Re = real part of the system transfer function s = Laplace transform variable t = time, sec t,v = time at which the response reaches steady state, sec T = system time,constant, sec r ( t ) = system input X ( s ) = Laplace transform of the input y(t) = systemoutput Y(s) = Laplace transform of the output Greek Symbols a = constants in the differentiation formula At = width of time interval between two data points, sec p = ensemble mean of the stochastic variable e ( t ) w = frequency, rad/sec Superscripts ', ", (i) = the derivatives * = deviation variable Subscripts i,k = arbitrary indices i l = presentwork i2 = previouswork
1 = major 2 = minor Literature Cited Carnahan, E., Luther, H . A., Wilkes, J. O., "Applied Numerical Methods," pp 128-130, Wiley, New York, N.Y., 1969. Clements. W. C., Jr.. Schnelle, K. B., Jr., lnd. Ens. Chem., Process Des. Dev., 2, 94 (1963). Filon, L. N. G., Proc. Roy. SOC.Edinburgh, 49, 38 (1928). Guillemin, E. A.. Proc. Nat. Electron. Conf., 10, 9 (1954). Himmelblau, D. M., "Process Analysis by Statistical Methods," pp 15-16, Wiley, New York. N.Y., 1970. Hougen, J. O.,Chem. Eng. Prog. Monogr. Ser., 60, No. 4 (1964). Hougen, J. 0.. Walsh, R. A.. Chem. Eng. Prog., 57, 69 (1961). Krishnaswamy, P. R., Shemilt, L. W., Can. J. Chem. Eng., 51, 680 (1973). Latour, P. R., Koppel. L. B., Coughanour, D. R.. lnd. Eng. Chem., ProcessDes. Dev., 6, 452 (1967). McCormick, J. M., Salvadori, M. G., "Numerical Methods in Fortran," pp 37-42, Prentice-Hall, New Delhi, 1968. Nyquist, J. K., Schindler, R. N., Gilbert, R. E., Chem. Eng. Prog. Symp. Ser., 59, No. 46, 98 (1963). Schechter, R. S . , Wissler, E. H., lnd. Eng. Chem., 51, 945 (1959). Stermoie, F. J., Larson. M. A., lnd. Eng. Chem., Fundam., 2, 62 (1963). Teasdaie, Jr., A. R., Control Eng., 2, 55 (1955).
Received f o r review June 13, 1974 Accepted January 22, 1975
Kinetics of the Methane-Steam Reaction D. W. Allen Girdler Chemical. lnc.. Louisville. Kentucky
E. R. Gerhard and M. R. Likins, Jr.*' Chemical Engineering Department, University of Louisville, Louisville. Kentucky
The reaction of methane and steam over a nickel catalyst in a fixed bed reactor has been studied. Conversion data at 1180°F, a steam to gas ratio of 3:l and six levels of pressure from 1.O to 18.0 atm were collected. These data have been correlated with a third degree polynomial and the initial reaction rates for metha-ne, carbon monoxide, and carbon dioxide were considered. Kinetic rate expressions were derived on the assumption that desorption of products was the rate-controlling step. This was found to give a reasonable representation of the data at atmospheric pressure.
Introduction The catalytic reaction of methane with steam is a n important industrial reaction. Usually the reaction is carried out using a catalyst consisting essentially of nickel deposited on some porous refractory carrier, such as alumina or silica. In spite of the reaction's importance, there has been little work done on the kinetics of the reaction. The reaction of methane and steam is a very complex reaction and a t least two primary reactions are required to predict all of the products. Among the many possible reactions are the following. CH,
+
HZO
CH, + 2HzO CO HZO CH, + COZ
+
CO COZ COZ 2CO
+
+
+
+
3Hz 4H2 H2 2Hz
(1) (21 (3) (4 )
Akers and Camp (1955) investigated the reforming reacAuthor to whom correspondence should be addressed at Applied AUtomation, Inc., Bartlesville, Okla. 74004.
