INDUSTRIAL AND ENGINEERING CHEMISTRY
March 1953
677
I
= intensity of turbulence, feet per second
Literature Cited
= fuel injection velocity (assuming tube running full),
feet per second = peak velocity of turbulent fluctuation of air, feet per
second
= air mass velocity, pounds per square foot per second
= fuel injection rate, pounds per second = = = =
= = = = = = = = =
mass, pounds axial distance, feet drop displacement from its mean position, feet maximum value of 2,feet maximum displacement of air eddy from its mean position, feet n t h root of J I ,dimensionless time, seconds viscosity, pounds per foot per second air density, pounds per cubic foot fuel density, pounds per cubic foot ring source function (see Equations 12 and 13), dimensionless disk source function (see Equations 14 and 15), dimensionless frequency, see.-’
(1) Carslaw, H. S., “Mathematical Theory of the Conduction of
Heat in Solids,” New York, Maomillan Co., 1921. ( 2 ) Dryden, H. L., IND.ENG.CHEM.,31, 416 (1939). (3) Kesler, G. H., Sc.D. thesis, Massachusetts Institute of Technology, 1952.
Langmuir, I., and Blodgett, K. B., “Mathematical Investigation of Water Droplet Trajectories,” A r m y A i r Forces Tech. Rept. 5418 (1946). (5) Little, B. H:, Jr., and Wilbur, S. W., “Turbulence-Intensity Measurements in a Jet of Air Issuing from a Long Tube,” Natl. Advisory Comm. Aeronaut., Rept. TN2361 (May (4)
1951). (6) Nikuradse, J., Forsch. Gebiete Ingenieurw., Forschungsheft, 356 (1932). ( 7 ) Taylor, G. I., Proc. London Math. SOC.,20, 196 (1921). (8) Taylor, G. I., Proc. R o y . SOC.London, A157, 537 (1936); A151, 444 (1935). (9) Towle, W. L., and Sherwood, T. K., IND. ENG.CHEM.,31, 457 (1939). RECEIVED for review September 18, 1952.
ACCEPTED October 20, l(l.52.
0
Reaction of Carbon with Steam at Elevated Temperatures B. E. HUNT’, SHlRO MORI, AND SIDNEY KATZ2, lnrfifute of Gas Technology, 3300 R. E. PECK, lllinoir lnstitufe of Technology, Chicago, 111.
T
HE importance of the reactions between carbon and steam in the manufactured gas industry as well as a large number
of synthesis processes has stimulated considerable interest in the controlling mechanisms. A variety of experimental techniques and materials has been employed by different workers, and it has not always been easy t o reconcile the reported results. The present discussion is concerned primarily with the reaction at temperatures above 2000’ F., the region of greatest interest t o the manufactured gas industry. At temperatures above 1700’ F. it has been shown that the equilibrium products of the reaction are almost entirely carbon monoxide and hydrogen ( 3 , 4). Experimentally, however, some carbon dioxide and water are usually present, even a t very high temperatures, indicating the incomplete nature of the reaction. I n the reactions of carbon with steam, the principal governing reactions are
+ H10 = CO + H, + 21320 = COZ + 2H2 c + coz = 2co CO + HlO COz + H, C C
.a
(1) (2)
(3)
(4)
Reaction 4 may occur either as a gas phase reaction or as n heterogeneous reaction at the solid-gas interface. All the other reactions must take place at the solid-gas interface. I n so far as a surface reaction is concerned, the rate controlling mechanism could be either the mass transfer of reactant gas between the main gas stream and the reacting surface, the adsorption or desorption of the gas at the solid surface, or the actual reaction on the carbon surface. Where several mechanisms may 1 2
Present address, Illinois Power Co., Deoatur, Ill. Present address, Armour Research Foundation, Chicago, Ill.
