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Catalysis kinetics of macro-reticular ion exchange resins
Chemical Engineering Science, 1962, Vol. 17, pp. 735-749.
Pergamon Press Ltd., London.
Printed in Great Britain.
Catalysis kinetics of macro-reticular ion exchange resins N. W. FRISCH Princeton Chemical Research, Inc., Princeton, New Jersey (Receiued 27 March 1961) Abstract-The development of a new class of ion-exchange resins which possesses macro-porosity superimposed on a conventional ion-exchange gel structure presents new kinetic problems. This paper considers the kinetics of this class of catalysts and presents the general analytical solution forasteadystate first-order reversible-reaction situation. The effect of pertinent physical parameters on both the concentration profiles and on reaction rate is indicated. Limiting rates for high surface area catalysts are predicted, and an estimate of the optimum catalyst porosity necessary to achieve maximum volumetric activity is presented. Finally, the maximum rate advantage of this new class of catalysts over conventional-ion-exchange catalysis is noted.
CONVENTIONAL ion-exchange resins may be considered as cross-linked polyelectrolyte gels with the exchange sites distributed, in a statistical fashion, throughout the entire resin particle. In addition to ion-exchange phenomena their utility encompasses catalytic applications. For information concerning specific catalytic reactions, comprehensive surveys by ASTLE [l], and by HELFFERICH [2] may be consulted. The strongly dissociated acidic? ion-exchange resins, in the H+ form, will catalyse many reactions which are normally catalysed by acids in homogeneous systems. In the absence of dissolved electrolyte these resins catalyse reactions at the locale of the exchangeable ion within the gel. Thus the active species, the Hf ion, must be accessible to the reacting species. Hence the mobility of both catalytic ion and of reactant in the gel is important. While, in general, rates observed in homogeneous systems are higher than those noted in the corresponding ion exchange catalyst case, there are exceptions to this general rule. Adsorption effects are often responsible for these reversals, permitting high concentrations of adsorbed reactant to t While the kinetic analysis is quite general, the limited use of strongly dissociated basic resins and both classes of weakly dissociated ion-exchange resins as catalysts, makes it practical and convenient to confine the discussion in this section to acidic catalysis.
accumulate on the catalyst, and consequently producing high rates of reaction. High reaction rate is not always the over-riding consideration in the selection of heterogeneous catalysts instead of a suitable homogeneous acid. Thus when expensive acids (i.e. BF,) may be required, and recovery is not practical, ion-exchange resin catalysts may be a feasible economic solution. In many instances, in the absence of poisoning and excessive temperature exposure, degradation rates may be sufficiently small to permit catalyst reuse, often without intermediate catalyst treatment. Another important advantage of ion-exchange catalysis is the ease of isolation of the catalyst from the reaction mixture. Product recovery by distillation, in the presence of soluble acid catalysts, is frequently accompanied by excessive product loss, by accelerated acid-cleavage and polymerization, or by equilibrium limitations at elevated temperatures. In other instances, the “specificity” of ion exchange catalysts is of prime consideration. This “specificity” may be manifested in several different ways. Thus a single ester species may be selectively hydrolysed in a mixture of esters; the direct esterification of acid-sensitive esters may proceed in good yield; and polymerization of unsaturates may occur only to a slight extent with the resin catalyst. A subsidiary advantage is the reduced corrosion rates often observed with heterogeneous systems. Unfortunately, the high equivalent cost of all
73s
N. W. FRISCH
synthetic ion exchange resins has limited the industrial development of catalytic processes based on these catalysts. In each situation the economics of the various competing processes must be individually assessed. As previously noted, the catalytic reaction occurs at the site of the active species in the resin gel. Consequently, non-polar reactants, which are not sorbed appreciably by these polar ion exchange resins, or reactants which possess low gel diffusivity rates, do not react at sufficient rates to warrant industrial interest. Thus if one examines the ratio of the esterification rates by ion-exchange catalysts to those observed in homogeneous systems, it is evident that this ratio decreases markedly as acids and alcohols of higher molecular weights are considered. Also, direct esterification of organic acids with olefins proceeds quite slowly. Similarly, direct alkylation of phenol with higher olefins becomes a marginal operation when compared with processing with available homogeneous acid catalysts. This situation can be improved somewhat by the use of small particle size catalyst, polar solvents, elevated temperatures and resins of lower degrees of cross-linking. However, in general, since the rate is at most proportional to the inverse of the particle size, only modest improvement can be effected in this nianner before handling difficulties become controlling. The use of polar solvents can also effect some rate improvement, but reactions requiring strongly acidic sites will not proceed in the presence of appreciable levels of polar solvents. (Optimum concentrations of these solvents exist). Similarly, temperature limitations of these catalysts, also equilibrium considerations, often restrict the benefits of operation at higher temperatures. Catalysts of low degree of cross-linking present stability and handling difficulties and offer only modest rate increases. Under these circumstances, it is evident that catalysts possessing macro-porosity would be useful to extend the range of utility to include reactions involving non-polar reactants. One type of macro-porous polymers may be produced by a polymerization process outlined in several patents [3, 41. In this technique, the polymerization of a mixture of two monomers, one of which contains at least two polymerizable double bonds, necessary to effect the cross-links, is carried
out in the presence of a third component. This component, a solvent for the monomers, but one largely incompatible with the cross-linked polymer, has been termed a non-solvent. This incompatibility manifests itself in a separation of phases during polymer gelation. With sufficiently low levels of non-solvent, holes or pores of molecular dimensions result in the polymer. Increases in the proportion of non-solvent in the monomer mixture result in a continuous polymer structure permeated by discontinuous pores of macroscopic dimensions, i.e. above molecular size. Above a critical nonsolvent level, the discontinuity of the pore structure is removed, and a continuous polymer, continuous pore structure results. Excessive levels of non-solvent are conducive to the precipitation of polymer during gelation, resulting in a largely discontinuous polymer phase dispersed in a continuous macro-pore structure of large dimensions. Thus this technique is capable of yielding a wide spectrum of pore sizes. The important sub-class of macro-porous polymers, containing a network of continuous polymer and continuous pores, which occurs by a mechanism which largely involves the expulsion of the nonsolvent liquid phase from the polymerizing gel, has been termed macro-reticular (MR) polymers. They are described [3] “as possessing a sponge-like structure, i.e. they are permeated by small veins in which non-swelling agents are capable of penetrating”. It is this important class of macroporous polymers with which we are concerned in the present analysis. The characteristics of macro-porous ion exchange resins has been discussed in detail [S]. Other studies concern the kinetics of macro-reticular ion exchange [6] and the surface characteristics of macro-porous ion exchange resins [7]. While these new physical structures mark a major advance in the field of ion-exchange catalysis, and the following analysis shows substantial kinetic advantages of MR catalysts over conventional ionexchange catalysts, certain limitations should be noted. MR catalysts possess serious limitations in some environments which are related to the chemistry of the polymer and ion-exchange function. In particular, the acidic variety, based on a sulphonic structure, is not one noted for its high acid strength, an important requirement in some reactions. The 736
Catalysis kinetics of macro-reticular ion exchange resins temperature stability threshold of the sulphonic acid functionally is well known to be about 160°C. Chemical resistance, in general, is a more complicated function of the porosity parameters and the degree of cross-linking. It should also be evident that MR catalysts do not always perform in a superior kinetic fashion compared to conventional ion-exchange catalysts. Thus the epoxidation of olefinic material with an organic peracid, the latter formed under the influence of the conventional catalyst, proceeds sufficiently rapidly and in good yield to justify industrial acceptance. The subsequent degradation of the epoxide product to form hydroxyacyloxy derivatives proceeds sufficiently slowly in this case because the epoxide is not sorbed appreciably by the catalyst. However, the catalytic sites of MR catalysts are more accessible to the epoxide, and the degradative hydroxylation reaction occurs to an excessive extent. Aspects of catalysis related to diffusional mechanisms have been considered by several authors. THIELE [8] has developed the effectiveness factor concept which has been comprehensively extended by WHEELER [9]. WEISZ and PRATER [lo] have treated more complex catalytic phenomena from a theoretical and experimental viewpoint. AMUNDSON and SMITH [l l] have discussed in detail the steadystate and transient kinetics of a reversible first-order reaction in a homogeneous gel ion exchange resin. The present paper is an analysis of the kinetic behaviour of macro-porous catalysts of the macroreticular class.
KINETIC ANALYSIS
Reversible reaction Consider a spherical non-swelling macro-reticular ion exchange resin of particle radius R, porosity P and specific surface S,. A model is assumed with these characteristics and radially oriented pores of effective radius ?. 2P
r=
%(I - P>P,
With the local porosity equal to the average value P, the number of pore mouths located on a spherical shell of radius r is 4r2P/f2. Thus each pore may be considered to be associated with a spherical gel area, normal to the pore axis, whose magnitude is independent of radial position and is expressed as &(l - P)/P. The pore serves as an access to the gel through a pore-wall transfer area of nr2 per unit length of pore. This mode of transfer complements the normal gel-diffusion mechanism occurring in conventional ion-exchange catalysts. Figure 1 depicts the idealized model of the catalysts and indicates the cylindrical pore and related gel structure. We now consider the performance of the catalyst in the case of a first-order reversible reaction Al;
B
b/K
which proceeds in the gel structure at local rates which are proportional to the gel-phase concentration of each species. Isothermal operation is assumed. In the absence of exchangeable ions or
Gel
FIG. 1.
