1.5-Fatty Acid Esterification in Reactive Distillation Columns_Example1

7182019 15-Fatty Acid Esterification in Reactive Distillation Columns_Example1

httpslidepdfcomreaderfull15-fatty-acid-esterification-in-reactive-distillation-columnsexample1 19

Published July 06 2011

r 2011 American Chemical Society 10176 dxdoiorg101021ie102327y | Ind Eng Chem Res 2011 50 10176ndash

10184

ARTICLE

pubsacsorgIECR

Computer Simulation of Fatty Acid Esterification in ReactiveDistillation Columns

Guilherme Duenhas Machadodagger Donato A G ArandaDagger Marcelo Castiersect || Vladimir Ferreira Cabral

dagger andLucio Cardozo-Filho

dagger

daggerDepartamento de Engenharia Quiacutemica Universidade Estadual de Maringa Av Colombo 5790 Maringa PR 87020-900 BrazilDaggerDepartamento de Engenharia Quiacutemica Escola de Quiacutemica Universidade Federal do Rio de Janeiro Av Horacio Macedo 2030Rio de Janeiro RJ 21941-909 BrazilsectChemical Engineering Program Texas A amp 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 reactivedistillation 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 casesfor 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 properdesign of processes that use reactive distillation columns for biodiesel production

rsquo INTRODUCTION

Investments in renewable energy sources are increasingly important due to economic issues and the problem of global warming12 Biodiesel (fatty acid alkyl esters) is a biodegradablefuel produced from renewable sources Recent studies34 show that biodiesel can be a viable substitute for fossil diesel Biodieselcan be obtained by esteri1047297cation or by transesteri1047297cation usinghomogeneous or heterogeneous reaction systems513 Recent

studies1415

show that theproduction of methylesters of biodiesel by transesteri1047297cation reaction can be improved by the use of metoxidesas catalyst In such papers theauthorsstatethat theuseof these catalysts can reduce the occurrence of the saponi1047297cationreaction Recently the noncatalytic reaction using alcohol undersupercritical conditions at high temperatures and pressures has been investigated as an alternative method for fatty acid estersproduction1620

Homogeneous transesteri1047297cation of vegetable oils has beenthe method most frequently used to produce biodiesel2122

However this technique has several drawbacks especially inrelation to the content of free fatty acids (FFA) and water in thefeedstock speci1047297cation In this process saponi1047297cation is undesired but may occur depending on the reaction conditions and the freeacid content of the vegetable oil used The existence of FFA and water content in the reaction bulk favor soap generation whichinhibits the separation of the alkyl esters and glycerol andcontributes to emulsion formation during the washing step2324

As ways of overcoming the limitations of the conventionalprocess alternative catalysts and chemical reactions can beevaluated The use of heterogeneous catalysis can be an alter-native to conventional homogeneous catalysis Production pro-cesses that use heterogeneous catalysis have the following bene1047297ts (1) better removal of the catalyst and easy separationof products(2) high purity of glyceroland (3)eliminationof thealkaline catalyst neutralization step2527

Moreover considering alternative types of chemical reactionshydroesteri1047297cationmdashhydrolysis followed by esteri1047297cationmdashis very promising with commercial biodiesel plants successfully using this technology (eg Biobrax in the Brazilian state of Bahia) This strategyhas twosteps(hydrolysis and esteri1047297cation)and uses any fat material as raw material because hydrolysisconverts the fat in FFA The biodiesel and glycerin produced inthis process have very high purity when compared with thecurrent method used to produce biodiesel Niobium oxide

(Nb2O5) can be used as catalyst for both hydrolysis andesteri1047297cation steps in biodiesel production2829

The esteri1047297cation of FFA with short-chain alcohols is another way to produce biodiesel In these processes a previous step of hydrolysis of oils andfats is used as a pretreatment to increase theFFA concentration producing a more complete conversion Sucha step increases the range of raw materials usable for biodieselproduction Studies show that this reaction of fatty acid ester-i1047297cation is faster and occurs in a single step unlike the threestages of the transesteri1047297cation of triglycerides3031 A catalyticprocess for the heterogeneous esteri1047297cation of fatty acids wasdeveloped32 and the technology was applied in a 12 000 tonyear biodiesel plant in Belem-PA-Brazil that started up in April 2005

This procedure however still requires steps of chemicalreaction and products separation This process could be evenmore attractive if it could be run in a single integrated step in which reaction and separation occur in a single device as in areactive distillation column

Heterogeneously catalyzed reactive distillation off ers advan-tages over the homogeneously catalyzed process The synthesis of methyl acetate by Eastman Chemicals using reactive distillation is

Received November 17 2010 Accepted July 6 2011Revised July 4 2011



10177 dxdoiorg101021ie102327y |Ind Eng Chem Res 2011 50 10176ndash10184

Industrial amp Engineering Chemistry Research ARTICLE

regarded as a textbook example of this process The process costs were reduced (sim80) by removing units and performing heatintegration The conventional process composed of 11 diff erentsteps carried out in 28 pieces of equipmentwas replaced by a singlehighly integrated reactive distillation column3335

The potential applicability of reactive distillation for biodieselproduction has motivated several publications such as those of Silva et al36 He et al37 and especially those of Kiss et al213843

In this way the objective of this work is to present new computersimulations of fatty acid alkyl esters production in reactivedistillation columns The simulation data obtained here can beuseful to develop and optimize processes to produce biodieselusing hydroesteri1047297cation In the simulations the formulationused assumes steady-state operation and the reaction rates areconsidered explicitly in the model of each stage In the 1047297rstexample presented here the formulation used in this work is validated by comparing its results with experimental data andsimulations results available in the literature56 Next two new simulations results of biodiesel production by esteri1047297cation arepresented using kinetic data of fatty acid esteri1047297cation thatemploy niobium oxide as heterogeneous catalyst4445

rsquoMETHODOLOGY

Reviews about the approaches used in these models of reactivedistillation columns are available in the literature4647 In thispaper we assume steady-state operation and consider the reac-tion rates explicitly in the model of each stage In all cases forsimplicity the Murphree efficiency of separation was set equal to100 The same assumptions were used by Chen et al46 and Alfradique and Castier47

