Chemical Reaction Engineering

5 Physical Phenomena in Catalysis and Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on December 11, 2014 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0109.ch005

in Gas-Solid Surface Reactions E. W I C K E Institut für Physikalische Chemie, Westfälische Wilhelms-Universität, 4400 Münster, Germany

Physical phenomena are understood as intraparticle and interparticle transport processes of mass and of heat in fixed bed reactors. Starting with measurements of temperature and of concentration profiles along short combustion zones in packed beds, our present knowledge about these processes and their influence on chemical reactions at solid surfaces is summarized. The main topics are the isothermal in-pore diffusion—the interior of porous catalyst pellets usually can be taken as isothermal—the gas-solid heat and mass trans fer, and the intensity of the dispersion effects in packed beds. Particular emphasis is given to the discussion of experi mental methods. Special attention is called to the differences between heat and mass interparticle transport processes, brought about in the range of medium and low Reynolds numbers by solid heat conduction and by radiation.

"Physical phenomena and catalysis is a broad field which has developed rapidly in recent years. Its increasing importance can be judged by the new extended and revised editions of the excellent book by FrankKamenetzky (2) and of the useful monograph by Satterfield (2). This review is restricted to prominent directions in this field. Within this framework it should be possible not only to review the knowledge ac cumulated, but to point to some difficulties and problems which have remained unsolved. In line with personal preferences, special emphasis is given to methods and to results of experimental investigations. Some interesting temperature measurements and concentration pro files in catalyst beds have been done recently by Fieguth (3). The ex perimental device used was a tubular reactor suitable for work under A

183 In Chemical Reaction Engineering; Bischoff, K.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on December 11, 2014 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0109.ch005

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CHEMICAL REACTION ENGINEERING

adiabatic conditions (Figure 1) [described i n detail elsewhere ( 4 ) ] , with a packed bed of catalyst particles. These were cylindrical pellets from alumina, about 3 mm i n diameter and height, containing 0.3 w t % platinum as active component. The oxidation of carbon monoxide i n air was chosen as the test reaction. One of the catalyst pellets was equipped with two thermocouples for temperature measurements i n the center and at the surface (Figure 1, right). This pellet was imbedded i n the cata lyst layer at the same level as the open end of a suction tube. A thermo couple i n the orifice of this tube measured the gas temperature, and the

suction tube

thermocouples

catalyst

vacuum inactive pellets

air + CO

Figure 1. Adiabatic tube reactor from quartz glass for measuring concentration and temperature profiles. Right side: 3 X 3 mm catalyst pellet with central and equatorial thermocouple.

In Chemical Reaction Engineering; Bischoff, K.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.


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Gas-Solid Surface Reactions

Figure 2. Profiles of C0 concentration, gas temperature, T , and pellet temperature (surface T , center T ) along moving combustion zone (3). Top: catalyst pellets, schematic. 4% CO in air, linear flow velocity u = 3.7 cm/sec. ff

2

s

c

0

gas flow withdrawn through the tube was analyzed continuously for C 0 . The inlet air flow contained a few percent C O ; if its temperature was raised to about 120 °C, a steep temperature increase built up i n the entrance of the catalyst bed, and the C O was oxidized completely along a distance of a few particle diameters. B y lowering the inlet gas tem perature, the combustion zone could be pushed back from the entrance and could then be shifted back and forth through the catalyst bed by changing the gas flow rate (4). A short reaction zone of this type was moved through the section of the bed where the measuring devices had been fixed; thus, the concentration and temperature profiles along the 2



186


zone were obtained. Figure 2 gives an example with an inlet gas com posed of 4 % C O and air preheated to 70°C. The reaction zone moves at 7.2 cm/hr opposite the direction of the gas flow. The concentration profile needs about 8 minutes to pass by the orifice of the suction tube; it extends therefore along about 1 cm or three particle diameters. The gas temperature profile is markedly broader, extending along five to six particle diameters. Regarding these profiles the following statements can be made: (1) The pellet interior is nearly isothermal; the temperature i n the center, T , exceeds the surface temperature T by only a few degrees. c

