511
I n d . E n g . C h e m . Res. 1989, 28, 511-518
Kinetics of Aryl Halide Hydrolysis Using Isothermal and Temperature-Programmed Reaction Analyses Stephen A. Birdsell* Mechanical Design Services,
P.O.Box 1663, M S J981, Los Alamos, N e w Mexico 87545
Bruce A. Robinson Los Alamos National Laboratory, Earth and Space Sciences Division, M S J981, Los Alamos, New Mexico 87545
Kinetics for the alkaline hydrolysis of aryl halides in an acetate-carbonate buffer are determined. These quantitative results corroborate qualitative relative reactivities from the literature for aryl halides with different substituent groups, location of substituent group, and species of halogen. Both temperature-programmed reaction (TPR) with a nonlinear temperature-rise rate and isothermal reaction analyses were used. T h e T P R technique provides results that are similar to isothermal reaction analysis in accuracy and ability to discriminate the most appropriate kinetic rate law, but the results are obtained in a much shorter experimental time. Chemically reactive tracer testing is a method of measuring temperature patterns in nonisothermal flow systems such as geothermal reservoirs, chemical reactors, and heat exchangers. Imperative to the success of reactive tracer testing is the use of tracers with appropriate reaction kinetics (Robinson et al., 1988). Aryl halides were investigated as chemically reactive tracers since the alkaline hydrolysis of these compounds was believed to have reaction rates in the range of interest for geothermal reservoir applications. Also, aryl halides of similar structure were known to vary widely in their kinetics. Thus, a catalog of reactive tracers suitable for a variety of geothermal reservoirs could be assembled from a family of compounds (Birdsell and Robinson, 1988). The primary motivation of the present study was to obtain rate constants for these hydrolysis reactions in a model geothermal fluid. Another requirement of our study was that the preexponential factor A , the activation energy E , and the reaction order be obtained quickly for a large number of compounds. The technique of temperature-programmed reaction (TPR) was employed to achieve these goals. Although T P R has been used in experimental gas-solid and catalytic reaction studies (Sohn and Kim, 1980; Falconer and Schwartz, 1983), few liquid-phase TPR studies have been performed. Along with examining the kinetics and mechanisms of aryl halide hydrolysis, we also critically evaluate the nonlinear temperature-rise TPR method for determining rate parameters and reaction order.
Background Aryl Halide Hydrolysis. Alkaline hydrolysis of aryl halides X
OH
X
where formation of the carbanion, called a Meisenheimer complex, is the rate-limiting step. The reaction rate increases as the stability of the carbanion increases. The presence of one or more electronwithdrawing groups will stabilize the carbanion as follows: X
X
X
X
1
I NOz 2 ortho, 1 p a r a
ortho
N0 2
I NOP para
ortho,para
(4)
Electron-withdrawinggroups para and ortho to the halogen result in faster rates than meta groups due to stronger electron induction and resonance. In addition to the location of a group on the benzene ring, the electron-withdrawing abilities of different groups will affect reactivity. Examples relevant to this work are X
X
X
I
I
I
I
I
1
CHO
NO2
COCH3
The choice of halogen X will also affect kinetics according to electron-withdrawing abilities. However, Morrison and Boyd (1975) point out that often only small differences in reactivity are seen between the halogens with the exception of F, which usually causes a marked increase in reactivity: F
is generally considered to occur through nucleophilic aromatic substitution (Morrison and Boyd, 1975). When an electron-withdrawinggroup is located at the ortho, para, or ortho and para positions, the halogen becomes activated toward displacement and reaction rate increases. The mechanism for reaction is bimolecular displacement
OH
OH
CI
I
NO2
Br I
I I
No2
The general rules just outlined are applicable to aryl halides with activating groups ortho or para to the halogen. For unactivated aryl halides reacting with weak bases, such as hydroxide ion, nucleophilic aromatic substitution occurs largely through an elimination-addition mechanism (Breslow, 1965). The reaction kinetics can be more com-
0888-5885/8912628-0511$01.50/0 0 1989 American Chemical Society
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Ind. Eng. Chem. Res., Vol. 28, No. 5, 1989
plex for this type of reaction. Furthermore, experiments performed on the unactivated compound l-bromo-3nitrobenzene exhibited numerous side reactions. Since this behavior is undesirable both in terms of identifying reactive tracers and for evaluating the TPR technique, meta compounds were eliminated from further consideration. The reaction solution for this study was chosen to be similar to that of the fluid in a geothermal reservoir. Typical geothermal fluids have an ionic strength of about lo-’ m and hydroxide ion concentrations in the 10-5-10-3-m range at temperatures of 200-300 “C. Some of the reactions in this study have been examined previously (e.g., Radhakrishnamurti and Sahu (1974) and Ritchie and Sawada (1977). Unfortunately, these studies were each conducted in solvents and at temperature ranges that make comparison to the present results inappropriate. Temperature-Programmed Reaction. In a TPR experiment, temperature is increased throughout the experiment. If the concentration-timetemperature behavior for a given rate law is modeled, optimal values of A and E are obtained. Although TPR data require a more sophisticated mathematical analysis than isothermal reaction data, the benefit of T P R is that only one experiment is necessary to evaluate the Arrhenius parameters. In contrast, isothermal reaction analysis requires a series of experiments to achieve the same results. Furthermore, the TPR technique, like isothermal reaction analysis, can be used to examine the “goodness of fit” for various rate laws to select the appropriate kinetic model for the reaction. As mentioned by Brown and Robinson (19861,researchers have avoided