The methodology takes additional considerations into ac-count analogous to the reactive distillation column using chemi-cal equilibrium Such considerations are detailed below In theenergy balance the heat of reaction is considered negligible whencompared to the value of heat of vaporization There is heat

transfer in the reboiler and in the condenser but the interiorstages of the column are adiabatic The chemical reactions occuronly in the liquid phase and are controlled by chemical kineticsThe possibility of vaporliquidliquid equilibrium (VLLE) isnot considered in the thermodynamic modeling The occurrenceof VLLE has a strong dependence on the temperature and formost systems at a given pressure there is a temperature above which two liquid phases do not form In all the simulations theassumption is that the operating temperatures along the reactivedistillation columns prevent the formation of two liquid phasesBesides the kinetic models used in the examples 2 and 3 areobtained from experiments4445 These experiments were con-ducted under temperatures ranging from 150 to 200 C and in

this range the occurrence of two diff erent liquid phases was notobserved

We consider pseudo-homogeneous kinetics that does notaccount for the in1047298uence of adsorption as a possible limitingstep to reaction rate Each stage is considered as a continuousstirred-tank reactor (CSTR) The stream of liquid and vaporleaving the stages are in phase equilibrium the vapor phase has

ideal gas behavior and the liquid phase is considered as anonideal solution Models of excess Gibbs free energy describethe liquid phase behavior

The general stage scheme used in this work is shown inFigure 1

The mass balance of component i on stage j is

f mi j frac14 ethR j thorn 1THORNnIIi j thorn ethZ j thorn 1THORNnI

i j

ethnIIi j thorn 1 thorn nI

i j 1 thorn F i j thorn sumnr

k frac14 1

νi k ξk jTHORN frac14 0 eth1THORN

where (R j + 1)ni jII is the molar liquid 1047298ow rate of component i

leaving stage j R jni jII is its 1047298ow in the liquid sidestream and ni j

II isits 1047298ow that reaches the next stage (Z j + 1)ni j

I is the molar 1047298ow

rate of component i in the vapor leaving stage j Z jni jI

is its 1047298ow rate in the vapor sidestream and ni j

I is its 1047298ow rate that reachesthe next stage In eq 1 F i j is the 1047298ow rate of of component i in thefeed 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 andnr represents thenumber of independent chemical reactions

Assuming that the streams leaving each stage are in phaseequilibrium and the fugacity coefficient in the vapor phase thePoynting factor and the fugacity coefficient of saturated vaporare equal to 1 the isofugacity criteria is

f eqi j frac14 lnethxI

i j P jTHORN lnethxIIi jγ

IIi j P sat

i j THORN frac14 0 eth2THORN

where xi jI and xi j

II arethe mole fractionsof component i in the vapor

and liquid streams leaving stage j P j is the pressure of stage j P i jsat

isthe saturation pressure of component i on stage j and γi jII is the

activitycoefficientof component i in the liquidphase leaving stage jThe rate of reaction expression is used as follows

f r k j frac14 ln k k j thorn sum

nc

i

Ri k lnxII

i j

vII j

ln ξk j frac14 0 eth3THORN

where v jII is the molar volume assuming an ideal liquid solution in

stage j k k j is the kinetic constant of reaction k in stage j Ri k is thekinetic order of component i in reaction k For kinetic datacorrelated as function of activities eq 3 becomes


nc

i

Ri k lnethxIIi jγ

IIi jTHORN ln ξk j frac14 0 eth4THORN

The energy balance in stage j is

f h j frac14 ethR j thorn 1THORNH II j thorn ethZ j thorn 1THORNH I j

ethH II j thorn 1 thorn H I j 1 thorn H F j thorn Q jTHORN frac14 0 eth5THORN

where (Z j + 1)H jI and (R j + 1)H j

II are the enthalpy 1047298ow rates of the vapor and liquid streams leaving stage j and Q j is the rate of heat added in each stage H F j is the enthalpy 1047298ow rate of the feedstream to stage j

An additional equation speci1047297es the behavior of the con-denser and reboiler based on a variable E j which is de1047297ned asthe ratio between the molar 1047298ow of vapor and liquid leaving

Figure 1 Schematic of each theoretical stage along the reactivedistillation column





stage j

f vl j frac14 ethZ j thorn 1THORN sum

nc

i frac14 1

nIi j E jethR j thorn 1THORN sum

nc

i frac14 1

nIIi j frac14 0 eth6THORN

For condensers and reboilers the value of E j is speci1047297ed asshown in Table 1 Foreach internal stage of thecolumn thevalueof E j is calculated

The equations and unknowns are organized as described indetail elsewhere4748 The formulation adopted here uses theNewtonRaphson method to solve the mass and energy bal-

ances phase equilibrium equations rates of reaction equationsand additional equations needed to match the number of degreesof freedom The Thermath package49 was used to obtain Fortransubroutines that implement these equations and their derivatives with respect to the process variables and the excess Gibbs freeenergy model used in the simulation The Fortran program usedin this work has about 10 800 lines of code

rsquoTHERMODYNAMIC MODELING

The calculation of thermodynamic properties is a key point insimulatingdistillation as thisoperationis basedon the separationof vapor andliquid phases Ideal vapor phaseis assumed (fugacity coefficient equal to unity) and the liquid phase is modeled

using excess Gibbs free energy equations such as UNIFAC50

UNIQUAC51 and UNIFAC Dortmund52

The molar enthalpies of the liquid (hL) and vapor (h V ) werecalculated using the following equations

hL frac14 sumnc

i frac14 1

xi

Z T

T ref

cL p idT thorn hE eth7THORN

h V frac14 sumnc

i frac14 1

yiethΔh vapi thorn

Z T

T ref

cL p idT THORN eth8THORN

whereΔhi vap is themolar enthalpy of vaporizationof component i

in the system hE is the molar excess enthalpy and c p iL the molar

speci1047297c heat of component i in the liquid phase The reference

temperature (T ref ) used was 29815 K The Antoine equation53

was used to calculate the vapor pressure

ln P sat frac14 A B

T thorn C eth9THORN

The molar enthalpy of vaporization was calculated using theClausiusClapeyron equation as follows

Δh vapi frac14 RT 2

dln P sat

dT eth10THORN

The values of speci1047297c heat of liquids (c p iL ) and the parameters

of Antoine equation were obtained from NIST54 and DIPPR 55

databases

rsquoRESULTS AND DISCUSSION

This section presents three examples of fatty acid esteri1047297cationin reactive distillation columns The 1047297rst example validates the

methodology used in this work by comparison of its results withother simulations and experimental data available in theliterature

