Ind. Eng. Chem. Res. 1987,26, 1395-1399
1395
this research was provided by the Office of Fossil Energy, US.Department of Energy, Morgantown Energy Technology Center. Registry No. Pd, 7440-05-3;COO,1307-96-6;MOO,, 1313-27-5; NiO, 1313-99-1; W 0 3 , 1314-35-8; Fe203, 1309-37-1; bauxite,
verting coal tars in the presence of simulated coal gas from a fBed-bed coal gasifier at 450-690 "C and 1010-1818 P a . Coke is the primary product, and periodic regeneration is required to maintain catalyst activity. Hydrocracking catalysts containing CoMo, NiW, or Pd reduced coke yield but lost activity a t a rate similar to LZ-Y82. The activity of LZ-Y82 could be completely restored by regeneration with a 75% steam, 25% air mixture at 450 "C on 1010 kPa. No permanent loss of catalytic activity was observed after five regeneration cycles. Higher regeneration temperatures resulted in some permanent catalyst degradation. The level of tar conversion required is not known and will likely vary depending on the application. The more severe the tar removal requirements, the more often regeneration will be required. Regeneration of the tar removal catalysts can be done in conjunction with hightemperature desulfurization sorbents. Development of a catalyst which would increase the gas yield from tar conversion at the expense of coke would reduce deactivation, increase conversion, reduce regeneration requirements, and increase the energy recovery from the tar. Nickel and iron catalysts have been shown to be effective for converting aromatics to gas in sulfur-free environments (Tamhankar et al., 1985; Stern, 1982; Baker and Mudge, 1984). In-bed desulfurization of coal using calcium-based sorbents is being studied (Cicero et al., 1986), and nickel- and iron-based catalysts may be effective for tar conversion with desulfurized gas from these gasifiers. Development of an improved catalyst for use with high sulfur gas is more challenging. The catalyst has to have cracking activity and a sulfur tolerant hydrogenation component. Sulfur tolerant methanation catalysts based on molybdenum are being developed (Happel et al., 1986), and they may have application in tar conversion.
1318-16-7; quartz, 14808-60-7.
Literature Cited Appleby, W. G.; Gibson, J. W.; Good, G. M. Ind. Eng. Chem. Process Des. Deu. 1962, 1, 102. Baker, E. G.; Mudge, L. K. J. Anal. Appl. Pyrolys. 1984, 6 , 285. Cicero, D. G.; Jain, S. C. paper presented at the American Chemical Society Symposium on High Temperature Fuel Gas Cleanup, Sept 8-13, 1985, Chicago, IL. Cicero, D. C.; Halow, J. S.; Jain, S. C. Chem. Sep. Deu. 1986,2, 175. Choudhary, N.; Saraf, D. N. Ind. Eng. Chem. Prod. Res. Deu. 1975, 14, 74. Crynes, B. L. "Processing Coal Liquefaction Products", In Chemistry of Coal Utilization; Ed.; Elliott, M. A., Wiley: New York, 1981; 2nd Suppl. Vol., p 1991. Ellig, D. L.; Lai, C. K.; Mead, P. W.; Longwell, J. P.; Peters, W. A. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 1080. Flinn, R. A.; Larsen, 0. A.; Beutner, H. Ind. Eng. Chem. 1960,52, 153. Happel, J.; Yoshikiyo, M.; Yin, F.; Otarod, M.; Cheh, H. Y. Ind. Eng. Chem. Prod. Res. Deu. 1986,25, 214. Haynes, H. W.; Parcher, J. F. L.; Helmer, N. E. Ind. Eng. Chem. Process Des. Deu. 1983, 22, 401. Janardanarao, M. Ind. Eng. Chem. Prod. Res. Dev. 1982, 21, 375. Kertamus, N. J.; Woolbert, G. D. Energy Sources 1976, 2, 203. Nace, D. M. Ind. Eng. Chem. Prod. Res. Deu. 1970,9, 203. Pater, K.; Headley, L.; Kovach, J.; Stopek, D. "Fixed-Bed Gasifier and Cleanup System Engineering Summary Report Through Test Run No. loo", DOE/METC/84-19, 1984; Morgantown Energy Technology Center, Morgantown, WV. Qadar, S. A.; Hill, G. R. Ind. Eng. Chem. Process Des. Deu. 1969,8, 450. Stern, E. W. "Bench-Scale Development of Catalysts for Reforming Aromatic and Heterocyclic Hydrocarbons", DOE/ET/ 11029-1191, 1982; Engelhard Corporation, Edison, NJ. Tamhankar, S. S.; Tsuchiya, K.; Riggs, J. B. Appl. Catal. 1985, 16, 103. Wen, W. Y.; Cain, E. Ind. Eng. Chem. Process Des. Deu. 1984, 23, 627.