(I)
Model of catalyst particle showing idealized pore structure. 737
N. W. FRLSCH
other poisoning phenomena the catalytic behaviour will be characterized by steady-state performance after the initial transient period. It is this steadystate rate which is of interest. The rate-controlling mechanism is assumed to be a diffusive one involving the transfer of reactant from the bulk fluid phase into the gel structure by diffusion in the pore and gel structure. The fluidfilm resistance at the external surface of the catalyst particle and at the pore-gel interface is assumed to be negligible in comparison with the low gel-diffusion rate. The diffusivities of reactant and product in each phase are assumed equal and independent of phase composition. Under these circumstances the following equations describe the process. Mass balances for each species taken about a spherical shell of radius’ I yield
+w 1 (1 -
-
d2c,
[
1
w,q, - &J =0 d2c,
+Dd’dr2+;dr
[
1 +
2dc,
-g+;-&.
(1 - P)(k”h -$)=O
2dc,
-
the pore concentration c at this radial position. A linear physical equilibrium isotherm is considered 5
%$(6)
552
(7)
In the bulk liquid phase the concentration reactant A is
of
CT,
(8)
CA =
The product is w
rate describing expressed on a
”
3k”(l -
R 0
R3
(2-9) catalyst. They are by application of groupings :
formation of particle volume
- ;
dr
(9)
the performance of in more convenient following dimensionless
(2)
1 +
(3)
Similar balances about a surface encompassing the pores in this shell indicate
1
(1 _
4D,P2
= [j(P)
-
w
2(hi - q*) (5)
where qi represents the gel-phase concentration of the indicated species at the pore-gel interface. The right-hand members are derived by considering the rate of transfer from the pore to the gel structure as proportional to the quantity (gel diffusivity) (transfer area)/(one-half the maximum gel-diffusion distance from the pore wall). The latter gel thickness is shown in Fig. 1 to be ?[,/(P) - P]/(2P). In the absence of a fluid-film resistance the value of qi at the pore-gel interface is in equilibrium with
E=
4P [J(P)
(17)
p)Q
D = 2
(18) G
R2 Q
- P] 7c;
(19)
F =
!@z D,
(20)
The significance of each of these quantities is readily discerned. The equilibrium saturation ratio, B, describes the relative quantity of reactant and product in the pore and gel structures. The surface-area parameter, E, is strongly dependent upon the magnitude of the specific surface of the catalyst. The kinetic modulus, F, describes the kinetic relationship between the intrinsic reaction rate and diffusion rate.
738
Catalysis kinetics of macro-reticular
Furthermore, let us define dimensionless groupings which occur in the solution of the system of equations (2-9)
([Q4
ion exchange resins
- aQ2 + /?I
[g4- (a+F(li K’)x
x P+[ a=E
(
B+;
1
+F
(22)
d2U, =+BD-
d2V,
dZ2
=FU,-;U, F
- a>]m = 0
(25)
xA
=
yA,
VA = v,
U,)
(26)
d2V, E = 5 (V, - U,) dZ2
(27)
x,
(28) U = 0,
Z 2 1
U = 6Z + i
Ej sinh J(zj)Z
(30)
V = 6Z + 2 2
9 R2 “=3F(I+$(U,-2)ZdZ and QD,
sinhJ(zj)Z
j=ly-Tj
(31)
The pore concentration eliminated from equations following pair of equations
(36)
(This form applies to both species). Equation (36) results from the more general form involving the eight roots (0, 0, _+ J(Zj) with j = 1,2, 3) of the auxiliary equation when one considers the necessity of limiting the concentrations at Z = 0 to finite values. Similarly the expression for the pore concentration profile is
= YBi (29) Z = 0
(35)
In addition to the zero root, there are, in general, three non-equal real roots of equation (35). Let these non-zero roots be denoted by zj (j = 1, 2, 3). Then the solution for the gel concentrationposition parameter is of the form j=l
d2VA E -=7j(VAdZ2
(34)
+
+ [(K + l)/K][P(F
(24)
dZ2 =KUB-FUA
u=o
+ [fl(K + 1)/K + a2 - aF(K - 1)/K - F2/K]m2+
In dimensionless form the pertinent equations become d2VA
)
The auxiliary equation related to (34) is of the eighth degree and possesses roots which are the square roots of the roots of the following quartic equation. m4 - [2a - F(K - l)/K]m”
(23)
d2U, dZZ+BD-
-;[@-r]’ I
(21)
(37)
Substitution of equations (36) and (37) in either (24) or (25) permits the development of relationships between the individual coefficients. These relationships are
terms V are readily (24-27) to yield the
(38) (~4-K~2+@u,+~(~2-y)U,=0
(32)
and &BI - = F(yK 7jj CP- a7j+ 73
a+F(l;K)]@+qU,+ K
%
,
+ F(g2 - y)u, = 0
(33)
where 9 represents the operator d/dZ. Equations (32) and (33) can be combined to yield an equation valid for either U, or U,
(39)
Additional relationships necessary to fix the coefficients result from the substitution of the boundary conditions (30) in (36) &d (37). The results are summarized below for the coefficients related to the reactant A. Let the quantity A be represented by:
739
N. W. FRISCH
1 1
1
1
p - at, + r:
1
p-crr,+z;
F(Y - r1)
CCC3+
p -
F(Y -
F(Y - 2)
A=
2:
r3)
(40)
Y
1 Y (P -
1
73
ax3 +
F(Y -
%Y
T3J2
Then
v
1
1-V
p-at,+r,2
K
1
1 p - cu2 + t2
F(Y - z1)
F(Y -
72)
p -
m3 +
F(Y -
z:
r3)
(41)
6,A = Y
V 1-V K
Similarly to the
Y
Y - t1 (P -
Y (P -
““1 + G)Y
JXY - tdZ
the value of &*?Ais represented
.
72
ar2 +
FiY -
below by altering
.
Y
G)Y
7212
the (j + 1)-st column
of the A determinant
sinh ,/(rj) 1-V K sinh ,/(tj)
.
.
.
.
. (42)
V
.
sinh J(rj) 1-V K sinh ,/(rj)
The important catalytic pactly expressed by 52 R2 -L= 3F(l - P) 2
rate parameter
x [J(rj)
EA, cash J(~j)
Limiting-area
- sinh J(rj)]
.
.
the concentration profile. Thus the solution of the general case of a first-order catalytic reaction is expressed by equations (35-43).
is com-
j=l
Q&i
.
(43)
Note that the 6 coefficient does not appear; its function is solely to define the equilibrium limits of 740
The action lyst is forms.
catalysts
important case of a being catalysed by a described by simple The pertinent value
reversible chemical rehigh surface area cataand particularly useful of r for large E values,
Catalysis kinetics of macro-reticular
approaching infinity, is [(K + l)fi]/Kcl. The solution is U,=
-+
Z
(K+
K+l x
[
1
l)VK+l
1 x
sinh,/{W + WIPIW
+ l>l>Z
sinh ,/{[(K + l)/K][F/(BD Ug=--
KZ
(K+
K+l
ion exchange resins
Figure 2 shows the calculated profiles (equation 44) for the reactant concentration in the gel structure of catalyst particles in equi-spaced sections of an isothermal fixed-bed reactor (K = 1.47). Profiles in a conventional ion-exchange catalyst are shown in Fig. 3 for an irreversible reaction as a function of
(44)
+ l)]}
1
l)v - 1 x K+l
sinh J{CW +
1YKI[FIW + l>]>Z c45j
’ sinh ,/{[(K + l)/K][F/(BD In the case of these concentration ratios in both the gel and and V, = U,. The corresponding W”R2
W
Q&J"
+ l)]}
fully developed catalysts, the for each species are the same pore phases; hence VA = VA, rate parameter is
= 3(1 - P)(BD + 1)
1
(K+
l)f;;:- 1 x (K + l)p
1 ’
(K+
x coth
-
1)
K
DIMENSIONLESS
F (BD + 1) I - ’ 1
FIG.
(46)
RADIAL
POSITION,
Z
3. Gel concentration profiles for a conventional ion-exchange catalyst.
modulus F. The latter profiles are based on the relationships of SMITH and AMUNDSON[l l] which are equivalent to our equations (44-46) with B = 0, i.e. zero porosity. It is evident that our relationships are extensions of the solution for the zero internal-porosity case which is useful for describing the performance of conventional ion-exchange catalysts. It is interesting to note that our analysis predicts that these infinite area catalysts perform as if the effective diffusivity of the reactants were of magnitude the kinetic
1.0,
I
I
I
n
I
Pc,D, + (1 - P)QD,
U-P)Q I OO
I
0.2 DIMENSIONLESS
I
I
0.4
0.6 RADIAL
I
I
0.6
POSITION.
FIG. 2.
I Z
Gel concentration profiles in MR catalyst particles in sections through fixed-bed (K = 1.47, co/Q = 100, D = 1000, F = 108, P = 0.5).
'
In all physical situations, this effective diffusivity is greater than the gel diffusivity, even in the unlikely case, co/Q = 1, and DJD, = 1. Irreversible-reaction case
A particularly useful set of relationships may be derived for the irreversible case, K = co. These 741
N. W. FRLSCH
expressions permit ready analysis of the performance of the catalysts as a function of the pertinent physical parameters. The remainder of this analysis treats the irreversible case. The solution is readily derived from equations (24) and (26) with K = co. Let us define the following dimensionless roots dl +
++=Jr
J(c? - 48) ] 2
porosity (P = 0.05, 0.1, 0.25, 0.5 and 0.75) were investigated in the case of the MR catalyst. In the region in which the intrinsic reaction rate is relatively slow compared to the gel diffusion rate (below F = 1 in this instance) the conventional resins possess slight rate advantages over MR catalysts.
