Relationships between physico-chemical properties and catalytic activity of polymer-supported palladium catalysts II. Mathematical model

~

A PA LE IY D CP AT L SS I A: GENERAL

ELSEVIER

Applied Catalysis A: General 142 (1996) 327-346

Relationships between physico-chemical properties and catalytic activity of polymer-supported palladium catalysts II. Mathematical model Andrea Biffis a Benedetto Corain b Zuzana Cvengro~o% c Milan Hronec c, Karel Je~ibek d, Milan KrAlik c,, a lnstitutfiir Organische Chemie und Makromolekulare Chemie, Heinrich-Heine-UniversitiJt D~sseldo~ Universitiitstrasse 1, D-40225 DiAsseldorf, Germany b Dipartimento di Chimica, lngegneria Chimica e Materiali, Universita' dell' Aquila, Coppito Due - Via Vetoio, 1-67010 L'Aquila, haly " Department of Organic Technology, Slovak Technical University, Radlinskeho 9, 812 37 Bratislat,a, Slocak Republic d Institute of Chemical Processes Fundamentals, Czech Academy of Sciences, 165 02 Praha 6 - Suchdol, Czech Republic

Received 17 October 1995; revised 5 February 1996; accepted 5 February 1996

Abstract A mathematical model including external mass transport, diffusion in the particle and chemical reaction inside the particle was developed to describe a hydrogenation process in an isothermal batchwise system with a polymer-supported metal catalyst. Various types of reaction kinetics were implemented into the model, e.g., the power law or the Langmuir-Hinshelwood type. The validity of the model was tested on data obtained from the hydrogenation of a 1 M methanol solution of cyclohexene at 25°C and 0.5-1.5 MPa. Diffusional coefficients inside the catalyst, the hydrogenation rate constant and the adsorption constant of hydrogen were estimated. The best model proved to be the model considering the dissociation of hydrogen and neglecting the adsorption terms in the denominator of the Langmuir-Hinshelwood kinetics. Using polymer supports of different swellability, a linear correlation between the logarithm of the diffusional coefficient of a solute inside the polymer and the reciprocal of the swelling volume of the polymer support was derived from ESR measurements. A comparison with values of diffusional coefficients obtained from catalytic tests confirmed the validity of this correlation.

* Corresponding author. Tel. (+ 42-7) 495242, fax. (+ 42-7) 493198. e-mail [email protected]. 0926-860X/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved. PH S0926- 860X(96)00063-4

328

A. Biffis et al. /Applied Catalysis A: General 142 (1996) 327-346

Keywords: Poly-dimethylacrylamide-p-styrylsulfonate-methylenebis(acrylamide); Palladium; Hydrogenation; Cyclohexene; Batchwise system; Diffusional coefficients; Isothermal mathematical model; LangmuirHinshelwood kinetics; Effectiveness factor

1. Introduction

The growing interest for functionalized polymers as catalysts or supports for heterogeneous catalysis is well documented by both industrial applications and theoretical investigations of these materials [1-7]. Synthesis of MTBE, and of methyl vinyl ketone, removal of oxygen to the ppb level from water used in power stations [1], hydration of alkenes [2], immobilization of catalytic metal complexes [3], synthesis of peptides [4], etc. underline the usefulness and perspectives of these materials. Polymer-supported metal catalysts are often employed in a three-phase slurry system, under mild temperature conditions. In accordance with examples given above, the liquid phase can be water, an organic solvent or an emulsion of both of them. The gas phase can be for example hydrogen, oxygen or alkenes. Knowledge of transport phenomena in systems involving polymer-supported metal catalysis is very important for the design of an optimal catalyst (hydrophilic-hydrophobic properties of the support, concentration and distribution of metal in the catalyst particle, size of particles) as well as for establishing the best operational conditions (pressure, temperature, residence time) of the process. Despite the extensive utilization of these materials, not much information dealing with these problems is available in the literature [5-11], particularly when the metal is supported on microporous polymers. For example, the evaluation of diffusional coefficients in porous materials is generally made through diffusional coefficients in bulk liquid, porosity and tortuosity factor [7,12]. These last two parameters, and especially the tortuosity factor, are difficult to determine for swollen microporous resins. At the end of the fifties, Mackie and Meares [8] developed a relationship between the diffusional coefficient and the volume fraction of polymer chains in swollen polymers, assuming that the mobility of the polymer chains is much lower than that of the solutes:

D'=D°

1 +Up]

(1)

Test of this equation on dowex resins (sulphonated polystyrene crosslinked with divinylbenzene) and phenol formaldehyde resins showed its validity and usefulness for the practice [9]. Similar equations were later proposed by other research groups [10]. In fact, the environment within swollen low-crosslinked microporous supports appears to be more conveniently depicted as a polymer solution than as a more or less rigid system of "cavities" defined by the polymer chains [5,6,10,13]. As a continuation of our previous work [14] aimed at synthetic and morphological (nanoscopic) aspects of microporous resins, we

