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Gas film coefficient of mass transfer in low Péclet number region for sphere packed beds
Chid
E&cfing
Science,1976,Vol. 31. pp. 9-13. PewamonPress. Printed in Great Britain
GAS FILM COEFFICIENT OF MASS TRANSFER IN LOW PfiCLET NUMBER REGION FOR SPHERE PACKED BEDS TERUKATSU MIYAUCHI, HIROSHI KATAOKA and TATSUJI KIKUCHI Departmentof Chemical Engineering, University of Tokyo, Tokyo 113,Japan (Received 15February 1975;accepted 15May 1975) A-t-The limiting Sherwood number between particles and Buid in the low P&let number region has been determined experimentally for gas phase mass transfer in packed beds. A value of Sh, = 8.33 (or Sh, = 12.5 at 4 = 0+50),was found where Sh,. and Sh, are the Sherwood numbers based on the particle diameter and the hydraulic diameter respectively and e, is the void fraction of the beds. A high accuracy of measurement was obtained by applying a pulse response of CO, tracer gas to determine the film coefficients.
the purpose of making the above situation more definite. The film coefficient of mass transfer utilized here is defined by the following equation:
Heat and mass transfer coefficients between particles and
fluid in sphere packed beds are one of basic informations needed for unit operations and chemical reactor design. The coefficients in the low Reynolds or PCclet number region are particularly important for such operations as adsorption, chromatography, fluid beds for catalytic reaction etc. where a dense phase of fine particles is utilized. Unfortunately, however, various inconsistencies have been experienced by many investigators in correlating rate data. This situation still continues even in the recent publications[l, 2, 4, 9, 11-13, IS]. The main difficulty encountered has been the limiting Sherwood number Sh,, (= k,J, /&) [ 161being not clear as to whether it goes down to zero or takes a finite constant as decreasing the flow rate of fluid to zero. Current status of progress is well understood by referring to Refs. [l, 2,3,4,6,12] and to the discussion given by Nelson and Galloway [121. Recently, Littman et al. [6] and Kato et al. [4] reported experimentally linear dependence of Sh, on Re,,, which is the dependence supported by Nelson from the concept of surface renewal. Kato’s data, however, are more than twenty times greater than the prediction of Nelson. Wakao and Tanisho[lS] gave an experimental quadratic dependence of Sh, on Rep. Their data are seemingly located in the region predicted by Nelson. On the other hand, several works have supported the limiting Nusselt or Sherwood number being finite constant. Of these, Sfirensen and Stewart[l3] derived numerically the limiting Nusselt number Nu,,. being about 3.9 for a simple cubic array of spheres. Also, Gunn and Souza[l] have indicated that Nb, may take the limiting value of about 10, although their data scatter considerably. A fairly large limiting Sherwood number of 8.7 was previously reported [2,11] for Sh,,, (= k&, /&), and more recently 7.41 for a liquid system[9]. The latter value corresponds to Sh,, = 16.7 at 9 = 0.40. With this large Sh,, it is probable that some experimental approaches utilized so far may be inadequate in some cases if relative contribution of correction terms suppresses that of film mass transfer. Experimental determination of the limiting Sherwood number has been presented here for gaseous systems with
+/ae
= Eazclaz2- aaclaz -k&
-c,).
(1)
The presentation here has been mostly confined to experimental works. Another experimental approach essentially different from the present one will follow to this. 1. OWLINEOF EXFZRIMENTAL APPROACH
To determine the gas film coefficient of mass transfer, a small amount of CO2gas is introduced, as a pulse wave at the bed inlet, into steadily flowing inert gas stream. The bed spheres are impregnated with concentrated aqueous KOH solution. The tracer CO2 gas reacts with KOH almost instantaneously in the sphere surface layer, and the residual CO2 gas response is measured at the bed outlet. The experimental lihn coefficient of mass transfer was quite high under the conditions utilized here, so that the residual pulse size was usually very small, sometimes the size being too small to measure accurately. Due to this, measurement of residual pulse tracer quantity is considered to give better accuracy for the extent of CO1 absorption than determining the percentage saturation for a steady state saturation method such as vaporization of liquid or sublimation of solid into a gas stream. This improvement in accuracy is an essential feature of the present experimental approach. Based on eqn (l), it has been shown elsewhere [8] that the overall film coefficient & is obtained by the following equation for correcting the effect of axial dispersion: 48 exp (Pez /2) % = (1 + fl)’ exp (/3Pe,/2) - (1 - /I)’ exp (+Pe, /2) (2)
where so and s are respectively the inlet and outlet quantities of CO1 tracer gas, Pe, = t?L/E, and fl = d1+4N,IPe, with N, = k,aL/U. Pe, included in eqn (2) is available from Ref. [7]. The 9
10
T.
