ENGINEERING AND PROCESS DEVELOPMENT tion, through the agency of hypochlorous acid. of the aldehydes t o the corresponding acetic acid, dichIoroacetic acid, and trichloroacetic acid. Both types of aide reaction can be controlled through proper arrangement of temperature and conditions pertaining t o the introduction of chlorine. The chlorination can be carried batchwise, but is most efficiently managed on a semicontinuous or completely continuous basis. Acknowledgment
Grateful acknowledgment is made t o Shawinigan Chemicals, Ltd., for permission t o publish; t o K. G. Blaikie for the helpful direction under which this work was carried out; t o T. P. Shaw for providing the analytical data; to D. J. Kennedy and G. E. Haddeland ( 3 , 4 )for the development of the tu-o-pump dispersion system; t o J. H. Alexander ( 9 ) for the investigation of holdup times for the third stage of the continuous system; and finally t o Armand Xadeau for able technical assistance.
literature Cited
(1) Bell, R. P., and Longuet-Higgins, H. C., J. Cfiem. S o c , 1946, 636. (2) Cave, W. T., Alexander, J. H., and hlcCoubrey, J. A. (to Shawinigan Chemicals, L a . ) , .U. S. Patent 2,606,864 (Aug. 12, 1952); Brit. Patent 634,938 (March 29, 1950). (3) Cave, R. T., and Haddeland, G. E. (to Shawinigan Chemicals, Ltd.), U. 9. Patent 2,552,934 (May 15, 1951): Brit. Patent 644,914 (Oct. 18, 1950). (4) Haddeland, G. E., and Kennedy, D. J. (to Shawinigan Chemicals. Ltd.). U. S. Patent 2,521,215 (Sept. 5. 1950): Can. Patent 470,578 (Jan. 2, 1981); Brit. Pakkt 633,378 (Dec. 12, 1949). (5) AlacMullin, R. B., and Weber, &I., Tram. Am. Inst. C h e n . Engrs., 31, 409 (1935). (6) Pinner, A., Liebigs Ann. Chenz., 179, 21 (1875). (7) Wohler, F., and Liebig, J., Ibid., 3, 262 (1832). (8) Wiirtz, A., Ibid., 102, 93 (1857). (9) Wiirtz, A., and Vogt, G., Compt. vend., 74, 777 (1872). RECEIVED for review January 21, 1963. A C C E P T E D hfay 4, 1963. Presented at the annual aonvention of the Chemical Institute of Canada, Halifax, N. S., June 1949.
Kinetics of Coal Gasification Proposed Mechanism of Gasification HOWARD R. BATCHELDER' AND ROBERT M. BUSCHE2, U. S. P. ARMSTRONG, Wcishingfon University, St. Louis,
AND WILLARD
I
N THE course of Fork in the development of the synthetic
liquid fuels program, attention has been centered primarily on coal as a source material for the necessary synthesis gas or hydrogen. Gasification of coal has been undertaken in a number of wags; most of the work of the Bureau of R h e s has been concentrated on the reaction in dilute suspension of powdered coal with oxygen and steam. Over a period of years, considerable scientific labor has been devoted to small-scale studies of certain single reactions t h a t are a part of the complex reaction system comprising coal gasification. Isolation of these reactions was, of course, necessary to obtain adequate and accurate data on reaction mechanism and rate, although in many cases competing reactions and the inherent difficulties of high temperature measurement required very ingenious experimental methods. Although such studieE serve as a basis for the understanding of the nature of the reactions involved, they do not integrate the kinetics of the individual reactions with the heat transfer and mass transport phenomenon, which are necessarily a part of the gasification process. Because of the significant influence of size on these phenomena, bench-scale x o r k has not been adequate for application to commercial-size units. On the other hand, empirical treatment of data obtained from the observation of pilot plant scale gasifiers has resulted in considerable information regarding the 1
2
Present address, Battelle Memoiial Institute, Columbus, Ohio. Present address, E. I. du Font de iiemours & Co., Ino., Belle, W. Va
1856
Bureau o f Mines, Louisiana, M o . , Ma.
operation and performance of each individual unit but does not clarify the complex physical processes involved and does not permit the design of other gasifiers in other than empirical fashion. For these reasons, it was decided to make this work an engineering study of the gasification process as a whole. An extensive search of the literature was made to obtain available rate data and to suggest a suitable mechanism of the over-all process, including heat and mass transfer. Theoretical equations expressing the kinetic changes in gasification were derived and applied in the calculation of conversion and product distribution to be expected in the gasification of powdered coal with such variable operating conditions as steam-coal ratio, oxygen-coal ratio, gasifier heat loss, and steam preheat. The results of this theoretical approach were then compared with data obtained experimentally from operation of suitable gasifiers. The theoretical calculations depend on the results of the literature survey, but not to the extent that might be thought. Three specific rate constants are involved, but the accuracy of these constants does not affect the form of the equations derived, and consequently does not affect the correlation of the chemical reactions and thermal and mass transfer involved in gasification. -4n extensive bibliography of the gasification literature has been published (44). The thermodynamics of the gasification system have been fairly well defined and may serve as a guide in choosing the variables to be studied and t o indicate the limits toward which a reacting system mag progress. Knmerous papers have presented
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 9
ENGINEERING AND PROCESS DEVELOPMENT methods of calculating gas compositions and temperatures to be achieved based on certain equilibria (14,46,68, 66, 93, 9.1,119, 137, 147, 149, $03,206-212). I n general, these papers develop material and heat balance equations and equilibrium equations commensurate with the number of unknowns t o be solved. I n particular, a recent paper by Batchelder and Sternberg emphasizes the practical application of equilibrium calculations for the proper choice of process variables (16). Recently, generalized flame equilibria equations have been derived by Brinkley utilizing high-speed electronic computers for the rapid solution of a large number of cases (34-38). General Kinetic Considerations. The thermodynamic properties are, by definition, point functions of the gasification process, indicating the conditions of a system a t equilibrium, regardless of the reaction path followed in attaining equilibrium or the time required. On t h e other hand, the kinetics of a reacting system define a particular sequence of reaction paths, as well as the rates at which the chemical changes take place. I n gasification, both homogeneous and heterogeneous reactions occur simultaneously in a complex reacting system. I n order to propose a suitable reaction mechanism, the results of a literature study are summarized b y considering individually each reaction t h a t is believed to take place. Classical discussions of the kinetics of either gas-phase or gassolid reactions are presented in a number of excellent texts (100, 102, 107, 134, 138, 167). The gasification reactions are made up of two general types: (1) exothermic reactions, which include the reactions of oxygen with carbon, hydrogen, and carbon monoxide; and (2) endothermic reactions, which include the reactions of carbon with carbon dioxide and steam. Reaction of Oxygen with Carbon I s Very Complex
The reaction of various forms of carbon with oxygen has been the subject of extensive kvestigation for a great number of years because of i h importance in the combustion and gasification processes. Although i t appears t o be a simple reaction, it is actually complex and no single study has been adequate t o clarify completely the kinetics involved. Consideration must be given t o such factors as the rate-controlling step, the order of reaction and the activation energy, the primary products of the reaction, and the chemical nature of the surface during oxidation. Rate-Controlling Step. Investigations into the rate of reaction have generally been directed to determining whether a diffusional or chemical process is rate-controlling. This is normally determined by varying the velocity of the gas past the surface a t constant temperature. Increase in the rate of reaction with increasing gas velocity then indicates mass-transport effects. From the work reported, it may be concluded, with reservation, t h a t diffusion controls the rate of oxidation of carbon a t temperatures greater than 1350' F. for velocities up to 50,000 feet per second (32, 54,69,60,98,126, 126, 213). The rate varies as the 0.4 t o 0.7 power of the mass velocity with an apparent energy of activation between 2.3 and 5.3 kcal. per gram-mole. Order of Reaction and Activation Energy. The order of the surface reaction must be determined under such conditions t h a t diffusion is unimportant. This may be achieved by maintaining a sufficiently high flow rate and a sufficiently low temperature or by the use of low pressure. Mayers (146)found the reaction to be first order between 930' and 1650' F. (For convenience, the connotation of a first-order heterogeneous reaction rate is applied t o a rate having a fractional order approaching unity.) Above 1650' F., however, diffusion controlled the reaction. Oreshko (166) reported energies of activation between 13.7 and 16.4 kcal. based on his experiments on t h e oxidation of coal. Scott and Jones (171)in experiments with air and anthracite concluded t h a t the reaction was
September 1953
