ENGINEERING, DESIGN, AND EQUIPMENT
Flow Experiments in Studying Kinetics Role of Diffusion and Influence of Flow Pattern in Gasification Reactions SABRI ERGUNl Coal Research Laborofory, Cornegie lnsfifufe of Technology, Pittsburgh, Po.
N
URTEROUSproblems of both scientific and experimental nature are encountered in attempting to explain the mechanisms of the heterogeneous reactions of oxygen, steam, and carbon dioxide with carbons. The rate a t which a gasification reaction takes place is not simply the result of appropriate molecular encounters such as two molecules of steam reacting with an atom of carbon to yield a molecule of carbon dioxide and two molecules of hydrogen. Auxiliary phenomena, such as rates of transfer of molecules and energy between phases, state of gases and solid state of carbons, play important roles in the over-all reaction rates. An understanding of the relative importance of these phenomena is essential to a complete description of data obtained in measurements of the over-all process. The choice of experimental method of investigation is often determined by the availability of the tools. One popular method of investigation involves passage of reactant gas streams through granular carbon beds. This method is one of the oldest, but analysis of the data thus obtained is probably the most difficult. It permits reaction a t a steady state and data obtained have practical application. The lack of agreement in the literature concerning the mechanism of the gasification reactions can be attributed to the difficulty in formulating the detailed mechanism of the reaction including the auxiliary transfer phenomena from the over-all rates. Work on the evaluation of flow processes in the interpretation of reaction mechanism was preceded by studies on fluid flow (6, 8), heat and mass transfer rates in both fixed and fluidized beds of granular solids ( 7 ) , and their aerodynamic and sorptive properties (8-4). These investigations led to the development of the method that was employed here for studying reaction rates in flow systems. The experiments were carried out in a high temperature porcelain tube, 2.22 cm. inside diameter, 56 cm. long, fitted with a porous disk to support the granular carbons. The tube was held vertically in a Globar furnace, the heated chamber of which was a square prismatic cavity of 11.5 X 11.5 X 23 cm. Borosilicate glass standard tapered joints were fused to both ends of the reaction tube for flexibility in operation. Closely screened and weighed amounts of carbons, ranging in size from 8 to 16 and 175 to 200 mesh, U. S. Standard, were introduced from the top by removing the upper half of the tapered joint. When a run was completed the solids were removed by suction through a 6-mm. porcelain tube inserted in the reaction tube. T o maintain fixed beds a t all flow rates, gas was introduced from the top of the tube and flowed downward. Reverse flow was employed whenever fluidization was desired. Reaction temperature was measured by means of a platinum versus platinum-lO~orhodium thermocouple placed vertically in the tube from the top. The position of the thermocouple could be adjusted easily. A second thermocouple was inserted horizontally through a hole on the side of the furnace and placed against the outside wall of the reaction tube. The inlet-gas flow rates were measured with a 1
Present address, U. 8. Bureau of Mines, Bruoeton, Pa.
October 1955
precision of &0.2y0 on an absolute scale (6). Product gases were passed through sampling tubes. Before any samples were taken the system was brought to a steady state and the loss in the weight of carbon-i.e., burnoff-usually was kept below 5% of the solid sample introduced. Corrections were made in sample weight for the amount of the burnoff a t the time of gas sampling. A sketch of the apparatus is shown in Figure 1. This apparatus has been used to study the reaction of carbon dioxide and steam with graphite, activated carbons, and metallurgical cokes in the temperature range of 700" to 1500" C., and some of the data obtained are the basis for this discussion. wher;couple to lotent iometer
f
Gas inlet or outlet
-=I/ _JSilicon carbide heating element
brick
disk
II
P
Figure 1.
Diagram of apparatus
INDUSTRIAL AND ENGINEERING CHEMISTRY
2075
ENGINEERING, DESIGN, AND EQUIPMENT Analysis of surface reaction sequence is a n objective
A reaction occurring a t a surface follows a sequence that may be separated into various steps, the slowest of which will have a greater, although not the only, influence on the rate of the over-all process. Analysis of this sequence is one of the objectives of kinetic studies. When a flow process is employed, only the rate of over-all process is readily calculated. The complete sequence of the reaction and the slowest step must be deduced from the effects of changing the experimental conditions, such as gas flow rate, partial pressure of reactant gases, amount of solids, physical properties of solids, reaction temperature, and pressure, and from correlative experiments.