A. Biffis et al. / Applied Catalysis A: General 142 (1996) 327-346

329

tried to develop new analytical methodologies for the evaluation of transport properties with chemical reaction inside microporous resins, based on ESR spectroscopy and mathematical modelling. A common method applied for the determination of reaction kinetics parameters in heterogeneous catalytic systems is based on the treatment of data obtained under the so-called kinetic regime [12,15]. However, attempts to achieve the kinetic regime with a given kind of catalyst can lead to experiments with very small catalyst particles, e.g., less than 10 t~m in radius. Such fine particles are uncomfortable to handle, for example, recycling experiments are difficult to be performed appropriately due to catalyst losses in the isolation from the reaction mixture. Another serious problem is caused by the swelling of the polymer support: usually shells near the surface are more swollen than those near the core of the polymer particle, which facilitates a release of metal crystallites at or near the particle surface. This effect is much more present in the case of small particles than in the case of bigger ones. It is also possible to decrease the loading of active moieties (functionalized groups, weight fraction of metal) for ensuring the kinetic regime. However, this method can be utilized only for heterogeneous catalysts representing heterogenized homogeneous catalysts [7] (acidic groups, metal complexes, etc.). In the case of metal supported catalysts, the specific metal catalytic activity depends on the loading. Therefore, results from experiments with catalysts loaded with various content of metal cannot be correlated straightforwardly [7,16]. If it is not possible to carry out experiments under kinetic regime, transport phenomena need to be taken into account. Evaluation of external mass transport resistance and internal diffusion can be done either using regressions given in literature, e.g., Ref. [12] or measuring them. In connection with a combined influence of transport and chemical reaction resistance on the overall rate of a process, a question arises: "Is it possible to estimate transport and intrinsic chemical reaction parameters from data reflecting the wide range of influences mentioned above ?". An attempt to answer this question in the context of polymer-supported metal catalysts is a key feature of the presented paper. For the investigation of catalytic properties of polymer-supported palladium catalysts, we chose the hydrogenation of cyclohexene to cyclohexane as a reaction often used for such purposes [17]. In the gas phase, at higher temperature a n d / o r low pressure of hydrogen, a dehydrogenation of cyclohexene to benzene can occur as described in the work of Chambers and Boudart [18] (254°C, pressure << 100 kPa). From kinetic measurements of the latter mentioned authors, at 100 kPa and higher pressure, and 25°C, the gas hydrogenation of cyclohexene to cyclohexane proceeds predominantly. The liquid phase hydrogenation of cyclohexene is thermodynamically favored to cyclohexane, which is inferred from the equilibrium constants: 1014 and 0.001 for the hydrogenation of cyclohexene to cyclohexane and the dehydrogenation of cyclohexene to benzene (calculated from standard Gibbs energies of formation in the liquid state: 101.6,

330

A. Biffis et a l . / Applied Catalysis A: General 142 (1996) 327-346

26.7 and 124,4 k J / m o l e for cyclohexene, cyclohexane and benzene, respectively [19]). Hence, with respect to the activity of hydrogen in the methanol solution [20], it follows that at a temperature of 25°C and a pressure of hydrogen higher than 0.5 MPa, the hydrogenation of cyclohexene is not accompanied by dehydrogenation to benzene and it is practically irreversible. As for the reaction mechanism, there are some general information in the literature dealing with hydrogenation of olefins [7,16,21-23]. Usually, a surface reaction is supposed to be rate controlling and a dissociative chemisorption of dihydrogen often occurs [22,7]. A relatively complex set of reactions, which has been well demonstrated by exchange between deuterium and organic compounds characterizes this system [22]. For a common use, the kinetics of hydrogenation is most frequently expressed by Langmuir-Hinshelwood models [12,22,23]. These are sometimes reduced to power law models for technological purposes [16,22]. The development of a suitable kinetic model for the conditions of liquid phase hydrogenation of cyclohexene on palladium supported over microporous anionic resin is the next topic of our work. Estimation of kinetic parameters in heterogeneous catalysis is a problem solved systematically following the famous example of the hydrogenation of iso-octenes given by Houghen and Watson [21], who linearized kinetic equations and applied the least-squares method. The proper model has been chosen on the basis of the physical significance of the model parameters (all needed to be non-negative) and the quality of fitting of experimental data. This basic principle for choosing the proper model has remained valid until now, but powerful algorithms of non-linear regression and statistical criteria for evaluating the estimation and description quality are employed (see e.g. Refs. [12,23]). In the presented work, we have followed the methodology and algorithms given by Froment [23], i.e., the Gauss-Newton-Marquardt method for finding out a minimum of the residual regression squares and the individual confidence limits for the obtained values of the model parameters, the correlation matrix to assess the "independence" of the model parameters and the F-criterion to evaluate fitting quality of the kinetic model applied. We have investigated the problem of transport phenomena and intrinsic reaction kinetics in one step, utilizing a full mathematical model without any simplifications dealing with assumptions under which the model was derived. Such an approach differs from the ones commonly applied, which utilize mainly effectiveness factors [11].

2. Experimental 2.1. Materials

Cyclohexene, cyclohexane, benzene and methanol were supplied by Aldrich. The catalysts used are described in Ref. [14]. Cyclohexene was purified by distillation prior to use.