MIYAUCHI
overall coefficient k, obtained in this way still includes the particle side resistance to mass transfer. To evaluate this resistance, unsteady state CO? diffusion through the impregnated aqueous KOH solution layer in the sphere surface region has been analysed under the following assumptions that the reaction taking place in the liquid layer is instantaneous and irreversible, and that the gas flows through the bed in piston flow manner. The local coefficient has been averaged over the entire active bed, by taking into consideration the concentration decrease of tracer wave along the bed. The final expression for a constant pulse size at the bed inlet has been given[9] as eqn (3). This is the same equation as the one utilized for neutralization reaction to know an aqueous film coefficients in packed beds of ion-exchange resin beads[9]. l/Sh,, = l/Sh, t A,$
(3)
where J, = (PDDl/d,)“‘(d,/L)Sh,,/~~ and A, = qd’*&,/24ti[(l-
~,)(amD#.
Here, Sh,,, is the experimentally obtained Sherwood number (= k&,,/&); Sh, = kfd, /DM; Ap a constant for constant er; q0 the initial pulse size (mol/cm’ of bed cross section) at 1.0 atm and the term A& the liquid film resistance to CO2 absorption. The above correction method is convenient to manipulate. Theoretically, eqns (2) and (3) are sufficiently accurate when the gas film resistance to mass transfer controls the overall mass transfer process, but becomes approximate when the liquid side resistance is controlling. Since the latter is generally not the case, the correction procedure is considered to be adequate191. 2. EXPERIMENTAL
EQUIPMENT AND PROCEDURES
et al.
placed in a gas chromatography equipment to maintain the temperature mostly at 22 + l”C, and to measure the outlet CO2 response by thermal conductivity change of the issuing gas. The inlet pulse size of CO* gas was always maintained at 0.10 cm” under the system pressure P. The carrier gases utilized were HZ, He, NZ and C9Hs respectively. Concentration of the aqueous KOH solution was carefully adjusted in the bed by regulating the water vapour pressure of carrier gas at 144- 2.14 mmHg, which was lower than that of 20N-KOH solution (1.55 mmHg at 20°C and 2.20 mmHg at 25”C), so that one gets the highest rate of liquid phase reaction. This procedure required a lot of skill and trial runs, but it constituted an essential part of this experimental work. Also, a bed packed with fresh particles impregnated with aqueous KOH solution was utilized for each run. Details of the equipment and experimental procedures have already been reported [8]. The experimentally utilized lowest gas velocity (or the P&let number) was limited by the accuracy of the measuring device for the residual CO2response size. The maximum extent of CO?: absorption was 99.7% for N&O2 at Pe,,( = Udh/DM)= 12, 99.5% for He-CO* at Pe,, = 3 and 99.8% for H&O* at Pe,, = 5 respectively. These figures were the upper accuracy limit of our device. Hence, it was not possible to measure the Sherwood number for the region, Pe,, ~2, due to the residual size being too small to measure accurately. When the extent of CO*absorption under the condition given here is compared with that calculated with the Nelson and Galloway correlation[l2], one will find quite different results. The initial pulse size was conveniently known from the outlet pulse size which had passed through the bed whose absorption capacity had been all exhausted. No residual CO*response was detected for much smaller Pe,, than two or for an active bed three times longer than the present one when the bed was operated at Pe,, 5 2. Hence, the initial pulse gas was considered essentially pure C@. Binary gaseous diffusivities at 1.0 atm are as follows[5]: 0~630cm*/sec for H&O2 at 22”C, 0*5%cm*/sec for He-CO2 at 23”C, 0.168 cm2/sec for NrC02 at 22”C, and 0.0835 cm*/sec for CsH&02 at 20°C.
Figure 1 shows a packed bed utilized for CO2 absorption by aqueous KOH. solution. It consisted of a 10mm i.d. stainless steel tubing equipped with pre- and after-calming packed sections. The bed height of the active test section, L, was kept at 3 - 4 mm, and the bed was packed with porous spheres (dp = 0*68, 1.04, 1.08, 1.15 3. EXPERlMEhTAL. RESULTS AND DISCUSSIONS and 1.42 mm respectively) which were impregnated with 20Naqueous KOH solution. The void fraction ef of the .3.1 Experimental overall film coeflcient % Figure 2 shows experimentally obtained overall gas film beds was 0.483 - 0.517. The ratio L/d,, was maintained at 3 - 5, which gave the column axial P&let number Pe, of coefficients as a function of the molecular P&let number Pe,,(= zid,,/DM). Dimensionless expression based on the 5.0 - 12.7 for the whole operating conditions. The bed constituted a kind of pulse reactor, and it was hydraulic diameter has been utilized in what follows, since this gives consistently better correlation for beds of different void fraction [ lo]. The Grashoff number Gr has been calculated to see the c gas inlet effect of natural convection. A possible severest case is taken as a COZpulse being sent into a HZstream flowing at Pe,+= 2. The pulse spreads by axial dispersion while calming sectran packed with C-22 particles for gas chmmatgmphy use. travelling through the calming section, and flows into the reaction section packed with reOct~~t active section. CO* concentration is highest in the liquid cooled C-22 particles. incoming stream and nearly zero on the active spheres. flange With these, Gr = 0.8 at the active bed inlet and about 80% volume of the initial COZ passes through the active bed Fig. 1. Packedbed for CO2absorption.