0 0
0
Federal St., Chicogo 76, 111.
be simultaneously operative, t h a t one which has the slowest rate will be rate controlling. In general, the rates of both sorption and chemical reactiom show an exponential dependence on temperature. The rate of mass transfer, on the other hand, is proportional t o T n where n varies from a value of 0.5 for a transfer system involving purely viscous flow t o a value close t o 0 for fully turbulent flow. At elevated temperatures, then, a careful consideration of these rate controlling mechanisms becomes necessary since a moderate temperature increase may increase the rates of sorption or chemical reaction t o the point where they exceed t h e rate of mass transfer. An understanding of the influence of the rate controlling fnctors can be used t o disclose the limits of temperature within which the desired conversion will occur a t a useful rate. For example, if the temperature a t uhich the transition t o a mass transfer controlling mechanism occurs is within the operating range, it is possible t o establish an upper temperature limit of useful operation since further temperature increases should yield negligible increases in the rate of conversion. The industrial importance of this type of study is a t once apparent. Experimental Procedures T h e experimental studies were conducted in a fixed carbon bed through which the gas phase passed in a vertical direction from bottom t o top. One of the reactors used in this work is shown in Figure 1. A vertical mullite tube, 3 inches in internal diameter, served as t h e reaction chamber in which the carbon bed was supported on a preheat zone of crushed mullite. The gas inlet line entered a t the top and passed down through the reactor t o the bottom of t h e preheat zone and the gaseous products of the reaction left a t the top. The depth of the carbon hed was maintained cohstant by means of a n overhead hopper and gravity feeder system which automatically maintained the coke a t R predetermined
INDUSTRIAL AND ENGINEERING CHEMISTRY
678
height. The temperature was monitored with sets of seven thermocouples placed in each of two thermocouple wells, one located axially along the center of the reactor and one near the reactor wall. External heating was provided by means of independently controlled electrical resistance heaters. For work a t temperatures below 2300" F.. the heaters were stacked one above the other, coaxially about the reactor. At higher temperatures, a set of silicon carbide resistance elements (globars) was arranged concentrically about t h e reactor. Temperature control is less sensitive with this arrangement; nevertheless, temperature variations of not more than 20" to 30" F. could be maintained in t h e carbon bed. All the experimental work under consideration here was carried out using a high temperature pitch coke (supplied by the Koppers Co.), whose analysis showed 99.5% carbon and 0.27% ash. The coke was crushed POSlTlONER and sized t o 10 t o 20 mesh (0.078 t o 0.033 inch), a size range which fed easily Figure 1 through the feed system without packing or bridging. Water vias metered accurately from burets into a steam boiler and the steam was superheated t o the reaction temperature before entering the reaction zone. The exit gases were passed through a drying train, and the dried gases were metered and sampled. Variables investigated included temperature, carbon bed depth, and rate of steam feed. Experimental data were obtained for the temperature range b e k e e n 1800' and 2500" F. The bulk of this discussion deals with the high temperature data, above 2000" F. Occasional reference will be made, however, t o some of the lower temperature data.
four reactions are indicated in the last four columns, for comparison with the equilibrium constants of these reactions. From a consideration of these data, it appears t h a t nithin the limits of the experimental measurements, the water gas equilibrium, Reaction 4, is established in the system, and that none of the other reactions enumerated reaches equilibrium. It is not therefore podsible to describe the rate of the reaction in terms of the disappearance of water. Instead, the rate of transfer of carbon from the solid to the gaseous phase has been taken as the index of reaction. Elsewhere in the course of this work it has been shown that the deposition of carbon by the r e v e r ~ eof Reaction 3 is negligible in this system, and the rate of carbon gasification is therefore a valid measure of the rate of the reaction. The experimental data may be represented a t any one temperature by a plot of carbon conversion per mole of entering steam against the reciprocal of the space velocity function, F/W. Here F is the feed rate of the entering steam and W is the mass of carbon in the reaction zone. A typical plot of this character is
1.0
,
I
I
I
I
I
o?I"
0.0 0.0
Treatment of Experimental Data
0.2
0.6
0.4
W/F(LB. CARBON) (HR.)/CU. FT. HzO
Representative experimental data are shown in Table I for a series of runs a t 2200" F. The product t o reactants ratios for the
Table I.
Vol. 45, No. 3
Figure 2
Reaction of Carbon with Steam-Gas Conversions at 2200' F. (Atmospheric pressure)
Product Gas Partial Pressure, Atm. Hz CO,
Run No.
