio de Janeiro, Av. Horacio Macedo 2030, Rio de Janeiro, RJ, 21941-909, Brazil § Chemical Engineering Program, Texas A & M University at Qatar, PO Box 23874, Doha, Qatar ‡
ABSTRACT: This work presents computational steady-state simulations of fatty acid esters (biodiesel) production in a reactive distillation column. Reaction rates were considered explicitly in the model of each stage. The procedures and formulation used here were initially validated by comparison of simulations results obtained in this work with data available in the literature. Two new cases for fatty acid esters (biodiesel) production are simulated. In both of them, conversions close to 99% are possible with the proper choice of operating conditions, as shown by sensitivity analyses. The simulations results obtained here can be useful for the proper design of processes that use reactive distillation columns for biodiesel production.
’ INTRODUCTION Investments in renewable energy sources are increasingly important due to economic issues and the problem of global warming.1,2 Biodiesel (fatty acid alkyl esters) is a biodegradable fuel produced from renewable sources. Recent studies3,4 show that biodiesel can be a viable substitute for fossil diesel. Biodiesel can be obtained by esterification or by transesterification using homogeneous or heterogeneous reaction systems.513 Recent studies14,15 show that the production of methyl esters of biodiesel by transesterification reaction can be improved by the use of metoxides as catalyst. In such papers the authors state that the use of these catalysts can reduce the occurrence of the saponification reaction. Recently, the noncatalytic reaction, using alcohol under supercritical conditions at high temperatures and pressures, has been investigated as an alternative method for fatty acid esters production.1620 Homogeneous transesterification of vegetable oils has been the method most frequently used to produce biodiesel.21,22 However, this technique has several drawbacks, especially in relation to the content of free fatty acids (FFA) and water in the feedstock specification. In this process, saponification is undesired but may occur depending on the reaction conditions and the free acid content of the vegetable oil used. The existence of FFA and water content in the reaction bulk favor soap generation, which inhibits the separation of the alkyl esters and glycerol, and contributes to emulsion formation during the washing step.23,24 As ways of overcoming the limitations of the conventional process, alternative catalysts and chemical reactions can be evaluated. The use of heterogeneous catalysis can be an alternative to conventional homogeneous catalysis. Production processes that use heterogeneous catalysis have the following benefits: (1) better removal of the catalyst and easy separation of products, (2) high purity of glycerol, and (3) elimination of the alkaline catalyst neutralization step.2527 r 2011 American Chemical Society
Moreover, considering alternative types of chemical reactions, hydroesterification—hydrolysis followed by esterification—is very promising, with commercial biodiesel plants successfully using this technology (e.g., Biobrax, in the Brazilian state of Bahia). This strategy has two steps (hydrolysis and esterification) and uses any fat material as raw material because hydrolysis converts the fat in FFA. The biodiesel and glycerin produced in this process have very high purity when compared with the current method used to produce biodiesel. Niobium oxide (Nb2O5) can be used as catalyst for both hydrolysis and esterification steps in biodiesel production.28,29 The esterification of FFA with short-chain alcohols is another way to produce biodiesel. In these processes, a previous step of hydrolysis of oils and fats is used as a pretreatment to increase the FFA concentration producing a more complete conversion. Such a step increases the range of raw materials usable for biodiesel production. Studies show that this reaction of fatty acid esterification is faster and occurs in a single step, unlike the three stages of the transesterification of triglycerides.30,31 A catalytic process for the heterogeneous esterification of fatty acids was developed32 and the technology was applied in a 12 000 ton/year biodiesel plant in Belem-PA-Brazil that started up in April 2005. This procedure, however, still requires steps of chemical reaction and products separation. This process could be even more attractive if it could be run in a single integrated step, in which reaction and separation occur in a single device, as in a reactive distillation column. Heterogeneously catalyzed reactive distillation offers advantages over the homogeneously catalyzed process. The synthesis of methyl acetate by Eastman Chemicals using reactive distillation is Received: November 17, 2010 Accepted: July 6, 2011 Revised: July 4, 2011 Published: July 06, 2011 10176
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Figure 1. Schematic of each theoretical stage along the reactive distillation column.