Acknowledgment We are indebted to Gary L. Roberts who conducted the experiments. We also thank Suresch C. Jain and V. P. Kothari of METC for their support. Financial support for
Received for review May 12, 1986 Accepted March 31, 1987
Prediction of Upper Flammability Limit by a Group Contribution Method M a r t i n S . High and Ronald P. D a n n e r * Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
A group contribution method has been developed to predict upper flammability limits of pure compounds. T h e method is applicable to many families of compounds which can be constructed from the group building blocks described in this paper. A companion procedure is described to calculate the confidence range of the predicted upper flammability limit. Flammability limits are important variables to consider when designing chemical processes involving flammable materials. The upper flammability limit is defined as the highest concentration of a flammable material in a gaseous mixture with air that is able to propagate flame in the presence of an ignition source. The lower flammability limit is analogously defined as the lowest concentration that will propagate flame. Both of these quantities are commonly reported as the volume percent or volume 0888-5885/87/2626-1395$01.50/0
fraction of the flammable component at 298 K. Experimental values of physical properties are the most accurate and should always be preferred over estimated values for design purposes. Experimental values of upper and lower flammability limits have been compiled by Daubert and Danner (1985). Unfortunately, experimental data are scarce and expensive to obtain. When experimental values are unavailable and determining them by experimental means is not practical, prediction methods 0 1987 American Chemical Society
1396 Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 Table I. Group Contributions for Proposed Prediction Method for Upper Flammability Limit i erouv h; 1 erouD h; 1 13 -0.8153 -0.9307 c1 CH, 14 1.311 -0.5225 2 2c1 CH, CH 15 3C1 -2.011 3 0.0 c 4 0.0 F 0.0 16 H 17 5 -0.5625 2F 0.0 OH 18 6 0.0 3F 0.0 0 1.458 19 7 n-Br 0.0 c=o 0.0 0.0 20 8 NH2 COOH 21 C=N 0.0 0.0 9 c=c 1.118 0.0 22 N 10 11 c=c 0.0 4.275 23 NO, 12 24 C(O)=O 0.0 Ca ring 0.0 Table 11. Comparison of Prediction Methods for Upper Flammability Limit method Nuzdha proposed no. of compds 117 181 av bias, vol % -5.9 -1.6 av % bias -2.2 8.3 max bias, vol % -88.9 -90.0 av abs. error, vol ’7~ 7.5 4.8 av abs. 7 G error 39.5 26.4
must be used to estimate the quantity. Reasonably accurate methods are available to preduct the lower flammability limit (Shebeko et al., 1983b).
