Kinetic Study of Carbon-Steam Reaction Bruce E. Riede and Deran Hanesian* Newark Co//egeof Engineering, Newark, New Jersey 07102
The experimental investigation into the kinetics of the carbon-steam reaction was made by suspending a %-in. diameter graphite rod in a thermally controlled vertical tube furnace. Steam passed into the furnace with nitrogen as a carrier gas. The weight loss of the graphite sample was measured by an externally mounted analytical balance located above the reaction tube. While the reaction pressure was maintained constant at about 1 atm, the variables explored were the reaction temperature between 500 and 900°C, the gas flow rate between 5 and 15 crn/sec, and the partial pressure of the water vapor between 7 and 12 cm Hg. A measured activation energy of 16,370 cal/rnol was close to reported values for similar temperatures. The data indicated an almost entirely surface reaction controlling model even at the highest temperature investigated. In the 700-900°C temperature range at the low partial pressure of water vapor, the diffusion model contributed only about 1-2% of the total resistance.
Introduction The pyrolysis of hydrocarbons in tubular furnaces results in the deposition of carbon on the reactor wall. For example, in the production of ethylene, in a steam cracking furnace from either light petroleum gases (ethane and propane) or heavier gas oil fractions, the carbon deposited on the furnace walls causes undesirable pressure drops and results in periodic furnace shutdowns for carbon burnout. The carbon which is deposited is a dense layer which takes the shape of the cylindrical tubes. Previous papers by Shah (1967) and Scott (1941) have discussed the kinetics of this reaction. Ergun and Menster (1965) have reviewed the reaction extensively and have discussed in detail the complexity of the reaction. This review shows that results vary with experimental conditions and the properties of the carbon used. The primary purpose of this study was to define the regions in which the rate of reaction was either controlled by surface reaction or gas film diffusion and to determine a rate expression applicable for use in hydrocarbon pyrolysis furnaces. Such knowledge is important for the reactions in a pyrolysis furnace but may not necessarily be important in the commercial units utilizing the water gas reaction. Thus, tests were made with carbon specimens similar to the carbon formed in steam cracking of hydrocarbons and the data were expressed in terms of penetration rate of the dense cylindrical layer formed on the furnace tube wall. Controlling Resistances The carbon-steam reaction is an example of a solidfluid reaction in which the solid carbon shrinks in size rather than forming an external ash layer and remaining dimensionally unchanged. For this reaction the following three steps occur in succession. (1) The water vapor diffuses from the main body of the gas through the gas film to the surface of the solid. (2) The reaction takes place between the carbon and the water vapor on the surface of the solid. (3) The reaction products diffuse from the surface of the solid through the gas film back into the main body of the gas. In similar, earlier studies, Yagi and Kunii (1955), Parker and Hottel (1936), and Tu, et al. (1934), investigated the carbon-oxygen reaction and showed that a t low temperatures chemical reaction predominates, while a t higher temperatures diffusion becomes controlling. Under some conditions, a combination of both resistances, gas film diffusion and chemical surface reaction, 70
Ind. Eng. Chem., Process Des. Develop., Vol. 14, No. 1, 1975
exists. When both resistances exist, a mean reaction rate constant, k,, is used in accordance with the equation
The combination of the resistances can be treated in an analogous manner t3 series resistances in heat transfer by the equation
and the relative importance of each resistance can then be determined by the estimation of the gas film resistance by extending the data given by Powell (1940) for the mass transfer factor us. Reynolds number. By comparison of k g with the mean rate constant, R , , the relative amount of each resistance can be calculated. Experimental Section The equipment flow diagram of the entire process is shown in Figure 1. Nitrogen Metering and Purification. Nitrogen was used as the carrier gas, as it is inert and should not interfere in the reaction. The nitrogen was purified by passage through a drying column containing anhydrous calcium sulfate to remove any traces of water vapor and by passage through a muffle furnace containing copper wire windings heated to about 800°C to remove any traces of oxygen. Saturator. In the saturator, moisture was added to the nitrogen stream by bubbling the gas through a series of two round-bottomed, three-necked flasks containing distilled water. The stirred water bath was maintained at a constant temperature by immersion heaters connected to a thermoswitch. Reaction Furnace. A detailed drawing of the vertical tube reaction furnace is shown in Figure 2 . The reaction tube consisted of a heavy-wall, fused quartz tube, measuring 11/4 in. i.d. and 1 1 ~ in. o.d., and having ground-glass high-vacuum seals with viton O-rings on each end. Six Chromel-Alumel thermocouples were tied with glass fiber cord to the outside of the reaction tube at positions 1, 4, and 8 in. above and below the vertical center of the furnace core to measure the temperature gradient along the heated length of the reaction tube. Another measuring Chromel-Alumel thermocouple was placed
