Ind. Eng. Chem. Res. 1989,28, 611-618 S u p p l e m e n t a r y Material Available: Experimental systems and conditions used in calculating each pair of ASOG parameters, the number of data points of each system, and 48 references to the literature (12 pages). Ordering inform a t i o n is given on a n y current masthead page.
Literature Cited Bagrov, I. V.; Dobroserdov, L. L.; Shakhanov, V. D.; Mikhailova, M. I. Liquid-Vapor Phase Equilibriums in the Methylene ChlorideEthyl Acetate System a t Atmospheric Pressure. Izu. Vyssh. Ucheb. Zaued., Khim. Khim. Tekhnol. 1970, 13(4), 499-502. Brown, I.; Smith, F. Liquid-Vapor Equilibria. VI. The Systems Acetonitrile+Benzene a t 45 "C and Acetonitrile Nitromethane at 60 "C. Austr. J . Chem. 1955,8, 62-67. Danciu, E. Liquid-Vapor Equilibrium. V. Binary Systems Acetone-Allyl Alcohol and Propylene Oxide-Allyl Alcohol under Isobaric Conditions. Rev. Chim. (Bucharest) 1971,22(2), 81-87. Dehmelt, Ch.; Finke, M.; Bittrich, H. J. Intermolecular Interaction of Diethylamine Systems with Aromatic Components. I. Heats of Mixing and Liquid-Vapor Equilibriums. 2. Phys. Chem. (Leipzig) 1974, 255(2), 251-260. Derr, E. L.; Deal, C. H. Analytical Solutions of Groups: Correlation of Activity Coefficients through Structural Group Parameters. Inst. Chem. Eng., Symp. Ser. London 1969, 32, 3:44-3:51. Dohnal, V.; Blahova, D.; Holub, R. Vapor-Liquid Equilibrium in Binary Systems Formed by Acetonitrile, 2-Butanone and 1,2-Dichloroethane. Fluid Phase Equilib. 1982, 9, 187-200. Engelman, K.; Bittrich, H. J. Isobaric Liquid-Vapor Equilibriums of the Systems Diethylamine/Ethyl Acetate, Diethylamine/l,4Dioxane, and Ethyl Acetate/l,4-Dioxane a t 760 mmHg. Wiss. 2. Tech. Hochsch. Chem. Leuna-Merseburg 1966,8(2-3), 148-153. Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Determination of UNIFAC Parameters. In Vapor-Liquid Equilibria Using UNIFAC. A Group-Contribution Method; Elsevier Scientific: Amsterdam, 1977. Khurma, J. R.; Muthu, 0.;Munjal, S.; Smith, B. D. Total Pressure Vapor-Liquid Equilibrium Data for Binary Systems of 1-Chlorobutane with Ethyl Acetate, Acetonitrile, Nitromethane, and Acetone. J . Chem. Eng. Data 1983a, 28, 86-93. Khurma, J. R.; Muthu, 0.;Munjal, S.; Smith, B. D. Total Pressure Vapor-Liquid Equilibrium Data for Binary Systems of Chlorobenzene with Nitromethane, Ethanol, Benzene, and 1-Chlorobutane. J . Chem. Eng. Data 1983b, 28, 100-107. Khurma, J. R.; Muthu, 0.;Munjal, S.; Smith, B. D. Total Pressure Vapor-Liquid Equilibrium Data for Binary Systems of Dichloromethane with Pentane, Acetone, Ethyl Acetate, Methanol, and
+
611
Acetonitrile. J . Chem. Eng. Data 1983c, 28, 412-419. Kojima, K.; Tochigi, K. Analytical Solutions of Groups (ASOG). In Prediction of Vapor-Liquid Equilibria by the ASOG Method; Kodansha Ltd.: Tokyo; Elsevier Scientific: Amsterdam, 1979. Komarov, V. M.; Krichevtsov, B. K. Liquid-Vapor Equilibriums in Systems Formed by Aliphatic Amines, Alcohols and Water. I. Liquid-Vapor Equilibriums in Systems Formed by Isopropylamines, Isopropyl Alcohol and Water. Zh. Prikl. Khim. 1969, 42(12), 2772-2776. Kristbf, E.; Orszlg, I.; Ratkovics, F. Static Vapour-Liquid Equilibrium Studies on (xC,H7NH2 + (l-x)C,H,OHI. J . Chem. Thermodyn. 1981, 13, 557-562. Letcher, T. M.; Bayles, J. W. Thermodynamics of Some Binary Liquid Mixtures Containing Aliphatic Amines. J . Chem. Eng. Data 1971, 16, 266-271. Linek, J.; Wichterle, I.; Polednovl, J. Liquid-Vapour Equilibrium. LIII. The Systems Benzene+Diisopropyl Ether, Diisopropyl Ether+Toluene, Diisopropyl Ether+ Ethylbenzene, Benzene+Dipropyl Ether, Dipropyl Ether+Toluene and Dipropyl Ether+Ethylbenzene. Collect. Czech. Chem. Commun. 1972, 37, 2820-2829. Mato, F.; Shchez, J. Equilibri? Liquido-Vapor de Mezclas Binarias de Acetonitrilo. I. An. Quim. 1967, 63-B, 1-11. Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. Comput. J . 1965, 7, 308-313. Ott, J. B.; Marsh, K. N.; Richards, A. E. Excess Enthalpies, Excess Gibbs Free Energies, and Excess Volumes for (Di-n-Butyl Ether+Benzene) and Excess Gibbs Free Energies and Excess Volumes for (Di-n-Butyl Ether+Tetrachloromethane a t 298.15 and 308.15 K. J. Chem. Thermodyn. 1981,13,447-455. Rao, K. V.; Raviprasad, A.; Chiranjivi, C. Isobaric Vapor-Liquid Equilibrium of Binary Mixtures of 1-Propanol+Chlorobenzene and 1-Butanol+Chlorobenzene. J . Chem. Eng. Data 1977, 22, 44-47. Suryanarayana, Y. S.; Van Winkle, M. Solvent Effect on Relative Volatility. n-Hexane+Hexene-1 System. J . Chem. Eng. Data 1966, 11, 7-12. Vijayaraghavan, S. V.; Deshpande, P. K.; Kuloor, N. R. Isobaric Vapour-Liquid Equilibrium Studies on Di(iso)Propyl Ether +Cyclohexane System. J . Indian Inst. Sci. 1965, 47, 57-63. Wilson, G. M.; Deal, C. H. Activity Coefficients and Molecular Structure. Activity Coefficients in Changing EnvironmentsSolutions of Groups. Ind. Eng. Chem. Fundam. 1962,1, 20-23. Received for review August 13, 1987 Revised manuscript received July 15, 1988 Accepted December 12, 1988
Heat-Transfer Parameters for an Annular Packed Bed William A. Summers,+Yatish T. Shah,*?*and George E. Klinzing Chemical a n d Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
Heat-transfer experiments are performed in an annular packed bed heat exchanger using ring-type packing. New empirical correlations are developed for the wall heat-transfer coefficient and the effective bed thermal conductivity. The wall heat-transfer coefficient is found to be significantly higher than the values predicted by previous investigators. The implications of the results are briefly discussed. The proper design of any chemical reactor requires knowledge of the transport properties of the reactor. In the case of a fixed bed catalytic reactor, the prediction of these properties is complicated by the existence of two phases and the potential for intraparticle and interparticle
* Author
