ARTICLE pubs.acs.org/IECR
Modeling Hydrolysis and Esterification Kinetics for Biofuel Processes Shujauddin 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, oleic acid esterification, in near- and supercritical ethanol. Hydrolysis was clearly autocatalytic. The experimental data, from reactions at 150-300 °C, times from 5 to 1440 min, and with different initial concentrations of reactants and products, were used to estimate thermodynamically and thermochemically consistent Arrhenius parameters for the forward and reverse reactions in an autocatalytic reaction model. The model provided a good correlation of the data and also exhibited the ability to make quantitatively accurate predictions within the parameter space investigated. The model also accurately predicted the experimental trends when extrapolated outside the original parameter space. Sensitivity analysis confirmed that data from both fatty acid esterification and fatty acid ester hydrolysis 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 and with solvents at elevated temperature and pressure, are gaining attention for the production of biofuels. Hydrothermal processes, for example, which use water as the solvent, can convert triglycerides in plant oils to fatty acids (green diesel feedstock)1 and convert wet algal biomass to crude bio-oils,2 crude lipids,3 or carbonized solids.4 This treatment in high temperature water (HTW) (T > 200 °C) hydrolyzes the ester linkages in the triglycerides present in algae. Thus, ester hydrolysis is an important reaction in biofuel production from the hydrothermal treatment of algal biomass and triglycerides. Another solvothermal process gaining attention is production of fatty acid alkyl esters (biodiesel) by reacting fats, oils, or free fatty acids with a supercritical alcohol.5-7 This process may be preferable to the traditional base-catalyzed transesterification for low-cost feedstocks, because it can tolerate impurities (e.g., water, free fatty acids) in the feedstock. Thus, fatty acid esterification in supercritical alcohol is an important reaction in biodiesel process development. The discussion above notes several biofuel production processes for which ester hydrolysis or fatty acid esterification is important. For some of these reacting systems, the fatty acid, ester, water, and alcohol will all be simultaneously present. Therefore, it is important to understand the reactivity of this multicomponent system as it reacts from both the hydrolysis and esterification directions. These two reactions are really one, since each is the reverse of the other. Though the literature contains many reports on the hydrolysis of triglycerides and mixtures of fatty acid esters in HTWs,8,9 very little literature exists for the hydrolysis kinetics for individual fatty acid 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 rate equation that was first order in ester. We note, however, that the initial ester concentration was low (∼5 10-5 M) in this work, which means that kinetics features that become important at higher concentrations would have gone unobserved. The kinetics of uncatalyzed esterification of different fatty acids in near or supercritical alcohols have been previously r 2011 American Chemical Society
studied.6,11,12 Aranda et al.11 suggested a simple kinetics model that was pseudo first order in fatty acid for esterification of palm oil extraction residue in supercritical alcohol. They did not include any reversible reaction in their model. Moreover, their experiments were all carried out at low temperatures of 130 °C. It is not clear whether a single fluid phase existed under those conditions. Minami and Saka12 included reversibility in their esterification model and also suggested that the fatty acid reactant can act as an acid catalyst for the reaction. They did not report any kinetics parameters, however. Pinnarat and Savage6 studied the kinetics for esterification of oleic acid in ethanol. Their model included reversibility but excluded catalysis by the fatty acid. Their experimental conditions were carefully chosen to ensure that a single phase existed in the reactor at the experimental conditions. This discussion of previous work in the field has identified several gaps in the literature related to the kinetics of hydrolysis of fatty acid ester or esterification of the fatty acid. The first-order kinetics determined for fatty acid ester hydrolysis is not definitive because of the low concentrations employed in the experiments.10 The reported kinetics for fatty acid esterification are also not definitive because none of the previous studies considered all of the essential elements of phase behavior, reversibility, and potential catalysis by fatty acid. Even without these issues, however, the existing literature would be inadequate because the kinetics of ester hydrolysis and fatty acid esterification have been studied as disparate topics. In reality, their kinetics are coupled since these reactions are the reverse of one another. This work provides new experimental data and presents a unified kinetics model for both the hydrolysis and esterification reactions. We used ethyl oleate (fatty acid ester) and oleic acid (fatty acid) as the model compounds for this work, since oleic acid is one of the most commonly occurring fatty acids in nature. Received: November 15, 2010 Accepted: January 14, 2011 Revised: January 8, 2011 Published: February 15, 2011 3206
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We use ethanol as the alcohol for the esterification reaction, as it is available from renewable resources and is safer than methanol.
