Ind. Eng. Chem. Res. 1999, 38, 1369-1375
1369
Kinetic Modeling of the Reaction between Hydrogen and Sulfur and Opposing H2S Decomposition at High Temperatures Norman I. Dowling* and Peter D. Clark Alberta Sulphur Research Ltd., c/o Chemistry Department, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4
The results of the previously reported kinetic study of the reaction between H2 and sulfur, H2 + 1/2S2 ) H2S, under Claus furnace conditions (Dowling; Hyne; Brown. Ind. Eng. Chem. Res. 1990, 29, 2327), have been reevaluated using a more rigorous analysis. The results of this reinvestigation were found to be consistent with a reversible kinetic model based on the rate expressions, -rH2 ) kr[H2][S2] and -rH2S ) kd[H2S][S2]1/2, for the H2/S2 recombination and H2S decomposition reactions, respectively. The kinetic parameters derived for these rate processes, over the studied temperature range from 600 to 1300 °C, were found to be as follows: Arecomb ) 3.46 × 106 m3/(mol.s), Ea,recomb ) 131.3 kJ/mol; Adecomp ) 2.26 × 109 m3/2/(mol1/2.s), and Ea,decomp ) 216.6 kJ/mol. This model has been shown to accurately predict the results of other published kinetic studies on H2S decomposition as well as equilibrium predictions for the system, H2S/ H2/Si (i ) 2-8), based on free energy calculations. A free-radical mechanism involving an initial bimolecular step between H2S and S2, as opposed to unimolecular decomposition, is put forward to account for the new form of the H2S decomposition rate expression. Introduction Studies on the noncatalytic thermal decomposition of H2S1-4 and the reverse reaction between H2 and sulfur5-7
H2S a H2 + 1/2S2
(1)
have been reported by a number of researchers in the literature. These studies have extensively examined the kinetics of this equilibrium system from both the forward and reverse reaction directions, over a wide temperature range. Recent studies have also cited interest in the kinetics of these processes at higher temperatures, as it relates to thermal cracking of H2S,8,9 and modeling of the Claus reaction furnace10 and associated waste heat boiler.11 Despite this type of scrutiny within the literature, the reported studies, so far, have failed to provide a unified picture of the overall kinetics within this system, often yielding conflicting results even as to the form of the rate expressions. In particular, Darwent and Roberts1 claimed a secondorder dependency on H2S for the rate of the decomposition reaction, whereas both Raymont2 and, more recently, Adesina et al.4 have suggested first-order kinetics. In their study of noncatalytic H2S decomposition, Kaloidas and Papayannakos3 also provided a reversible kinetic treatment of the system. These authors, however, implicitly relied on the available kinetic models within the literature. For their model they chose to use first-order kinetics for the H2S decomposition reaction and a form, -d[H2]/dt ) k[H2][S2]1/2, for the rate expression of the reverse H2/S2 reaction first proposed by Aynsley et al.6 at lower temperatures, containing terms first order in H2 but half-order in S2. More recently, the reverse reaction involving H2 and S2 was extensively studied by Dowling et al.,7 over the temperature range from 600 to 1300 °C. They reported * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: (403) 284-2054.
an experimental rate expression for this reaction different from that used by Kaloidas and Papayannakos. The form of the rate expression given by these authors was as follows, -d[H2]/dt ) k[H2][S2], containing terms first order in both H2 and S2. As part of this study a reversible kinetic treatment of the system was also performed that included the assumption of strict firstorder kinetics for H2S decomposition and pseudo-firstorder behavior for the H2/S2 reaction under the conditions of the study. In light of the apparent lack of agreement on the kinetics of this system evident within the literature, a reevaluation of the kinetic data for the H2/S2 reaction reported in the study by Dowling et al.7 was undertaken. In so doing the scope of the current study, was to implement a more rigorous reversible kinetic model as well as to utilize a more robust data regression technique than originally available. As part of the study, a comparison of the model with available reported kinetic data for the H2S decomposition reaction as well as free energy based