Applied Catalysis, 18 (1985) 87--103 87 Elsevier Science Publishers B.V., Amsterdam -- Pr inted in The Netherlands

A KINETIC MODEL OF STEADY STATE ETHYLENE EPOXIDATION OVER A SUPPORTED SILVER

CATALYST

L. PETROV, A. ELIYAS and D. SHOPOV

Ins t i t u t e of Kinet ics and Catalysis, Bulgarian Academy of Sciences, Sofia 1113,

Str. Acad. G. Bonchev bi .11, Bulgaria.

(Received 12 December 1984, accepted 16 Apr i l 1985)

ABSTRACT

A k inet ic study of select ive ethylene oxidat ion to ethylene oxide over a s i l ve r cata lyst has been carr ied out by the c i r cu la t i on f low method. The s i l ve r was promoted by a Ca addi t ive and was supported on alumina. The experiments were con- ducted under steady state condit ions in the temperature in terva l 210 - 292°C and at atmospheric pressure. As a resu l t of th i s k ine t ic study two rate equations, fo r the par t ia l and fo r the complete ox idat ion reactions, are proposed. A reaction scheme is put forward, according to which adsorbed molecular oxygen produces ethylene oxide, whereas the atomic oxygen is responsible for the complete oxidat ion react ion. The empirical k inet ic model corresponds to a Rideal-Eley type of mecha- nism. Se lec t i v i t y decreased with temperature increase and with decrease of the oxygen content in the feedstock.

INTRODUCTION

Since the pioneering work of Lefort [ I ] in 1931 and the f i r s t indus t r ia l rea l i za t ion

of d i rec t c a t a l y t i c ethylene epoxidation in 1937 a great number of invest igators

have studied the k inet ics of th is process in order to elucidate i t s mechanism.

A wide range of physical methods has also been applied to gain knowledge of the

intermediates ex is t ing on the s i l ve r surface under the reaction condi t ions.

The existence of adsorbed atomic and molecular oxygen on the s i l ve r surface

seems to have found almost general acceptance. However, the opinions of the authors

d i f f e r as far as the role of these two species is concerned. Three working hypo-

theses have been put forward up to now:

ZO 2 ÷ C2H40 ~ C 2 H 4 0 Z O , ~ C2H40 ZO 2~,,)~

ZO ~ CO 2 + H20 CO 2 + H20 CO 2 + H20

Scheme I Scheme I I Scheme I I I

Most invest igators favour reaction scheme I , according to which adsorbed molecular

oxygen produces ethylene oxide, whereas the atomic oxygen is responsible for the

complete oxidat ion reaction [2-7] . Other authors argue in favour of scheme I I .

0 1 6 6 - 9 8 3 4 / 8 5 / $ 0 3 . 3 0 © 1985 Elsevier Science Publishers B.V.

88

They consider adsorbed atomic oxygen as a common precursor fo r both C2H40 and for

CO 2 ÷ H20 [8-13]. A number of studies suggests a scheme in which the molecular

oxygen species reacts with ethylene to give both epoxide and carbon dioxide -

scheme I I I [14-18,39].

A Rideal-Eley mechanism is proposed by the major i ty of the authors. They conclud~

that gaseous or weakly adsorbed ethylene in teracts with chemisorbed oxygen [2-4,6,

8,10-15,17,18]. Other authors, contemplating the data on the dependence of reaction

rate on C2H 4 par t ia l pressure, which is not l i near over the en t i re range, propose

a Langmuir-Hinshelwood type of mechanism, according to which both ethylene and

oxygen are chemisorbed and in teract in the adsorbed state on the Ag surface [7,9,

19-21]. There is also spectroscopic evidence suggesting an adsorbed ethylene in te r -

mediate [9,16].

The prevai l ing number of studies support a single s i te mechanism. In the case

of a Langmuir-Hinshelwood mechanism, a competit ive adsorption of oxygen and ethylen~

on the same type of act ive si tes is assumed. The nature of the act ive s i te is Ag20,

according to [4,14,15,17] or a single s i l v e r surface atom [22]. A dual s i te mechani!

is proposed in [19,20,23,24]. According to t he i r concept, oxygen adsorbs on com-

p le te ly reduced s i l v e r atoms, while ethylene adsorption requires a pos i t i ve l y

charged s i l ve r atom.

Twigg concluded in ear ly work [8] that oxygen adsorption is the slowest and

therefore the ra te -con t ro l l i ng step. However, in more recent studies, an agreement

exists between the invest igators that the rate-determining step is a surface

reaction. This i s , in fac t , the only point in the mechanism that has found general

acceptance.