the use of liquid-phase T P R primarily because the heat effects of the reaction complicate the task of producing a linear temperature-rise rate. A linear temperature-rise rate has been a requirement for the analytical expressions traditionally used to determine the preexponential factor and the activation energy (Koch, 1977). In the present study, since the kinetic parameters were found by using nonlinear regression, there was no need for a linear temperature-rise rate. Thus, the TPR experiments are much simpler to carry out, requiring only an accurate measurement of the time-temperature history. Reactions with significant heat effects could also be easily analyzed by using nonlinear regression, although in this case heat effects are negligible. Previous studies have evaluated the use of liquid-phase TPR. Ortiz Uribe et al. (1985a,b) developed a graphical method for integrating linear temperature-rise kinetic data and sequentially discriminating between potential kinetic models. Brown and Robinson (1986) determined the kinetics of the alkaline hydrolysis of ethyl acetate by using TPR, but they used nonlinear temperature-rise rates. Their use of nonlinear regression to analyze TPR data is similar to the present study, but only two experiments were analyzed. Furthermore, these two TPR experiments consisted of only five and six data points, respectively. Matsuda and Goto (1984) have developed a differential thermal analysis (DTA) method, which they used to determine the kinetics of the hydrolysis of acetic anhydride. In this technique, the heat of reaction causes a nonlinear increase in the temperature. However, the initial concentrations of reactants are limited so that the increase in temperature is small. A reaction rate constant is then calculated from the thermal data and is assumed to be the reaction rate constant a t the average temperature of the experiment. Subsequently, experiments are conducted at different average temperatures, and the kinetic parameters are evaluated from an Arrhenius plot. If the nonlinear regression technique of the present study were to be used
with this DTA technique, the temperature increase would not be limited and the kinetic parameters could be evaluated from a single experiment. Using numerical simulation techniques, Brown and Robinson (1986) examined the relative accuracies of isothermal, linear temperature-rise rate TPR, and nonlinear temperature-rise rate TPR. They stressed that linearization of the reaction rate expression for analytical analysis of constant temperature-rise rate data can implicitly weight the data, whereas nonlinear regression uses the data to the fullest extent possible. Another conclusion is that, for a given number of data points, isothermal experiments may yield slightly more accurate results than TPR experiments. This does not necessarily favor isothermal experiments since a larger number of samples can be taken in a much shorter experimental time with TPR. In the present study, TPR was used for the more reactive compounds. For the less reactive compounds, autoclave temperature and pressure limitations precluded the use of TPR, and isothermal experiments were performed.
Experimental Section Equipment and Experimental Procedures. Experiments were conducted in a 2-L Parr Instruments (Model 4522) stirred autoclave. The aryl halide and a buffer solution described below were charged to the autoclave, and the temperature was allowed to increase along the saturation vapor pressure of the solution (0.79-8.6 MPa). Since the fluid evolved COz, disrupting equilibrium calculations, it was charged in quantities such that the vapor space in the reactor was minimized at the experimental temperature. Also, care was taken to avoid loss of CO, to the atmosphere before the autoclave was sealed. For isothermal experiments a temperature controller (f1 “C) was used. Once the temperature had stabilized, samples were removed periodically through a sampling port connected to a cooling coil so that the reaction was quenched immediately upon sampling. For TPR experiments, a power control was used to control the quantity of heat delivered to the heating jacket. By adjusting the power delivered to the heating jacket, the temperature-rise rate could be increased or decreased as required for different experiments. When the temperature was believed to be high enough for significant reaction to occur, sampling began. Between 6 and 18 samples were taken per experiment. Collection of a sample required about 20 s. so the mean time-temperature for each sample was recorded. Analytical Procedures. The extent of reaction was determined by analysis for the liberated halides. This measurement was made with Orion ion-specific electrodes. Since these electrodes are sensitive to ionic strength, the buffer solution was used to produce the electrode standards. For a few experiments, a Dionex 4000i high-pressure liquid chromatograph was used to check for the possibility of side reactions. Buffer Solution. The buffer solution is a sodium bicarbonate-acetic acid mixture that was previously mathematically modeled to calculate equilibrium concentrations by Robinson and Tester (1988). This solution was chosen to simulate the behavior of a geothermal fluid at elevated temperatures. Equilibrium dissociation equations for HAC, H,CO,, HC03-, and H 2 0 were solved simultaneously with the resulting [OH-] used in the kinetic analysis. The charge balance in Robinson and Tester (1988) was modified to include [X-], which is liberated by reaction of ArX. Also, since it was not possible to completely eliminate the vapor space in the autoclave at all times, evolution of COP into the vapor space was accounted for through calculation
Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989 513 Table I. Structural Formulas of the Aryl Halides Investigated structure compound ~~
~
Br
4-bromoacetophenone (p-BrC6H4COCH3)
I
COCHa
Br
p-bromobenzaldehyde @-BrC6H4CHO) 106
'
17
21
1.9
2.3
I
I 2.5 CHO
10oorr (K')
Figure 1. Model of the carbonate-acetate buffer system for the ranges encountered in this study. In addition to the HAC, 7.5 g of NaHC03 was added to 1.625 L of water.