t o whom all correspondence should be addressed. Present address: Westinghouse Electric Corporation, Advanced Energy Systems Division, Pittsburgh, P A 15236. f Present address: College of Engineering and Applied Sciences, T h e University of Tulsa, Tulsa, OK 74104.
temperature and concentration gradients. Most of the reported literature on packed bed heat transfer is based on measurements taken f o r n o n r e a c t i n g beds with welld e f i n e d particles such as sphere or cylinders. The objective of this paper is to present new empirical correlations for the heat-transfer parameters within an annular packed bed heat exchanger, which simulates the geometry of a new annular fixed bed steam reformer. The annular reformer (Hoover et al., 1982) catalyst bed consists of an annular packed bed with a small tube diameter to particle diameter ratio. The p a c k i n g is composed of cat-
0888-5885/89/2628-0611$01.50/0 0 1989 American Chemical Society
612 Ind. Eng. Chem. Res., Vol. 28, No. 5, 1989 1
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Figure 1. Comparison of correlation for wall heat-transfer coefficient.
CIRCUMFERENTIAL POSITION (DEGREES1 AXIAL LOATION A E C 0 E F 0 I80 0 0 0 I80 0 180 no 90 0 270 90 180 0 270
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alyst rings, which result in a large void fraction of over 50%. Data for this type of reactor geometry have not been reported previously in the literature. A large number of investigators have measured heat transfer from the wall to flowing gas in packed tubes, and many correlations for the wall heat-transfer coefficient have been reported in the literature. Unfortunately, there has been no general agreement on either the form of the correlation or the empirical constants that are employed. Various Nu, versus Re, correlations reported in the literature are shown in Figure 1. These correlations show the wide range of experimental conditions and the discrepancies in the correlations, including Re, dependency as indicated by the slopes of the curves. In the present paper, a similar correlation for the annular fixed bed geometry is presented. Experimental Equipment The experimental apparatus used in this study consisted of a double-pipe heat exchanger with a packed annulus, two high-temperature furnaces, a digital data recorder, a compressed air supply system, and associated instrumentation, piping, valves, and controls. A simplified experimental setup is shown in Figure 2. Compressed air at approximately 100 psig was filtered and the pressure was reduced to 30 psig by a pressure regulator. The flow was then split and directed through two rotameters. Air from the first rotameter was heated successively by two high-temperature electric furnaces. The heated air at approximately 200-250 "C was passed upward through
the central tube of the double-pipe heat exchanger. The heat-exchanger tube was filled with l/*-in. aluminum spheres to enhance heat transfer from the heated air. After passing through the central tube, the air exited at the top of the heat exchanger. Air from the second rotameter was introduced through a side connection in the heat exchanger and passed downward through the annular gap between the two tubes of the heat exchanger. The annular gap was filled with heat-exchanger packing consisting of approximately 1/4-in.x ll4-in. x '/*-in. alumina reforming catalyst support rings supplied by United Catalysts, Inc. Since the objective of the study was to measure heat transfer without reactions, only catalyst support material was employed. After passing through the packed annulus countercurrently to the hot air stream, the air exited from a side connection at the bottom of the heat exchanger. Both air streams were vented through a ventilation hood. Gas pressures were measured by means of four Ashcroft pressure gauges. Temperatures were measured by 47 chromel-alumel Type K thermocouples (see Figure 3). The packed bed temperatures were measured by 0.040-in.-diameter sheathed thermocouples inserted through the outer annulus wall. The sheathed thermocouples had a glass-sealed exposed junction to prevent error caused by heat conduction along the thermocouple sheath. The small diameter stainless steel sheaths were chosen to minimize disruption of the packed bed by thermocouples. Temperature readings were recorded automatically by a data recorder. The annular packed bed heat exchanger used in the present study was a tube-in-tube double-pipe heat exchanger packed with catalyst support rings. The outer tube was constructed of a 48-in.-long piece of 3h-diameter Schedule 40 pipe of 304 stainless steel. The inner tube was a 60-in.-long, 1 1/2-in.-o.d.aluminum tube with a 0.035in.-thick wall. The two pipes were held together by a pair of 304 stainless steel flanges at each end. The inner tube was centered in the end flanges by use of Swagelok connectors. High-temperature graphite gaskets were used for sealing. The entire heat exchanger, including the flanges and inlet/outlet connections, was insulated by several inches of mineral wool insulation. The annular gap be-
Ind. Eng. Chem. Res., Vol. 28, No. 5, 1989 613 INNER WALL
Table I. Annular Bed Heat-Exchanger Test Conditions hot air cold inlet hot inlet cold air flow flow rate, temp, "C temp, "C test rate, SCFM SCFM 1 15.0 20.0 64.7 189.0 2 10.0 15.0 83.6 237.2 177.2 3 18.0 24.0 59.8 241.1 4 5.0 10.0 95.4 248.4 5 7.5 12.0 84.8 215.3 6 12.5 16.0 71.2 221.6 75.4 9.0 7 6.0 71.1 236.0 8 11.25 15.0 254.2 12.0 75.2 9 8.75 238.4 10.0 80.3 10 6.75 11 14.25 206.3 22.0 78.9 211.4 22.0 84.3 12 13.50 13 16.00 223.8 22.0 77.7 14 17.00 222.1 22.5 75.9
tween the two tubes was 20-mm (0.784-in.) wide and was packed with alumina catalyst support rings, 'I4-in. high, 'I4-in. diameter, with a 'I8-in. hole. The tube diameter to particle diameter ratio (using the hydraulic diameter of the annulus) was 6.3, which was approximately the same as the proposed ratio for the annular bed reformer.