A para l le l -consecut ive scheme dominates over the para l le l scheme of the reaction

which means that fu r the r oxidat ion of C2H40 is considered h igh ly probable by most

of the authors.

The object of the present paper was to study the k inet ics of ethylene oxidat ion

over a supported s i l v e r cata lys t and to propose a reaction scheme and a k inet ic

model of the process.

EXPERIMENTAL

Apparatus

The reaction rates were measured by a glass c i r cu la t i on f low system at atmos-

pheric pressure. The block diagram of the apparatus is shown in Figure I . The

pressure regulators (P) f i x the same pressure (1.5 atm) for the three gases fed

in to the system - C2H 4, 02 and Ar. The gases are dried in the f i l t e r s (F), con-

ta in ing molecular sieve 5A. The Matheson mul t ip le mass f low con t r o l l e r , model 8249

(M), controls the f low rates (the precision is ±1% of the set f low rate) . The

i n i t i a l gas mixture flows through the six-way sampling valve (C) and then i t is

fed into the reactor (R). The f ixed bed reactor with preheater contains 25 g of

cata lys t and i t is placed in an oven (0). The e lec t ron ic thermoregulator (T)

89

FIGURE I C i rcu la t ion f low system. P: pressure regulator , F: molecular sieve f i l t e r ,

M: mass flow con t ro l l e r , C: six-way valve, $I: 0.25 ml sampling loop, $ 2 : 2 ml

sampling loop, R: f ixed bed reactor, O: reactor oven, T:thermoregulator, PP:

c i r cu la t ion pump, Q:Porapack Q column, DC:thermal conduct iv i ty detector, MP:

microprocessor system, T1:thermostat, T2: column thermostat, T3: detector thermostat.

maintains the desired oven temperature constant: the deviat ion does not exceed ±I°C.

The electromagnetic four valve piston pump (PP) provides fo r the intensive c i rcu-

la t ion of the react ion mixture: the rate is about 700 - 800 1 h - I .

The converted gas mixture flows out of the c i r cu la t i on cycle and passes through

the second s ix way sampling valve (C) so that a sample is taken fo r analysis of

the ou t le t gas composition. The c i r cu la t i on cycle and the valve are placed in the

thermostat (TI) at 110°C to avoid water vapour condensation.

Gas chromatographic analysis

The analysis was carried out by means of a Tsvet 110 gas chromatograph, equipped

with a thermal conduct iv i ty detector (DC) and a 2 m Porapack Q column (Q). Column

temperature was 115°C and the car r ie r gas was Ar (f low rate 30 ml min-1). Detector

response was spec ia l l y cal ibrated fo r each of the reagents .... C2H 4, 02 , C02, H20

and C2H40. The volumes of the sampling loops are 0.25 ml fo r the i n l e t gas sample

($I) and 2 ml fo r the ou t le t gas sample ($2). The microprocessor system ISOTCHROM

(MP) automat ical ly processes the data from the GC analysis.

Conditions

The experiments were carried out at atmospheric pressure and at four d i f f e ren t

temperatures of the cata lys t bed - 2 i0, 240, 264 and 292°C. At each temperature

90

four series of experiments were conducted wi th four d i f f e ren t feedstock compositions:

I ) 50.0% 02 , 25.0% C2H 4, 25.0% Ar

2) 33.3% 02 , 33.3% C2H 4, 33.3% Ar

3) 25.0% 02 , 50.0% C2H 4, 25.0% Ar

4) 20.0% 02 , 60.0% C2H 4, 20.0% Ar

Within each series the cata lys t bed temperature and the feedstock composition

were kept constant and only the contact time was varied. The contact time was

defined by W/F e, where W is the cata lyst mass in grams and F e is the ethylene f low

rate in moles h - I and i t varied from 119 to 1905 g-cat h mole-1. The degree of

etht lene conversion varied from 0.5% to 70.0%.

Catalyst

The cata lyst used in th is k inet ic study of ethylene epoxidation was synthesized

in our laboratory. I t has the fo l lowing charac ter is t i cs :

- 20% s i l ve r supported on alumina, promoted by a Ca addi t ive

- spheroidal pe l l e t s , 6 mm in diameter

spec i f ic surface area, 0.14 m 2 g-cat - I , determined by the BET method (adsorption

of Kr)

to ta l pore volume, 0.06 cm 3 g-cat - I

- prevai l ing pore radius, 200

Steady state

About 30 minutes a f te r the beginning of the operation the system comes to a

steady state. This was established by the s t a t i s t i c a l method of Wald-Wolfowitz [27].

That the reaction was proceeding in the k ine t i c region was checked by the

Corrigan c r i t e r i on [26].