1-bromo-2-nitrobenzene (o-BrC6H4N02)
of the partial pressures of COz, HzO, and HACin the vapor space. The effect of acid dissociation of the phenolic reaction products was studied parametrically and was found to have no effect on [OH-] for the concentrations encountered in this study. Values of [OH-] are shown graphically in Figure 1for the ranges of temperatures and concentrations of this study. Kinetic Modeling. The bimolecular displacement mechanism shown in eq 2 and 3 leads to the following second-order, overall reaction rate expression:
1-bromo-4-nitrobenzene (p-BrC6H4N02)
A N 0 2
n Br I
NO2
1-fluoro-2-nitrobenzene (o-FC6H4NO2)
d[ArX]/dt = -kll[ArX][OH-] (7) where kll is the reaction rate constant, assumed to be of Arrhenius form kll = A exp(-E/RT) (8)
1-iodo-2-nitrobenzene ( O - I C B H ~ N O ~ )
I
For isothermal experiments, integration of eq 7 leads to
where [OH-] is a constant, buffered by the reaction solution. This model should be appropriate for aryl halides with activating groups. The form of the kinetic model for T P R is
,5103.
-
.
'
$02
[ArX]/[ArX], = -AJt[OH-] 0
exp(-E/RT) dt
(10)
where T and [OH-] are functions of t. Values of [ArX] and T a r e experimentally determined functions of t , while [OH-] is calculated by using the carbonate-acetate buffer model. Optimal values of the Arrhenius parameters A and E can then be calculated by using a nonlinear least-squares regression (Brown and Robinson, 1986). In the present study, the buffer model was solved first to give smooth functions of [OH-] and T versus t using cubic splines. The integral of eq 10 could then be calculated numerically for various A and E. Optimal values of the Arrhenius parameters were obtained by nonlinear regression to minimize the sum of the squared residuals between data and calculated concentrations. Parameters were calculated without data weighting, since the Monte Carlo error analysis described in the Result and Discussion section suggested that weighting the data based on the concentration measurement error would have little effect on the accuracy of the results.
Results and Discussion This section presents results of the two aspects of the work: the aryl halide hydrolysis rate parameters and the temperature-programmed reaction technique. Since the goal of this study is to identify chemically reactive tracers
0 $510' Y
10
loo
'
.
i
102'
17
"
18
'
"
19
"
2.0
'
I
21
lOOOR (K.' )
Figure 2. Arrhenius plots for the investigated compounds.
with a range of applicability, aryl halides that were predicted to have widely varying reaction rates were chosen. Structural formulas of the investigated aryl halides are shown in Table I. Sites occupied on the benzene ring were ortho, para, and ortho-para to the halogen; attached a t these sites were the electron-withdrawing groups NOz, CHO, and COCH,; halogen species were F, Br, and I. Figure 2 shows that the results of this study agree with the expected relative reactivities of aryl halides with different substituent groups (eq 5 ) , group location (eq 4), and species of halogen (eq 6). Kinetic Analysis. Table I1 is a summary of the experimental conditions and results for individual experiments, and Table I11 lists the Arrhenius parameters obtained. Since p-BrC6H4CH0is the only compound for which both isothermal and TPR experiments were run,
514
Ind. Eng. Chem. Res., Uol. 28, No. 5 , 1989
Table 11. Summary of Individual Experiments. Initial Aryl Halide Concentrations Ranged from 5 run p-BrC6H4COCH3-1 p-BrC,HdCOCH,-2 >-BrC,H;COCH,-3 p-BrCeHdCOCH3-4 p-BrC6H4COCH3-5 p-BrC6H4CHO-1 p-BrC6HdCHO-2 p-BrC6H4CHO-3 p-BrC6H4CHO-4 p-BrC6H4CHO-5 p-BrC6H4CHO-6 o-BrC6H4NO2-1 o-BrC6H4N02-2 p-BrC6H4NOz-l BrC6H3(N02)2-1 BrC6H3(NO2)2-2 BrC6H3(N02)2-3 0-FCGHdN02-1 0-ICsH4NO2-1 o-IC6H4NO2-2
T range, "C 235" 252" 270" 291" 295.5" 223" 247.5' 248.5" 296.5" 296.5" 259-293' 229-268' 251-295' 225-300' 170-204' 201-228' 170-205* 204-226' 231-271' 228-265'
no. of data pts 8 4 4
11 6
15 5 8 8
4 18 9 10 18 8 9 10
I
i
10
Isothermal reaction analysis.