regarded as a textbook example of this process. The process costs were reduced (∼80%) by removing units and performing heat integration. The conventional process, composed of 11 different steps carried out in 28 pieces of equipment, was replaced by a single, highly integrated reactive distillation column.3335 The potential applicability of reactive distillation for biodiesel production has motivated several publications such as those of Silva et al.,36 He et al.,37 and especially those of Kiss et al.21,3843 In this way, the objective of this work is to present new computer simulations of fatty acid alkyl esters production in reactive distillation columns. The simulation data obtained here can be useful to develop and optimize processes to produce biodiesel using hydroesterification. In the simulations, the formulation used assumes steady-state operation and the reaction rates are considered explicitly in the model of each stage. In the first example presented here, the formulation used in this work is validated by comparing its results with experimental data and simulations results available in the literature.56 Next, two new simulations results of biodiesel production by esterification are presented using kinetic data of fatty acid esterification that employ niobium oxide as heterogeneous catalyst.44,45
’ METHODOLOGY Reviews about the approaches used in these models of reactive distillation columns are available in the literature.46,47 In this paper, we assume steady-state operation and consider the reaction rates explicitly in the model of each stage. In all cases, for simplicity, the Murphree efficiency of separation was set equal to 100%. The same assumptions were used by Chen et al.46 and Alfradique and Castier.47 The methodology takes additional considerations into account, analogous to the reactive distillation column using chemical equilibrium. Such considerations are detailed below. In the energy balance, the heat of reaction is considered negligible when compared to the value of heat of vaporization. There is heat transfer in the reboiler and in the condenser, but the interior stages of the column are adiabatic. The chemical reactions occur only in the liquid phase and are controlled by chemical kinetics. The possibility of vaporliquidliquid equilibrium (VLLE) is not considered in the thermodynamic modeling. The occurrence of VLLE has a strong dependence on the temperature and, for most systems at a given pressure, there is a temperature above which two liquid phases do not form. In all the simulations, the assumption is that the operating temperatures along the reactive distillation columns prevent the formation of two liquid phases. Besides, the kinetic models used in the examples 2 and 3 are obtained from experiments.44,45 These experiments were conducted under temperatures ranging from 150 to 200 °C and, in
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this range, the occurrence of two different liquid phases was not observed. We consider pseudo-homogeneous kinetics that does not account for the influence of adsorption as a possible limiting step to reaction rate. Each stage is considered as a continuous stirred-tank reactor (CSTR). The stream of liquid and vapor leaving the stages are in phase equilibrium, the vapor phase has ideal gas behavior, and the liquid phase is considered as a nonideal solution. Models of excess Gibbs free energy describe the liquid phase behavior. The general stage scheme used in this work is shown in Figure 1: The mass balance of component i on stage j is f mi,j ¼ ðR j þ 1ÞnIIi, j þ ðZj þ 1ÞnIi, j ðnIIi, j þ 1 þ nIi, j 1 þ Fi, j þ
nr
∑ νi, kξk, j Þ ¼ 0 k¼1
ð1Þ
where (Rj + 1)nIIi,j is the molar liquid flow rate of component i leaving stage j, RjnIIi,j is its flow in the liquid sidestream, and nIIi,j is its flow that reaches the next stage. (Zj + 1)nIi,j is the molar flow rate of component i in the vapor leaving stage j, ZjnIi,j is its flow rate in the vapor sidestream, and nIi,j is its flow rate that reaches the next stage. In eq 1, Fi,j is the flow rate of of component i in the feed stream to stage j, νi,k is the stoichiometric coefficient of component i in reaction k, ξk,j is the extent of reaction k in stage j, and nr represents the number of independent chemical reactions. Assuming that the streams leaving each stage are in phase equilibrium and the fugacity coefficient in the vapor phase, the Poynting factor, and the fugacity coefficient of saturated vapor are equal to 1, the isofugacity criteria is: eq