s

(2) The pellet as a whole is superheated appreciably above the gas flow; the excess temperature T — T attains values up to 100 °C. (3) The steepness of the concentration profile indicates that the axial dispersion of mass is very small under these conditions (modified Reynolds number Re « 10); in particular there is no back mixing of mass. (4) The axial dispersion of heat is appreciably larger, as shown by the gas temperature profile, T . There is also back mixing of heat against the gas flow; the temperature profile extends upstream to particles which have no chemical heat production as yet. (5) The first increase of C 0 concentration, indicating the onset of reaction and chemical heat production, should coincide with the start of the pellets' superheating over the gas flow. Contrary to this, the C 0 concentration in Figure 2 starts to increase about one particle diameter later. Such shifts in the profiles are characteristic for measurements of this type because the distance of one particle diameter represents the general uncertainty in fixing the position of a reaction zone i n a packed bed. 8

g

p

g

2

2

(6) In view of the heterogeneous nature of the packed bed the question arises as to how far the smooth profiles are meaningful, or if stepwise functions would not be better approximations. Fundamentally, would it not be more advantageous to work with difference equations and with cell methods instead of differential equations? Along with this is the problem of the behavior of catalyst particles i n steep gradients of concentration and temperature which has been studied recently by several groups of authors ( 5 - 9 ) . The background of these temperature and concentration profiles in theory and experience contains the whole field of physical phenomena in catalysis and in gas-solid reactions; a compilation of these phenomena is shown in Table I. Intraparticle Problems—Isothermal The predominant internal problem of porous solids in catalysis and in surface reaction with gases is in-pore diffusion. Measurements as well as theoretical considerations are made usually with countercurrent dif-


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fusion through porous plates. The general transport equation for sta tionary multicomponent diffusion at constant temperature and pressure is: ι


-c

\ ^ JiXk

JkX%

grad Xi = 2^

Γη

ι

Ji

(λ \

1" η κ

W

This represents the balance between the driving force for the molecular species i and the resistances to transport, as they are induced by intermolecular collisions (normal gas diffusion according to Stefan-Maxwell) and by wall collisions (Knudsen flow). Here χ* and x are the mole frac tions, Ji and J are the molar fluxes of the species i and k; c is the total molar concentration in the gas phase. The D represent the binary bulk diffusion coefficients, the factor ψ accounts for the restrictions of bulk diffusion by the porous network (structural factor), and D* ff is the effective Knudsen diffusion coefficient of species i. For counter diffusion k

k

ik

K

Table I.

e

Physical Phenomena

Intraparticle

(internal problems)

Isothermal:

Non-isothermal:

in-pore diffusion, normal gas diffusion, Knudsen diffusion, stoichiometry

internal superheating and stability

Interparticle (external problems) ι interphase transport ι dispersion effects

/

\

of mass : of heat : diffusion, conducton, convection, convection irradiation (gas phase only) (gas and solid phase) of two components, with equal pressures on both sides of the porous plate (open system), the molar fluxes are inversely proportional to the roots of the molecular masses: Ji/Ji

= -

VM /M 1

2

= α -

1

(2)

This holds for both Knudsen flow and in the pressure range where normal gas diffusion occurs in the porous medium, as was shown first by Hoogschagen i n 1953 (10,11). For binary counter diffusion (Components 1,2) : J ι = — Di eff c grad Xi


(3)


188

with

γ~ L>1

=

.J**

1

(3a)

+ γτ^-

1

eff

*Λ

. ρ ( Torr)

Figure 6. Pressure dependence of self-diffusion coefficient of hy drogen in a nuclear graphite at room temperature (Bosanquet dia gram) after different burnoffs. The line for 0% burnoff has been shifted upward and drawn with a 10-fold reduced scale (36, 37).