[OH'] range, m x io4 0.41 0.57 1.4 5.3 2.0 0.30 0.58
A , kg! (mol.min)
2.0 2.1
1.83 x 1014 1.12 x 1011 2.34 X 1 O I 2 1.28 X 10" 2.62 X 10l6 1.68 x 1019 9.8 x 1015 8.07 x 1015 4.72 X 10" 6.37 x 1014
1.35 x 9.52 x 1.08 X 1.08 X 1.15 X 1.43 x 1.12 x 1.19 x 9.78 X 1.29 x
lo-' to 1
k ? kg/ (molamin) 1.44 4.65 7.06 17.1 70.3 1.75 9.71 9.95 101 61.4
E , J/mol
2.1
5.8-13 2.8-7.9 1.3-4.5 0.31-2.4 0.11-0.39 0.12-0.27 0.11-0.42 0.94-1.8 3.6-9.3 5.8-10
X
X
lo-' m sum of the squared residuals
1.81 x 1.44 X 4.53 x 4.35 x 4.81 X 7.00 X 1.22 x 1.60 X 5.03 X 1.64 X
105 104 lo5 lo5
lo5 105 105
105 lo4 105
.
100
I 0 03
lo-'
10-2 10-2
lo-* 10-1
lo-'
IO-'
'Temperature-programmed reaction. Table 111. Arrhenius Parameters A , kg/(mobmin) compound p-BrC6H4COCH, 2.91 x 1013 4.62 X 10l2 p-BrC6H4CH0 1.72 X 10" o-BrC6H4N02 p-BrC6H4N02 1.28 X 10" 6.01 x 1015 BrC6H3(N02)2 8.07 x 1015 o-FC~H~NO~ o-IC~H~NO~ 7.09 X 10''
32
10-1
0 06
0 09
0 15
3 '2
E , J/mol 1.30 X s 1.17 X lo5 1.07 x 105 1.0sx 105 1.10 x 105 1.19 x 105 1.10 x 105
Individual Isothermal Experiments
t [OH.] (min-m)
Figure 3. Isothermal kinetics experiments for p-BrC6H4CH0
-5 g 10 . h
m
i 5 Y
1
1.75
1 .
!
I
1
I
I
1
10
20
30
'I0
51
1.80
1.85 1.90 1.95 1OOOR (K-' )
2.00
2.05
Figure 5. Comparison of Arrhenius plots of the isothermal and T P R techniques for p-BrC6H4CH0. 25:
Time (min)
Figure 4. T P R kinetic experiment for p-BrC6H4CH0.
comparison of speed and accuracy of the two techniques will focus largely on p-BrC6H4CH0. In addition, representative cases in which only T P R was used will be used to evaluate the technique. Isothermal data for p-BrC6H4CH0 experiments are shown on a semilog plot in Figure 3. This large quantity of experimental work, representing 5 experiments and nearly 4 days of reaction time, is in contrast to the T P R experiment shown in Figure 4, which yields the same information but lasted only 47 min. The goodness of fit shown in Figure 4 is typical of all TPR experiments in this study. Furthermore, the Arrhenius plots from T P R and isothermal data compare well (Figure 5). Our convention for plotting T P R results in Arrhenius form is to choose as the end points of the line segment the range of tempera-
10
I 175
I
I
I
I
180
185
190
195
2 00
1ooom (IC' )
Figure 6. Arrhenius plots for the two o-BrC6H4NOzTPR experiments.
tures over which the reaction took place, thereby denoting the range of applicability of the results.