(47)
4_ $-J(;-41)]
(48)
It is readily shown that a2 > 4/I for all situations involving finite B values. The case, /I = 0, leads to a trivial solution, W, = 0. The solution is u, =
B
+‘_(& - y) sinh 4+Z sinh 4+ Y(& - &2-) _
1
d(+“- - Y)sinh4-Z sinh c$_
C#J:sinh 4-Z ~$5 sinh 4+Z + sinh 4+ sinh 4__ I
(49)
(50)
The volumetric reaction-rate expression is
“uR’_ _ QW’
x
FIG. 4. Predicted catalytic rate behaviour ventional and macro-reticular ion-exchange (co/Q = 100, D = 1000).
3F(l - P)
~(4: - 4-2) ’
4’-(4: - Y)(++coth 4+ - 1) _ 4: _ 4:(4’- - ~)(4- coth 4- - 1)
$5
(51)
1
Comparison of conventional and MR catalyst performance
The contrast between these two classes of catalysts may be conveniently demonstrated by comparing the rates in a given situation. Fig. 4 is a plot of the dimensionless rate parameter vs. the kinetic modulus for various catalysts. A comparison is made at reasonable values of the parameters, D = 1000 and c,/Q = 100. Several values of 742
for concatalysts
Since this F value corresponds to near saturation of the gel with slow-reacting A, the introduction of finite porosity into the catalyst serves only to dilute the active gel structure with inert pores. At F values of 10 to IO*, gel concentrations in conventional ionexchange.catalysts are sufficiently small (Fig. 3) so that the MR resins begin to exhibit advantages. In the region of F = lo3 to about lo4 the MR catalyst plots begin to exhibit the effect of variation in the surface-area parameter, E. Each plot, corresponding to a specified porosity, is drawn to show two branches, one for low E (= 500) value and the other (shown dotted) representing the limiting rate curve for infinite E. At low F values, for all values of E, it is apparent from Fig. 4 that the reaction rate is proportional to
Catalysis kinetics of macro-reticular ion exchange resins
1.0
6
6
SPECIFIC
IO SURFACE
12
14
AREA,
S,f*
16
16
;
FIG. 5. Effect of surface area on catalytic rate (B = 100, D = 1oo0, P = 0.5, R = 0.05cm, ps = IXi g/cm%
the intrinsic reaction constant; here the apparent activation energy coincides with the true value. In the case of the limiting area catalysts, at high F values, the reaction rate becomes proportional to the square root of the reaction constant, and only one-half of the actual activation energy will be observed. At finite E values, and large F values, the observed activation energies will be a small fraction of the true values.
higher in value. At a level of 6.06 m2/g the profiles approach each other at reasonable concentration values corresponding to an appreciable increase in rate. The equations which describe the irreversible reaction case with infinite area follow directly from equations (44) to (46) with K = co.
lZj”ect of surface area From equation (1) it is evident that for a given system of fixed skeletal density and specified porosity, specific surface area is inversely proportional to pore size. The role of surface area in influencing reaction rate is shown in Fig. 5 at two levels of the kinetic modulus. At high levels of F the gel concentrations can be increased significantly by the incorporation of an increased level of specific surface. At lower Fvalues the effect is much less pronounced. In all instances there is a limiting rate which is approached as surface area is increased unbounded. The effect of changes in surface area on the gel and pore profiles is shown graphically in Fig. 6. At S, = Q-333 m’lg the gel concentrations ar?, in general, quite small, while the pore profile is much
0
.2
DIMENSIONLESS
.4 RADIAL
.6 POSITION,
I
.8 t
FIG. 6. Influence of surface area on dimensionless concentration profiles (B = 100, D = 1000,F = 107, P = 0.5, R = 0.05 cm, ps = l-50 g/cmS).
743
N. W. FRISCH
Effect of porosity
B which satisfies
The effect of porosity is essentially a two-fold one. In addition to the dilution, there is a beneficial result accompanying the introduction of an increase in porosity. At a fixed specific-surface level, increased porosity results in an improvement in the gel concentrations of the reactant, thus improving the reaction rate per unit gel volume. Thus an optimum porosity level exists at which the volumetric reaction rate 9” is a maximum. Fig. 7
[
D?&-i$‘]j[(BD:
l)jcothJ[(B:+
l)j
(52) The values of P,,,, corresponding to maximum 9, are noted on Fig. 4 on the upper curve at the various F levels. This upper curve, which represents the maximum rate for infinite-area catalysts prepared at optimum porosity levels, envelopes the limiting rate curves for these fully developed resins. As F increases without limit, the optimum level of porosity increases, approaching as a limit the value (53)
DIMENSIONLESS
RADIAL
POSITION,
t
FIG. 7. Effect of porosity on dimensionless gel concentration profiles for constant surface-area catalysts (co/Q = 100,D = 100, ;‘,:$‘:I -P ,/[l - PI2 = 1000,
depicts this porosity effect on the profiles at a fixed surface level. While the profiles become more attractive at higher porosity levels, on a particle volume basis, the intermediate porosity catalyst is more active than either of the extreme porosity ones. In Fig. 8 the effect of porosity on the limiting value (for infinite area catalysts) of W,, for three levels of the kinetic modulus, is shown. Optimum porosity levels are indicated. At low F values, P,,, -+ 0 since it is not economical to dilute active gel with inert pores. For fully developed ion exchange catalysts the optimum level of porosity is defined by the value of 744
POROSITY,
P
FL. 8. Influence of kineticmodulus on optimum porosity (co/Q= lOO,D= 1000,E-t w).
Catalysis kinetics of macro-reticular
At the usual Dca/Q values, P,,,, approaches the quantity + as F approaches infinity. It is axiomatic that, as the reaction conditions become more unfavourable (high F values or depressed B or D values) the optimum porosity increases. Since the optimum porosity levels possess a finite limit at high F values, it is possible to estimate the maximum rate advantage of MR catalysts relative to conventional ion-exchange catalysts. This rate performance, relative to that of the conventional resin, levels off, at high F values, at a Maximum relative rate = i J [ coD~~GQ”G]
(54)
ion exchange resins
calculated for the MR catalyst at E + co levels. Fig. 9 illustrates the particle size effect for intermediate surface area catalysts at F = 10’. In both cases, the reaction rate is nearly inversely proportional to particle diameter. E#ect of @id-phase
concentration
With conventional catalysts the rate is predicted to be independent of total solution concentration. In the case of high area catalysts, at high F values, the rate is nearly proportional to the square root of co. Fig. 10 depicts the effect of the co/Q ratio for a finite area catalyst. At low co/Q values theeffect on
For the parameters represented in Fig. 4 this relative rate corresponds to a value of 158; at F = 10’ the actual ratio is 143. Effect of particle size
With the conventional catalyst, at low values of the kinetic modulus, the reaction rate W, is independent of particle size. At high levels of the modulus the reaction rate becomes inversely proportional to particle diameter. Similar effects are
0
CONCENTRATION
RATIO,
2
FIG. 10. Effect of fluid-phase concentration on catalytic rate. (D = 100, E == 5[1016, F = [1015,P = 0.25.)
is somewhat less than proportional to the square root of c o ; at higher co/Q values, as gel concentrations become more significant, the effect of concentration on reaction rate becomes even less important.
W,
E#ect of d@usivity ratio
RELATIVE
PARTICLE
SIZE,
R/R,
FIG. 9. Effect of particle size on catalytic rate (co/Q = 100, D = 100. E/Ro2 = 5[102]), for low area catalyst, E/R02 = 5(10)6 for high area catalyst. F/Ro2 = 105, P = 0.3.) C
With high surface-area catalysts and at high values of the kinetic modulus, the reaction rate is nearly proportional to the square root of the diffusivity ratio, being of course, independent of D at low F values. Also the effect of the diffusivity ratio on reaction rate is less significant in the case of low 745
N. W. FRISCH
area catalysts. Fig. 11 illustrates the diffusivity ratio effect on the gel profile of a MR catalyst at F = IO’.
bulk diffusion to Knudsen diffusion in a series of catalysts of fixed porosity but decreasing pore size. A liquid-phase reaction would proceed with a rate which would be largely independent of pore size once sufficient area is introduced into the structure. In the case of the gas-phase reaction, as the diffusion rate decreases in proportion to pore size, the over-all reaction rate suffers. Poisoning
DIMENSIONLESS
RADIAL
POSITION,
Z
FIG. 11. Intluence of ditTusivity ratio on dimensionless gel-concentration profiles. (R = 100, E = 5[1016, F = 107, P
=
0:5).
In the case of gas-phase reactions at low pressures Knudsen flow may control the diffusion rate in small pores. Fig. 12 illustrates the transition from
IO
Two types of uniform or homogeneous poisoning of MR catalysts will be considered. In the case of exchange poisoning, low levels of dissolved ionic materials are exchanged by the resin, replacing active ions in the gel, such as H+ or OH-. There are several effects which accompany this exchange which result in reduced activity. Neglecting catalyst volume change, they are (1) the reduced intrinsic activity due to the dilution effect, (2) the reduction of gel diffusivity of the reactants and (3) the reduced solubility of the reactant in the gel. In Fig. 13 we have shown a particular poisoning situation, indicating an approximately linear decrease in rate in proportion to the fraction of catalytic sites which have been replaced. This is in agreement with experimental findings.