f i, j ¼ lnðxIi, j Pj Þ lnðxIIi, j γIIi, j Psat i, j Þ ¼ 0
ð2Þ
where xIi,j and xIIi,j are the mole fractions of component i in the vapor and liquid streams leaving stage j, Pj is the pressure of stage j, Psat i,j is the saturation pressure of component i on stage j and γIIi,j is the activity coefficient of component i in the liquid phase leaving stage j. The rate of reaction expression is used as follows: ! nc xIIi, j r ð3Þ f k, j ¼ ln kk, j þ Ri, k ln II ln ξk, j ¼ 0 vj i
∑
where vIIj is the molar volume assuming an ideal liquid solution in stage j, kk,j is the kinetic constant of reaction k in stage j, Ri,k is the kinetic order of component i in reaction k. For kinetic data correlated as function of activities, eq 3 becomes: f rk, j ¼ ln kk, j þ
nc
∑i Ri, klnðxIIi, j γIIi, jÞ ln ξk, j ¼ 0
ð4Þ
The energy balance in stage j is: f hj ¼ ðR j þ 1ÞH IIj þ ðZj þ 1ÞH Ij ðH IIj þ 1 þ H Ij 1 þ H Fj þ Q j Þ ¼ 0
ð5Þ
where (Zj + 1)HjI and (Rj + 1)HjII are the enthalpy flow rates of the vapor and liquid streams leaving stage j, and Qj is the rate of heat added in each stage. HFj is the enthalpy flow rate of the feed stream to stage j. An additional equation specifies the behavior of the condenser and reboiler, based on a variable Ej, which is defined as the ratio between the molar flow of vapor and liquid leaving 10177
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Table 1. Ej Parameter Values for Each Mode of Operation of Condenser and Reboiler reboiler (stage 1) partial
condenser (stage N)
total
partial
total
Z1 = 0
Z1 6¼ 0
ZN = 0
ZN = 0
R1 = 0
R1 = 0
RN = 0
RN 6¼ 0
E1 6¼ 0
E1f ∞
EN 6¼ 0
EN = 0
stage j: f vlj ¼ ðZj þ 1Þ
nc
nc
∑ nIi, j Ej ðRj þ 1Þ i∑¼ 1 nIIi, j ¼ 0 i¼1
ð6Þ
For condensers and reboilers, the value of Ej is specified as shown in Table 1. For each internal stage of the column, the value of Ej is calculated. The equations and unknowns are organized as described in detail elsewhere.47,48 The formulation adopted here uses the NewtonRaphson method to solve the mass and energy balances, phase equilibrium equations, rates of reaction equations, and additional equations needed to match the number of degrees of freedom. The Thermath package49 was used to obtain Fortran subroutines that implement these equations and their derivatives with respect to the process variables and the excess Gibbs free energy model used in the simulation. The Fortran program used in this work has about 10 800 lines of code.
’ THERMODYNAMIC MODELING The calculation of thermodynamic properties is a key point in simulating distillation, as this operation is based on the separation of vapor and liquid phases. Ideal vapor phase is assumed (fugacity coefficient equal to unity) and the liquid phase is modeled using excess Gibbs free energy equations such as UNIFAC,50 UNIQUAC,51 and UNIFAC Dortmund.52 The molar enthalpies of the liquid (hL) and vapor (hV) were calculated using the following equations: Z T nc L xi cLp, i dT þ hE ð7Þ h ¼
∑
i¼1
h ¼ V
nc
∑ i¼1
T ref
Z vap yi ðΔhi
þ
T
T ref
cLp, i dTÞ
ð8Þ
where Δhvap i is the molar enthalpy of vaporization of component i L the molar in the system, hE is the molar excess enthalpy, and cp,i specific heat of component i in the liquid phase. The reference temperature (Tref) used was 298.15 K. The Antoine equation53 was used to calculate the vapor pressure ln Psat ¼ A
B T þ C
ð9Þ
The molar enthalpy of vaporization was calculated using the ClausiusClapeyron equation as follows: dln Psat ð10Þ dT L ) and the parameters The values of specific heat of liquids (cp,i of Antoine equation were obtained from NIST54 and DIPPR55 databases. vap
Δhi
Figure 2. Schematic of the reactive distillation column in all cases.
