Znd. Eng. Chem. Res. 1995,34, 1539-1547
1539
Kinetics of Thymol Hydrogenation over a Ni-Cr203 Catalyst Ayaz I. Allakhverdiev, Natal’ya V. Kul‘kova, and Dmitry Yu. Murzin* Department of Catalysis, Research Centre “Karpov Institute”, Vorontsovo pole 10, Moscow,103064, Russia
The kinetics of thymol hydrogenation over commercial nickel-chromia catalyst with formation of four menthol diastereoisomers have been investigated in a batch reactor at constant hydrogen pressure (0.4-4 MPa) at temperatures between 373 and 433 K in n-hexane and cyclohexane solutions. The rate of thymol consumption was independent of conversion. Initially mainly more thermodynamically unstable cis isomers (neomenthol and neoisomenthol) were produced and only at relatively high conversions trans isomers (menthol and isomenthol) were formed. However the stereoselectivity values at a particular conversion were seen to be independent of hydrogen pressure and reaction temperature. The observed kinetic regularities were modeled based on a n elementary step mechanism.
Introduction The stereochemistry of different heterogeneous catalytic reactions was a subject of considerable interest throughout the years (Augustine, 1976; Bartok, 1985; Bunvell, 1957; Clarke and Rooney, 1976; Siegel, 1966; Siegel and Dunkel, 1957). Selective and stereoselective catalytic hydrogenation in the liquid phase is probably the most widely used reaction for the production of fine chemicals and pharmacologically active molecules; therefore not surprisingly special attention was focused on this reaction. A large amount of qualitative information was obtained, and activity and stereoselectivity were seen to depend on the nature of the catalyst and of the compound t o be hydrogenated, reaction conditions, solvents, etc. The rather complex, still partly speculative mechanistic proposals were advanced, basing mainly on physical-chemical and surface science studies. Kinetic analysis of these complex reaction systems is rather scarce; however as pointed out by Froment (1987) kinetics contribute to a better understanding of reaction mechanisms and of the effect of catalyst upon these. Several studies were devoted to the kinetics of the liquid-phase catalytic hydrogenation of monoalkylphenols. In this case industrial interest is offered only by the cis form of the corresponding monoalkylcyclohexanol (Murzin and Konuspaev, 1992). A kinetic analysis was presented for the hydrogenation of o-cresol (Takagi et al., 1967,1968), 2-tert-butylphenol (Kut et al., 19881, and 4-tert-butylphenol (Murzin, 1993; Murzin et al., 1993a,b). The liquid-phase hydrogenation of dialkylphenols is an even more complicated reaction as it in principle leads to a mixture of four diastereoisomers of dialkylcyclohexanol and two isomers of dialkylcyclohexanone. The most frequently studied alkylphenol is thymol, because its liquid-phase catalytic hydrogenation is used in the fragrance industry for the manufacture of menthols. (Davis, 1978). The industrial process needs separation and recycling of useless diastereoisomers. Various catalysts were reported to be active in this reaction, which was conducted in the gas phase (Tungler et al., 19851, liquid phase (Allakhverdiev et al., 1993a,b, 1994a,b; Besson et al., 1993; Kologrivova et al., 1963, 1965, 1966; Tungler et al., 19911, and even in the solid state (Lamartine et al., 1980; Repellin et al., 1977). The study of Allakhverdiev et al. (1993a,b) was a continu-
* To whom correspondence should be addressed at ZAK/HM301,BASF AG, D-67056,Ludwigshafen, Germany. 0888-5885/95/2634-1539$09.00/0
ation of a research program in our laboratory devoted to kinetic modeling of the liquid-phase hydrogenation of substituted aromatic compounds (Kotova et al., 1991; Murzin et al., 1989; Murzin and Kul‘kova, 1990; Murzin, 1991, 1993; Temkin et al., 1988, 1989). The kinetic model was presented in the instance of thymol hydrogenation over supported Pt (Besson et al., 1993), Rh, Pd, and Ir catalysts (Allakhverdiev et al., 1993b). The kinetic study of Besson et al. (1993) was performed on a well-characterized Pt catalyst, and all the possible reaction products were detected. Unfortunately the experiments of Besson et al. (1993) were conducted only at one hydrogen pressure and the actual reaction network was oversimplified; the values of constants were determined graphically without any data fitting. In the thymol hydrogenation over Rh and Pd catalysts (Allakhverdiev et al., 1993b) menthol and isomenthol were not obtained, the ratio of menthones and neoisomenthoheomenthol was independent of conversion and hydrogen pressure, and the reaction order toward thymol was zero. The kinetic model presented by Allakhverdiev et al. (1993a,b) took that into account: the design of the kinetic model was based upon the theory of complex reactions (Horiuti and Nakamura, 1967; Temkin, 1979; Happel and Sellers, 1983) and the parameter estimation was performed. However in industrial conditions stereoselective thymol hydrogenation (Kologrivova et al., 1965) is carried out over nickel-chromia catalyst. Recently we performed a study on the effects of various promoters on activity, selectivity, and stereoselectivity in thymol hydrogenation over Ni catalyst (Allakhverdiev et al., 1994a), and in this work we present the kinetic modeling of this reaction over a commercial nickel-chromia catalyst at conditions close to industrial.