100 PORE
RADIUS,
T , 8
FIG. 12. Effect of pore size on catalytic rate in Ii uid- and gas-phase systems at low pressures at 7 = 5000 A, Er2 -7% 2 = 6(10)‘0, F = 104, P = 0.36.
746
B = 56.25, D = 100
Catalysis kinetics of macro-reticular
I SURFACE
”
ion exchange resins
LC,(Vf - v) =
FOULING
wow
(1 -
PIPS
(5%
and -Lc,
EXCHANGE
the latter form being directly integrable in all but the general case (equation 43). Rather than dealing with catalyst particles of uniform size, a distribution of particle sizes occurs in commercial batches of catalyst. For that region in which the reaction rate 9” is inversely proportional to particle size, the average particle radius which defines the effective volumetric reaction rate &, for a log-normal distribution of particle sizes, is simply K exp[(-log’o)/2], where R is the weight geometrical mean particle size and (Tis the standard deviation of the log-normal distribution of particle sizes.
POISONING
\-
o-
0
DEGREE
.4
.P
OF
POISONING,
.B
.6
f
FIG.13. Effect of poisoning on catalytic rate. Exchange poisoning, f=O, co/Q = 100, D = 500, E=4(10)6, F = lOs,f= 1.0, co/Q = 250, D = 1500, E= 1*6(10)‘3, F = 0, P = O-25. Surface fouling f = 0, as in exchange poisoning case above Ecr (1 -f).
CONCLUSIONS
A second type of poisoning, due to the fouling of pore surfaces with suspended material or polymeric products, is also shown. In this instance, it is assumed that the area available for transfer to the gel decreases in proportion to the degree of fouling. In this case, unless we are dealing with low area catalysts, the reaction rate does not suffer to a significant extent until the pore surfaces are nearly completely fouled. In cases of non-homogeneous fouling, the detrimental effects will be more pronounced than those noted above since the gel sites near the external surface will be the ones which are most completely deactivated. The second type of poisoning is less frequently observed in practice. DESIGN CONSIDERATIONS The analysis presented here yields, in an explicit manner, the steady-state reaction rate for monosized spherical catalyst particles immersed in a fluid phase of specified composition. These relationships, including the limiting forms, are directly applicable to the cases of continuous stirred-tank reactors and fixed-bed isothermal reactors. The mass balances for these situations are respectively
(56)
A model has been described which permits the analysis of the catalysis kinetics with macroreticular ion-exchange resins. The present paper discusses the general analytical solution for a steadystate first-order reversible reaction situation. In the case of a specific catalytic reaction the variables which affect the rate of conversion concern the physical parameters of the catalyst-reactant system. Among these are several important ones which require definition in a catalyst design programme. Reaction rate, rate of conversion per unit catalyst volume, is nearly a linear function of specific surface at low? surface-area values; it reaches a limiting value as the area increases without limit. Porosity is important in fixing over-all performance. Too little porosity restricts access of the reactants to the active gel through the pore structure; too much reduces the number of active sites contained in the reactor volume. The optimum porosity value is strongly affected by the kinetic modulus which expresses the relative rate of reaction and diffusion in the gel. In the unfavourable region which is defined by a kinetic modulus of large magnitude, the rate advantage of an optimum macro-reticular catalyst 7 In the case of zero internal surface area, the reaction rate is given by (1 - porosity) (reaction rate of an equivalent conventional ion exchange catalyst).
747
N. W
relative to a conventional ion-exchange one approaches a maximum, and is 0.5 J[(c,,D, + QDJ (QD,)]. This important relationship defines, in simple fashion, the limits of utility of the MR class of catalysts. NOTATION Equilibrium saturation ratio defined dimensionless in (17) c Fluid-phase concentration of indicated species in pore lb mole/f@ at radial position r E Bulk fluid-phase concentration of species A lb mole/fts of reactant and product co Total fluid-phaseconcentration lb mole/ft3 9 Operator, d/dZ dimensionless D Diffusivity ratio defined in (18) ft2/min Gel diffusivity of reactant and product DG ft2/min Pore diffusivity of reactant and product DP E Surface-area parameter defined in (19) dimensionless dimensionless F Kinetic modulus defined in (20) dimensionless f Degree of poisoning fE Fraction of external voids in fixed-bed reactor dimensionless ft h Depth of catalyst in fixed-bed reactor K Equilibrium constant for first-order reaction dimensionless min-l kv Intrinsic gel activity for forward reaction L Fluid-phase flow rate in CSTR or fixed-bed reactor ft3/min m Variable in (35) P Catalyst porosity, pore volume/total particle volume dimensionless P0pt Optimum value of porosity for iniinite area catalysts dimensionless Q Total gel-phase concentration corresponding to total lb mole/f@ fluid-phase concentration, co 4 Gel-phase concentration of indicated species lb molejfta lb mole/f@ 4t Value of q at pore-gel interface ft R Particle radius B
[l] [2] [3] [4] [5] [6] [7] [S] [9] [lo] [ll]
FRISCH Weight geometrical mean particle size ft Volumetric reaction rate based on total particle volume lb mole/fts min Value of W, for unpoisoned catalyst lb mole/fts min Effective value of gR, for a distribution of particle sizes lb mole/f@ mm Radial distance measured within catalyst particle ft Effective pore radius ft Specific surface area of catalyst ft2/lb Cross-sectional area of fixed-bed reactor fts Gel concentration rat&radial position product defined in (14) dimensionless Pore cdncentration ratio-radial position product defined in (15) dimensionless Value of VA in (30) at Z = 1 dimensionless Value of V in feed to CSTR dimensionless Value of V in inlet and exit of fixed-bed reactor. respectively dimensionless Weight of catalyst in CSTR lb Pore-phase concentration ratio defined in (10, 11) dimensionless Gel-phase concentration ratio defined in (12, 13) dimensionless Value of Y at gel-pore interface dimensionless Radial position defined in (14) dimensionless Parameter defined in (21) dimensionless Parameter defined in (22) dimensionless Parameter defined in (23) dimensionless Determinant in (40) dimensionless Coefficient in (36, 37) defined by (38,41) dimensionless Coefficients in (36, 37 and 43), defined in (39, 42) dimensionless Skeletal density of catalyst lb/ft Standard deviation of a log-normal distribution of dimensionless particle sizes dimensionless Non-zero roots of equation (35) dimensionless Root defined in (47) dimensionless Root defined in (48) General subscripts A Refers to reactant species B Refers to product species j Refers to quantity related to jth (j = 1, 2 or 3) root of equation (35)
ASTLEM. J., Zon Exchangers in Organic and Biochemistry (Edited by CALMONC. and KRFSMAN Interscience, New York 1957. HELFFERICHF. Angew. Chem. 1954 66 241. Coarn H. and MEYERA., German Pat. 1045102, 1958. MILLARJ. R., Brit. Pat. 849122, 1960. KUN~N R., FRISCH N. W. and FISHER S. A., Characteristics of macro-reticular ion-exchange Chem. Prod. Research and Development 1962 1 140. FR~SCHN. W., Kinetics of macro-reticular ion exchange. To be published. FIUSCHN. W., Surface Characteristics of macro-porous ion-exchange resins. To be published. TULLE E. W., Zndustr. Engng. Chem. 1939 31 916. WHEELERA., Catalysis, (Edited by Emmett P. H.) Vol II, pp. 1.05-165. Reinhold, New York WEISZ P. B. and PRATERC. D., Advances in Catalysis, Vol. VI, pp. 143-196. Academic Press, SMITHN. L. and AMUNDSONN. R., Zndust. Engng. Chem. 1951 43 2156.
748
T. R. E.) pp. 658-687,
resins. Zndustr. Engng.
1955. New York 1954.
Catalysis kinetics of macro-reticular
ion exchange resins
Resume-Le developpement dune nouvelle categoric de resines echangeuses d’ions qui possedent une grande porosite jointe a la structure conventionnelle dun gel 6changeur d’ions, presente de nouveaux problemes de cinetique. Dans cet article on considere la cinetique de cette cattgorie de catalyseurs, et on presente la solution analytique generale dans le cas d’une reaction reversible d’ordre 1 en regime permanent. On indique l’influence des parametres physiques a la fois sur le profil des concentrations et sur la vitesse de reactions. Ces vitesses limite pour de grandes surfaces de catalyseurs sont prevus ainsi que la porosite optimum du catalyseur necessaire pour realiser l’activite volumttrique maximum. Enfin on note l’avantage de la vitesse maximum de cette nouvelle classe de catalyseur sur les catalyseurs d%change d’ions conventionnels. Zusammenfassung-Die Entwicklung einer neuen Klasse von Ionenaustauscherharzen, bei der eine Makroporositlt der konventionellen Gel-Struktur der Ionenaustauscher iiberlagert ist, bringt neue kinetische Probleme. Diese Arbeit bertlcksichtigt die Kinetik dieser Klasse von Katalysatoren und gibt eine allgemeine analytische Losung fiir eine stationare reversible Reaktion erster Ordnung. Der Einfluss passender physikalischer Parameter sowohl auf die Konzentrationsverteilung als such auf die Reaktionsgeschwindigkeit wird aufgezeigt. Grenzgeschwindigkeiten filr Katalysatoren mit grosser Oberllache werden vorausgesagt; es wird eine Methode zur Abschltzung der fur eine maximale, volumetrische Katalysatoraktivitat erforderlichen optimalen Poriisitlt angegeben. Schliesslich wird der Vorteil durch grossere Reaktionsgeschwindigkeit dieser neuen Klasse von Katalysatoren gegentiber den bisher iiblichen Ionenaustauschkatalysatoren mitgeteilt.