Experimental Results Test Matrix. A total of 14 separate test runs were made with cold air flow rates ranging from 8.0 normal m3/h (5.0 SCFM) to 29.0 normal m3/h (18.0 SCFM). Test conditions for each of the tests are shown in Table I. The cold air entered the top of the heat exchanger a t ambient temperature and was preheated to approximately 75 "C before reaching the uppermost thermocouple location. The hot air flow rate was maintained at approximately 150% of the cold air flow rate, and the furnace settings were adjusted to maintain a hot air temperature (measured at the lowest heat-exchanger thermocouple location) of 200-250 "C. This resulted in packed bed temperatures at the midpoint of the heat exchanger of 125-150 "C. Temperature readings were recorded at specified time intervals. When steady-state operating conditions were assured, a final set of data was taken. A typical experimental run required approximately 2-3 h for the heat exchangers to reach operating temperatures, and an additional 1 h to ensure steady state. A complete run, including cool-down, required approximately 5-6 h. Data Analysis. The central 12-in. portion of the heat exchanger was used as a control volume for the data analysis. The data from a typical test run are shown graphically in Figure 4. Radial temperature data were taken at each of five axial locations: 0, 3, 6, 9, and 12 in. from the inlet of the control volume. At each axial location, the inner wall temperature, the outer wall temperature, and four bed temperatures were measured. The thermocouple probes were placed in order to record the bed temperatures at 'I8,'I4, and 'Iz in. from the inner tube wall, corresponding to lI2, 1,11/2, and 2 particle diameters from the wall. The data were well-ordered, showing increasing temperatures both axially (in the direction of cool air flow) and radially (from the outer wall inward). Circumferential variations in temperature were examined, and the data were found to be rotationally invariant. For the purpose of data analysis, it was necessary to fit a continuous curve to the discrete data points. The inner wall axial temperature profile was well-represented by a linear fit. The root-mean-square error from the leastsquares linear approximation was generally less than 0.5 "C. The bed radial temperature profile at each of the five axial levels was approximated by a least-squares fit to a
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Figure 4. Test 12 temperature measurements.
quadratic polynominal, and the root-mean-square error was 2-4 "C. The majority of the previous heat-transfer studies on packed beds have used cylindrical tubes with the outer wall contained within a steam jacket. This arrangement permits the assumption of a constant wall temperature and with the further assumptions of constant effective bed thermal conductivity and constant wall heat-transfer coefficient leads to the well-known analytical solution for a cylindrical geometry. This solution is then used along with the measured temperature profiies to calculate k , and h,. Li and Finlayson (1977) discuss four widely used methods for performing this calculation. In the case of an annular packed bed, the analytical solution becomes more difficult. For the case of variable wall temperatures, the analytical solution is not known at this time. Yagi and Kunii (1960) and Baddour and Yoon (1961) overcame this difficulty by designing an annular packed bed heat exchanger in which heat flow was purely radial and the flowing gas was not a heat sink. The values of k,, and h, could then be calculated from the temperature gradient in the bed and the total amount of heat transferred, which was based on the water vapor condensation rate by Yagi and Kunii (1960) and electric power input to a Calrod heater by Baddour and Yoon (1961). The experimental apparatus chosen to simulate the annular bed steam reformer, as discussed above, results in a variable wall temperature and requires a different data analysis approach. Van Dame et al. (1984) analyzed the data from their experimental annular bed steam reformer by calculating overall heat-transfer coefficients (h,) based on heat balances for a control volume. They did not measure radial temperature profiles, and the individual contributions of k,, and h, could not be determined. The analysis approach chosen here is different from those discussed above and is believed to represent an improved method of determining k,, and h, from experimental data for packed beds with variable wall temperatures. The analysis consists of using a computer program to calculate temperature profiles throughout the packed bed based on the measured axial wall temperature profile and the inlet bed temperature profile. The expressions
614
Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989
for calculating k,, and h, are then modified until the best fit to the measured temperature data throughout the bed is obtained. The equation to be solved is