Prediction of Upper Flammability Limits A few methods are available for the prediction of upper flammability limit. Nuzdha et al. (1979), Zabetakis (1965), and Shebeko et al. (1983a) proposed prediction methods. Zabetakis’s method is based on the stoichiometric amount of air needed to completely burn the flammable component and the Shebeko method is a group contribution method. In our initial study the methods of Zabetakis and Shebeko et al. were found to be very inaccurate with average errors of 8.2 and 7.6 vol 70,respectively. Nuzdha’s method uses the equation 4” = A e~p(-0.15t’/~) (1) where e is calculated from the expression t = ( N , - 1)4.93 + Miso (2) Nuzdha refers to t as the “energy of formation of the carbon skeleton”. The first term in eq 2 accounts for the formation of the n-alkane containing n carbon atoms. The second term corrects for branching and multiple bonds present in the compound of interest. This definition is ambiguous and leads to difficulty in calculating AHisofor
some compounds. It is not clear what structure has an energy of formation of t. A in eq 1is calculated by a group contribution method using the equation A = c + XAA, (3) where AA is the contribution for group i. The parameter A takes into account effects of functional groups in the upper flammability limit, but these functional groups also contain portions of the carbon skeleton. We assumed that AHisois the difference between enthalpy of formation of the branched hydrocarbon with the same structure as the compound of interest and the enthalpy of formation of the n-alkane with the same number of carbon atoms. A is then intended to correct for the functional groups added to this branched hydrocarbon. This interpretation can also lead to difficulties as, for example, in the case of ethers. An n-alkane can be identified with the same number of carbon atoms as the ether, but a hydrocarbon does not exist that has the same structure as the ether because of the 0 group. An evaluation of the Nuzdha method was carried out by comparing estimates calculated from the Nuzdha method with experimental values for 117 compounds listed in Daubert and Danner (1985). This method predicted upper flammability limit with an average error of 7.5 vol %. There were cases, however, where the method was in error as much as 88.9 vol %. The purpose of this work was to develop a group contribution method to predict upper flammability limit that is more accurate than Nuzdha’s method and can be applied to more classes of compounds with less difficulty. Equation 4 was developed to estimate the upper flammability limit from the structure of the compound:
4’ = exp(3.817 - 0.2627Nc + 1.02 X 10-2N:
24
+ Chi$i) i=l
(4)
Here hiis a group contribution as listed in Table I. $$is the fraction of all the groups in the molecule which are of type i. $ = - ni 24
i=l
(5)
n,
Equation 4 was chosen from a number of possible equation forms. Only equation forms that could be made linear in the regression parameters were chosen for reasons that will be discussed later. For these linear forms, a standard statistical computer package was used to analyze the significance of the regression parameters. It was found that the group fractions $iwere better independent variables
Table 111. Comparison between the Nuzdha Method and the Proposed Group Contribution Method for Prediction of Upper Flammability Limit (vol 70) method proposed Nuzdha exptl pred. pred. UFL UFL error UFL error methyl chloride 12.4 14.8 2.4 19.4 7.0 trans- 1,2-dichloroethylene 12.8 20.2 -7.2 7.4 5.6 ethyl chloride 15.4 13.2 -2.2 -1.5 13.9 2-chloropropene 16.0 16.0 0.0 -3.1 12.9 2-methoxyethanol 24.5 20.4 -4.1 12.9 -11.6 trans-crotonaldehyde 15.5 -0.9 14.6 -5.4 10.1 isobutyl alcohol 10.9 11.6 -0.2 10.7 0.7 ethyl propyl ether 11.4 9.1 2.4 9.0 0.1 aniline 11.0 11.4 9.1 -1.9 0.4 2,2-dimethylbutane 7.0 6.7 7.8 0.8 -0.3 5.7 3,3-diethylpentane 4.7 -1.0 0.3 6.0 n-decane 5.4 5.0 0.3 -0.4 5.7
Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 1397 Table IV. t Distribution Values for Various Confidence Limits (Bever. 1981)
2.576 1.960 1.645
99 95 90