in low P&let number regionfor spherepackedbeds
Gas filmcoefficient of mass transfer
-co*( 0 lkhm
3 2
‘He -C02(
I
1
EI lIK)mn,
, 1.0 atm)
1.6 atm)
\
He-CO, ( 0 1.08mm , 1.0 atm) I.3
2
Il111.1
345 7 10 P% = C&/o,
I.8
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11
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I.,JJl
34507
N,-CO, I
10
2
.I
($
1.08mm
, 2.0ah )
I111111
34507 no Pq, = ii&/D,
2
3 2
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Fig.2. Measuredoverallcoefficientk, as a functionPe,,. within about 0.11 sec. Gr is too small to induce natural convection. Hence, this effect is considered to be negligible. Essential feature of the plot given in Fig. 2 may be summarized as follows for Pe,, 5 lOO- 150, where the mechanism of mass transfer is in the regime of molecular diffusion controlling for liquid systems [9]. (a) bj responds enough sensitively to the change in such physical parameters as d,, P and D,. (b) k, tends to remain less dependent on Peh in comparison with the behaviour in the Pohlhausen regimeHO], where the boundary layers for velocity and concentration are developing simultaneously and Sh, is proportional to RehlnSc I”. (c) When dp is decreased under constant P, N-XOz system shows definite increase in b,, but H&O2 system reveals only slight increase. (d) When P is increased under constant d,, kO, decreases for both of N&Z02 and He-CO* systems, although the decrease is smaller for the latter. (e) When /c,, for various systems are compared with one another under constant P and d,, the systems with higher D, (such as He-CO2 and H&02) show generally larger /c,f than those with lower DM(such as N&JO* and C,HXO& However, kO,for He and HZ are not much different from those of NrC02 for the large difference in D,. C~H&OZ system shows definitely smaller lc,, than the rest. In the molecular diffusion controlling regime for the gas film coefficient, k,dV/Dnr should remain constant for geometrically similar beds[ll]. Hence, the above b. suggests the region of Peh 5 100 - 150 being the molecular diffusion controlling regime, although bf still includes the influence of liquid side resistance to mass transfer. In this mass transfer regime, the Sherwood number is constant, or kf is proportional to DM/dp Hence, /c,, should be approximately proportional to D, /d, when kf is controlling. The behaviour given in c. and d. satisfies this relation (note that DM m l/P) with an exception of H&JO*. This system shows only slight increase in hf with decreasing dp The reason seems to come from the aqueous KOH solution side resistance being controlling due to very high k,. The behaviour given in e. is also best understood in the same manner as above. In contrast to these, the gas film resistance controls the
Fig. 3. Sh,,, as a functionof Pe,.
overall mass transfer process for Nz-CO* and C,HL02 systems. 3.2 Sherwood number To observe the above mechanism of mass transfer more clearly, Sh,,, (= k&,, /DM) is shown in Fig. 3 as a function of Peh(=Udh/DM). Obviously, the systems with smaller D, (NrC02 and CsH&02) have higher Sh,, than those with larger DM (He-CO2 and HrC02). Also, the former shows Sh,, being less dependent on Peh than the latter. The systems with larger D, have higher kf so that the liquid side resistance to mass transfer becomes increasingly noticeable. This is the reason why HZ and He show lower Sh,, than Nf and CJHs. The gradient of each mean curve has been obtained from the final correlation eqn (4) below. It is seen that the limiting Sherwood number Sh,,(= k,d,/D,) is well more than 10 when the liquid film side resistance to mass transfer is adequately eliminated from Sh,,. To eliminate this resistance, the data taken for Peh s 100 are processed according to eqn (3) as follows. The arithmetic mean value of experimental l/Sh,, and that of IJ are tirst calculated for the runs taken under a given set of 4, P and a gaseous system. The mean values thus obtained are plotted in ‘Fig. 4 for different sets of experimental conditions. Although the data scatter
T.
MNAUCHI et 01.
molecular diffusion controlling regime (Peh s 100). Further, an average Sherwood number of 7.87 has been found for both of gas and liquid systems. NOTATION
4 refer to eqn (3), [atmcm/sec]+ DM molecular diffusivity of gas phase, cm*/sec DL CO* diffusivity .in liquid phase, cm*/sec E superficial axial dispersion coefficient, cm’/sec Gr d,‘gAplpv= L active bed length, cm P mean system pressure, atm lldhI DM Peh ULlE dJJlv d,,ti/v VIDM
Pe, Rep Reh
SC
Fig. 4. l/Sh,,, vs # plot.
considerably, l/S&, seems to be about linearly combined with JI as expected from eqn (3), i.e. l/S!!,, = 0.080 + 0*045$.