Pergamon Press Ltd., London.
Printed in Great Britain.
Catalysis kinetics of macro-reticular ion exchange resins N. W. FRISCH Princeton Chemical Research, Inc., Princeton, New Jersey (Receiued 27 March 1961) Abstract-The development of a new class of ion-exchange resins which possesses macro-porosity superimposed on a conventional ion-exchange gel structure presents new kinetic problems. This paper considers the kinetics of this class of catalysts and presents the general analytical solution forasteadystate first-order reversible-reaction situation. The effect of pertinent physical parameters on both the concentration profiles and on reaction rate is indicated. Limiting rates for high surface area catalysts are predicted, and an estimate of the optimum catalyst porosity necessary to achieve maximum volumetric activity is presented. Finally, the maximum rate advantage of this new class of catalysts over conventional-ion-exchange catalysis is noted.
CONVENTIONAL ion-exchange resins may be considered as cross-linked polyelectrolyte gels with the exchange sites distributed, in a statistical fashion, throughout the entire resin particle. In addition to ion-exchange phenomena their utility encompasses catalytic applications. For information concerning specific catalytic reactions, comprehensive surveys by ASTLE [l], and by HELFFERICH [2] may be consulted. The strongly dissociated acidic? ion-exchange resins, in the H+ form, will catalyse many reactions which are normally catalysed by acids in homogeneous systems. In the absence of dissolved electrolyte these resins catalyse reactions at the locale of the exchangeable ion within the gel. Thus the active species, the Hf ion, must be accessible to the reacting species. Hence the mobility of both catalytic ion and of reactant in the gel is important. While, in general, rates observed in homogeneous systems are higher than those noted in the corresponding ion exchange catalyst case, there are exceptions to this general rule. Adsorption effects are often responsible for these reversals, permitting high concentrations of adsorbed reactant to t While the kinetic analysis is quite general, the limited use of strongly dissociated basic resins and both classes of weakly dissociated ion-exchange resins as catalysts, makes it practical and convenient to confine the discussion in this section to acidic catalysis.
accumulate on the catalyst, and consequently producing high rates of reaction. High reaction rate is not always the over-riding consideration in the selection of heterogeneous catalysts instead of a suitable homogeneous acid. Thus when expensive acids (i.e. BF,) may be required, and recovery is not practical, ion-exchange resin catalysts may be a feasible economic solution. In many instances, in the absence of poisoning and excessive temperature exposure, degradation rates may be sufficiently small to permit catalyst reuse, often without intermediate catalyst treatment. Another important advantage of ion-exchange catalysis is the ease of isolation of the catalyst from the reaction mixture. Product recovery by distillation, in the presence of soluble acid catalysts, is frequently accompanied by excessive product loss, by accelerated acid-cleavage and polymerization, or by equilibrium limitations at elevated temperatures. In other instances, the “specificity” of ion exchange catalysts is of prime consideration. This “specificity” may be manifested in several different ways. Thus a single ester species may be selectively hydrolysed in a mixture of esters; the direct esterification of acid-sensitive esters may proceed in good yield; and polymerization of unsaturates may occur only to a slight extent with the resin catalyst. A subsidiary advantage is the reduced corrosion rates often observed with heterogeneous systems. Unfortunately, the high equivalent cost of all
73s
N. W. FRISCH
synthetic ion exchange resins has limited the industrial development of catalytic processes based on these catalysts. In each situation the economics of the various competing processes must be individually assessed. As previously noted, the catalytic reaction occurs at the site of the active species in the resin gel. Consequently, non-polar reactants, which are not sorbed appreciably by these polar ion exchange resins, or reactants which possess low gel diffusivity rates, do not react at sufficient rates to warrant industrial interest. Thus if one examines the ratio of the esterification rates by ion-exchange catalysts to those observed in homogeneous systems, it is evident that this ratio decreases markedly as acids and alcohols of higher molecular weights are considered. Also, direct esterification of organic acids with olefins proceeds quite slowly. Similarly, direct alkylation of phenol with higher olefins becomes a marginal operation when compared with processing with available homogeneous acid catalysts. This situation can be improved somewhat by the use of small particle size catalyst, polar solvents, elevated temperatures and resins of lower degrees of cross-linking. However, in general, since the rate is at most proportional to the inverse of the particle size, only modest improvement can be effected in this nianner before handling difficulties become controlling. The use of polar solvents can also effect some rate improvement, but reactions requiring strongly acidic sites will not proceed in the presence of appreciable levels of polar solvents. (Optimum concentrations of these solvents exist). Similarly, temperature limitations of these catalysts, also equilibrium considerations, often restrict the benefits of operation at higher temperatures. Catalysts of low degree of cross-linking present stability and handling difficulties and offer only modest rate increases. Under these circumstances, it is evident that catalysts possessing macro-porosity would be useful to extend the range of utility to include reactions involving non-polar reactants. One type of macro-porous polymers may be produced by a polymerization process outlined in several patents [3, 41. In this technique, the polymerization of a mixture of two monomers, one of which contains at least two polymerizable double bonds, necessary to effect the cross-links, is carried
out in the presence of a third component. This component, a solvent for the monomers, but one largely incompatible with the cross-linked polymer, has been termed a non-solvent. This incompatibility manifests itself in a separation of phases during polymer gelation. With sufficiently low levels of non-solvent, holes or pores of molecular dimensions result in the polymer. Increases in the proportion of non-solvent in the monomer mixture result in a continuous polymer structure permeated by discontinuous pores of macroscopic dimensions, i.e. above molecular size. Above a critical nonsolvent level, the discontinuity of the pore structure is removed, and a continuous polymer, continuous pore structure results. Excessive levels of non-solvent are conducive to the precipitation of polymer during gelation, resulting in a largely discontinuous polymer phase dispersed in a continuous macro-pore structure of large dimensions. Thus this technique is capable of yielding a wide spectrum of pore sizes. The important sub-class of macro-porous polymers, containing a network of continuous polymer and continuous pores, which occurs by a mechanism which largely involves the expulsion of the nonsolvent liquid phase from the polymerizing gel, has been termed macro-reticular (MR) polymers. They are described [3] “as possessing a sponge-like structure, i.e. they are permeated by small veins in which non-swelling agents are capable of penetrating”. It is this important class of macroporous polymers with which we are concerned in the present analysis. The characteristics of macro-porous ion exchange resins has been discussed in detail [S]. Other studies concern the kinetics of macro-reticular ion exchange [6] and the surface characteristics of macro-porous ion exchange resins [7]. While these new physical structures mark a major advance in the field of ion-exchange catalysis, and the following analysis shows substantial kinetic advantages of MR catalysts over conventional ionexchange catalysts, certain limitations should be noted. MR catalysts possess serious limitations in some environments which are related to the chemistry of the polymer and ion-exchange function. In particular, the acidic variety, based on a sulphonic structure, is not one noted for its high acid strength, an important requirement in some reactions. The 736
Catalysis kinetics of macro-reticular ion exchange resins temperature stability threshold of the sulphonic acid functionally is well known to be about 160°C. Chemical resistance, in general, is a more complicated function of the porosity parameters and the degree of cross-linking. It should also be evident that MR catalysts do not always perform in a superior kinetic fashion compared to conventional ion-exchange catalysts. Thus the epoxidation of olefinic material with an organic peracid, the latter formed under the influence of the conventional catalyst, proceeds sufficiently rapidly and in good yield to justify industrial acceptance. The subsequent degradation of the epoxide product to form hydroxyacyloxy derivatives proceeds sufficiently slowly in this case because the epoxide is not sorbed appreciably by the catalyst. However, the catalytic sites of MR catalysts are more accessible to the epoxide, and the degradative hydroxylation reaction occurs to an excessive extent. Aspects of catalysis related to diffusional mechanisms have been considered by several authors. THIELE [8] has developed the effectiveness factor concept which has been comprehensively extended by WHEELER [9]. WEISZ and PRATER [lo] have treated more complex catalytic phenomena from a theoretical and experimental viewpoint. AMUNDSON and SMITH [l l] have discussed in detail the steadystate and transient kinetics of a reversible first-order reaction in a homogeneous gel ion exchange resin. The present paper is an analysis of the kinetic behaviour of macro-porous catalysts of the macroreticular class.
KINETIC ANALYSIS
Reversible reaction Consider a spherical non-swelling macro-reticular ion exchange resin of particle radius R, porosity P and specific surface S,. A model is assumed with these characteristics and radially oriented pores of effective radius ?. 2P
r=
%(I - P>P,
With the local porosity equal to the average value P, the number of pore mouths located on a spherical shell of radius r is 4r2P/f2. Thus each pore may be considered to be associated with a spherical gel area, normal to the pore axis, whose magnitude is independent of radial position and is expressed as &(l - P)/P. The pore serves as an access to the gel through a pore-wall transfer area of nr2 per unit length of pore. This mode of transfer complements the normal gel-diffusion mechanism occurring in conventional ion-exchange catalysts. Figure 1 depicts the idealized model of the catalysts and indicates the cylindrical pore and related gel structure. We now consider the performance of the catalyst in the case of a first-order reversible reaction Al;
B
b/K
which proceeds in the gel structure at local rates which are proportional to the gel-phase concentration of each species. Isothermal operation is assumed. In the absence of exchangeable ions or
Gel
FIG. 1.