2. EXPERIMENTAL SECTION We used batch mini reactors assembled from 316 stainless steel Swagelok tube fittings. Prior to using these reactors, we conditioned them by filling them with water and placing them in a fluidized sand bath at 250 °C for 30 min. This conditioning helped remove any residual materials on the reactor walls and also exposed them to the HTW environment. The conditioned reactors were cooled by quenching them in a water bath. Each reactor was then washed thoroughly before use. All chemicals were purchased from Sigma Aldrich in high purity and used as received. Hydrolysis reactions were carried out at 240, 260, 280, and 300 °C for batch holding times between 0 and 180 min. The reactors (capacity 1.5 mL) were loaded at room temperature with 40 μL of ethyl oleate. The amount of water loaded for each experiment was such that the aqueous phase would occupy about 95% of the reactor volume at reaction conditions. The loaded and sealed reactors were then immersed in a preheated isothermal fluidized 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 time of 1440 min to obtain information at chemical equilibrium. Other experiments were done with added water and added ethyl oleate to discover the influence of added product on the esterification kinetics. The procedure for esterification is the same as that described in our previous work.6 The amount of each compound present in the multicomponent mixtures produced by ethyl oleate hydrolysis and oleic acid esterification was determined using the analytical procedure outlined previously.6 The sole exception is that in this work, we used a Zorbax ODS HPLC column (4.6 mm i.d. 250 mm length) with 5 μm particle size packing, which gives peaks corresponding to oleic acid and ethyl oleate at around 17 and 24 min, respectively. Once again, we used ASPEN Plus version 2006.5 for fluid phase equilibrium calculations, which verified that the reactions were conducted in a single fluid phase. 3. RESULTS This section presents results from ethyl oleate hydrolysis in high temperature liquid water and oleic acid esterification in near- and supercritical ethanol. In all cases, the conversion is calculated using the yields of the reactant and product and assuming that the small difference between their sum and 100% (perfect mass balance) can be apportioned equally between the two yields. Experimental uncertainties reported herein are the run-to-run variations, which we determined as the standard 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, and 300 °C. The initial concentration of ester (CoEO) in these experiments was 0.075 mol/L. The line segments connecting sequential 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 for the first 60 min or so, but then the rate increases sharply. This type of behavior is entirely inconsistent with a simple power-law rate equation used by previous researchers.10 Rather, it is indicative of autocatalysis. The literature does provide precedent
Figure 1. Temporal variation of ethyl oleate conversion.