equilibrium calculation predictions would also be undertaken in order to establish the validity of the model. Experimental Section Data Set and Reactor Temperature Profiles. The experimental data set previously reported by Dowling et al.7 and reproduced in Table 1 was used as the basis for all of the kinetic modeling experiments performed in this study. Details of the experimental design used in this work have been fully reported, including the essential nonisothermal reactor design imposed by the experimental furnace. To improve the accuracy of the modeling, measurement of the actual temperature distribution along the length of one of the reactors was also performed to more accurately define the nonisothermal reaction temperature profile. These measurements were carried out under nonreactive flow conditions (500 mL/min argon) in a 1.0 cm i.d. reactor using
10.1021/ie980293t CCC: $18.00 © 1999 American Chemical Society Published on Web 03/12/1999
1370 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 1. Analyzed H2 Concentrations in the Exit Stream and Calculated % H2 Consumption Valuesa for the Reaction of H2 with Sulfur Vapor reactor tube diameter 0.2 cm
0.4 cm
0.6 cm
1.0 cm
hot-zone temp, °C
mol % exit
% H2 consumption
mol % exit
% H2 consumption
mol % exit
% H2 consumption
mol % exit
% H2 consumption
602 702 815 930 1038 1146 1290
0.94 0.93 0.91 0.78 0.47 0.35 0.41
0.0 1.2 3.7 16.8 50.0 62.4 56.6
0.93 0.88 0.77 0.44 0.22 0.29 0.31
1.3 6.2 17.6 52.8 76.9 69.5 66.5
0.90 0.83 0.61 0.19 0.19 0.23 0.24
4.6 12.2 35.6 79.9 79.9 76.1 75.0
0.78 0.58 0.18 0.08 0.11 0.13 0.14
17.2 38.7 80.8 91.1 88.4 86.1 85.0
a Initial inlet H concentration ) 0.94 mol %. % H consumption ) [(mol % H inlet - mol % H exit)/mol % H inlet] 100. (Dowling et 2 2 2 2 2 al., 1990.)7
a retractable 0.5 cm o.d. S-type thermocouple, to a resolution of 2.5 cm over the entire length of the furnace. The experimental temperature profiles obtained in this manner at nominal hot-zone settings of 815 and 1146 °C were used to estimate the remaining profiles at the other hot-zone temperatures. This was done by simple projection from the measured data for the middle hot-zone section of the reactor. This procedure was based on the similar profile observed in this region relative to the actual furnace hot-zone setting for the two experimentally determined profiles. For the end zones of the reactor, the estimated profiles in these regions were obtained by proportional extrapolation from the measured data, again using the actual hotzone settings. While this approach is not as ideal as attempting to directly measure the reactor profiles at all hot-zone settings, it does, nonetheless, retain the basic semblance of a nonlinear temperature profile within the various sections of the reactor. This represents an improvement over the simplified assumption of a true isothermal hot-zone section and linear profile within the ramp-up and cool-down zones of the furnace. All of the temperature profiles determined in this manner were regressed to separate Gaussian fits of the form
y ) a0 + a1 exp(-0.5((x - a2)/a3)2)
(2)
for each of the ramp-up, hot-zone, and cool-down sections of the reactor for use in the modeling. Model Development. A discrete element approach was adopted in implementing the model as a spreadsheet-based solution. The model itself was implemented as a set of separate calculation modules for simulating the extents of reaction for the complete data set reported in Table 1, under the experimental conditions used, by adjusting the kinetic parameters for both the H2 + S2 and H2S decomposition reactions. The model calculations were based on a plug flow assumption12 and the nonisothermal temperature profile of the reactor. Use of the plug flow assumption was checked and shown to be justified by the type of nondimensional group analysis reported by Cutler et al.12 This type of analysis which is designed to judge the validity of the plug flow idealization to kinetic analysis of tubular flow reactor data showed that, in general, the criteria were well met for all of the reactors despite the low Reynolds numbers. While the criteria for assumption of negligible Poiseuille flow was not found to be completely satisfied at the highest temperatures for the largest (1.0 cm i.d.) reactor used, even in this case satisfactory criteria were achieved once the temperature was lower than 1000 °C.