W/F
HzO
482 481 480 483 484 490 491
0.032 0,041 0.054 0.092 0.142 0.225 0.382
0.366 0.264 0.213 0.158 0,132 0.056 0.066
0.358 0.402 0.425 0.450 0.458
472
466 468 474 473 475 476
0.076 0.098 0,172 0.198 0.290 0,457 0.718
0.088 0.078
495 493 492 496
0.159 0.233 0.436 0.884
0.055 0.052 0.049
0.486
0.028 0.018
0.218 0,272 0.308 0.339 0.361 0.434 0.430
0.474 0.478
0.029 0.029 0.022
0.410 0.415 0.414
0.488
0.102 0.051 0.038
0.462
0.071 0.039
0.479 0.497 0.499
0.014 0.005
0.022
0.012
0.486 0.487 0.498 0.494
0.492
0.067
co
0.062
0.022
0.440
0.010 0.010 0.003
0.466 0,478 0.497
0.017 0.013
0.433 0.451 0.474
0.006
0.010
0.485
Conversion, Cu.Ft. (CO Coz)/ Cu. Ft. Feed
+
K1 =
Px%z K z = P%PZHz PHzO
p2H20
Ka = ?!?
pcoz
Ka
PC02PHz ~
PCOPHzO
3-Inch Fuel Bed 0.394 0.219 0.485 0.414 0.555 0.615 0.632 0.966 0.862 1.253 0.832 3.782 0.867 3.215
0.068 0.144 0.219 0 . 604 0.590 1.745 1.005
0.71 1.19 1 I73 2.21 2.66 8.19 10.27
0.300 0.347 0.356 0.436 0.470 0.481 0.313
5-Inch Fuel Bed 0.745 2.208 0.779 2.543 0.839 1.875 0.846 4.192 0.910 4.969 0.935 17.003 49.103 1.011
0.842 1.089 0.452 1.998 1.647 12.65 29.20
5.80 5.94 7.79 8.80 21.62 22.85 82.33
0.380 0.428 0.240 0.476 0.276 0.744 0.596
7-Inch Fuel Bed 0.871 2.921 0.859 5.747 0.918 10.751 19.926 0.944
0.774 2.113 3.113 17.29
11.03 15.65 37.45 23.62
0 265 0.367 0.287 0,843
March 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY rm
Table II.
Rates'of Carbon Conversion
F. 1800
0.64 3.3 5.3 10.0 10.0 10.0 12.7
79.7 76.3 73.2 70.3 67.7 65.2 60.8
1900 2000 2100 2200 2300 2500
(diffusion) and
ro = rn = rr TEMPERATURE,
2400
2200
I
I
1800 I
I
4.0
2.0 I .O
a6 70
80
1 / T X 10-6, "K.
Figure 3
e
To
= KO
(PA
- PA%*)
(4)
where
The gas film thickness is related t o gas flow velocity by the relation Nu' = K (Re)m(Sc)" (6)
6.0
0.4 60
(3)
where r,, is the over-all rate of reaction. It is easily shown t h a t
OF.
2000
(1) (2)
where rm and r, refer, respectively, t o the rate of mass transfer and the rate of chemical or sorption controlled reaction. p,, pAi,pAk* are, respectively, the partial pressures of the diffusing gas in the gas stream, at the solid-gas interface and a t equilibrium on the solid surface. With steady state conditions prevailing,
+
(Cu. Ft. CO Cdh/ (Lb.Carbon) (Hr.)