Ind. Eng. Chem. Res., Vol. 28, No. 5, 1989 515 105
I
Table V. Estimated Measurement Errors in a Typical TPR Experiment std dev (in units of measure measurement or normalized, as noted) volume of acetic acid 0.4% mass of sodium bicarbonate 0.15% mass of water 0.1% mass of aryl halide 0.005 g sample collection time 5s temp 0.5 “C 2 70 Br- concn 100000
2.0
2.1
2.2
2.3
loO0rr (IC’)
i
Figure 7. Arrhenius plots for the three BrC6H3(N02)2TPR experiments. Table IV. Maximum Percent Differences in Reaction Rate Constant for Compounds in Which More Than One Experiment Was Conducted TPR 70 diff o-BrC6H4NO2 25 O-IC~H~NOZ 31 BrCRHJNOd? 64 isothermal reaction % diff p-BrC6H4COCH3 79 p-BrC6H4CH0 31
The results of the individual T P R experiments for oBrC6H4N02are shown in Figure 6. The two experiments agree well. However, Figure 7 shows the results of the individual experiments for BrC6H3(NOz)z,a compound for which the individual experiments did not agree so well. This is true even though the kinetic model fits the individual T P R experiments for BrC6H3(N0J2as well as the T P R experiments for any other compounds. In exploring the possible reasons for this discrepancy, we must distinguish between errors introduced by the T P R technique only and errors common to both TPR and isothermal reaction experiments. The latter is more likely, as shown in the following analysis. Table IV gives the maximum percent difference in the values of kll. For T P R results, this is the maximum percent difference between kll determined from different experiments, but only calculated for temperature ranges common to each of the individual T P R experiments. Therefore, compounds for which only one T P R experiment was performed are not covered in Table IV. For isothermal reaction results, Table IV shows the maximum percent difference between the least-squares line of the Arrhenius plot and the data point that deviated most from that line. Since isothermal and TPR maximum percent errors are similar, a large portion of the error probably resides in the experimental technique and solution-chemistry modeling common to both isothermal and TPR, rather than in the T P R technique itself. To further evaluate the propagation of errors, a Monte Carlo approach to error analysis was used. First, a theoretical experiment was simulated numerically assuming perfect measurement accuracy and precision. Next, estimates of the standard deviation of error for each laboratory measurement were made. To perform a Monte Carlo realization, error was simulated by randomly generating “experimental” data from the standard deviation of error. These synthetic data were then analyzed to determine the values of A and E for the realization. An Arrhenius plot of a large number of realizations provides an estimate of the overall error introduced by the individual measurement errors. Since BrC6H3(N02)z showed the most discrepancy in kll from one T P R experiment to
100
1I T
Figure 8. Actual TPR results compared to 100 realizations. Errors in the realizations are calculated from the standard deviation of error.
the next, our error analysis will focus on it. Table V shows the estimated absolute or percent error of each measurement in the experiment. Figure 8 shows 100 realizations of the Monte Carlo analysis, using the kinetics parameters for experiment BrC6H3(N0z)2-1 as the exact values. The spread in the simulated curves is similar in magnitude to that in the experimental results, suggesting that the experimental results are within the range expected. More reproducible results could have been obtained by improving the precision of the measurements listed in Table V, especially the concentration of each sample and the weight of the aryl halide charged to the reactor. Nonetheless, the measurements were accurate enough for our purpose, which was to screen potential reactive tracers for use in geothermal reservoirs. The Monte Carlo simulations also illustrate that the so-called compensation effect, often present in isothermal kinetics analyses, is also present in our TPR results. Due to measurement errors, the individual estimates of A and E determined may differ greatly from one experiment to the next, but estimation of the rate constant a t a given temperature is much closer. For example, the standard deviation for the activation energy in the Monte Carlo simulations is 8.3 kJ/mol, which on an absolute basis seems large. However, the combination of A and E determined in each simulation is such that the standard deviation of the rate constant at 184 “C is only 127 kg/(mobmin) or 5.9% of the rate constant at that temperature. Thus, as is generally the case with isothermal experiments, the TPR technique is best used to measure the rate constant in a given temperature range rather than to provide an exact measurement of the activation energy and preexponential factor. For comparison with the TPR error analysis just presented, a Monte Carlo simulation of a series of isothermal experiments was also carried out. For this experiment, the same measurement errors listed in Table V were used.
