Ind. Eng. Chem. Process Des. Dev. 1984, 23, 805-808 Mlchelsen, M. L. J . Fluid Phese €9u/llb. 1982a, 9 ,1. Mlchelsen, M. L. J . FluM Phase Equilib. 1982b, 9 ,21. Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15. 59. Prausnitz, J. M. Ind. Eng. Chem. Process Des Poling, B. E.; Edward, A. 0.; D e v . 1981. 20, 127. Redllch, 0.; Kwong, J. N. S. Chem. Rev. 1949, 4 4 , 233. Schmidt, G.; Wenzel, H. Chem. Eng. Sci. 1980, 35, 1503. Shah, M. K.; Bishnoi, P. R. Can. J . Chem. Eng. 1978. 56, 470.
805
Soave, G. Chem. Eng. Sei. 1972, 2 7 , 1197.
Received for review December 29, 1982 Accepted January 16,1984
Part of this work was presented at the Third Austrian-ItalianYugoslav Chemical Engineering Conference, Graz, Austria, Sept 1982.
Prediction of Gas-Particle Heat Transfer Coefficients by Pulse Technique Abdelhafeez N. Mousa Chemical Engineering Department, Kuwait Universlty, Kuwait
The heat transfer coefficient between a gas and a solid was studied by Introducing a pulse of heat in the stream of a gas flowing through a bed packed with solids. The variation of temperature with respect to time was measured at the inlet and outlet of the packed bed. The first moments were calculated from the temperature-time curves. The DC model (dispersion concentric model) was used to predict the heat transfer coefflclent. The particles used were spherical glass beads of 2.1 mm diameter, and air was used as the gas. The particle Reynolds number was varied from 14 to 50.
Introduction The determination of heat transfer coefficients between a flowing fluid and the particles of a packed bed by direct steady-state techniques is usually very difficult to realize. As an alternative, heat transfer coefficients may be obtained either by transient heat-transfer techniques or by performing mass transfer experiments from which heat transfer coefficients may be predicted by employing the analogy between the transfer of heat and mass. Gas-particle heat transfer coefficients in packed beds are available at high Reynolds numbers ranging from about 100 to 100000. Dayton et al. (1952), Meek (1961), and Shearer (1962) have successfully used sinusoidal input technique a t high Reynolds numbers to predict heat transfer coefficients. However, at low Reynolds numbers data are not only scarce, but their reliability is questionable. The reason for the scarcity of data at low Reynolds numbers may be due to the fact that the method of Gamson et al. (1943) is inapplicable in this region. Data for Reynolds numbers of less than 100 have been reported by Kunii and Smith (1960, 1961), Eichorn and While (19521, Pulsifer (1965), Wilke and Hougen (1945), Glaser and Thodos (1958) and De Acetis and Thodos (1960). Several models have been suggested for analyzing sinusoidal inputs. Gunn and Pryce (1969) used a one-parameter model, while models with four parameters have been used by Asbjornsen and Wang (1971) and Asbjornsen and Amundsen (1970). The dispersion concentric model (DC model), based on a fluid existing in dispersed plug flow with intraparticle temperatures leaving in radial symmetry, was used by Turner and Otten (1973) and Bradshaw et al. (1970), who reported heat transfer coefficients by step response measurements. The continuous solid-phase model (CS model), based on the assumptions of a fluid being in dispersed plug flow and a solid through which axial heat conduction is taking place in continuous phase, was used by Littman et al. (1968). Discussions of the DC
model and CS model are given by Kaguei et al. (1977). Wakao et al. (1979) have shown that, for the determination of heat transfer coefficients, the DC model is perhaps better. In the present study, the pulse technique was applied to determine the heat transfer coefficients between a flowing gas and a packed bed. The gas used was air and the bed was packed with spherical glass beads. The DC model was used to analyze the results. Theory According to the DC model proposed by Kaguei et al. (1977) and Wakao (1981) the instantaneous heat balance between a flowing fluid and a packed bed gives the following equations
with the following prevailing boundary conditions
aTP dr
k - = h,(TF - Tp)(atr = R) TF =
Tp = 0
TF = TF1(t) TF
= T&t) TF
=0
(3)
(at t = 0)
(44
(at x = XI)
(4b)
(at x = XI+ L )
(44
(atx =
(44
m)
aTP (at r = 0) (44 ar The solution of eq 1and 2 with the boundary conditions represented by eq 3 and 4 in the Laplace domain between -= 0
0 1984 American Chemical Society
806
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
TF1at X , and function
F(s) =
TFIIat
[
LU = exp - (1- [l + 2% TFICStdt
JfTF1le-at dt
s,
mc
X1 + L give the following transfer
1
COMPRESSED AIR
(5) where
Figure 1. The apparatus.