’ RESULTS AND DISCUSSION This section presents three examples of fatty acid esterification in reactive distillation columns. The first example validates the methodology used in this work by comparison of its results with other simulations and experimental data available in the literature. The next two examples present new simulations of fatty acid esterification. In Example 2, the simulations show the conventional operation of a reactive distillation column, while in Example 3 the simulations try to reproduce the concept of reactive absorption. In both cases, we use kinetic data of fatty acid esterification using a niobium oxide catalyst.44,45 The reactive distillation column setup shown in Figure 2 is used in all simulations performed in this paper. The liquid phase was modeled by the UNIFAC DORTMUND model45 in all cases. Example 1: Esterification of Decanoic Acid with Methanol. Steinigeweg and Gmehling56 studied this system experimentally. Thus, these experimental data will be used to validate the mathematical modeling applied in this work. Kiss et al.3840 used the Aspen Plus software to simulate the same system in reactive distillation columns. In those works, the authors used a reaction kinetics model that considered metal oxides such as niobic acid, sulfated zirconia, sulfated titania, and sulfated tin oxide as catalyst. Here, the esterification of decanoic acid (1) with methanol (2) producing methyl decanoate (3) and water (4) is given by the following stoichiometric relationship: C9 H19 COOH þ CH 3 OH S C9 H19 COOCH 3 þ H2 O ð1Þ
ð2Þ
ð3Þ
ð4Þ
ð11Þ The chemical reaction of esterification is considered to be of first order with respect to decanoic acid and methanol. The inverse reaction (hydrolysis) is considered to be of first order with respect to methyl decanoate and water. These assumptions are the same as those employed by Steinigeweg and Gmehling56 to develop a pseudo-homogeneous reaction rate model dependent on the activity of reagents: r ¼
¼ RT 2
1 1 dni ¼ k1 a1 a2 k1 a3 a4 mcat vi dt
ð12Þ
The catalyst used was a strongly acid ion-exchange resin commercially called Amberlyst 15. The constants of the rate equation for the catalyst according to the Arrhenius equation are 10178
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Table 2. Specifications of the Reactive Distillation Column for Example 1 variable
specifications
pressure stages condenser
all stages
1.0132 bar
total
20 stage 20
reboiler
partial
stage 1
reflux ratio
condenser
0.5
reactive zone
stages 714 Katapak-SP packing filled with
catalyst
189.6 g
Amberlyst 15 resin feed 1
0.250 (gmol/min)
stage 14
1.0132 bar, 331.19 K decanoic acid feed 2
0.483 (gmol/min))
stage 06
1.0132 bar, 337.65 K
Figure 3. Liquid phase composition along the reactive distillation column of Example 1: Comparison of simulation results with experimental and simulated data.56
methanol
Table 3. Comparison between Simulation Results for Example 1 and Data from Literature56
top
bottom
liquid phase
Steinigeweg and
this
mole fraction
Gmehling (2003) experimental
work
1
0.000
0.000
0.000
2
0.716
0.760
0.763
3
0.000
0.000
0.000
4
0.277
0.240
0.237
1 2
0.366 0.303
0.428 0.220
0.511 0.103
3
0.303
0.332
0.386
4
0.001
0.000
temperature stage 1
0.000
363.53
-
363.49
stage 11
347.28
-
338.83
stage 20
341.27
-
341.39
42.99
-
42.99
conversion (% - decanoic acid)
given by the following:56 68710½J=gmol 5 k1 ¼ 9:1164 10 exp ðmol=ðgsÞÞ, TðKÞ RT
k1
In the extremes (top and bottom of the column), the results are in excellent agreement with the experimental values. More pronounced deviations occur in the intermediate stages. These differences between the simulation results of this study and the literature56 can be attributed to some modeling issues. Here, eq 12, a pseudo-homogeneous model, is used to model the reaction rate, while the cited literature results are based on a heterogeneous model that considers adsorption as a limiting step. Figure 4 shows that the esterification reaction is favored close to the feed location of fatty acid. This region has the highest temperature of the reactive zone. The good agreement between the simulation results and the literature data suggests that the methodology adopted here is valid. Example 2: Esterification of Oleic Acid with Methanol. De Pietre et al.55 and Alvarez et al.56 studied this reaction system with emphasis on the development of catalysts. This example evaluates a reactive distillation column for the esterification of oleic acid (1) with methanol (2) producing methyl oleate (3) and water (4) according to the following stoichiometric relationship: C17 H33 COOH þ CH 3 OH S C17 H33 COOCH 3 þ H2 O ð1Þ
ð2Þ
ð13Þ
64660½J=gmol ¼ 1:4998 104 exp ðmol=ðgsÞÞ, TðKÞ RT
ð14Þ The simulated column had 20 stages (reboiler, 18 adiabatic plates, and condenser). The specifications of the feed are presented in Table 2. The liquid phase was modeled by the UNIFAC DORTMUND model.45 Table 3 shows the results obtained in the simulations of this work. Figure 3 shows the mole fraction profiles in the liquid phase. In general, the profiles obtained in this work show the same tendency as the experimental and simulation data available. The largest deviations occur between stages 2 and 15. Figure 4 shows the temperature and the extents of the esterification (direct) and hydrolysis (reverse) reactions along the column.