516 Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989 '13OCO
j
I
I
C3 "'^
I
I
"
I 0 3C24
1 T
Figure 9. Realizations showing the effect of experimental error on isothermal results. Errors are calculated from the standard deviation of error
Several six-data-point isothermal experiment simulations (the same number of data points as was used in the TPR realizations) were made at different temperatures to estimate the relative error of the rate constant measurement. Figure 9 is an Arrhenius plot showing the effect of experimental error on the isothermal experiment. At 184 "C, the standard deivation of error in the isothermal experiments is 5.4%, virtually identical with the error of 5.9% found for the T P R technique. Thus, for this reaction system, measurement techniques, and the particular set of error parameters chosen, the two techniques appear to provide similarly accurate estimates of the rate constant. However, we caution that this conclusion is specific to our kinetics study and may not be valid for other studies. Factors that might result in a clear-cut choice of the isothermal or TPR technique are as follows: 1. The type of error in the concentration measurement. In our study, since the concentration of the reaction product Br- was measured to follow the reaction progress, the absolute error in the calculated reactant concentration increased as the reaction proceeded. If the reactions had been measured directly, the error would have decreased with reaction progress, and the results of the error analysis might have been different. In fact, direct measurement of the reactant along with different criteria in comparing the isothermal and T P R realizations was used by Brown and Robinson (1986) when they concluded that, for a given number of data points, isothermal analysis is more accurate than TPR analysis. 2. The extent of reaction at the end of the experiment. We found this parameter to have a larger effect on the scatter of the rate constant estimates for the isothermal experiments than for the T P R experiments. Therefore, an error analysis such as the Monte Carlo study carried out here should be performed whenever a choice between the isothermal and T P R techniques must be made. A final possible source of error common to both the TPR and isothermal reaction techniques is occurrence of consecutive or competing reactions. The kinetic model shown in eq 7 is first order in [ArX] and [OH-]. Therefore, OHmust be positively identified as the nucleophile since the anions bicarbonate, acetate, and dissociated reaction product (Le., phenoxide ion) also exist in the reaction solution. Nebergall et al. (1980) give these relative nucleophilicities OH- > HC03- > Ac-
(11)
and Solomons (1978) gives these relative nucleophilicities
OH- > ArO- > Ac(12) for anions existing in the buffer solution. Hydroxide ion should dominate as the nucleophile over phenoxide, bicarbonate, and acetate ion. Analysis of the p-BrC6H4N02 and o-IC6H4N02experiments by using liquid chromatography verified that OH- was the dominant nucleophile. For p-BrC6H4No2,the reactant and product were positively identified, the mass balance was within the analytical precision of the instrument, and no unidentified peaks appeared in the chromatogram. For o-IC6H4NO2,one unknown peak was observed in the chromatogram, but its concentration was estimated to be well below 10% of that of m-nitrophenol, the dominant reaction product. Stock (1968) mentions that a side reaction of hydrolysis of chlorobenzene is the nucleophilic aromatic substitution involving chlorobenzene and phenoxide to produce diphenyl ether. Therefore, similar side reactions may be taking place to a limited extent in this study, but for the ortho- and para-substituted aryl halides studied, their effect was small. By contrast, an experiment with mBrC6H4NO2produced a chromatogram with about 10 unknown peaks by the end of the experiment. Clearly, kinetics analysis of this type of reaction system by simply monitoring [Br-] would be inappropriate. Discrimination of Reaction Order. The isothermal data of Figure 3 indicate a first-order reaction in [ p BrC6H4CHO]since the data fall on a straight line in the In C versus t[OH-] plot. To support this analysis, the data were also analyzed as zero order in [ArX] d[ArX]/dt = -k,,[OH-] and second order in [ArX]
(13)
d[ArX]/dt = -k21[ArX]2[0H-] (14) Plots of [p-BrC6H4CHO]versus t[OH-] for a zero-order reaction and l/[p-BrC6H4CHO]versus t[OH-] for a second-order reaction do not fall on a straight line, suggesting that the reaction is first order in [p-BrC6H4CHO]. In addition to providing a rapid method to determine kinetic parameters, the TPR technique should also provide a method to distinguish between kinetic models of different reaction order. To verify first-order dependence on [ArX] for TPR experiments, the optimal Arrhenius parameters for the zero- and second-order models were calculated by using nonlinear least-squares regression. Parts a and b of Figure 10 show that first-order dependence on [ p BrC6H4CHO] fits the data better than the zero- or second-order reaction assumptions. Although the data fits for the three models appear to be close, the zero- and second-order fits both exhibit significantly larger sumof-the-squares error and systematic deviations between the data and optimal fit. The sum of the squared dimensionless concentration residual is 1.8 X loW3for first-order, 4.5 X for second-order, and 2.1 X for zero-order dependence in the cases shown in Figure 10. In all TPR experiments, the sum of the squared residuals showed the reaction to be first order in [ArX], consistent with the assumed model. Thus, an added feature of the nonlinear temperature-rise T P R technique is the ability to distinguish between models of different reaction order. Verification of first-order dependence on [OH-] cannot be achieved in this manner since [OH-] is buffered by the reaction solution. To show first-order dependence, the rate law for zero-order dependence on [OH-] d[ArX]/dt = -k,,,[ArX] (15) and the rate law for second-order dependence on [OH-] (16) d[ArX] /dt = -k12[ArXl [OH-]*
Ind. Eng. Chem. Res., Vol. 28, No. 5, 1989 517
k12 resulting from the isothermal experiments (smaller [OH-]). Likewise, klo resulting from the TPR experiment is greater than kIo resulting from the isothermal experiments.
