Ind. Eng. Chem. Res. 1991, 30, 428-430
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RESEARCH NOTES Measurement of the Effective Diffusion Coefficient of Nitrogen Monoxide through Porous Monolith-Type Ceramic Catalysts This Research Note describes a straightforward experimental technique t o measure the effective diffusion coefficient of nitrogen monoxide through the porous walls of a monolith-type ceramic catalyst. The method takes explicit advantage of the geometric shape of a monolith-type catalyst to measure the steady-state diffusion flux of nitrogen monoxide through the porous catalyst. It is found that the tortuosity factor of the commercial titania-supported catalysts used in this study and employed for the selective catalytic reduction of NO by NH3 ranges from 2.0 t o 2.3. Introduction The selective catalytic reduction (SCR) of NO by NH3 over titania-supported monolith-type catalysts is a technology used in Japan and West Germany for the removal of NO from power plant stack gas. SCR may also find commercial application in the United States pending stringent emission regulations. It is well-known that the performance of these catalysts is hampered by pore diffusion. It is therefore important to measure and predict the effective diffusion coefficient of the reactants in order to develop catalysts with enhanced NO removal performance. This Communication outlines a simple experimental technique that takes advantage of the monolith structural shape for measuring the steady-state diffusion flux of nitrogen monoxide through the porous catalyst.
channel, the channel weight, and the catayst bulk density, the last obtained from mercury porosimetry.
Experimental Procedure The experimental apparatus is shown in Figure 1 and consists basically of the diffusion cell, a Model 10 AR NO analyzer from Thermo Electron, and a gas metering device. The method is in principle similar to the technique used by Wicke and Kallenbach (1941) but takes advantage of the monolith structural shape for measuring the steadystate diffusion of nitrogen monoxide through the porous catalyst. The catalyst used is a single-channel cutout of an industrial-sized monolith shown in Figure 2. Stainless steel tubing (1/4 in.; 316SS) shaved down on one end to a square shape is inserted 1/4 in. into the single channel and glued with Epoxy to the catalyst. The catalyst and tubing are then inserted into the Pyrex glass enclosure of the diffusion cell and sealed tight by means of a clamp on the center O-ring closure shown in Figure 1. Gas with a certified m o u n t of NO in N2from MG Industries is passed at a known flow rate (typically 400 L/h at STP) internally through the catalyst channel. Externally, pure N2 sweep gas is passed over the catalyst at typically 400 L/h at STP and carries along the NO which diffuses through the wall of the catalyst. The pressure difference between the inside and outside of the catalyst channel is measured by means of a U-tube water manometer during each experiment and is found to be negligible (less than 0.3 mm of HzO). On the basis of the flow rate and the NO content of the exiting sweep gas, the total diffusion molar flux expressed in moles of NO per second can be calculated. The catalyst geometric area open to pore diffusion is taken as the internal area of the channel between Epoxy glue points. The average wall thickness of the channel is calculated from the length of the catalyst piece, the outside diameter of the
(4)
Results a n d Discussion Figure 3 shows a schematic representation of the diffusion cell. A material balance over an infinitesimal distance dx axially along the cell yields the following equations: dClb F1 - - -A (Clb - Cls)kl dx
(1)
Bil(Clb - CIS) = CIS - czs
(2)
Biz(C,s - C?) = CIS - c 2 s
(3)
with boundary conditions: at x = 0
Clb = Clb,o C2b = 0
atx=L
(5)
(6)
In eqs 1-6, variables relating to the inside of the channel have a subscript 1 while variables relating to the outside of the channel have a subscript 2. Equation 1 relates the drop of the bulk gas phase concentration of NO, Clb, to the flux through the boundary layer a t the inside of the channel. Equation 2 relates the flux through the boundary layer inside the channel to the flux through the catalyst. In eq 2, Bil is the Biot number of NO given by
Bil
kl W / D
(7)
Equation 3 then equates the flux through the catalyst to the flux through the boundary layer at the outside of the channel while eq 4 then describes the increase of the NO concentration in the sweep gas. In eqs 2 and 3 it is assumed that the catalyst has a uniform pore structure across the wall; i.e., that there is no skin effect. Equations 1-6 can easily be solved analytically and yield the following expression when the flow rate inside and outside of the channel are kept the same:
where L is the total length of the channel and CZbveis the
0888-5885/91/ 2630-0428$02.50/0 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 2,1991 429
i l
p
Table I. Pore Structure Data of Catalyst EmdoYeda
I
A
B C
0.504 0.443 0.425
0.014 0.021 0.014
137 243 228
5000 5000 5000
147 73 74
" A 6WA pore diameter was used to discriminate micropores from macropores. From mercury porosimetry. From d, = 4c,/S. dPore volume averaged (Hegedus, 1980). CFromN2 BET measurements. A:catolyrt c h m l
F :O-ring closure
B:Epoxy $ue C : l N inch steel tubing
G: Pyrex enclosur*
D:NoandyZCW
J : vent
E:gosmeter
K: 3 - w ~VOIV~
Table 11. Geometrical Measurements of the Single-Channel Catalysts length, internal wall catalyst cm oDen diam. cm thickness. cm 0.597 0.140 A 13.33 0.559 0.163 B 4.95 0.594 0.145 C 5.35
I: " e t e r
Figure 1. Experimental setup of the diffusion cell.