(4)
Hence, the limiting Sherwood number Sh,, is given as follows:
superficial gas velocity, cmlsec u N, kOfllL/U NUI hd,, lk Sh, ktdpID, Sh,, 44 IDM Shp k,fd, ID, Shh, k,dh IDM S cross sectional area of bed, cm’ a surface area per unit bed volume, cm*/cm’ C
Sh,, = l/O.080 = 12.5.
(5) 2
Since the mean void fraction of the beds is 0.50, the above Sherwood number gives
dp
Sh,,,, = k,od,,/D, = 8.33.
k/ 4 4 m
(6)
The limiting Sherwood number determined for aqueous electrolyte solutions[9] is Sh,,, = 7.41, close to eqn (6). Considering the accuracy of experimental approach utilized here, we take an average Sherwood number aho as follows for both of gas and liquid systems:
h k
40 S S0
shh, = (7.41+ &33)/2 = 7.87.
n
(7)
2
For the gaseous systems, the mechanism of mass transfer seems to move to the Pohlhausen regime [ lo] for Peh 2200 (ref. to Figs. 2 and 3 for N&IO2 system, SC = 0904). The limiting Sherwood number eqn (7) is fairly greater than those by Serensen and Stewart[l31 (Nub = hdJk = 2-6 at ef =0*5) and by Gunn and Souzalll (Nu,. = 4.4 at e, = 0.4; this limiting value is not always obvious). Sh,,, by Sorensen is about the same as that given by Shirai[l4] (Sh, = 2.6 at l, = O-5).
concentration of CO?, mol/cm’ surface concentration of CO*, mol/cm’ (2/3)[e,/(l- q)]dp, hydraulic dia., cm particle dia., cm film coeff. of heat transfer, Cal/cm’ sec”C thermal conductivity, Cal/cm secT film coeff. of mass transfer, cm/set limiting film coeff. of mass transfer, cm/set overall coeff. of mass transfer, cm/set partition ratio of CO, betw. carrier gas and KOH sol% q/P, with q = s,/S, mol/cm* atm final size of tracer wave, mol initial size of tracer wave, mol interstitial velocity, U/e,, cmlsec axial distance coordinates, cm
Greek symbols a capacity ratio, mol-COz/cm3-KOH sol’n P ql t 4N,IPe, AP Ef e V
;
density difference, g/cm’ void fraction of packed bed time, set kinematic viscosity, cm*/sec density, g/cm3 refer to eqn (3), [atmcmlsec]‘”
4. CONCLUSIONS
(1) Gas film coefficients of mass transfer in sphere packed beds have been measured in the low P&let number region, by applying a pulse response method of CO2 gas through a packed bed of aqueous KOH impregnated spheres. The gaseous systems studied are H&O*, He+C02, N&O2 and C,H&02. (2) A constant Sherwood number of S& = 8.33 (or Sh, = 12.5 at lI = 0.50) has been obtained for the
REFERENCES
[l] Gunn D. J. and De Souza J. F. C., Chem. Engng Sci. 197429 1363. [2] Ikeda K., Ohya H., Kanemitsu 0. and Shimomura K., Chem. Engng Sci. 197328 227. [3] Karabelas A. J., Wegner T. H. and Hanratty T. J., Chem. Engng Sci. 197126 1581. [4] Kato K., Kubota H. and Wen C. Y., Chem. Engng Progr., Symp. Series 197066 No. 105, 87.
Gas filmcoefficient of mass transfer in low P&let number region for sphere packed beds [5] Kagaku-Kogoku-Benran, 3rd. Edn, (Edited by Sot. Chem. Engrs). Maruzen, Tokyo, 1968. [6] Littman H., Barile R. G. and Pulsifer A. H., Ind. Engng Chem. Fundls 19687 554. [I MiyauchiT. andKikuchi T., C/rem.EngngSci. 197530,343. 181Miyauchi T., Kikuchi T. and Kataoka H., Kaguku-Kogaku 197135 1148;also in Int. Chem. Engng 197212 373. [9] Miyauchi T., Matsumoto K. and Yoshida T., J. Chem. Engng Japan 19758 228. [IO] Miyauchi T., Kagaku-Kogaku 197236 633.
13
1111Miyauchi T., 4th CHISA Congress, Session 10, Fundls of Heat and Mass Transfer, Sept. 1972,Praha. 1121NelsonP. A. andGalloway T.R., Chem.Engng Sci. 197530 1. 1131Sorensen J. P. and Stewart W. E., Chem. Engng Sci. 197429 818. [14] Shirai T., Dr. Engng dissertation, Tokyo Institute of Technology, Tokyo, 1955. [IS] Wakao N. and Tanisho S., Chem. Engng Sci. 197429 1991. [16] Zabrodsky S. S., Int. J. Heat and Mass Transfer 1%3 6 23, 991.