first order, as did Sihvonen (183, 191) while working at low oxygenpressures and at temperatures between 1470' and 3270' F. Meyer (148) used pressures less than 5 X lo-* 111111. of mercury with graphite filaments and reported a firsborder rate up to 2240" F. with an activation energy of 20 t o 30 kcal., whereas above 2780' F. the reaction was of zero order with a n energy of activation of 70 kcal. Gulbransen and Andrew (91, 92) found that between 800' and 1070' F. the reaction waa of first order with a n activation energy of 36.7 kcal. above 100 111111. but was zero order below 10 mm. Strickland-Constable (198, %OO) and Barrer (13)had reported t h a t the rate of oxidation of freshly outgassed samples decreased as oxidation proceeded and contended that the reaction was initially first order and was controlled by chemisorption. Lambert (127) reported energies of activation between 27 and 31 kcal. At temperatures between 512' and 897' F., a fractional order mechanism was proposed closer t o zero order than first order. This result WM reported with reservation, however, as secondary oxidation of carbon monoxide complicated the analysis. Primary Products of Combustion. Bone, Finch, and Townend (24) proposed that in the combustion of carbon there are three steps: (1) a fixation of oxygen a t the carbon surface, (2) adjustment of the surface complexes formed, through the attainment of mobile equilibrium a t the surface in the system carboncarbon monoxide-carbon dioxide, and ( 3 ) evolution of these complexes as oxides of carbon. The equilibrium described must be a surface equilibrium between the complexes and not a n equilibrium between solid carbon and molecules of carbon dioxide and carbon monoxide in the gas phase. The latter would incorrectly presuppose t h a t the reaction of carbon dioxide with carbon is so rapid t h a t equilibrium is maintained. Oxygen, on the other hand, might be expected to react rapidly with the carbon surface, as it is a biradical, or has two unpaired electrons per molecule (220), and as such has a great affinity for the carbon surface. This mechanism suggests t h a t both carbon monoxide and carbon dioxide may be formed as primary products of the surface reaction and that the ratio of monoxide to dioxide is a function of temperature, with the dioxide predominating a t very low temperature and carbon monoxide predominating at high temperature. This relationship was partly shown by Lambert's work (127) on the low temperature oxidation of coconut charcoal. H e found, when using mixtures of oxygen with carbon monoxide or nitrogen, that at 512' F. the gas-phase oxidation of carbon monoxide had a negligible rate. Carbon monoxide acted merely as a diluent, and its concentration was slightly increased; the primary product was carbon dioxide. However, as the temperature was raised t o 836" F. the oxidation of carbon monoxide completely overshadowed the primary reaction a t the carbon surface. Many experimental methods have been used that prevented or suppressed the gas-phase oxidation of carbon monoxide formed as a primary product and permitted the study of the extent of this formation. These methods included: outgassing oxidized carbon surfaces under high vacuum (3, 139); reacting carbon filaments with oxygen a t very low pressures (130,169, 201); supporting the combustion of a glowing particle in a flow of cold oxygen (214); varying the velocity of gas flow under diffusion-controlled conditions so t h a t the rate of the surface reaction is varied in relation to a relatively constant rate of gasphase reaction (48-53, 62, 88-90, 118, 129, 162); and adding substances t h a t are known t o inhibit the gas-phase reactions (6, 7 , 11, 33, 71, 79). Whatever the method, the results showed that carbon dioxide can be formed as a primary product at low temperature, but t h a t its formation decreases and that of carbon monoxide increases as the temperature is raised. Above 1470' F. the formation of carbon monoxide is predominant.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1857
ENGINEERING AND PROCESS DEVELOPMENT Nature of Surface Complexes. The mechanisms of the reactions of carbon v i t h oxygen, steam, and carbon dioxide are dependent 1vgPly on the nature and mode of formation of surface comp1exc.s of oxides of carbon. Historically, de Sauserre (61) iu 1811 first observed that charcoal adsorbs oxygen slowly and releases it upon outgassing as osides of carbon. The idea of a carbon-oxygen coinpleu TWS first suggested in 1905 b y hrmstrong ( b ) ,who believed that the oxidized carbon surface should be represented as complexes of C, and 0,. The simple oxide eventually obtained mas considered to be formed by the decompobition of this oxidized coniplev through the breakdown of six-membered carbon rings. The oxides of carbon theory was developed further by others (74, 85,161,163-166, 175-178, 180, 181, 183, 186-189, 190-196, 215).
carbon dioxide reaction always accompanies the steam reaction ; and, because thew is strong indication in the literature that both are similar in rate and mechanism, the relatively simpler carbon dioxide reduction is discussed first,, to assist. in developing the mechanism of the stcani reaction. Early investigations of the carbon dioside reaction were made hy Bouclounrd (31) (for whoin t8hereaction waa named), Rheitd and JVheeler (160), H u b h r d and Recs (109))Broom arid Triivers (.GO), and Langmuir (150). Mayers (1.49)proposed a two-stage mechanism for t'he reaction oi carbon dioxide with carbon in the temperature range 1560" to 2370" F. €€e maintained that in the range 1560" to 1740" F. the niechmism is explained by retention of half of the oxygen of the carbon dioxide by graphite. This unsteady-state reaction :
Reaction of Carbon Monoxide and Oxygen Is Extremely Rapid
presumably controls the rate in the low temperature range. A sinal1 contribution to the rate of format,ion of the monoside is due to the slow decomposition of the solid complex. However, as the temperature is increased, the surface complex decomposes as rapidly as it is formed by the reaction:
The oxidation of carbon monoxide as a secondary reaction accompanying the combustion of ctii bon and the oxidation of hydrogen are extremely rapid gas-phase reactions. This reaction has been studied by :t number of investigators ( 5 , l r , 20, 117, 152, 173). Falk (75), through a measurement of ignition temperatures, found that the reaction b e h e e n hydrogen and oxygen was bimolecular, with a temperature coefficient of 1.31 per 18" F. rise a t 980" F. and of 1.13 a t 1160" F. The reaction between carbon monoxide and oxygen was trimolecular with a temperature coefficient of 1.24 a t 1160" F. and of 1.14 a t 1340" F. On the other hand, in a study of the simultaneous combustion of hydrogen and carbon monoxide, Haslam (96) found that between 1160' and 2730' F. both reactions are trimolecular. He proposed that the niecnhnnism of combustion of either hydrogen or carbon monoxide alone differs from that of the combustion oi a miltuie of these two gases in the ordinary industrial furnace where both gases are burning simultaneously, or, in other words, that hydrogen can be considered as affecting the combustion of carbon monoxide. This catalytic effect of hydrogen species had been reported by a number of investigators ( 0 , 10, 21-25, 26-29, 63, 186, 193, 195). Griswold (87) has presented two mechanisms for the chain reaction conhuetion of carbon monouide--one for the reaction in the presence of moistuie, the othpr for the dry reaction. Wheland (220)hna d i s c w e d the requirements of a chain mechanism. Reaction of Hydrogen and Oxygen Proceeds by Chain Mechanism
The oxidation of hydrogen, like that of carbon monoxide, is known t o proceed a t an extremely rapid rate by a chain mechanism. Hinshelwood and his apsociates (102, 105, 106) have examined the whole course of the gaseous reaction, by a st:i tic method a t constant teniperature and volume, from thc legion where it is a heterogeneous surface reaction to near the point at nhich it passes into euplosion. Above 968" F. the rate is strongly autocatalyzed by steam and has a high temperature coefficient. It exhibits on the average a fourth-order rate. Lewis and Von Elbe (13.5) presented a very rigorous expeiimental and mathematical treatment of the reaction. From a critical analysis of all the imaginable reactions of the system, they deduced a complel, chain-reaction mechanism. Hinshelwood and Garstang ( 10.4) showed that the oxidation of hydrogen is inhibited by halides in a manner analogous to the inhibition of the oxidation of carbon monoxide.
c + cog
-+
Co
c-o,,iid
+
-.+
C-osolid
co
so that in the high temperature range 1740" to 2370" F. the steady-stat'e rate is cont~rolledby chemisorption. In this temperature range and a t 745-mm. pressure, the rate of formation of emboli monoxide expressed as A , = cc./(sq. cm.)(second) is given by the forniula: logm41 = 5.07
0.04
- (38,700 i 8)/4.575 T o K.
Bonrier and Turkevich ( J O I , working with radioactive tracers (197), and Frank-Kamenetzkj, (78) both reported results that supported Mayers' mechanism. The data of the latter correlated by an equation of the form of the Langmuir adsorption isotherm (85): k,pco. r = (1 k,Pco lC~PCo2)
+
+
The data of Gadshy, Long, Sleight~holm,and Sykes (89)and Lewis, Gilliland, and McBritle (1%) also followed thie rate equation. Vulis and Vitman (216) reported the reaction to be of first order between 1650' and 1940' F. with an energy of activation of 59 kcal. Strickland-Constable (199, 202) investigated reactions of carbon filaments with carbon dioxide, steam, and oxygen. The carbon dioxide reaction was 0.7 order a t 2000" F. and first order a t 3270" F. The steam reaction was of zero order a t 1300" F., 0.6 a t 2000" F., and first order a t 3270" F. The rates for the carbon dioxide and steam reactions were equal a t all temperatures investigated and were only 0.01 the rate of the carbon-osygen reaction. Graham (86') found that a t atmospheric pressure, the order of both the steam and carbon dioxide reactions varied from 0.3 to 0.95 for temperatures of 1350" and 1800' F., respectively. The order changed with both temperature and pressure, approaching unity with increasing temperature and decreasing toward zero with increasing pressure. From a review of these studies, the following mechanism is suggested for the carbon-ctirhon dioxide reaction a t atmospheric pressure.
Reaction of Carbon with Carbon Dioxide Always Accompanies Steam Reaction
1. A carbon dioxide molecule approaches the carbon surface, where it dissociates on the surface into an atom of oxygen, which forms a keto-type complex with a surface carbon molecule and into a molecule of carbon monoxide, which emapes t o the gas phase. Only one carbon-oxygen bond is broken in the dissociation. 2. The adsorbed complex of carbon and oxygen subsequently is decomposed by rupture of the carbon-carbon bonds in the graphite lattice, and a molecule of carbon monoxide is desorbed into the gas phase.