(7) Wakao (1976) has shown that the axial gas thermal dispersion coefficients, am,can be expressed as am =
ke + R U
~CFPF For flows with Reynolds numbers less than 0.5, the second term on the right-hand side of eq 8 can be neglected. For flows with Reynolds numbers greater than 5.0 the first term on the right-hand side of eq 8 can be neglected. The first moment of a pulse, as defined by Andrieu and Smith (1980), is P = JcTF
dt
so the first moment of the input heat pulse becomes
and the first moment of the output heat pulse is
Experimental Procedure Figure 1shows the experimental apparatus used in this investigation. I t consists of a polystyrene foam cylinder (A) of 65 mm inside diameter packed with spherical glass beads (B) of 2.1 mm diameter. Compressed air was made to flow through a rotameter (C), then downward through the bed. A heating coil ( D ) , in an empty section of the polystyrene foam cylinder, gives the required heating pulse by closing switch (H) for about 5 s. Thermocouple (E), at x = xl, records the input heat pulse as temperature (TJ) with respect to time at the center of the tube. Thermocouple (F), at x = x1 + L , records the output heat pulse as temperature (TFII) with respect to time. A two-pen recorder (G) was used to obtain the temperatures of TF1, and TFrr with respect to time. The distance, L, between the two thermocouples was 20 mm. The thermocouples were properly protected in order to prevent touching the solid particles. The temperature peaks were found to be within 10 "C above the inlet air temperatures, which was about 25 OC. The void fraction, c, was found to be 0.35. The two-pen recorder (G) used in this work was an Omniscribe chart recorder made by Houston Instrument. I t has a response of 0.5 s and a writing speed of 50 cm/s independent of line frequency. It has an overall accuracy of 0.3%. Calculations and Results The CD model has the three parameters, a=, k ,and h . Since all flow rates in this work were such that all heynoldb numbers were above 5.0, cyBr was calculated using eq 8 by neglecting the first term on the right-hand side of the equation. The thermal conductivity of glass beads is given as, k , = 0.88 W m-l K-l. Therefore, the remaining parameter to be determined is the heat transfer coefficient hP*
These mooments are related to the transfer function by the following equation
where F'(s) is the first derivative of F(s) with respect to S.
Therefore, by differentiating eq 5 and substitution in eq 12, we get
which can be expressed as
A t a given flow rate of air, the signal recorded by thermocouple (E), which is TFrvs. time ( t ) ,was used to integrate the expressions
numerically using the trapezoid rule and a PDP-11 computer, 90 the first moment of the input p1 is calculated from eq 10. Similarly, using the signal recorded by thermocouple (F), pI1 is calculated. The input signal and the output signal returned to the zero line during a time of about 30 s and there was no tailing of the recorded signal, so practically the integration was with respect to time from t = 0 to t = 30 s. Thus there was no tailing problem during the integration of the signals. Then using eq 14 the heat transfer coefficient (h,) is calculated. Following this procedure, the flow rate of air was then changed and pl, $I, and h, were calculated. The results are tabulated in Table I.
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 807
I
L
.I
-
r"
I
Re
'i' 1
I!
DE L C E T I S AND TKODOS (1960) L I I T V A N E 1 P,L, (19b8) EICHORN AND KHlK (1152) cp EICHOPJI AND WHlTE (1152) dD EICIIORH AND KI-IITE (L952) d ?
C 3 E F
I .
1
=
0.655m
=
0,523mm
=
0,2/'im L
01
1
1
L
5
6 7 8 9 1 . 0
I
1
L
5
6 7 8 9 1 0
I
1
L
5
6
7 8 9
N"
Figure 2. Plots of Nusselt number Table I. Calculated Results h,, W m-2 K-l 453 461 402 527 645 623 516 628 775 644 633
VS.
Reynolds number.
