Modeling Hydrolysis and Esterification Kinetics for Biofuel Processes

Published: February 15, 2011

r 2011 American Chemical Society 3206 dx.doi.org/10.1021/ie1023047 | Ind. Eng. Chem. Res. 2011, 50, 3206–3211

ARTICLE

pubs.acs.org/IECR

Modeling Hydrolysis and Esterification Kinetics for Biofuel ProcessesShujauddin Changi, Tanawan Pinnarat, and Phillip E. Savage*

Chemical Engineering Department, University of Michigan, Ann Arbor, Michigan 48109-2136, United States

ABSTRACT:We determined the kinetics for ethyl oleate hydrolysis in high-temperature water and for the reverse reaction, oleicacid esterification, in near- and supercritical ethanol. Hydrolysis was clearly autocatalytic. The experimental data, from reactions at150-300 �C, times from 5 to 1440 min, and with different initial concentrations of reactants and products, were used to estimatethermodynamically and thermochemically consistent Arrhenius parameters for the forward and reverse reactions in an autocatalyticreaction model. The model provided a good correlation of the data and also exhibited the ability to make quantitatively accuratepredictions within the parameter space investigated. Themodel also accurately predicted the experimental trends when extrapolatedoutside the original parameter space. Sensitivity analysis confirmed that data from both fatty acid esterification and fatty acid esterhydrolysis need to be used together if one desires reliable estimates for all of the Arrhenius parameters in the autocatalytic model.

1. INTRODUCTION

Solvothermal processes, which make use of reactions in andwith solvents at elevated temperature and pressure, are gainingattention for the production of biofuels. Hydrothermal pro-cesses, for example, which use water as the solvent, can converttriglycerides in plant oils to fatty acids (green diesel feedstock)1

and convert wet algal biomass to crude bio-oils,2 crude lipids,3 orcarbonized solids.4 This treatment in high temperature water(HTW) (T > 200 �C) hydrolyzes the ester linkages in the trigly-cerides present in algae. Thus, ester hydrolysis is an importantreaction in biofuel production from the hydrothermal treatmentof algal biomass and triglycerides. Another solvothermal processgaining attention is production of fatty acid alkyl esters (bio-diesel) by reacting fats, oils, or free fatty acids with a supercriticalalcohol.5-7 This process may be preferable to the traditionalbase-catalyzed transesterification for low-cost feedstocks, because itcan tolerate impurities (e.g., water, free fatty acids) in the feedstock.Thus, fatty acid esterification in supercritical alcohol is an importantreaction in biodiesel process development.

The discussion above notes several biofuel production processesfor which ester hydrolysis or fatty acid esterification is important. Forsome of these reacting systems, the fatty acid, ester, water, andalcohol will all be simultaneously present. Therefore, it is importantto understand the reactivity of this multicomponent system as itreacts from both the hydrolysis and esterification directions. Thesetwo reactions are really one, since each is the reverse of the other.

Though the literature contains many reports on the hydrolysisof triglycerides and mixtures of fatty acid esters in HTWs,8,9 verylittle literature exists for the hydrolysis kinetics for individual fattyacid esters. Khuwijitjaru et al.10 studied the hydrolysis of C8—C16 fatty acid methyl esters from 210-270 �C in a batch reactor.The ester disappearance kinetics were consistent with a rateequation that was first order in ester. We note, however, that theinitial ester concentration was low (∼5� 10-5 M) in this work,which means that kinetics features that become important athigher concentrations would have gone unobserved.

The kinetics of uncatalyzed esterification of different fattyacids in near or supercritical alcohols have been previously

studied.6,11,12 Aranda et al.11 suggested a simple kinetics modelthat was pseudo first order in fatty acid for esterification of palmoil extraction residue in supercritical alcohol. They did notinclude any reversible reaction in their model. Moreover, theirexperiments were all carried out at low temperatures of 130 �C. Itis not clear whether a single fluid phase existed under thoseconditions. Minami and Saka12 included reversibility in theiresterification model and also suggested that the fatty acidreactant can act as an acid catalyst for the reaction. They didnot report any kinetics parameters, however. Pinnarat andSavage6 studied the kinetics for esterification of oleic acid inethanol. Their model included reversibility but excluded catalysisby the fatty acid. Their experimental conditions were carefullychosen to ensure that a single phase existed in the reactor at theexperimental conditions.