196


burnoff (with C 0 at 1 0 0 0 ° C ) . Figure 7 represents pore size distribu tions of some of the probes obtained b y H g porosimetry. The measure ments on the original material give a straight line i n the 1/D vs. Ρ plot as expected for a uniform group of transport pores. F r o m the slope of the line, according to Equation 4, the structural factor (permeability) can be calculated: ψ = 2 X 10~ , from the intercept on the ordinate the effective Knudsen diffusion coefficient, and from this the mean radius of the transport pores: r = 1, 2 χ 10" cm. [The self-diffusion coefficient of hydrogen at 20°C was taken as D = 1.43 cm /sec] This value agrees well with the macropore peak i n the pore size distribution ( F i g ure 7) for 0 % burnoff. W i t h increasing burnoff the micropore peak shifts from very small radii to larger values, obviously because narrow connections (micropores) between macropore voids burn out to larger diameters and finally merge i n the group of macropores. The simul taneous influence of two different pore groups on the diffusional transport gives rise to deviations from straight lines i n the Bosanquet diagram ( Figure 6 ). The deviations at low pressures are induced by the influence of the macropores; to account for this a two term relation like Equation 5 has to be used (22, 23). It is interesting that the measurements of Cun ningham and Geankoplis (18) on Sample 1 in Figure 4 also give a straight 2

et{


3

4

H

2

2

1 àV M dig r

1

J"—

001

1

1 — ι — I

Q05

Figure 7.

I

I

I

ι

φ

1

ι

1

1—ι—ι

» » ι

1

1

1

1

QS

W 5 Pore radius in/u Pore size distributions of the nuclear graphite after different burn offs (36, 37)

line when plotted i n a 1/D vs. Ρ diagram as demonstrated i n Figure 8. The values of the structural factor and the mean pore radius, derived from the slope and intercept of this line, agree well with the values given by the authors, thereby confirming that i n this bidispersed system the macropores dominate i n diffusional transport. [The evaluation was based on e



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Figure 8.

197


1 / D vs. Ρ plot of the measurements of Cunningham and Geankoplis (18) on Sample 1 (see Figure 4) e

Equation 7; by substituting a by 1 — λ / M / M > according to Equation 2, and Xi, 1 — x by Xi, x> respectively, the equation given i n the figure is obtained.] The steady-state diffusion methods, useful and reliable as they are in basic research, have some disadvantages for direct application to cat alyst pellets i n industrial practice. Single samples only can be used after special preparation, and erroneous results must be expected if the ma terial contains blind pores or anisotropic pore distributions. Unsteady state methods are often more generally applicable; among these the pulse technique, developed first by Deisler and Wilhelm (38) i n 1953, seems to be of particular importance. Supported b y experiences i n gas chro matography this method is now in progress at several places (39, 40, 41). From the pulse technique readily applicable test methods are to be ex pected, suitable for supervising catalysts in practice, because their results w i l l be statistical mean values from a number of catalyst pellets. t

l

x

Intraparticle Problems (Non-isothermal) The problem of internal superheating of catalyst particles by chem ical heat production has received much interest i n recent years. The coupling of reaction rate as a strongly nonlinear function of temperature with the essentially linear transport processes of heat and mass may give rise to multiple stationary solutions of the balance equations—i.e., to multiple steady states of the reaction system. M u c h theoretical work has been done to investigate the conditions under which multiple steady-


198


state profiles of concentration and temperature occur in the interior of a catalyst pellet and to determine the criteria of stability of the steady states. A survey of these problems and of the extended literature has been given by Aris (42) (see also V . Hlavâcek (8)). The boundary con ditions at the external surface of the pellet are usually choosen in such a way (43) that the surface temperature T and the surface concentration c remain fixed. In addition to the Thiele modulus φ, the characteristic parameters are the maximum relative excess temperature i n the pellet center, β, and the dimensionless activation energy, y:


8

8

(-AH) D kT

=

e{{

*

e

s

c _ AT T s

max

J2_ RT

=

'

s

T

S

(AH = reaction enthalpy; k = heat conductivity of the pellet material). For multiple steady states to occur in the interior of the pellet—with fixed surface temperature and with a first-order reaction—the product yβ must exceed a value of about 5. Recently Hlavâcek et al. (44) have accumu lated data of γ, β, and φ from industrial catalytic processes and from experimental studies (see Table II). In no case is the limit yβ ^ 5 at tained; i n most industrial processes the values are much smaller. As a €

Table II.