Experimental Section The pellets of industrial Ni/CrzOs (Proskurnin et al., 1985) were crushed, and those less than 50 pm in particle size were taken and reduced in flowing hydrogen a t 623 K. The Ni loading was 50% and Ni surface area was 52 m2/g (determined by oxygen chemisorption a t 298 K). The kinetic experiments were performed in a shaked reactor with a n external heating-cooling system. The volume of the reactor was 75 mL. The frequency of vibration of the reactor was 150 min-l and the amplitude was 15 cm. The pressure in the reactor was measured with a standard manometer and was constant
0 1995 American Chemical Society
1540 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995
1 .--c 0
e!
-L
E
0"
40
20
0 1 1.2 1.4 1.6 1.8 2 time, h Figure 1. Thymol hydrogenation at 443 K and 2.9 MPa in n-hexane solution. (0) thymol; (dotted 0)menthone; (+) isomenthone; (a) menthol; (W isomenthol; (0)neomenthol; ( x ) neoisomenthol.
0
6o
0.2
0.6
0.4
0.8
L Q
50
0
l o o
E.
401
Q
0 O
OO 0
0
0
0
0
0
0
0
Q 0
w
c
0
B
0
0
0
0 0
20
O
O
x
IO
0
40 eo 80 100 Thymol concentration, mol % Figure 2. Product concentration (mol S ) as a function of thymol concentration (temperature region 373-443 K, pressure region 0.4-4 MPa; n-hexane and cyclohexane): ( x ) neomenthol; (dotted 0)neoisomenthol; (+) menthol; (dotted 0 ) isomenthol.
0
20
during the experiment. The reactor temperature was kept within a range of 1 K of the fixed values. The hydrogenation reactions were carried out between 373 and 433 K and a t hydrogen pressures between 0.4 and 4 MPa. n-Hexane and cyclohexane were chosen as solvents, and the initial amount of thymol was 3 g. The volume of used solvents was 25 mL. The catalyst concentration was usually below 10 wt % thymol. Before an experiment the reactor, containing thymol and catalyst, was flushed with H2 a t room temperature (for 1 h). During the course of the reaction samples of the solution were taken and analyzed by flame ioniza-
tion detector gas chromatography (15%LAC-3R-446 on chromosorb W). Menthones and menthols were separated a t 413 K (2 m). Thymol was separated using the same phase (1m) at 458 K. A fresh portion of catalyst was taken for each experiment. The absence of diffusion limitations was verified using the published procedure (Murzin and Kul'kova, 1992). The proportionality of the efficiency of the reactor to the amount of catalyst, the calculation of the rate of diffusion of dissolved hydrogen to the outside surface of the catalyst particles, and the efficiency factor show that the reaction took place in the kinetic region.
Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 1541 Trans- 1 -hydroxy-2 -isopropyl - 5 -metliylcyc l o h e x e n e
OH
Thymol (T)
'I
0
n Isomenthone (IMN)
A
Menthone (MN)
Neomenthol (NML)
/
Menthol (ML)
Isomenthol (IMLI
OH
Neoisomenthol (NIML)
Figure 3. Reaction scheme.