r dr Axial thermal conduction in the packed bed has been neglected in eq 1. This simplification is the so-called "conventional" heat balance used for packed bed reactors. Paterson and Carberry (1983) have qualitatively reviewed the application of this simplification. Froment and Bischoff (1979) and Smith (1981) have pointed out that axial thermal conduction is negligible in most industrial reactors. The significance of axial thermal conduction depends on packed bed length and fluid velocity. Froment and Hofmann (1987) justify the omission of axial dispersion terms in both mass and heat balances in the two-dimensional pseudohomogeneous model for packed beds. For the present case, the importance of axial thermal conduction can be assessed by considering the following dimensionless differential heat balance for the bed: az
dT
- - -1 - + - -a2T PrLRepn
dz
"(rk*F)=O r dr
Pr$e,m
(2)
where PrL = PPCP/XL
n = L/d, Pr, = p g c p / k e r r e f
m = R2/d$, k* = ker/kerref An order of magnitude analysis (Whitaker, 1977) shows that, in order to neglect the first term in comparison with the second one, the following condition has to be fulfilled: PrLRepn>> 1 (3) For the present case, we use the most conservative value for Re,, which is its lower bound for the present experimental set: Re, = 200. In addition, n = 48. The evaluation of Pr, involves the estimation of the effective axial thermal conductivity, XL, for the packed bed. Here we use a conservative estimate of X L 10 J/(m.s-K) (Perry and Green, 1986). If we take an average value of k, = 4 X J/(ms.K) (Cheung et al., 1962), then we can compute
-
-
k, PrL = -Pr XL
which for Pr 0.7 gives PrL N 2.8 x If we use this value in eq 3 along with the values for Re, and n, we obtain PrLRe,n = 26. Thus, axial thermal conduction can be safely neglected in the present analysis. Li and Finlayson (1977) presented the following relationship to estimate the relative error caused by the omission of axial dispersion in determining k,, and h, in packed beds without reaction:
In this work, we use the hydraulic radius R instead of the outer radius of the packed bed. When this expression is used for the present case, a maximum relative error of 1% is obtained over the entire range of 200 5 Re, 5 800.
This estimate once again shows that the axial thermal dispersion can be safely neglected in the evaluation of the present experimental data. The boundary conditions are obtained by assuming that the heat exchanger is well-insulated, and therefore there is no heat transfer through the outer wall. The boundary conditions are written as r = R1, 0 I z 5 L , -ker d T / & = h,(T, - T ) (5a) r = R2, 0 i z 5 L , dT/dr = 0
(5b)
The bed temperature profile a t the control volume inlet ( z = 0) is represented by a quadratic fit to the data, and the final boundary condition becomes R1 I r i R2, z = 0 , T = Ar2 Br + C (5c)
+
The correlation for calculating the effective bed thermal conductivity and the wall heat-transfer coefficient were assumed to follow the expressions he,/k, = a1 + a2PrRe, (6) (7)
Equations 1 and 5 were solved numerically by use of Galerkin procedure combined with /3-splines. The solution permitted the use of pointwise physical properties. In eq 5 and 6, the particle diameter is the nominal diameter. The Reynolds number did not include the bed void fraction because of the somewhat uncertainty involved in determining the radial void fraction profile. The variables a l , a*, and /3 are empirical constants that were adjusted until the root-mean-square error between the temperature calculated at each thermocouple location and actual temperature reading was minimized. A twopattern search based on the mathematical technique of Hooke and Jeeves (Beveridge and Schechter, 1970) was used to perform this optimization. The use of this method of analysis permits all of the data points to be considered in the solution, thus minimizing errors that might be caused by one or two inaccurate temperature measurements. The analysis also permits the use of point values for the gas-transport properties, the specific heat, gas viscosity, and gas thermal conductivity, which were varied throughout the bed based on the gas temperature. In most cases, variation in these properties was approximately 10% across the length of the control volume. The inner wa1.l temperature and the radially averaged gas temperature along with the calculated heat flux were used to calculate the overall heat-transfer coefficients at each of the axially measured positions. Typical results are shown in Table 11. Correlation of Data. The results of the data analysis for all 14 test runs are shown in Table 111. The modified Reynolds number varied from 200 to approximately 800. The test results of test 3, however, were considered unreliable due to the required high flow rates and the relatively low gas temperature that could be obtained. These results were, therefore, not included in further correlation of the data. The data for h, and h, were fitted to a number of different types of correlations. The overall heat-transfer coefficient is calculated on the basis of the difference in temperatures between the wall and the bulk. This includes the effects of both the wall film resistance and the internal bed heat-transfer resistance. The effective bed thermal conductivity was fitted by a linear correlation. The results are shown in Table IV. A final correlation form that was tested was the use of a Biot number, rather than a Nusselt