*^
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ROTAFURNACE
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Figure 1. Equipmenr flow diagram
within a fused quartz thermocouple probe, 5 mm i.d. and 7 mm o.d., to record the apparent temperature of the sample during reaction. The furnace core consisted of an externally threaded Alunduni tube 24 in. in length with a 11/3-in. bore, 2li4-in. 0.d.. and a lh-in. thread pitch. In the threaded grooves of the core were placed three separate windings of 24-gauge Nichrome V resistance wire, each covering 8 in. of tube length. A controlling Chromel-Alumel thermocouple, located in the probe with the measuring thermocouple, was connected to a Leeds and Northup Speedomax H recorder with a Duration adjusting type control unit which recorded the apparent sample temperature and regulated the power input to the central coil cia a relay and the variable transformer. 'The carhon rod specimen was placed. with its longitudinal axis parallel with the direction of flow, in a basket made from a 60-mesh nickel wire screen. The wire screen basket was suspended by a 0.0125-in. diameter nickel-chrome wire. The wire passed through a 1 to 2-mm hole a t the top of the reaction tube ana was attached to the external weighing pan of an analytical balance located on a platform directly above the vertical tube furnace. 'The bottom of the wire screen basket containing the rod was about +4 in. from the thermocouple probe containing the measuring and controlling thermocouples. ITnder t,hese conditions, calculations indicated that the temperature difference between the thermocouple and th.e rod would be about l-*%"C.This difference is within the range of experimental error. 580-Grade Graphite Characteristics. The 580-gr:~de graphite used was a manufactured graphite possessing the physical properties listed in Table I and containing the impurities noted in Table 11. The 580-grade graphite used was a pure grade of carbon which was fully graphitized at approximately 2500°C. Consequently. because of the high graphitization temperature, the graphite did not contain any volatile organics to interfere with the experimental carbon weight rneasurements. The graphite samples also possessed a low ash content. which further aided the experimental reaction. In Table I, the particle size indicates the maxim'um size of the particles in the grain used to fabricate the rod. Hence, it is an indication of the coarseness of the structure. Procedure. A prepared graphite rod sample, approximately 1 in. in length by l/i in. in diameter and 5 . 5 g in weight, was precisely dimensioned with A micrometer. The graphite sample was placed in the nickel wire mesh basket and after about 10 min of nitrogen, flow was low-
A S B E S T O S INSULATION 3 COILS OF *24 NICHROME P RESIST A N C E WIRE
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HE A S URlNQ T H ERMOCOUPLC
BRDUND BLASS JOINT W I T H 0-RlNO
CON+R o L THERMOCOUPLE
Figure 2. Vertical tube furnace
Table I. Typical Physical Properties of 580-Grade Graphite Density Specific resistance Flexural strength (min) Particle size (max) Ash (max) Average porosity How formed
1.73 g/cm' 0.00042 ohm-in.
2500 lb/in. 0.008 in. 0.15% 24%
Extruded
Table 11. Impurity Level of 580-Grade Graphite
Impurity Calcium Iron Alu minu in Silicon Vanadium Titanium Boron Sulfur Total ash Gas content, cm' 'g to 1 0 0 0 " ~
Amount of impurity, PPm 100
1500 20 65 110 20
0.7 120 1500
1.00
ered by means of the nickel-chrome wire into the reaction tube to within 114 in. of the thermocouple probe. The temperature control units on the reaction furnace and saturator bath were permitted to stabilize at their respective control points, which generally took about 3h-l hr. The entire start-up period usually was about llh hr. The sample weight and other variables were continuously monitored and recorded throughout the entire reaction period, which lasted from 1to 2 hr. Ind. Eng. Chern.. Process Des. Develop., Vol. 1 4 , No. 1, 1975
71
0
10 20 REICTION
3 0 TIME
4 0
XIO.'
5 0 SECS I
Figure 3. Cumulative carbon weight loss u 9 reaction time. Curve I ( 0 ) :temperature, 879.8"C; partial pressure of water. 11.69 cm Hg; gas velocity, 14.90 cm/sec. Curve I1 (HI:temperature, 921°C; partial pressure of water. 7.34 c m Hg; gas velocity, 14.90 cm/sec.