106,
- pAJ
r7 = k , (pAi - p A z * ) (first order chemical reaction)
Rate a t Zero Conversion
(i/z)z
Temp.,
= km ( p ,
679
shown in Figure 2. The derivative of this form of plot yields the rate of the reaction directly. The over-all reaction mechanism involves a complex series of steps, each proceeding a t a rate characteristic of the associated temperature. It is not, therefore, possible t o make a general comparison of reaction rates at different temperatures. However, this may be done if a set of comparable conditions can be selected. This condition is satisfied in two regions only, near the point of zero conversion, where W / F approaches zero, or the region of equilibrium conversion, where W / F is very large and the rate is approaching zero. The latter is unsuitable for rate studies. I n the former region, where the conversion is close t o zero, and no secondary or reverse reactions are taking place, the rate of the reaction is proportional t o the rate constant. It is therefore possible t o plot these data t o obtain an energy of activation. The rates of carbon conversion where W / F is zero are listed in Table 11, and a plot of the rates on logarithmic paper against the reciprocals of the corresponding temperatures is shown in Figure 3. From this figure it appears t h a t the reaction controlling mechanism undergoes a transition in the neighborhood of 2100' F. An estimate of the energy of activation below 2100' F yields a value of at least 45 kcal. per gram-mole. Above 2100' F. the energy of activation is much lower. The higher figure is consistent with a chemical or surface controlled reaction mechanism, whose exact nature will not be considered further here. At higher temperatures, a diffusion controlling mechanism appears t o be the most logical explanation of the extremely low activation energy. An alternative approach t o the analysis of the high temperature mechanism has been made, based on the assumption of a dual mechanism in which chemical reaction and diffusion are both assumed t o be contributing t o t h e control of the reaction rate. The carbon-steam reaction may be treated as a pseudo-first order reaction ( 9 ) . Then, following the treatment of Wilhelm (6)
where the Reynolds number is equal t o DG/p and the Schmidt number is p / p D v . D is the effective diameter of the path of gas flow, p is the gas viscosity, p is the gas density, G is the mass velocity, and D, is the gas diffusivity. Exponent m varies from about 0.4 when the Reynolds number is small, t o 0.8 for very large Reynolds numbers (1). Adopting a value of 0.5 in the present case, and recalling that t h e modified Nusselt number is directly proportional t o the mass transfer coefficient, Equation 6 may be rewritten k , = K'FO.6 (7) since F is proportional t o the G term of the Reynolds number. Equation 5 may now be written
+ l/kr
1 / K , = 1/K'FQa6
(8)
Thus a plot of 1 / P 6against l / K o will be a straight line with a n intercept of l/k, and a slope of l/K'. Plotting 1/K, against 1/FO.6 and noting that l/Ko = l / K m l/Kp, the following results are t o be expected: 1. Where the reaction is controlled by a chemical or surface reaction mechanism KOwill be independent of the gas velocity. 2. Where the reaction is controlled by mass transfer, K Owill be dependent on the gas velocity. At high velocities the boundary film will approach zero thickness-and the rate will be very large. On the above plot, the curve should approach the origin.
+
An analytical expression relating KO t o the experimentally available data of the carbon-steam reaction has been derived, The expression is somewhat approximate in character; however, a t high temperatures where little carbon dioxide forms, it is fairly accurate. The relation between the over-all rate coefficient and the experimentally observed conversion may be derived by using the simplifying assumption t h a t the carbonsteam reaction is predominantly Reaction 1
C
+ H,O
=
CO
+ H2
At elevated temperatures, the carbon dioxide content of the gas is low, and this equation is fairly descriptive of the reaction. If x moles of hydrogen be produced from F moles of steam in a x, since 2 given time interval, the total moles of gas are F moles of product gas replace one of steam. Then, dx = Koa d V (pH,* pH,) (9)
+
-
where K, is the over-all reaction rate coefficient, a is the surface area of the solid phase per unit volume, and dV is a differential element of volume. pHz*is t h e equilibrium partial pressure of hydrogen a t the solid surface, and p E z is the partial pressure of hydrogen in the gas stream.
INDUSTRIAL AND ENGINEERING CHEMISTRY
680
Assuming a total reactor pressure,
T,
Table 111.
X
F+z '
PHz
Vol. 45, No. 3
Combining Equations 9 and 10
Run No.