The next two examples present new simulations of fatty acidesteri1047297cation In Example 2 the simulations show the conven-tional operation of a reactive distillation column while inExample 3 the simulations try to reproduce the concept of reactive absorption In both cases we use kinetic data of fatty acid esteri1047297cation using a niobium oxide catalyst4445 Thereactive distillation column setup shown in Figure 2 is used inall simulations performed in this paper The liquid phase wasmodeled by the UNIFAC DORTMUND model45 in all cases

Example 1 Esterificationof Decanoic Acid with MethanolSteinigeweg and Gmehling56 studied this system experimentally

Thus these experimental data will be used to validate themathematical modeling applied in this work Kiss et al3840

used the Aspen Plus software to simulate the same system inreactive distillation columns In those works the authors used areaction kinetics model that considered metal oxides such asniobic acid sulfated zirconia sulfated titania and sulfated tinoxide as catalyst

Here the esteri1047297cation of decanoic acid (1) with methanol (2)producing methyl decanoate (3) and water (4) is given by thefollowing stoichiometric relationship

C9H19COOH eth1THORN

thorn CH 3OH eth2THORN

S C9H19COOCH 3eth3THORN

thorn H2Oeth4THORN

eth11THORN

The chemical reaction of esteri1047297cation is considered to be of 1047297rst order with respect to decanoic acid and methanol Theinverse reaction (hydrolysis) is considered to be of 1047297rst order with respect to methyl decanoate and water These assumptionsare the same as those employed by Steinigeweg and Gmehling56

to develop a pseudo-homogeneous reaction rate model depen-dent on the activity of reagents

r frac14 1

mcat

1

vi

dni

dt frac14 k 1a1a2 k 1a3a4 eth12THORN

The catalyst used was a strongly acid ion-exchange resincommercially called Amberlyst 15 The constants of the rateequation for the catalyst according to the Arrhenius equation are

Table 1 E j Parameter Values for Each Mode of Operation of Condenser and Reboiler

reboiler (stage 1) condenser (stage N)

partial total partial total

Z 1 = 0 Z 1 6frac14 0 Z N = 0 Z N = 0

R 1 = 0 R 1 = 0 R N = 0 R N 6frac14 0

E1 6frac14 0 E1finfin EN 6frac14 0 EN = 0

Figure 2 Schematic of the reactive distillation column in all cases





given by the following56

k 1 frac14 91164 105exp 68710frac12 J=gmol

RT

ethmol=ethgsTHORNTHORN T ethK THORN

eth13THORN


RT


eth14THORNThe simulated column had 20 stages (reboiler 18 adiabatic

plates and condenser) The speci1047297cations of the feed arepresented in Table 2

The liquid phase was modeled by theUNIFAC DORTMUNDmodel45 Table 3 shows the results obtained in the simulations of this work

Figure 3 shows themole fraction pro1047297les in the liquid phase Ingeneral the pro1047297les obtained in this work show the sametendency as the experimental and simulation data availableThe largest deviations occur between stages 2 and 15 Figure 4shows the temperature and the extents of the esteri1047297cation(direct) and hydrolysis (reverse) reactions along the column

In the extremes (top and bottom of the column) the results

are in excellent agreement with the experimental values Morepronounced deviations occur in the intermediate stages Thesediff erences between the simulation results of this study and theliterature56 canbe attributedto some modeling issues Here eq 12a pseudo-homogeneous model is used to model the reaction rate while the cited literature results are based on a heterogeneousmodel that considers adsorption as a limiting step

Figure 4 shows that the esteri1047297cation reaction is favored closeto the feed location of fatty acid This region has the highesttemperature of the reactive zone

The good agreement between the simulation results and theliterature data suggests that the methodology adopted hereis valid

Example 2 Esterification of Oleic Acid with Methanol DePietreet al55 andAlvarez et al56 studied thisreactionsystem withemphasis on the development of catalysts

This example evaluates a reactive distillation column for theesteri1047297cation of oleic acid (1) with methanol (2) producingmethyl oleate (3) and water (4) according to the followingstoichiometric relationship

C17H33COOH eth1THORN



thorn H2Oeth4THORN

eth15THORN

The chemical reaction of esteri1047297cation is considered as secondorder with respect to oleic acid and of zeroth order with respect

to methanol It is assumed that the reverse reaction (hydrolysis)does not occur ie the esteri1047297cation is irreversible Gonc)alves44

used these assumptions in the development of a pseudo-homo-geneous kinetic model as function of reagent concentration asfollows

r frac14 1

mcat

1

vi

dni

dt frac14 kC 1

2 eth16THORN

where C 1 is the concentrations (gmolL) of oleic acid in thereaction mixture Data for the kinetics of this reaction wereobtained from the cited experimental work The kinetic con-stant in eq 16 is given by the Arrhenius equation

Table 2 Speci1047297cations of the Reactive Distillation Columnfor Example 1

variable speci1047297cations

pressure all stages 10132 bar

stages 20

condenser total stage 20

reboiler partial stage 1re1047298ux ratio condenser 05

reactive zone stages 714

catalyst Katapak-SP packing 1047297lled with

Amberlyst 15 resin

1896 g

feed 1 0250 (gmolmin) stage 14

10132 bar 33119 K

decanoic acid

feed 2 0483 (gmolmin)) stage 06

10132 bar 33765 K

methanol

Figure 3 Liquidphase composition along thereactive distillation columnof Example 1 Comparison of simulation results with experimental and simu-lated data56

Table 3 Comparison between Simulation Results for Exam-ple 1 and Data from Literature56

liquid phase

mole fraction

Steinigeweg and

Gmehling (2003) experimental

this

work

top 1 0000 0000 0000

2 0716 0760 0763

3 0000 0000 0000

4 0277 0240 0237

bottom 1 0366 0428 0511

2 0303 0220 0103

3 0303 0332 0386

4 0001 0000 0000

temperature stage 1 36353 - 36349stage 11 34728 - 33883

stage 20 34127 - 34139

conversion ( - decanoic acid) 4299 - 4299





k frac14 113exp 27209frac12 J=gmol

RT

eth L=eth g catmin gmolTHORNTHORN T ethK THORN

eth17THORN

The simulated column has 15 stages 1 reboiler 13 adiabaticplates and 1 condenser The speci1047297cations of the feed arepresented in Table 4