Ind. Eng. Chem. Res., Vol. 28, No. 5, 1989 615 Table 11. Calculated Results and Radial Temperature Profile ("C) from Heat-Exchanger Test 12 overall reactor heat-trans length, av gas heat flux, coeff, cm temp,"C W/m2 Re W/(m2."C) 422.7 24,263 611.4 0.00 122.1 576.7 209.1 7.62 152.7 9,913 569.8 207.0 159.3 8,448 15.24 208.7 7,430 563.9 22.86 165.1 208.7 6,571 558.4 30.48 170.6 reactor length, wall gas at temp, "C wall, "C cm d, 1.5dp 2.0dp 0.5dP 166.6 122.1 177.6 113.6 110.0 106.9 0.00 7.62 170.5 152.7 139.8 129.8 122.4 117.3 15.24 174.4 159.3 148.3 139.6 133.1 128.6 155.5 148.0 142.3 138.3 178.3 165.1 22.86 170.6 162.0 155.4 150.4 146.9 30.48 182.2 Table 111. Data Analysis Results test SCFM Re, Nu, 1 15.0 659 99.3 410 85.5 2 10.0 114.4 3 18.0 797 60.2 4 5.0 200 5 7.5 304 80.0 6 12.5 524 98.3 7 6.0 254 62.9 8 11.25 745 84.9 77.0 9 8.75 364 278 71.7 10 6.75 609 102.5 11 14.25 12 13.5 570 101.6 13 16.0 680 101.1 14 17.0 726 104.9
Nu, 40.8 26.9 42.0 15.0 22.5 34.3 19.8 32.5 27.2 22.5 39.7 37.6 42.9 44.8
Table IV. Correlation of Experimental Data correlation a b Nu, = a(Re )* 5.9 0.44 N U , = a + &Rep) 62.6 0.056 0.23 0.80 Nu, = a(Re,)* Nu, = a + b(Re,) 6.0 0.054 0.6 0.157 k,,/k, = a + b(PrRe,) Bi = a(Re,)* 155 -0.55 Bi = a + b(Re,) 9.4 -0.0076
transfer data for a packed bed heat exchanger with a variable wall temperature, an additional check was made by using a different approach in determining the empirical correlation for the overall heat-transfer coefficient. The purpose of this approach was to obtain another measurement of the total heat transfer occurring within the heat exchanger, thus assuring that the results were a true representation of the data and not a function of the method of data analysis. The second method of data analysis was a straightforward approach of performing a heat balance around the control volume and calculating the average overall heattransfer coefficient based on the calculated heat flux and the log-mean temperature difference between inner reactor wall and the bulk gas temperature (AT,,):
The average gas temperature at each end of the control volume was calculated by curve fitting a quadratic function to the temperature data and then integrating the function to determine the average temperature. The following equations were utilized:
k,,jk, 70.9 40.5 67.8 20.7 32.2 54.1 29.7 53.9 42.8 33.8 67.3 62.2 76.5 80.1
T =A
+ Br + Cr2
(14)
2 f R * r Tdr J!?
Once the average gas temperatures were determined, the total heat duty, Q, could be calculated as follows:
Q = k c p ( 7 ' z = 1 2 i n , - Tz=o)
(16)
The log-mean temperature difference was based on the differences between the measured wall temperature and the calculated average gas temperature at each end of the control volume. The results are represented by the following empirical correlation:
correl coeff 0.969 0.785 0.994 0.995 0.993 -0.931 -0.901
Nu, = 0.19Rep0.s4
number, as suggested by Li and Finlayson (1977). The Biot number is the ratio of the internal bed heat-transfer resistance to the wall film resistance. It, therefore, includes the effects of both hwand ker, The Biot number is defined as follows:
The results are included in Table IV, and they show a somewhat poorer fit to the Biot number correlations than the Nusselt number correlations. The final correlations that best fit the present data were the following:
Nu, = 5.9Re,0,44
(9)
Nu, = 0.23Re,0.s0 k e , / k , = 0.6 + 0.157PrRep
(10)
Bi = 155Re,.d.55
(12)
(11)
Equations 9-11 should be used for annular packed beds with ring-type packing in the range 200 < Re, < 800 and D,/dp = 6 Although the method of data analysis chosen was considered the most accurate method of analyzing heat-
(17)
The overall heat-transfer coefficients calculated from eq 17 are within 2-7 % of those calculated from eq 10 in the Reynolds number range of this study. This is excellent agreement particularly considering that the latter method of data analysis only utilized data at the two ends of the control volume and had to assume average gas transport properties. It can, therefore, be safely assumed that the empirical correlations presented previously, eq 9-12, are true representations of the experimental data. Overall Heat-Transfer Coefficient. The empirical correlation for the overall heat-transfer coefficient, h,, is plotted in Figure 5 , along with several other correlations reported in the literature. The results indicate an overall heat-transfer coefficient slightly higher than that predicted by the correlation of Li and Finlayson (1977), which is based on selected data taken from various experiments utilizing cylindrical packing in round tubes, with a tube diameter to particle diameter ratio in most cases greater than 10. The present experiments used catalyst support ring packing in an annular bed with a tube diameter to particle diameter ratio of 6.3. It can be expected that the packing states in the two cases would be considerably different. The center hole in the catalyst support ring packing permits additional gas flow in the radial direction and increases gas mixing. The annular geometry results in two wall/particle interfaces rather than one and further modifies the voidage profile in the bed. The void fraction in the annular heat ex-
616 Ind. Eng. Chem. Res., Vol. 28, No. 5, 1989
I
100
200
I
3 0 0 40d
1
600 800 1000
PARTICLE REYNOLDS NUMBER, R e P =
dP .G.p
Figure 5. Correlations for the overall heat-transfer coefficient. (1) Best fit to data: Nu, = 0.23RePom. (2) Li and Finlayson (1977): cylinders, Nu, = 0.077Re,”95. (3) Li and Finlayson (1977): spheres, Nu, = 0.125Re,080. (4) DeWasch and Froment (1972): Nu, = 3.4 + 0.024Rep. ( 5 ) Leva (1947): Nu, = 0.05Re;”.