ð3Þ
ð4Þ
ð15Þ The chemical reaction of esterification is considered as second order with respect to oleic acid and of zeroth order with respect to methanol. It is assumed that the reverse reaction (hydrolysis) does not occur, i.e., the esterification is irreversible. Gonc) alves44 used these assumptions in the development of a pseudo-homogeneous kinetic model as function of reagent concentration, as follows: r ¼
1 1 dni ¼ kC1 2 mcat vi dt
ð16Þ
where C1 is the concentrations (gmol/L) of oleic acid in the reaction mixture. Data for the kinetics of this reaction were obtained from the cited experimental work. The kinetic constant in eq 16 is given by the Arrhenius equation: 10179
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Figure 4. Temperature profile and extents of reaction along the reactive distillation column of Example 1.
Figure 5. Composition profile in the liquid phase along the reactive distillation column of Example 2.
Table 4. Specifications of the Reactive Distillation Column for Example 2 variable
specifications
pressure
all stages
stages
1.0132 bar 15
condenser
total
stage 15
reboiler reflux ratio
partial condenser
stage 1 0.001
reactive zone
stages 612
catalyst
niobium oxide powder
14.0 kg
feed 1
97.15(gmol/min)
stage 13
1.0132 bar, 418.1 K oleic acid feed 2
98.12 (gmol/min))
stage 06
1.0132 bar, 338.6 K methanol
k ¼ 1:13exp
27209½J=gmol ðL=ðg cat min gmolÞÞ, TðKÞ RT
ð17Þ The simulated column has 15 stages: 1 reboiler, 13 adiabatic plates, and 1 condenser. The specifications of the feed are presented in Table 4. Figure 5 shows the profiles of the liquid phase mole fractions and Figure 6 shows the temperature and extent of the esterification reaction along the column. The results of Figure 5 show that, in the liquid phase, the mole fractions of the least volatile components, oleic acid and methyl oleate, are higher at the bottom of the column. In the same figure, the mole fraction of oleic acid decreases rapidly in the region close to its feed stage, where a large rate of product formation (methyl oleate) also occurs. The temperature profile presented in Figure 6 is similar to that of the previous example. The reactive zone presents higher temperatures than neighboring stages where the reaction rates are negligible. The highest temperature in the reactive zone is close to the feed location of oleic acid, which is fed at a temperature of 418 K. The conversion obtained was 97.1% and can possibly be increased by adding more reactive stages to the reactive zone of the simulated column.
Figure 6. Temperature profile and extents of reaction along the reactive distillation column of Example 2.