256
Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 3, 1975
tion over a reduced nickel catalyst and concluded that both carbon monoxide and carbon dioxide were primary reaction products. They correlated their data with a simple first-order, gas-phase decomposition which cannot predict the formation of products. Y = kP,Hd (5) The most common assumption of the mechanism of the reaction is eq 1 followed by eq 3. This would indicate that only carbon monoxide is a primary product. Gerhard and Moe (1965) have presented calculations which indicate that the "shift reaction'.' (eq 3) is not at equilibrium and probably the reverse reaction is occuring. Their results indicate that eq 2 is occuring followed by the reverse shift reaction. Schnell (1970) has studied the steam reforming of a mixture of propane and butane over nickel catalysts. He concluded that first methane and low olefins and some hydrogen are formed followed by the reaction of methane and olefins with steam to form carbon dioxide and hydrogen and finally a slower establishment of equilibrium among the products. Shevtov and Al'tshuler (1967) stud-
f
Y
/ /
0.41
o.2E n---
0.00
Figure 1. Flow diagram of reactor apparatus: A, gas cylinder; C, condenser; F, rotameter; H, preheater; M, wet test meter; P, metering pump; R, reactor; w, water receiver.
ied the reaction of methane with a mixture of steam and carbon dioxide. They concluded that eq 1 and 4 and the reverse shift reaction are important above 1472°F. Volgina and Rozhdestvenskii (1969) studied the reaction of methane and steam on a sintered nickel monoxide catalyst in a fluidized bed using a steam to gas ratio of 2:l. They postulated that methane reacted first to form carbon dioxide. Bodrov et al. (1967, 1968) have published two articles on the reforming of methane. For a particular nickel a-alumina catalyst, they found that, in the range 752-1112"F, the rate of reaction was inhibited by the presence of hydrogen. In this range, their data could be correlated by the expression
2
4
I
8 10 T I M E FACTOR, W/F
6
.J
12
14
16
12
14
16
Figure 2. Conversion data, 1.0 atm.
A
-COP FORMED
-1 Y
p 0.2 0.
2
0
4
6 8 10 TIME FACTOR, W/F
Figure 3. Conversion data, 4.4 atm.
Above 1292"F, the rate of reaction is not inhibited by the presence of hydrogen. In this range, they correlated their data with the expression
A
- C O 2 FORMED
kpCH4
Y =
(7)
PC Hq
1 +a-
p9
+ bPco
They predicted a mechanism for this reaction based on the surface reaction between a chemisorbed oxygen atom and a chemisorbed CH2 radical.
I
0.0
0
2
4
6
8 1 0 T I H E FACTOR. W/F
12
14
16
Figure 4 . Conversion data, 7.8 atm.
Experimental Procedure For this study, analytical grade (>99%) methane and distilled water and a commercial nickel catalyst, Girdler G-56B, were used. The catalyst pellets were cylindrical, x 3hs in. The apparatus used is shown in Figure 1. Methane and water flow into a preheater, where vaporization occurs, and then into the reactor itself. The reactor consisted of a stainless steel pipe, 3/4 in. schedule 40, 2 f t long located in an electrically heated furnace. The reaction mixture leaving the reactor is cooled and unreacted water removed in a large expansion chamber. The gases were then sampled and vented to the atmosphere. Methane, carbon monoxide, and carbon dioxide were analyzed by gas chromatography. Unreacted water was collected and measured volumetrically; hydrogen concentration was found by difference. The exit dry gas flow rate was measured and compared to a calculated exit flow rate based on carbon balance. For all data points, the largest error was 23% while the average error was only 7%. Results The experimental results are shown in Figures 2-7. These figures show the conversions of methane in terms of
Figure .?I.Conversion data, 11.2 atm.
moles reacted per mole of methane in the feed and production of carbon monoxide and carbon dioxide in terms of moles formed per mole of methane in the feed. All of the data were collected a t 1180°F and a steam to gas ratio of3:1. These data were fitted to a third-degree polynomial by regression analysis. These constants are shown in Table I. Ind. Eng. Cham., Process Des. Dev., Vol. 14, No. 3, 1975
257
1. o
r-EXPERIMENTAL
E
o,8-
LL w
0.0
2
0
4
6 8 10 TIME FACTOR, W/F
12
14
16
"."