Figure 5 shows the pro1047297les of the liquid phase mole fractionsand Figure 6 shows the temperature and extent of the esteri1047297ca-tion 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 methyloleate are higher atthe bottom of the column In the same1047297gurethe mole fraction of oleic acid decreases rapidly in the regionclose to its feed stage where a large rate of product formation(methyl oleate) also occurs

The temperature pro1047297le presented in Figure 6 is similar to thatof the previous example The reactive zone presents highertemperatures than neighboring stages where the reaction ratesare negligible The highest temperature in the reactive zone isclose to the feed location of oleic acid which is fed at atemperature of 418 K The conversion obtained was 971 andcan possibly be increased by adding more reactive stages to thereactive zone of the simulated column

Example 3 Esterification of Lauric Acid with Ethanol Silvaet al36 studied experimentally a system similar to this example

and Kiss et al38 used the Aspen Plus software to simulate thissystem in reactive distillation columns In the latter work theauthors modeled the reaction kinetics considering different typesof catalyst(ion-exchange resins calcium and metal oxides) In allcases the authors simulated the conventional operation of areactive distillation column

In the previous cases simulated here the conventional opera-tion of a reactive distillationcolumnwas used too Reagents enterthe column as liquids and the heat transfer rate in the reboiler ishigh in all cases favoring the exposure of the product to hightemperatures in the reboiler However according to Kiss40 it is better to have a lower temperature pro1047297le in the column toprevent 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 fedat a temperature close to its saturation

The esteri1047297cation of lauric acid (1)with ethanol (2) producingethyl laurate (3) and water (4) follows the equation


thorn C2H5OH eth2THORN

S C11H23COOC 2H5eth3THORN

thorn H2Oeth4THORN

eth18THORN

The esteri1047297cation reaction was considered to be of 1047297rst order with respect to concentrations of lauric acid and ethanol whilethe inverse reaction (hydrolysis) follows a 1047297rst order kinetic withrespect to the concentrations of ethyl laurate and water From




stages 15


reboiler partial stage 1

re1047298ux ratio condenser 0001


catalyst niobium oxide powder 140 kg

feed 1 9715(gmolmin) stage 13

10132 bar 4181 K

oleic acid


10132 bar 3386 K

methanol

Figure 5 Composition pro1047297le in the liquid phase along the reactivedistillation column of Example 2

Figure 6 Temperature pro1047297le andextents of reaction along thereactivedistillation column of Example 2






these assumptions Le~ao45 proposed the following pseudo-

homogeneous model

r frac14 1

mcat

1

vi

dni

dt frac14 k 1C 1C 2 k 1C 3C 4 eth19THORN

The constants k 1 and k 1 in eq 19 obey the Arrhenius equation

as follows


RT


eth20THORN

k 1 frac14 7 323 exp 3500581frac12 J=gmol

RT eth L=eth g catmin gmolTHORNTHORN T ethK THORN

eth21THORN

In this case the column has 20 stages 1 reboiler 18 adiabaticstages and 1 condenser The feed speci1047297cations are presented inTable 5

Figure 7 shows the pro1047297le of the mole fractions in the liquidphase of all compounds Figure 8 shows the temperature pro1047297leand extents of reaction along the column

From Figure 7 we verify that the bottom product has asigni1047297cant amount of ethanol This is due to the lower heattransfer rate used in the reboiler Such heat transfer rate only provides the heat needed for ethanol evaporation In thissituation almost all water is removed from the top as desired

In Figure 8 the temperature in the reactive zone hasmaximum value between stages 6 and 17 This range of conditions favorsthe esteri1047297cation reaction compared to the hydrolysis reaction because the kinetic constant k 1 is higher than the kinetic constantk 1 (see eqs 20 and 21)

In this example the temperature at the bottom of the reactivedistillation column simulated is signi1047297cantly lower when com-pared to the previous case (Figure 6) This is due to the strategy used in this example to minimize the heat tranfer rate in thereboiler thus turning the case into a reactive absorption columnThis approach tends to reduce utilities consumption in thecolumn and prevent degradation of the ester formed in thechemical reaction

Sensitivity Analysis The influence of some variables such asreflux ratio number of stages and the heat-tranfer rate in thereboiler was observed

In the sensitivity analysis of the re1047298ux ratio such parameterhad its value 1047297 xed between 0002 and 10 for a column with 15stages In case the number of stages we analyzed columns with1523 theoretical stages while for heat-tranfer rate in thereboiler values between 135 and 105 MJmin were used in acolumn with 15 theoretical stages




stages 20






10132 bar 48015 K

lauric acid


10132 bar 35115 K

ethanol



Figure 9 Composition surfaceof ethyl laurate (3) in theliquidphase of the column simulated in Example 3 Eff ect of re1047298ux ratio





The manipulation of the reboiler heat transfer rate was doneindirectly In this case the relationship between the vapor andliquid in the reboiler ( E1) was changed in order to obtain aspeci1047297c value of heat transfer rate in the reboiler (Q R )

Figure 9 showsthe ester mole fraction in theliquid phase alongthe reactive distillation column as function of the re1047298ux ratio andFigure 10 presents the temperature as function of the re1047298ux ratio

Figures 11 and 12 present results for the variation of heattransfer rate in the reboiler along thesimulated column Figure13exhibits the relationship between lauric acid conversion and

number of theoretical stagesThe increase in the re1047298ux ratio in the condenser increases the

water concentration in the reactive zone favoring the hydrolysisreaction (eq 21) Figure 9 shows that higher concentrations of ethyl laurate are obtained in the bottom product when lower values of re1047298ux ratio are used in the column The increase of the water concentration in the reactive zone also causes the decreasein the temperature pro1047297le mainly in the reactive zone as shownin Figure 10

From Figure 12 it is veri1047297ed that an 8-fold increase in the heattransfer rate in the reboiler increases lauric acid conversion by only 24 while there is a considerable increase in temperature inthis equipment varying in the range of 382531 K approximately

(see Figure 11) As the risk of product degradation raises withhigher bottom product temperature increasing the heat transferrate in the reboiler is not advisible It is preferable to use a heatexchanger for preheating the alcohol stream before entering thereactive distillation column This procedure reduces the heattransfer in the reboiler and may avoid exposing the bottomproduct to high temperatures

Figure 13 shows that an increase in the number of stagesincreases the conversion of lauric acid The column with 20theoretical stages converts 987 of the lauric acid This value ishigher than the minimum purity of 965 required by the