A. Biffis et al. / Applied Catalysis A: General 142 (1996) 327-346

331

2.2. Apparatus and procedure Catalytic experiments were carried out in a 50 cm ~ glass-lined stainless steel reactor connected with a flexible metal capillary to an apparatus for measuring the hydrogen consumption at constant pressure [24]. Experiments were considered to be completed when the hydrogen consumption stopped, i.e., the consumption increased in 10 min by less than 0.1% of the last recorded value. A chromatographic analysis of the reaction mixture after hydrogenation showed a 100% yield of cyclohexane. Typically, 10 ml of a 1 M solution of cyclohexene in methanol was employed, with an amount of catalyst yielding an analytical concentration of Pd of 0.4 mmol/l. The same sample of catalyst was utilized for experiments at different pressure. Hydrogen consumption was recalculated to the conversion by dividing a given value of the consumption by the final value of the consumption. The reproducibility of catalytic measurements using the apparatus [24] is given by: (i) adjusting the pressure of hydrogen at the start (during the experiment the pressure is kept within + 5 Pa), (ii) circumstances occurring during performance of the experiment (e.g. changes in shaking, changes in mechanical resistance of driving pumps, etc.). In order to increase the precision of data obtained, each kind of experiment was repeated two times and an average conversion curve was calculated from pairs of these curves. Values of the conversion corresponding to the time of the 50% conversion given by the average conversion curve, were read from the first and the second (repeated measurement) curve. In this way a set of data consisting of twice the number of values in respect to the number of runs was obtained and the pure error variance of measurements was calculated (Table 2). To estimate the model parameters, values of the average conversion curves were treated. After the catalytic tests, size distribution measurements of catalyst particles in the employed sample, swollen in methanol, were performed. Particle size distributions were evaluated with a Zeiss optical microscope (4 × ), equipped with an Ibas 2000 image analyzer. The dimension of about 100 particles were recorded for each sample. In order to determine the pycnometric density of a catalyst, the sample was dried at 40°C and 1 kPa for 12 h (constant weight of the sample). The dried sample (about 1.000 g) was put into a 25 ml pycnometer and 20 ml of methanol was added. The catalyst was let to swell for 12 h, thermostated at 25°C and then the pycnometer was filled up to the mark with methanol, thermostated, and weighed. From the weights of the empty pycnometer, the pycnometer filled with methanol, the pycnometer filled with the swollen catalyst in methanol, and the weight of the dry catalyst sample, the pycnometric density P was calculated. 3. Mathematical model

3.1. Development of the model The mathematical model for the hydrogenation process was derived under the following assumptions:

332

A. Biffi's et al. /Applied Catalysis A: General 142 (1996) 327-346

1. Isothermal regime. 2. Ideal stirring of bulk liquid. 3. Constant concentration of hydrogen in the bulk liquid (no hindrance due to gas-liquid transport). 4. Spherical catalyst particles with equivalent diameter determined by size distribution measurements. 5. Constant diffusional coefficients throughout the particles. 6. Constant liquid-solid mass transfer coefficient (independent of the radius of particles). 7. Homogeneous porosity of the particles. 8. The adsorption of reaction components on the polymer backbone does not influence the concentration in the void volume of a swollen polymer. 9. Homogeneous distribution of catalytic sites throughout the particles. 10. No chemical reaction in the bulk liquid. Some of the above listed assumptions are somewhat drastic, e.g., it is well-known that the liquid-solid mass transfer coefficient depends on the size of the catalyst particles [12]. However, for reactors stirred by shaking, it is very difficult to predict this dependence; therefore, it was decided to keep this parameter constant, under the same conditions of stirring. The assumption about the equilibrium partition of the reaction components between the void volume of swollen polymer and the bulk solution (viii) can also be far from reality, particularly when strong enthalpic interactions between reaction components and the polymer backbone exist [10,11]. Moreover, for the development of a truly exhaustive model for the catalytic activity of these materials, inhomogeneity in the microporous polymer support [5,6] is a feature that should be accounted for. In spite of all these potential inaccuracies, we have considered these materials as homogenous and having no significant interaction substrate-polymer backbone, which is as approximation commonly accepted in the literature [7].

Table 1 Values of input parameters Name

Value

Ref.

Diffusional coefficient for cyclohexene Diffusional coefficient for hydrogen Solubility of hydrogen in methanol at 298 K Pycnometric density (P4N) Pycnometric density (P8N) Swellability (P4N) Swellability (P8N) Porosity (P4N) Porosity (P8N) L i q u i d - s o l i d mass transfer coefficient Diffusional parameter

2.0 × 10 9 m 2 s i 1.7 )< 10 -8 m 2 s - 1 0.3869 ( m o l / m 3 ) / M P a 1240 kg m - 3 1250 kg m 3 0.00244 m 3 kg J 0.00186 m 3 k g - L 0.67 0.57 0.0002 m s i ~ 0.004 m 3 k g - ~ "

[17] [17] [20] This This This This This This [12] This

a Initial estimate.

work work work work work work work

A. Biffis et al. /Applied Catalysis A: General 142 (1996) 327-346

333

The mathematical model is expressed by Eqs. (2)-(5) • Component balance in the bulk liquid t/f

dCi.L = -

dt

~-"fjajkLs(Ci,sj--Ci,L) VL j = i Vp

with initial values Cen,t° = Cen,0 ; Can,t ° ~Component balance in the particle

Oci,j Ot

0", C H 2 , t ° =

(2)

const.

Oi O f r2OCi,j ] _k_Vi~v £r2

Or k

(3)

with initial values for all catalyst particles: ce.,,,, = Ce,,0; Can,,,, = 0; Cn:.,,, = 0 Boundary conditions for the particle OCi Or'J r=O = 0

-D

i ~~Ci ' j r=rpj = k L s ( C i , s j -- Ci, L )

i = 1,2 . . . . . n c j = 1,2 . . . . . nf

(4)

Rate of the chemical reaction

v=CPd[1+(K.2;.=),,]cCen k r c "H~

(5)

Coefficients a, b, c in Eq. (5) take values depending on the type of kinetic model, e.g., a = 1, c = 0 for the power law kinetics; for Langmuir-Hinshelwood kinetic models [12] coefficients a, b, c can vary as Table 2 indicates. Preliminary treatment of experimental data showed a very low adsorptivity of cyclohexene and cyclohexane (values were close to zero and individual confidence intervals of these parameters included zero), therefore the adsorption terms concerning these two components are not involved in the denominator of Eq.