The basic function of the model was executed by calculating the overall rate of disappearance of H2 as a function of the nonisothermal temperature profile along the reactor length. The model was operated at constant pressure based on the open tubular reactor design with all species concentrations being expressed in mole/m3. Starting concentrations were based on the adjusted feed composition following sulfur pick-up of H2 0.87 mol %, sulfur vapor 7.4 mol % (expressed as S2), and Ar 91.73 mol % at an inlet flow of 500 mL/min and reactor pressure of 0.88 atm (ambient barometric conditions). Initial and final concentrations of all species, H2S, H2, S2, and Ar, were explicitly calculated within each successive element down the length of the reactor while allowing for the effects of molar changes due to reaction and temperature difference between successive elements. Data Regression. The model just described was used to regress the Arrhenius preexponential factors, A, and activation energies, Ea, of both reactions by minimizing the objective function n
(1/n)
(Xj - X h j)2 ∑ j)1
(3)
where n is the number of experimental runs and Xj and X h j are the experimental and calculated extents of reaction for the jth run. The regression was performed using the Solver utility provided as an add-in in Microsoft Excel while utilizing a stepping function to guide successive choices for the initial parameter selection. This function was implemented as a separate Visual Basic for Applications code module fully automating the solution process. Two types of data regression were examined using this solving routine based either solely on the fit to the experimental data set in Table 1 or including an additional equilibrium constraint. The latter constraint was imposed on the solution to the model by additional calculation modules that simulated the equilibrium extent of reaction starting from the same initial feed conditions for a choice of temperatures within the range examined. The form of the objective function shown in eq 3 was modified in these cases to also include the difference between the theoretically calculated and model-based equilibrium extents of reaction. Results and Discussion Kinetic Model Investigations. The base set of models for H2S decomposition/H2 + S2 recombination
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1371
considered in this work were all based on the experimental kinetic rate law for the H2 + S2 reaction of the form
-rH2 ) kr[H2][S2]
(4)
first reported by Dowling et al.7 A series of empirical reversible kinetic models were investigated on this basis by choosing various forms for the H2S decomposition rate expression which corresponded to either strict firstorder, kd[H2S], or second-order, kd[H2S]2, dependencies as well as the mixed H2S and S2 dependencies, kd[H2S][S2]1/2 and kd[H2S][S2]. The individual models studied therefore corresponded to the overall form
-rH2 ) kr[H2][S2] - kd[H2S]R[S2]β
(5)
for opposing reactions, where R and β represent the kinetic orders with respect to H2S and S2 respectively for decomposition of H2S. For all of the models investigated regression provided a set of kinetic parameters that were consistent with the experimental H2 + S2 reaction data in Table 1 as well as equilibrium predictions for the specific experimental system. These models, however, could be differentiated on the basis of their behavior with respect to consistency, in general, toward equilibrium for the H2S/H2/S2 system. Hence, investigation of all of the models in terms of equilibrium behavior for the system, showed that only the overall form of the rate expression
-rH2 ) kr[H2][S2] - kd[H2S][S2]1/2
(6)
containing the half-order term in S2 for the decomposition rate law was generally consistent with the predictions of equilibrium. Regression of this model provided values for the kinetic parameters of the H2/S2 recombination process over the 600-1300 °C temperature range as Arecomb ) 3.46 × 106 m3/(mol.s) and Ea,recomb ) 131.3 kJ/mol, and corresponding H2S decomposition rate parameters as Adecomp ) 2.26 × 109 m3/2/(mol1/2.s) and Ea,decomp ) 216.6 kJ/mol. The difference of 85.3 kJ/mol between the activation enthalpies determined by this model, is in excellent agreement with the relationship
∆HR = ∆Hqdecomp - ∆Hqrecomb ) 84.8 kJ/mol (7) where ∆HR corresponds to the standard enthalpy of H2S dissociation. The correlation between this model and the experimental H2 consumption values in Table 1, for the given parameters, is clearly shown in Figure 1. It should be noted that the temperature displayed along the abscissa in this plot corresponds only to the set hot-zone temperature and that the observed H2 consumption is associated with a very specific temperature profile within the experimental reactor. Nonetheless, this figure shows the significant correlation (coefficient 0.992) between experiment and the proposed reversible kinetic model that can be obtained by actual simulation of this temperature profile. The high-temperature region of the curves in Figure 1 also deserves some comment. The reported H2 consumption values beyond equilibrium in this region, shown by the dotted equilibrium consumption curve, is due to reaction between H2 and sulfur during slow
Figure 1. Correlation between experimental H2 consumption values and model predictions for the kinetic model, -rH2 ) kr[H2][S2] - kd[H2S][S2]1/2.