Table 1. Effect of Added Oleic Acid and Ethanol on Ethyl Oleate Conversion (30 min, CoEO = 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
240 300
1.0 0
0 0
569 495
0.58 ( 0.07 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
for autocatalysis during ester hydrolysis in high temperature water.13,14 The carboxylic acid product is generally viewed as the autocatalytic agent. Khuwijitjaru et al.10 used low concentrations of ester (∼510-5 mol/L), which prevented them from observing this 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. We denote the initial molar ratios (R) of oleic acid (OA) and water (W) to the limiting reactant (ethyl oleate, EO) to be ROA and RW, respectively. As shown in the first four rows of Table 1, the conversion of the ester increases with an increasing initial amount of oleic acid present. This increase is so large that an equimolar addition of oleic acid is functionally equivalent to about a 60 °C increase in temperature. That is, both changes lead to a conversion of about 60% after 30 min. The results in Table 1 clearly demonstrate that the presence of oleic acid catalyzes the hydrolysis reaction. We also determined the effect of added ethanol (EtOH), one of the hydrolysis products, on the extent of hydrolysis. We used three different conditions with varying initial molar ratios of ethanol to ethyl oleate at a fixed temperature of 300 °C (30 min). The molar ratio of water to ethyl oleate (RW) necessarily decreased in these runs as the ethanol ratio increased because the total fluid volume was roughly constant. The final four rows of Table 1, which show the results, indicate that an increase in the ethanol ratio leads to a decrease in conversion. This effect is probably due to the reverse reaction (esterification), becoming more important, which reduces the hydrolysis rate. 3.2. Esterification. As mentioned earlier, we have carried out esterification experiments for long batch holding times that supplement the data set we reported previously.6 Table 2 shows the conversion obtained for esterification of oleic acid from 150 to 290 °C at 1440 min. Long batch holding times were used here 3207
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Table 2. Oleic Acid Conversion from Esterification at 1440 min T (°C)
COAo (mol/L)
REtOH
X
150
1.11
7.5
0.83
200 230
1.11 0.63
7.0 9.8
0.97 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 Oleic Acid Conversion (250 °C, 30 min, REtOH = 10) COAo (mol/L)
RW
REO
X 0.75 ( 0.04
0.61
0
0
0.34
0
2
0.59 ( 0.03
0.24 0.18
0 0
4 6
0.55 ( 0.07 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
so that we could obtain results near equilibrium, when the reverse reaction would be important. The conversions were close to unity for most of the experiments, owing to the large excess of ethanol (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), to determine the effect of having one of the products present initially. Water is also relevant because it is frequently present as an impurity in low cost feedstocks (e.g., waste greases and used cooking oils) used for producing biodiesel. The first four rows in Table 3 show that as the molar ratio of ethyl oleate (REO) to limiting reactant (oleic acid) increases, the conversion of oleic acid decreases. The final three rows show the same behavior as the molar ratio of water (RW) to limiting reactant increases. These trends are as expected, because one expects an increase in the rate of the reverse reaction (hydrolysis), when product (ester, water) is present initially in the reaction system. Also note that addition of water or ethyl oleate led to a reduction in the oleic acid initial concentration, and this dilution effect might also have played a role in reducing the conversion.
4. KINETICS MODEL In this section, we use the experimental data in the previous section and that reported in Figure 5 of Pinnarat and Savage6 to develop and validate a unified kinetics model for hydrolysis and esterification. The sigmoidal trends in Figure 1 and the acceleration of hydrolysis upon addition of oleic acid lead us to propose an autocatalytic model for this hydrolysis/esterification system. The phenomenological model comprises two reversible reactions as shown below: k1
EO þ Water h OA þ Ethanol k-1
k2
EO þ Water þ OA h 2OA þ Ethanol k-2
ð1Þ ð2Þ
The first reaction is a reversible hydrolysis of ester to produce the fatty acid. In the second step, the fatty acid formed can catalyze the reaction to give another mole of the acid and ethanol.