This discussion of previous work in the field has identifiedseveral gaps in the literature related to the kinetics of hydrolysisof fatty acid ester or esterification of the fatty acid. The first-orderkinetics determined for fatty acid ester hydrolysis is not definitivebecause of the low concentrations employed in the experi-ments.10 The reported kinetics for fatty acid esterification arealso not definitive because none of the previous studies con-sidered all of the essential elements of phase behavior, reversi-bility, and potential catalysis by fatty acid. Even without theseissues, however, the existing literature would be inadequatebecause the kinetics of ester hydrolysis and fatty acid esterifica-tion have been studied as disparate topics. In reality, their kineticsare coupled since these reactions are the reverse of one another.This work provides new experimental data and presents a unifiedkinetics model for both the hydrolysis and esterificationreactions.

We used ethyl oleate (fatty acid ester) and oleic acid (fattyacid) as the model compounds for this work, since oleic acidis one of the most commonly occurring fatty acids in nature.

Received: November 15, 2010Accepted: January 14, 2011Revised: January 8, 2011

3207 dx.doi.org/10.1021/ie1023047 |Ind. Eng. Chem. Res. 2011, 50, 3206–3211

Industrial & Engineering Chemistry Research ARTICLE

We use ethanol as the alcohol for the esterification reaction, as itis available from renewable resources and is safer than methanol.

2. EXPERIMENTAL SECTION

We used batch mini reactors assembled from 316 stainlesssteel Swagelok tube fittings. Prior to using these reactors, weconditioned them by filling them with water and placing them ina fluidized sand bath at 250 �C for 30 min. This conditioninghelped remove any residual materials on the reactor walls andalso exposed them to the HTW environment. The conditionedreactors were cooled by quenching them in a water bath. Eachreactor was then washed thoroughly before use. All chemicalswere purchased from Sigma Aldrich in high purity and used asreceived.

Hydrolysis reactions were carried out at 240, 260, 280, and300 �C for batch holding times between 0 and 180 min. Thereactors (capacity 1.5mL)were loaded at room temperature with40 μL of ethyl oleate. The amount of water loaded for eachexperiment was such that the aqueous phase would occupy about95% of the reactor volume at reaction conditions. The loaded andsealed reactors were then immersed in a preheated isothermalfluidized sand bath for the desired batch holding time.

The esterification of oleic acid was studied from 150 to 290 �C.Some experiments were completed at a long batch holding timeof 1440min to obtain information at chemical equilibrium.Otherexperiments were done with added water and added ethyl oleateto discover the influence of added product on the esterificationkinetics. The procedure for esterification is the same as thatdescribed in our previous work.6

The amount of each compound present in the multicompo-nent mixtures produced by ethyl oleate hydrolysis and oleic acidesterification was determined using the analytical procedureoutlined previously.6 The sole exception is that in this work,we used a Zorbax ODS HPLC column (4.6 mm i.d. � 250 mmlength) with 5 μm particle size packing, which gives peakscorresponding to oleic acid and ethyl oleate at around 17 and24 min, respectively. Once again, we used ASPEN Plus version2006.5 for fluid phase equilibrium calculations, which verifiedthat the reactions were conducted in a single fluid phase.

3. RESULTS

This section presents results from ethyl oleate hydrolysis inhigh temperature liquid water and oleic acid esterification innear- and supercritical ethanol. In all cases, the conversion iscalculated using the yields of the reactant and product andassuming that the small difference between their sum and100% (perfect mass balance) can be apportioned equally be-tween the two yields. Experimental uncertainties reported hereinare the run-to-run variations, which we determined as thestandard deviations calculated from replicated experiments.3.1. Hydrolysis. Figure 1 shows the conversion (X) of ethyl

oleate at different batch holding times and 240, 260, 280, and300 �C. The initial concentration of ester (Co