(I)
Model of catalyst particle showing idealized pore structure. 737
N. W. FRLSCH
other poisoning phenomena the catalytic behaviour will be characterized by steady-state performance after the initial transient period. It is this steadystate rate which is of interest. The rate-controlling mechanism is assumed to be a diffusive one involving the transfer of reactant from the bulk fluid phase into the gel structure by diffusion in the pore and gel structure. The fluidfilm resistance at the external surface of the catalyst particle and at the pore-gel interface is assumed to be negligible in comparison with the low gel-diffusion rate. The diffusivities of reactant and product in each phase are assumed equal and independent of phase composition. Under these circumstances the following equations describe the process. Mass balances for each species taken about a spherical shell of radius’ I yield
+w 1 (1 -
-
d2c,
[
1
w,q, - &J =0 d2c,
+Dd’dr2+;dr
[
1 +
2dc,
-g+;-&.
(1 - P)(k”h -$)=O
2dc,
-
the pore concentration c at this radial position. A linear physical equilibrium isotherm is considered 5
%$(6)
552
(7)
In the bulk liquid phase the concentration reactant A is
of
CT,
(8)
CA =
The product is w
rate describing expressed on a
”
3k”(l -
R 0
R3
(2-9) catalyst. They are by application of groupings :
formation of particle volume
- ;
dr
(9)
the performance of in more convenient following dimensionless
(2)
1 +
(3)
Similar balances about a surface encompassing the pores in this shell indicate
1
(1 _
4D,P2
= [j(P)
-
w
2(hi - q*) (5)
where qi represents the gel-phase concentration of the indicated species at the pore-gel interface. The right-hand members are derived by considering the rate of transfer from the pore to the gel structure as proportional to the quantity (gel diffusivity) (transfer area)/(one-half the maximum gel-diffusion distance from the pore wall). The latter gel thickness is shown in Fig. 1 to be ?[,/(P) - P]/(2P). In the absence of a fluid-film resistance the value of qi at the pore-gel interface is in equilibrium with
E=
4P [J(P)
(17)
p)Q
D = 2
(18) G
R2 Q
- P] 7c;
(19)
F =
!@z D,
(20)
The significance of each of these quantities is readily discerned. The equilibrium saturation ratio, B, describes the relative quantity of reactant and product in the pore and gel structures. The surface-area parameter, E, is strongly dependent upon the magnitude of the specific surface of the catalyst. The kinetic modulus, F, describes the kinetic relationship between the intrinsic reaction rate and diffusion rate.
738
Catalysis kinetics of macro-reticular
Furthermore, let us define dimensionless groupings which occur in the solution of the system of equations (2-9)
([Q4
ion exchange resins
- aQ2 + /?I
[g4- (a+F(li K’)x
x P+[ a=E
(
B+;
1
+F
(22)
d2U, =+BD-
d2V,
dZ2
=FU,-;U, F
- a>]m = 0
(25)
xA
=
yA,
VA = v,
U,)
(26)
d2V, E = 5 (V, - U,) dZ2
(27)
x,
(28) U = 0,
Z 2 1
U = 6Z + i
Ej sinh J(zj)Z
(30)
V = 6Z + 2 2
9 R2 “=3F(I+$(U,-2)ZdZ and QD,
sinhJ(zj)Z
j=ly-Tj
(31)
The pore concentration eliminated from equations following pair of equations
(36)
(This form applies to both species). Equation (36) results from the more general form involving the eight roots (0, 0, _+ J(Zj) with j = 1,2, 3) of the auxiliary equation when one considers the necessity of limiting the concentrations at Z = 0 to finite values. Similarly the expression for the pore concentration profile is
= YBi (29) Z = 0
(35)
In addition to the zero root, there are, in general, three non-equal real roots of equation (35). Let these non-zero roots be denoted by zj (j = 1, 2, 3). Then the solution for the gel concentrationposition parameter is of the form j=l
d2VA E -=7j(VAdZ2
(34)
+
+ [(K + l)/K][P(F
(24)
dZ2 =KUB-FUA
u=o
+ [fl(K + 1)/K + a2 - aF(K - 1)/K - F2/K]m2+
In dimensionless form the pertinent equations become d2VA
)
The auxiliary equation related to (34) is of the eighth degree and possesses roots which are the square roots of the roots of the following quartic equation. m4 - [2a - F(K - l)/K]m”
(23)
d2U, dZZ+BD-
-;[@-r]’ I
(21)
(37)
Substitution of equations (36) and (37) in either (24) or (25) permits the development of relationships between the individual coefficients. These relationships are
terms V are readily (24-27) to yield the
(38) (~4-K~2+@u,+~(~2-y)U,=0
(32)
and &BI - = F(yK 7jj CP- a7j+ 73
a+F(l;K)]@+qU,+ K
%
,
+ F(g2 - y)u, = 0
(33)
where 9 represents the operator d/dZ. Equations (32) and (33) can be combined to yield an equation valid for either U, or U,
(39)
Additional relationships necessary to fix the coefficients result from the substitution of the boundary conditions (30) in (36) &d (37). The results are summarized below for the coefficients related to the reactant A. Let the quantity A be represented by:
739
N. W. FRISCH
1 1
1
1
p - at, + r:
1
p-crr,+z;
F(Y - r1)
CCC3+
p -
F(Y -
F(Y - 2)
A=
2:
r3)
(40)
Y
1 Y (P -
1
73
ax3 +
F(Y -
%Y
T3J2
Then
v
1
1-V
p-at,+r,2
K
1
1 p - cu2 + t2
F(Y - z1)
F(Y -
72)
p -
m3 +
F(Y -
z:
r3)
(41)
6,A = Y
V 1-V K
Similarly to the
Y
Y - t1 (P -
Y (P -
““1 + G)Y
JXY - tdZ
the value of &*?Ais represented
.
72
ar2 +
FiY -
below by altering
.
Y
G)Y
7212
the (j + 1)-st column
of the A determinant
sinh ,/(rj) 1-V K sinh ,/(tj)
.
.
.
.
. (42)
V
.
sinh J(rj) 1-V K sinh ,/(rj)
The important catalytic pactly expressed by 52 R2 -L= 3F(l - P) 2
rate parameter
x [J(rj)
EA, cash J(~j)
Limiting-area
- sinh J(rj)]
.
.
the concentration profile. Thus the solution of the general case of a first-order catalytic reaction is expressed by equations (35-43).
is com-
j=l
Q&i
.
(43)
Note that the 6 coefficient does not appear; its function is solely to define the equilibrium limits of 740
The action lyst is forms.
catalysts
important case of a being catalysed by a described by simple The pertinent value
reversible chemical rehigh surface area cataand particularly useful of r for large E values,
Catalysis kinetics of macro-reticular
approaching infinity, is [(K + l)fi]/Kcl. The solution is U,=
-+
Z
(K+
K+l x
[
1
l)VK+l
1 x
sinh,/{W + WIPIW
+ l>l>Z
sinh ,/{[(K + l)/K][F/(BD Ug=--
KZ
(K+
K+l
ion exchange resins
Figure 2 shows the calculated profiles (equation 44) for the reactant concentration in the gel structure of catalyst particles in equi-spaced sections of an isothermal fixed-bed reactor (K = 1.47). Profiles in a conventional ion-exchange catalyst are shown in Fig. 3 for an irreversible reaction as a function of
(44)
+ l)]}
1
l)v - 1 x K+l
sinh J{CW +
1YKI[FIW + l>]>Z c45j
’ sinh ,/{[(K + l)/K][F/(BD In the case of these concentration ratios in both the gel and and V, = U,. The corresponding W”R2
W
Q&J"
+ l)]}
fully developed catalysts, the for each species are the same pore phases; hence VA = VA, rate parameter is
= 3(1 - P)(BD + 1)
1
(K+
l)f;;:- 1 x (K + l)p
1 ’
(K+
x coth
-
1)
K
DIMENSIONLESS
F (BD + 1) I - ’ 1
FIG.
(46)
RADIAL
POSITION,
Z
3. Gel concentration profiles for a conventional ion-exchange catalyst.
modulus F. The latter profiles are based on the relationships of SMITH and AMUNDSON[l l] which are equivalent to our equations (44-46) with B = 0, i.e. zero porosity. It is evident that our relationships are extensions of the solution for the zero internal-porosity case which is useful for describing the performance of conventional ion-exchange catalysts. It is interesting to note that our analysis predicts that these infinite area catalysts perform as if the effective diffusivity of the reactants were of magnitude the kinetic
1.0,
I
I
I
n
I
Pc,D, + (1 - P)QD,
U-P)Q I OO
I
0.2 DIMENSIONLESS
I
I
0.4
0.6 RADIAL
I
I
0.6
POSITION.
FIG. 2.
I Z
Gel concentration profiles in MR catalyst particles in sections through fixed-bed (K = 1.47, co/Q = 100, D = 1000, F = 108, P = 0.5).
'
In all physical situations, this effective diffusivity is greater than the gel diffusivity, even in the unlikely case, co/Q = 1, and DJD, = 1. Irreversible-reaction case
A particularly useful set of relationships may be derived for the irreversible case, K = co. These 741
N. W. FRLSCH
expressions permit ready analysis of the performance of the catalysts as a function of the pertinent physical parameters. The remainder of this analysis treats the irreversible case. The solution is readily derived from equations (24) and (26) with K = co. Let us define the following dimensionless roots dl +
++=Jr
J(c? - 48) ] 2
porosity (P = 0.05, 0.1, 0.25, 0.5 and 0.75) were investigated in the case of the MR catalyst. In the region in which the intrinsic reaction rate is relatively slow compared to the gel diffusion rate (below F = 1 in this instance) the conventional resins possess slight rate advantages over MR catalysts.