We assumed that the reaction orders are equal to the stoichiometric coefficients, vi. Thus, rate equations for the consumption of ester (for hydrolysis experiments) and the consumption of oleic acid (for esterification experiments) can be written. For example, the rate equation for ethyl oleate hydrolysis is as follows: - r EO ¼ k1 CEO CW - k-1 COA CEtOH þ k2 CEO CW COA - k-2 COA 2 CEtOH
ð3Þ
We next combined the rate equations with the design equation for a constant volume batch reactor. Substituting the expressions for the concentration of each component (Ci) in terms of the conversion of the limiting reactant, Ci = Cio (Ri þ νiX), into eq 3 leads to a differential equation describing how the ethyl oleate conversion changes with batch holding time. dX ¼ k1 CoEO ð1 - XÞðRW - XÞ dt - k-1 CoEO ðROA þ XÞðREtOH þ XÞ þ k2 CoEO 2 ð1 - XÞðRW - XÞðROA þ XÞ - k-2 CoEO 2 ðROA þ XÞ2 ðREtOH þ XÞ ð4Þ One can write a similar equation for oleic acid esterification. We assume that the rate constants follow Arrhenius form (eq 5), where 10ai and Ei are the respective pre-exponential factor and activation energy. -Ei ki ¼ 10ai exp , i ¼ 1, 2, - 1, 2 ð5Þ RT The ratios of forward and reverse rate constants for the first (uncatalyzed) and second (catalyzed) reactions should be the same, because they share a common equilibrium constant. This thermodynamic constraint leads to eqs 6 and 7, and it reduces the total 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
ð7Þ
We numerically integrated the differential equations using Euler’s method and simultaneously performed parameter estimation to get estimates for a1, a2, a-2, E1, E2, and E-2. These calculations were performed using Microsoft Excel 2007 and its Solver function. The objective function to be minimized was the sum of the squared differences between the experimental and calculated conversions. We combined and used together the experimental data in Figure 1 (except the data at 60 min for each temperature), Table 1 (first four rows), and Table 2, along with the data we reported previously6 for oleic acid esterification in single-phase systems, to estimate numerical values for the parameters in the model. To the best of our knowledge, this report is the first to treat ester hydrolysis and fatty acid esterification data together 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 the parameters in Table 4 to correlate the experimental results for both hydrolysis and esterification. These parity plots compare the calculated and experimental conversions. If the model provided a perfect fit for all the data, then all points would fall on the diagonal line. Clearly, the model fit is not perfect, but it is very good. Moreover, the data are scattered on both sides of the diagonal indicating the absence of systematic errors. 3208
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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 4. Parity plot for model validation (( hydrolysis, 60 min, Figure 1, 9 esterification, 10 min, 270 and 290 °C (ref 6) 2 hydrolysis with 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) and predicted ester yields Figure 2. Parity plot for ethyl oleate conversion from hydrolysis.
Figure 3. Parity plot for oleic acid conversion from esterification.
To verify that the parameters in Table 4 are reasonable on a thermochemical basis, we calculated the heat of reaction for hydrolysis of ethyl oleate (using the estimated activation energies) and compared it to the value obtained using heats of formation of the reactants and products. The heat of reaction is simply the difference between the activation energies for the forward and reverse reaction. The activation energies in Table 4 lead to ΔHr = -36.9 kJ/mol. Heats of formation for ethyl oleate, water, oleic acid, and ethanol were taken from Vatanai et al.15 to obtain the theoretical ΔHr = -42.4 kJ/mol (at 298 K). Our experimental estimate for ΔHr is in good agreement with this thermochemical estimate. Khuwijitjaru et al.10 used a first order model to describe the hydrolysis kinetics for different fatty acid esters (acyl chain length C8-C16). They observed no autocatalysis at their low initial concentrations, so our Reaction 1 probably provides an appropriate comparison with their results. They reported the activation energy for hydrolysis of methyl palmitate to be 70 kJ/mol. This value is similar to but slightly lower than our E1 value of 87 kJ/mol for uncatalyzed hydrolysis of ethyl oleate. The small difference likely exists because the two studies used different fatty acid esters, different experimental conditions, and different kinetic models. Pinnarat and Savage6 report activation energies for hydrolysis of ethyl oleate as 66 ( 14 kJ/mol and that for esterification of oleic acid to be 56 ( 2 kJ/mol. Since their experiments had a high concentration of fatty acid, it is probably most appropriate to compare their activation energies with E2 and E-2. Our estimate for E2 (51 kJ/mol) is within the uncertainty of their value,
reaction time (min)
Warabi et al.16
model
4
0.49
0.50
6
0.57
0.61
8 10
0.67 0.74
0.67 0.72
14
0.96
0.79