EO) in theseexperiments was 0.075 mol/L. The line segments connectingsequential data points serve to make the trends more apparent.At the lower temperatures, the trend of conversion with time

exhibits sigmoidal behavior. That is, the rate at 240 �C is slow forthe first 60 min or so, but then the rate increases sharply. Thistype of behavior is entirely inconsistent with a simple power-lawrate equation used by previous researchers.10 Rather, it isindicative of autocatalysis. The literature does provide precedent

for autocatalysis during ester hydrolysis in high temperaturewater.13,14 The carboxylic acid product is generally viewed as theautocatalytic agent. Khuwijitjaru et al.10 used low concentrations ofester (∼5�10-5 mol/L), which prevented them from observingthis kinetic feature that became important at higher concentrations.To test for autocatalysis by the fatty acid produced during

hydrolysis, we conducted three additional experiments at 240 �C(30 min) with varying amounts of oleic acid present initially. Wedenote the initial molar ratios (R) of oleic acid (OA) and water(W) to the limiting reactant (ethyl oleate, EO) to beROA andRW,respectively. As shown in the first four rows of Table 1, the con-version of the ester increases with an increasing initial amount ofoleic acid present. This increase is so large that an equimolaraddition of oleic acid is functionally equivalent to about a 60 �Cincrease in temperature. That is, both changes lead to a conver-sion of about 60% after 30 min. The results in Table 1 clearlydemonstrate that the presence of oleic acid catalyzes the hydro-lysis reaction.We also determined the effect of added ethanol (EtOH), one

of the hydrolysis products, on the extent of hydrolysis. We usedthree different conditions with varying initial molar ratios ofethanol to ethyl oleate at a fixed temperature of 300 �C (30 min).The molar ratio of water to ethyl oleate (RW) necessarilydecreased in these runs as the ethanol ratio increased becausethe total fluid volume was roughly constant. The final four rowsof Table 1, which show the results, indicate that an increase in theethanol ratio leads to a decrease in conversion. This effect isprobably due to the reverse reaction (esterification), becomingmore important, which reduces the hydrolysis rate.3.2. Esterification. As mentioned earlier, we have carried out

esterification experiments for long batch holding times thatsupplement the data set we reported previously.6 Table 2 showsthe conversion obtained for esterification of oleic acid from 150to 290 �C at 1440 min. Long batch holding times were used here

Figure 1. Temporal variation of ethyl oleate conversion.

Table 1. Effect of Added Oleic Acid and Ethanol on EthylOleate Conversion (30 min, Co

EO = 0.075 mol/L)

T (�C) ROA REtOH RW X

240 0 0 569 0.07( 0.03

240 0.25 0 569 0.35( 0.04

240 0.5 0 569 0.43( 0.05

240 1.0 0 569 0.58( 0.07

300 0 0 495 0.57( 0.08

300 0 25 450 0.35( 0.07

300 0 50 375 0.23( 0.05

300 0 75 300 0.18( 0.07



so that we could obtain results near equilibrium, when the reversereaction would be important. The conversions were close tounity for most of the experiments, owing to the large excess ofethanol (driving the esterification reaction nearly to completion).We also carried out esterification experiments with different

amounts of added water and ethyl oleate at 250 �C (30 min), todetermine the effect of having one of the products presentinitially. Water is also relevant because it is frequently presentas an impurity in low cost feedstocks (e.g., waste greases and usedcooking oils) used for producing biodiesel. The first four rows inTable 3 show that as the molar ratio of ethyl oleate (REO) tolimiting reactant (oleic acid) increases, the conversion of oleicacid decreases. The final three rows show the same behavior asthe molar ratio of water (RW) to limiting reactant increases.These trends are as expected, because one expects an increase inthe rate of the reverse reaction (hydrolysis), when product (ester,water) is present initially in the reaction system. Also note thataddition of water or ethyl oleate led to a reduction in the oleicacid initial concentration, and this dilution effect might also haveplayed a role in reducing the conversion.