changer was measured and found to be 65%, compared to values of approximately 40% for packed tubes. Apparently this packing arrangement promotes both wall/particle heat transfer and lateral mixing. Van Dame et al. (1984) reported overall heat-transfer coefficients slightly higher than those calculated herein for an annular packed bed measured under reacting conditions. They attributed the high heat-transfer rate to a reaction enhancement effect, but it was more likely due to the physical nature of the reactor bed. This implies that perhaps the overall heat-transfer coefficient should include a void fraction. The Reynolds number exponent of 0.80 in eq 10 approximates the Reynolds number dependency of an open tube, which may be due to the large void fraction in the bed. Wall Heat-Transfer Coefficient. The empirical correlation for the wall heat-transfer coefficient, eq 9, is shown in Figure 6 along with several other correlations reported in the literature. It can readily be observed that the present results indicate much higher wall heat-transfer coefficients than previous correlations. This is an important result for the design of an annular bed reformer, since the reactor performance is strongly influenced by the wall heat-transfer coefficient. As discussed above for the overall heat-transfer coefficient, the annular heat-exchanger geometry is considerably different from that used in previous studies, and the differences in results are not surprising. In particular, it should be noted that the wall heat-transfer coefficient does not truly represent a physical phenomenon but is rather a sort of correction term used to compensate for the decreased effective thermal conductivity in the near-wall region. Several investigators (Schuler et al., 1952; Hall and Smith, 1949; Bunnell et al., 1949) handled this problem by utilizing a variable effective thermal conductivity that decreased near the wall. The mathematical model utilized herein is based on the assumption of a constant effective bed thermal conductivity and accounts for the increased thermal resistance near the wall by use of the wall heattransfer coefficient. The wall heat-transfer coefficient represents a film drop at the wall/bed interface and is defined by the boundary condition
-ker a T / a r = h,(T,,,,
- T,)
(18)
Since the wall heat-transfer coefficient compensates for the discrepancy caused by the use of a constant effective
PARTICLE REYNOLDS NUMBER, R e p =
Gd
3 ps
Figure 6. Correlations for the wall heat-transfer coefficient. (1) Best fit to data: Nu, = 5.9Re,0w. (2) Li and Finlayson (1977): cylinders, Nu, = 0.16Re,093. (3) Paterson and Carberry (1983): Nu, = 0.35Rep0738 + 66.2Rep4 262. (4) Calderbank and Pogorski (1957): N u , = 4.21Rep0365.(5) DeWasch and Froment (1972): Nu, = 12.5 + 0.048Re . (6) Drew et al. (1962): cylinders, Nu, = 2.29Re,033 + 0.082Re,0Bb. (7) Yagi and Kunii (1960): Nu, = 15 + 0.029Rep. (8) LI and Finlayson (1977): spheres, Nu, = 0.17Re,079
thermal conductivity from wall to wall across the bed, it follows that the value of h, would be dependent on the relative magnitudes of the effective thermal conductivity in the bulk of the bed and that near the wall region. When this ratio is high, h, will be small. This is the case for round tubes with large tube diameter to particle diameter ratios and relatively low void fractions. The effective bed thermal conductivity is nearly constant over the bulk of the bed and decreases rapidly near the wall. Baddour and Yoon (1961) found the radial effective thermal conductivity within one-half particle diameter distance of the wall to be significantly less than that in the interior of the bed. On the other hand, when the effective thermal conductivity in the near-wall region is similar to that in the bulk of the bed, a smaller “correction factor” is necessary and h, is correspondingly larger. This appears to be the case with the annular packed bed heat exchanger. The large void fraction caused by having an annular width of only slightly greater than three particle diameters, coupled with catalyst support ring packing and the presence of two wall/particle interfaces, results in physical conditions from wall to wall that are considerably different than those existing in previous studies. The wall heat-transfer coefficient for this case should therefore be calculated according to the reported empirical correlation. It is cautioned, however, that if the physical geometry is significantly altered, this correlation may not be applicable. The Reynolds number dependency of h, shows an exponent of 0.44. This is very similar to that reported by a number of other investigators (Beek, 1962; Paterson and Carberry, 1983; Hanratty, 1954; Calderbank and Pogorski, 1957). The slope is less, however, than that reported by Li and Finlayson (1977), who found a Reynolds number exponent of 0.93. The Reynolds number dependency of h, found in this study is consistent with that determined for h,. The overall heat-transfer coefficient includes the effects of both h, and internal bed heat transfer. Since the internal bed heat transfer increases with increased radial mixing caused by larger Reynolds number, h, should increase more rapidly with increased Reynolds number than h,. This is seen by the Reynolds number exponent of 0.80 for h, and 0.44 for h,. At very high Reynolds
Ind. Eng. Chem. Res., Vol. 28, No. 5 , 1989 617
t
,
I
l
400
800
PARTICLE REYNOLDS NUMBER, Re,=>
L
Gd PLP
Figure 7. Correlations for the effective bed thermal conductivity. (1)Yagi and Kunii (1957): Raschig rings, k,,/k, = 8 + 0.12ReP. (2) Lerou and Froment (1977): cylinders, k,,/k, = 13 + 0.084ReP. (3) Best fit to data: Raschig rings, k,,/k, = 0.6 + O.llRep. (4)Calderbank and Pogorski (1957): cylinders, k,/k, = 9.5 + 0.077Rep. (5) Yagi and Kunii (1957): cylinders, spheres, k,,/k, = 5 + 0.07ReP. (6) DeWasch and Froment (1972): cylinders, k,,/k, = 10 + 0.045Re,.