Example 3: Esterification of Lauric Acid with Ethanol. Silva et al.36 studied experimentally a system similar to this example, and Kiss et al.38 used the Aspen Plus software to simulate this system in reactive distillation columns. In the latter work, the authors modeled the reaction kinetics considering different types of catalyst (ion-exchange resins, calcium, and metal oxides). In all cases, the authors simulated the conventional operation of a reactive distillation column. In the previous cases simulated here, the conventional operation of a reactive distillation column was used too. Reagents enter the column as liquids and the heat transfer rate in the reboiler is high in all cases, favoring the exposure of the product to high temperatures in the reboiler. However, according to Kiss,40 it is better to have a lower temperature profile in the column to prevent thermal degradation of the fatty esters product. With this motivation, in this example, we use a strategy that minimizes the heat load in the reboiler. Therefore, ethanol is fed at a temperature close to its saturation. The esterification of lauric acid (1) with ethanol (2) producing ethyl laurate (3) and water (4) follows the equation:
C11 H23 COOH þ C2 H5 OH S C11 H23 COOC2 H5 þ H2 O ð1Þ
ð2Þ
ð3Þ
ð4Þ
ð18Þ The esterification reaction was considered to be of first order with respect to concentrations of lauric acid and ethanol, while the inverse reaction (hydrolysis) follows a first order kinetic with respect to the concentrations of ethyl laurate and water. From 10180
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Table 5. Specifications of the Reactive Distillation Column for Example 3 variable pressure
specifications all stages
1.0132 bar
stages condenser
total
20 stage 20
reboiler
partial
stage 1
reflux ratio
condenser
0.002
reactive zone
stages 617
catalyst
niobium oxide powder
54.5 kg
feed 1
109.80(gmol/min)
stage 18
1.0132 bar, 480.15 K lauric acid 98.12 (gmol/min))
feed 2
stage 06
Figure 7. Composition profile in the liquid phase along the reactive distillation column of Example 3.
1.0132 bar, 351.15 K ethanol
these assumptions, Le~ao45 proposed the following pseudohomogeneous model: r ¼
1 1 dni ¼ k1 C1 C2 k1 C3 C4 mcat vi dt
ð19Þ
The constants k1 and k1 in eq 19 obey the Arrhenius equation as follows: 35027:62½J=gmol k1 ¼ 1:54637 102 exp ðL=ðg cat min gmolÞÞ, TðKÞ RT
ð20Þ k1 ¼ 7:323 exp
Figure 8. Temperature profile and extents of reaction along the reactive distillation column of Example 3.
35005:81½J=gmol ðL=ðg cat min gmolÞÞ, TðKÞ RT
ð21Þ In this case, the column has 20 stages: 1 reboiler, 18 adiabatic stages, and 1 condenser. The feed specifications are presented in Table 5. Figure 7 shows the profile of the mole fractions in the liquid phase of all compounds. Figure 8 shows the temperature profile and extents of reaction along the column. From Figure 7, we verify that the bottom product has a significant amount of ethanol. This is due to the lower heat transfer rate used in the reboiler. Such heat transfer rate only provides the heat needed for ethanol evaporation. In this situation, almost all water is removed from the top as desired. In Figure 8, the temperature in the reactive zone has maximum value between stages 6 and 17. This range of conditions favors the esterification reaction compared to the hydrolysis reaction, because the kinetic constant k1 is higher than the kinetic constant k1 (see eqs 20 and 21). In this example, the temperature at the bottom of the reactive distillation column simulated is significantly lower when compared to the previous case (Figure 6). This is due to the strategy used in this example to minimize the heat tranfer rate in the reboiler thus turning the case into a reactive absorption column. This approach tends to reduce utilities consumption in the column and prevent degradation of the ester formed in the chemical reaction.
Figure 9. Composition surface of ethyl laurate (3) in the liquid phase of the column simulated in Example 3: Effect of reflux ratio.
Sensitivity Analysis. The influence of some variables such as reflux ratio, number of stages, and the heat-tranfer rate in the reboiler was observed. In the sensitivity analysis of the reflux ratio, such parameter had its value fixed between 0.002 and 10 for a column with 15 stages. In case the number of stages, we analyzed columns with 1523 theoretical stages, while for heat-tranfer rate in the reboiler, values between 1.35 and 10.5 MJ/min were used in a column with 15 theoretical stages. 10181
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Figure 12. Conversion of lauric acid versus reboiler heat transfer rate in Example 3. Figure 10. Temperature surface along the reactive distillation column in Example 3: Effect of reflux ratio.
Figure 11. Temperature surface along the reactive distillation column in Example 3: Effect of reboiler.