whereas our estimate for E-2 (89 kJ/mol) is not. This discrepancy possibly arises because Pinnarat and Savage6 used only the esterification data to estimate the activation energies, whereas the present model uses both the hydrolysis and esterification data simultaneously. Pinnarat and Savage6 also did not explicitly include 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 predictive ability of the model. These data are the points at 60 min batch holding time from Figure 1 and the results displayed in the final four rows of Table 1 and in Table 3. These results came from experiments done both within and outside the parameter space used to determine the model parameters. Thus, they provide an opportunity to assess the predictive ability of the model as it interpolates within the parameter space and also as it extrapolates beyond. The parity plot in Figure 4 summarizes the results from this model validation study. First, we tested the ability of the model to predict the outcome of experiments done within the parameter space used to determine the model parameters. The diamonds in Figure 4 compare model predictions and experimental results from hydrolysis for 60 min at 240, 260, 280, and 300 °C. The squares show the results for esterification at 270 and 290 °C for 10 min each. It is clear that the points nearly fall on the diagonal, indicating that the model can be used to predict experimental conversions for such cases. Next, we tested the ability of the model to predict experimental conversions for cases where one of the reaction products was added to the reactor. No data from experiments with added product ethanol, ester, or water were used to determine the model parameters. Thus, the comparisons test the predictive ability of the model outside its parameter space. The triangles in Figure 4 show results from hydrolysis experiments with added ethanol, and these outcomes are predicted well by the model. 3209
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Table 6. Normalized sensitivity coefficients normalized sensitivity coefficient run
reaction
t (mins)
T (°C)
Xmodel
Rw
REtOH
REO
E1
a1
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
The circles and asterisks in Figure 4 show results from esterification experiments with varying initial ester and water amounts, respectively. The model does a poorer job of predicting the experimental conversions in these cases, but it does predict the proper trends (i.e., adding ester and water reduces the conversion for esterification). One possible reason for the model’s lack of quantitative predictive ability in these cases when extrapolated is that the model is phenomenological and is not based on the elementary steps that govern the reaction chemistry. For example, one could build a detailed mechanistic model that includes charged intermediates, dissociation of oleic acid in high temperature water, and catalysis by Hþ. Such a model is currently under 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 of ethyl oleate from oleic acid esterification at 300 °C, 150 bar, and REtOH = 42. Table 5 compares their experimental results at different batch holding times with the yields predicted by the kinetics model. Even though the experimental conditions used by Warabi et al.16 are not within our parameter space, the model still gives a nearly quantitatively accurate prediction of the product yields, except at the longest time. To sum up this section on model validation, we have demonstrated that the model makes quantitatively accurate predictions within, and at times outside, the parameter space. It also accurately predicts trends when extrapolated outside the original parameter space. 4.2. Sensitivity Analysis. To determine the sensitivity of the calculated conversion to small changes in the estimated Arrhenius parameters, we calculated normalized sensitivity coefficients as shown in eq 8, where P represents one of the parameters. Dln X ð8Þ S¼ Dln P These coefficients indicate the relative change in conversion that would result from some small change in a parameter. A normalized sensitivity coefficient of unity, for example, indicates that a small relative change (of, say, 1%) in a parameter leads to an identical relative change in conversion. We used Berkeley Madonna 8.3.18 to compute the sensitivity coefficients, which are functions of the initial concentrations, reaction time, and temperature. We conducted this sensitivity analysis at the experimental conditions used to test the predictive capability of the model, as discussed in the previous section. Table 6 summarizes 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 forward rate constants for both reactions 1 and 2, but not sensitive to a-2 and E-2. This result is reasonable since the calculated conversion is low under these conditions as are the product concentrations.
One would not expect the reverse reaction to be important under these conditions. Run 2, however, shows that at a higher temperature (and higher conversion), not only does the model become sensitive to all six parameters, but the magnitude of the sensitivity to the parameters also decreases. Again this outcome is reasonable because at high conversion, products are present in higher concentration, and the reverse reaction should have some influence on the calculated conversion. Moreover, the magnitude of the sensitivity coefficients decreases because as the conversions approach unity, it is not capable of undergoing much additional increase. Run 3 shows that for esterification at moderate conversion, the model is sensitive to only a-2 and E-2, the kinetics for the esterification reaction. Collectively, runs 1-3 show that to estimate reliable values for all six of the model parameters one needs to use data from both hydrolysis and esterification reactions. Run 4 shows the normalized sensitivity coefficients for hydrolysis with added ethanol. The calculated conversion is still most sensitive to E1 and E2 (as in Run 1), but the added ethanol brings with it a sensitivity to the Arrhenius parameters for esterification (a-2 and E-2). This sensitivity arises because of an increase in the 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 that the hydrolysis path is also important when water or ester is present during esterification under those conditions. To summarize, this section describes the sensitivity of the calculated conversions to the model parameters under different conditions. For hydrolysis, E1 and E2 are most important with a-2 and E-2 being least important. The latter becomes important only in the presence of added ethanol. Similarly for esterification, a-2 and E-2 are most important. Thus, one needs a combination of both the hydrolysis and esterification data to get accurate estimates for all of the kinetics parameters.
