Shoneman, K. F., Gerster, J. A., AIChE J., 16, 1080 (1970). Shunta, J. P., Luyben, W. L., AZChE J., 17, 92 (1971). Thomas, W. J., Campbell, M., T r a m . Inst. C h m . Eng., 44, T314, IlRIX'I.
Wahl, E. F., Ph.D. Thesis, Cornel1 University, Ithaca, N . Y., 1967. Wahl, E. F., Harriott, P., Ind. Eng. Chem., Proc. Des. Develop., 9,
_ _ _ (imn).
296
T&jala,'K., Acta Acad. Aboensis $lath. Phys., 31, Xo. 5 (1971); 32, Xo. 2 (1972). Toijala, K,, Fagervik, K., Acta Acad. Aboensis JIath. Phys., 32 KO. 1 (1972). Toijala, K., Jonasson, D., Acta Acad. Aboenszs X d h . Phys., 31 No. 11 (1971).
\--
- I
RECEIVED for review October 7, 1969 January 24, 1973 RESUBMITTED ACCEPTED &lay 17, 1973 Presented at the JACC meeting, Boulder, Colo., Aug 1969.
Two-Stage Catalytic Converter. Transient Operation George 1. Bauerle and Ken Nobe" School of Engineering and Applied Science, Cniversity of California, Los Angeles, California 90024
A mathematical model for two-stage catalytic exhaust converters has been developed b y extending the work of others for single-stage converters. It has been shown that computations of the operational characteristics of the first stage are not in serious error by assuming temperatures of the gas and solids phases as equal. O n the other hand, computations for the second stage are more in error but not substantially. The effectiveness of two-stage, axial-flow converters to decrease pollutant emissions has been shown to vary with reactor diameter; the effect of secondary air rate was not as appreciable. Furthermore, warm-up time varied with diameter much more for the second stage than for the first stage.
F e d e r a l standards foil 1975-1976 auto exhaust emissions have spurred considerable research and development work in catalytic control methods. The purpose of this work is to extend the mathematical modeling of single-stage catalytic exhaust converters by Vardi aiid Biller (1968), who studied the thermal response of catalyst beds without reaction and by Kuo and coworkers (1971), who examined the transient behavior of the oxidatjon converter to a two-stage catalytic converter. The analysis of steady-state, two-stage catalytic Converters has been given in an earlier paper (Bauerle and Xobe, 1973) and will be referred to as part I. Mathematical Model
I n deriving the present mathematical model for a trvo-stage converter, it is assumed that t x o cylindrical reactors in series are employed. Only axial flow of gases is considered. I t rras shown in p i r t I that the longitudinal arid radial diffusioii terms are negligible in practical design applications. Thus, the mass balance simplifies to
to be operating adiabatically. Thus, the energy balances for the gas phase and solids phase, respectively, can be expressed as
and
It has been assumed that the heats of reactions are developed initially 111 the solids phase. The model included a computational scheme suggested by Kuo, et al. (1971). Temperature was assumed to remainat an average value over each time arid length step. It was also assumed that the species in excess remained a t the initial value during the time step. Equation 1 can now be written for the j t h length step
Khere the a\ erage temperatures are taken as Vardi and Hiller (19168) showed that the heat capacity of the solids is about three orders of magnitude greater than the heat capacity of the gas aiid that the thermal conduction terms are very small comliared t o gas-solid heat exchange aiid the bulk flow t e r m . Kuo, et al. (1971); found that the thermal behavior of the solid phase dominated the dynamic response of the entire system. K i t h these consideratioils the transient energy term for the gas phase and all thermal conduction terms can be neglected, Furthermore, in part I it was showii that for all practiral piirposes the converter can be considered
T
=
(T
+ 2"')
2
(5)
For illuatratir e purpo>es, the catalyst i n the fir3t qtage nil1 be assumed to be higlilj selective for the reaction
so
+ co
=
?S?t co,
(6)
I n addition. it 1.; a5wmed that the oudation reactions in the second .tage can be represented by the reaction
co +
?02
=
co2
Ind. Eng. Chern. Process Des. Develop., Vol. 12, No. 4, 1973
(7) 407
SREO,
YPH
50
Table 1. Mass Rates of Converter Output Calculated with and without Gas-Solid Heat Exchange for Two Reactor Diameters”
:piL&d!L 20 10
PPY NO
Reactor diameter, ft
2000
Mass rates of converter output, g/miIe
co
NO
Time to reach 1 OOOOF a t ‘/4-length point In reactor, sec
1.13 0.50
Without Gas-Solid Heat Exchange 1.08 40.1 1.80 17.0
907 182
1.13 0.50
With Gas-Solid Heat Eschange 1.10 42.1 1.81 21.9
960 232
1000 40
O 0
120
80
TIME,
0
40
BO
120
SECONDS
Figure 1 . Typical input data
Modified forms of the rate equations obtained by using combined data of Baker and Doerr (1965) and Bauerle, et al. (1972). for the KO-CO reaction on copper chromite and by Blunienthal and Nobe (1966) for the CO-0, reaction on copper ovide have been selected for this analysis. For the YO-CO reaction =