than the number of group i in the compound; i.e., upper flammability limit could be correlated more accurately if the group fractions were used. Many of the group contributions in Table I are zero. Statistical treatment showed that these groups did not significantly influence the upper flammability and, thus, these group contributions should be zero. The value of the upper flammability limit estimate, however, will be affected by the presence of a group with a contribution of zero. The presence of any group makes the denominator in eq 5 larger and thus dilutes the effect of the groups with non-zero contributions. Most hydrocarbon and hydrocarbon derivatives can be treated with eq 4. The method is applicable to ring compounds as well as straight chain compounds. Sulfur-containing compounds are the most notable exceptions. Upper flammability limit data for sulfur compounds were too sparse to be included in the analysis. The proposed method does not require the ambiguous t as in the Nuzdha method. Values are not needed for the heat of formation of the n-alkane or the alkane homomorph. Example calculations are given in the Appendix. A comparison of the proposed method to the Nuzdha method is given in Table 11. The proposed method performs considerablybetter than the Nuzdha method. Some of the improvement is to be expected since the data used in the comparison were used to regress the group contributions for the new method. However, the proposed method is easier to use and can be applied to a larger number of families of compounds. Table I11 is a comparison of the two methods for several compounds. These compounds were chosen as representative members of several chemical families. Confidence Limits for Upper Flammability Limits We only considered models that could be made linear in the contributions so that standard statistical methods could be applied to the estimation of confidence limits. Upper flammability limits are difficult to predict, and the new method performs poorly on some compounds. Since the model can be made linear with respect to the group contributions, however, a confidence limit of the predicted value can be calculated. Thus, in addition to an estimate of the upper flammability limit, the range that contains the true value within a certain probability can be predicted. The lower and higher confidence limits are calculated from
+gW = In (+ired) - u.t(a) In &gh = In ($:red) + u.t(a) In
(6)
(7)
Values of t ( a ) for the 9070, 9570, and 99% confidence limits are given in Table IV. The standard deviation of the natural log of the predicted upper flammability limit is calculated from 12 12
u2 =
0.1544z C V,VjAij i=lj=1
(8)
where Aij is an 12 X 12 matrix of constants given in Table V. Vi is a vector with the 12 elements listed in Table VI. The 9;s in Table VI are the group fractions defined in eq 5. Equation 8 involves the double summation of the elements of the vector V and the matrix A. Vi is equal to
3 m 1 i N 3 3 N 1 1 3 3 Q Q Q Q Q Q O Q Q Q Q O
r l m m 3 1 3 N 3 3 1 3 3
Q Q O Q Q Q O O O O O O
1398 Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 Table VI. Elements of the Vector VTo Be Used in Confidence Limit Calculations VI = 1 v 5 = $2 v9 = $11 V, = N , v6 = $5 = $13 V , = NC2 v 7 = $7 VI, = $14 v 4
=
$1
V8 =
$10
VI, = $IS
Table VII. Confidence Range (95%) for Prediction of Upper Flammability Limits (vol % ) lower high exptl limit pred. limit methyl chloride 12.4 10.8 14.8 20.2 16.0 20.2 25.4 trans-1,2-dichloroethylenen 12.8 15.4 10.7 13.2 16.2 ethyl chloride 16.0 2-chloropropene 13.6 16.0 18.8 24.5 17.5 20.4 23.9 2-methoxyethanol" 15.5 12.8 14.6 16.6 trans-crotonaldehyde 10.6 11.6 12.8 isobutyl alcohol 10.9 9.0 9.8 11.4 13.1 ethyl propyl ether" aniline 11.0 7.3 9.1 11.4 7.0 2,2-dimethylbutane 5.8 6.7 7.6 3,3-diethylpentane 5.7 3.7 4.7 5.9 5.4 n-decane 4.1 5.0 6.1 a
Missed confidence range.
V, when i = j in the summation. Table VI1 gives the confidence limits for the compounds listed in Table 111. Three of the compounds have experimental upper flammability limits that do not fall within the calculated 95% confidence range. Only a t the limit of a large number of compounds will 95% of the experimental values fall within the confidence limits. The predicted value is used to calculate the high and low limit (cf. eq 6 and 7) and will always lie between the high and low limit. The upper range value of the UFL can be used for a more conservative design. In addition, the width of the confidence range can be used as a qualitative measure of the accuracy of the prediction. In general, the higher the carbon number of the compound, the more accurate the UFL prediction and the narrower the confidence range.
Conclusions We developed a group contribution method for the prediction of upper flammability limit. Even though this method is the most accurate method available, large errors sometimes occur. Since the upper flammability limit is an important parameter in the design of processes involving flammable compounds, it is valuable to be able to estimate the error in the predicted values. Therefore, we have also presented a method to calculate the confidence limits of the estimated upper flammability limit. If a more conservative estimate of the upper flammability limit is needed, the high confidence limit should be used. Acknowledgment We gratefully acknowledge financial support from the AIChE Design Institute for Physical Property Data during the course of this work. We thank T. Selover of SOH10 for his many helpful comments and suggestions.