01
260
I
I
I
270
260
290
1 300
Temperature ('C) (8)
104
-
z-
102 100
t f
Acknowledgment
.
This work was carried out under the auspices of the U.S. Department of Energy, Geothermal Technology Division. We thank Lee F. Brown for providing a subroutine that found optimal Arrhenius parameters, Dale A. Counce and Patricio E. Trujillo, Jr., for analytical chemistry assistance, and Cheryl Rofer for her excellent review of this manuscript.
.
Second-Order In [OH.]
*
First-Oldel In [OH.]
Conclusions Reaction rates were measured for the alkaline hydrolysis of a variety of aryl halides. Relative reactivities for different substituent groups, group location, and species of halogen agreed with those expected for aryl halide hydrolysis. The reactions were also shown to have first-order depmdence on both aryl halide and hydroxide ion concentrations. Temperature-programmed and isothermal experiments were used to evaluate the kinetic parameters. The T P R experiments required shorter experimental time and fewer experiments, while retaining the ability to discriminate between correct and incorrect kinetic models. The nonlinear least-squares curve-fitting technique made the experiments much easier to carry out by eliminating the need to produce a linear temperature rise. Individual T P R experiments fit the kinetic model well, but disagreement between the results of different TPR experiments occurred. However, since error also existed in the isothermal reaction experiments, it cannot be attributed to the TPR technique. In fact, a Monte Carlo analysis of experimental errors showed that for this reaction system the isothermal and TPR techniques result in equally accurate estimates of the rate constant. However, this conclusion is specific to our reaction system; other studies using T P R should employ a similar error analysis to evaluate the technique.
-
Nomenclature - __
.
TPR Isothermal
A = preexponential factor, kg/(mol-min) ArX = aryl halide
10-6
175
165
195
205
1TT (K.' )
Figure 11. Zero-, first-, and second-order in [OH-] for T P R and isothermal analysis of pBrC6H4CH0.
were analyzed for the isothermal and T P R data for p BrC6H4CH0. The results of these models are shown in Figure 11along with the first-order results. The isothermal experiments of p-BrC6H4CHO-2and p-BrC6H4CHO-3were operated at essentially the same temperature, but their OH- concentrations differed by a factor of about 4 (Table 11). Comparison of klo, kll, and k12 for these experiments indicates that the reaction is first order in [OH-]. Comparison of the T P R results (p-BrC6H4CHO-6)with the isothermal results furthers this conclusion, since [OH-] for the TPR experiment was as much as 43 times greater than the isothermal experiment of lowest [OH-] ( p BrC6H4CHO-1). Furthermore, when modeled assuming a zero- and second-order dependence on [OH-], all experiments disagree with the model in a manner that is consistent with first-order behavior. That is, the k12 resulting from the TPR experiment (large [OH-]) is less than
C = dimensionless concentration E = activation energy k, = reaction rate constant for reaction order i in [ArX] and order j in [OH-], kg/(mol.min) R = universal gas constant, J/(mol.K) T = temperature, K X = halogen Registry No. p-BrC6H4COCH3, 99-90-1; p-BrC6H4CH0, 1122-91-4; o-BrCsH4N02, 577-19-5; p-BrC6H4N02, 586-78-7; BrC6H4(N02)2,584-48-5; o-FC6H4NO2,1493-27-2; O - I C ~ H ~ N O ~ , 609-73-4.
Literature Cited Birdsell, S. A.; Robinson, B. A. Prediction Of Thermal Front Breakthrough Due To Fluid Reinjection In Geothermal Reservoirs. Presented at Energy-Sources Technology Conference and Exhibition, New Orleans, Jan 1988. Breslow, R. Organic Reaction Mechanisms; W. A. Benjamin, Inc.: New York, 1965; p 149. Brown, L. F.; Robinson, B. A. Chem. Eng. Sci. 1986,41, 963. Falconer, J. C.; Schwartz, J. A. Catal. Rev. Sci. Eng. 1983, 25, 141-227. Koch, E. Non-Isothermal Reaction Analysis; Academic Press: New York, 1977; Chapter 3.
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I n d . Eng. Chem. Res. 1989, 28, 518-523
Morrison, R. T.; Boyd, R. N. Organic Chemistry, 3rd ed.; Allyn and Bacon, Inc.: Boston, 1975; pp 826-841. Matsuda, H.; Goto, S. Can. J . Chem. Eng. 1984, 62, 103-111. Nebergall, W. H.; Holtzclaw, 3. F., Jr.; Robinson, W. R. College Chemistry With Quantitatiue Analysis, 6th ed.; D. C. Heath and Company: Lexington, MA, 1980; p 360. Ortiz Uribe, M. I.; Romero Salvador, A.; Irabien Gulias, A. Thermochim. Acta 19858, 94, 323-331. Ortiz Uribe, M. I.; Romero Salvador, A.; Irabien Gulias, A. Thermochim. Acta 198513, 94, 333-343. Radhakrishnamurti, P. S.; Sahu, T. Indian J . Chem. 1974, 12(4), 370-372. Ritchie, C. D.; Sawada, M. J . Am. Chem. Soc. 1977, 99(11), 3754-3761.