4. KINETICS MODEL

In this section,we use the experimental data in the previous sectionand that reported in Figure 5 of Pinnarat and Savage6 to develop andvalidate a unified kinetics model for hydrolysis and esterification. Thesigmoidal trends in Figure 1 and the acceleration of hydrolysis uponaddition of oleic acid lead us to propose an autocatalytic model forthis hydrolysis/esterification system. The phenomenological modelcomprises two reversible reactions as shown below:

EOþWaterhk1

k-1

OA þ Ethanol ð1Þ

EOþWaterþOAhk2

k-2

2OA þ Ethanol ð2Þ

The first reaction is a reversible hydrolysis of ester to produce thefatty acid. In the second step, the fatty acid formed can catalyzethe reaction to give another mole of the acid and ethanol.

We assumed that the reaction orders are equal to the stoichio-metric coefficients, vi. Thus, rate equations for the consumption ofester (for hydrolysis experiments) and the consumption of oleicacid (for esterification experiments) can be written. For example,the rate equation for ethyl oleate hydrolysis is as follows:

- rEO ¼ k1CEOCW - k-1COACEtOH þ k2CEOCWCOA

- k-2COA2CEtOH ð3Þ

Wenext combined the rate equations with the design equationfor a constant volume batch reactor. Substituting the expressionsfor the concentration of each component (Ci) in terms of theconversion of the limiting reactant, Ci = Ci

o (Riþ νiX), into eq 3leads to a differential equation describing how the ethyl oleateconversion changes with batch holding time.

dXdt

¼ k1CoEOð1- XÞðRW - XÞ

- k-1CoEOðROA þ XÞðREtOH þ XÞ

þ k2CoEO

2ð1- XÞðRW - XÞðROA þ XÞ- k-2C

oEO

2ðROA þ XÞ2ðREtOH þ XÞ ð4ÞOne can write a similar equation for oleic acid esterification. Weassume that the rate constants follow Arrhenius form (eq 5),where 10ai and Ei are the respective pre-exponential factor andactivation energy.

ki ¼ 10aiexp-EiRT

� �, i ¼ 1, 2, - 1, 2 ð5Þ

The ratios of forward and reverse rate constants for the first(uncatalyzed) and second (catalyzed) reactions should be thesame, because they share a common equilibrium constant. Thisthermodynamic constraint leads to eqs 6 and 7, and it reduces thetotal number of adjustable parameters in the model to six.

a-1 ¼ a1 - a2 þ a-2 ð6Þ

E-1 ¼ E1 - E2 þ E-2 ð7ÞWe numerically integrated the differential equations using

Euler’s method and simultaneously performed parameter estima-tion to get estimates for a1, a2, a-2, E1, E2, and E-2. Thesecalculations were performed using Microsoft Excel 2007 and itsSolver function. The objective function to be minimized was thesum of the squared differences between the experimental andcalculated conversions. We combined and used together theexperimental data in Figure 1 (except the data at 60 min for eachtemperature), Table 1 (first four rows), and Table 2, along withthe data we reported previously6 for oleic acid esterification insingle-phase systems, to estimate numerical values for the para-meters in the model. To the best of our knowledge, this report isthe first to treat ester hydrolysis and fatty acid esterification datatogether to develop a unified model for this reaction system.Table 4 displays the parameter estimates.

Figures 2 and 3 demonstrate the ability of the model with theparameters in Table 4 to correlate the experimental results forboth hydrolysis and esterification. These parity plots comparethe calculated and experimental conversions. If the modelprovided a perfect fit for all the data, then all points would fallon the diagonal line. Clearly, the model fit is not perfect, but it isvery good. Moreover, the data are scattered on both sides of thediagonal indicating the absence of systematic errors.