Relation between Rate of Steam Feed and Over-all Rate Coefficient
Cu. Ft. Steam/Hr. ("
Cu. Ft. €12,' Cu. Ft. Steam
F.)
l/Fo.s
1/Ko a
V
2000° F.
which may be arranged in the form
420 430 452 423 455 45 1 427 438 460
8.54 8.32 7.68 7.37 6.90 4.71 3.98 3.25 1.86
394 391 399 364 387 381 397 392
25.05 22.78 8.58 8.47 7.79 5.00 4.54 3.05
472 466 468 474 473 475
12,23 9.47 5.40 4.68 3.19 2.03
499 485 498 469 497 478
10.42 9.49 8.22 4.62 3.55 1.34
0 0 0 0 0 0 0 0 0 21000
r
I
I
I
1
I
0.06 0.02
435 506 686 437 710 749 731 802 910
0.342 0,347 0.361 0.369 0.381 0.460 0,555 0.734
0 05 1 0 . 043 0 . 048 0 .0b9 0 . 029 0 . 039 0 048 0 . 048 0 . 0,56
0.200 0.210 0,342 0.344 0.358 0.448 0.469 0.572
0.051 0.035 0.033 0.025 0.024 0.041 0.041 0.047
0.286 0.326 0.430 0.463 0.560 0.703
0.017 0.019 0 026 0,030 0.032 0.048
0.310 0.324 0,360 0.465 0.568 0.864
0.012 0.020 0.011 0,022 0.017 0,066
0.502
F. 0,290 0 404 0.714 0.793 0.822 0 803 0.826 0.887
22000 I?.
0.02
0.805 0.839 0.889 0.890 0.944 0.953 2300O I.". 0.991 0.708 0.961 0,947 0.991 0.963
0.02
0.06
-
0 / '
02
04 llFo
06
08
'
Figure 4
Integrating 12 along the length of the reactor yiclds
(13) where the limits of hydrogen concentration along the length of the reactor are 0 and XF, and the reactor volume limits are 0 and V. Equation (13) may be written in the more convenient form
volume terms, respectively, and are related to the experimental conditions in the reaction vessel. Figure 4 shows that the transition from surface or chemical reaction controlling t o diffusion controlling is indicated by this treatment. At 2000" F., the rate appears to be independent of the gas velocity term while a t 2200' and 2300" F. the plot is of the form anticipated n-here mass transfer controls. A transition region occurs a t 2100" F. These studies were all made on a single high temperature coke, sized t o a rather narrow range. No comparative data for other carbons or other sizes are available a t this time. The implications of these findings are of considerable interest in the manufactured gas industry. If they are applicable t o other carbons generally, it would appear that the reaction rate is increased very slightly, if a t all, by increasing the temperature beyond this comparatively low transition temperature. It is planned t o extend this work t o higher and lox-er temperatures t o determine the validity of these correlations ovei' a broader range of temperatures.
Acknowledgment
(14) Since the terms on the left are available experimentally, it becomes possible t o evaluate KOa V for the correlations discussed previously. Example. The application of Equation 14 to the experimental data mag be shown by reference to run 466 (Tables I and 111). I n this run the terms have the following values: x
This work is a portion of a study of the reactions of c~arlion, oxygen, and steam, a project sponsored by the Gas Production Research Committee of the American Gas Association as a part of its PAR program. The sponsor's permission to publish this paper i b gratefully acknowledged. Literature Cited
(total pressure) = 1 atmosphere
F (inlet steam feed) = 9.47 cu. ft. per hour Pa,* (equilibrium hydrogen partial = 0.5 atmospheres pressure) X P (hydrogen) = 7.95 cu. ft. per hour
These figures substitute into Equation 14 t o yield the value of 53.6 which is used for KOa 8. The data for the carbon-steam reaction in this form are given in Table 111 and Figure 4 a t 2000°, 2100", 2200°, and 2300" F., using KOa 8 in place of K O . Terms a and V are surface area and
(1) Hilpert, Fomch. Gebiete ZngcnieuTw., 4 , 215 (1933). ( 2 ) Hougen and Watson, "Chemical Process Principles," pp. 961.-3, Kew York, John Wiley C? Sons, 1947. ( 3 ) P a r e n t a n d K a t z , "Equilibrium Compositions and E n t h a l p y Changes in Reactions of Carbon, Oxygen, and S t e a m , " Institute of Gas Technology, 1948. (4) Wagman, Kilpatrick, Taylor, Pitzcr, and Rossini, J . Research Natl. Bur. Standards, 34, 143 (1945). (5) Wilhelm, Chem. Eng. Progr., 45, 208 (1949). I ~ E ~ E I ~for E D review
J u l y 31, 1951.
ACCEPTEDNovember 10. 1952.