I
I
I
\ CJ
s
-I
0.6
0.7
\3 0.9
0.8
RECIPROCAL T E M P E R A T U R E , l000/'K.
Figure 2.
Typical plot of reaction rate
Inert g a s experiments should be planned carefully
I n planning the experiments to determine the influence of inert gases certain factors should be considered carefully, For example, a given change in the partial pressure can be brought about a t a constant total flow rate by introducing a stream of inert gas and correspondingly decreasing the rate of flow of reactant gas. An investigation of this type is illustrated in Figure 4 utilizing the reaction of carbon dioxide with a metallurgical coke. At the reaction temperature indicated, llOOo C., experiments were carried out with 3-gram carbon samples while the total rates of gas flow a t the inlet were maintained a t 180 cc. per min. a t standard temperature and pressure (STP). The
specific
Most carbonaceous materials are porous. I n a bed of porous particles the space between the particles is spoken of as the void volume. Gas flowing through such a bed, even where the pores of the material may form continuous channels in the direction of the flow, passes practically through the void space (8). The volume surrounded by the flowing gas is the aerodynamic volume of the solids, the enveloping surface is the aerodynamic surface. These aerodynamical properties of crushed porous carbons are essential in estimating resistance to gas flow and rates of heat and mass transfer in flow processes and can be determined with precision by two gas flow methods outlined previously by the author (a, 9). Consequently, one phase of the problem of reaction rates that can be considered without ambiguity is the transfer of reactant and product gases between bulk of gas stream and aerodynamic surface. The rate of the maas transfer in the gas phase, often called diffusion, is distinct from other possible steps in heterogeneous reactions in its dependence on temperature. Also, the dependence of diffusion rates on partial pressure is well established. Yet, the role of diffusion in over-all rates of reaction in flow processes has been controversial. Estimates of rates of mass transfer based on independent studies in packed columns invariably led to higher results than the actual rates of gasification. For example, the ratio of the maximum rate of mass transfer to the actual rate of reaction of steam with a metallurgical coke a t 1200' C. a t the aerodynamic boundary can be calculated to be over several thousand-cf., calculations. On the other hand, conventional specific reaction rates-Le., amount gasified a t unit partial pressure, per unit time, and per unit weight of solid-
2076
exhibit change in slopes a t higher temperatures in the Arrheniustype plots shown in Figure 2. There is no general agreement on the temperature and other conditions a t which this change occurs, but it is generally concluded that the change corresponds to the onset of diffusion control. Such a conclusion might be justified only if calculated rate constants were absolute rate constants. I n Figure 3 the log of apparent specific rate-i.e., amount of carbon gasified per unit time and per unit weight of carbon sample-is plotted against reciprocal temperature, and a similar behavior is observed. The data were obtained in this investigation, and a careful analysis of them indicated that the reaction was far from being affected by diffusion rates and that, the constants employed were not absolute rate constants. A detailed account of the analysis that was made would be desirable to demonstrate that a change in the slope of an Arrhenius-type plot of specific rate constants does not necessarily indicate the onset of diffusional control. But such a presentation would require much anticipation as to the reaction mechanism, a complete kinetic analysis of which has been done and will be forthcoming. However, it is possible to examine the role of diffusion on gasification reactions simply by observing the influence of inert gases on reaction rates.
IOOOl'K
Figure 3.