Chemicals

Ethylene (grade Purum), produced by Fluka, with pu r i t y >98%, containing 1.2%

ethane, 0.33% ni t rogen, 0.21% methane, 0.06% carbon dioxide and traces of carbon

monoxide, was used.

Technical grade oxygen and high pur i t y argon (99.9%) were u t i l i z e d .

PROCESSING OF EXPERIMENTAL DATA

The experimental data were processed by means of special programs in BASIC on

a 9845 B Hewlet t - Packard computer. These programs perform the fo l lowing calculation~

CHROM Program fo r chromatogram processing

- calculates the pa r t i a l pressures of a l l the reactants and products ( in atm) both

in the feedstock and in the converted gas mixture, f lowing out of the c i r cu la t ion

cycle from the chromatographicall determined (ISOTCHROM) compositions.

- computes the material balance of each experiment wi th respect to carbon,

91

hydrogen and oxygen

- f igures out the degree of conversion o f a l l the reactants AX i in %

- ca lcu lates the s e l e c t i v i t y S fo r ethylene oxide as the f r a c t i o n of ethylene

converted in the epoxidat ion reac t ion in the to ta l amount of ethylene converted

- computes the rates of consumption or accumulation of the reagents W i ( rates fo r

substances):

W i = AXi.Fi/W ( I )

where AX i is the degree of conversion o f the reagent i . Here i = I means ethy lene,

i = 2 is oxygen, i = 3 is ethylene ox ide , i = 4 is carbon d iox ide and i = 5 is

water. When we ca lcu la te the rate f o r oxygen F i is the oxygen f low rate in moles h - I ,

whi le in a l l o ther cases F i is the ethylene f low rate. W i is ca lcu la ted in moles h - I g-cat - I .

LINF Program

In our reac t ion system there are on ly two l i n e a r l y independent react ion routes:

I) C2H 4 + ½02 = C2H40 (2)

I I ) C2H 4 + 302 = 2C02 + 2H20 (3)

The program computes the rates along independent routes - R(1)of the p a r t i a l

ox ida t ion and R(2) of the complete ox ida t i on . Rj are ca lcu la ted on the basis of

the rates f o r reagents W i , a l ready determined by CHROM. The re l a t i onsh ip between

Rj and W i is given by the expression:

n

Z Ci j .R j = W i (4) j=1

where Ci j are the elements of the transposed s to ich iomet r i c mat r i x , i = 1,2 . . . . .

m is the number o f the reagent and j = 1,2 . . . . . n is the number o f the independent

route; n and m are re la ted by the f o l l o w i n g equa l i t y :

n = m - q (5)

where q is the rank of the atomic mat r i x . Applying (4) and (5) f o r the epoxidat ion

of ethylene we obta in :

W ° = -0.5 R(|) - 3 R(2)

W e = - R(1) - R(2)

Weo = R(1)

W = 2 R(2) C

W = 2 R(2) W

(6)

g2

where W o is the rate for oxygen, W e is the rate for ethylene, Weo is the rate for

ethylene oxide, W c is the rate for carbon dioxide and W w is the rate for water.

The system (6) consists of f i ve equations with two unknowns, R(1) and R(2)

(W i are determined experimental ly) , so i t is preset. Due to the errors in the

determination of W i the system becomes inconsistent. For this reason we have to

f ind i ts approximate solut ion. Overdetermined systems of l inear equations may be

solved by means of the Chebyshev approximation. Mathematically the problem is

reduced to f inding such a vector ~(RI,R 2 . . . . . R n) for which the minimum of the

maximum deviation is achieved, i . e . the problem is equivalent to the l inear pro-

gramming problem to f ind min ~ with the l im i ta t ions [28-30,32].

I ! i C i j Rj - Wi < ~ (7)

I t has been shown that a re la t i ve s t a b i l i t y of the solutions exists at small

experimental errors of the substance formation rates [31]. The appl icat ion of the

standard programs for l i near programming requires observance of the Haar condit ion,

which means that a l l the main minors of the stoichiometr ic matrix should necessarily

be d i f fe ren t from zero. This condit ion, however, is not always va l id and that is

why we used the algorithm of Abdelmalek [38], which also holds good for the cases

when the Haar condit ion is not observed. The experiments with greater error give

nonfeasible solutions and thus an addi t ional check on the qua l i t y of the experi-

ments is carried out.