The two important endotherniic gasification reactions are those of carbon with carbon dioxide and steam. The carbon-
13eIox about 1700' F. st,ep 1 is rapid and step 2 is slow, so that two effects may be present:
1858
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Vol. 45, No. 9
s
ENGINEERING AND PROCESS DEVELOPMENT
1. If the surface of the carbon is initially clean, owing, for example, to outgassing or storage in an inert atmosphere, so that a very small quantity of oxides is present, the rate is controlled by an unsteady-state chemisorption with a slight contribution to the rate by the slow desorption of the oxide. In this case slightly mere than one carbon monoxide molecule is obtained {or every molecule of carbon dioxide reacted. The rate decreases as more of the surface is covered with complex, and the adsorption step thus approaches equilibrium. 2. When the surface is sufficiently covered with oxygen complexes, the rate is controlled by the slow desorption of the complex as carbon monoxide into the gas interface. In this steady state, two carbon monoxide molecules are obtained for every molecule of carbon dioxide that reacts, and the reaction is of zero order.
The rate of the steam reaction a t 745-mm. vapor pressure in the. high temperature range, 1832" to 2120" F., waa expressed GI = (micromoles of gas-phase carbon)/(sq. cm.)(second) an& was given by the equation: logioG1 = 6.20
25
Figure 1. Effect of Hydrogen and Steam on Rate of Carbon-Steam Reaction
-
Between approximately 1700" and 2000" F., the rate of desorption approaches the rate of adsorption, and a transition from a zero-order reaction to a first-order reaction takes place. Above 2000" F., the rate of desorption is high enough so that equilibrium is maintained in this step and the rate is first order, controlled by the Chemisorption of the reacting carbon dioxide molecules. Only qualitative work has been done a t elevated pressures. The transition temperature region described above probably is shifted upward as the pressure is increased. Reaction of Carbon with Steam Is Similar to Carbon-Carbon Dioxide Reaction
The carbon-steam reaction has been found to be similar in mechanism to the carbon-carbon dioxide reaction, although secondary reactions that occur simultaneously in the steam system make the study of this reaction more complex. The work by Mayers on the carbon dioxide reduction (148) has been discussed. In later experiments on the reaction of carbon with steam, he observed a similar discontinuity in the Arrhenius curve that he had attributed in his work with carbon dioxide to a change in mechanism. In the lower temperature range the steady-state desorption of the product carbon monoxide from the surface appears t o control the reaction, whereas a t some temperature, probably near 1800° F., the rate of desorption of the solid complex exceeds its rate of formation, as indicated by the lower energy of activation of the adsorption step, and a transition i s made from a zero-order, desorption-controlled rate to a firstorder, adsorption-controlled rate of reaction.
September 1953
T o K.)
An apparent order of 0.66 a t 2000" F. waa obtained by Pilcher (169). Haslam and Thiele (101 j reported that the rate of .reaction increased only slightly with pressure below 1850" F. Above 1850" F. the rate varied inversely aa pressure between 200 and 800 mm., or had a -1 order. This haa not been confirmed by the work of others. Haslam and coworkers (99) found that both carbon monoxide and carbon dioxide are formed monomolecularly, and advanced the theory that a monomolecular mechanism precludes the occurrence of the shift reaction to any great extent in the gas phase. The "bimolecular" steam reaction is the result of a sequel to the monomolecular reaction in which the keto complex reacts with steam. Key and Cobb (121) deduced that the primary formation of carbon monoxide in the water gas reaction was first order and was retarded by hydrogen a t 1800" F. The rate of the shift reaction approached equilibrium a t the surface. Key (120) also advanced Mayers' two-step mechanism and derived a rate equation in which (1) a t low pressure the velocity of the reaction becomes proportional to the concentration of reactant, and ( 2 ) a t high pressure i t becomes independent of pressure. Hydrogen was again found to inhibit the reaction, although this effect diminished with an increase in temperature. The data of Gadsby, Hinshelwood, and Sykes (81)were correlated by a form of the Langmuir adsorption isotherm:
r =
17 19 21 23 TEMPERATURE (IOO'F:)
- (35,130/4.575
klP1
1
+ k2P2 + kam
where p l and pz' are, respectively, the pressures of steam and hydrogen for the steam reaction, and carbon dioxide and carbon monoxide for the carbon dioxide reaction. It waa found that the retarding effect of hydrogen approached a limit above 75 mm. of hydrogen pressure. The above pseudo-firsborder rate law also correlated the data of Chen (46,112). Chen has reported values for the constants of this equation in which kl increases exponentially with temperature, and k2 and ka decrease exponentially with temperature in the temperature range studied, 1580" to 1720" F. The temperature coefficients of the constants suggest a t once that some temperature may be reached a t which the retarding effects of hydrogen and steam are negligible, or mathematically when the value of the function (1 k2p2 ksp1) approaches unity. Values of this function have been calculated using Chen's constants a t zero conversion and plotted against temperature a t various gas compositions for 1-atm. total pressure in Figure 1. It may be noticed that above 2500" F., the retarding effect is negligible and the reaction rate equation reduces to a simple firsborder rate law. The equation for k1 given by Chen when converted to the units of (pound-moles of carbon)/(sq. foot)(second)(atm.) reduces t o the form:
+
logioki
+
0.12227
-
12,873.8/T0 R
Mayers' constant, on the other hand, is: logioko = 0.51097
-
13,822/T0 R
The excellent agreement between the rate constants calculated from these equations is shown in the following examples: A t 1540" F., IC1 = 4.8 X 10-7, ko = 4.0 X 10-7; at 2540" F., kl =1 6.6 X 10-8, k5 = 8.0 X 10-6. In addition, Warner (217, 218) found that the rates of gasification of electrode carbon, in an atmosphere of essentially steam at 1-atm. pressure, ranged from 0.18 X 10-6 (gram-molea)/(sq. cm.) (second) a t 1560" F. to 4.0 X 10-8 a t 1740" F. At these tem-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1859
ENGINEERING AND PROCESS DEVELOPMENT peraturea and unit steam partial pressure, Mayers obtained values of 0.2303 X l0-eand 0.8346 X 10-0, respectively. From experiments made at normal pressure, Sihvonen (184, 186), believed that the water-gas process generally produces carbon monoxide as a primary product, but may also produce the dioxide by the action of activated water molecules, especially at moderak temperatures and high pressures. Fom a n analysis of the review presented, the following mechanism is summarized for the reaction of carbon and steam a t atmospheric pressure under such conditions t h a t diffusion does not control :
A water molecule migrates to the carbon surface, where it dissociates; the oxygen atom is chemisorbed t o form a keto complex, G O ; the h drogen fragments either unite t o form a hydrogen molecule andkscape to the gas interface or are chemisorbed by the unsaturated surface. Adsorption equilibrium is probably maintained in the adsorption of h drogen, owing t o its rapid rate. The oxygen complex is d e n either desorbed as carbon monoxide or reacts with a n adjacently adsorbed oxygen atom or with steam to form carbon dioxide, which is desorbed into the gas interface. Water-gas shift equilibrium is maintained in this step. Below approximately 1800" F. the adsorption step is rapid and desorption slow, so that the latter rate controls and the reaction is zero order. Between 1800' and 2000" F., the greater energy of activation of the desorption step causes its rate t o approach the rate of adsorption, and a transition between zero order and first order begins. Above 2000' F. this transition is completed, and the reaction rate approaches first order. The similarity between this mechanism and t h a t for the carbon dioxide reaction is apparent. It may be qualitatively stated that an increase in pressure will displace the reaction toward a zero-order mechanism-that is, the transition period will take place a t higher temperatures. Water-Gas Shift Reaction I s More Rapid at Carbon Surface
I n analyzing the data given in the literature covering the watergas shift reaction these factors must be considered: ( 1 ) the extent of water-gm equilibrium a t the carbon surface, (2) the relative approach t o equilibrium a t the carbon surface and in the gas phase, and (3) the effect of the gas-phase reaction upon gasification. The extent of attaining shift equilibrium at the surface of carbon may be best obtained in evacuation experiments in which gas-phase reactions are eliminated. Muller and Cobb (161) reacted outgassed charcoal with steam a t 572' F. Upon heating the charcoal containing the complex and evacuating in stages up to 1922' F., gases were desorbed whose composition corresponded t o equilibrium of the shift reaction a t that temperature. Gwosdz ( 9 6 ) concluded that, at the surface of charcoal, carbon dioxide is produced by the interaction of carbon monoxide and steam and the reaction is strongly affected by the ash content. The gases carbon monoxide and carbon dioxide are produced in proportions corresponding t o the equilibrium established a t the surface. Haslam (97), as did Fritsche ( Y O ) , discussed the pseudoequilibrium constants calculated from gas compositions and concluded that there is very little actual gas-phase shift. In a seriea'of papers, Dolch (64j 66-69) reported on the effect of the carbon surface on the attainment of shift equilibrium. Experiments with mixtures of carbon dioxide and hydrogen over wood charcoal a t 1112' to 1832" F. indicated that these gases first react to form carbon monoxide and steam a t about 1112"F., whereas carbon dioxide first begins to react n ith carbon a t about 1382' F. His experiments shoil-ed that in quartz apparatus, a temperature of 1832" F. was required before carbon dioxide and hydrogen would react in the gas phase, and equilibrium was not reached until 2552" F. However, when the reaction was deter-
1860
mined in the presence of a carbon surface, shift equilibrium \\ as reached a t temperatures as low as 1292' F. Terres and coworkers (204) and Neumann, Kroger, an$ Fingas (154) reported similar results. -4 number of papers have discussed the use of commercial catalysts in the shift reaction (12, 133). The preceding discussion indicates that water-gas shift equilibrium is attained much more rapidly a t a carbon surface than in the gas phase. It does not state, however, that the homogeneous reaction does not occur. Certain qualitative deductions can, on the other hand, be made concerning the contribution of homogeneous shift t o gasification. The chemical combinations of oxygen with hydrogen and carbon monoxide occur by extremely rapid chain reactions, and furthermore, the presence of hydrogen species accelerates the carbon monoxide oxidation. As these reactions are faster than any of the carbon reactions, they tend to approach equilibrium very quickly in the flame. This also imposes shift equilibrium on the system, as is apparent on inspecting the equations of the equilibrium constants:
CO
+ HzO
F)c
CO,
+ Hz
It is conceivable that the homogeneous shift reaction tnlres place as a part of the complex chain mechanisms of the Oxidation reactions. Kondratjev and Ziskin (1.23) have intimated this. They noticed a feeble glow of heated water gas similar t o that of a carbon monoxide flame and considered the reaction to be a chain reaction conjugated t o the chain oxidation of hydrogen and carbon monoxide by traces of oxygen in the gas. Behrens (16, 18) believed the reaction occurred by thc simplified chain mechanism:
From the concentration of the radicals, the reaction velocity was derived as a function of temperature. This, in combination with the rate of cooling. led him to an estimation of the "freeeingin" temperature of the shift reaction. Above 1340' F. Reaction 1 is fader than 2. If the cooling time per 180" F. exceeds three times the half life of the radicals, equilibrium conditions n 111 prevail; if this cooling time is less than one third the half ]if?, the equilibrium will be frozen-in. With respect to gasification, when the above equilibria are approached in the flame, the net rate of reaction by the homogeneous shift reaction is zero and will remain zero as long as equilibrium prevails. In the substantial absence of oxygen, as the temperature of the system drops owing to the endothermic reactions, a dynamic equilibrium will be maintained a t the surface by adjustments in the proportions of carbon monoxide and carbon dioxide produced. However, the maximum evolutiori of the monoxide or dioxide is limited by the rates of formation of carbon monoxide and subsequent surface reaction with additional steam or oxygen complexes t o form carbon dioxide. If these rates are insufficient t o keep pace with the changing equilibrium requirements caused by the decrease in temperature, the equilibrium will be "frozen." Two factors are suggested in summary: 1. After oxygen has been depleted, homogeneous shift reaction has only a small contribution t o gasification; a dynamic shift is maintained, in accordance n-ith the temperature, a t the carbon surface through the rearrangement of surface complexes. 2. Instead of being gradually approached in gasification, shift equilibrium is established very early in the flame because of the rapid rates of oxidation of hydrogen and carbon monoxide. -4fter this, during lower-temperature periods oi gasification, the y s -
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vol. 45, No. 9
ENGINEERING AND PROCESS DEVELOPMENT tem may fali away from shift equilibrium because of an inability of the surface reactions to maintain the equilibrium corresponding t o rapidly falling temperatures. Diffusion Has a Complex Effect on Heterogeneous Reactions
-
*
'
The generalized mechanism for a heterogeneous reaction is generally considered t o be represented by the following steps: diffusional transport of gaseous reactant from the homogeneous gas phase through a film of counterdiffusing products to the gassolid interface; sorption and chemical reaction a t the surface; and counterdiffusion of the products into the gas phase. Furthermore, any one of these steps may be said to control the reaction rate if its rate is slow enough with respect to the others, and it is conceivable that transitions from one controlling step to another may be caused by changes in temperature or pressure. The present concepts of diffusion are based upon kinetic theory and were developed primarily by Maxwell and Stefan. An extensive treatment of the theory of diffusion has been given by Jeans (111). From inspection of the Stefan equation (107)and the Gilliland equation for difhsivity (84) i t is apparent that: (1) diffusion is a function of the one-half power of temperature and as such would have an "energy of activation" (slope of the Arrhenius curve) of approximately 1.84 times T (' K.); and (2) the product, DP, is independent of total pressure, and hence in this respect the rate of diffusion would conform kinetically to a zero-order rate. With regard to the gasification reactions in particular, the diffusivity for oxygen diffusing through steam, hydrogen, etc., has about the same value as the diffusivity for steam diffusing through oxygen, hydrogen, etc. Therefore, it may be stated without reserv&ion t h a t when diffusion controls both the carbonoxygen reaction and the carbon-steam reaction, the rates of both will be substantially equal. It has been deduced from the work of a large number of investigators t h a t diffusion controls the rate of the carbon-oxygen reaction a t the temperatures attained in combustion and gasification. On the other hand, the rate of the carbon-steam reaction is generally considered to be much slower than the combustion reaction. Consequently, the rates of adsorption or surface reaction for the carbon-steam reaction must be slower than the corresponding steps for the oxygen reaction; therefore, a higher temperature must be attained in the carbon-steam reaction before the transition from chemical to diffusional stepcontrolling begins. These suppositions find support in various studies. Clement, Adams, and Haskins (55,56)studied the reactions of carbon with steam and carbon dioxide, using charcoal, coal, and coke crushed to a uniform 5-mm. size. At velocities between 0.5 and 5.0 feet per second and at constant contact time, the yield of carbon monoxide wm constant and unaffected by velocity of flow. Energies of activation may be calculated from their data, which vary between 30 and 45 kcal. They also gave, for their temperature range, the observed increase in rate, as compared with the calculated increase in rate of diffusion and stated:
It seems probable from the high values of the increase in kl with rising temperature found in our experiments, that the determining factor in speeds of the reactions under consideration is the velocity of chemical combination and not diffusion. The carbon-carbon dioxide reaction was studied by Vulis and Vitman (216)using 4- to 6-mm. carbon tubes. The reaction rate measured by analysis of the gas leaving was shown t o be independent of Reynolds number a t 1652' F., and practically so at 1940" F. Within this temperature interval, the reaction was first order with an energy of activation of 59 kcal. I n the '[intermediate region" where kinetic and diffusional processes became of equal importance, a graphic method permitted an approximate separation of the two phenomena. At
September 1953
temperatures still higher than those used in their investigations (2370' to 2730' F.), they calculated that t h e reaction rate WBB controlled entirely by diffusion, and i t became commensurate with the rate of the diffusion-controlled reaction of carbon and oxygen. Haslam and Thiele (101) found that diffusion did not control the carbon-steam reaction a t 1850' F. for particle sizes of 8 t o 14 mesh as did Gadsby, Hinshelwood, and Sykes (81) using two different types of 8 to 10 British Standard Screen charcoal between 1292' and 1472" F., even with a relatively low flow rate of 1.76 feet per minute based on open tube area. Hunt, Mori, and Kate (110) found, in their study of the steamcarbon reaction in a cylindrical reactor, that below 2100" F. either cheniical reaction or sorption controlled the rate, whereae a t higher temperatures the rate was explained by a mass-transfercontrolling mechanism. In addition to the effect of temperature upon diffusion, an extremely important but little-considered fact is t h a t the rate of diffusion of a gaseous component t o or from a small spherical particle or droplet is directly proportional to its radius and not to ita surface area. This observation was first made by Sresnewsky in 1883 (196). The effect was verified by Morse (160) in experiments in which the changes in weight owing t o evaporation from small solid spheres of iodine of less than 2-mg. mass were meaaured by a microbalance. H e found t h a t the rate of weight loss is given by the formula -dm/dt = Icnl'a, wherein m is the mass of the sphere. Langmuir (181)made an analogy between diffusion and his experimentally verified theory concerning the convection of heat from small wires. His deductions led t o tbe equation that WBB supported by diffusional experiments:
wherein m is the mass of the sphere; t, time; r, the radius; D, the diffusion coefficient; M , the molecular weight; p , the ambient pressure of the diffusing substance; TI the absolute temperature; and R, the gas constant. Langmuir also estimated the thickness of the stagnant gas film t o be about 4 mm., which is large in comparison to the size of a powdered coal particle. Topley and Whytlaw-Gray (206) found that Stefan's general theory of diffusion applied t o evaporation from a sphere leads t o the result:
in which -dm/dt is the rate of evaporation in gama per second; MI the molecular weight of vapor; D, the diffusional coefficient, sq. cm. per second; p , saturated pressure of the vapor, dynes per sq. em.; r, the radius of the evaporating sphere; r,, the radius of spherical shell of adsorbent; R, the gas constant, ergs per degree; T , absolute temperature; and P , total (constant) pressure of the atmosphere, dynes per sq. cm. This expression reduces t o the Langmuir equation where p is small and ro is large. In connection with the burning of small carbon spheres weighing 2 to 70 grams, Smith and Gudmundsen (194) concluded that the specific surface reaction rate for carbon sphefes burned in dry and in moist air is a complex function of the particle size. It is enormously larger for a small particle than for a large one. Mayers (142) derived an equation for the rate of combustion similar in form t o those discussed:
r = 12
@=a+$)
in which PI is the partial pressure of oxygen in the ambient atmosphere and d is the particle diameter.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1861
ENGINEERING AND PROCESS DEVELOPMENT ~
RIayers (145) also concluded, upon correlating the data of others, that: (1)the rate of combustion for small particles varies as the radius of the particle and the 0.4 power of the relative velocity between particle and atmosphere; and (2) for a gratefired furnace (large particles), on the other hand, the ratenolonger depends on particle size but primarily on velocity. I n summary, certain qualitative deductions can be made regarding the effects of particle size and temperature:
An increase in temperature increases the rate of the chemical steps with respect t o the rate of d8usion because of the low energy of aativation for diffusion and hence results in a shift in the mechanism toward diffusional control. An increase in particle size for fine particles causes a relative reduction in the specific rate of diffusion and also favors diffusional control. T h e effect of temperature is greater, the lower the temperature; and the effect of particle size is greater, the smaller the particle. lnorganic Salts Serve as Surface Catalysts
There is considerable evidence in the literature that, in addition to the surface catalysis of the water-gas shift reaction, certain inorganic salta, particularly oxides and carbonates, serve as catalysts for the primary surface reactions of carbon with steam, carbon dioxide, and oxygen (8,7b, 16%’,14l, 156,156). White and coworkers (76, 77, 219, 291) in an extensive study investigated the effect of various catalyets on the steam reaction. They found t h a t sodium carbonate accelerated the carbonsteam-carbon dioxide reactions up to 1742’ F., above which the effect was reduced. It wa8 believed that the reaction of impregnated graphite gave products that ruptured the layer of carbon monoxide around each graphite granule, making it possible for water and carbon dioxide to react with fresh carbon surfaces. The diminishing catalytic effect above 1742’ F. may be compared to the previously suggested mechanism for the steam reaction in which desorption ceases to control above this temperature. Reactivity Determinations Have limited Value in Kinetic Work
The study of the “reactivity” of various fuels may be discussed briefly. The use of such a comparative index as reactivity, for the rate a t which different forms of carbon react under uniform conditions, is in itself recognition of the inability t o separate the effects of many simultaneously occurring phenomena. Reactivity determinations have been made by a large number of workers in this field (1, 2, 19, 67, 70, 113-116, 156, 17‘8). They serve, principally, as a qualitative bash for the selection of fuel and have only limited value in kinetic n-ork.