Table 2. Oleic Acid Conversion from Esterification at 1440min

T (�C) COAo (mol/L) REtOH X

150 1.11 7.5 0.83

200 1.11 7.0 0.97

230 0.63 9.8 0.99

270 0.08 35.2 0.96

290 0.08 35.2 0.98

Table 3. Effect of Added Ethyl Oleate and Water on OleicAcid Conversion (250 �C, 30 min, REtOH = 10)

COAo (mol/L) RW REO X

0.61 0 0 0.75 ( 0.04

0.34 0 2 0.59( 0.03

0.24 0 4 0.55( 0.07

0.18 0 6 0.52 ( 0.10

0.51 10 0 0.46( 0.05

0.38 30 0 0.24( 0.04

0.31 50 0 0.20 ( 0.03



To verify that the parameters in Table 4 are reasonable on athermochemical basis, we calculated the heat of reaction forhydrolysis of ethyl oleate (using the estimated activation en-ergies) and compared it to the value obtained using heats offormation of the reactants and products. The heat of reaction issimply the difference between the activation energies for theforward and reverse reaction. The activation energies in Table 4lead toΔHr =-36.9 kJ/mol. Heats of formation for ethyl oleate,water, oleic acid, and ethanol were taken from Vatanai et al.15 toobtain the theoretical ΔHr = -42.4 kJ/mol (at 298 K). Ourexperimental estimate for ΔHr is in good agreement with thisthermochemical estimate.

Khuwijitjaru et al.10 used a first order model to describe thehydrolysis kinetics for different fatty acid esters (acyl chain lengthC8-C16). They observed no autocatalysis at their low initialconcentrations, so our Reaction 1 probably provides an appro-priate comparison with their results. They reported the activationenergy for hydrolysis of methyl palmitate to be 70 kJ/mol. Thisvalue is similar to but slightly lower than our E1 value of 87kJ/mol for uncatalyzed hydrolysis of ethyl oleate. The smalldifference likely exists because the two studies used different fattyacid esters, different experimental conditions, and differentkinetic models.

Pinnarat and Savage6 report activation energies for hydrolysisof ethyl oleate as 66 ( 14 kJ/mol and that for esterification ofoleic acid to be 56( 2 kJ/mol. Since their experiments had a highconcentration of fatty acid, it is probably most appropriate tocompare their activation energies with E2 and E-2. Our estimatefor E2 (51 kJ/mol) is within the uncertainty of their value,

whereas our estimate for E-2 (89 kJ/mol) is not. This discre-pancy possibly arises because Pinnarat and Savage6 used only theesterification data to estimate the activation energies, whereas thepresent model uses both the hydrolysis and esterification datasimultaneously. Pinnarat and Savage6 also did not explicitlyinclude autocatalysis.4.1. Model Validation. We used most of the experimental

results to determine reliable values for the model parameters.Several sets of results were reserved, however, to test the pre-dictive ability of the model. These data are the points at 60 minbatch holding time from Figure 1 and the results displayed in thefinal four rows of Table 1 and in Table 3. These results came fromexperiments done both within and outside the parameter spaceused to determine the model parameters. Thus, they provide anopportunity to assess the predictive ability of the model as itinterpolates within the parameter space and also as it extrapolatesbeyond. The parity plot in Figure 4 summarizes the results fromthis model validation study.First, we tested the ability of the model to predict the outcome

of experiments done within the parameter space used to deter-mine the model parameters. The diamonds in Figure 4 comparemodel predictions and experimental results from hydrolysis for60 min at 240, 260, 280, and 300 �C. The squares show theresults for esterification at 270 and 290 �C for 10 min each. It isclear that the points nearly fall on the diagonal, indicating that themodel can be used to predict experimental conversions for suchcases.Next, we tested the ability of themodel to predict experimental

conversions for cases where one of the reaction products wasadded to the reactor. No data from experiments with addedproduct ethanol, ester, or water were used to determine themodel parameters. Thus, the comparisons test the predictiveability of the model outside its parameter space. The triangles inFigure 4 show results from hydrolysis experiments with addedethanol, and these outcomes are predicted well by the model.

Table 4. Estimated Parameters (min, L, mol)

reaction i ai Ei (kJ/mol)

1 4.3 86.7

2 3.1 51.1

-1 8.6 123.6

-2 7.5 87.9

Figure 2. Parity plot for ethyl oleate conversion from hydrolysis.

Figure 3. Parity plot for oleic acid conversion from esterification.

Figure 4. Parity plot for model validation (( hydrolysis, 60 min,Figure 1, 9 esterification, 10 min, 270 and 290 �C (ref 6) 2 hydrolysiswith added ethanol, Table 1, b esterification with added ethyl oleate,Table 3, * esterification with added water, Table 3).