(9)
Table 111. Effective Diffusion Coefficient Measurements catalyst D measd at 20 "C, cm2/s B(pred)/D(measd) A 0.00452 1.12 B 0.00726 0.9 1 C 0.005 10 1.10
Figure 4 shows a typical response of the specific molar flux with the flow rate (internal and external flow rates are kept the same). As can be observed, the specific molar flux increases initially with the flow rate but becomes constant above 400 L/h a t STP. A t flow rates above 400 L/h a t STP,it can easily be shown that (based on estimates of the effective diffusion coefficient and the external mass transfer coefficient) the term W I D in eq 9 is approximately 50 times larger than l / k , and l/k2. Under these conditions, then, the specific molar flux becomes proportional to the effective diffusion coefficient. In this Research Note, three catalysts are investigated, hereafter referred to as A, B, and C. Table I gives the pore structure data as determined from mercury porosimetry
and nitrogen BET and shows that the catalysts have appreciably different micropore diameters and microporosities and therefore are expected to lead to significant differences in the effective diffusion coefficient. Table I1 shows the geometrical measurements of the single-channel cutouts for the three catalysts. Table 111 gives the results of the measurements of the effective diffusion coefficients of NO through the three catalysts. The predicted values are obtained from the Wakao and Smith (1962) model. The prediction for all three catalysts is quite good, showing only a 10% difference between the predicted effective diffusion coefficient and the measured value. It can further be shown from the classical definition of the effective diffusion coefficient (Satterfield, 1970) that the tortuosity factor for all three titania-supported catalysts investigated here is in the range of 2.0-2.3.
concentration of NO in the sweep gas a t the exit of the diffusion cell. The specific molar flux 6 is then given by
-+-+. D kl
Figure 2. Commercial SCR catalyst.
kz
I n d . Eng. C h e m . Res. 1991,30,430-434
430
Bi
= Biot number C = NO gas-phase concentration, mol/cm3 D = effective diffusion coefficient, cm2/s d = pore diameter, cm F = volumetric gas flow rate, cm3/s k = external mass transfer coefficient, cm/s L = length of the channel, cm S = catalyst internal surface area, cm2/cm3 x = axial coordinate, cm W = catalyst wall thickness, cm
catalyst
0
x
x+dx
L
__. Figure 3. Diffusion cell schematic.
Greek Symbols
specific molar flux, mol/(sec-cm2) = porosity, cm3/cm3
@ = t 41
Subscripts
m = micropore M = macropore 1 = inside of the channel 2 = outside of the channel Superscripts
01 50
100
150
i
200
Flow rate (cm3/rec at STP)
Figure 4. Specific molar flux dependence on gas flow rate.
The experimental technique presented in this Research Note can be extended for high-temperature measurements using an adequate sealant material between the catalyst and the stainless steel tubing and inserting the entire diffusion cell in a temperature-controlled furnace. Effective diffusion coefficients for other support materials besides titania can also be determined with this technique as long as they can be extruded as uniform straight hollow bodies. Acknowledgment
b = bulk gas phase s = interface e = exit o = inlet Registry No. NH3, 7664-41-7; NO, 10102-43-9; T i 0 2 , 1346367-7.
Literature Cited Hegedus, L. L. Catalyst Pore Structures by Constrained Nonlinear Optimization. Znd. Eng. Chem. Prod. Res. Deo. 1980,19,533-537. Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; Krieger: Malabar, FL, 1970; Chapter 1. Wakao. N.: Smith, J. M. Diffusion in Catalvst Pellets. Chem. Eng. Sci. '1962, 17, 825. Wicke, E.; Kallenbach, R. Die Oberflachendiffusion von Kohlendioxyd in Aktiven Kohlen. Kolloid 2. 1941, 97, 135-151.
Jean W.Beeckman
I thank Ronald J. Majeran for setting up the diffusion cell and performing the experiments.
Research Division W . R. Grace & Company-Conn. 7379 Route 32 Columbia, Maryland 21044
Nomenclature A = specific geometric area of the catalyst channel, cmz/cm
Received for review February 21, 1990 Accepted October 8, 1990
Steady-State Cubic Autocatalysis in an Isothermal Stirred Tank In this paper, we demonstrate how the recently proposed procedure for global steady-state multiplicity analysis by Balakotaiah and Luss may be used to map regions in parameter space having a specific number of feasible solutions. The system chosen is a generalized scheme of autocatalytic reaction taking place in an isothermal CSTR. Both reversible and irreversible cases were considered. For each case, two possible forms of kinetic rate expressions leading to cubic steady-state manifold equations were examined. The influence of the Damkohler number (residence time and feed concentration) and stoichiometry of the autocatalyst have been studied. While stoichiometry may influence the steady-state solution pattern of the irreversible autocatalytic reaction, it was found that the behavior of the reversible reaction is independent of the stoichiometric coefficient of the autocatalyst. Introduction The genesis of the investigation of chemically reacting systems characterized by steady-state multiplicity is probably found in Aris and Amundson (1958). Further research has since shown that what would have easily passed for mere experimental artifacts are indeed real 0888-5885/91/2630-0430$02.50/0
phenomena not uncommon in the analysis of nonlinear systems. It is now becoming increasingly acceptable that not only does preliminary analysis of steady-state multiplicity serve as a useful guide in delineating regions of interest for experimental investigation, but also the associated question of the stability of such solutions is of equal 0 1991 American Chemical Society