Brazilian laws for trading fatty acid esters (biodiesel)

rsquoCONCLUSIONS

In this work fatty acid esteri1047297cation in reactive distillationcolumns was simulated computationally The results obtainedhere showed good agreement with experimental and simulateddata available in literature validating the simulation proceduresThe second and thirdexamples presented new simulation data of fatty acid esteri1047297cation in reactive distillation columns In thethird example a sensitivity analysis permitted determination of suitable conditions for column operation With these operatingconditions conversions above 98 were obtained which are

Figure 10 Temperature surface along the reactive distillation columnin Example 3 Eff ect of re1047298ux ratio

Figure 11 Temperature surface along the reactive distillation columnin Example 3 Eff ect of reboiler

Figure 12 Conversion of lauric acid versus reboiler heat transfer rate inExample 3

Figure 13 Conversion of lauric acid versus number of stages inExample 3





higher than the legal purity requirements for biodiesel trading inBrazil This mode of operation minimizes the heat transfer rate inthe reboiler simulating the operation of a reactive absorptioncolumn As remarked by Kiss40 in such equipment the absenceof a reboiler tends to lower the 1047297 xed and variable costs compared with those of a reactive distillation column However economicstudies must be performed because some articles show that

reactive distillation is not of economic advantage althoughequipment may be reduced The techniques and procedurespresented here can be used for the design and optimization of biodiesel production using reactive distillation

rsquoAUTHOR INFORMATION

Corresponding AuthorTel +55-4432614749 Fax +55-4432614774 E-mail vladimirdequembr

Present Addresses )On leave from the Federal University of Rio de Janeiro Brazil

rsquoACKNOWLEDGMENTThis work was supported by CNPq (Grant 1454652010-1)

and CAPES

rsquoNOMENCLATURE A B C = constants of Antoine equationai = activity of component iC i = molar concentration of component ic p i L = liquid heat capacity of component i

E j = relation between the liquid and vapor streams in stage jF i j = molar 1047298ow rate of the feed stream of component i to stage j

f i jeq = phase equilibrium function of component i in stage j

f i jm = mass balance function of component i in stage j

f jh = energy balance function at each stage f j

lv = function relating the liquid and vapor streams

f k jr = chemical equilibrium function

H jI = total enthalpy of stream I at stage j

H j+1I = total enthalpy of stream I at stage j+1

h E = molar excess enthalpy

hV = molar enthalpy of vapor stream

h L = molar enthalpy of liquid stream

H F j = total enthalpy 1047298ow rate of feed stream to stage j

k k j = rate constant of reaction k in each stage j

mcat = catalyst mass per reactive stage

ni jI

= molar 1047298ow rate of component i in stream I of stage jni j

II = molar 1047298ow rate of component i in stream II of stage j

P i jsat = saturation pressure of component i in stage j

P j = pressure at stage jQ j = heat load to stage jR = universal gas constantR j = liquid side stream fraction at stage j

T j = temperature at stage j

v jII = liquid molar volume at stage j

xi jI = mole fraction of component i in stream I of stage j

xi jII = mole fraction of component i in stream II of stage j

Z j = vapor side stream fraction at stage j

Greek lettersRi k = kinetic order of component i in reaction k

γi jII = 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

SubscriptsSuperscripts

L II = liquidV I = vaporsat = saturationi = componentk = reactionF = feed j = stagecomponent

rsquoREFERENCES

(1) Madras G Kolloru C Kumar R Synthesis of Biodiesel inSupercritical Fluids Fuel 2004 83 2029

(2) ValliyappanT Bakhshi NDalaiA K Pyrolysisof Glycerol forthe Production of Hydrogen or Syn Gas Bioresour Technol 2008

99 4476(3) Altin R C)etinkaya S Yucesu H S The Potential of Using

Vegetable Oil Fuels as Fuel for Diesel Engines Energy Convers Manage2001 42 529

(4) Ma F Hanna M A Biodiesel Production A Review BioresourTechnol 1999 70 1

(5) Darnoko D Cheryan M J Kinetics of Palm Oil Transester-i1047297cation in a Batch Reactor J Am Oil Chem Soc 2000 77 1263

(6) Dorado M P Ballesteros E Mittelbach M Lopez F JKinetic Parameters A ff ecting the Alkali-Catalyzed Transesteri1047297cationProcess of Used Olive Oil Energy Fuels 2004 18 1457

(7) Freedman B Butter1047297eld R O Pryde E H Transesteri1047297cationKinetics of Soybean Oil J Am Oil Chem Soc 1986 63 1375

(8) Knothe G Van Gerpen J Krahl J The Biodiesel Handbook AOCS Press Champaign IL USA 2005

(9) Martinez M Vicente G Aracil J Kinetics of Sun1047298

ower OilMethanolysis Ind Eng Chem Res 2005 44 5447(10) Martinez M Vicente G Aracil J A Comparative Study of

Vegetable Oils for Biodiesel Production in Spain Energy Fuels 2006 20 1722

(11) Oliveira D Luccio M Faccio C Dallarosa C Bender J PLipke N Amroginski C Dariva C Oliveira J V Optimization of

Alkaline Transesteri1047297cation of Soybean Oil and Castor Oil for BiodieselProduction Appl Biochem Biotechnol 2005 121 231

(12) Singh A K Fernando S D Transesteri1047297cationof Soybean OilUsing Heterogeneous Catalysts Energy Fuels 2008 22 2067

(13) Trakarnpruk W Porntangjitlikit S Palm Oil Biodiesel Synthe-sized with Potassium Loaded Calcined Hydrotalcite and Eff ect of Biodiesel Blend on Elastomers Properties Renewable Energy 2008 33 1558

(14) Balasubramainian R K Obbard J P Heterogeneous catalytictransesteri1047297cation of phosphatidylcholine Bioresour Technol 2011 102 1942

(15) Yoo S J Lee H S Veriansyah B Kim J Kim J D Lee Y W Synthesis of biodiesel from rapeseed oil using supercriticalmethanol with metal oxide catalysts Bioresour Technol 2010 101 8686

(16) Demirbas A Biodiesel Production Via Non-Catalytic SCFMethod and Biodiesel Fuel Characteristics Energy Convers Manage2006 47 2271

(17) Kusdiana D Saka S Biodiesel Fuel from Rapeseed Oil asPrepared in Supercritical Methanol Fuel 2001 80 225