Table 5. Comparison of experimental (Warabi et al.16) andpredicted ester yields

reaction time (min) Warabi et al.16 model

4 0.49 0.50

6 0.57 0.61

8 0.67 0.67

10 0.74 0.72

14 0.96 0.79



The circles and asterisks in Figure 4 show results from esterifica-tion experiments with varying initial ester and water amounts,respectively. The model does a poorer job of predicting theexperimental conversions in these cases, but it does predict theproper trends (i.e., adding ester and water reduces the conversionfor esterification). One possible reason for the model’s lack ofquantitative predictive ability in these cases when extrapolated isthat the model is phenomenological and is not based on theelementary steps that govern the reaction chemistry. For exam-ple, one could build a detailed mechanistic model that includescharged intermediates, dissociation of oleic acid in high tem-perature water, and catalysis by Hþ. Such a model is currentlyunder development.As a final test of the predictive ability of the model, we use it to

predict results in the literature. Warabi et al.16 report yields ofethyl oleate from oleic acid esterification at 300 �C, 150 bar, andREtOH = 42. Table 5 compares their experimental results atdifferent batch holding times with the yields predicted by thekinetics model. Even though the experimental conditions used byWarabi et al.16 are not within our parameter space, the model stillgives a nearly quantitatively accurate prediction of the productyields, except at the longest time.To sum up this section on model validation, we have demon-

strated that the model makes quantitatively accurate predictionswithin, and at times outside, the parameter space. It alsoaccurately predicts trends when extrapolated outside the originalparameter space.4.2. Sensitivity Analysis. To determine the sensitivity of the

calculated conversion to small changes in the estimated Arrhe-nius parameters, we calculated normalized sensitivity coefficientsas shown in eq 8, where P represents one of the parameters.

S ¼ Dln XDln P

ð8Þ

These coefficients indicate the relative change in conversion thatwould result from some small change in a parameter. A normal-ized sensitivity coefficient of unity, for example, indicates that asmall relative change (of, say, 1%) in a parameter leads to anidentical relative change in conversion. We used BerkeleyMadonna 8.3.18 to compute the sensitivity coefficients, whichare functions of the initial concentrations, reaction time, andtemperature. We conducted this sensitivity analysis at theexperimental conditions used to test the predictive capability ofthe model, as discussed in the previous section. Table 6 sum-marizes the sensitivity analysis results.Run 1 shows that for hydrolysis, at a lower temperature, the

model is highly sensitive to a1, E1, a2, and E2, i.e., to the forwardrate constants for both reactions 1 and 2, but not sensitive to a-2

and E-2. This result is reasonable since the calculated conversionis low under these conditions as are the product concentrations.

One would not expect the reverse reaction to be important underthese conditions. Run 2, however, shows that at a highertemperature (and higher conversion), not only does the modelbecome sensitive to all six parameters, but the magnitude of thesensitivity to the parameters also decreases. Again this outcome isreasonable because at high conversion, products are present inhigher concentration, and the reverse reaction should have someinfluence on the calculated conversion. Moreover, the magnitudeof the sensitivity coefficients decreases because as the conver-sions approach unity, it is not capable of undergoing muchadditional increase. Run 3 shows that for esterification atmoderate conversion, the model is sensitive to only a-2 andE-2, the kinetics for the esterification reaction. Collectively, runs1-3 show that to estimate reliable values for all six of the modelparameters one needs to use data from both hydrolysis andesterification reactions.Run 4 shows the normalized sensitivity coefficients for hydro-

lysis with added ethanol. The calculated conversion is still mostsensitive to E1 and E2 (as in Run 1), but the added ethanol bringswith it a sensitivity to the Arrhenius parameters for esterification(a-2 and E-2). This sensitivity arises because of an increase inthe esterification rate under those conditions.Runs 5 and 6 list the normalized sensitivity coefficients for the

cases of added ester and water, respectively, for esterification.The calculated conversion is sensitive not only to E-2 and a-2,but is also modestly sensitive to E2 and a2. This result implies thatthe hydrolysis path is also important when water or ester ispresent during esterification under those conditions.To summarize, this section describes the sensitivity of the

calculated conversions to the model parameters under differentconditions. For hydrolysis, E1 and E2 are most important witha-2 and E-2 being least important. The latter becomes importantonly in the presence of added ethanol. Similarly for esterification,a-2 and E-2 are most important. Thus, one needs a combinationof both the hydrolysis and esterification data to get accurateestimates for all of the kinetics parameters.