r\-0
7 0(10)9e-8250’R’TC\ 7 0 CCOmol’hr Ib of catalyst
(8)
and for the CO-O1 reaction rCo
= 3 6(10)’3e~*~ 2°0’R’TC~oCo2 mol/hr lb of catalyst
(9)
For the NO-CO reaction, integration of eq 4 gives Y ’ N ~ , ]=
[(a
+
PYNO
,)epAs -
~I/P
(10)
where = = - RTgG
~ ! 7 ’ , ~ y \ - ~ , ~ - ~ / ~ ~ z ~ i(11) p
e&JIp [p,(l
-
e)ABcop/~RT,]e-~’~’~ (12) -”
Similar appropriate relationships were developed for the
CO-O? converter. I n difference form, eq 2 and 3, respectively, become
T t g ,=
+ hA,T’,,Az/GC,]/[l + hA,AzlGC,]
[T’g,3-l
(13)
and
\\-here the primes refer to conditions a t the end of the time step. Time steps are “fonvard” differences while length steps are “backward” differences. For the two-stage converter, the model determines concentration distribution and temperature as a function of time and position in each reactor. The efRuent from the first stage is mised with secondary air before entering the second stage. Results
The model was tested using input data derived from emissions test results typical of automobiles undergoing the Federal Test Procedure (Federal Register, Vol. 33, Yo. 108, June 4, 1968). (Data for typical instantaneous emissions using the current Federal driving schedules (i.e., Federal Register, Vol. 35, KO.136, July 15, 1970) were not available a t the time this 408
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
Uncontrolled Exhaust (Input to Converter) 4.0 70.0 a Secondary air rate = 0.5Q, reactor length = 0 . 5 Et, lb/cu ft, and C, = 0.25 Btu/lb “F.
p. =
104
analysis mas completed.) Figure 1 shows typical data for a single cycle of the seven-cycle test. For effective KO reduction with CO in the first stage the exhaust entering the converter is required to be in a reducing condition. In a typical seven-cycle test, first cycle eshaust is highly reducing due to the choked operation of the carburetor and the low temperat’ure. To ensure t,hat the eshaust entering the converber is in a reducing condit,ion during the entire test the first cycle data for the CO concentrations has also been used for the remaining sis cycles. A comparison was made of calculated conversions and catalyst temperatures in a two-stage catalytic reactor by first considering gas-solid heat exchange (eq 13 and 14) and then by assuming that gas and solids temperatures are equal. Secondary air was t’aken as 5097, of the primary air flow and was assumed to be preheated to the temperature of the firststage exhaust. For T , = T,, the following difference equation is obtained
T’,
=
T,[1 - C,jAOG~C,p,(l
- e)&]
cf AOTj-iCg, j-1 Csp,(l - ailhe fouiid elsen-here jl3auerle and S o b e , 1971). The re,*;ultq-ho\\-ii i l l the tables and figures iiidicates that a m i i 4 e r a h l y greater :icti\-ity catalyht is required for the semiid ctage to niiiiimixe the thermal inertia iii that stage and to iiiert tlie 1975-1 976 Federal auto emissioii ,-taiidards for C'O aiid 1iydrovari)oiis. .I catalyst x i t h a substantially greater
A
drrhenius preexponential factor catalyst superficial area, sq ft/cu ft of catalyst C = concentration, lb mol/cu ft C, = specific heat of gas, Btu/lb "F C, = specific heat of solids, Btu/lb O F E = activation energy, Btu/mol G = mass velocity, Ib/hr sq ft A H k = heat of reaction, Btu/mol h = gas-solid heat exchange coefficient, 13tu:hr sq ft ?)z = number of reactions occurring -11 = average molecular weight', lbl'lb mol n = number of reacting species p = pressure, atm Q = primary air flow rate, scfni Rik = reaction rate, lb rnolihr lb of cat'alyst R = gas constant, atm cu ftjmol "R R' = gas const'ant', Btulmol OR TCO = rate of CO oxidation, mol/hr lb of catalyst = rate of S O reductioii, mol/hr lb of catalyst' T = average temperature, O R T , = gas temperature, "R T , = solids temperature, "It f = average mole fraction y i = mole fract,ion of component i z = asial length, ft =
-4,
=
c-0
GREEKLETTERS CY
=
p
= A = e = 8 = p. = pg =
function in eq 11 function in eq 12 increment void fraction time, hr solids density, lb/cu ft gas density, lb/cu ft
SUBSCRIPTS CO = carbon moiioside g
i ,f
k
S s
gas index for species ( e . g . , NO or CO, etc.) length step index = index for specific reaction O = nitric oxide = solids = = =
Primed values denote conditions a t eiid of a time step. Ind. Eng. Chem. Process Des. Develop., Vol. 1 2 ,
No. 4, 1973
409
literature Cited
Baker, R. A., Doerr, R. C., Ind. Eng. Chem., Process Des. Develop., 4 , 189 (1963). Bauerle, G. L., Nobe, K., UCLA Engineering Report No. 7156, pp 1-51, Aug 1971. Bauerle, G. L., Nobe, K., Ind. Eng. Chem., Process Des. Develop., 12, 137 (1973). Bauerle, G. L., Service, G. R., Nobe, K., Ind. Eng. Chem., Prod. Res. Develop., 11, 54 (1972). Blumenthal, J. L., Nobe, K., Ind. Eng. Chem., Process Design Develop., 5 , 177 (1966).