Conventional representation of rate data Carbon dioxide on activated carbon
specific reaction rates show an increase with the partial pressure; but it is difficult to conclude whether the resulting change in the reaction rate is due t o the partial pressure per se-Le., diffusional hindering due to the presence of inert gas-or whether the change is due to the change of the net flow rate of the reactant gas. To clarify this point, experiments were conducted at a constant reactant gas flow rate, with the change in partial pressure brought about by introducing inert gas a t successively increased rates.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47. No. 10
ENGINEERING, DESIGN, AND EQUIPMENT
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However, the addition of inert gas in this manner increases the total rates of gas flow through the reactor and thus causes changes in the gas-flow pattern, which in turn might affect the concentration gradient of gases. (Heat requirements for isothermal reaction conditions were assumed to be satisfied. I n adiabatic reactors addition of inert gases affects the reaction temperature.) Accepting, for the moment, the existence of a range where addition of limited amounts of inert gases will not cause appreciable changes in the gas-flow pattern in so far as it affects the concentration gradient along the path of gases as is illustrated in Figure 5, investigation of this type would indicate whether or not the infiuence of inert gases is of a diffusional nature. The experiments were carried out a t 1100" C. with coke samples of 3.0 grams while the flow rate of carbon dioxide was maintained a t 77 cc. per min. (STP). Inert gases, whether helium or nitrogen, have little or no influence on the reaction rates, contrary to what one might expect from diffusional control. Minor effects observed are attributable to the change in flow conditions with the increased total gas-flow rates. Experiments of this type conducted on the reactions of carbon dioxide and steam with an activated carbon, a metallurgical coke, and a natural graphite in the temperature ranges of 700' to 1050', 900" to 1200°, and 1000" to 1400" C., respectively, indicated no marked influence of diffusion on reaction rates. I n studying the gasification reactions in these temperature ranges, therefore, the attention must be focused on the sequence of reaction between the aerodynamic boundary and the reaction sites. Over-all reaction rates do not give the sequence of the reaction between the aerodynamic boundary and reaction sites, but this sequence may be deduced from the effects of changing experimental conditions and from correlative experiments-for example, with tracer reactants. The direct influence of flow conditions is on the composition of the gas a t the aerodynamic boundary; special attention, therefore, should be given to the effect of flow conditions in order to arrive a t the proper sequence. Evaluation of the role of partial pressure was particularly important for this purpose. Partial pressures, however, have been employed largely in correlating experimental data. The popular method of determining the role of partial pressure is to observe its influence on reaction rate at constant total flow rates as shown in Figure 4. The slope of such plots leads to an apparent order of reaction and the intercept a t the right to the specific reaction rate a t unit partial pressure. The question of the order of reaction is also controversial (Table I). ~
Table 1.
Order of Reaction and Energy of Activation Data for Reaction of Carbon Dioxide on Carbon
Literature Source (16) (16)
(9)
Order of Reaction Zero order below 950' C. First order above 950' C. Zero order above 3000' C. Zero order 600-750' C. TO,w_&_:d_first order 750-
Energy of Activation, Cal./Mole 39 ,000 90,000
yuu- u.
(18) (17)
(10)
(14)
(1)
First order 900-1060° C. Zero order at 700' C. 0.7 order a t llOOo C. First order a t 1800' C. First order 700-800° C. (hinderance) First order (hinderance)
59,000
58,800 69,000 86,000
(Anthracite) (Coke)
Zero order below 850' C.
Apparent orders are largely empirical factors that find use in reproducing the results of limited experimental work. To date the use of the concept of order of reaction in gasification studies has not resulted in any reliable formulation. The influence of flow conditions on reaction rates must necessarily be analyzed on more basic grounds. Gas and solid mixing
October 1955
in fluidized beds was investigated by Gilliland and Mason ( I d , 13). Their experimental program involved
...
two techniques for studying gas mixing. I n the first, called back-mixing studies, tracer gases were introduced into the fluidized bed and gas samples were taken from various positions (both below and above point of injection), and analyzed, I n the second, termed "residence-time" studies, the solid was fluidized with a mixture of tracer gas and air and the composition of the exit gas from the bed was determined as a function of time after the tracer-gas addition was discontinued. From back-mixing ,experiments Gilliland and Mason conclude that gas mixing is relatively small while from residence-time experiments, gas mixing is excessive. Considerable by-passing of gas in the form of rapidly rising bubbles is believed to be the cause of this seemingly contradictory result. The authors conclude that in fluidized beds back-mixing of the pas does occur, but that the nonuniform flow of the gas is probably more important.
0
20
30
40
60
80
100
PERCENT CARBON DIOXIDE
Figure 4.