(18) Madras G Kolluru C Kumar R Synthesis of Biodiesel inSupercritical Fluids Fuel 2004 83 2029

(19) Silva C Weschenfelder T A Rovani S Corazza F CCorazza M L Dariva C Oliveira J V Continuous Production of





Fatty Acid Ethyl Esters from Soybean Oil in Compressed Ethanol Ind Eng Chem Res 2007 46 5304

(20) Bertoldi C Silva C Bernardon J P Corazza M LCardozo-Filho L Oliveira J V Corazza F C Continuous Productionof Soybean Biodiesel in Supercritical Ethanol Water Mixtures EnergyFuels 2009 23 5165

(21) Kiss A A Omota F Dimian A C Rothenberg G C Study of Heterogeneous Base Catalysts for Biodiesel Production Top Catal

2006 40 141(22) Fukuda H Kondo A Noda H Biodiesel Fuel Production by

Transesteri1047297cation of Oils J Biosci Bioeng 2001 92 405(23) Van Gerpen J Shanks B Pruszko R Clements D Knothe

G Biodiesel In Production Technology National Renewable Energy Laboratory NREL Golden CO 2004

(24) Van Gerpen J Biodiesel Processing and Production Fuel Process Technol 2005 86 1097

(25) Di Serio MCozzolino MGiordano M Tesser R PatronoP Santacesaria E From Homogeneous to Heterogeneous Catalysts inBiodiesel Production Ind Eng Chem Res 2007 46 6379

(26) Di Serio M Tesser R Pengmei L Santacesaria E Hetero-geneous Catalysts for Biodiesel Production Energy Fuels 2008 22 207

(27) Ondrey G Biodiesel Production Using a HeterogeneousCatalysts Ind Eng Chem Res 2004 10 13

(28) Aranda D A Gonc)

alves J A Peres J S Ramos A L deMelo C A R Antunes O A C Furtado N C Taft C A The Use of Acids Niobium Oxide and Zeolite Catalysts for Esteri1047297cation Reac-tions J Phys Org Chem 2009 22 709

(29) Rocha L L L Ramos A L D Antoniosi Filho N RFurtado N C Taft C A Aranda D A G Productionof Biodiesel byaTwo-Step Niobium Oxide Catalyzed Hydrolysis and Esteri1047297cation LettOrg Chem 2010 7 571

(30) Warabi Y Kusdiana D Saka S Reactivity of Triglyceridesand Fatty Acids of Rapeseed Oil in Supercritical Alcohols BioresourTechnol 2004 91 283

(31) Kusdiana D Saka S Kinetics of Transesteri1047297cation in Rape-seed Oil to Biodiesel Fuels as Treated in Supercritical Metanol Fuel2001 80 693

(32) Aranda D A G Antunes O A C Catalytic process for the

esteri1047297

cation of fatty acids WIPO Patent WO 081644 2006(33) Peuroopken T Steinigeweg S Gmehling J Reactive Distillationfor the Synthesis and Hydrolysis of Methyl Acetate using StructuredCatalytic Packings Experiments and Simulation Ind Eng Chem Res2001 40 1566

(34) Krafczyk J Gmehling J Use of Catalyst Packages for theProduction of Methyl Acetate by Reactive Recti1047297cation Chem Ing Tech1994 66 1372

(35) Steinigeweg S Gmehling J n-Butyl Acetate Synthesis viaReactive Distillation Thermodynamic Aspects Reaction Kinetics Pilot-Plant Experiments and Simulation Studies Ind Eng Chem Res 2002 41 5483

(36) Silva N L Santander C M G Batistella C B Maciel FilhoR Maciel M R W Biodiesel Production from Integration BetweenReaction and Separation System Reactive Distillation Process Appl

Biochem Biotechnol 2010 161 245(37) He B B Singh A P Thompson J C A Novel Continuous-

Flow Reactor Using Reactive Distillation for Biodiesel ProductionTrans ASAE 2006 49 107

(38) Kiss A A Omota F Dimian A C Rothenberg G TheHeterogeneous Advantage Biodiesel by Catalytic Reactive DistillationTop Catal 2006 40 141

(39) Dimian A C Bildea C S Omota F Kiss A InnovativeProcess for Fatty Acid Esters by Dual Reactive Distillation ComputChem Eng 2009 33 743

(40) Kiss A Novel Process for Biodiesel by Reactive AbsorptionSep Purif Technol 2009 69 280

(41) Kiss A ADimian A CRothenbergG Biodieselby CatalyticReactive Distillation Powered by Metal Oxides Energy Fuels 2008 22 598

(42) Kiss A A Separative Reactors for Integrated Production of Bioethanol and Biodiesel Comput Chem Eng 2010 34 812

(43) Kiss A A Heat-Integrated Process for Biodiesel by Reactive Absorption Adv Synth Catal 2010 348 75

(44) Gonc)alves J A Esteri1047297cac)~ao de Compostos Modelos sobre Acido Niobico para a Produc)~ao de Biodiesel MSc Thesis UFRJ 2007

(45) Le~ao L S Estudo Empiacuterico e Cinetico da Esteri1047297cac)~ao de Acidos Graxos Saturados sobre Oxido de Niobio MSc Thesis UFRJ

2009(46) Chen F Huss R S Malone M F Doherty M F Multiple

Steady States in Reactive Distillation Kinetic Eff ects Comput Chem Eng 2000 24 2457

(47) Alfradique M F Castier M Automatic Generation of Proce-dures for the Simulation of Reactive Distillation Using Computer

Algebra Comput Chem Eng 2005 29 1875(48) Henley E J Seader J D Equilibrium-Stage Separation Opera-

tions in Chemical Engineering Wiley New York 742 1981

(49) Castier M Automatic Implementation of ThermodynamicModels Using Computer Algebra Comput Chem Eng 1999 23 1229

(50) Smith J M Van Ness H C Abbott M M Introduction toChemical Engineering Thermodynamics 5th ed McGraw-Hill New

York 2000(51) Okur H Bayramoglu M The Eff ect of the Liquid-Phase

Activity Model on the Simulation of Ethyl Acetate Production by Reactive Distillation Ind Eng Chem Res 2001 40 3639(52) Gmehling J Li J Schiller M A Modi1047297ed UNIFAC Model 2