The sample, upon removal from the reaction tube and after further cooling, was again dimensionally calibrated and inspected for changes in appearance. Additional details about the apparatus and procedure have been published (Riede, 1969) and supplementary material has been submitted for the microfilm editions. (See the paragraph a t the end of the paper regarding supplementary material .) Observations. The apparent sample temperature, as observed by these two thermocouple wires, was controlled to within 05°C under most experimental conditions. A t several of the higher temperature runs, the controller was able to regulate the temperature to only 1 5 ° C because of powerstat instability. The longitudinal temperature gradient along the outside wall of the central 8-in. vertical section of the fused quartz reaction tube seldom exceeded 6-8"C, as observed by four of the six thermocouples attached to the tube wall. The temperature sensed by the thermocouples in the probe and the adjacent wall thermocouples usually agreed within 5°C. The graphite samples examined a t the end of each run were blackened in appearance, but the exterior surface remained relatively smooth. Only at the highest temperature runs was the sample surface slightly roughened. The nitrogen gas flow rate was monitored and maintained to within an accuracy of 5%, and the reaction pressure was regulated by means of the air bleed to 4 mm Hg. The saturator water bath could easily be controlled to within 0.4"C of the desired temperature, and therefore the equilibrium partial pressure of water could be maintained within 0.20-0.30 cm Hg. Discussion of Results General Reaction Results. The initial portions of the reaction rate curves were linear but started to curve after 1.5-2 hr. This curvature was probably because the surface of the rods became pitted along the graphite grain after the initial reaction period and resulted in a slightly irregular surface. At the start of the weight measurements only about 0.1-0.2% weight change had occurred for the worst cases. In most runs, the initial weight change was negligi72
Ind. Eng. Chem., Process Des. Develop., Vol. 14, No. 1 , 1975
ud
09 VVERSC
IO 1 1 12 I3 I ABSOLUTE TEMDERbTU9E
15 0'
"K
Figure 4. Mean reaction rate constant us inverse absolute temperature (partial pressure of water = 7.27 cm Hg): 0 , 4.97 cm/ sec, m, 9.94 cm/sec; A , 14.90 cm/sec gas velocity.
ble. Typical weight loss us time curves are shown in Figure 3. The slope of these graphs represents the rate of reaction. The mean reaction rate constant, h,, was plotted against the inverse absolute reaction temperature for the various gas flow rates as shown in Figures 4 and 5. Below 500°C it was difficult to obtain good kinetic rate data because there was almost no reaction and the change in specimen weight could not be measured. Above 9OO"C, instability in the variable transformer controlling the reaction temperature became a problem and reliable data could not be obtained. Hence, only the data obtained between 500 and 900°C were felt to be accurate for inclusion in this study. Controlling Resistances. As indicated in the study of carbon-oxygen reaction by Yagi and Kunii (1955), at the lower temperatures the curves shown in Figure 4 were approximately linear, denoting chemical surface reaction controlling, and then became curved a t the higher ternperatures. The curved plots were noticeable a t the lower partial pressure of water and no curvature is observed at the higher partial pressure of water. Similarly, some effect of velocity is observed at the lower partial pressure of water. Estimation of the diffusion resistance by the extending of the mass transfer factor correlation given by Powell (1940) for vertical cylinders indicated that a t the highest temperatures, lowest gas velocities, and lowest water partial pressure this resistance, considering the total rod surface, amounted to only 1-2%. Hence, the reaction under conditioiis of this study is almost entirely surface reaction controlling. Deviations in Chemical Reaction Kinetics. Theoretically, the linear portions of Figure 4 should be independent of gas-velocity. However, experimentally small differences in k, values were measured in this region. There is no apparent explanation for these differences, although some deviation may have been caused by experimental error. There were several possible causes of experimental error which may have resulted in these variations. Slight
loor
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5
Figure .i.Mean reaction rate constant u s . inverse absolute temperature (partial pressure of water = 11.85 cm Hg): 0 , 4.97 cm/ sec; m, 9.94 cm/sec; A , 14.90 cmisec gas velocity. changes in the saturator water bath temperature, although small if any, would have altered the water vapor concentration during the run. Also, because of the endothermicity of the reaction, the higher steam flow rates would have created a small cooling effect on the carbon sample which might not have been completely detected by the thermocouples. Finally, even though a fresh sample was used for each run to minimize surface area differences and prevent changes in porosity, there still might have been slight variations in the surface contact area since the sample was probably composed of carbon particles of various sizes. In addition to small experimental error, some complications in the boundary layer around