Results and Discussion Kinetic Experiments. The time dependence of thymol conversion and product formation a t some temperatures is presented in Figure 1. Experiments with different solvents demonstrated that the activity, selectivity, and stereoselectivity a t the same conditions (temperature, pressure, catalyst concentration) were the same for both n-hexane and cyclohexane. That demonstrates the weak adsorption of solvents on the catalyst surface; therefore below we will use instead of concentrations values of mole fractions or mole percents, setting the initial amount of thymol equal to 100 mol %. As it can be seen from Figure 1,the rate of thymol consumption is independent of conversion, thus indicating the zero order toward thymol. At the beginning of the reaction a t low temperatures mainly neomenthol and neoisomenthol are formed and only after the formation of menthol and isomenthol was observed. The yields of menthone (MN) and isomenthone (IMN)clearly exhibit maximum, however the concentrations were very low (around 1%for MN and 3-5% for IMN). No hydrogenolysis was observed. The menthol isomer distribution in distinction from Pd and Rh catalyst (Allakhverdiev et al., 1993 a,b) was changing as the reaction proceeded; thus the isomerization reaction of menthols takes place. In Figure 2 the product distribution as a function of conversion is presented. As can be seen from Figure 2, the dependence of mole fractions of menthols as a function of conversion is approximately the same within the temperature and pressure region studied for both solvents used. Kinetic Modeling: Reaction Mechanism. The thymol hydrogenation can be represented by the reac-
tion network in Figure 3 (Allakhverdiev et al., 1993a,b). On the basis of kinetic data and taking into account similarity in homogeneous and heterogeneous catalysis, it was proposed (Murzin et al., 1993a) that the step which governs the total selectivity and stereoselectivity in alkylphenol hydrogenation is the step of keto-enol transformation in the same way as it is established for acid-base homogeneous catalyzed transformation of ketone and enol. Such tautomeric transformation is a key step, which can greatly influence stereoselectivity of the overall complex reaction of alkylphenol hydrogenation. cis-Alkylcyclohexanols were thought t o be produced from corresponding cyclohexanones and trunsalkylcyclohexanolsfrom direct hydrogenation of adsorbed enols (cyclohexen-1-01s). That proposal was first introduced in the earlier studies of Takagi et al. (1967). Thus, for thymol menthol and isomenthol are produced from enol forms and neomenthol and neoisomenthol from ketones. The kinetic modeling of the liquid-phase thymol hydrogenation was based upon the kinetic schemes advanced before for the instance of hydrogenation of unsaturated compounds (Temkin et al., 1988): stage 1:
ZA
ZAH,
stage 2: stage 3: net:
+ H,
ZB
+A
--
ZAH,
ZB
3
ZA
A+H,=B
+B (1)
where A is the substrate, B is the product, and A H 2 is an intermediate complex; stage 3 is an equilibrium one.
1542 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 Table 1. Reaction Mechanism basic routesa
+
-
1. ZA Hz Z A H z 2.ZAH2 Hz ZAH4 3.ZAH4 ZEi 4 . Z E i e ZY1 5. ZYi Hz ZYlHz 6.ZYlH2 ZC1 7.ZE1+ H2 ZEiHz 8. ZEiHz ZTi 9.ZAH4 ZEz 10. ZEz ZYz 11.Z Y z + H2 ZYzHz 12. ZY2Hz ZCz 13. ZEz Hz ~1 ZEzHz 14.ZEzH2 ZTz 15. ZCz ZTz 16. ZCz 9 ZCi 17.ZC2 ZT1 18.ZCz+A-ZA+Cz 19. ZCz + Tz w ZTz Cz 20. ZCz C1- ZTz C1 21.ZC2 + Ti * ZTi + Ci 22.ZYi+AwZA+Yi 23. ZYz + A- ZA + Yz e;)
+
+
1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 -1 0 0 0
c=)
-
=)
+
-
4
4
+
a
+ +
N(1), N(6),A + 3Hz = C1; N(2), N(7), A
= Yz.