(5). It is worthwhile to add a few comments to the component balance with respect to catalyst porosity and diffusivity. In Eq. (3), Eq. (), the porosity (void fraction in the catalyst) e is considered, that is, we are expressing in the model " t r u e " concentration of species inside the void fraction of the swollen polymer, in accordance with approaches commonly applied for balances of components in porous materials [12,25]. An advantage of such an approach is that distribution coefficients of components between bulk liquid and the liquid in the swollen polymer [10,11] can be approximately set to 1 (i.e. they do not need to be considered) for the cases without strong enthalpic interactions between reaction components and polymer backbone (assumption (viii) listed above). Our approach to the mass balance is not so unusual. A possibility to express concentration of the component in the swollen polymer in this way is described, e.g., by Muhr [10]. The relationship between diffusional coefficients ( D i) employed in

334

A. B(flfis el al. /Applied Catalysis A: General 142 (1996) 327 346

Eq. (3) with those ones (DI.) utilized for the description of transport phenomena, considering the total volume of a swollen polymer as the basis for the evaluation of concentration of components, is expressed by:

(6)

Di=ED;

In our previous work [14], the microporous polymer supported catalysts were characterized by swelling volume measurements, inverse steric exclusion chromatography (ISEC), X-ray diffraction, and ESR spectroscopy. A linear correlation between the logarithm of the correlation time of the "spin probe" employed and the reciprocal of the swelling volume of the resin was found: "ri = 'ri0ex p ~-

(7)

with value a, = 0.004 m 3 kg-1. It is well known that the rotational diffusion coefficient of the probe is inversely proportional to the correlation time [26]. An evidence has been given that in various liquids and polymers the rotational diffusion coefficient is directly proportional to the translational coefficient [27]. Therefore, the following expression linking the translational diffusion coefficient and the swelling volume can be obtained

This expression was utilized in the mathematical model instead of the more commonly employed relationship involving the void fraction and the tortuosity factor [7,12], or the expression proposed by Mackie and Meares (Eq. (1)). The diffusional parameter a D was assumed to be constant for all solutes. The porosity • developed by the catalysts in methanol was evaluated on the basis of their swelling volume S, determined by ISEC measurements [14], and their pycnometric density p (Table 1), through the expression 1

• =1---

pS

(9)

The concentration of palladium inside the swollen polymer was calculated using the expression Xea. 10 3 ( k g m -3) cea = • S

(10)

This expression predicts an increase of the concentration of palladium with decreasing swellability, i.e. the concentration of palladium is higher in the more crosslinked polymer with lower swellability than in a less crosslinked polymer. Another important feature deals with the porosity. Due to the relatively free motion of the polymer chains, we suggest to consider all crystallites of palladium as accessible for the reaction species, and therefore to be present only in the void fraction of the swollen polymer; this explains the introduction of • in the denominator of Eq. (10).

A. Biffis et a l . / Applied Catalysis A: General 142 (1996) 3 2 7 - 3 4 6

335

3.2. Procedure of the parameter estimation For both mathematical modelling and parameter estimation, an effective algorithm and computer method for the solution of the partial differential equations expressing the mathematical model is necessary. Probably one of the best is the collocation method developed for chemical-engineering systems by Villadsen [25]; in our case, we have utilized program modules from Soerensen [28]. For solving the set of ordinary differential equations obtained, the RungeKutta-Hanna algorithm was employed [29]. A computer program was developed in FORTRAN, by which an arbitrary number of components, fractions of catalyst particles, collocation points, and catalytic tests can be treated. Limitations are given by computer memory and mainly by computational time. Preliminary computation tests have shown that, as a good compromise between acceptable accuracy of calculation and computational time, three collocation points and three fractions of particles could be considered. As a maximum, one needs to estimate 4 parameters in the arbitrary model from Table 2: (i) the mass transfer coefficient, (ii) the diffusional parameter aD,

Table 2 Estimated values of parameters k~, KH2, a D, their individual confidence intervals, minimal sum of the squared errors SS~ and F~. value for various kinetic models characterized by the rate determining step implying coefficients a, b, c in Eq. (5) Model no.

Rate determining step

1

H 2 +A

a

t

b

-

c

0

kr

KH~

a D X 10 3

Ak r

AK-H2

A a D × 103

-

4.00

3.35 0.22

2

H 2 * +A *

3

H 2 * +A

4

H ~ +A*

5

H * +A

6

H * +A ~

1 1 0.5 0.5 0.5

1 1 0.5 0.5 -

2 1 2 1 0

H * +A 7

2H * +A

1

0.5

2

10.34

4.28

0.56

1.61

0.09

6.67

31.08

4.31

0.71

5.62

0.08

0.61

9×10

0.02

6. ×

10 -4

0.06

0.61

7×10 -~

4.52

0.02

6 x 10 4

0.06

8

2H * +A ~

1

0.5

3

5

4.52

0.61

4.52

0.02

0.06

3.18 10.0 1.58

Fc a

3323

4.94

1304

1.91

1187

1.73

925

1.33

925

1.33

923

1.32

1121

1.63

1046

1.51

0.13

5.94

17.7

SS e

51.2

4.49

7.12

0.08

6.00

4.35

0.72

0.08

Notation: A = c y c l o h e x e n e , * = component chemisorbed on the active site. Dissociation of hydrogen can be homolytic ( 2 H * ) or heterolytic ( H + * + H - * ). F~, ~ [ ( S S e - P e ) / ( n m t - n B - 2 n r + 1 ) ] / [ ( P e / ( 2 n r - 1)]; nmt = 239, n~ = 8. r

Pe = ~

-

~ , (Yi.j . . . . . . 'm,.50 -- 50)2' w h e r e Yij .......... 50 r e p r e s e n t s a value of the conversion corresponding to

i=lj=l

the time in which the 50% conversion is predicted by the average conversion curve YMi- The pure error variance of measurements [23] was 2 . 5 2 % . F ( n t > 120, n 2 = 15, a = 0 . 0 5 ) = 2.11 [31].