the carbon cylinder may result and affect the measured rate of reaction. The gas flow past the graphite sample was laminar throughout, as the Reynolds number was always under 25. The contact time between the steam and the graphite sample ranged from 0.20 sec a t the fastest velocity to 0.45 sec at the lowest velocity, with the average contact time being about 0.30 sec. The amount of steam by-passing the carbon sample during reaction was constant and, therefore, had no relative effect on the reaction rate. Activation Energy, Kinetic Order, a n d Other Results. The data in this study were correlated by a simple Arrhenius model and first-order rate law. Numerous models based upon the Langmuir-Hinshelwood approach and given by Yang and Hougen (1950) were tested using Marquardt’s statistical method for nonlinear parameter estimation. In addition, adjustment of the Arrhenius preexponential factor by T-1 2 as used for the carbon-oxygen reaction by Parker and Hottel (1936) and T u (1934) was attempted. However, the statistical results did not justify the more sophisticated models and a simple Arrhenius correlation with first-order rate law was used. This rate law form was
The Arrhenius preexponential factor and the activation energy were obtained from Figure 5 , and eq 3 becomes
At the lower partial pressures, the activation energy was given by the linear portion of Figure 4 and was 13,450 cal/ mol. The preexponential factor was 13,933 cm/hr. Scott (1941) reported second-order kinetics for the temperature range 700-1000°C for lignite char particles and indicated the activation energy was 26,000 cal/mol. Shah (1967) indicated a first-order reaction and activation energy of 21,300 cal/mol based upon Scott’s data. Johnstone, et al (1952), used a Langmuir-Hinshelwood approach and reported the activation energy decreased from 32.700 cal/ mol to 13,100 cal/mol as the per cent carbon consumed increased from 0 to 7.5%. A cylindrical, porous graphite tube was used in their study which was for temperatures between 850 and 940°C. Mayers (1934) indicated an activation energy of 22,000 cal/mol for temperatures between 860 and 960°C and a graphite sample. Scott (1941) indicated that the nature of the carbon can vary results considerably and that the presence of catalytic materials in the ash is an important factor. This fact probably accounts for the wide variation in activation energies reported in the literature at temperatures above 1000°C for this reaction. In this study, the rate of reaction was normalized based upon the external surface area of the carbon. The rate was calculated proportional to external surface area and, hence, the units of the rate constant are the same as a penetration rate. This rate constant can, therefore, be more easily related to the penetration of the dense carbon deposits on the cylindrical walls of the ethane-propane pyrolysis furnaces. However, since the carbon specimens were 24% porous, diffusion into the pores is important. An estimate of the Thiele modulus under extreme conditions indicates that the water vapor could penetrate into the pores and some reaction could occur inside the specimen. The specimens in this study were carefully machined to 0.5 in. in diameter by 1 in. long such that the external surface area was within 0.1 to 0.2 cm2 (total surface 12.6 cm2) for all runs. Under these conditions the external surface area to specimen weight ratio was 2.3 cm2/g. This ratio can therefore be used to convert all rate data from the penetration basis of this study to a sample weight basis. Details on the pore size, pore size distribution, and total surface area are not available for these specimens and hence, a rate constant based on total surface area could not be calculated. Conclusions The following conclusions were made. At atmospheric pressure and at a reaction temperature range of 500%x)oC, the carbon-steam reaction data fit first-order kinetics, having an activation energy of 16,370 cal/mol with the principal .products probably being carbon dioxide and hydrogen. The reaction is almost entirely surface reaction controlling in this temperature range with mass transfer resistances of only 1-2% under the most extreme cases. Acknowledgment The authors wish to thank Mr. Richard W . J . Robertson, Kewark College of Engineering, for his assistance with the computer analysis of the various models tested using Marquardt’s Method for Non-Linear Estimation of Parameters. Ind. Eng. Chem., Process Des. Develop., Vol. 14, No. 1, 1975
73
Nomenclature a, b = stoichiometric coefficients for water vapor, carbon C.4 = concentration of water vapor in nitrogen, mol/cm3 D = diffusion coefficient, cm2/sec dL, = diameter of graphite rod, cm E = activation energy, cal/mol k,, = Arrhenius preexponential factor, cm/hr k , = diffusion reaction rate constant, cm/hr ks = surface controlling reaction rate constant, cm/hr k s = mean reaction rate constant, cm/hr N r 4 = moles of carbon P.\* = equilibrium partial pressure of water vapor in ni-
trogen, cm Hg P = total pressure in saturator, cm Hg R = ideal gas law constant Sex = exterior surface area of graphite rod, cm2 t = time, hr T = reaction temperature, "K Sc = Schmidt number Re = Reynoldsnumber y.\ = mole fraction of water vapor Literature Cited Ergun, S., Menster. M.. "The Chemistry and Physics of Carbon," Vol. I , pp 203-263, P. L. Walker, Jr., Ed., Marcel Dekker, Inc., New York. N.Y., 1965.