Robinson, B. A.; Tester, J. W., submitted for publication in Int. J . Chem. Kinetics 1988. Robinson, B. A.; Tester, J. W.; Brown, L. F. SPE Reservoir Eng. 1988, 28(3), 227-234. Sohn, H. Y.; Kim, S.K. Ind. Eng. Chem. Process Des. Deu. 1980,19, 550-555. Solomons, T. W. G. Organic Chemistry, revised; Wiley and Sons: New York, 1978; p 649. Stock, L. M. Aromatic Substitution Reactions; Prentice Hall, Inc.: Englewood Cliffs, NJ, 1968; p 132.
Received for review May 31, 1988 Reuised manuscript receiued December 19, 1988 Accepted January 4, 1989
Unification of Coal Gasification Data and Its Applications K. Raghunathant and Ray Y. K. Yang* Department of Chemical Engineering, West Virginia University, Morgantown, West Virginia 26506-6101
Various research groups have reported that their char conversion versus time data from different experiments can be unified into a single curve when conversion is plotted against normalized time, t / t l j z ,where t l j 2is the half-life of the reaction, or time taken for 50% conversion of char. On the basis of two-parameter rate models, the grain model and the random pore model, unification curves ( x versus t / t I j 2 with ) one adjustable parameter are derived for each model. For coal gasification, each model parameter lies within a range, and for this range, the plotted unification curves lie close to each other u p to about 70% conversion. With the aid of correlations reported in the literature for unification curves, a master curve is derived to approximate conversion-time data from most gasification systems. With an extension of the unification approach, it is shown that for steam and C 0 2 gasification, the product of half-life and average reactivity is nearly a constant with a value of 0.38. Since half-life is simply related to the average reactivity, it can be directly used as a reactivity index for characterizing the char-gas reaction. In the absence of structural or kinetic data, half-life data a t a few temperatures can be used to predict char conversion up to 70% over a reasonably wide range of temperatures. When char particles are gasified, the solid undergoes changes in pore structure and surface area with conversion or time, depending on the gasification conditions. There have been many attempts to unify these dynamic changes through various normalizing parameters such as half-life, reactivity, or surface area (Mahajan et al., 1978; Chin et al., 1983; Adschiri and Furusawa, 1987). According to the unification approach proposed by Mahajan et al. (1978), char gasification curves in the form of char conversion x versus gasification time t for different temperatures, pressures, gasifying agents, and chars approximately reduced to a single curve when x is plotted against the dimensionless time -7, where -7 = t/t,,,, t I j z being the half-life of the char-gas reaction. Kasaoka et al. (1985) and Peng et al. (1986) have also unified their data successfully by using this approach. The objective of this paper is to present a detailed analysis of this normalizing scheme and discuss useful applications. In the following discussions, a set of conversion-time data, when approximated by a single x--7 curve, is referred to as the “unified data” and the x--7 curve as the “unification curve”.
Experimental Section Kinetic studies of the charsteam reaction were carried out in a TGA apparatus a t atmospheric pressure. The
* To whom correspondence should be addressed. ‘Present address: Department of Chemical Engineering, The Ohio State University, Columbus, OH 43210.
0888-5885/89/2628-0518$01.50/0
reaction was studied in the range 800-1200 “C for a North Dakota lignite. The chars were generated in situ by devolatilization in a steam-nitrogen atmosphere and were gasified in the same environment without interruption. The weight loss of the sample was continuously recorded on a microcomputer and analyzed. The mean particle size of the coal sample was 178 km, and the steam concentration was 76 mol 9’0. Details of the experiments are described by Peng et al. (1986). Only the conversion-time data from our experiments will be presented in this paper, and a more detailed analysis of the results can be found in Raghunathan (1988).
Correlations for Unification Curves Mahajan et al. (1978) correlated their data for four gasifying agents separately and together up to x = 0.7 using the cubic form x = AT
+ Br2 + Cr3
(1)
Kasaoka et al. (1985) observed that data from 19 different chars can be reduced to a single curve for steam and COP gasification. For each gasifying agent, they fitted a modified volume reaction model of the form x = 1 - exp(-ATB)
(2)
and reported good approximations up to high conversions. Peng et al. (1986) normalized their data at different temperatures for each of the six chars and obtained good correlations for the cubic form above. C 1989 American Chemical Society