~~
Period of Predominantly Exothermic Reaction. During this period oxygen diffuses to the carbon surface, where carbon monoxide is formed as the primary product by the reaction: 2C f 0 2 -+ 2CO. The diffusion step is believed to control the rate of reaction. The product carbon nionovide counterdiffuses into the homogeneous gas space, where it is oxidized to carbon dioxide by the 0 2 2C02. This rerapid homogeneous reaction: 2CO action approaches equilibrium as the carbon dioxide concentration increases and the oxygen concentration decreases. T h e carbon monoxide concentration during the fimt stages of combustion quickly reaches the relatively low value a t which it is held i n dynamic stability controlled by the relative rate of the gas phase oxidation and the surface reaction. Steam diffuses simultaneously with oxygen to the carbon surface, where it is decomposed by the reaction: C RzO -+ CO Hg. At the high flame temperature, carbon monoxide is the main product of reaction, and but little carbon dioxide is formed by the bimolecular steam reaction. Product hydrogen and carbon monoxide diffuse into the gns phase, where they are oxidized t o steam and carbon dioxide, respectively. Equilibrium is probably maintained continuously in the reaction HZ I/lO2 & HzO. Hence, during this period the net effect of the steam reaction is to augment the oxygencarbon reaction, and the steam present is equivalent to an increase in the partial pressure of oxygen a t the high temperatures a t which diffusion controls both reactions. Attainment of equilibrium in the reactions Hz f- 1 / 2 0 2 ~f HzO and 2CO 0 2 ~t ~ C Oalso Z imposes water-gas shift equilibrium on the system. Upon continued depletion of the oxygen pressure, the rates of the exothermic reactions are reduced to such an extent t h a t the heat requirements of the system balance the reaction heat evolved, and a peak in the flame temperature occurs. The ovygen concentration at this point is very low. Period of Endothermic Reaction. After the temperature niaximum and continuing throughout the remainder of the reaction time, the temperature of the systpm falls because of the heat rrquirements of the endothermic reactions rand gasifier heat loss. During this latter period both steam and carbon diosidt, migrate to the carbon surface, where the surface reactions previously described take place. Water-gaa shift equilibrium is dynamically maintained a t the surface between the components steam, carbon dioxide, carbon monoxide, and hydrogen. Depending upon the temperature and particle size, diffusion, cheniical surface reaction, or both may be significant in controlling the reactions. Since, a t the beginning of the gasification period, shift equilibrium already existed on ing to the rapid gas-phase oxidation reactions, little net homogeneous shift reaction (CO H20 e COP Hz) takes place. As the temperature decreases, the rates of the heterogeneous reactions also decrease. It is possible to achieve a condition under which the declining reaction rates cannot maintain the changing shift requirements caused by the drop in temperature, and the so-called “frozen shift” results, in which the system falls away from equilibrium. The gas composition a t this time corresponds t o shift equilibrium a t a higher temperature than the actual temperature of the system. Gasification, for all practical purposes, ceases after the temperature falls sufficiently or aftrr the carbon is exhausted. The most important variable in this regard is the temperature. Steam is usually in excess so that the change in its partial pressure is small and, thus, does not greatly influence the ratcs of reaction.
+
+
+
+
+
+
Mechanism Is Proposed for Powdered-Coal Gasification
From a critical analysis of the literature survey, the following mechanism for the gasification of powdered coal is proposed. Preheat Period. The first stage in the gasification sequencr is t h e devolatilization of the coal particles, which has been discussed in detail by Fuchs and Sandhoff (80). hlaycrs (145) describes this as follows: The particle is swept into the combustion zone by a stream of oxygen, where it is subjected to the radiation from the walls and flame. The particle heats up in a matter of milliseconds, and volatile matter is driven off. This matter may ignite, further raising the temperature. At a point in the neighborhood of 1100’ F., the coked particle can ignite, and the temperature rises more rapidly.
+
(Continued)
1862
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No, 9
ENGINEERING AND PROCESS DEVELOPMENT
(Kinetics o f Coal Gasification)
Development of Reaction Rate Equations
I
X A kinetic analysis of gasification, account must be taken of the simultaneous changes in material composition and temperature and of their mutual interdependence. Equations are herein derived to express the rates of the reactions occurring. These rates are incorporated in a series of simultaneous, linear, first-order, differential equations that may be used to calculate the changes in composition of the system.
DIFFUSION Derivation of Individual Rate Equations. GENERAL EQUATION. In a complex system of gases reacting with or in the presence of a solid phase, the individual rates of the heterogeneous reactions will be controlled by the rate of the slowest step in the complete reaction. In this analysis it is assumed that diffusion, surface reaction, or both are controlling.
I e
Adiabatic Preheat Temperature M a y Be Calculated from Thermodynamic Considerations
+ 02 2 C 0 . 2CO + Oz e 2CO2 .r2 HZ+ HzO . . .r3
(4)
, ,
1/z02
C C C
+ H e 0 CO + H2 . . + 2Hz0 * COz + 2H2 . . .TS .TP
+
+ COz .+ 2CO
...re
I
I
1
I
I
34
(3)
, .r1
4
I
h
In the very short period of time after the reactants enter the gasifier and during ignition, a considerable physical and chemical change occurs in the coal particles. The temperature rises very rapidly and volatile matter is evolved. Because of the extreme difficulty in expressing these changes kinetically, a method has been used baaed upon thermodynamics for calculating the temperature attained by the system upon the devolatiliaation and combustion of the hydrogen content of the coal corrected for sulfur. In this calculation are included the heat effects accompanying the transitions of the coal elements to their standard molecular states. The resulting compositions and temperatures of the system for various inlet conditions have been calculated t o serve as a basis for the kinetic calculations. Volatile matter carbon is calculated as fixed carbon in order to follow the entire course of carbon conversion during reaction. This introduces an error in the oxidation time, which is small compared t o the total reartion time. The method, in brief. consists of equating to zero the sum of the reaction heat and the enthiilpies of reactants and products relative t o 0" absolute temperature. A simple trial-and-error solution is used to evaluate the temperature and composition. The temperatures so calculated for the Rock Springs, Wyo., coal analysis used in this study are given in Figure 2. Equations of Continuity. The following sequence of reactions and their corresponding reaction rates has been proposed:
2C
I
(5) (6)
(7) (8)
The differential change in any component, A , is given by:
IY 0
0
0
-32 w
a
3
g30 a 2
r 28 0.4
0.8
0.6
1.0
LE. STEAM/LB. COAL Figure 2. Adiabatic Preheat Temperature for Rock Springs, Wyo., Coal Analysis
B
A thorough development of the theory of diffusion from kinetic theory is given by Jeans (111). I n the gasification system wherein a number of components are diffusing simultaneously, a rigorous treatment of the diffusion mechanism would be too awkward for use. However, Hougen and Wataon (108)have suggested a n approximate equation based on the assumption that, in a complex system of diffusing gases, the diffusional gradient established for any component A is equal to the sum of the gradients that would result from the separate diffusion of A with each of the other components in separate binary systems in which the concentrations and rates are the same as in the complex system. For the general reaction a A bB -+ rR sS, proceeding in contact with solid phase B and in the presence of an inert gas I, their equation is of the form:
+
+
d A = rAd0 where
For the gasification components therefore:
+ 2r5 - ra)de dHzO = + 2r6 - r8)& dCO = (2rl - 2r2 + r4 + 2re)d8
(10)
dCOa = (2rz
(12)
&I2 = (r,
-(rq
dC
do2 dna September 1953
+ r6 - rdde = - ( 2 f 1 + r4 + + re)& = + rz + l/zrddO = dH2 + dHzO + dCO + dCO2 + dOz y6
-(r1
(9) (11) and
(13)
(14) (15)
84
r+s-a a
For each of the heterogeneous carbon reactions,
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
&A
= 1.