Kuo, J. C. W., Morgan, C. R., Lassen, H. G., SAE Paper No. 710289, presented to Automotive Engineering Congress, Detroit, Mich., 1971. Vardi, J., Biller, W. F., Ind. Eng. Chem., Process Design Develop., 7, 83 (1968). RECEIVED for review May 1, 1972 ACCEPTED May 21, 1973 Work supported by Grant No. AP00913, Air Pollution Control Office, Environmental Protection Agency and, in part, by Air Resources Board Project No. 2-009, State of California.
Gas Absorption Rates at the Free Surface of a Flowing Water Stream. Effects of a Surfactant and of Surface Baffles Murray Moo-Young* and Makota Shoda Department of Chemical Engineering, Cniversity of Waterloo, Waterloo, Ontario, Canada
Gas absorption rates a t the free surface of a flowing water stream in a horizontal channel were measured with and without the presence of traces of a common soluble surfactant (Tween 20) for hydraulic radiusbased channel Reynolds numbers between 200 and 2000. It was found that the surfactant significantly reduced mass transfer rates and that the reduction i s related to the surface tension changes induced b y the surfactant in the system. The mass transfer reduction could also be predicted from measurements obtainable from a relatively simple non-flowing stirred-cell system. It i s shown that simple surface baffles can cause an enhancement of mass transfer rates in these systems b y a factor of 2 or more, and the practical implications of surface-baffle applications to the aeration of polluted water streams and in pipeline fermentors have been noted.
A d e q u a t e oxygen transfer into flolving waters is of practical importance to the alleviation of water-pollution problems in natural bodies of xater. It is also of importance in the design and operation of surface-aeration systems for treating fluids such as waste waters and unsparged fermentation media. I n order to obtain a understanding of the gas-liquid mass transfer mechanism involved in these processes, several studies have recently been carried out on the uptake rates of a soluble gas from the atmosphere into open channel liquid f l o ~ sThis . paper deals with an experimental study on (a) the feasibility of enhancing gas absorption rates into a channelflow water stream by means of simple surface baffles, and (b) the inhibition effects of a soluble surfactant on the mass transfer rates in these systems. Davies (1972) seems to have made the only report so far on mass transfer enhancement by deliberate channel geometry modification, in t,liis case, by increasing the surface roughness of t'he bottom of the channel. Our present work seems to be the first study dealing with surface-baffling effects. The effects of surfactants on gas-liquid mass transfer have previously been considered, e.g., Burnett and Himmelblau (1970) Byers and King (1967), and Davies and Rideal (1963). However, a comprehensive explanation of these effects is still lacking and more extensive experimental data for these systems seem to be required. Here we have presented additional dat'a. 410
Ind. Eng. Chem. Process Des. Develop., Vol. 1 2 , No.
4, 1973
Experimental Section
-4schematic diagram of the equipment used is shown in Figure 1. A channel, 15.2 em wide X 10.2 ern high X 246 cm long, was used to investigate the mass transfer of carbon dioxide into flowing tap water. The high aspect ratio was used to minimize wall effects. The channel was made of transparent acrylic sheets and supported horizontally on antivibration pads. Tween 20 (polyoxyethylenesorbitan monolaurate), supplied by Fisher Scientific, was selected as the surfactant. This surfactant is commonly used in fermentation and related systems. Water was fed into the channel from an overhead tank. At the inlet of the channel, a 14.5-cm long calming section made of common drinking straws (id. = 0.7 cm) was used to minimize entrance end effects. J l a t e r flowed from the overhead tank under gravity to the channel via a rotameter, the flow rate requiring only minimal manual control during an experiment. The water then flowed into a rectangular outflow slot (7.5 cm x 15.2 cm) and the depth of the water in the channel (0.4-0.8 em) was fixed and controlled by a variable external weir. Eyit end effects viere minimized by adjusting the height of the liquid on the overflotv slot to about 0.5 cm below the height of the main channel flow so that any stagnant end zones would not spread back into the channel section. Small end effects are not expected to affect the present comparisons between gas absorption rates for free and baffled