Parameters of Some Exothermic Catalytic Reactions

Reaction

(44)

Y

29.4 Synthesis of N H (45) Synthesis of higher alcohols 28.4 from C O and H (45) 16.0 Oxidation of C H O H to C H 0 (45) Synthesis of vinyl chloride 6.5 from C H and HC1 (45) 23-27 Hydrogénation of C H (46) 6.75-7.52 Oxidation of H (47) Oxidation of C H to ethylene oxide (45) 13.4 22.0 Decomposition of N 0 (49) Hydrogénation of C H (50) 14-16 Oxidation of S 0 (45) 14.8 3

2

3

2

2

2

2

4

2

2

4

2

6

6

2

0.0018

1.2

0.024 0.175

1.1

1.65 1.0-2.7 0.21-2.3 1.76 1.0-2.0 1.7-2.0 0.175

0.27 0.2-2.8 0.8-2.0 0.08 1.0-5.0 0.05-1.9 0.9

—

matter of fact, multiple steady states in the interior of catalyst pellets have not been observed experimentally, even in cases where high internal superheating was obtained, as i n studies of the hydrogénation of ethylene [(46), AT = T - T up to 3 7 ° C ] , the oxidation of hydrogen [(47, 48), AT more than 1 0 0 ° C ] , and the decomposition of N 0 [(49), AT up to 36 ° C ] , The reason for the failure to observe multiple steady states is that with increasing temperature in the pellets' interior the concentration of the reactants, within a small temperature interval, recedes towards c

8

2


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199

the external surface. Only a thin reaction zone remains, with steep con centration gradients. Hence, induced b y the small diffusivities i n the porous structure, the interior of the catalyst particles usually can be taken as isothermal.


Interphase Transport W h e n overheating by an exothermic reaction occurs, the catalyst particles usually overheat as the whole, as shown i n Figure 2. The tem perature gradients appear predominantly i n front of the external pellet surface, where the resistance of heat transfer to the bypassing gas flow must be overcome. It is the limitation i n the intensity of this external heat transfer compared with the chemical heat production within the particle which really gives rise to multiple steady states of the system. In this external problem three steady states are possible, and the medium one is unstable (51, 52). The particles i n these states have tempera tures more or less different from the gas flow. Their interiors, how ever, are essentially isothermal, for the reasons stated above [(see also Hugo and Wicke ( 2 2 ) ] . In this case also it seems unlikely that the internal problem should have multiple solutions. The phenomenon of more than three steady states, as calculated b y combining the external and internal problem (53), should scarcely be observed experimentally. A n instructive discussion of the possible situations has been given by Cresswell (54) (Figure 9 ) . Here the Thiele modulus is defined by the re action rate under the conditions of the bypassing gas flow as a reference value; an increasing Thiele modulus therefore means increasing tem peratures of gas flow. Cresswell distinguishes four regions with different behavior of the system. In the kinetic region 1 the reaction parameters are the same throughout the porous pellet. In Region 2 the temperature i n the pellet increases, but the interior remains essentially isothermal; the reaction is confined more and more to a thin shell at the pellet surface. This is why the effectiveness factor normally does not increase i n this range but decreases. In Region 3 the limitation of external heat transfer gives rise to appreciable superheating of the pellet; this causes a dramatic increase of the effectiveness factor, connected with three steady states. In Region 4 the pellet is i n the upper stable state where the external mass transfer controls the rate of conversion. Mass and heat transfer between particles and gas flow i n packed beds has been studied increasingly i n the last years. This is especially true for the range of low Reynolds numbers, below about 100, which is most important for gas-solid reactions and catalysis. The traditional method



200


THIELE MODULUS

φ

>

Figure 9. Main rate-controUing regions of an exo thermic reaction at a catalyst pellet. Region 1: kinetic; Region 2: in-pore diffusion, non-isothermal; Region 3: multiple steady states; Region 4: interphase mass trans fer, after Cresswell (54). of measurement (the adiabatic evaporation of liquids from wetted porous particles) is difficult to perform i n this range because the gas stream at the outlet of the test section w i l l be nearly saturated with the vapor. The test section, therefore, must be short, two or three layers of particles only, suitably sandwiched between beds of solid dry pellets of the same size. Such a short arrangement, of course, has strong entrance and exit effects, whose influence can be observed i n the fact that the wetted par ticles approach the wet-bulb temperature of the inlet air only at high air velocities. The same is true when the wetted particles are interspersed randomly i n a bed of solid dry pellets ("expanded" or "dispersed" bed of wetted particles) (55). The temperatures of the wet surfaces, there fore, must be measured carefully if reliable results of mass transfer are to be obtained. Petrovic and Thodos (56) recently performed such measurements with uniformly packed and with dispersed beds at low Reynolds numbers: 3 < Re < 230. They correlated the values found for the mass transfer factor j b y : d

ej

d

= 0.357 ββ-°·

359


(14)