5. CONCLUSIONS

This work is the first to explore the dynamics of esterhydrolysis and fatty acid esterification reactions in tandem. Thekinetics are autocatalytic, and a two-step phenomenologicalmodel with six adjustable parameters fit the experimental con-version data obtained over a range of temperatures, initialconcentrations, and batch holding times. The parameter valuesare thermodynamically consistent and reasonable on a thermo-chemical basis. The model makes reliable quantitative predic-tions within the experimental conditions used to determine itsparameters. It makes reliable qualitative predictions when extra-polated outside this parameter space. A mechanistic, rather thanphenomenological, model would provide a better platform for

Table 6. Normalized sensitivity coefficients

run reaction t (mins) T (�C) Xmodel Rw REtOH REO

normalized sensitivity coefficient

a1 E1 a2 E2 a-2 E-2

1 hyd. 60 240 0.18 569 0 0 7.70 -16.47 7.01 -11.07 0.00 0.00

2 hyd. 60 300 0.96 510 0 0 0.29 -0.57 0.88 -1.30 -0.26 0.28

3 est. 10 270 0.40 0 35 0 0.00 0.00 0.00 0.00 5.07 -5.68

4 hyd. 30 300 0.45 450 25 0 4.51 -8.30 5.49 -7.84 -2.94 3.10

5 est. 30 250 0.62 0 10 2 0.01 0.01 -0.15 0.23 6.68 -7.88

6 est. 30 250 0.70 10 10 0 -0.04 0.08 -1.34 2.14 7.52 -8.90



making accurate extrapolative predictions. Sensitivity analysisshowed that the model is mostly sensitive to a2 and E2 forhydrolysis and a-2 and E-2 for esterification. Sensitivity analysisalso confirms the need of using both hydrolysis and esterificationdata to obtain reliable estimates of the kinetics parameters foreach forward and reverse reaction.

Finding autocatalysis for ester hydrolysis has implications forprocess design and optimization for this hydrothermal biofuelproduction process. Autocatalytic reactions exhibit a maximumin their rate at some intermediate conversion, and for stronglyautocatalytic reactions this maximum is at X = 0.5. Thus, onecould minimize the total reactor volume required for fatty acidester hydrolysis by using a reactor sequence (continuous stirredtank reactor followed by a plug flow reactor) rather than a singlereactor. The first reactor should be designed to operate at theintermediate conversion that maximizes the reaction rate. Asecond process implication is that recycling a portion of thehydrolysis product stream could serve to reduce the reactorvolume. This product stream would contain a high concentrationof fatty acids, which would accelerate the hydrolysis rate. Ofcourse, the advantage gained in reaction rate would need to bebalanced against the disadvantage of processing a larger volumeof fluid through the reactor.

’AUTHOR INFORMATION

Corresponding Author*Tel: 734-764-3386; Fax: 734-763-0459; E-mail: [email protected].

’ACKNOWLEDGMENT

We thank Prof. Charles Monroe for his guidance and sugges-tions regarding numerical methods and Jongyoon Bae for helpwith esterification experiments. We also acknowledge financialsupport from NSF Grant EFRI 0937992 and the Royal ThaiGovernment.

’ABBREVIATIONSHTW = High Temperature WaterFFAs = Free Fatty AcidsEO = Ethyl OleateOA = Oleic AcidEtOH = EthanolCi

o = Initial concentration of component iRi = Initial molar ratio of component i to the limiting reactantνi = Stoichiometric coefficient of component iX = Conversion of component iak = Log of pre-exponential factor for reaction kEk = Activation energy for reaction kΔHr = Heat of reactionS = Normalized sensitivity coefficient

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Modeling Hydrolysis and Esterification Kinetics for Biofuel Processes