numbers, the radial mixing is nearly complete, and the overall heat-transfer coefficient should be equal to the wall heat-transfer coefficient. It can be shown that based on eq 9 and 10 the values for h, and h, would coincide at a modified Reynolds number of 8200. This is well beyond the experimental range of the correlations, but it demonstrates that they have the proper functional dependency. Effective Bed Thermal Conductivity. The measured value of the effective radial bed thermal conductivity was found to be in excellent agreement with previous work. The linear k,,-Re, relationship of eq 11 is consistent with the results of several other investigators (Yagi and Kunii, 1957; Calderbank and Pogorski, 1957; DeWasch and Froment, 1972). (See Figure 7.) The stagnant conductivity is low compared to other data, but this can be explained by the large void fraction in the bed and the low solid thermal conductivity of the alumina catalyst support particles. The relatively low operating temperature also minimized radiant heat transfer. The coefficient of the dynamic term in eq 11 is 0.157, indicating a modified Peclet number for heat transfer due to turbulent eddy diffusion of 6.4. (The Peclet number for eddy diffusion is the inverse of the Prandtl number-Reynolds number coefficient.) Ranz (1952) determined a theoretical value of the eddy diffusion Peclet number for rhombohedral packing of spheres of 5.9. Extensive experimental data (Lerou and Froment, 1977; Yagi and Kunni, 1957; Schertz and Bischoff, 1969; Agnew and Potter, 1970; DeWasch and Froment, 1972) for tubular packed beds shows Peclet number values of 7-10, dependent somewhat on the solid conductivity and the particle to tube diameter ratio. Data by Maeda and Kawazoe (1951) for Berl saddles and Raschig rigs indicate Peclet numbers of 4-6. The Peclet number measured in this study is therefore consistent with expected results. Conclusions 1. New experimental data have been obtained for an annular packed bed heat exchanger with ring-type packing. The results vary significantly from those reported previously for other packed bed geometries. 2. An improved data analysis procedure was developed that permitted the simultaneous determination of the individual heat-transfer parameters and utilized all of the measured data points along with point values of the gastransport properties.
3. The overall heat-transfer coefficient was found to be a power function of the particle Reynolds number as shown in eq 10. A void fraction dependency was suggested as an explanation for the slightly higher results predicted by this correlation as compared to other correlations found in the literature. 4. The wall heat-transfer coefficient was found to be a power function of the particle Reynolds number as shown in eq 9. This result predicts much higher heat-transfer coefficients than other correlations reported in the literature. This discrepancy was attributed to the unique geometry of the annular packed bed with ring-type packing. This correlation should be used with caution if the physical geometry is significantly altered. 5 . The effective bed thermal conductivity was found to be a linear function of particle Reynolds number as shown in eq 11. The low stagnant conductivity was due to the large bed void fraction and the low thermal conductivity of the packing. The dynamic portion of the effective bed thermal conductivity was consistent with previously reported results. Acknowledgment The helpful discussion and calculations provided by Dr.
C. G. Dassori are gratefully acknowledged. Nomenclature A , B , C = constants in eq 14 Bi = wall Biot number (=[h,(Dt/2)]/k e J , dimensionless c p = gas mixture specific heat, J/(kg.K) d, = particle diameter, m D,= tube diameter (or equivalent tube diameter), m G = mass flow velocity, kg/(m2.s) h, I= overall or global heat-transfer coefficient, J/ (m2.s.K) Lo = average overall heat-transfer coefficient over control volume, J/(mz.s."F) h, = wall heat-transfer coefficient, J/ (m2.s.K) k,, = effective radial bed thermal conductivity, J/ (m.s.K) k,,ref = reference value for k,, k , = fluid thermal conductivity, J/(m.s.K) m = mass flow rate, kg/s Nu, = modified wall Nusself number (=h,d,/k,) Nu, = modified overall Nusselt number (=h,d,/k,) Pr = Prandl number ( = p g c p / k g ) ,dimensionless Q = heat transfer, J/s r = radial dimension, m R = hydraulic radius, m R1,R z = catalyst bed inner and outer radii, respectively, m Re, = modified Reynolds number (=Gd,/p,) T = temperature, K T , = wall temperature, K z = axial dimension, m Greek Symbols a l , aZ,,8 = constants in eq 5 and 6 p,
= gas viscosity, kg/(m.s)
Subscripts g = gas o = initial condition or outer wall p = particle r = radial direction w = inner wall z = axial direction Literature Cited Agnew, J. B.; Potter, 0. E. Heat Transfer Properties of Packed Tubes of Small Diameter. Trans. Znst. Chem. Eng. 1970, 48, T15-T20. Baddour, R. F.; Yoon, C. Y. Local Radial Effective Conductivity and the Wall Effect in Packed Beds. Chemical Engineering Progress
618
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Symposium Series. Heat Transfer-Buffalo; Wiley: New York, 1961; Vol. 57, NO. 32, pp 35-50. Beek, J. Design of Packed Catalytic Reactors. In Advances in Chemical Engineering; Drew, T. B., Hooper, J. W., Vermeulen, T., Eds.; Academic Press: New York, 1962; Vol. 3, pp 203-270. Beveridge, G. S.; Schechter, R. S. Optimization;McGraw-Hill: New Yorkr 1970; p 384. Bunnell. D. G.: Irvin. H. B.: Olson. R. W.: Smith. J. M. Ind. E m- . Chek. 1949,’41, 1977. ’ Calderbank, P. H.; Pogorski, L. A. Heat Transfer in Packed Beds. Trans. Inst. Chem. Eng. 1957, 35, 195-207. Cheung, H.; Bromley, L. A.; Wilke, C. R. Thermal Conductivity of Gas Mixtures. AIChE J. 1962,8, 221-228. DeWasch, A. P.; Froment, G. F. Heat Transfer in Packed Beds. Chem. Eng. Sci. 1972,27, 567-576. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; McGraw-Hill: New York, 1979. Froment, G. F.; Hofmann, H. Design of Fixed-Bed Gas-Solid Catalytic Reactors. In Chemical Reaction and Reactor Engineering; Carberry, J. J., Varma, A., Eds.; Marcel Dekker: New York, 1987. Hall, R. E.; Smith, J. M. Chem. Eng. Prog. 1949, 45(7), 459. Hanratty, T. J. Nature of Wall Heat Transfer Coefficient in Pack Beds. Chem. Eng. Sci. 1954, 3, 209-214. Hoover, D. Q., et al. Cell Module and Fuel Conditioner Development Final Report. Prepared for NASA Lewis Research Center, Cleveland, OH, Feb 1982. Lerou, J. J.; Froment, G. F. Velocity, Temperature and Conversion Profiles in Fixed Bed Catalytic Reactors. Chem. Eng. Sci. 1977, 32. 853-861.