336

A. Bgff~s et al. /Applied Catalysis A: General 142 (1996) 327-346

(iii) the rate constant k r and (iv) the adsorption constant KH2. These parameters will be considered as components of the vector B. Estimation of B was made by the least-squares method with a minimization criterion in the form: nr

SSe = E

tlp,i

meas.

E wi.j( Yi,j

calc. ] 2

- Yi,j ,

(l l)

i=1 j = l

In order to find a minimum of the sum of the squared errors SS e, the Gauss-Newton-Marquardt technique was applied [23]. In connection with the evaluation of derivatives we can give a piece of practical advice, stemming from our observations. Using computer compilers working with 15 valid digits (decimal), a direct evaluation of derivatives from Eq. (11) was not successful when the minimization procedure was close to the minimum. This behavior is due to the round-off errors, whose role increases with increasing number of data treated. Therefore, the first derivatives utilized in this method need to be evaluated using numerical derivatives of elements of the Jacobi matrix [23]. The algorithm was complemented with a check of parameters values in order to ensure b s >~ 0. The searching procedure was started from the following initial estimates: the rate constant was estimated from experiments with the smallest catalyst particles, the adsorption constant supposed to be a very small value and the diffusional parameter was the value obtained from treatments of the rotational correlation time (see Table 1). Then, calculations starting from different initial estimates were done to verify that the global minimum has been found. Individual confidence limits for the estimate of parameters A b s were calculated using the o~/2-percentage point of the t-distribution with nmt n B degrees of freedom. The adequacy of the model was checked by the F-criterion. The probability level for all statistic tests was 95% (e~ = 0.05). -

-

4. Results and discussion In our previous work we have observed that the rate of the hydrogenation process employing polymer supported metal catalysts is very often under mass-transport-controlled regime, and thus, depending significantly on the size of catalyst particles [14,30]. Therefore, a precise size distribution measurement for the employed catalyst particles was necessary. The size distributions were determined with samples in the working state, that is, swollen in methanol. Fractions of the catalyst were calculated assuming spherical particles with radius of equivalent circles of areas projected by the catalyst particle (so-called the projected area radius). Results are given in Fig. 1. The first two entries represent samples of catalyst P4NPd2 [14] with different size distributions, which were separated by sieving. Sample I had a particle size in the dry state of < 0.1 ram, and exhibited a specific area in the swollen state

A. Biffis et al. / Applied Catalysis A: General 142 (1996) 327-346

1,0-t

~I

337

~rp'(104m) fp, (-)

0,5

0

, P4-I:I

0 ~ 2 3 P4-II:l 2 3 P 8 : 1 Catalyst: fraction

2 3

Fig. 1. Particle size distribution for P4NPd2(I)-P4-1, P4NPd2(II)-P4-1Iand P8NPd2-P8.

of 702 c m 2 / c m 3. Sample II had a particle size between 0.1 and 0.3 ram, and its specific area was 422 c m 2 / c m 3. The last entry refers to a fraction of catalyst P8NPd2 [14] with a particle size between 0.1 and 0.3 mm (specific area 325 cm2/cm3). Three sets of experiments were carried out. The first one (Fig. 2) was performed with the smaller particles of catalyst P4NPd2 at 1.5 and 1.0 MPa. The 1.5 MPa pressure was the highest working pressure for the apparatus employed; using this pressure and the smaller catalyst particles we tried to approach the kinetic regime. To evaluate the effect of increased particle size on the rate of the process, a second set of experiments (Fig. 3) was run with bigger particles of P4NPd2. The third set (Fig. 4) was performed with catalyst P4NPd8, to investigate the effect of increased crosslinking of the support (and therefore of decreased swelling volume). The expected behavior of the hydrogenation rate was found, i.e. it increased with decreasing particle size, increasing pressure, and decreasing crosslinking degree.

100

o

",~ 50

Sd ~

P (MPa)

0 0

500

time (s)

1000

Fig. 2. Hydrogenation of cyclnhexene at different pressures with P4NPd2(I). Solid curves denote calculated conversions model No. 6.

338

A. BiJfis et a l . / Applied Catalysis A: General 142 (1996) 327-346

100

o

~, 50

0

~

~

~.A °

p ~)

0.5

*

I

I

I

0

1000

2000

time (s)

Fig. 3. Hydrogenation of cyclohexene at different pressures with P4NPd2(II). Solid curves denote calculated conversions model No. 6.

All catalytic tests from Figs. 2 - 4 (eight runs) were treated simultaneously by the procedure described in Section 3.2. Each run consisted approximately of 20 points, the total number of experimental points was 168, the statistical weight was put equal to 2 for experiments with the P8N catalyst (71 experimental points). The input parameters are shown in Table 1. The small difference in the sizes of Pd crystallites in P8NPd2 and P4NPd2 [14] (both about 2 nm in diameter) was neglected. As an initial estimate for a D we took the value a~, derived from the ESR measurements [14]. A high value of the external mass transport coefficient (about 0.002 m s - ' ) was obtained from the first stage of data treatment and a comparison with a model with an extremely high value of the mass transport coefficient (10 ]6) showed that the external mass transport of species in the hydrogenation of cyclohexene under the conditions of our investigation can be omitted. Further estimation contained only three parameters as a maximum. The estimated values

100

o

50

o.5

o

.5 0 0'

1000 200"0 ' time (s)

3000 '

Fig. 4. Hydrogenation of cyclohexene at different pressures with P8NPd2. Solid curves denote calculated conversions model No. 6.