Present Parameter Matrix and Results for Diff erent ThermodynamicProperties Ind Eng Chem Res 1993 32 178

(53) Hala E Boulblik T Fried V Vapour Pressure of PureSubstances Elsevier Amsterdam 17 972 1984

(54) NIST Chemistry WebBook NIST Standard Reference Data- base Number 69 2008

(55) DIPPR Information and Data Evaluation Manager Public Version 120 2000

(56) Steinigeweg S Gmehling J Esteri1047297cation of a Fatty Acid by Reactive Distillation Ind Eng Chem Res 2003 42 3612

(57) De Pietre M K Almeida L C P Landers R VinhasR C G Luna F J H3PO4

and H2SO4 Treated Niobic Acid as

Heterogeneous Catalyst for Methyl Ester Production React Kinet Mech Catal 2010 99 269(58) Alvarez M Ortiz M Ropero J Nino M Rayon R

Tozompantzi F Gomez R Evaluation of Sulfated Aluminas Synthe-sized Via the Sol-Gel Method in the Esteri1047297cation of Oleic Acid withEthanol Chem Eng Commun 2009 196 1152

rsquoNOTE ADDED AFTER ASAP PUBLICATION

The version of this paper that was published ASAP July 282011 was missing some text corrections The revised version waspublished August 9 2011





regarded as a textbook example of this process The process costs were reduced (sim80) by removing units and performing heatintegration The conventional process composed of 11 diff erentsteps carried out in 28 pieces of equipmentwas replaced by a singlehighly integrated reactive distillation column3335

The potential applicability of reactive distillation for biodieselproduction has motivated several publications such as those of Silva et al36 He et al37 and especially those of Kiss et al213843

In this way the objective of this work is to present new computersimulations of fatty acid alkyl esters production in reactivedistillation columns The simulation data obtained here can beuseful to develop and optimize processes to produce biodieselusing hydroesteri1047297cation In the simulations the formulationused assumes steady-state operation and the reaction rates areconsidered explicitly in the model of each stage In the 1047297rstexample presented here the formulation used in this work is validated by comparing its results with experimental data andsimulations results available in the literature56 Next two new simulations results of biodiesel production by esteri1047297cation arepresented using kinetic data of fatty acid esteri1047297cation thatemploy niobium oxide as heterogeneous catalyst4445

rsquoMETHODOLOGY

Reviews about the approaches used in these models of reactivedistillation columns are available in the literature4647 In thispaper we assume steady-state operation and consider the reac-tion rates explicitly in the model of each stage In all cases forsimplicity the Murphree efficiency of separation was set equal to100 The same assumptions were used by Chen et al46 and Alfradique and Castier47

The methodology takes additional considerations into ac-count analogous to the reactive distillation column using chemi-cal equilibrium Such considerations are detailed below In theenergy balance the heat of reaction is considered negligible whencompared to the value of heat of vaporization There is heat

transfer in the reboiler and in the condenser but the interiorstages of the column are adiabatic The chemical reactions occuronly in the liquid phase and are controlled by chemical kineticsThe possibility of vaporliquidliquid equilibrium (VLLE) isnot considered in the thermodynamic modeling The occurrenceof VLLE has a strong dependence on the temperature and formost systems at a given pressure there is a temperature above which two liquid phases do not form In all the simulations theassumption is that the operating temperatures along the reactivedistillation columns prevent the formation of two liquid phasesBesides the kinetic models used in the examples 2 and 3 areobtained from experiments4445 These experiments were con-ducted under temperatures ranging from 150 to 200 C and in

this range the occurrence of two diff erent liquid phases was notobserved

We consider pseudo-homogeneous kinetics that does notaccount for the in1047298uence of adsorption as a possible limitingstep to reaction rate Each stage is considered as a continuousstirred-tank reactor (CSTR) The stream of liquid and vaporleaving the stages are in phase equilibrium the vapor phase has

ideal gas behavior and the liquid phase is considered as anonideal solution Models of excess Gibbs free energy describethe liquid phase behavior

The general stage scheme used in this work is shown inFigure 1

The mass balance of component i on stage j is

f mi j frac14 ethR j thorn 1THORNnIIi j thorn ethZ j thorn 1THORNnI

i j

ethnIIi j thorn 1 thorn nI

i j 1 thorn F i j thorn sumnr

k frac14 1

νi k ξk jTHORN frac14 0 eth1THORN

where (R j + 1)ni jII is the molar liquid 1047298ow rate of component i

leaving stage j R jni jII is its 1047298ow in the liquid sidestream and ni j

II isits 1047298ow that reaches the next stage (Z j + 1)ni j

I is the molar 1047298ow

rate of component i in the vapor leaving stage j Z jni jI

is its 1047298ow rate in the vapor sidestream and ni j

I is its 1047298ow rate that reachesthe next stage In eq 1 F i j is the 1047298ow rate of of component i in thefeed 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 andnr represents thenumber of independent chemical reactions

Assuming that the streams leaving each stage are in phaseequilibrium and the fugacity coefficient in the vapor phase thePoynting factor and the fugacity coefficient of saturated vaporare equal to 1 the isofugacity criteria is

f eqi j frac14 lnethxI

i j P jTHORN lnethxIIi jγ

IIi j P sat

i j THORN frac14 0 eth2THORN

where xi jI and xi j

II arethe mole fractionsof component i in the vapor

and liquid streams leaving stage j P j is the pressure of stage j P i jsat

isthe saturation pressure of component i on stage j and γi jII is the

activitycoefficientof component i in the liquidphase leaving stage jThe rate of reaction expression is used as follows


nc

i

Ri k lnxII

i j

vII j

ln ξk j frac14 0 eth3THORN

where v jII is the molar volume assuming an ideal liquid solution in

stage j k k j is the kinetic constant of reaction k in stage j Ri k is thekinetic order of component i in reaction k For kinetic datacorrelated as function of activities eq 3 becomes


nc

i

Ri k lnethxIIi jγ

IIi jTHORN ln ξk j frac14 0 eth4THORN

The energy balance in stage j is

f h j frac14 ethR j thorn 1THORNH II j thorn ethZ j thorn 1THORNH I j

ethH II j thorn 1 thorn H I j 1 thorn H F j thorn Q jTHORN frac14 0 eth5THORN

where (Z j + 1)H jI and (R j + 1)H j

II are the enthalpy 1047298ow rates of the vapor and liquid streams leaving stage j and Q j is the rate of heat added in each stage H F j is the enthalpy 1047298ow rate of the feedstream to stage j