E&cfing
Science,1976,Vol. 31. pp. 9-13. PewamonPress. Printed in Great Britain
GAS FILM COEFFICIENT OF MASS TRANSFER IN LOW PfiCLET NUMBER REGION FOR SPHERE PACKED BEDS TERUKATSU MIYAUCHI, HIROSHI KATAOKA and TATSUJI KIKUCHI Departmentof Chemical Engineering, University of Tokyo, Tokyo 113,Japan (Received 15February 1975;accepted 15May 1975) A-t-The limiting Sherwood number between particles and Buid in the low P&let number region has been determined experimentally for gas phase mass transfer in packed beds. A value of Sh, = 8.33 (or Sh, = 12.5 at 4 = 0+50),was found where Sh,. and Sh, are the Sherwood numbers based on the particle diameter and the hydraulic diameter respectively and e, is the void fraction of the beds. A high accuracy of measurement was obtained by applying a pulse response of CO, tracer gas to determine the film coefficients.
the purpose of making the above situation more definite. The film coefficient of mass transfer utilized here is defined by the following equation:
Heat and mass transfer coefficients between particles and
fluid in sphere packed beds are one of basic informations needed for unit operations and chemical reactor design. The coefficients in the low Reynolds or PCclet number region are particularly important for such operations as adsorption, chromatography, fluid beds for catalytic reaction etc. where a dense phase of fine particles is utilized. Unfortunately, however, various inconsistencies have been experienced by many investigators in correlating rate data. This situation still continues even in the recent publications[l, 2, 4, 9, 11-13, IS]. The main difficulty encountered has been the limiting Sherwood number Sh,, (= k,J, /&) [ 161being not clear as to whether it goes down to zero or takes a finite constant as decreasing the flow rate of fluid to zero. Current status of progress is well understood by referring to Refs. [l, 2,3,4,6,12] and to the discussion given by Nelson and Galloway [121. Recently, Littman et al. [6] and Kato et al. [4] reported experimentally linear dependence of Sh, on Re,,, which is the dependence supported by Nelson from the concept of surface renewal. Kato’s data, however, are more than twenty times greater than the prediction of Nelson. Wakao and Tanisho[lS] gave an experimental quadratic dependence of Sh, on Rep. Their data are seemingly located in the region predicted by Nelson. On the other hand, several works have supported the limiting Nusselt or Sherwood number being finite constant. Of these, Sfirensen and Stewart[l3] derived numerically the limiting Nusselt number Nu,,. being about 3.9 for a simple cubic array of spheres. Also, Gunn and Souza[l] have indicated that Nb, may take the limiting value of about 10, although their data scatter considerably. A fairly large limiting Sherwood number of 8.7 was previously reported [2,11] for Sh,,, (= k&, /&), and more recently 7.41 for a liquid system[9]. The latter value corresponds to Sh,, = 16.7 at 9 = 0.40. With this large Sh,, it is probable that some experimental approaches utilized so far may be inadequate in some cases if relative contribution of correction terms suppresses that of film mass transfer. Experimental determination of the limiting Sherwood number has been presented here for gaseous systems with
+/ae
= Eazclaz2- aaclaz -k&
-c,).
(1)
The presentation here has been mostly confined to experimental works. Another experimental approach essentially different from the present one will follow to this. 1. OWLINEOF EXFZRIMENTAL APPROACH
To determine the gas film coefficient of mass transfer, a small amount of CO2gas is introduced, as a pulse wave at the bed inlet, into steadily flowing inert gas stream. The bed spheres are impregnated with concentrated aqueous KOH solution. The tracer CO2 gas reacts with KOH almost instantaneously in the sphere surface layer, and the residual CO2 gas response is measured at the bed outlet. The experimental lihn coefficient of mass transfer was quite high under the conditions utilized here, so that the residual pulse size was usually very small, sometimes the size being too small to measure accurately. Due to this, measurement of residual pulse tracer quantity is considered to give better accuracy for the extent of CO1 absorption than determining the percentage saturation for a steady state saturation method such as vaporization of liquid or sublimation of solid into a gas stream. This improvement in accuracy is an essential feature of the present experimental approach. Based on eqn (l), it has been shown elsewhere [8] that the overall film coefficient & is obtained by the following equation for correcting the effect of axial dispersion: 48 exp (Pez /2) % = (1 + fl)’ exp (/3Pe,/2) - (1 - /I)’ exp (+Pe, /2) (2)
where so and s are respectively the inlet and outlet quantities of CO1 tracer gas, Pe, = t?L/E, and fl = d1+4N,IPe, with N, = k,aL/U. Pe, included in eqn (2) is available from Ref. [7]. The 9
10
T.