Re 14 16 17 19 21 23 24 26 46 50 46
Nu 43 47 31 49 41 47 39 48 59 49 48
The particle Reynolds number and Nusselt number defined as
RE =
UdpPF
-
F
I
dPhP
NU = kF
were also calculated and tabulated in Table I. The calculated Nusselt and Reynolds numbers were plotted on log-log paper as shown in Figure 2 together with values found in the literature. The leashquare method was used to find the best straight line that fits these values. Discussion and Conclusion As seen from Figure 2 there is a great difference between the values of the heat transfer coefficients reported by different workers. The data of Eichorn and White (1952) show a large particle size effect, while for the data of Littman et al. (1968) this effect was absent. The measured heat transfer coefficients in the present study agree w i t h data previously reported in the literature. In fact, they all possess almost the same slope as shown in Figure 2. De Acetis and Thodos (1960) used the vaporization method which, as shown by Littman et al. (1968), fails at low Reynolds numbers because the mean temperature difference in the bed cannot be measured accurately. They also ignored the gas phase dispersion.
The data of Eichorn and White (1952) are far away from the data of this work due to the fact that these investigators used the vaporization method, and the temperature difference between the gas and particles at the outlet was large, which accounted for their low Nusselt number. Also, a Nusselt number of 0.1 seems very low from a theoretical point of view. Since the recorder used in this study had an overall accuracy of f0.3% and repeatability of f0.1% of the full scale, the data obtained can be considered to be of high accuracy. The line representing the data of this study, when extended to a value of Re of 0.01, gives a value of Nu that approaches 2. This is a fact that has been shown by a number of workers. The equation suggested by Schlunder (1975) predicts Nusselt numbers which are believed to approach 2 at low flow rates. This leads to the conclusion that the method used in this study and the results of this study are internally consistent and therefore may be considered to be reliable. Acknowledgment The author thanks Professor N. Wakao for his great help and valuable discussions. He also wishes to thank Hameeda Dashti for her experimental assistance. The financial help from the Research Council of the University of Kuwait (EC006) is highly appreciated. Nomenclature C = specific heat d = particle diameter f i s ) = transfer function h, = particle-to-gas heat transfer coefficient k = thermal conductivity k, = effective thermal conductivity of quiescent packed bed L = bed length Nu = Nueselt number R = particle radius Re = Reynolds number S = Laplace operator T = temperature t = time U = interstitial gas velocity = u/c
000
Ind. Eng. Chem. process
ms. mv. 1904, 23,aoa-aw
u = superficial gas velocity Subscripts F = gas P = particle Superscripts I = input I1 = output (response) Greek Letters a, =
axial gas thermal dispersion coefficient
= bed void fraction I.L = gas viscosity p = density e
Literature Cited Andrleu, J.; Smith, J. M. Chem. Eng. J . 1980, 20, 211. AsbJornsen, 0. A.; Amundsen, K. Chem. €ng. Sd. 1970, 25, 943. Asbpnsen, 0.A.; Wang, B. Chem. Eng. Scl. 1971, 26, 585. Bradshaw. A. V.; Johnson, A.; McLachlan, N. H.; Chiu, Y. T. Trans. Inst. Chem. Eng. 1970, 48, T77. Dayton, R. W.; Fawcett, S.L.; (Llmble, R. E.; Seelander, C. E. Batelle Memorial Institute, Columbus, OH. 1952; Report EMI-747.
De Acetls, J.; Thodos, G. Ind. Eng. Chem. 1960, 52, 1003. Eichorn, J.; White, R. R. Chem. Eng. h o g . Symp. Ser. 1952. 48(4), 11. Gamson, B. W.; Thodos, G.;Hougen, 0. A. Trans. Am. Inst. Chem. Eng. 1943, 39, 1. Glaser, M. 6.; Thodos, G. AIChE J. 1958, 4 , 63. Gunn, 0. J.; Pryce, C. Trans. Inst. Chem. Eng. 1969, 47, T341. Kaguei, S.; Shiorawa, 6.; Wakao, N. Chem. Eng. Sci. 1977, 3 2 , 507. Kunii, D.; Smith, J. M. AIChf J. 1960, 6 , 71. Kunii, D.; Smith, J. M. AIChP J . 1961, 7 , 29. Littman, H.; Barile, R. G.: Pulsifer, A. H. Ind. Eng. Chem. Fundam. 1968, 7, 554. Meek, R. M. G. International Heat Transfer Congress, ASME, New York, 1961, p 770. Pulsifer, A. H. Ph.D. Dissertation, Syracuse University, 1965. Schlunder, E. U. “Elnfuhrung In die Warme- und Stoffubertragung”, 2 Aufl.; Vieweg-Verlag: Braunschwelg, 1975; p 75. Shearer, C. J. Nat. Eng. Lab. East Kilbridge, Glasgow, N.E.L. Rept. 1962; 55. Turner, G.A.; Otten, L. Ind. €ng. Chem. Process Des. Dev. 1973, 12, 417. Wakao, N. Chemlcal Engineering Department, Yokohama National University Japan, Personal Contact, 1981. Wakao, N. Chem. Eng . Sci. 1976, 31, 1115. Wakao, N.; Kaguel, S.; Funazkrl, T. Chem. Eng. Sci. 1979, 3 4 , 325. Wilke, C. R.: Hougen, 0. A. Trans. Am. Inst. Chem. Eng. 1945, 4 1 , 445.