1863
ENGINEERING AND PROCESS DEVELOPMENT Allowance must also be made for the fact that the diffusional aurface is spherical. It has been pointed out by Tu, Davis, and Hottel(81S) t h a t if d equals the diameter of the particle, the rate of difiusion t o the surface is obtained by multiplying Equation 16 by the geometric-mean film area: [ r d 2 X n(d 2X)2]1/2, so that
+
rA
=
DAmp x RTX
- pa') x [dx Pf
+ 2X)2]1/2
r(d
(19)
I oc
Because of the critical effects of temperature and particle size on the rate of diffusion and the transitions that occur at gasification temperatures between a diff usion-controlled rate and chemical reaction-controlled rate, neither chemical reaction nor diffusion is explicitly stated in this paper to control the reactions of carbon with steam or carbon dioxide. Instead, the rate of diffusion has been incorporated with the rate of chemical reaction into a single rate equation t h a t may be used over the entire range of gasifier temperature and particle size. Equation 22 may be used in general for any of the heterogeneous reactions in the gasification system. The denominator of this expression consists of the reciprocals of two factors: a diffu-
(& + 1)
2Da,P
sional function,
and a chemical-reaction-rate
* .
- IC
constant, k . If the reaction-rate constant, k , is small compared with the diffusional function, then the chemical reaction step controls, and the equation simplifies to the first-order rate law:
3
1
r
0 l-
0 + 0
a
w
IL
0.'
.oI
I
20
!
!
25 30 35 40 45 TEMPERATURE (100°F.)
To return to a formulation of specific rate of diffusion based upon carbon surface area, the expression is divided by the surface area, r d 2 : =
DA,P
RT
The partial pressure,
(PA
-
PA^)
Pf PA%, a t
the carbon surface may be expressed as a function of the rate of surface reaction. For the general monoinolecular reaction given: TA
= kpA,
(21)
where k is the specific reaction rate constant expressed in poundmoles per unit area per unit time per unit pressure. Substituting for p l i in Equation 20
To convert Equation 22 to a form expressing the total rate of reaction of a unit weight of carbon, let a = total particle area per mole of carbon fed. Furthermore, if the diameter of the particle ie small and the relative velocity of gas t o particle is low, such that X is large, the equation reduces to:
in which 7.4 = rate of reaction, moles per mole of carbon fed per unit time.
1864
As $ approaches infinity, chemical reaction controls; as L,I approaches zero, diffusion controls; as $ approaches unity, both steps have equal rates. The transition region has been arbibetween 0.1 and 10. Values of trarily taken for values of have been calculated for the carbon-steam reaction, using available physical data and Mayers' rate constant (144), for various temperatures and particle diameters, and assuming an effective film thickness for diffusion of 4 mm. The use of this value for film thickness has a significant effect only on the values of I,L calculated for particle sizes approaching infinite diameter (or plane surface). For small particle sizes the film thickness is essentially infinite. These values are plotted in Figure 3. Fair agreement is obtained between the data of such investigators as Clement, Adams, and Haskins (65, 56), Vulk and Vitnian (616), Haslam and Thiele ( I O I ) , Gadsby, Hinshelwood, and Sykes ( 8 1 ) , Hunt, Mori, and Katz ( I I O ) , and Mayers (143, 144). A notable exception is the work of Pexton and Cobb (168). The data of Tu, Davis, and Hottel (918) for the carbon-oxygen reaction showed a break point-Le., the upper teniperature limit of chemical reaction-controlling-at about 1580" F. It is significant that this temperature varied only slightly for various rates of gas flow. From the foregoing plot, this temperature would indicate a value of $ about 100 times as great as the value of $ a t the carbon-steam reaction break point, and therefore indicates that the chemical reaction rate for oxidation is about 100 times as fast as t h a t for the carbon-steam reaction, since the diffusivities in the tm-o cases are about equal. This is of the order of magnitude found by Meyer (148) and others. Reaction rate equations may be derived for each reaction occurring. REACTION 3. 2C OS + 2CO. The chemical rate of oxidation is fast compared with the rate of diffusion of oxygen t o the surface, and therefore Equation 23 reduces t o
+
Figure 3. Ratio of Diffusional Rate to Chemical Rate for Carbon-Steam Reaction as Function of Temperature
f A
= kapA.
Conversely, if IC is large relative to the diffusional function, diffusion controls and the equation reduces t o the form of the simple diffusion rate equation. When both functions are of the same order of magnitude, the rate is in the transition region. An index t o which step controls the carbon-steam reaction (and also the carbon-carbon dioxide reaction) can be obtained from the magnitude of $, where
a a I z
+
+
+
+
REACTION 4. 2 C O 0 9 S 2C02. This gas-phase oxidation has been studied by Haslam (96) with the conclusion that it
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 9
ENGINEERING AND PROCESS DEVELOPMENT approximates a third-order mechanism in accordance with the stoichiometric equation. The rate may be expressed by the clasRical third-order rate law 7.2
=
kl
[(pco)’ (poi)
- (PCO~/KZI
(26)
where rz = rate of consumption of oxygen based on gas-phase volume, (pound-moles)/( cu. foot) (second). The specific rate constant is given by the equation (108) l0gmk9 = 7.1899
-
16,523.5/T0 R
Exponential equations for the temperature variation of the equilibrium constants for Reactions 4 and 6 have been calculated from the data of Rossini and coworkers (167,168)
Kz =
elZ0,96Q.4/TQR,-.20.8&343
Ks = e64,3?0.S/T0
(32)
R,-6.00242
(33)
By differentiating’ with respect to time and suhtituting theae functions in Equation 31
with the units of (pound-moles of oxygen)/(cu. foot) (second) (atm.)g. The gas-phase volume must now be expressed as a function of the carbon fed. Assuming that the perfect gas law holda a t gasification temperatures u s - n&To
(27)
P
*
where no = total gaseous moles per mole of carbon fed. fore,
There-
with the units of (pound-moles of oxygen)/(pound-mole of carbon fed)(second). This kinetic expremion for the rate of Reaction 4 is rigorous over all conditions of temperature and composition. However, when equilibrium is approached in this reaction, the bracketed function, and hence the rate, approaches zero, and small variations in any of the partial pressures can cause considerable fluctuations in reaction rate. This is particularly detrimental to the accuracy of numerical integration methods used in highepeed machine calculations, because it forces the operation to select a smaller time interval and hence prolongs the calculation time. To avoid this mathematical instability, a conditional transfer may be set up 80 that, when a gas composition close to equilibrium is attained, the rate of Reaction 4 may be replaced by an expression involving equilibrium alone. The equilibrium constant for this reaction is given by
728 may
This equation is less sensitive to changes in gas composition than the previous kinetic expression and may be used in ita place when equilibrium is approached. REACTION 5. HZ 1/202 e H20. The oxidation of hydrogen is the fastest reaction in the gasification system and occurs by a complex chain mechanism. On the other hand, the steam reactions that produce hydrogen take place by a slower heterogeneous mechanism. It is to be expected in a system of reactions occurring consecutively and simultaneously that the fastest reaction will approach equilibrium and will be held in dynamic balance by the slower rates of the opposing reactions. The time required to attain equilibrium will depend upon the relative reaction rates. In gasification, hydrogen is not present initially; hence, any hydrogen formed by the carbon-steam reactions ia simultaneously oxidized, and Reaction 5 is substantially a t equilibrium throughout the entire period. The equilibrium constant for Reaction 5 k expressed by the equation:
+
(35) The total number of gaseous moles, ~EQ, may again be considered constant during the oxidation period; rn that upon differentiating
be considered constant, so that, upon differentiating
By suitable manipulation similar to the derivation of Equation 34, the rate of Reaction 5 is obtained as
””1 1
108,741.0 O2 To4 dB
co
p = 1 -2 1
4
0 2
xi-T-m
Making these substitutions in Equation 29 using Equations 11, 12, and 14, and solvingfor r2:
September 1953
(37)
REDUGTIOM OF STEAM BY CARBON. There are strong indications from the work of many investigators that the primary product of the surface reaction of steam with carbon is carbon monoxide. Secondary surface phenomena involving rearrangements of the complexes present maintain shift equilibrium a t the surface with respect to the component carbon monoxide, carbon dioxide, hydrogen, and steam. It is apparent, therefore, that rate constants obtained experimentally for the carbon-steam system are complicated functions of the complete reaction chain and do not represent any single step. The rate constant obtained by Mayers (144) has been discussed. I n his experiments, a large excess of steam was used, so that the partial pressure of the steam was essentially the total pressure of
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
186s
.