Nomenclature A = preexponential factor for Nuzdha's method A, = matrix of constants defined in Table V AA, = group contribution for the preexponential factor in the Nuzdha method c = constant for Nuzdha method h, = group contribution for group i AH,8o= correction factor for carbon branching N , = number of carbon atoms n, = number of group type i
t ( a ) = value of the t distribution with confidence level a VI = vector defined in Table VI Greek Symbols t = energy of formation of the carbon skeleton 4" = upper flammability limit, vol % u
= standard deviation of the natural log of the predicted
upper flammability limit $, = fraction of groups of type i dUpred= predicted value of the upper flammability limit
Appendix. Example Calculations Example I. Calculate the upper flammability limit of toluene 1
n1 1 5 1
cs ring H CH3
$1
hl
117 517 __ 117
0.0 -0.5625 -0.9307
Note that only the carbon skeleton is considered in the benzene ring contribution. Five H groups must be added to complete the structure. There are seven carbon atoms in toluene, so N , = 7, N,2 = 49. By use of eq 4, the upper flammability limit is estimated to be 7.0 vol %. Tryon (1962) reported an experimental value of 7.1 vol %. To calculate the confidence limits for the upper flammability limit prediction, we identify the elements of the vector V t o be V2 = N , = 7
V, = 1 V4 =
$1
= 1/7
v, = $7
V5 =
$2
=0
v, = $10
Vi0 = $13 = 0
Vi1 = $14
V3 = N,2 = 49 V, =
=0 =0 =0
$5
v, = $11 Vi2 =
= 5/7
=0 =0
So there will be a contribution to the double summation only when i and j are equal to 1, 2, 3, 4,or 6. Also, the calculations are simplified by noting that A, = AJl. Then, 12 12
E
CA,V,V, = VI2A11 + VZ2Azz + V32A33 + V42A44 +
1=1 J = 1
V62A66 2V1VzA12 2VIV3A13 + 2V1V4A14 1V6A16 + 2V2VsA23 + 2VzV4A24 + 2V2V6A26 + 3V4A34 + 2V3VsA36 + 2V5Vp446 12 12
C C A,, V ,V, = 0.07043 1=1J=1
So, from eq 8 12 12
u2 =
0.1544Z C KV,AIJ= 0.01087 r=l]=l
So, u = 0.1042. For a 95% confidence limit t(0.95) = 1.960 (from Table IV). From eq 6 and 7, In dk,,, = In (7.0) - 0.1042(1.960) = 1.74
f$yow = 5.7 In
dXlgh
= In (7.0) + 0.1042(1.960) = 2.15 @kgh
= 8.6
Therefore, the 95% confidence range for the true value of the upper flammability limit of toluene is between 5.7 and 8.6 vol %. Example 11. Calculate the upper flammability limit of ethyl propyl ether 1
n,
$1
h,
CH3 CH, 0
2 3
216 3/6 1/6
-0.9307 -0.5225 1.458
1
Ind. Eng. Chem. Res. 1987, 26, 1399-1407
There are five carbon atoms in this molecule, so N , = 5. By use of eq 4,the upper flammability limit is estimated to be 11.4 vol %. Sax (1984) reported an experimental value of 9.0 vol 90. Example 111. Calculate the upper flammability limit of dimethylamine i
n,
$i
hi
CH, H
1 2 1
1/4 2/4 1/4
0.0 -0.9307 -0.5625
N
Two carbon atoms are in dimethylamine, so N , = 2. By use of eq 4, the upper flammability limit is estimated to be 15.3 vol %. Tyron (1962) reported an experimental value of 14.0 vol %. Registry No. Methyl chloride, 74-87-3; trans-1,2-dichloroethylene, 156-60-5; ethyl chloride, 75-00-3; 2-chloropropene, 557-98-2; 2-methoxyethanol, 109-86-4; trans-crotonaldehyde, 123-73-9; isobutyl alcohol, 78-83-1; ethyl propyl ether, 628-32-0; aniline, 62-53-3; 2,2-dimethylbutane, 75-83-2; 3,3-diethylpentane,
1399
1067-20-5; decane, 124-18-5; toluene, 108-88-3.