A. Biffis et al. / Applied Catalysis A: General 142 (1996) 327-346

339

together with individual confidence limits of parameters are given in Table 2. All correlation coefficients except for models No. 7 and No. 8 were less than 0.9. In models No. 7 and No. 8, the rate constant and the adsorption constant were strongly correlated having values of the correlation coefficients about 0.96. Table 2 indicates the power law kinetics (model No. 1) as the worst one of all the models tested. The other models possessed a comparable quality of description. The problem of choosing the best kinetic model from the data we have treated is indicated by the F-statistics. For the given degrees of freedom and the probability level of 95%, all models, except the No. 1, satisfy the necessary condition: F c < F; not to be rejected. However, models No. 4 and No. 5 can be excluded because the adsorption constants are close to zero. Thus, these models can be reduced to model No. 6. This is also indicated by the values of individual confidence intervals of adsorption constants. Model No. 6 which involves dissociation of hydrogen and neglects all adsorption terms, can be considered to be the best one for the hydrogenation of cyclohexene in methanol at pressures from 0.5 up to 1.5 MPa and ambient temperature. Calculated conversion curves for this model are given in Figs. 2-4. As shown in Table 2, all models have the value of diffusional parameter close to 4. In order to analyze why the diffusional parameter is independent of the kind of kinetic model, the hydrogen kinetic term fH (the fraction in Eq. (5)) was calculated as a function of the concentration of hydrogen. This can vary from zero up to the value of the saturated liquid at 1.5 MPa. Fig. 5 shows that all Langmuir-Hinshelwood kinetic equations have similar values of the hydrogen kinetic term, and the discrimination of the models could be better made at low pressures (less than 0.5 MPa) or at higher pressures (more than 1.5 MPa). This can serve as an advice for future investigation of the hydrogenation of cyclohexene in methanol on this kind of catalysts.

0,2

~

0,1 . .--"/;:"" ......... 1 0,0 / f ' ' ' " 0,00

4,5,6,7 I

t

0,03

0,06 cm (M)

Fig. 5. The dependence of the hydrogen kinetic term fH

," on the concentration of

hydrogen in the liquid CH,. Coefficients a, b, c for models 1 - 8 are listed in Table 2.

340

A. Biffis et al. /Applied Catalysis A: General 142 (1996) 327-346

S-1

2 -2

-3

I

I

0,2

I

0,4 0,6 1/S (kgm -3) x 10-3

Fig. 6. The logarithm of the ratio of the diffusional coefficient in a swollen polymer to the diffusional coefficient in bulk liquid (In D / D o) versus the reciprocal value of the swellability (S) calculated on the basis of Eq. (12) (dot line) and Eq, (8) (solid line), a n = 0.00453, p = 1245 kg m 3 (the mean for P4N and P8N from Table 2).

The agreement between the values of the diffusional parameter and the rotational correlation time parameter confirms the proposed dependence of the diffusional coefficients on the swelling volume. Thus, a quantitative evaluations of this dependence can be based on ESR measurements, through the analysis of the correlation times t of suitable paramagnetic spin probes (a T -~ an). If the dependence of "r on the swellability is known, the diffusional coefficient in a swollen polymer can be calculated from the relevant "r value or from the swellability, utilizing Eq. (8). However, it must be pointed out that an accurate and precise measurement of swellability is not so easy (bulk expanded volume cannot be utilized directly). Probably more accurate values are obtained from ISEC measurements. For a comparison of our approach to the determination of diffusional coefficients in a swollen polymer with that of Mackie and Meares, we transformed the Mackie and Meares Eq. (1) by the aid of Eq. (6). After substitution of the polymer fraction Up , and the porosity ~, in terms of the pycnometric density p and the swellability S, the following expression was obtained: In( D/Do)=21n

pS-~l

(

+In 1

1

9S

(12)

Fig. 6 shows a dependence of the term l n ( D / D o) on the reciprocal value of the swellability applying Eq. (12) and Eq. 0 and (8). The shape of the curve given by (12) approaches a straight line up to the value of 1/S equal to 600 k g / m 3, i.e., the swellability S is higher than 0.0017 m3/kg, which is the value for a relatively little swollen polymer. Closeness of both curves gives a possibility to choose one or another relationship. We can speculate that for low-crosslinked materials (higher swellability) the equation

A. Biffis et a l . / Applied Catalysis A: General 142 (1996) 327-346

341

developed by us is slightly better, while for more crosslinked (lower swellability) Meares equation is preferable. This statement is justified by considering the mobility of polymer chains, which is higher in low-crosslinked polymers (collisions between molecules and polymer chains are elastic and the motion of species is not significantly hindered) than in more crosslinked polymers (polymer chains practically do not move and hinder the motion of species [8]). For both theoretical investigations and practical purposes an analysis in terms of an effectiveness factor is useful. The present work started from the observation that metal charged onto a microporous resin represents a very active catalytic species and therefore the overall rate of the process is usually hindered by transport phenomena. A quantification of this behavior is possible having a mathematical description of the process. The effectiveness factor ~q is defined as

[12]: (actual reaction rate in the pellet) (13)

~q = (rate in the pellet at pore-mouth concentration)

For simple reactions, i.e. monomolecular non-reversible or reversible, the effectiveness factor can be calculated analytically using the Thiele modulus [12]. An analytical solution is not available for the bimolecular reaction: A + B products, and other more complicated reactions. Therefore, we calculated the effectiveness factor numerically; the nominator into Eq. (13) was obtained by integration of the reaction rate throughout the radius of the particle. The rate in pellet at pore-mouth concentration of components (denominator) was calculated using actual concentrations in the batch reactor due to the zero resistance of the transport of reaction species between the bulk liquid and surface of the catalyst. Calculations were made for the P4NPd2 catalyst with various particles radiuses

1

\

\ \ \ "'~ 0.75 0.5

S

0.25 0 rp (m) x 105

-~o

Fig. 7. Effectiveness factor ('q) versus radius of the particle (rp) and conversion (y) of cyclohexene. The model No. 6 with parameters given in Table 2. Catalyst P4NPd2 2.3 w / w % Pd, analytical concentration 0.4mM of Pd, 1M cyclohexene in methanol at the start, 1 MPa of hydrogen.