ENGINEERING AND PROCESS DEVELOPMENT t h e system. This rate is designated as ko, the gasification constant, in the nomenclature of this paper. To arrive at a suitable kinetic expression for the rate of reaction, steam is assumed to react with carbon by the reactions:
+ HzO C + 2H20 C
-+
-+
+ Hz C02 + 2H2 CO
(6)
+
li4
+ kg
+ HzO C + 2Hz0 c + coz
-+
+
+ Hz COz + 2H2
CO
-+
2CO
With respect t o the over-all reaction rates, it is a necessary condition that, in the steady state, the rate of diffusion of stenm t o the carbon surface must equal the rate of reaction of steam with carbon, and therefore
where
Substituting and solving for p,?:
(39)
It remains, therefore, to calculate k4 and kg in terms of kc to complete the rate data required. The ratio of kq to le6 is an index t o the extent of water-gas shift a t the surface. After all ovygen has been consumed, the water-gas components enter into reaction in the following manner: C
15,226/T0 R. (pound-moles of carbon)/ (3q. foot)(second)(atni.)
(38)
Under the conditions of Mayers' experiments, in n-hich pHZo 1.0 atm.,
k~ =
-
(7)
Reaction 7 is a simplified equation for the surface rearrangementa taking place. In terms of classical rate equations: ka = ~ ~ ( P H ~ ok~(prr,o)* )
logloka = 0.72940
(6)
Let
Solving the quadratic equation and taking only the positive root, since p s must be positive:
(7) (8)
These rates of these reactions may be expressed by the simple rate equations (neglecting inhibiting factors which are small a t high temperature and atmospheric pressure) :
PS =
Pa
orps = P,
27
x-k
(& + 7) + @ +
+ 4rP,]"z
-Yy
(53)
Xf(r)
For the monomolecular reaction, C 7-4
=
-+
CO
+ 112 (54)
= X.dapJ(-t)
For the bimolecular reaction, C rj
+ €120
+ 2H20
+
COS
+ 2IIZ (55)
k~a~,~[f(r)l~
If the surface reaction rate constant is small relative to thc diffusional function, y + 0 3 , and f ( y ) -+ 1.0, so that the r.Ltc eqiiations reduce t o the limiting case of chemical reaction rnte controlling. If, on the other hand, diffusion controls (using the second form of the quadratic solution for greater numerical accuracy), y -+ 0, and
Hence:
Differentiating Equation 46 with respect to time:
+
RIDCCTIONOF CARBOYDIOXIDE B Y C ~ R B O Y C: . Con-+ The mechanism of the carbon dioxide reaction is v e i y sinii1:tr to that of the steam renctioiis, but is uncomplicated hy secondary reactions. Conversely, the simultaneously occuri in g carbon dioxide reduction must be considered in calculati~igthe rate of the steam reaction in an atmosphere of steam and carbon dioxide. Referring to Equation 48, it may be noted that the specific reaction rate constant, he, for the carbon d i o d e reaction must be known to permit calculation of the rate constants Tor the steam reactions. Equation 23 for the rate of a heterogeneous reaction may llr used t o express the rate of the carbon dioxide reaction. The reverse reaction is negligible a t gasification temperatures. 2 0 .
Substituting the rates of change of the various components and solving for kq:
This relationship permits the calculation of rate constants k4 and k5 from the gasification constant, kc, and constant kb. These latter values may be obtained by the formulas (143, 144): 1OgdCkO = 0.51097
1866
-
13,822/T0 R, (pound-moles of carbon)/ (sq. foot)(second)(atm.)
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 9
ENGINEERING AND PROCESS DEVELOPMENT Equations Have Been Developed for Calculations of Particle Surface Area
In the reaction rate equations derived, the area of the particle system has been expressed by a, the particle surface area per mole of carbon fed. T h e rate constants reported by Mayers t h a t were used in this study are based upon the geometric area of the graphite samples. Consequently the same area basis was used in calculating a for pulverized coal. Differences in internal structure between the two forms of carbon and the effect, if any, of these differences on the reaction rate data have not been determined. It is assumed that, for pulverized coal, reaction occurs primarily at the surface, and ash is continuously removed in the process t o maintain a homogeneous surface of decreasing area. By definition:
residue and ash collected are not representative of the bulk of he particles leaving the gasifier are only partly consumed and account for unconverted carbon. Most of the er, is gasified, and the ash accompanying carbon in the coal, instance has carbon been found in the it enters the slag. slag.
M M.
ad2
a =
(59)
The weight of carbon per particle is c = pnord3
6 and carbon conversion is defined as: rJ
=
Ca
-c CO
so that d = d,(l -
325 200 100 60 U.S. STD. MESH
OT)'/r
Figure 4.
and the area equation becomes:
Both the specific diameter function, d/d,, and the specific area function ala,, can be plotted as straight lines with conversion on logarithmic paper. Use of the foregoing equations necessitates prior knolvledge of average particle diameter, surface area, and density. These functions are dependent upon the grind of coal used and may be calculated from size-distribution data by methods outlined by Kraemer (124). Samples of the pulverized coal feed to the eyperimental gasifier were s y s t e m a t i d l y collected and analyzed for chemical composition and size distribution. Samples of coked residue and fly ash were similarly analyzed. Fly ash consisted of particles that passed through the gasifier and waste-heat boiler and were collected in a cyclone separator. Residue consisted of coal particles that passed through the flame but were trapped a t the bottom of the gasifier in the slag-tap port. Chemical analysis of the residue and ash showed that the volatiles were reduced t o about 370, substantiating the belief t h a t volatile matter is driven off during the first part of the oyidation. T h e ash-carbon ratios of these samples also showed an interesting trend. T h e ratio in the coal feed was approximately 0.08: in the residue, 0.2; and in the fly ash, 0.4. This variation suggests a progreasive concentration of the ash in the particle, although t h e extent is only small when it is considered that the ratio could increase a hundredfold or more. It has been assumed in the kinetic calculations t h a t the ash-carbon ratio remains constant throughout the reaction time. The deviation from this assumption i s n o t serious and should not affect the accuracy of the computations. However, these observations are purely qualitative, as the
Particle Size Distribufion of Coal Feed and Residue
. T h e results of sieve tests have been plotted in %sin-Rammler form, as recommended by Landers and Reed (188), in Figure 4. Extremely close reproducibility of grinding is evidenced by the fact t h a t 24 pulverized-coal sieve analyses, representing composites of each run, have plotted on a single line. Other r e d t s show t h a t the Rosin-Rammler curves may not be extrapolated below the lower limit of resolution of the sieve method. Turbidimeter measurements of the subsieve sizes disclosed a break point near the minus 325-mesh size followed by a greater slope, and hence more uniformity of size in the fines. This is not simply the result of differences in analytical method, as the studies of others showed similar trends (140). Sieve analyses of the residue are plotted on the same chart as the coal feed. The greater slope of the former is probably due t o a partial classification of the larger particles after leaving the nozzle. On the other hand, the fly ash is too fine t o be meisured by sieve methods. Subdivision of the ash largely results from reaction rather than classification, as the small particles are more a p t t o react completely, leaving the partly consumed remains of the originally large particles. Decrepitation may also affect t h e size of the ash, although the data are inconclusive in this regard. Photomicrographs were taken of the coal, residue, and ash to permit studying the influence of heat and gas evolution on the particle shape. T h e pictures showed no evidence of a swelling phenomenon such as the formation of cenospheres. T h e shape of the particles mas irregular, as was expected, although the size-distribution d a t a have been correlated in terms of equivalent diameter spheres for simplicity in use.