5. CONCLUSIONS This work is the first to explore the dynamics of ester hydrolysis and fatty acid esterification reactions in tandem. The kinetics are autocatalytic, and a two-step phenomenological model with six adjustable parameters fit the experimental conversion data obtained over a range of temperatures, initial concentrations, and batch holding times. The parameter values are thermodynamically consistent and reasonable on a thermochemical basis. The model makes reliable quantitative predictions within the experimental conditions used to determine its parameters. It makes reliable qualitative predictions when extrapolated outside this parameter space. A mechanistic, rather than phenomenological, model would provide a better platform for 3210
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Industrial & Engineering Chemistry Research making accurate extrapolative predictions. Sensitivity analysis showed that the model is mostly sensitive to a2 and E2 for hydrolysis and a-2 and E-2 for esterification. Sensitivity analysis also confirms the need of using both hydrolysis and esterification data to obtain reliable estimates of the kinetics parameters for each forward and reverse reaction. Finding autocatalysis for ester hydrolysis has implications for process design and optimization for this hydrothermal biofuel production process. Autocatalytic reactions exhibit a maximum in their rate at some intermediate conversion, and for strongly autocatalytic reactions this maximum is at X = 0.5. Thus, one could minimize the total reactor volume required for fatty acid ester hydrolysis by using a reactor sequence (continuous stirred tank reactor followed by a plug flow reactor) rather than a single reactor. The first reactor should be designed to operate at the intermediate conversion that maximizes the reaction rate. A second process implication is that recycling a portion of the hydrolysis product stream could serve to reduce the reactor volume. This product stream would contain a high concentration of fatty acids, which would accelerate the hydrolysis rate. Of course, the advantage gained in reaction rate would need to be balanced against the disadvantage of processing a larger volume of fluid through the reactor.
’ AUTHOR INFORMATION Corresponding Author
*Tel: 734-764-3386; Fax: 734-763-0459; E-mail: psavage@ umich.edu.
’ ACKNOWLEDGMENT We thank Prof. Charles Monroe for his guidance and suggestions regarding numerical methods and Jongyoon Bae for help with esterification experiments. We also acknowledge financial support from NSF Grant EFRI 0937992 and the Royal Thai Government.
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’ ABBREVIATIONS HTW = High Temperature Water FFAs = Free Fatty Acids EO = Ethyl Oleate OA = Oleic Acid EtOH = Ethanol Cio = Initial concentration of component i Ri = Initial molar ratio of component i to the limiting reactant νi = Stoichiometric coefficient of component i X = Conversion of component i ak = Log of pre-exponential factor for reaction k Ek = Activation energy for reaction k ΔHr = Heat of reaction S = Normalized sensitivity coefficient ’ REFERENCES (1) Li, L.; Coppola, E.; Rine, J.; Miller, J. L.; Walker, D. Catalytic Hydrothermal Conversion of Triglycerides to Non-Ester Biofuels. Energy Fuels 2010, 24, 1305–1315. (2) Brown, T. M.; Duan, P.; Savage, P. E. Hydrothermal Liquefaction and Gasification of Nannochloropsis sp. Energy Fuels 2010, 24 (6), 3639–3646. (3) Levine, R. B.; Pinnarat, T.; Savage, P. E. Biodiesel Production from Wet Algal Biomass through in Situ Lipid Hydrolysis and Supercritical Transesterification. Energy Fuels 2010, 24 (9), 5235–5243. 3211
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