Effect
of inlet partial pressure at constant total flow rates
Coke samples reacted at 1 100' C. Total flow rate = 180 cc./min.,STP Weight of carbon = 3.0 grams
Gas mixing effect on reaction rate can be illustrated on theoretical as well as experimental grounds. For example, if the reaction of carbon dioxide with carbon is assumed to be firit order, the composition of the gas can be calculated as a function of distance from the inlet or as a function of weight of the carbon in the bed for any given rate constant. Figure 6 (left) illustrates the case when no longitudinal mixing of gases occurs, and Figure 6 (right) the case of complete mixing. The same amount of solids-Le, a relative distance of 5 from the inletresults in 89.5% conversion of carbon dioxide for the case of no mixing and 60% for the case of complete mixing. When these two cases are compared on the basis of equal conversion-for example, 60%-the relative amounts of solids required are 2.3 for no mixing and 5 for complete mixing. Flow pattern effect on gasification rates was studied
The experiments shown in Figure 7 were undertaken to investigate the direct infiuence of flow pattern ongasificationrates. The procedure was identical with that in the experiments shown in Figure 5. The data shown in Figure 7a were obtained a t relatively high carbon dioxide rates, 480 cc. per min. (STP). The amount of the carbon in the bed was 8 grams. By introducing helium, the partial pressure of carbon dioxide a t the inlet was reduced from 1.00 to 0.33 a t atmospheric pressure. The maximum rate of flow of helium was 1000 cc. per min. The fraction of carbon dioxide reacted remained independent of its partial pressure a t the inlet provided the amount of the solids
INDUSTRIAL AND ENGINEERING CHEMISTRY
2077
ENGINEERING, DESIGN, AND EQUIPMENT and the flow rate of carbon dioxide remained the same. It would seem that the initial concentration of carbon dioxide does not affect the rate of reaction. On the other hand, when low flow rates of carbon dioxide were employed-for example, 180 cc. per min. (STP)-introduction of helium caused a n increase in the reaction rate of carbon dioxide (Figure 7b). Eventually the rate assumed a n asymptotic value. This behavior would seem to be perplexing in that i t not only deviates from the plot 7a, but also shows an inverse dependence on the partial pressure of carbon dioxide. The behavior can, however, be explained on the basis of gas mixing. I n the plot 7a, the rate of flow of carbon dioxide was sufficiently high, and back diffusion, although always
. E
d.
* - a
E
W
B z
0 0
9
He 0 N2
0
b
a v)
0
0.2 0.4 0.6 0.8 PARTIAL PRESSURE OF CARBON DIOXIDE
1.0
Figure 5. Effect of inlet partial pressure at constant rate of flow of reactant gas Coke sample reacted at 1 100' C. Carbon dioxide flow rate = 77 cc./min., Weight of carbon = 3.0 grams
STP
present, could not appreciably alter the concentration gradient of the gases in the bed. The system, therefore, approximates the case where no longitudinal mixing of gases occurs. The addition of helium, therefore, has no marked influence on the reaction rates. I n the experiments shown in 7b, the flow rate of carbon dioxide is low and extensive mixing of the gases occurs in the gas phase. Introduction of helium increases the flow rate and thus reduces the mixing. With the increase in the flow rate of helium (indicated by the decrease in the partial pressure of carbon dioxide in the plot), the effect of mixing decrease3 and ultimately becomes negligible. Partial mixing forms a transition region. The flat portion at the right of the plot approximates the conditions in which near complete mixing occurs; the one a t the left, negligible mixing. Experiments shown in Figure 7c were obtained under conditions identical with those in 7a except that gas flow was upward vertically, resulting in fluidization a t linear gas velocities in excess of 16 cm. per sec. (based on an average viscosity of 0.047 cp.), which corresponded to a carbon dioxide flow rate of 480 cc. per min. (STP) at 80% conversion. At this flow rate an average fractional void volume of about 0.47 is maintained. The flow rate is high enough to minimize back diffusion (Figure 7 a ) . When successively increased rates of helium are introduced with carbon dioxide, no detectable change in the reaction rate is observed until the average linear velocity of the gases is in excess of 34 om. per sec., approximately 1000 cc. per min. (STP), a t which velocity a fractional void volume of about 0.56 is maintained. With additional increase in the rate of flow of helium the reaction rate is reduced rapidly. The latter effect is due to 2078