MIYAUCHI
overall coefficient k, obtained in this way still includes the particle side resistance to mass transfer. To evaluate this resistance, unsteady state CO? diffusion through the impregnated aqueous KOH solution layer in the sphere surface region has been analysed under the following assumptions that the reaction taking place in the liquid layer is instantaneous and irreversible, and that the gas flows through the bed in piston flow manner. The local coefficient has been averaged over the entire active bed, by taking into consideration the concentration decrease of tracer wave along the bed. The final expression for a constant pulse size at the bed inlet has been given[9] as eqn (3). This is the same equation as the one utilized for neutralization reaction to know an aqueous film coefficients in packed beds of ion-exchange resin beads[9]. l/Sh,, = l/Sh, t A,$
(3)
where J, = (PDDl/d,)“‘(d,/L)Sh,,/~~ and A, = qd’*&,/24ti[(l-
~,)(amD#.
Here, Sh,,, is the experimentally obtained Sherwood number (= k&,,/&); Sh, = kfd, /DM; Ap a constant for constant er; q0 the initial pulse size (mol/cm’ of bed cross section) at 1.0 atm and the term A& the liquid film resistance to CO2 absorption. The above correction method is convenient to manipulate. Theoretically, eqns (2) and (3) are sufficiently accurate when the gas film resistance to mass transfer controls the overall mass transfer process, but becomes approximate when the liquid side resistance is controlling. Since the latter is generally not the case, the correction procedure is considered to be adequate191. 2. EXPERIMENTAL
EQUIPMENT AND PROCEDURES
et al.
placed in a gas chromatography equipment to maintain the temperature mostly at 22 + l”C, and to measure the outlet CO2 response by thermal conductivity change of the issuing gas. The inlet pulse size of CO* gas was always maintained at 0.10 cm” under the system pressure P. The carrier gases utilized were HZ, He, NZ and C9Hs respectively. Concentration of the aqueous KOH solution was carefully adjusted in the bed by regulating the water vapour pressure of carrier gas at 144- 2.14 mmHg, which was lower than that of 20N-KOH solution (1.55 mmHg at 20°C and 2.20 mmHg at 25”C), so that one gets the highest rate of liquid phase reaction. This procedure required a lot of skill and trial runs, but it constituted an essential part of this experimental work. Also, a bed packed with fresh particles impregnated with aqueous KOH solution was utilized for each run. Details of the equipment and experimental procedures have already been reported [8]. The experimentally utilized lowest gas velocity (or the P&let number) was limited by the accuracy of the measuring device for the residual CO2response size. The maximum extent of CO?: absorption was 99.7% for N&O2 at Pe,,( = Udh/DM)= 12, 99.5% for He-CO* at Pe,, = 3 and 99.8% for H&O* at Pe,, = 5 respectively. These figures were the upper accuracy limit of our device. Hence, it was not possible to measure the Sherwood number for the region, Pe,, ~2, due to the residual size being too small to measure accurately. When the extent of CO*absorption under the condition given here is compared with that calculated with the Nelson and Galloway correlation[l2], one will find quite different results. The initial pulse size was conveniently known from the outlet pulse size which had passed through the bed whose absorption capacity had been all exhausted. No residual CO*response was detected for much smaller Pe,, than two or for an active bed three times longer than the present one when the bed was operated at Pe,, 5 2. Hence, the initial pulse gas was considered essentially pure C@. Binary gaseous diffusivities at 1.0 atm are as follows[5]: 0~630cm*/sec for H&O2 at 22”C, 0*5%cm*/sec for He-CO2 at 23”C, 0.168 cm2/sec for NrC02 at 22”C, and 0.0835 cm*/sec for CsH&02 at 20°C.
Figure 1 shows a packed bed utilized for CO2 absorption by aqueous KOH. solution. It consisted of a 10mm i.d. stainless steel tubing equipped with pre- and after-calming packed sections. The bed height of the active test section, L, was kept at 3 - 4 mm, and the bed was packed with porous spheres (dp = 0*68, 1.04, 1.08, 1.15 3. EXPERlMEhTAL. RESULTS AND DISCUSSIONS and 1.42 mm respectively) which were impregnated with 20Naqueous KOH solution. The void fraction ef of the .3.1 Experimental overall film coeflcient % Figure 2 shows experimentally obtained overall gas film beds was 0.483 - 0.517. The ratio L/d,, was maintained at 3 - 5, which gave the column axial P&let number Pe, of coefficients as a function of the molecular P&let number Pe,,(= zid,,/DM). Dimensionless expression based on the 5.0 - 12.7 for the whole operating conditions. The bed constituted a kind of pulse reactor, and it was hydraulic diameter has been utilized in what follows, since this gives consistently better correlation for beds of different void fraction [ lo]. The Grashoff number Gr has been calculated to see the c gas inlet effect of natural convection. A possible severest case is taken as a COZpulse being sent into a HZstream flowing at Pe,+= 2. The pulse spreads by axial dispersion while calming sectran packed with C-22 particles for gas chmmatgmphy use. travelling through the calming section, and flows into the reaction section packed with reOct~~t active section. CO* concentration is highest in the liquid cooled C-22 particles. incoming stream and nearly zero on the active spheres. flange With these, Gr = 0.8 at the active bed inlet and about 80% volume of the initial COZ passes through the active bed Fig. 1. Packedbed for CO2absorption.