In [40] two of the authors of the present paper have studied the problem of the

app l i cab i l i t y of d i f f e ren t computing procedures for the determination of the

reaction rates along independent routes. I t has been shown that in the cases when

the law of error d i s t r i bu t i on is not known the best resul t is achieved by using

nonlinear programming methods with a minimization c r i t e r ion :

W calc _ wexp E = minmax i l (8)

wexp 1

When the experimental errors are small the l inear and nonlinear programming give

the same result . That is why we used l inear programming as the faster calculat ing

procedure,

NEM Program

By means of the NEM program a kinet ic equation best f i t t i n g the experimental

results for each route is selected and the values of the preexponents and the

act ivat ion energies for each k inet ic constant as well as the reaction orders are

determined. The program makes use of the par t ia l pressures (determined by CHROM)

and of the rates along routes (determined by LINF). I t is based on a nonlinear

programming method and in par t icu lar the Nelder-Mead algorithm [33]. In the

93

calculat ions the fo l lowing minimization c r i t e r i a were used:

N (RCalc Rexp)2 El = Z .. - -.

i=I I j 1J

corresponding to a normal error d i s t r i bu t i on and:

(9)

N (RCalc exp 2 Rexp) 2. (10) E2 = Z I j - Ri~ j ) / ( i j

i= I

corresponding to a normal re la t i ve er ror d i s t r i bu t i on . Here N is the to ta l number

of experiments, taking into account d i f f e ren t temperatures; j = 1,2 is the route

number; R~ Ic is the theoret ical rate along route, calculated on the basis of the ]J

k inet ic model" R~ p is the experimental rate along route, i . e . the one already ' l J

determined by LINFo

The NEM program calculates also the model deviat ion for each tested equation

by the formula:

(11) N

D : I c - Rexpi.1OO/R xP).I/, I j

i=I J J

The k inet ic constants were also calculated by the Marquardt procedure [41] . The

values were the same as those calculated by NEM. The confidence in terva ls of the

estimates were computed only by the Marquardt procedure.

RESULTS

Figure 2 shows the concentrations of a l l the reactants as a funct ion of the

contact time fo r one of the experimental series: the one at 264°C and feedstock

composition C2H4:O2:Ar = 1:1:1. I t can be seen from the f igure that the product

concentrations gradual ly increase wi th the increase of the contact time, whi le the

reactant concentrations decrease with the contact time. Oxygen concentration

decrease is more rapid than that of ethylene, as could be expected from the s t o i -

chiometry of the react ion.

The dependence of the rates along routes R(1) and R(2) on the ethylene par t ia l

pressure fo r the series: (240°C, C2H4:O2:Ar = 1:1:1) is shown in Figure 3. Both

rates increase wi th the increase of ethylene par t ia l pressure Pe at the e x i t of

the reactor. At one and the same ethylene content in the feedstock the smaller

the contact time is the greater is the ethylene par t ia l pressure at the reactor

ex i t . At th is comparatively low temperature (240°C) the epoxidation rate (R(1)

is higher than that of complete ox idat ion R(2). But at the higher temperatures

( for example 292°C, Figure 4) the rate of complete combustion is already much

higher than the epoxidation rate. This means that the ac t i va t ion energy of the

complete ox idat ion reaction is higher than that of the epoxidat ion and that is

why the combustion rate r ises more speedi ly wi th the temperature.

Se lec t i v i t y decreases with the increase of temperature (Figure 5) as could be

94

Io 60

O ,,.-------.~ c02' 'H20

"ZOO 300 500 700 900 1100 CONTACT rlME W / Fo(g-c~.hP.mo/e -t)

FIGURE 2 Concentrations of the reagents versus contact time at 264°C and feedstock

composition: 33.3% C2H 4, 33.3% 02 , 33,3% Ar.

6- .

X ~ 4 " 9")

0 I I I I I I I l : ~, ,59 41 4,5 4,5 4 7 4 9 ^

C2H 4 PARTIAL PRES.SURE, P E × IO-ZATM

FIGURE 3 Computed rates along routes versus ethylene partial pressure at 240°C

and feedstock composition: 50.0% C2H4, 25.0% 02, 25.0% Ar.

expected from the comparison of figures 3 and 4. Another factor which turned out

to exert influence on the select iv i ty is the feedstock composition (Figure 6):

this result is interesting and somewhat unexpected. As can be seen from the figure,

the select ivi ty drops with the decrease of oxygen content in the feedstock. A

mathematical expression for the select iv i ty that reflects both factors (see S m

on Figures 5 and 6) is derived from our kinetic equations and wi l l be discussed

later. Figures 5 and 6 i l lus t ra te the model deviation graphically.

95

%j f ~22t

0

R(2)

1 2! 0 J2 '2'4 '26 '2~ Jo\ C21"-I 4 PARTIAL PRE,S,SURE, PE X'IO-WATM

FIGURE 4 Computed rates along routes versus ethylene part ial pressure at 292°C

and feedstock composition: 33.3% C2H 4, 33.3% 02 , 33.3% Ar.