(47)
4_ $-J(;-41)]
(48)
It is readily shown that a2 > 4/I for all situations involving finite B values. The case, /I = 0, leads to a trivial solution, W, = 0. The solution is u, =
B
+‘_(& - y) sinh 4+Z sinh 4+ Y(& - &2-) _
1
d(+“- - Y)sinh4-Z sinh c$_
C#J:sinh 4-Z ~$5 sinh 4+Z + sinh 4+ sinh 4__ I
(49)
(50)
The volumetric reaction-rate expression is
“uR’_ _ QW’
x
FIG. 4. Predicted catalytic rate behaviour ventional and macro-reticular ion-exchange (co/Q = 100, D = 1000).
3F(l - P)
~(4: - 4-2) ’
4’-(4: - Y)(++coth 4+ - 1) _ 4: _ 4:(4’- - ~)(4- coth 4- - 1)
$5
(51)
1
Comparison of conventional and MR catalyst performance
The contrast between these two classes of catalysts may be conveniently demonstrated by comparing the rates in a given situation. Fig. 4 is a plot of the dimensionless rate parameter vs. the kinetic modulus for various catalysts. A comparison is made at reasonable values of the parameters, D = 1000 and c,/Q = 100. Several values of 742
for concatalysts
Since this F value corresponds to near saturation of the gel with slow-reacting A, the introduction of finite porosity into the catalyst serves only to dilute the active gel structure with inert pores. At F values of 10 to IO*, gel concentrations in conventional ionexchange.catalysts are sufficiently small (Fig. 3) so that the MR resins begin to exhibit advantages. In the region of F = lo3 to about lo4 the MR catalyst plots begin to exhibit the effect of variation in the surface-area parameter, E. Each plot, corresponding to a specified porosity, is drawn to show two branches, one for low E (= 500) value and the other (shown dotted) representing the limiting rate curve for infinite E. At low F values, for all values of E, it is apparent from Fig. 4 that the reaction rate is proportional to
Catalysis kinetics of macro-reticular ion exchange resins
1.0
6
6
SPECIFIC
IO SURFACE
12
14
AREA,
S,f*
16
16
;
FIG. 5. Effect of surface area on catalytic rate (B = 100, D = 1oo0, P = 0.5, R = 0.05cm, ps = IXi g/cm%
the intrinsic reaction constant; here the apparent activation energy coincides with the true value. In the case of the limiting area catalysts, at high F values, the reaction rate becomes proportional to the square root of the reaction constant, and only one-half of the actual activation energy will be observed. At finite E values, and large F values, the observed activation energies will be a small fraction of the true values.
higher in value. At a level of 6.06 m2/g the profiles approach each other at reasonable concentration values corresponding to an appreciable increase in rate. The equations which describe the irreversible reaction case with infinite area follow directly from equations (44) to (46) with K = co.
lZj”ect of surface area From equation (1) it is evident that for a given system of fixed skeletal density and specified porosity, specific surface area is inversely proportional to pore size. The role of surface area in influencing reaction rate is shown in Fig. 5 at two levels of the kinetic modulus. At high levels of F the gel concentrations can be increased significantly by the incorporation of an increased level of specific surface. At lower Fvalues the effect is much less pronounced. In all instances there is a limiting rate which is approached as surface area is increased unbounded. The effect of changes in surface area on the gel and pore profiles is shown graphically in Fig. 6. At S, = Q-333 m’lg the gel concentrations ar?, in general, quite small, while the pore profile is much
0
.2
DIMENSIONLESS
.4 RADIAL
.6 POSITION,
I
.8 t
FIG. 6. Influence of surface area on dimensionless concentration profiles (B = 100, D = 1000,F = 107, P = 0.5, R = 0.05 cm, ps = l-50 g/cmS).
743
N. W. FRISCH
Effect of porosity
B which satisfies
The effect of porosity is essentially a two-fold one. In addition to the dilution, there is a beneficial result accompanying the introduction of an increase in porosity. At a fixed specific-surface level, increased porosity results in an improvement in the gel concentrations of the reactant, thus improving the reaction rate per unit gel volume. Thus an optimum porosity level exists at which the volumetric reaction rate 9” is a maximum. Fig. 7
[
D?&-i$‘]j[(BD:
l)jcothJ[(B:+
l)j
(52) The values of P,,,, corresponding to maximum 9, are noted on Fig. 4 on the upper curve at the various F levels. This upper curve, which represents the maximum rate for infinite-area catalysts prepared at optimum porosity levels, envelopes the limiting rate curves for these fully developed resins. As F increases without limit, the optimum level of porosity increases, approaching as a limit the value (53)
DIMENSIONLESS
RADIAL
POSITION,
t
FIG. 7. Effect of porosity on dimensionless gel concentration profiles for constant surface-area catalysts (co/Q = 100,D = 100, ;‘,:$‘:I -P ,/[l - PI2 = 1000,
depicts this porosity effect on the profiles at a fixed surface level. While the profiles become more attractive at higher porosity levels, on a particle volume basis, the intermediate porosity catalyst is more active than either of the extreme porosity ones. In Fig. 8 the effect of porosity on the limiting value (for infinite area catalysts) of W,, for three levels of the kinetic modulus, is shown. Optimum porosity levels are indicated. At low F values, P,,, -+ 0 since it is not economical to dilute active gel with inert pores. For fully developed ion exchange catalysts the optimum level of porosity is defined by the value of 744
POROSITY,
P
FL. 8. Influence of kineticmodulus on optimum porosity (co/Q= lOO,D= 1000,E-t w).
Catalysis kinetics of macro-reticular
At the usual Dca/Q values, P,,,, approaches the quantity + as F approaches infinity. It is axiomatic that, as the reaction conditions become more unfavourable (high F values or depressed B or D values) the optimum porosity increases. Since the optimum porosity levels possess a finite limit at high F values, it is possible to estimate the maximum rate advantage of MR catalysts relative to conventional ion-exchange catalysts. This rate performance, relative to that of the conventional resin, levels off, at high F values, at a Maximum relative rate = i J [ coD~~GQ”G]
(54)
ion exchange resins
calculated for the MR catalyst at E + co levels. Fig. 9 illustrates the particle size effect for intermediate surface area catalysts at F = 10’. In both cases, the reaction rate is nearly inversely proportional to particle diameter. E#ect of @id-phase
concentration
With conventional catalysts the rate is predicted to be independent of total solution concentration. In the case of high area catalysts, at high F values, the rate is nearly proportional to the square root of co. Fig. 10 depicts the effect of the co/Q ratio for a finite area catalyst. At low co/Q values theeffect on
For the parameters represented in Fig. 4 this relative rate corresponds to a value of 158; at F = 10’ the actual ratio is 143. Effect of particle size
With the conventional catalyst, at low values of the kinetic modulus, the reaction rate W, is independent of particle size. At high levels of the modulus the reaction rate becomes inversely proportional to particle diameter. Similar effects are
0
CONCENTRATION
RATIO,
2
FIG. 10. Effect of fluid-phase concentration on catalytic rate. (D = 100, E == 5[1016, F = [1015,P = 0.25.)
is somewhat less than proportional to the square root of c o ; at higher co/Q values, as gel concentrations become more significant, the effect of concentration on reaction rate becomes even less important.
W,
E#ect of d@usivity ratio
RELATIVE
PARTICLE
SIZE,
R/R,
FIG. 9. Effect of particle size on catalytic rate (co/Q = 100, D = 100. E/Ro2 = 5[102]), for low area catalyst, E/R02 = 5(10)6 for high area catalyst. F/Ro2 = 105, P = 0.3.) C
With high surface-area catalysts and at high values of the kinetic modulus, the reaction rate is nearly proportional to the square root of the diffusivity ratio, being of course, independent of D at low F values. Also the effect of the diffusivity ratio on reaction rate is less significant in the case of low 745
N. W. FRISCH
area catalysts. Fig. 11 illustrates the diffusivity ratio effect on the gel profile of a MR catalyst at F = IO’.
bulk diffusion to Knudsen diffusion in a series of catalysts of fixed porosity but decreasing pore size. A liquid-phase reaction would proceed with a rate which would be largely independent of pore size once sufficient area is introduced into the structure. In the case of the gas-phase reaction, as the diffusion rate decreases in proportion to pore size, the over-all reaction rate suffers. Poisoning
DIMENSIONLESS
RADIAL
POSITION,
Z
FIG. 11. Intluence of ditTusivity ratio on dimensionless gel-concentration profiles. (R = 100, E = 5[1016, F = 107, P
=
0:5).
In the case of gas-phase reactions at low pressures Knudsen flow may control the diffusion rate in small pores. Fig. 12 illustrates the transition from
IO
Two types of uniform or homogeneous poisoning of MR catalysts will be considered. In the case of exchange poisoning, low levels of dissolved ionic materials are exchanged by the resin, replacing active ions in the gel, such as H+ or OH-. There are several effects which accompany this exchange which result in reduced activity. Neglecting catalyst volume change, they are (1) the reduced intrinsic activity due to the dilution effect, (2) the reduction of gel diffusivity of the reactants and (3) the reduced solubility of the reactant in the gel. In Fig. 13 we have shown a particular poisoning situation, indicating an approximately linear decrease in rate in proportion to the fraction of catalytic sites which have been replaced. This is in agreement with experimental findings.