Received f o r review November 4, 1982 Revised manuscript received December 5 , 1983 Accepted January 26, 1984
Flue Gas DenHrMcation. Selectlwe Cataiytic Oxidation of NO to NOz Hans T. Karkront and Harvey S. Rosenberg’ Battelk Memoriel Institute, Columbus Laboratmles, Columbus, Ohio 4320 1
A study was conducted on the selective catalytic oxidation of NO in simulated flue gas. Oxidation of NO to the more reactive &Os and N204(NO,) would enable wet scrubbing of NO, simultaneously with SO,. Fourteen catalysts were tested in a fixed-bed reactor at a space velocity of at least 1500 h-’ in the temperature range of 150 to 800 OF. The experimental results comprise a screening program for an engineering analysis rather than a full kinetic study. Eight catalysts exhibited optknwn performance at 200 O F , a temperatwe which is very suitable for an add-on process at a 00aCR.d power plant. Six catalysts yielded greater than 50% oxidation at this temperature. However, deactivation of the catalysts was observed after about 14 h of exposure to the flue gas. The experimental results indicate that it may be possible to solve the deactivation problem by modifying the catalysts.
Introduction Generally speaking, two types of technologies have been considered for NO, control on power plant boilerscombustion modification and flue gas denitrification. The latter technology is required only for very stringent emission regulations. However, flue gas desulfurization (FGD)is required on new power plant boilers. Since the leading FGD processes involve wet scrubbing, there is considerable interest in developing a wet scrubbing process for the simultaneous removal of NO, and SO2. Wet methods for NO, removal are limited by the relatively inert nature of NO. The NO, in flue gas is approximately 90% NO. This difficulty can be overcome by oxidation of NO to the more reactive NOz in the gaseous phase using ozone or C102prior to absorption (oxidation absorption). Ozone is the be& oxidizing agent but it is very expensive. The cost of C102is 30 to 40% lower than that of ozone, but the use of C102 introduces a considerable amount of chloride into the scrubbing liquor, thus causing Energy Technology R&D,Southern Sweden Power Supply,
S-21701 Malmo, Sweden.
waste disposal problems. Ozone and CIOz oxidize NO to NO2 within a 1-s residence time. NO can be oxidized by the oxygen in flue gas, but with low NO concentrations the noncatalytic reaction is very slow and the rate decreases with increasing temperature. For flue gas containing 5% oxygen and 750 ppm NO, a residence time of about 150 min (space velocity of about 0.4 h-l) is required to convert 90% of the NO to NO2 at a temperature of 300 O F . Several oxidation absorption-reduction processes are under development in Japan for the simultaneous removal of NO, and SOz from flue gas. In this type of process, NO is first oxidized to the more reactive NO2 which is then absorbed. Because of the nature of the process chemistry in the liquid phase, usually 3 to 4 mol of SO2 are needed for each mole of NO, for efficient removal of NO,. This mole ratio is not a problem for flue gas from a boiler fired with high-sulfur coal. Most of the absorbed NO, is reduced to nitrogen or NH3 by sulfite ions (absorbed SOz) so that the formation of undesirable nitrites and nitrates is greatly reduced or eliminated. Any NH3 produced must be recovered for use, decomposed, or disposed of after appropriate waste treatment.
0196-4305/84/ 1123-0808$01.50/0 0 1984 American Chemical Society