,o6o

( J ~ I I I I | I I I ! - - ~

200 220 240 260 280 300 T E M P E R A T U R E ~ P C

FIGURE 5 Select iv i ty S versus temperature at feedstock composition: 50.0% C2H 4,

25.0% 02 , 25.0% Ar ( 0 - model se lec t i v i t y Sm, 0 - experimental se lec t iv i ty Se).

The degree of conversion of ethylene AX e does not affect the select ivi ty con-

siderably as follows from Figure 7. This fact may be considered as evidence in

favour of the parallel scheme of reaction, rather than the parallel-consecutive

scheme.

96

80

°"~ 6 0

2of

' ~ ' ~ ' ' 4 . . . . 5 FEED RATIO C2H 4 : 0 2

FIGURE 6 Select iv i ty S versus feedstock composition at 292°C ( 0 - model selec-

t i v i t y Sm, 0 - experimental se lect iv i ty Se).

~'lO- I I I I I I I I 1 - ' -

0 0 qO 30 50 70 90 DEGREE OF CQIVVERSION

z~xc, , . . %

FIGURE 7 Select iv i ty S versus degree of conversion of ethylene ~X e at 264°C and

feedstock compositions:/~60% C2H 4, 20% 02 , 20% Ar ;033.3% C2H 4, 33.3% 02 , 33.3%

Ar ;025% C2H 4, 50% 02 , 25.0% Ar.

97

Kinet ic analys is

Various publ ished k ine t i c equations f o r ethylene epox ida t ion , corresponding to

a Rideal-Eley or a Langmuir-Hinshelwood type of mechanism, and also other equations

possible from a physical po in t of v iew, were tested to f i t our experimental resu l t s .

We d iscr iminated between these r i va l models not only on the basis of the min imizat ion

c r i t e r i o n and the model dev ia t ion . We re jected models wi th implaus ib le ac t i va t i on

energy values (below 5 kcal mole - I or wel l over 60 kcal mole - I ) and also models

wi th systematic e r r o r of the model rates along routes. The ra te equations f i t t i n g

our experimental data best ( i . e . , g iv ing values of the model rates along routes

nearest to those of the experimental rates) are the f o l l ow ing :

KI.Po.P e R(1) = (12)

I + K3.Po + K4.Pe

K2.P .P o e

R(2) = (13) I + K3.P o + K4.P e

where P is the oxygen p a r t i a l pressure and P is the ethylene p a r t i a l pressure. o e

These equations have the same denominator: a s im i l a r r esu l t has been obtained by

many other authors [14,18,22,34] . This fac t means that the mechanisms of both

react ions are c lose ly re la ted [35]. The average model dev ia t i on of our k ine t i c

equations is about 20%. The values of the preexponents and of the ac t i va t i on energies

(ca lcu lated in conformi ty wi th the Arrhenius law) as wel l as the values o f the

corresponding k i n e t i c constants fo r a l l react ion temperatures are reported in

Table I . The quan t i t i es are measured in the fo l l ow ing un i t s : [P ] = [Pe ] = atm,

[R(1) ] = [R(2) ] = mole h - I g-cat - I , [K I ] = [K2] = mole h - I g-c~t - I atm -2, [K3] =

[K4] = atm - I .

I t should be noted that the denominator does not r e f l e c t i n h i b i t i o n by the

react ion products. In fac t the i n h i b i t i o n of both react ions by the products has

been establ ished by many inves t iga to rs [3 ,8 ,21,35,36] . Nevertheless, i t has not

been considered in some other rate equations [18,34] . Probably, under cer ta in

react ion condi t ions or in the presence o f cer ta in add i t i ves to the ca ta l ys t , i t

may be compensated and may not show i t s e l f (as in our case).

S e l e c t i v i t y equat ion

The s e l e c t i v i t y of the react ion can be expressed as fo l l ows :

S - R(1) (14) R(1) + R(2)

A f te r subs t i t u t i ng R(1) and R(2) wi th our k i ne t i c equat ions, we obta in :

98

TABLE I

Values of preexponents, act ivat ion energies and k inet ic constants

Preexponent Ko Ea/cal mole -I 210°C 240°C 264°C 292°C

K1 13.53 8087 0.00297 0.00486 0.00693 0.0101

K2 2253.00 13559 0.00166 0.00378 0.00685 0.0128

K3 0.0004507 7378 0.980 0.625 0.453 0.321

K4 0.0051330 7897 19.2 11.8 8.38 5.81

TABLE 2

90% Confidence in te rva ls for preexponents and act ivat ion energies

Preexponent Ko

Lower l im i t Upper l im i t

Ea/cal mole - I

Lower l i m i t Upper l i m i t

K1 12.98 14.08 7861 8313

K2 2181.00 2315.00 13125 13993

K3 0.0004394 0.000462 7194 7562

K4 0.005011 0.005255 7621 8173

S = KI___1___ (15) KI + K2

According to this expression, select iv i ty depends only on the temperature, as KI