Leva, M. Heat Transfer to Gases Through Packed Tubes. Ind. Eng. Chem. 1947, 39(7), 857-862. Li, C. H.; Finlayson, B. A. Chem. Eng. Sci. 1977, 32, 1055-1066. Maeda, S.; Kawazoe, K. Chem. Eng. Jpn. 1951, 15, 5. Paterson, W. R.; Carberry, J. J. Chem. Eng. Sci. 1983,38(1), 175-180. Perry, R. H.; Green, D. W. Chemical Engineers Handbook; McGraw-Hill: New York, 1986. Ranz, W. E. Chem. Eng. Prog. 1952, 48, 247. Schertz, W. W.; Bischoff, K. B. Thermal and Material Transport in Monisothermal Packed Beds. AZChE J . 1969, 15(4), 597-604. Schuler, R. W.; Stallings, V. P.; Smith, J. M. Heat and Mass Ransfer in Fixed-Bed Reactors. Chem. Eng. Prog. Symp. Ser. 1952,48(4), 19-30. Smith, J. M. Chemical Engineering Kinetics; McGraw-Hill: New York, 1981. Van Dame, S. E.; Smith, R. A.; Christner, L. G. Experimental Steam-Methane Reformer Heat Transfer Correlations. Proceedings of the A.S.M.E./A.I.Ch.E National Heat Transfer Conference. Niagara Falls, NY, Aug 5-8, 1984. Yagi, S.; Kunii, D. Studies on Effective Thermal Conductivities in Packed Beds. AZChE J . 1957,3(3), 378-381. Yagi, S.; Kunii, D. Studies on Heat Transfer Near Wall Surface in Packed Beds. AIChE J. 1960,1, 97-104. Whitaker, S.Fundamental Principles of Heat Transfer;Pergamon Press: New York, 1977.
Received for review June 13, 1988 Accepted January 17, 1989
Determination and Use of Isothermal Adsorption Constants of Jet Fuel Lubricity Enhancer Additives Bruce H. Black, Dennis R. Hardy,* and Margaret A. Wechtert Code 6180, Naval Research Laboratory, Washington, DC 20375-5000
In order to assess the hypothesis of adsorptive loss of surface-active carboxylic acid lubricity enhancer additives from jet fuel, adsorption constants for a variety of materials were determined. These materials included 70:30 copper/nickel alloy, cold-rolled steel, zinc-plated steel, and glass. Care was taken t o determine the adsorption at additive concentrations below 4 ppm (v/v) and surface area to volume ratios of 0.1-0.001 cm-l. Given the worst case surface area to volume ratio for a typical fuel pipeline, approximately 0.4 cm-’, a fuel with a lubricity additive concentration of 9 ppm would lose less then 3% by adsorption on pipeline walls. At present, a lubricity enhancer additive is required in
U.S. military jet fuel (JP-4 and JP-5). The required concentration range is between 9 and 22.5 ppm (QPL-2501714, 1984). This additive was previously used to decrease corrosion to fuel-handling and -storage systems (Goodger and Vere, 1985). The additive is effective as a corrosion inhibitor due to its surface-active nature, usually imparted by an organic acid or alcoholamine. The acid forms a monolayer boundary which hinders surface attack by dissolved oxygen and free water. This additive’s current important use is to increase the lubricity of low-lubricity jet fuel (Vere, 1969; Moses et al., 1984; Petrarca, 1974; Hillman et al., 1977; Grabel, 1977; Masters et al., 1987). Qualitatively, lubricity is defined as the relative abilities of two fluids, which have the same viscosity, to resist wear and friction (Moses et al., 1984; Goodger and Vere, 1985). Lubricity is recognized as one of the most critical properties degraded by refining processes such as hydrotreatment and clay treatment. These processes effectively remove the trace polar compounds that naturally impart lubricity (Biddle et al., 1987; Masters
* Author t o whom correspondence should be addressed. Present address: Department of Chemistry, Southeastern Massachusetts University, North Dartmouth, MA 02747.
0888-588518912628-0618$01.50/0
et al., 1987; Vere, 1969; Moses et al., 1984; Petrarca, 1974; Goodger and Vere, 1985; Grabel, 1977). A number of problems associated with the use of lowlubricity fuels have occurred in the past 20 years. Aircraft components which derive lubrication from fuel have been experiencing increased wear and mechanical failure. Since this additive is surface active and also contains a long hydrocarbon chain structure, it was serendipitously found to impart increased lubricity to fuels that had been severely processed in order to improve thermal stability. In early 1966, the Air Force designated corrosion inhibitor as a mandatory additive in JP-4 and, hence, JP-5 as a lubricity enhancer. More recent fuel lubricity problems have been experienced by military aircraft (Biddle et al., 1987; Moses et al., 1984; Grabel, 1977). These recent fuel lubricity related problems are believed to be a result of lubricity additive loss from fuel. It has been postulated that corrosion inhibitor, added as a fuel lubricant at the refinery, may be depleted from the fuel during storage and handling by adsorption. Once below a critical minimum, the additive would be unable to achieve its intended purpose. In the late 1970s, a series of experiments were performed in the United Kingdom to measure the adsorption of the active ingredient in most lubricity enhancer additives 1989 American Chemical Society