Literature Cited Beyer, W. H., ed. CRC Standard Mathematical Tables, 26th ed.; CRC: Boca Raton, FL, 1981. Daubert, T. E.; Danner, R. P. Data Compilation: Tables of Properties of Pure Compounds; American Institute of Chemical Engineers: New York, extant 1985. Nuzdha, L.; Glinkin, M. A,; Rafales-Lamarka, E. E.; Tyupalo, N. F. Soviet Chem. Ind. 1979, 11, 230. Sax. N. I. Dangerous Properties of Industrial Materials, 6th ed.; Van Nostrand Reinhold: New York, 1984. Shebeko, Y. N.; Ivanov, A. V.; Alekhina, E. N.; Barmakova, A. A.; Soviet Chem. Ind. 1983a, 15, 1203. Shebeko, Y. N.; Ivanov, A. V.; Dmitrieva, T. M. Souiet Chem. Ind. 1983b, 15, 311. Tryon, G. H., ed. Fire Protection Handbook, 12th ed.; National Fire Protection Association: Boston, 1962. Zabetakis, M. G. Estimating Techniques for Vapor Flammability; Bureau of Mines: Washington, DC, 1965; Bull. 627, Appendix B. Received for review April 3, 1986 Revised manuscript received March 26, 1987 Accepted April 10, 1987
A Kinetic Modeling Approach to the Design of Catalysts: Formulation of a Catalyst Design Advisory Program James A. Dumesic,* Beth A. Milligan, Leonard0 A. Greppi, Vijay R. Balse, K e n n e t h T. Sarnowski, C h a r l e s E. Beall, T a k u o Kataoka, a n d Dale F.R u d d Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706
A n d r e s A. T r e v i n o Shanahan Valley Associates, Madison, Wisconsin 53711
We describe an approach to catalyst design that allows the coordination, interpretation, and generalization of theoretical and experimental catalysis studies. Our approach allows for the rapid estimation of catalyst performance from reaction mechanism considerations and serves to direct the catalyst designer toward experiments which are likely to yield the catalytic properties sought. We apply the approach to two test catalyst design problems: that of predicting the reactions of n-hexane and hydrogen on platinum catalysts and that of predicting the conversion of methanol to olefins on a zeolite H-ZSM-5 catalyst. We also show how this simple approach forms the basis for a Catalyst Design Advisory Program capable of being implemented on a computer. Portions of the advisory program have been made available commercially and are being used in industry under the name of CATALYST 11. Background Heterogeneous catalysts are key components of many industrial chemical processes, such as ammonia synthesis, methanol synthesis, cracking of fuel oils to gasoline products, reforming of hydrocarbons to enhance combustion performance,polymerization, and partial oxidation of hydrocarbons. Despite the importance of these catalytic processes, the search for new catalysts or the improvement of existing catalysts has been empirical. Our current understanding of chemical processes occurring on solid surfaces is not yet sufficiently well developed to allow the design of heterogeneous catalysts without extensive experimental studies. This empirical search for new or improved catalysts, however, should be based on fundamental science. Before an experimental program is undertaken, it is important to determine its probability of success in terms of creating the desired catalytic properties. The purpose of the present paper is to formulate a methodology for the evaluation of catalyst performance that incorporates both chemical expertise and experimental work. 0888-5885/ 87 / 2626- 1399$01.50 / 0
A Modeling Approach to t h e Design of Heterogeneous Catalysts An important problem facing the designer of heterogeneous catalysts is how to coordinate, interpret, and generalize the results of experimental studies. The catalyst designer must assimilate the existing experimental data for a given catalytic process to predict how a new catalyst can be formulated or to improve the performance of an existing catalyst. Alternatively, the catalyst designer must extrapolate the results from studies of known catalysts and reactions for use in the generation and performance estimation of a catalyst for an entirely new chemical process. Here we propose a catalyst design approach based on a kinetic model of the reaction/catalyst system to be used in conjunction with experimental studies. Specifically, the performance of a catalyst is simulated by automated modeling of proposed chemical reaction mechanisms, and this modeling is then used in directing experimental work. It is through the combination of modeling and experimental studies that the kinetic model is altered and refined 0 1987 American Chemical Society