and K2 are functions only of the temperature. The values of the select iv i ty

according to (15) for the dif ferent reaction temperatures are as follows: 64.1%

(210°C), 56.2% (240°C), 50.3% (264°C) and 44.1% (292°C). R(1) and R(2) are the

approximate solution of the system (6), so i t is to be expected that the values

of the select iv i ty , calculated direct ly from the experimental data, w i l l be some-

what different. In fact the select iv i t ies (16-18), although not quite dif ferent

from those of (15) show dependence also on the feedstock composition. So we were

faced with the problem to derive from our kinetic model an expression describing

the dependence of select iv i ty on both factors - temperature and feedstock compo-

si t ion. Several formulae for the calculation of select iv i ty from experimental data

were used (16-18).

aCeo.lO0 $I - (16)

AC e

ACeo.lO0 $2 = (17)

ACeo + 0.5AC c

99

6ACeo. 100 $3 - (18)

5ACeo + 2AC o

where AC i is the d i f fe rence between the concentrat ions of the corresponding reagent

i in the converted gas mixture and in the feedstock. The index e denotes ethy lene,

eo is ethylene ox ide, o means oxygen and c is carbon d iox ide .

We can express the degree of conversion AX i of each substance i from ( I ) . For

example:

W .W eo (19)

AXe° = f e

Then fo r AC we obta in : eo

ACeo = AXeo.100 = Weo.W. IOO/F e (20)

In the same way we can der ive expressions fo r each AC i . I f we subs t i tu te the

corresponding expressions fo r ACeo and AC ° in (18) we obta in :

6W S3 = eo (21)

5Weo + 2Wo.(Fe/F o)

We can use (6) to subs t i tu te the absolute values of W o and Weo with R(1) and

R(2). Then we use (12) and (13) to subs t i tu te R(1) and R(2). In the end we have:

$3 = I (22) 0.83 + (0.17 + K2/KI).Fe/F o

This is our s e l e c t i v i t y equat ion, der ived from our k i n e t i c model, which describes

both factors in f luenc ing the s e l e c t i v i t y , the temperature (through the K2/KI term)

and the feedstock composit ion (through the Fe/F ° term). In Figures 5 and 6, S e is

the experimental s e l e c t i v i t y and S m is the model s e l e c t i v i t y , ca lcu la ted from (22).

We can judge the accuracy and adequacy o f our model from them.

Mechanism

Now we can make use of our k i ne t i c model (12-13) to draw some conclusions about

the mechanism of both react ions. Temkin [37] has deduced a general equation fo r

the rate of a steady state react ion accounting fo r the reac t ion proceeding along

d i f f e r e n t pathways:

i00

Z r(N) n

~Sl (N) r (N) r o (N) + -SlaS2 + , , . + r-s1 - s 2 " " s m

r s l r r rs I rs I rs 2 s2" ' " s m

r r . . . r -s I -s 2 -s m

= I - (23) r r . . . r s I s 2 s m

where s I , s~ s are the step numbers, r s_ and r_ s are the rates of the correspon- z " " m m m (N)

ding step in the forward and reverse d i r e c t i o n , ~s- is the s to ich iomet r i c

number of the s m step p a r t i c i p a t i n g in the route N andmr £NJ' ' is the ra te along

route N.

This equation a l lows us to der ive k i n e t i c models d i r e c t l y from the presumed

mechanism. The unique mechanism, which leads to our k ine t i c model, is represented

by the react ion scheme (24).

Steps 2) and 4) are i r r e v e r s i b l e . Step 4) obviously combines several fas t

consecutive steps. The mechanism assumes both nondissoc ia t ive and d i ssoc ia t i ve

adsorpt ion of oxygen on the s i l v e r surface, r esu l t i ng in adsorbed molecular as

wel l as atomic oxygen. Adsorbed molecular oxygen produces ethylene ox ide, whereas

the atomic oxygen is responsible fo r the complete ox ida t ion reac t ion . I t is im-

possib le to make an assumption about the nature of the ac t ive s i t e Z only on the

basis of our k i n e t i c study.