gas bubble formation that was easily observed when the behavior of the solids a t fluidized states was studied independently in glass tubes at room temperatures. Fluidization of the solids starts when the bed attains a fractional void volume of about 0.47. With the increase in gas velocity the bed continues to expand uniformly, although fluidized, and more agitation of the solids is observed. When the fractional void volume reaches a value of about 0.56, bubble formation begins and with increased rate of flow a two-phase behavior of bubbles and solid phase prevails. When spheres of uniform size-e.g., glass beads-are employed (8),fluidization and bubble formation start after a fractional void volume of about 0.47 is obtained which corresponds to the loosest stable configuration of spheres (simple cubical arrangement results in a fractional void volume of 1 n / 6 = 0.4764). The uniform expansion of crushed particles beyond the incidence of fluidization is apparently caused by the irregularity of their shape. Bubble or slug formations in fluidized beds alter flow patterns considerably and the effect almost corresponds to gas by-pass. Referring to Figure 7c, the apparent change in the rate of reaction with partial pressure is not caused by the partial pressure effect, but by the accompanying excessive fluidization. Experiments shown in Figure 7d were obtained under the same conditions as those in 7b except the direction of flow was upward. Again fluidization was attained a t linear velocities in excess of 16 cm. per sec. The increase in the rate of reaction with the decrease in the partial pressure of carbon dioxide, as indicated on the right side of the plot, corresponds to the transition range in mixing effects. Following a range of maximum reaction rate, a decline is observed that was caused by excessive fluidization. The plot, therefore, comprises the effects shown in Figures 7b and c. Influences of gas mixing and excessive fluidization on reaction rates were confirmed
I n order to substantiate further the influences of gas mixing and excessive fluidization on reaction rates, experiments were conducted with carbon dioxide alone at a wide range of flow rates while a constant ratio of weight of carbon to rate of flow of carbon dioxide a t the inlet was maintained. Similar effects were ob-
t ;.4N c
i
.4
5 .2 a
8
I 2 3 4 5 RELATIVE DISTANCE FROM THE INLET
0
Figure 6.
RELATIVE DISTANCE FROM THE INLET
Concentration gradient of gases as result of reaction and flow (Left) No longitudinal mixing of gases (Right) Gases completely mixed
served from the experiment.s as shown in Figure 8. The plot of 8a belonged to experiments in fixed beds. Again a n increase is observed in the reaction rate with the flow rate owing to the establishment of a concentration gradient in transition region,
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 10
ENGINEERING, DESIGN, AND EQUIPMENT
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beyond which linear gas velocity has no effect on the reaction rate. The plot of 86 was obtained with upward gas flow. Similarly an increase in the reaction rate accompanies the gas flow rate in the transition region. There is a range of flow rate, Figure 8b, where reaction rate is constant, but at a maximum beyond which excessive fluidization sets in. The shapes and points of breaks of the plots shown in Figures 5, 7, and 8 are functions of the physical properties of both solids and gases, such as particle size, aerodynamic density and surface area, diffusivity, viscosity, reaction rates, and other experimental conditions. For example, the figures show that inert gases have little or no i d u e n c e on the reaction rate whenever they do not alter the flow pattern. This condition is true for the carbon dioxide-carbon as well as for the steam-carbon reaction, but may
CO, rote = 480 cc./min., weight of carbon, 8 g m .
'
80 10)
0 0 0
Downward gas flow 0
0
0
.
1
n
-- --I 2
I
X
P
I
Pa-
9
O
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I
I
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gas I
COz r a t e = 180 cc./min. weight of carbon: 3 gm.
9 80
Id)
.boo
0
0
& 70 0
O
?