The manipulation of the reboiler heat transfer rate was done indirectly. In this case, the relationship between the vapor and liquid in the reboiler (E1) was changed in order to obtain a specific value of heat transfer rate in the reboiler (QR). Figure 9 shows the ester mole fraction in the liquid phase along the reactive distillation column as function of the reflux ratio and Figure 10 presents the temperature as function of the reflux ratio. Figures 11 and 12 present results for the variation of heat transfer rate in the reboiler along the simulated column. Figure 13 exhibits the relationship between lauric acid conversion and number of theoretical stages. The increase in the reflux ratio in the condenser increases the water concentration in the reactive zone, favoring the hydrolysis reaction (eq 21). Figure 9 shows that higher concentrations of ethyl laurate are obtained in the bottom product when lower values of reflux ratio are used in the column. The increase of the water concentration in the reactive zone also causes the decrease in the temperature profile mainly in the reactive zone, as shown in Figure 10. From Figure 12, it is verified that an 8-fold increase in the heat transfer rate in the reboiler increases lauric acid conversion by only 2.4%, while there is a considerable increase in temperature in this equipment, varying in the range of 382531 K approximately
Figure 13. Conversion of lauric acid versus number of stages in Example 3.
(see Figure 11). As the risk of product degradation raises with higher bottom product temperature, increasing the heat transfer rate in the reboiler is not advisible. It is preferable to use a heat exchanger for preheating the alcohol stream before entering the reactive distillation column. This procedure reduces the heat transfer in the reboiler and may avoid exposing the bottom product to high temperatures. Figure 13 shows that an increase in the number of stages increases the conversion of lauric acid. The column with 20 theoretical stages converts 98.7% of the lauric acid. This value is higher than the minimum purity of 96.5% required by the Brazilian laws for trading fatty acid esters (biodiesel).
’ CONCLUSIONS In this work, fatty acid esterification in reactive distillation columns was simulated computationally. The results obtained here showed good agreement with experimental and simulated data available in literature, validating the simulation procedures. The second and third examples presented new simulation data of fatty acid esterification in reactive distillation columns. In the third example, a sensitivity analysis permitted determination of suitable conditions for column operation. With these operating conditions, conversions above 98% were obtained, which are 10182
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’ AUTHOR INFORMATION Corresponding Author
*Tel.: +55-4432614749. Fax: +55-4432614774. E-mail: vladimir@ deq.uem.br. )
Present Addresses
On leave from the Federal University of Rio de Janeiro, Brazil.
’ ACKNOWLEDGMENT This work was supported by CNPq (Grant 145465/2010-1) and CAPES. ’ NOMENCLATURE A, B, C = constants of Antoine equation ai = activity of component i Ci = molar concentration of component i L = liquid heat capacity of component i cp,i Ej = relation between the liquid and vapor streams in stage j Fi,j = molar flow rate of the feed stream of component i to stage j fi,jeq = phase equilibrium function of component i in stage j fi,jm = mass balance function of component i in stage j fjh = energy balance function at each stage fjlv = function relating the liquid and vapor streams r fk,j = chemical equilibrium function I Hj = total enthalpy of stream I at stage j HIj+1 = total enthalpy of stream I at stage j+1 hE = molar excess enthalpy hV = molar enthalpy of vapor stream hL = molar enthalpy of liquid stream HFj = total enthalpy flow rate of feed stream to stage j kk,j = rate constant of reaction k in each stage j mcat = catalyst mass per reactive stage nIi,j = molar flow rate of component i in stream I of stage j nIIi,j = molar flow rate of component i in stream II of stage j Psat i,j = saturation pressure of component i in stage j Pj = pressure at stage j Q j = heat load to stage j R = universal gas constant Rj = liquid side stream fraction at stage j Tj = temperature at stage j vIIj = liquid molar volume at stage j xIi,j = mole fraction of component i in stream I of stage j xIIi,j = mole fraction of component i in stream II of stage j Zj = vapor side stream fraction at stage j
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Greek letters
Ri,k = kinetic order of component i in reaction k γIIi,j = activity coefficient of component i in stream II of stage j νi,k = stoichiometric coefficient of component i in reaction k ξk,j = extent of reaction k at stage j Subscripts/Superscripts
L, II = liquid V, I = vapor sat = saturation i = component k = reaction F = feed j = stage/component
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’ NOTE ADDED AFTER ASAP PUBLICATION The version of this paper that was published ASAP July 28, 2011, was missing some text corrections. The revised version was published August 9, 2011.
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