1) Z + 02 ÷ ÷ ZO 2

2) ZO 2 + C2H 4 ÷ ZO + C2H40

3) 2 ZO ÷ ÷ 2 Z + 02

4) C2H 4 + 6 ZO ÷ 2 CO 2 + 2 H20 + 6Z

I I I

2 0

2 0

1 - 3

0 I

(24)

I) 2 C2H 4 + 02 = 2 C2H40

I I ) C2H 4 + 3 02 = 2C02 + 2 H20

Temkin assumes tha t Z is a molecule of the surface compound AgO 2. The ZO and ZO 2

are also surface ox ides, respect ive ly Ag202 and Ag203 [14,15] . In th i s way our

k i ne t i c study supports a s ing le s i te R idea l -E ley type o f mechanism wi th the

ethylene molecule p a r t i c i p a t i n g from the gas phase.

Any o f the fou r steps (24) may be considered as the f i r s t one in the sequence.

In th is way , beginning each time wi th a d i f f e r e n t step, we obtained four d i f f e r e n t

equations from equat ion (23). Now we can subs t i tu te the step rates rsm with the

corresponding expressions from the Law o f Mass Act ion. We have:

rs l = k1. [Z] .P o and r_s I = k~1.[Z02]

rs2 = k2.[ZO2].P e and r_s 2 = 0 (25)

i01

= = rs3 k3.[ZO]2 and r_s 3 k_3. [Z ]2 .p °

rs4 k4.[ZO]~P e and r s 4 = 0

Thus we obtained a system of four equat ions wi th f i v e unknowns - the surface

concentrat ions [Z ] , [ZO] and [ZO 2] plus R(1) and R(2). We need a f i f t h equation

to solve the system. I f [Z ] , [ZO] and [Z02] are measured in mole f r ac t i ons then:

[Z] + [ZO] + [Z02] = I (26)

In t h i s way we have the fo l l ow ing system:

R(1) . (2.k2.P e + 2 .k_ I )

k l .k2.Po.P e = [ Z ]

2.R(1)/k2.P e = [Z02]

R(1).k4.Pe.[ZO]6 + R(2).k_3.Po.[Z]2 - 3.R(2).k4.Pe.[ZO]6

!R 2L 1,16 k4" Pe~

= [ z o ]

k3.k4.P e = [ZO] 8 (27)

[ ~ + [ZO] + [Z02] = I

We can solve the system in t roduc ing some approximations. The values of R(1)

and R(2) are of the order of n x 10 -5 mole h - I g-cat - I . Therefore R. 2 are of the i0-I0 1

we can assume that Ri2 = O. The same holds t rue , of course, fo r order of and

Ri3, Ri4 etc. I t is apparent from (26) t ha t , f o r ins tance, [ZO] < I so the terms

we can assume in the t h i r d equation of the system (27) the term [ZO] 8 = O.

F i na l l y we obta in :

a,P .P O,33a.Po.Pe R(1) = o e and R(2) = (28)

I + b.P ° + c.P e I + b.P ° + c.P e

where

k1"k 2 k l . k 2 + 36 .k l . k 4 k 2 a = - - b = and c - (29)

12.k_ I 36.k 1.k 4 k_1

102

Unfortunately, the expressions (29) do not offer the possib i l i ty of determining

the rate constants of the steps k I , k_1, k 2 and k 4. The equations (29) i l lus t ra te

the complex nature of our kinetic constants in (12-13). The ratio KI/K2 of the

constants in the numerators of our kinetic equations (12-13) is not equal to 3,

as follows from (28), in the whole experimental temperature interval . Our kinetic

constants KI and K2 change independently from each other with the change in tem-

perature. Nevertheless, we think that our kinetic equations support the mechanism

(24) because as a result of (28) a rea l is t ic value for the se lect iv i ty , 75%, is

obtained, which is achieved industr ia l ly .

CONCLUSIONS

As a result of a steady-state kinetic study of ethylene epoxidation over a

supported si lver catalyst at atmospheric pressure and in the temperature interval

210 - 292°C, a kinetic model of the process is proposed. The model consists of

two equations for the partial and for the complete oxidation reactions. The

equations have the same denominator due to the closely related mechanisms of the

two reactions. No inhib i t ion by products is reflected in these equations: probably

under these reaction conditions i t is compensated in some way. The equations

correspond to a single site Rideal-Eley type of mechanism with the ethylene mole-

cule participating from the gas phase. Adsorbed molecular oxygen interacts with

ethylene to produce ethylene oxide, while the atomic oxygen is the precursor of

carbon dioxide and water. Selectivity depends on two factors, temperature and

feedstock composition, and this is described by a model select iv i ty equation,

derived from the kinetic model.