0
o-CH, REACTED A -COz FORMED
2
6 8 10 TIME FACTOR, b'F
4
12
14
16
Figure 8. Solution of kinetic model, 1.0 atm
Figure 6. Conversion data, 14.6 atm.
Reaction Mechanism Yang and Hougen (1950) have shown that the effect of total pressure can be important in determining the mechanism of a solid-gas reaction. The initiai rate of reaction is the constant C1 in Table I. This appears to be independent of total pressure which indicates that the overall rate is controlled by a step involving desorption of products. In the following mechanism, eq 8, 9, and 11 are assumed to be a t equilibrium and eq 10 and 12 are controlling the overall reaction.
-1
p 0.4-
0.0
0
2
4
6 8 10 TIME FACTOR, W/F
12 .
11 ,.
HzO(g)
16 ._
Figure 7. Conversion data, 18.0 atm.
HzO(g)
+
c0 -0.0037 -0.0024 -0.0013 0.0058 0.0007 0.0067 0.0083 0.0009 0.0074 0.0082 0.0009 0.0074 0.0076 -0.0004 0.0082 0.0066 -0.0028 0.0097
c1
1.0 atm 0.1877 0.0369 0.1508 4.4 atm 0.1934 0.0295 0.1592 7.8 atm 0.1896 0 -0265 0.1624 11.2 atm 0.1693 0.0198 0.1499 14.6 atm 0.1860 0.0249 0.1616 18.0 atm 0.1696 0.0299 0.1391
c2
c3
-0.0310 -0.0059 -0.0252
0.0019 0.0004 0.0015
- 0.0287
0.0034 0.00009 0.0013
-0.0024 -0.0253 -0.0255 -0.0011 -0.0242
0.0012 -0.00003 0.0012
-0.0277 -0.0007 -0.0271
0.0015 -0.00005 0.0016
-0.0356 -0.0031 -0.0327
0.002 2 0.0002 0.0021
-0.0300 -0.0042 -0.0256
0.0017 0.0002 0.0015
By application of a simple continuity balance, the rate of reaction can be shown to be the slope of these conversion curves. The rate of reaction is therefore indicated by the first derivative of these cubic equations. 258
Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 3, 1975
S
+=+ H2O.S
+ +s
CO'S e C02.S
CO2-s
Table I. Correlation of Conversion Data X = Co + Ci(T.F.) + Cz(T.F.)' + C3(T.F.)3
+
+ H20'S + COOS + co-s i CO(g) + s
CH,(g)
COz(g)
%==
3Hz(g)
(8) (9 1
(10) Hz(g)
(11) (12)
Applying the methods of Hougen and Watson (1943), the following rate equations may be derived.
Kpl and Kp2 are the normal thermodynamic equilibrium constants for eq 1 and 2 and may be evaluated independently. This model was solved and compared to the experimental data at 1.0 atm. Figure 8 shows that this model does give a reasonable representation of the data at 1.0 atm. Conclusion Conversion data for the reaction of methane and steam have been collected a t 1180°F and six levels of Dressure from 1.0 to 18 atm. These data were correlated with a cubic equation and the rate of reaction examined from the slope of these curves. A heterogeneous model for the reaction was presented on the assumption that the desorption
of carbon monoxide and carbon dioxide were controlling steps. This model gave a reasonable representation of the data at 1.0 atm.