342

A. Biffis et al. /Applied Catalysis A: General 142 (1996) 327-346

0.75

"7"

0.5 0.25 0

105 Fig. 8. The average effectiveness factor (rim) versus the radius of the particle rp and palladium loading in the dry catalyst (xpd). Model No. 6 with parameters given in Table 2. Other properties of the catalyst are the same as for P4NPd2 (Table 1). 1M cyclohexene in methanol at the start, 1.85 kg m -3 of the catalyst in the reaction mixture, 1 MPa of hydrogen.

(Fig. 1) and various pressures of hydrogen from 0.5 MPa up to 1.5 MPa. Calculations showed that the effectiveness factor is practically independent on the pressure of hydrogen, slightly changes during the hydrogenation process, and strongly depends on the particle radius (Fig. 7). Attainment of the kinetic regime with the catalyst P4NPd2 would have be possible only with extremely low values of radius. For the optimization of the metal content in the catalyst, the dependence of the effectiveness factor on the metal loading is of interest. The average value of the effectiveness factor (calculated by integration from the zero conversion up to the value of 99.5%) as a function of particle radius and metal loading is shown in Fig. 8. It is apparent that catalysts charged only with a low content metal (less than 0.5 w / w % ) and particle sizes less than 0.02 mm in radius exhibit the effectiveness factor close to 1. The latter facts are of respect in large-scale industrial applications, in which catalysts with low metal loading a n d / o r a non-uniform distribution of a metal (only near the surface of a bigger catalyst particle) are applied [1]. Of course, one need to take into account that the specific activity with respect to the unit weight of metal depends on the route of the catalyst preparation, i.e., the way of charging metal, activation, local concentration of metal in the resulting catalyst, size of metal crystallites, etc.

5. Conclusions Catalytic tests utilizing the hydrogenation of cyclohexene at room temperature and 0.5-1.5 MPa showed both good molecular accessibility of the investi-

A. Biffis et al./ Applied Catalysis A: General 142 (1996) 327-346

343

gated catalytic materials and the effect of mass transfer phenomena taking part in the process. An isothermal mathematical model considering different size fractions of catalyst particles, liquid-solid mass transfer, internal diffusion and chemical reaction in the particles was developed to describe the kinetics of the catalytic process. The parameters that are necessary for the model can be estimated from a wide set of catalytic tests at various conditions under which, different kinds of regimes can be maintained. A merit of this model is the possibility of involving arbitrary kinetic models, which makes it possible to study also the mechanism of the surface chemical reaction. The validity of the kinetic model and the next plans of experiments can be proposed on the basis of statistical characteristics. The liquid phase hydrogenation of cyclohexene over palladium catalysts at ambient temperature and pressures 0.5-1.5 MPa is supposed to take place with dissociation of dihydrogen. Under these conditions the adsorption terms of all species can be neglected. This model is also suitable for the design of catalytic processes with related materials, after the estimation of relevant parameters. The values of effectiveness factor calculated on the basis of obtained mathematical model have confirmed sufficiency of low loading (less than 0.5 w / w % in the dry catalyst) of the noble metal in catalyst for large scale applications. Simple ESR measurements on suitable "spin probes" confined in swollen microporous polymer supports provide valuable information on the hindrances to the diffusivity within these materials. Through the evaluation of the correlation time of the spin probe, useful relationships between swellability and diffusional coefficient in the swollen polymer can be obtained, under the assumption that the translational diffusion coefficient is inversely proportional to the correlation time.

6. List of symbols a aD ar

aj b bi

B Ab i c Can Cen CH~

Coefficient in the rate Eq. (5), Eq. 0, see Table 2 Diffusional parameter in Eq. (8) (m 3 kg - l ) Rotational correlation time parameter in Eq. (7) (m 3 kg - j ) Specific surface area of particles from fraction j (m: m -3) Coefficient in the rate Eq. (5), Eq. 0, see Table 2 Parameters of a model Vector of the components b z Individual confidence interval of the parameter b z Coefficient in the rate Eq. (5), Eq. 0, see Table 2 Concentration of cyclohexane (kmol m-3) Concentration of cyclohexene (kmol m -3) Concentration of hydrogen (kmol m -3)

A. Biffis et al. / Applied Catalysis A: General 142 (1996) 327-346

344 Cpd

Ci,j Ci,L Ci,Sj

Di

Concentration of palladium (kg m 3) Concentration of component i in particle fraction j (kmol m -3) Concentration of component i in bulk liquid (kmol m -3) Concentration of component i on the surface of particles from fraction j (kmol m -3) Diffusional coefficient of component i in a swollen polymer (m 2 S- l )