100 PORE
RADIUS,
T , 8
FIG. 12. Effect of pore size on catalytic rate in Ii uid- and gas-phase systems at low pressures at 7 = 5000 A, Er2 -7% 2 = 6(10)‘0, F = 104, P = 0.36.
746
B = 56.25, D = 100
Catalysis kinetics of macro-reticular
I SURFACE
”
ion exchange resins
LC,(Vf - v) =
FOULING
wow
(1 -
PIPS
(5%
and -Lc,
EXCHANGE
the latter form being directly integrable in all but the general case (equation 43). Rather than dealing with catalyst particles of uniform size, a distribution of particle sizes occurs in commercial batches of catalyst. For that region in which the reaction rate 9” is inversely proportional to particle size, the average particle radius which defines the effective volumetric reaction rate &, for a log-normal distribution of particle sizes, is simply K exp[(-log’o)/2], where R is the weight geometrical mean particle size and (Tis the standard deviation of the log-normal distribution of particle sizes.
POISONING
\-
o-
0
DEGREE
.4
.P
OF
POISONING,
.B
.6
f
FIG.13. Effect of poisoning on catalytic rate. Exchange poisoning, f=O, co/Q = 100, D = 500, E=4(10)6, F = lOs,f= 1.0, co/Q = 250, D = 1500, E= 1*6(10)‘3, F = 0, P = O-25. Surface fouling f = 0, as in exchange poisoning case above Ecr (1 -f).
CONCLUSIONS
A second type of poisoning, due to the fouling of pore surfaces with suspended material or polymeric products, is also shown. In this instance, it is assumed that the area available for transfer to the gel decreases in proportion to the degree of fouling. In this case, unless we are dealing with low area catalysts, the reaction rate does not suffer to a significant extent until the pore surfaces are nearly completely fouled. In cases of non-homogeneous fouling, the detrimental effects will be more pronounced than those noted above since the gel sites near the external surface will be the ones which are most completely deactivated. The second type of poisoning is less frequently observed in practice. DESIGN CONSIDERATIONS The analysis presented here yields, in an explicit manner, the steady-state reaction rate for monosized spherical catalyst particles immersed in a fluid phase of specified composition. These relationships, including the limiting forms, are directly applicable to the cases of continuous stirred-tank reactors and fixed-bed isothermal reactors. The mass balances for these situations are respectively
(56)
A model has been described which permits the analysis of the catalysis kinetics with macroreticular ion-exchange resins. The present paper discusses the general analytical solution for a steadystate first-order reversible reaction situation. In the case of a specific catalytic reaction the variables which affect the rate of conversion concern the physical parameters of the catalyst-reactant system. Among these are several important ones which require definition in a catalyst design programme. Reaction rate, rate of conversion per unit catalyst volume, is nearly a linear function of specific surface at low? surface-area values; it reaches a limiting value as the area increases without limit. Porosity is important in fixing over-all performance. Too little porosity restricts access of the reactants to the active gel through the pore structure; too much reduces the number of active sites contained in the reactor volume. The optimum porosity value is strongly affected by the kinetic modulus which expresses the relative rate of reaction and diffusion in the gel. In the unfavourable region which is defined by a kinetic modulus of large magnitude, the rate advantage of an optimum macro-reticular catalyst 7 In the case of zero internal surface area, the reaction rate is given by (1 - porosity) (reaction rate of an equivalent conventional ion exchange catalyst).
747
N. W
relative to a conventional ion-exchange one approaches a maximum, and is 0.5 J[(c,,D, + QDJ (QD,)]. This important relationship defines, in simple fashion, the limits of utility of the MR class of catalysts. NOTATION Equilibrium saturation ratio defined dimensionless in (17) c Fluid-phase concentration of indicated species in pore lb mole/f@ at radial position r E Bulk fluid-phase concentration of species A lb mole/fts of reactant and product co Total fluid-phaseconcentration lb mole/ft3 9 Operator, d/dZ dimensionless D Diffusivity ratio defined in (18) ft2/min Gel diffusivity of reactant and product DG ft2/min Pore diffusivity of reactant and product DP E Surface-area parameter defined in (19) dimensionless dimensionless F Kinetic modulus defined in (20) dimensionless f Degree of poisoning fE Fraction of external voids in fixed-bed reactor dimensionless ft h Depth of catalyst in fixed-bed reactor K Equilibrium constant for first-order reaction dimensionless min-l kv Intrinsic gel activity for forward reaction L Fluid-phase flow rate in CSTR or fixed-bed reactor ft3/min m Variable in (35) P Catalyst porosity, pore volume/total particle volume dimensionless P0pt Optimum value of porosity for iniinite area catalysts dimensionless Q Total gel-phase concentration corresponding to total lb mole/f@ fluid-phase concentration, co 4 Gel-phase concentration of indicated species lb molejfta lb mole/f@ 4t Value of q at pore-gel interface ft R Particle radius B
[l] [2] [3] [4] [5] [6] [7] [S] [9] [lo] [ll]
FRISCH Weight geometrical mean particle size ft Volumetric reaction rate based on total particle volume lb mole/fts min Value of W, for unpoisoned catalyst lb mole/fts min Effective value of gR, for a distribution of particle sizes lb mole/f@ mm Radial distance measured within catalyst particle ft Effective pore radius ft Specific surface area of catalyst ft2/lb Cross-sectional area of fixed-bed reactor fts Gel concentration rat&radial position product defined in (14) dimensionless Pore cdncentration ratio-radial position product defined in (15) dimensionless Value of VA in (30) at Z = 1 dimensionless Value of V in feed to CSTR dimensionless Value of V in inlet and exit of fixed-bed reactor. respectively dimensionless Weight of catalyst in CSTR lb Pore-phase concentration ratio defined in (10, 11) dimensionless Gel-phase concentration ratio defined in (12, 13) dimensionless Value of Y at gel-pore interface dimensionless Radial position defined in (14) dimensionless Parameter defined in (21) dimensionless Parameter defined in (22) dimensionless Parameter defined in (23) dimensionless Determinant in (40) dimensionless Coefficient in (36, 37) defined by (38,41) dimensionless Coefficients in (36, 37 and 43), defined in (39, 42) dimensionless Skeletal density of catalyst lb/ft Standard deviation of a log-normal distribution of dimensionless particle sizes dimensionless Non-zero roots of equation (35) dimensionless Root defined in (47) dimensionless Root defined in (48) General subscripts A Refers to reactant species B Refers to product species j Refers to quantity related to jth (j = 1, 2 or 3) root of equation (35)
ASTLEM. J., Zon Exchangers in Organic and Biochemistry (Edited by CALMONC. and KRFSMAN Interscience, New York 1957. HELFFERICHF. Angew. Chem. 1954 66 241. Coarn H. and MEYERA., German Pat. 1045102, 1958. MILLARJ. R., Brit. Pat. 849122, 1960. KUN~N R., FRISCH N. W. and FISHER S. A., Characteristics of macro-reticular ion-exchange Chem. Prod. Research and Development 1962 1 140. FR~SCHN. W., Kinetics of macro-reticular ion exchange. To be published. FIUSCHN. W., Surface Characteristics of macro-porous ion-exchange resins. To be published. TULLE E. W., Zndustr. Engng. Chem. 1939 31 916. WHEELERA., Catalysis, (Edited by Emmett P. H.) Vol II, pp. 1.05-165. Reinhold, New York WEISZ P. B. and PRATERC. D., Advances in Catalysis, Vol. VI, pp. 143-196. Academic Press, SMITHN. L. and AMUNDSONN. R., Zndust. Engng. Chem. 1951 43 2156.
748
T. R. E.) pp. 658-687,
resins. Zndustr. Engng.
1955. New York 1954.
Catalysis kinetics of macro-reticular
ion exchange resins
Resume-Le developpement dune nouvelle categoric de resines echangeuses d’ions qui possedent une grande porosite jointe a la structure conventionnelle dun gel 6changeur d’ions, presente de nouveaux problemes de cinetique. Dans cet article on considere la cinetique de cette cattgorie de catalyseurs, et on presente la solution analytique generale dans le cas d’une reaction reversible d’ordre 1 en regime permanent. On indique l’influence des parametres physiques a la fois sur le profil des concentrations et sur la vitesse de reactions. Ces vitesses limite pour de grandes surfaces de catalyseurs sont prevus ainsi que la porosite optimum du catalyseur necessaire pour realiser l’activite volumttrique maximum. Enfin on note l’avantage de la vitesse maximum de cette nouvelle classe de catalyseur sur les catalyseurs d%change d’ions conventionnels. Zusammenfassung-Die Entwicklung einer neuen Klasse von Ionenaustauscherharzen, bei der eine Makroporositlt der konventionellen Gel-Struktur der Ionenaustauscher iiberlagert ist, bringt neue kinetische Probleme. Diese Arbeit bertlcksichtigt die Kinetik dieser Klasse von Katalysatoren und gibt eine allgemeine analytische Losung fiir eine stationare reversible Reaktion erster Ordnung. Der Einfluss passender physikalischer Parameter sowohl auf die Konzentrationsverteilung als such auf die Reaktionsgeschwindigkeit wird aufgezeigt. Grenzgeschwindigkeiten filr Katalysatoren mit grosser Oberllache werden vorausgesagt; es wird eine Methode zur Abschltzung der fur eine maximale, volumetrische Katalysatoraktivitat erforderlichen optimalen Poriisitlt angegeben. Schliesslich wird der Vorteil durch grossere Reaktionsgeschwindigkeit dieser neuen Klasse von Katalysatoren gegentiber den bisher iiblichen Ionenaustauschkatalysatoren mitgeteilt.