W = mass of catalyst, g X = conversion, mol reacted/mol of feed
Nomenclature Co, C1, Cp, Cz = regression coefficients F = feed rate, mol/hr k = velocity constant, mol/hr g of cat. atm k' velocity constant, mol/hr g of cat. k l = velocity constant for eq 10 k p = velocity constant for eq 12 K , = equilibrium constant for eq 8 KD, = equilibrium constant for eq 10 KD, = equilibrium constant for eq 12 Kpl = equilibrium constant for eq 1 KP2 = equilibrium constant for eq 2 K s , = equilibrium constant for eq 9 K S z = equilibrium constant for eq 11 N = mol present/mol of feed P = partial pressure, atm r = rate of reaction, mol/hr g of cat. ro = initial rate of reaction, mol/hr g of cat. S = active site on catalyst surface T.F. = time factor, g of cat. hr/mol
Akers, W. W., Camp, D. P., AIChEJ.. 1,471 (1955). Bodrov, I. M., Apel'baum, L. O., Timkin, M. I . , Kfnet. K a t a l , 8, 821 (1967). Bodrov. I. M., Apel'baum, L. O., Timkin, M. I,, Kinet K a t a l . 9, 1065 (1 968). Gerhard, E. R., Moe, J. M., "Chemical Reaction and Heat Transfer Rates in the Steam Methane Reaction," AlChE Symposium, Fifty-sixth National Meeting, San Francisco, Calif., May 1965. Hougen. 0. A.. Watson, K . M., Ind. Eng. Chem.. 35, 529 (1943) Likins, M. R., Ph.D. Thesis, University of Louisville, Louisville, Ky.. 1970. Schnell, C. R., J. Chem. SOC.6.158 (1970). Shevtsov, V. P., Al'tshuier, V. S., Gazov. Protesessy. Poluch. Energ. Tekhnol. Gazov. Akad. Nauk. SSSR. Inst. Goryuch. I s k i p . , 140 (1967). Volgina, L. M., Rozhdestvenskii, V. R., Zh. Priki. K k i m . . 42, 2055 (1969) Yang, K. H., Hougen. 0. A,, Chem. Eng. Prog.. 46, 146 (1950).
Literature Cited
Received for recieu J u n e 19, 1974 Accepted January 13. 1975 This work was m a d e possible b y a grant from the N a t i o n a l Aeronautics a n d Space Administration. T h e authors wish t o t h a n k Girdler Chemical, Inc., for their generous support a n d assistance.
Two-Dimensional Recirculating Bed Data with Simulated Heat Transfer Surface in the Downcomers Wen-Ching Yang* and
D. L. Keairns
Research Laboratories, Westmghouse Electric Corporation. Pittsburgh. Pennsyivania 15235
Experimental data from a two-dimensional recirculating fluid bed with simulated heat transfer surface in the downcomers are presented. Mathematical models proposed earlier (Yang and Keairns, 1974) for the case without simulated heat transfer surface can also be applied here with a correction factor taking into account the presence of the simulated heat transfer surface in the downcomers. The accuracy of the correlations is f25% for the solid circulation rate, f 5 % for the pressure drop in the downcomer. Jet penetration depth can also be predicted reasonably well.
The recirculating fluid bed concept for industrial application has been presented previously (Yang and Keairns, 1974) along with data obtained in a two-dimensional recirculating bed df dimensions 8.5 X 1.5 in. For convenience, the schematic of the two-dimensional cold model is again shown in Figure 1. Air is fed into the base of an open draft tube section through an air jet nozzle. The superficial velocity of air flowing up the riser ranges between 20 and 40 ft/sec for the present experiments. The solids are picked up pneumatically in the draft tube and are then disengaged in a fluid bed of expanded cross-section above the draft tube. Solids from the fluid bed above the draft tube flow into the downcomers and enter the base of the draft tube again. This creates a solid circulation pattern upward through the draft tube and downward in the downcomer. Gas is introduced at the base of the down-
comer at a rate necessary to permit the downward flow of solids. A deep recirculating fluidized bed combustion boiler was conceived as an alternative to the proposed pressurized fluid bed combustion boiler concept which was evaluated under a contract to EPA (Keairns et al., 1973). In a recirculating fluid bed combustion boiler, combustion would take place in the draft tube. The heat generated from combustion is then carried away by the recirculating solids to the downcomers where the primary heat transfer surface for steam generation is located. The fluid bed above the draft tube can be used for sulfur removal when lime sorbents are used as bed material. In order to study the feasibility of this concept, the experimental two-dimensional unit was operated with and without simulated imbedded heat transfer surface in the downcomers. Ind. Eng. Chem., Process Des. Dev., Vol. 14, No. 3, 1975
259