An additional equation speci1047297es the behavior of the con-denser and reboiler based on a variable E j which is de1047297ned asthe ratio between the molar 1047298ow of vapor and liquid leaving

Figure 1 Schematic of each theoretical stage along the reactivedistillation column





stage j


nc

i frac14 1


nc

i frac14 1










hL frac14 sumnc

i frac14 1

xi

Z T

T ref


h V frac14 sumnc

i frac14 1

yiethΔh vapi thorn

Z T

T ref







ln P sat frac14 A B

T thorn C eth9THORN



dln P sat

dT eth10THORN



databases









C9H19COOH eth1THORN



thorn H2Oeth4THORN

eth11THORN



r frac14 1

mcat

1

vi

dni






Z 1 = 0 Z 1 6frac14 0 Z N = 0 Z N = 0

R 1 = 0 R 1 = 0 R N = 0 R N 6frac14 0









RT


eth13THORN


RT















thorn H2Oeth4THORN

eth15THORN




r frac14 1

mcat

1

vi

dni

dt frac14 kC 1

2 eth16THORN





stages 20





Amberlyst 15 resin

1896 g


10132 bar 33119 K

decanoic acid


10132 bar 33765 K

methanol



liquid phase

mole fraction

Steinigeweg and


this

work

top 1 0000 0000 0000

2 0716 0760 0763

3 0000 0000 0000

4 0277 0240 0237

bottom 1 0366 0428 0511

2 0303 0220 0103

3 0303 0332 0386

4 0001 0000 0000


stage 20 34127 - 34139







RT


eth17THORN















thorn H2Oeth4THORN

eth18THORN





stages 15







10132 bar 4181 K

oleic acid


10132 bar 3386 K

methanol









homogeneous model

r frac14 1

mcat

1

vi

dni



as follows


RT


eth20THORN



eth21THORN











stages 20






10132 bar 48015 K

lauric acid


10132 bar 35115 K

ethanol

















rsquoCONCLUSIONS
















and CAPES
















ni jI















rsquoREFERENCES











































esteri1047297







































stage j


nc

i frac14 1


nc

i frac14 1










hL frac14 sumnc

i frac14 1

xi

Z T

T ref


h V frac14 sumnc

i frac14 1

yiethΔh vapi thorn

Z T

T ref







ln P sat frac14 A B

T thorn C eth9THORN



dln P sat

dT eth10THORN



databases









C9H19COOH eth1THORN



thorn H2Oeth4THORN

eth11THORN



r frac14 1

mcat

1

vi

dni






Z 1 = 0 Z 1 6frac14 0 Z N = 0 Z N = 0

R 1 = 0 R 1 = 0 R N = 0 R N 6frac14 0









RT


eth13THORN


RT















thorn H2Oeth4THORN

eth15THORN




r frac14 1

mcat

1

vi

dni

dt frac14 kC 1

2 eth16THORN





stages 20





Amberlyst 15 resin

1896 g


10132 bar 33119 K

decanoic acid


10132 bar 33765 K

methanol



liquid phase

mole fraction

Steinigeweg and


this

work

top 1 0000 0000 0000

2 0716 0760 0763

3 0000 0000 0000

4 0277 0240 0237

bottom 1 0366 0428 0511

2 0303 0220 0103

3 0303 0332 0386

4 0001 0000 0000


stage 20 34127 - 34139







RT


eth17THORN















thorn H2Oeth4THORN

eth18THORN





stages 15







10132 bar 4181 K

oleic acid


10132 bar 3386 K

methanol









homogeneous model

r frac14 1

mcat

1

vi

dni



as follows


RT


eth20THORN



eth21THORN











stages 20






10132 bar 48015 K

lauric acid


10132 bar 35115 K

ethanol

















rsquoCONCLUSIONS
















and CAPES
















ni jI















rsquoREFERENCES











































esteri1047297









































RT


eth13THORN


RT















thorn H2Oeth4THORN

eth15THORN




r frac14 1

mcat

1

vi

dni

dt frac14 kC 1

2 eth16THORN





stages 20





Amberlyst 15 resin

1896 g


10132 bar 33119 K

decanoic acid


10132 bar 33765 K

methanol



liquid phase

mole fraction

Steinigeweg and


this

work

top 1 0000 0000 0000

2 0716 0760 0763

3 0000 0000 0000

4 0277 0240 0237

bottom 1 0366 0428 0511

2 0303 0220 0103

3 0303 0332 0386

4 0001 0000 0000


stage 20 34127 - 34139







RT


eth17THORN















thorn H2Oeth4THORN

eth18THORN





stages 15







10132 bar 4181 K

oleic acid


10132 bar 3386 K

methanol









homogeneous model

r frac14 1

mcat

1

vi

dni



as follows


RT


eth20THORN



eth21THORN











stages 20






10132 bar 48015 K

lauric acid


10132 bar 35115 K

ethanol

















rsquoCONCLUSIONS
















and CAPES
















ni jI















rsquoREFERENCES











































esteri1047297








































RT


eth17THORN















thorn H2Oeth4THORN

eth18THORN





stages 15







10132 bar 4181 K

oleic acid


10132 bar 3386 K

methanol









homogeneous model

r frac14 1

mcat

1

vi

dni



as follows


RT


eth20THORN



eth21THORN











stages 20






10132 bar 48015 K

lauric acid


10132 bar 35115 K

ethanol

















rsquoCONCLUSIONS
















and CAPES
















ni jI















rsquoREFERENCES











































esteri1047297








































homogeneous model

r frac14 1

mcat

1

vi

dni



as follows


RT


eth20THORN



eth21THORN











stages 20






10132 bar 48015 K

lauric acid


10132 bar 35115 K

ethanol

















rsquoCONCLUSIONS
















and CAPES
















ni jI















rsquoREFERENCES











































esteri1047297
















































rsquoCONCLUSIONS
















and CAPES
















ni jI















rsquoREFERENCES











































esteri1047297













































and CAPES
















ni jI















rsquoREFERENCES











































esteri1047297























































esteri1047297



































Date post:	10-Jan-2016
Category:	Documents
Upload:	carlos-manuel-castillo-salas
View:	7 times
Download:	2 times

1.5-Fatty Acid Esterification in Reactive Distillation Columns_Example1

Documents