4
o o
0
0
z 70'
O
solids. The volume is, however, easily determined by simple experiments. For spheres, it closely approaches the value for the simple cubical arrangement, E = 1 - a/6, and it also corresponds to the start of bubble formation. For various carbonaceous materials fractional void volume a t the incidence of fluidization is slightly higher, but the theoretical value serves as a good approximation whenever the value used for the density of the solids is determined aerodynamically. For crushed carbons, bubble formation starts a t fractional void volumes of about 0.55. Gas mixing formulation i s a complex problem
Formulation of the gas mixing alone is not a simple problem as its effect is intimately involved with those of the reaction mechanism and reaction rates in addition to the experimental conditions cited. Estimation of concentration gradient is particularly difficult; it is, however, possible to ascertain under what conditions the reaction proceeds. Only the extreme cases of flow conditions-Le., complete mixing and no mixing of gases-readily permit mathematical analysis. Therefore, the experiments should be carried out as close to either extreme condition as possible. I n cases where such is not done or where it is not permissible, the data should be analyzed on the basis of both complete mixing of gas and negligible mixing and the results should be averaged. Excessive fluidization should be avoided in kinetic studies; when it occurs, the results are difficult to analyze. Yumerical answers to absolute rate constants and equilibrium constants require that the experiments be planned for such purposes. Qualitative experiments, therefore, are needed for
0
I
I
0
0.2
0.4
0.6
0
0
0
0.8
1.0
PARTIAL PRESSURE OF CARBON DIOXIDE
Figure 7. Reaction of activated carbon (20 to 30 mesh) with carbon dioxide ai
900' C.
a
e
-
~
or may not be true for other solid-gas reactions. I n the examples given, observed gas velocities a t the incidence of fluidization are close to those required for the elimination of mixing effects. For coarser materials the effects of mixing are eliminated first and in plots similar to those of Figure 7c, 7 4 and 8b, sections corresponding to maximum reaction rates cover a wider range. For smaller particles, 175 to 200 mesh and smaller, fluidization velocities are much less than those required to minimize mixing, no increase in the reaction rate with the increase in velocity is observed. Excessive fluidization, on the other hand, reduces the rate of reaction. Gas velocities required to fluidize particles smaller than 1 mm. and with a density less than 2 grams per cu. cm. can be calculated from the expression (8)
where u = the gas velocity based on empty tube, cm. per 8ec. g = gravitational acceleration, cm. per sq. sec. E = fractional void volume pa = aerodynamic density of the solids, gram per cu. cni. I.L = viscosity of the gas, poise S,= aerodynamic specific surface area of the particles, sq. cm. per cu. cm. of solid particles The fractional void volume that a bed attains a t the incidence of fluidization may depend on the characteristic shape of the
October 1955
I
65
0
N
8
75
I 400
200
t
I
800
I
1000
I I200
1400
0 0
70t O 0
0
I
600
200
Upward goo f l o w
Fluidization
O
600 BOO IO00 Cop FLOW RATE, cc / min.
400
1200
-I I
1400
Figure 8. Reaction of activated carbon (20 to 30 mesh) with carbon dioxide at 900" C. Constant ratio of carbon weight to carbon dioxide flow rate
planning. I n kinetic studies it is often very difficult to carry out experiments over wide ranges of temperature under identical conditions. Higher flow rates and different flow conditions must be utilized a t higher temperatures in order to prevent nearly complete conversion. It is therefore easy to see the importance of evaluating flow conditions in order to carry out experiments over wide ranges of temperature. The foregoing experiments were primarily planned for studying the role of diffusion and for evaluating the influence of flow pattern on the reaction rates. Some additional important conclu-
INDUSTRIAL AND ENGINEERING CHEMISTRY
2079