in low P&let number regionfor spherepackedbeds
Gas filmcoefficient of mass transfer
-co*( 0 lkhm
3 2
‘He -C02(
I
1
EI lIK)mn,
, 1.0 atm)
1.6 atm)
\
He-CO, ( 0 1.08mm , 1.0 atm) I.3
2
Il111.1
345 7 10 P% = C&/o,
I.8
2
11
I
I.,JJl
34507
N,-CO, I
10
2
.I
($
1.08mm
, 2.0ah )
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2
3 2
3450071ooo
Fig.2. Measuredoverallcoefficientk, as a functionPe,,. within about 0.11 sec. Gr is too small to induce natural convection. Hence, this effect is considered to be negligible. Essential feature of the plot given in Fig. 2 may be summarized as follows for Pe,, 5 lOO- 150, where the mechanism of mass transfer is in the regime of molecular diffusion controlling for liquid systems [9]. (a) bj responds enough sensitively to the change in such physical parameters as d,, P and D,. (b) k, tends to remain less dependent on Peh in comparison with the behaviour in the Pohlhausen regimeHO], where the boundary layers for velocity and concentration are developing simultaneously and Sh, is proportional to RehlnSc I”. (c) When dp is decreased under constant P, N-XOz system shows definite increase in b,, but H&O2 system reveals only slight increase. (d) When P is increased under constant d,, kO, decreases for both of N&Z02 and He-CO* systems, although the decrease is smaller for the latter. (e) When /c,, for various systems are compared with one another under constant P and d,, the systems with higher D, (such as He-CO2 and H&02) show generally larger /c,f than those with lower DM(such as N&JO* and C,HXO& However, kO,for He and HZ are not much different from those of NrC02 for the large difference in D,. C~H&OZ system shows definitely smaller lc,, than the rest. In the molecular diffusion controlling regime for the gas film coefficient, k,dV/Dnr should remain constant for geometrically similar beds[ll]. Hence, the above b. suggests the region of Peh 5 100 - 150 being the molecular diffusion controlling regime, although bf still includes the influence of liquid side resistance to mass transfer. In this mass transfer regime, the Sherwood number is constant, or kf is proportional to DM/dp Hence, /c,, should be approximately proportional to D, /d, when kf is controlling. The behaviour given in c. and d. satisfies this relation (note that DM m l/P) with an exception of H&JO*. This system shows only slight increase in hf with decreasing dp The reason seems to come from the aqueous KOH solution side resistance being controlling due to very high k,. The behaviour given in e. is also best understood in the same manner as above. In contrast to these, the gas film resistance controls the
Fig. 3. Sh,,, as a functionof Pe,.
overall mass transfer process for Nz-CO* and C,HL02 systems. 3.2 Sherwood number To observe the above mechanism of mass transfer more clearly, Sh,,, (= k&,, /DM) is shown in Fig. 3 as a function of Peh(=Udh/DM). Obviously, the systems with smaller D, (NrC02 and CsH&02) have higher Sh,, than those with larger DM (He-CO2 and HrC02). Also, the former shows Sh,, being less dependent on Peh than the latter. The systems with larger D, have higher kf so that the liquid side resistance to mass transfer becomes increasingly noticeable. This is the reason why HZ and He show lower Sh,, than Nf and CJHs. The gradient of each mean curve has been obtained from the final correlation eqn (4) below. It is seen that the limiting Sherwood number Sh,,(= k,d,/D,) is well more than 10 when the liquid film side resistance to mass transfer is adequately eliminated from Sh,,. To eliminate this resistance, the data taken for Peh s 100 are processed according to eqn (3) as follows. The arithmetic mean value of experimental l/Sh,, and that of IJ are tirst calculated for the runs taken under a given set of 4, P and a gaseous system. The mean values thus obtained are plotted in ‘Fig. 4 for different sets of experimental conditions. Although the data scatter
T.
MNAUCHI et 01.
molecular diffusion controlling regime (Peh s 100). Further, an average Sherwood number of 7.87 has been found for both of gas and liquid systems. NOTATION
4 refer to eqn (3), [atmcm/sec]+ DM molecular diffusivity of gas phase, cm*/sec DL CO* diffusivity .in liquid phase, cm*/sec E superficial axial dispersion coefficient, cm’/sec Gr d,‘gAplpv= L active bed length, cm P mean system pressure, atm lldhI DM Peh ULlE dJJlv d,,ti/v VIDM
Pe, Rep Reh
SC
Fig. 4. l/Sh,,, vs # plot.
considerably, l/S&, seems to be about linearly combined with JI as expected from eqn (3), i.e. l/S!!,, = 0.080 + 0*045$.