(Confinued)
September 1953
INDUSTeIAL AND ENGINEERING CHEMISTRY
1867
ENGINEERING AND PROCESS DEVELOPMENT
(Kinetics o f Coal Gasificafion)
Development of Heat Transfer Equations and Method of Calculation
IK
COKSIDERIXG the case of an incandescent coal particle suspended in a medium of heat-absorbing gases and surrounded by refractory surfaces, a number of individual points must be taken into account before arriving a t the complete mechanism of heat transfer in the system. The temperature level ie the most important single variable in gasification. Inability to maintain the proper temperature majresult in reaction rates PO s l o i ~that no practical conversion can be achieved. This temperature dependence of the rate, however, has a different meaning than the rlassical concept of a controlling step in a reaction. The latter differentiates between such niechxnisms as diffusion, adsorption, desorption, etc., and a definite temperature level is implied. Reactors May Be Isothermal or Nonisothermal
ture, and so on. The oxygen content of the system is finally diminished to such an extent that a peak flame temperature is reached. The endothermic reatztions predominate after this temperature maximum, and the progression is reversed. A n y small amount of reaction will absorb heat, causing the temperature to drop, which in turn lowers the reaction rate. Finally the reactants are so depleted, or more probably, the temperature falls so low, that further reaction is negligible. Equations Are Derived from Studies of Heat Transfer Rate
9 study of the heat transfer phenomena in gasification must consider the following rates of heat transfer: rate of change of enthalpy of the pasticle rate of change of enthalpy of the gas rate of heat generation by surface reactions rate of heat generation by gas-phas reactions net radiant heat exchange b e h e e n coal surface and refractory x all net radiant heat evchange betxieen coal surface nnd absorbing gases net radiant heat exrhange hrtween absorbing gases and refractory wall rate of heat transfer b3- conduction through stagnant film from solid to ambient gas enthalpy difference betiwen counterdiffusing gaseouq componenta rate of heat loss from the gasifiei
Two major types of reactors may he compared. having a diameter of the 1. I ~ O T H E Rh IU4 B~ALT I C REICTOR same order as the longitudinal dimension. Under certain flow coiiditions extreme Iongitudinal turbulence may cause thorough mixing of the contents of the reactor, v hich results in a substantially uniform tempei atui e and composition throughout the reactor, that are the same as that of the product discharged from it. ADI ~ B A T I C RIXCTOR having a dlametei 2. SOLISOTHERMAL. that is small compared n ith the longitudinal dimension. Such a design would essentially prevent the mixing of the contents and would result in a progressive temperature and coniposition change throughout the reactor. In the case of an endotheimic reaction and for any pitrticular inlet condition and conversion, the temperature level throughout, the isothermal reactor n-ould be constant and would equal the adiabatic reaction temperatuie a t the conversion attained. Cnder the same circumstances, a nonisothermal reactoi would have a progressive temperature diop from a high initial temperature doxn to an exlt gas temperature that \Todd equal the uniform temperature in the isothermal reactor. It is apparent, therefore, that a long, tubular-type reactor would maintain a higher average temperature level than a reactor of, for instance, cubical shape, and would consequently iequire a shorter residence time for the same conversion owing to the higher average late of reaction. In a tubular-type reactoi, a coal particle may, for simplicity, be considered to be at the centei of a sphere of heat-absorbing gases. This concept is complicated by the fact that radiation is possible betm-een particles of varying temperatures and also f i om radiating gas masses of different temperatures throughout the gas volume. However, it is likely that the main heat transfer a ill be between the particle and the immediate gas body associated a i t h it. Furthermore, if the particle is suspended-that is, the relative velocity of the particle v i t h respect to the gas is close to zerothe temperature-time-composition history of the gas-solid system may be calculated by simplified methods. In gasification the folloiving thermal process is folloived: K h e n the exotheimic reactions predominate and foi any time interval, an increment of reaction will release a certain amount of reaction heat t o the system. This heat raises the temperature, which in turn raises the reaction rate. The increased reaction rate increases the heat evolved and consequentlv the temperit1853
T h e following heat balances may be derived: Heat balance around coal particle QP = QRS
- QC -
QRSW
-
QRSG
-
(62)
qR
Heat balance around gas volume q G == QRG
+
QC
- qRtW
+
qRSG
f qS - q L
(W
Heat balance over system of particle and gas volume qP
+
QG = Q R S
f
qRG
-
qRSW
qRGW
- qL
(64)
The equations for these rates must now be derived. Rate of Change of Enthalpy of Particle. If 3: is the fraction of inlet carbon converted a t time 8, then (1 -z) is the carbon remaining unconverted. Let 2 equal the molar ratio of ash to carbon in the coal. The rate of change of particle ciithnlpy is then given b y the rquation:
where C,, and C, arc t h e molar heat capacities of carbon : m l ash, respectivel;-. Rate of Change of Enthalpy of Gas. Let C,, equal thcl m r a n molar heat capacity of the gas. Then w C ~ , , ,= ~ A C , ~ B C , , ncCpc . , SO that,
+
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
+
Vol. 45, No. 9
ENGINEERING AND PROCESS DEVELOPMENT Rate of Heat Generation by Surface Reactions. Let rp equal the rate of any surface reaction, and A{, its heat of reaction. Then:
c
T(b+l)=
[s-)(
+
( T s b f ' - To"+')]
(66)
Xiri
qRS
Substituting Equation 71 for qc:
S
Rate of Heat Generation by Gas-Phase Reactions. Similarly, let rj equal the rate of any gaseous reaction, and Xj, its heat of reaction. Then: qRQ
=
c
br,
let
(67)
=
G
9RSW =
aam(Ts4- Tw4)N
(68)
However, for an actual gasifier the effective emissivity, €8, is a rather complicated function of reactor geometry and interference by absorbing gases and adjacent particles. Consequently, a simpler heat-loss eqwtion is derived below (rate of heat loss from gasifier) t o include radiation effects. Net Radiant-Heat Exchange between Absorbing Gases and Coal Particles or Walls. For simplicity i t is assumed that are negligible. This is not strictly true, as large qRSQ and concentrations of heat-absorbing gases, such as steam and carbon dioxide, are present. Nevertheless, gas absorption is small compared with the other rates of heat transfer and may be neglected. Rate of Heat Transfer by Conduction from Solid to Ambient Gas through Stagnant Film of Gas. Following the analysis given by Burke and Schumann (41-43), a derivation may be made to express the rate of heat conduction between gas and solid. Assuming that a steady state is reached so that the rate of change of the temperature of the particle is slow, as compared with the establishment of thermal equilibrium throughout the film, the heat conducted away per unit time across any stagnant spherical boundary is given by Fourier's law as:
where
K r T N
= thermal conductivity of the film a t temperature = radius of any differential film boundary
T
= temperature of the film a t radius r = number
of particles per pound-mole of carbon fed
The thermal conductivity of the film may be calculated by the following expression:
K
=
- ryTsb+']
(77)
- rs
Net Radiant-Heat Exchange between Coal Surface and Refractory Wall. If a coal particle is considered to be at the center of a sphere of refractory material in a nonabsorbing atmosphere, the net rate of heat exchange between particle and refractory is: *
Cr,Td+'
Hence
Enthalpy Difference between Counterdiffusing Gaseous Components. The enthalpy difference between the components of a system involving diffusing substances is given by the equation: qH =
2
RD,CP,(TS
TG)
i
=
1, 2, 3,
. . . 12
(79)
However, preliminary calculations have shown that this term is small compared with other rates of heat transfer and can be neglected for simplicity. Rate of Heat Loss from a Gasifier. I n connection with the vertical gasifier runs made by the Bureau of Mines a t Louisiana, Mo., temperature traverses have been made of gasifier skin temperature and inside refractory temperatures. Gasifier heat losses calculated from these studies are in good agreement with the heat unaccounted for in over-all heat balances. These overall heat-loss figures must, for the purposes of kinetic evaluation, be related to the instantaneous rates of heat loss over the reaction time. A simple relationship is proposed to accomplish this, which also includes t o some degree internal radiant-heat transfer. It is a logical deduction that incremental conversion and heat loss should have the same time curve. Thus, a t high temperature, conver,+ion is high owing to the rapid rates of reaction, and heat loss is also high owing to the large temperature driving forces. In addition, high particle temperatures would cause a net exchange of radiant heat to cooler particles and the refractory wall. In cooler sections of the gasifier, the reaction rates are not as great, resulting in a lower rate of conversion; and the cooler particles, although radiating t o the walls, are receiving radiant heat from the particles in the flame. Consequently, the net rate of heat loss is also lower. Therefore, let
T b KO( E )
qL
Substituting for K and integrating Equation 69: b # 1
-
2=1
ax a0
hL -
where = instantaneous rate of heat loss, B.t.u./(pound-mole carbon fed)(second) h~ = over-all gasifier heat loss, B.t.u. per pound-mole of carbon converted x = carbon conversion, pound-moles per pound-mole of carbon fed 8 = reaction time, seconds qL
Furthermore, if rs is small compared with the film thickness:
The temperature of the film a t a n y radius may also be calculated from Equation 69 by integrating without limits as follows:
(73) For the boundary condition, T = Ta a t r = ra
September 1953
Complex Calculations Predict Variations in Composition and Temperature with Reaction Time
Equations derived tQexpress the kinetic changes occurring in powdered coal gasification cansist essentially of material and heat balances, which are functions of the appropriate rates of chemical change and heat transfer and are part of a complex series of calculations that predict the variations in composition and tempera-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1869
ENGINEERING AND PROCESS DEVELOPMENT ture with reaction time in a tubular-type, pseudo-adiabatic, nonisothermal gasifier. I n the kinetic calculation there are eight unknowns: steam, hydrogen, oxygen, carbon monoxide, carbon dioxide, x,the carbon conversion, Ta,the gas temperature, and Ts,the particle temperature, which necessitate the simultaneous solution of eight equations. The formation of methane was not considered in this analysis, because the calculations were carried out for hightemperature atmospheric pressure operation. However, a t high pressures methane formation becomes substantial and would be included in an analysis of pressure gasification.
(GI = G P S COMPOSITION
co 4
2
3
H 2 + 112 0 2 * HZ;O
02.
2
1.0
cop
2
.I
5
.Ol
.GO4
.002 REACTION
Figure
.006
1. Choose any arbitrary set of operating conditions: steamcoal ratio, s / ~ ;oxygen-coal ratio, O / C ; steam temperature: Dart i d e size; and heat loss. 2 . Take the start for the calculation as that time after the adiabatic combustion (as niolecular hydrogen) of any net hydrogen in the coal. This is admittedly an approximation that disregards the form in which hydrogen is present in the mal. I t s basis is the belief t h a t the volatiles are thermally cracked during the initial preheat period before combustion begins. Because of the difficulty in expressing this process kinetically, the simplification justifies the theoretical inaccuracy involved. KO consideration was given to the nitrogen and sulfur content of the coal, except that hydrogen equivalent t o the sulfur was subtracted from the system. 3. Having established the initial conditions by step 2, proceed as follows: For the various conditions a t the start of any time interval, A8, such auxiliary functions as (1 - x)'/3, (1 - ~ ) ~ /etc., 3 , may be calculated. The specific reaction rate constants and the equilibrium constants are calculated from power-sei ies expansions of their normal equations if an electronic computei is used, or are obtained fiom graphs if the calculation is carried out manually These terms are then inserted into the reaction rate equations, and the individual rates are calculated. The incremental change in the number of nioles of any constituent is then calculated as a function of the reaction rates. These incremental change