Johnstone. H. F., Chen. C. F., Scott. D . , Ind. Eng. Chem., 4 4 (7). 1564 (1952). Mayers, M. A . , J . Amer. Chem. Soc., 56, 1879 (1934). Parker, A . S.. Hottel, H. C., Ind. Eng. Chem., 28, 1334 (1936). Powell, R. W.. Trans. lnst. Chem. Eng., (London), 18, 36, (1940). Riede, 8. E.. M.S. Thesis, Newark College of Engineering, Newark, N.J., 1969. Scott, G . S., Ind. Eng. Chem., 33, 1284 (1941). Shah, M. J., Ind. €ng. Chem., 59 (5), 74 (1967). Tu, C. M., Davis. H . , Hottel. H. C., Ind. Eng. Chem., 26, 749 (1934). Yagi, S..Kunii, D.. "5th Symposium (International) on Combustion,'' p 231, Reinhold. New York, N.Y.. 1955. Yang, K. H.. Hougen, 0. A , , Chem. Eng. Progr., 46, 146 (1950).
Recezuedfor reuieu March 11, 1974 Accepted September 5, 1974
Supplementary Material Available. Additional experimental details will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the ,Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number PROC-75-70.
A Simplified Analytical Design Method for Differential Extractors with Backmixing. I. Linear Equilibrium Relationship
H. R . C . Pratt University of Melbourne, Victoria, Australia
Approximate solutions are presented to Miyauchi's equations (1957) for mass transfer with backmixing in differential extractors. Given values of the Peclet numbers P x and P,, and of H o x (or the mass transfer coefficient), these permit the column length to be calculated directly for the case of a linear equilibrium relationship. Comparisons of exact and approximate solutions indicated that, with a high degree of backmixing in both phases and values of the extraction factor between 0.50 and 2.0, the results are accurate to well within 5% when the length > 4 ft and Nox > 2.
Introduction General. In spite of a voluminous literature on the theory of two-phase mass transfer, the precise design of contacting equipment from first principles is unreliable in the absence of experimental data for the particular system and contactor to be used. This is a result of the complexity of the interacting factors which control performance. Liquid-liquid extraction is no exception in this regard, to the extent that the extensive published data for droplet contactors ( e . g . , packed columns) are virtually useless for design purposes outside the exact range of conditions reported. This is largely due to the effect of backmixing (longitudinal dispersion) of the phases, which reduces concentration gradients and adversely affects performance. In an extensive programme of work some years ago by the author and coworkers on packed columns (Gayler and Pratt. 1951, 1957a,b; Pratt, 1955), the need was recognized to consider separately the questions of interfacial 74
Ind. Eng. C h e m . , Process Des. Develop., Vol. 14, No. 1 , 1 9 7 5
area of contact of the phases, individual phase mass transfer coefficients, and "longitudinal mixing" of the phases, and methods were devised for predicting these in the absence of interfacial (Marangoni) effects. The backmixing correction was, however, based on a relatively crude graphical method and more recently Eguchi and Nagata (1958), Sleicher (1959) and Miyauchi (1957) proposed a more realistic diffusional model. This yields a rather complex analytical solution which can be used to obtain the concentration profile directly, but requires trial and error to calculate the column length required for a specified duty. To overcome this difficulty, a simple approximate solution to the model is presented which gives the length directly. This possesses useful advantages over other proposed methods, summarized later. Theoretical Basis. Mass balances over a differential length of contactor, taking into account axial diffusion, yield the following equations for one-dimensional steadystate countercurrent flow (Miyauchi, 1957; Miyauchi and