Oio

f, f. Fc F(nl,n 2) kLS

kr KH~ nB /'/c nf nr Ylp nmt

r rpj

S SSe t to Up

v. Wi,j Xp d

Y Ymi

nq "rim E

vi

P

Diffusional coefficient of component i in the bulk solution (m 2 s - l ) Volume fraction j of particles Hydrogen kinetic term (m 3 kg ' s - l ) Value for the statistical F-test, see Table 2 oL-percentage of the F-distribution with n I and n 2 degrees of freedom, respectively Liquid-solid mass transfer coefficient ( m / s ) Rate constant (m 6 kmol i kg-1 s - l ) for models l, 2, 3, 7, 8 and (m 45 kmol- 05 kg- l s- l) for models 4, 5, 6 Adsorption constant of hydrogen (m 3 kmol- ~) Number of parameters bg Number of components Number of fractions of particles Number of runs Number of points in the run Total number of points with respect to statistical weights on runs Radial coordinate (m) Radius of particles from fraction j (m) Swelling volume (m 3 kg-1) Sum of the squared residuals (squared errors in the minimum) Time (s) Initial time for the solution of differential equations (s) Volume fraction of the polymer chains in the swollen polymer Volume of bulk liquid (m 3) Volume of swollen catalyst (m 3) Statistical weight on the point " i " in the run " j " (1 or 2) Mass fraction of palladium in a resin of the dry state Rate of chemical reaction (kmol m-3 s 1)) Conversion of cyclohexene (%) Average conversion of cyclohexene for the conditions of the run " i " Effectiveness factor Average effectiveness factor Porosity of the catalyst Stoichiometric coefficient for the component i Pycnometric density (kg m -3)

A. Biffis et al. /Applied Catalysis A: General 142 (1996) 327-346

q'i

tio

345

Rotational correlation time of the probe inside a polymer (ps) Rotational correlation time of the probe in a bulk liquid (ps)

Acknowledgements This work was partially supported by Progetto Finalizzato Chimica Fine ll (CNR Rome), by MURST 40% (Rome), and by the project Nove Syntezy Katalytickymi Postupmi financed by the Slovak Ministry of Education. A.B. wishes to thank the Ing. Aldo Gini Foundation, Padova, for a scholarship.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

R. Wagner and P.M. Lange, Erd61, Erdgas, Kohle, 105 (1989) 414. H.J. Paneman and A.C.M. Beenackers, Ind. Eng. Chem. Res., 31 (1992) 1425. V.I. Smeshanjuk, Nefteldaimija, 35 (1995) 127. G.B. Fields and R.L. Noble, Int. J. Peptide Prot. Res., 35 (1990) 161. A. Guyot, in D.C. Sherrington and P. Hodge (Editors), Syntheses and Separation Using Functional Polymers, Wiley, New York, 1988, p. 1. A. Guyot, Pure Appl. Chem., 60 (1988) 365. B.C. Gates, Catalytic Chemistry, Wiley, New York, 1992. J.S. Mackie and P. Meares, Proc. Roy. Soc. London A, 232 (1955) 498. P. Meares, in J. Crank and G.S. Park (Editors), Diffusion in Polymers, Academic Press, New York, 1968, p. 373. A.H. Muhr and J.M.V. Blanshard, Polymer, 23 (1982) 1012. J.G. Ekerdt, in W.T. Ford (Editor), Polymeric Reagents and Catalysts (ACS Symposium Series, Vol. 0097-6156/86/0308), ACS, Washington DC, 1986, p. 68. L.K. Doraiswamy and M.M. Sharma, Heterogeneous Reactions: Analysis, Examples and Reactor Design, Wiley, New York, 1984. A. Biffis, B. Corain, M. Zecca, C. Corvaja and K. Jerabek, J. Am. Chem. Soc., 117 (1995) 1603. A. Biffis, B. Corain, Z. Cvengrosova, M. Hronec, K. Jerfibek and M. Krgdik, Appl. Catal. A. 124 (1995) 355. M. Boudart, AIChE J., 18 (1972) 465. Ch.N. Satterfield, Heterogeneous Catalysis in Practice, McGraw-Hill, New York, 1980. J. Hanika, K. Sporka, V. Ruzicka and J. Deml, Coll. Czech. Chem. Commun., 37 (1972) 951. R.P. Chambers and M.Boudart, J. Catal., 5 (1966) 517. D.R. Stull, E.F. Westrum, Jr. and G.C. Sinke, The Chemical Thermodynamics of Organic Compunds, Wiley, New York, 1969. K. Radhakrishnan, P.A. Ramachandran, P.H. Brahme and R.V. Chaudhari, J. Chem. Eng. Data, 28 (1983) 1. O.A. Houghen and K.M. Watson, Chemical Process Principles Ii1, Kinetics and Catalysis, Wiley, New York, 1947. R.L. Burwell Jr., in J.R. Anderson and M. Boudart (Editors), Catalysis-- Science and Technology. Vol. 9, Springer, Berlin, 1991, p. 1. G.F. Froment and L.H. Hosten, in J.R. Anderson and M. Boudart (Editors), Catalysis-- Science and Technology, Vol. 2, Akademie Verlag, Berlin, 1983, p. 97. M. Hronec and J. Ilavsky, Chem. Papers, 39 (1985) 705. J. Villadsen and M.J. Michelsen, Solution of Differential Equation Models by Polynomial Approximation, Prentice Hall, Englewood Cliffs, NJ, 1978.

346

A. Biffis et al. /Applied Catalysis A: General 142 (1996) 327-346

[26] A.L. Buchachenko, A.L. Kovarskii and A.M. Vasserman, in Z.A. Rogovin (Editor), Advances in Polymer Science, Wiley, New York, 1974, p. 26. [27] A.L. Kovarskii, A.M. Wasserman and A.L. Buchachenko, J. Magn. Reson., 7 (1972) 225. [28] J.P. Soerensen, Simulation, Regression, and Control of Chemical Reactors by Collocation Techniques, Polyteknisk Forlag, Lyngby, 1982. [29] S.S. Ashour and O.T. Hanna, Comput. Chem. Eng., 14 (1990) 267. [30] M. Kralik, M. Hronec, S. Lora, G. Palma, M. Zecca, A. Biffis and B. Corain, J. Mol. Catal., 101 (1995) 143. [31] D.C. Montgomery and G.C. Runger, Applied Statistics and Probability for Engineers, Wiley, New York, 1994.