REFERENCES

I T.E. Lefort , French patent, 729 952 (1931). 2 P.A. K i l t y and W.M.H. Sachtler, Catal. Rev. Sci. Eng., 10 (1974) I . 3 A. Ayame, H. Kano, T. Kanazuka and H. Baba, Bul l . Japan Petrol. Ins t . , 15

(1973) 150. 4 Sh.L. Guseinov, I.T. Frolkina, L.A. Vasilevich, A.K. Avetisov, A.I. Gelbshtein,

Kinet. Catal., 18 (1977) 1455. 5 D.W. Park, S. Ghazali and G. Gau, Appl. Catal., 6 (1983) 175. 6 M. Kobayashi, Chem. Eng. Sci., 37 (1982) 403. 7 S. Kagawa, M. lwamoto and T. Seiyama, Chemtech, 11 (1981) 426. 8 G.H. Twigg, Proc. Roy. Soc. London, 188A (1946) 92. 9 E.L. Force and A.T. Bell, J. Catal., 40 (1975) 356.

10 K. Miyahara and S. Yokoyama, J. Res. Inst. Catal., Hokkaido Univ., 19 (1972) 127 11 A.V. Khasin, S.N. Filimonova and S.N. Goncharova, React. Kinet. Catal. Lett . ,

15 (1980) 321. 12 N. Giordano, J.C.J. Bart, R. Maggiore, Z. Physik. Chemie, 127 (1981) 109. 13 R. Haul, D. Hoge, G. Neubauer and O. Zeeck, Surface Sci. Let t . , 122 (1982) 622. 14 Yu.V. Yonov, E.M. Temkina, D. Kamensky, N.V. Kulkova, M.I. Temkin, Kinet.

Catal., 21 (1980) 1269. 15 D. Kamensky, D. Bonchev, N.V. Kulkova, M.I. Temkin, Kinet. Catal., 19 (1978) 633 16 N.W. Cant, W.K. Hall, J. Catal., 52 (1978) 81. 17 V.A. Rastaturin, ZH. Prikl. Khimii, 51 (1978) 1929. 18 M.S. Kharson, A. Kh. Mamedov, S.L. Kiperman, Kinet. Catal., 25 (1984) 353. 19 S. Kagawa, M. lwamoto, H. Mori, J. Phys. Chem., 85 (1981) 434.

108

20 M. Akimoto, K. Ichikawa and E. Echigoya, J. Catal . , 76 (1982) 333. 21 P.D. KlugherzandP. Harr io t t , AIChE J. , 17 (1971) 856. 22 P. Kripylo, L. Mogling, H. Ehrchen, I . Harkanyi, D. Klose and L. Beck, Chem.

Techn., 31 (1979) 82. 23 H.T. Spath, Proc. Fi f th Int . Cong. Catal . , 2 (1973) 945. 24 H.T. Spath and K.D. Haydel, Adv. Chem. Ser., 133 (1974) 395. 25 M.I. Temkin, S.L. Kiperman and L . I . Lukyanova, Dokl. Akad. Nauk. SSSR, 74

(1950) 763. 26 T.E. Corrigan, Chem. Eng. Fundam., 199 (1955). 27 D. Himmelblau, Analiz protsesov stat is t icheskimi metodami, Mir, Moscow (1973). 28 S.I . Spivak, V. I . Timoshenko, M.G. Slinko, Dokl. Acad. Nauk. SSSR, 192 (1970)

580. 29 M.M. Andrushkevich, R.A. Buyanov, V. I . Timoshenko and S.I . Spivak, Kinet. Catal . ,

11 (1970) 1419. 30 M.G. Slinko, S. I . Spivak and V.I. Timoshenko, Kinet. Catal . , 13 (1972) 1570. 31 S.I. Spivak, M.G. Slinko and V.I . Timoshenko, React. Kinet. Catal. Le t t . ,

I (1974) 99. 32 S.I. Zhukhovitski i , L . I . Avdeeva, Lineinoe i vypukloe programmirovanie, Nauka,

Moscow (1968). 33 J.A. Nelder, R. Mead, The Computer Journal, 7 (1965) 308. 34 S. Ghazali, D.W. Park and G. Gau, Appl. Catal . , 6 (1983) 195. 35 P.L. Metcalf and P. Harr io t t , Ind. Eng. Chem., Process Des. Dev., 11 (1972) 478. 36 A. Orzechowski and K.E. MacCormak, Can. J. Chem., 32 (1954) 415 and 443. 37 S.L. Kiperman, Osnovv khimicheskoi k ine t i k i v geterogennom kata l ize, 180,

Moscow, Khimia (1979). 38 N. Abdelmalek, BIT 15 (1975) 117. 39 D. Kamensky and L. Petrov, Bulg. Acad. Sci. , Commun. Dept. Chem., 16 (1983) 86. 40 L.A. Petrov and D.M. Shopov, React. Kinet. Catal. Le t t . , 7 (1977) 261. 41 D. Marquardt, J. Soc. Indust. and Appl. Math., 11 (1963).