1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0
1 1 0 0 0 0 0 0 1
0 1 1 1 1 0 0 0 1 0 0 0 0 0
stage 2: stage 3:
ZAH, ZY
stage 4:
ZB + A
ZAH, ZAH,
ZY
+ H,
stage 3':
net:
--
+ H, ZAH, + H, ZA
(=)
1 0 0 0 0 0 0 0 0 1 -1 0 0 0 0
1 1 0 0 0 0 0 0 1
1 1 0 0 0 0 0 0 1
0
0
1 1 0 0 0 1 0 1 0 -1 0 0 0
1 1 0 0 0 0 1 1
0 0 -1 0 0
1 1 1 1 0
0 0
1 1 0 0 0 0 0
0
0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
cyclohexene or derivative, and A H 2 and A H 4 are intermediate complexes; stage 3' is a fast one. In order t o develop a kinetic model for the more complicated case of thymol hydrogenation, we used the theory of complex reactions (Horiuti and Nakamura, 1967; Temkin, 1979). This theory permits an efficient algorithm for estimating the rates of complex multistep reactions. Elementary reactions are grouped into steps (stages), and chemical equations of steps contain reactants and surface species in a similar way as in the eqs 1and 2. Overall reaction equations can be obtained by the summation of chemical equations of steps multiplied by stoichiometric numbers (positive, negative, or zero); these numbers must be chosen such that the overall equations contain no surface species. A set of stoichiometric numbers of steps is defined as a reaction route (Temkin, 1979). Routes must be essentially different, and it is impossible to obtain one route through multiplication of another by a number, although their respective overall equations can be identical. The proposed basic reaction routes for a network of reactions of thymol hydrogenation are given in Table 1. On the right hand side of the equations, stoichiometric numbers for the different routes are reported. In Table 1 Z represents a surface site, A, YI,Yz,TI, CI, CZ,and TOrepresent molecules of thymol (TI,menthone (MN), isomenthone (IMN), menthol (ML), neomenthol (NML), neoisomentho1 (NIML) and isomenthol (IML), respectively, and AH,,etc. represent intermediate complexes. In the case of thymol hydrogenation when overall reactions are irreversible, the reaction mechanism can be described by nine reaction routes. The number of basic routes, P , is determined by the following equation:
P=S+W-J
ZAH,
= ZA + B
A+3H,=B
0 0 0 0 0
1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 -1 0 0 0 0
+ 3Hz = Ti; N(3), A + 3H2 = Cz; N(4), N(5), A + 3Hz = T2; N(8), A + 2H2 = Y1; N(9), A + 2H2
This mechanism explains the simultaneous zero orders with respect to A and H2 at high hydrogen pressures which is often observed because it assumes the formation of a complex A H 2 on the surface of the catalyst which slowly isomerizes into B. At high values of P H ~ the surface of the catalyst is completely covered with this complex and the reaction rate ceases to depend on either hydrogen pressure or the concentration of A. The role of hydrogen in catalytic hydrogenation can be viewed in the following way. Hydrogen does not compete for sites with the molecules adsorbed on the surface. If the adsorbed hydrogen is in equilibrium with the hydrogen dissolved in the liquid phase, the reaction rate will not depend on the extent of filling of the sites for hydrogen adsorption. That means that from the viewpoint of transition state theory activated complexes will be in equilibrium with both the adsorbed and the dissolved hydrogen. As pointed out by Temkin et al. (1989), the reaction rate will be the same whether the activated complexes are formed from the adsorbed hydrogen or from the dissolved hydrogen; therefore it is convenient to express the reaction rate as a function of hydrogen pressure in the gas phase in equilibrium with the liquid phase rather than as a function of hydrogen concentration in the liquid phase. In the instance of aromatic compounds the formation of adsorbed cyclohexadiene or its derivatives is forbidden by thermodynamic reasons (Temkin et al., 1989). Therefore the reaction mechanism for the liquid-phase hydrogenation of aromatic compounds is given as stage 1:
1 1 0
(2)
where A is the substrate, B is the product, Y is
(3)
where S is the number of stages, W is the number of balanced equations, and J is the number of intermediates. Balanced equations determine the relationships between adsorbed intermediates. For example, such equations can correspond to the total coverage equal to unit. For Table 1it follows from eq 3 that there are 23