ENGINEERING, DESIGN, AND EQUIPMENT sions can be drawn from the experiments shown in Figures 7 and 8. The reaction rate is independent of the concentration of the inert gas. On the other hand, the presence of the effects of flow conditions-that is, whether or not mixing of the gases and/or of solids occurs-shows that composition of the gas has something to do with the rate of reaction. The most likely explanation, which incidentally can be established unequivocally, is that the relative amounts of the reactant and product gases in the gas phase are important. I n the case of carbon dioxide reactions this effect is better known as the inhibition effect of carbon monoxide. Substitution of carbon monoxide in place of a n inert gas leads to reduced reaction rates. Similarly hydrogen and carbon monoxide definitely influence the reaction rates of both steam and carbon dioxide. The role of carbon monoxide or hydrogen in the gasification reactions should furnish a clue to the reaction sequence. These gases do not undergo appreciable reaction with carbons a t higher temperature, yet their presence in the gas phase has a definite effect on the reaction rate. This effect, not being of a diffusional character, should lead to additional details of the reaction mechanism. The inference to be drawn here is that the evaluation of the flow pattern is a prerequisite in such studies. Calculations compare reaction rate with mass transfer
- -d C l d L
= E1 l n Ci c=ki 1
For 80% conversion, neglecting the volume changes due to reaction
This represents approximate differential change in the concentration as a result of actual reaction. Mass transfer rate would be a t a maximum when the concentration of steam a t the aerodynamic surface boundary approaches zero. The maximum possible differential change in the concentration due to diffusion, when calculated by the equation derived by Ergun (6)
is over 24,000 cm.-l When the Gamson, Thodes, and Hougen (11) equation is used, d C / d L / C can be calculated to be between 2000 and 8000. Although the equations used in estimating maximum possible diffusion require large extrapolations, it can safely be said that diffusional rates are several hundred, if not thousand, fold greater than gasification rates of metallurgical cokes with steam a t 1200' C. Acknowledgment
Experimental conditions (Run No. 40): 40 to 50 mesh coke, 5.0 gram sample, temperature = 1473'
Flow rate of water = 3.65 cc./sec. (STP) Flow rate of nitrogen = 1.27 cc./sec. (STP) Fraction of water converted = 0.802 Particle density = 1.30 gram/cc. Specific surface area = 210 em.-'
K.
It is a pleasure to acknowledge the advice and encouragement given by H. H. Lowry, former director of the Coal Research Laboratory, to the author in planning the work and in preparing the manuscript. The author wishes to thank Daniel T. Muth for assistance in carrying out the experimenk.
Calculations :
literature cited
Estimated fractional void volume = 0.50 Estimated height of bed = 2.0 cm. Av. viscosity of gases = 0.00057 gram/sec. cm. Diffusivity of water vapor in nitrogen = 2.98 sq. cm./sec. Superficial gas velocity, a t entrance = 6.4 cm./sec. a t exit = 9.3 Density of water vapor a t atmospheric pressure = 1.49 X 10-4 gram/cc.
(1) Bonner, F.,and Turkevich, J. Am. Chem. SOC.,73, 561 (1951). (2) Ergun, S.,A n a l . Chem., 23, 151 (1951). (3) Ibid.. 24. 388 (19521. i 4 j Ibid.; 25; 1222'(1953). (5) Ibid., p. 790. (6) Ergun, S.,Chem. Eng. Proer., 48, 89 (1952). (7) Ibid., p. 227. ( 8 ) Ergun, S.,and Orning, A. A,, INDENG.CHEM.,41,1179 (1949). (9) Frank-Kamenetskii, D. A., Compt. rend. acad. aci. U.R.S.S., 23, 663 (1939). (10) Gadsby, J., Long, S. J., Sleightholm, P., and Sikes, K. W., Proc. Roy SOC.London, A193, 357 (1948). (11) Gamson, B. W.,Thodos, G., and Hougen, 0. A., Trans. Am. Inst. Chem. Engrs., 39,1 (1943). (12) Gilliland, E. R.,and Mason, E. A,, IND.ENQ.C H ~ M 41, . , 1191 (1949). (13) Ibid., 44,218 (1952). (14) . , Lewis. W.K..Gilliland. E. R., and McBride, G. P., Ibid., 41, 1213 (1949). (15) Mayers, M.A., J. Am. Chem. SOC.,56, 70 (1934). (16) Meyer, L.,Trans. Faraday SOC.,34, 1056 (1938). (17) Strickland-Constable,R. F., Ibid., 43, 769 (1947). (18) Vulis, L. A.,and Vitman, L. A., J. Tech. Phys. (U.S.S.R.), 11 (1941).
For a first order reaction, change in reactant concentration with time can be expressed as
I n a flow system
dL u can be substituted for dt ( L is the length
of the bed, u gas velocity)
- -daCh/ d- L C
1 U
When a suitable average velocity is chosen, integration of the left-hand side of the expression becomes permissible.
2080
RECEIVED for review July 31, 1954.
INDUSTRIAL AND ENGINEERING CHEMISTRY
ACCEPTED April 18. 1965.
Vol. 47, No. 10
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