(4)
Hence, the limiting Sherwood number Sh,, is given as follows:
superficial gas velocity, cmlsec u N, kOfllL/U NUI hd,, lk Sh, ktdpID, Sh,, 44 IDM Shp k,fd, ID, Shh, k,dh IDM S cross sectional area of bed, cm’ a surface area per unit bed volume, cm*/cm’ C
Sh,, = l/O.080 = 12.5.
(5) 2
Since the mean void fraction of the beds is 0.50, the above Sherwood number gives
dp
Sh,,,, = k,od,,/D, = 8.33.
k/ 4 4 m
(6)
The limiting Sherwood number determined for aqueous electrolyte solutions[9] is Sh,,, = 7.41, close to eqn (6). Considering the accuracy of experimental approach utilized here, we take an average Sherwood number aho as follows for both of gas and liquid systems:
h k
40 S S0
shh, = (7.41+ &33)/2 = 7.87.
n
(7)
2
For the gaseous systems, the mechanism of mass transfer seems to move to the Pohlhausen regime [ lo] for Peh 2200 (ref. to Figs. 2 and 3 for N&IO2 system, SC = 0904). The limiting Sherwood number eqn (7) is fairly greater than those by Serensen and Stewart[l31 (Nub = hdJk = 2-6 at ef =0*5) and by Gunn and Souzalll (Nu,. = 4.4 at e, = 0.4; this limiting value is not always obvious). Sh,,, by Sorensen is about the same as that given by Shirai[l4] (Sh, = 2.6 at l, = O-5).
concentration of CO?, mol/cm’ surface concentration of CO*, mol/cm’ (2/3)[e,/(l- q)]dp, hydraulic dia., cm particle dia., cm film coeff. of heat transfer, Cal/cm’ sec”C thermal conductivity, Cal/cm secT film coeff. of mass transfer, cm/set limiting film coeff. of mass transfer, cm/set overall coeff. of mass transfer, cm/set partition ratio of CO, betw. carrier gas and KOH sol% q/P, with q = s,/S, mol/cm* atm final size of tracer wave, mol initial size of tracer wave, mol interstitial velocity, U/e,, cmlsec axial distance coordinates, cm
Greek symbols a capacity ratio, mol-COz/cm3-KOH sol’n P ql t 4N,IPe, AP Ef e V
;
density difference, g/cm’ void fraction of packed bed time, set kinematic viscosity, cm*/sec density, g/cm3 refer to eqn (3), [atmcmlsec]‘”
4. CONCLUSIONS
(1) Gas film coefficients of mass transfer in sphere packed beds have been measured in the low P&let number region, by applying a pulse response method of CO2 gas through a packed bed of aqueous KOH impregnated spheres. The gaseous systems studied are H&O*, He+C02, N&O2 and C,H&02. (2) A constant Sherwood number of S& = 8.33 (or Sh, = 12.5 at lI = 0.50) has been obtained for the
REFERENCES
[l] Gunn D. J. and De Souza J. F. C., Chem. Engng Sci. 197429 1363. [2] Ikeda K., Ohya H., Kanemitsu 0. and Shimomura K., Chem. Engng Sci. 197328 227. [3] Karabelas A. J., Wegner T. H. and Hanratty T. J., Chem. Engng Sci. 197126 1581. [4] Kato K., Kubota H. and Wen C. Y., Chem. Engng Progr., Symp. Series 197066 No. 105, 87.
Gas filmcoefficient of mass transfer in low P&let number region for sphere packed beds [5] Kagaku-Kogoku-Benran, 3rd. Edn, (Edited by Sot. Chem. Engrs). Maruzen, Tokyo, 1968. [6] Littman H., Barile R. G. and Pulsifer A. H., Ind. Engng Chem. Fundls 19687 554. [I MiyauchiT. andKikuchi T., C/rem.EngngSci. 197530,343. 181Miyauchi T., Kikuchi T. and Kataoka H., Kaguku-Kogaku 197135 1148;also in Int. Chem. Engng 197212 373. [9] Miyauchi T., Matsumoto K. and Yoshida T., J. Chem. Engng Japan 19758 228. [IO] Miyauchi T., Kagaku-Kogaku 197236 633.
13
1111Miyauchi T., 4th CHISA Congress, Session 10, Fundls of Heat and Mass Transfer, Sept. 1972,Praha. 1121NelsonP. A. andGalloway T.R., Chem.Engng Sci. 197530 1. 1131Sorensen J. P. and Stewart W. E., Chem. Engng Sci. 197429 818. [14] Shirai T., Dr. Engng dissertation, Tokyo Institute of Technology, Tokyo, 1955. [IS] Wakao N. and Tanisho S., Chem. Engng Sci. 197429 1991. [16] Zabrodsky S. S., Int. J. Heat and Mass Transfer 1%3 6 23, 991.