Ind. Eng. Chem. Res., Vol. 34, No. 5 , 1995 1543 step equations, 15 intermediates, and 1balanced equation, and therefore 9 basic routes. The thymol molecule is thought t o be adsorbed with the aromatic ring parallel to the metal surface, and the substituent groups tend to keep away from the surface and take a cis position upon hydrogenation of thymol (Besson et al., 1993). That results in the formation of relatively high amount of neoisomenthol (route N(3)), where all the substituent groups are in cis position. This thermodynamically unstable stereoisomer then isomerizes into more stable ones (steps 15-17 in Table 1). The adsorption in the liquid phase (steps 18-23) is thought t o have "adsorption-assisted desorption" (Tamaru, 1989) nature (Murzin et al., 1990). More specifically the adsorption-desorption steps can be either quasiequilibria or not. As the adsorption strength can be different for alkylphenols, alkylcyclohexanones, and alkylcyclohexanols the adsorption-desorption step can have a nonequilibrium character. Nonequilibrium adsorption of the intermediate cyclohexanone or its derivative was proposed by Kut et al. (1988) and Schumann et al. (1989a,b). This approach can be applied also for replacement of alkylcyclohexanols; however the replacement of one alkylcyclohexanol by another one could be equilibrated. Kinetic Modeling: Rate Law Computation. The kinetic modeling was simplified by not taking into account the menthones formation as their amount was very low. Therefore only basic routes N(l)-N(7) from Table 1 remain in the reaction mechanism. For adsorption-desorption steps 19-21 from Table 1 a quasiequilibrium approach was used, thus leading t o the following expressions: 'CaT2
K -l9 - ' T a C 2
(12)
The fractional coverage of
C2
can be determined from
+ rg = r18
r3 Therefore ('3
+ k9)eAH4 = ' 1 8 ' C a A
- k-18'ANC2
and
where
The steady state conditions imply that
r(= r6 rl = r,
(4)
rll
= r12
r13
= '14
and therefore we easily arrive a t K20
=
'C2NCl c1
c2 eY1H2
and
=k
k5pH2 -5
+ k 6' Y 1
1 lPH2 uT1lv C2
where O c 2 is the surface coverage of C Z ,etc. and N c 2 denotes the mole fraction of C 2 , etc. Following Temkin et al. (1989) in the derivation of kinetic equations, it is assumed that the surface of the catalyst is uniform or quasiuniform and that organic compounds form an ideal liquid mixture, hence their activities are equal to their mole fractions. The mole fraction of hydrogen in the liquid phase can be neglected, because its solubility is low. The steady state conditions require that
r1 = r2 = r3
+ r,
=k
r3
= k3'A€I4
=k
'E2H2
+ k,?
'IPH2 -7
+ k 8' E l
'13'H2 -13
+ k14
'Yl
Assuming the equilibrium character of steps 4 and 10
(7)
1 8 ~ P ~ k2 - 1 O A H p
=k
'ElHZ
The rates of steps 1, 2, 3, and 9 are given by r1
= k -11
'YZH2
'E 1
= 'Y
1IK4
(26)
'E2
= 'YfiIO
(27)
The fractional coverage of Y1 and Y 2 can be expressed as a function of O m 4 taking into account that (10)
r3 = r6
+ r,
(28)
= '12
+ '14
(29)
and Here k 1 is the rate constant for stage 1in the forward direction, etc. The fractional coverage of species A H 2 and A can be therefore obtained after a straightforward procedure:
r9
Expressing the rates of steps implying the mass action law and using eqs 26 and 27, we arrive at
1644 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995
(30) and =
Y '2
4HA's'
+ '12) + k13k14PHd((k-13
kllkl$Hd(k-ll
+ '14IKl0) (31)
The site balance equation is given by
+ 'AH2 + 'AH4 + 'El + 'Yl + 'YlH2 + 'Cl + 'ElH2 $- 'Tl + 'E2 + 'Y2 + 'Y2H2 + 'C2 + 'E2H2 +
A '
eT2= 1 (32)
n
rc2
m c 2 -
=mdt -
As the reaction order toward thymol is equal to zero, that means that surface coverages of 6 A 0 ~ ~0 2~ ~ 4 are essentially higher than those of other species; therefore
+
(
eAH4=w=I + '-,
;i2+
kg
+
+R ) l
(33)
Defining the differential stereoselectivity as the ratio of rates
The rate of consumption of thymol is given by --A=
n CW, ---= m dt
(3 '
+ 'g)W
STI= r ~ i l r ~ (34)
where n is the initial amount of thymol in the system (moles), m is the mass of the catalyst, and t is time. As the solvent adsorption on the catalyst is weak, it is convenient t o use initial thymol mole fraction equal to unity
N ~ = N O ~ = Ia t
t=O
(35)
and integrating eq 34, the following equation was obtained
+
mtln = (1- NA)Wl(k3 kg)
The rate equation for substances other than thymol are given by
'C2
= r8
+ r14
(37)
'T2
= r14
+ r15
(38)
rC1
= r6 + r16
(39)
= '12 - '14 - r15 - r16
(40)
From eqs 16, 22-27, 30, 31, and 37-40 the rate equations are obtained: rT1
=
n cW,i-
dt-
ST,
= 'TdrA
(46)
SCl
= rc1k4
(47)
C '2
= 'CdrA
(48)
we can arrive at the stereoselectivity expressions for reaction products which do not contain time as a parameter (Beriinek, 1975). For the case of zero order reactions (Kiperman, 1979) the differential selectivity is equal to integral selectivity, which is expressed in the following way:
(36)
rT1
(45)
S T ~NTJNA
(49)
'T2
=" d N A
(50)
'Cl
= NC1lNA
(51)
'C2
= NCdNA
(52)
This allows essential simplification in the data fitting as instead of solving a set of differential eqs 41-44 only algebraic equations can be used for the parameter estimation. As at the beginning of kinetic runs the concentrations of some of the products were rather low in order to avoid statistical problems in the parameter estimation we used instead of eqs 49-51 the rearranged ones 'Cl+C2
= 'C1IrA
+ 'CdrA
(53)
'TZ+C2
= rTl'rA
+ 'CdrA
(54)
'Tl+T2+Cl+C2
=
(55)
Equations 52-55 along with eq 36 were used for the parameter estimation.
Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 1545
a
1 0.8 0.6
0.4
0.2 C
. 9 L
n
0 -0.2 -0.4
-0.6 -0.8 -1
0.2
0
0
5
0.6 Thymol mole fraction
10
15
20
mtln
25
1
0.8
0.4
30
35
40
Figure 4. Fitting results. (a) Deviation in stereoselectivity as a function of thymol mole fraction: (0) stereoselectivity to neoisomenthol; (+I stereoselectivity to neoisomenthol + neomenthol; (0)stereoselectivity to neoisomenthol + isomenthol. (b) Thymol mole fraction as a function of mtln (g Wmol) in thymol hydrogenation at 433 K in cyclohexane solution: (dotted 0)0.4 MPa; (+) 1.4 MPa; (dotted 0 ) 2.4 MPa.
Parameter Estimation. The estimation of the stereoselectivity and mtln values was performed by the minimization of the sum of residual squares. The minimization of the residuals in mtln data was carried out separately a t each temperature using the objective function
WSRS = [wi(mt/nexp - ~ t / ~ , , , , J 2 1 (56) where WSRS denotes the weighted sum of residual squares. An equal weight was given to every experimental point in the estimation. However the minimiza-
tion of the residuals in stereoselectivity data was carried for all temperatures with the objective function from eq 56. The minimization was carried out numerically using the Marquardt-Levenberg method adopted to the kinetic nonlinear regression program package Reproche (Vajda and Valko, 1985). The algebraic model option was used; the hydrogen pressures and mole fractions of the components were the independent variables and the experimental values of mtln and stereoselectivity were the dependent variables. The mathematical structure of the kinetic model is relatively complicated; therefore a strong correlation between the rate con-
1646 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 Table 2. Values of Estimated Parameters from mtln Data Sei?
T,K 373 393 413 423 433 443
fib
f3b
WSRSC
MRSC
MRC
130 50 30 25 15 5
93.9 48.8 20.8 20.4 10.3 4.4
0.60 0.36 0.41 0.19 0.22 0.25
0.060 0.024 0.026 0.014 0.014 0.027
0.24 0.15 0.16 0.11 0.12 0.17
a Standard deviation of parameters 5-15% of an estimated value. f i in gl-dmol; f3 in g-h.MPa/mol. WSRS, weighted sum of residual squares; MRS, mean residual square; MR, mean residual.
*
Table 3. Values of Estimated Parameters from Selectivity Data Seta*b f4
f5
fs
f7
f6
0.31 0.64 8.1 5 x
2x
fs
lo-*
fio
1.2 x
0.05
WSRS' MRS' MR' 10.7
0.027 0.16
Standard deviation of parameters 5-15% of an estimated value. f d - f l o , dimentionless. WSRS, weighted sum of residual squares; MRS, mean residual square; MR, mean residual. a
stants was expected. In order to avoid this correlation, a search of parameters f 1 - f ~ was performed. Those parameters are given by the following expressions: fl
= U k 3+ k g )
(57)
f8
= k16'k18
(64)
f9
= k17/k18
(65)
= k-18
(66)
f10
The results of the fits are presented in Figure 4 and Tables 2 and 3. It can be seen from Figure 4 that the descriptions are rather good; therefore the kinetic model describes experimental data with good accuracy. The value of fdPm was negligibly small in comparison with f 1 and f3/PH2 cfi