quenching of the gases leaving the furnace. This provides sufficient time for the H2/S2/H2S equilibrium to readjust within the cool-down zone of the reactor, causing H2 consumption to increase relative to the equilibrium conditions established within the hot-zone of the furnace. Equilibrium Predictions of the Model. For the form of the H2S dissociation equilibrium shown in eq 1, the equilibrium constant expression for the reaction is given as
Keq )
[H2][S2]1/2 [H2S]
(8)
It follows from the general restriction imposed on the rates for the forward and backward reactions by the limiting condition of equilibrium, which can be stated as13,14
vf (H2S,H2,S2) vb(H2S,H2,S2)
[
) Keq
[H2S] [H2][S2]
]
z
1/2
, where
kf ) Keqz kb (9)
where vf and vb are the forward and backward reaction rates respectively, and are some function of concentration terms, that the proposed forms of the rate expressions in the model satisfy this condition shown by
vd kd [H2S][S2]1/2 kd [H2S] ) ) (for z ) 1) (10) vr kr [H ][S ]1/2 kr [H2][S2] 2 2 where subscripts d and r have been substituted for f and b in the general expression. To properly validate the model, a series of consistency checks against the required equilibrium behavior for the system were also run. The overall decomposition of H2S was investigated by obtaining the equilibrium conversions for a series of H2S/N2 mixtures as a function of initial composition, temperature, and pressure by free energy minimization calculations and comparing to the corresponding conversions obtained by the model. Since
1372 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 2. Comparison between the Kinetic Model and Experimental H2S Decomposition Data Reported by Kaloidas and Papayannakos at 740-860 °C3 H2S conversion Tma (°C)
P (atm)
104FOb (mol/s)
exptl (%)
model (%)
740 860 740 860
1.28 1.28 2.96 2.96
1.2 1.1 1.5 1.6
0.3 3.3 0.6 4.7
0.02 2.8 0.12 5.3
a T ) maximum in furnace temperature. b F ) molar feed m O flow rate.
Figure 2. Comparison of free energy and kinetic model based equilibrium H2S conversions.
the rate expression used for decomposition of H2S in the model also contains a half-order term in [S2], this meant that some small nonzero value must be initially assigned to this concentration if the model is to operate properly. The model itself, however, remains relatively insensitive to this initial choice for values of 1 × 10-6 mol % or less. The physical significance of this term in the rate law for H2S decomposition must be interpreted in terms of a separate induction period mechanism in order to account for the initial appearance of S2. Such a mechanism has already been proposed by others working in this area based on unimolecular decomposition of H2S with initial H-S bond fission3,4 or S atom elimination15-17 as the rate-controlling step. The results of this comparison between the free energy calculated equilibria and kinetically based steadystate conversions for H2S decomposition are shown in Figure 2. These plots demonstrate the necessary correlation between the theoretical equilibrium conversions for the system and corresponding kinetically based values, fully validating the model with respect to equilibrium behavior. Correlation with Other Kinetic Studies. A similar comparison has also been made between reported kinetic data and the current model on the basis of several of the published studies on the noncatalytic thermal decomposition of H2S. These comparisons provide a further crucial test for the validity of the model in terms of accurately predicting the observed kinetic behavior. Experimental conversions for a pure H2S feed over the temperature range from 740 to 860 °C at pressures of 1.28-2.96 atm were afforded on the basis of the study performed by Kaloidas and Papayannakos.3 Reported conversions from this work were obtained as a function of the molar feed flow rate, and the model was also modified to reflect the nonisothermal temperature distribution along the length of the reactor. More recently, the available kinetic data on decomposition of H2S was extended to even higher temperatures by the study of Hawboldt et al.10 These authors reported results over the temperature range from 850 to 1150 °C and residence times from 0.09 to 1.24 s, in a 2.25
Figure 3. Correlation between the experimental H2S decomposition data of Hawboldt et al.10 and corresponding model conversions.
mol % H2S, balance N2, system, under essentially 1 atm of pressure and isothermal conditions. Comparisons between the model and reported data from these studies were performed by using the model to simulate the appropriate experimental system and conditions in each case, with the results shown in Tables 2 and 3, respectively. Comparison with the results of Kaloidas and Papayannakos in Table 2 shows that the model provides a reasonable fit to the experimental data at the highest conversions reported by these authors, on the order of 3-5%, although agreement is less satisfactory at the very low conversions reported in some of the experiments. The low overall experimental conversions in this study reflect the lower temperatures used. The corresponding comparison with the more extensive data set of Hawboldt et al. in Table 3 however provides somewhat more convincing support for adopting the current model. Both the reported experimental results and corresponding conversions from the model are plotted in Figure 3. The residence times quoted by these authors are for the actual time spent by the gases at temperature under the near-isothermal design of their system. Details of the experimental setup in terms of reactor design and inlet and quenching of the gases are provided by Hawboldt et al.10 Inspection of Figure 3 shows that the model provides a reasonable match to the experimental data over all of the reported conditions (correlation coefficient 0.996). Actual differences between the data sets at lower temperatures and hence conversions, where experimen-
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1373 Table 3. Comparison Between the Experimental Results of Hawboldt et Al.10 and the Kinetic Modela 850 °C residence time (s) 0.12 0.25 0.54 0.77 1.24 a
950 °C
% H2S conversion exptl model 0