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201


where c is the fraction of voids i n the fixed bed. The factor c i n Equa tion 14 originates from the work of McConnachie (57), who measured mass and heat transfer into air from spheres held fixed i n space by wires in a body-centered cubic arrangement, a "distended" bed. H i s results, obtained i n the range 0.416 < e < 0.778; 100 < Re < 2000, could be approximately related to: j — 1/c at Re = constant, as Sen Gupta and Thodos (58) have shown. Petrovic and Thodos, i n deriving Equation 14 from their measurements, tried to account for the influence of axial mixing by using a mixing cell model instead of the usual method of logarithmic mean driving force. W i t h the same model they recalculated results of earlier investigations (55, 59, 60) on packed and dispersed beds and thereby extended Equation 14 to the range 3 < Re < 1000. O n the other hand, however, important parameters are missing i n this correlation. F o r uniformly packed beds, for example, the dimensionless length of the test section—i.e., the number of wetted particle layers used—is expected as parameter to account for end effects. F o r dispersed bed arrangements the mean value of shortest distance (or the number density) of the wetted particles should be implicit i n Equation 14. Neglect of these parameters may be the reason for the broad scatter ing of experimental data with respect to Equation 14; hence, the corre lation w i l l have to be refined i n future, especially i n the low Reynolds number range. Interphase heat transfer i n this range is characterized by the fact that influences of heat conduction and of radiation between the particles in question and their surroundings can no longer be neglected, as is nor mally done at high Reynolds numbers. These effects favor the rate of interphase heat transport, but there are no comparable effects i n mass transfer. The ratio of heat to mass transfer rates, therefore, should increase with decreasing Re number. D e Acetis and Thodos i n their investiga tions (55) of heat and mass transfer with wetted particles i n short test sections and in dispersed beds, obtained values of j /j « 1.5 for the ratio of heat to mass transfer factor ( especially at low Re numbers ) compared with only 1.07 i n the classical work of Hougen et al. (59, 60) at higher Reynolds numbers, Re > 350 [(see also Sen Gupta and Thodos (58)]. Satterfield and Cortez (61 ) have reported on différencies between mass and heat transfer data obtained with woven-wire screens i n gas flow, (they call it "discrepancies") which can be attributed to longitudinal heat conduction. In 1950 Wilhelm (62) compiled the effective mechanisms for heat transport i n packed beds, and together with Singer he worked out the scheme shown i n Figure 10. It considers the heat conduction from particle to particle through the contact areas and through the fluid fillets around them, the interphase heat transfer, and the molecular and eddy


d

h

d


202



conductivity i n the fluid phase. The diagram can be taken as a program for research i n this field; until today this program has not been com pletely worked out. Remarkable progress has been achieved i n recent years b y Schlunder (63) i n investigations of combined heat and mass transfer between gas flow and single bodies enclosed i n packed beds. F r o m his numerous important results the one shown i n Figure 11 seems

R

MF

= T h e r m a l resistance of particle it self. 11 r = T h e r m a l resistance of fluid fillet between particles. Tic = T h e r m a l resistance of contact area. Ni = T h e r m a l resistance of i m p u r i t i e s : oxides, grease, etc. 7?// = T h e r m a l resistance f o r heat flow f r o m particle to m a i n b o d y of fluid. 7?.wp = T h e r m a l resistance of fluid at rest (molecular conductive effect). RR = T h e r m a l resistance of turbulent flow. R,

Figure 10. Scheme of mechanisms for heat flow in packed beds, after Singer and Wilhelm (62)


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Gas-Solid Surface Reactions Pr-0.71 Pr'*0.59

*

A Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on December 11, 2014 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0109.ch005

Chemical Reaction Engineering

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