Kinetics of Methanol Synthesis 2

8/10/2019 Kinetics of Methanol Synthesis 2

1/11

Chemical Engineering Science, Vol. 43, No. 12, pp. 3185-3195, 1988.

ooo9-X09/88 3.00 + 0.00

Printed in Great Britain. 0 1988 Pergamon Press

plc

KINETICS OF LOW-PRESSURE METHANOL SYNTHESIS

G.

H. GRAAF,+ E. J. STAMH UIS

and A. A. C. M. BEENACKERSZ

Department of Chemical Engineering, State University of Groningen, Nijenborgh l 9747 AC Groningen,

Netherlands

R e c e i v e d

11 June 1987;

accepted fo r

publication 1 June 1988)

Abstract-ThB

kinetics of low-pressure methanol synthesis, starting from CO, CO, and hydrogen over a

commercial

Cu-Zn-Al

catalyst, were studied in a spinning basket reactor at p= 15-50 bar and

T = 21&245C. The results show that methanol can be formed from both CO and CO,. Besides these two

reactions the water-gas-shift reaction takes place. Based on these three reactions and a dual-site adsorption

mechanism, 48 kinetic rate models are derived. Hydrogen is believed to adsorb dissociatively. Th e

experimental results support this assumption. Based on X2-statistics and consistency tests a final kinetic rate

model is selected. This kinetic model gives a significantly better agreement with the experimental results than

kinetic

models taken from recent literature.

INTRODUCTION

Kinetic data often play an important role in designing

a chemical reactor and methanol synthesis is no

exception to this. Unfortu nately, there is still no

agreement in the literature on the kinetics of methanol

synthesis, not even for the same types of catalyst. The

objectives of this paper are to clarify w hich reactions

are involved in methanol synthesis and to derive

kinetic rate equations for these reactions.

LITERATURE

Although low-pressure methanol synthesis is an

importan t industrial process, the kinetic studies on

this subject as published in the open literatu re are very

often conflicting. The role of CO, especially is in-

sufficiently understood . This can be seen in Table 1.

Most models published up till now describe methanol

formation from CO only. The role of CO, in these

models, if present, is restricted to comp etitive adsorp-

tion on the active sites of the catalyst. Contrary to this

some authors (Dybkjaer, 1985; Chinchen et al., 1984)

claimed that methanol

i s

formed from CO, only.

According to Dybkjaer this is because strong adsorp-

tion of CO, preven ts the co-adsorption of CO.

Chinchen et a l . based their conclusions on exper-

iments with labelled carbon in CO,. A third group of

authors concluded that methanol is formed from both

CO and CO,. Liu et

a l .

(1985) came to this conclusion

based on experiments with labelled oxygen in CO*.

Denise and Sneeden (1982) and Klier et al. (1982)

reached the same conclusion based on kinetic exper-

iments.

Most of the authors m entioned in Table 1 presented

kinetic rate expressions. The rate expressions pub-

lished more recently are listed in Table 2.

TPresent address: N.V. Nederlandse Gasunie, Laan

Corpus den Hoom 102, 9728 JR Groningen, Netherlands.

*To whom correspondence should be addressed.

Seyfert and Luft (1985) (see Table 2) assum ed a

Langmuir-Hinshelwood mechanism in which CO and

H, are believed to be non-dissociatively adsorbed on

the same kind of active sites. Methanol is made in a

two-step reaction: in the first step formaldehy de is

formed in an equilibrium reaction; the second ste p, in

which adsorbed H, and adsorbed formaldehyde react

to form meth anol, is believed to be rate-controlling.

Villa

et a l .

(1985) (see Table 2) also assumed a

Langmuir-Hinshelwood mechanism in combination

with non-dissociative adsorption of CO and H,. The

rate-controlling step is believed to be a trimolecular

surface reaction between adsorbed CO and two ad-

sorbed H, molecu les as proposed originally by Natta

(1955).

Klier

et a l .

(1982) (see Table 2) presented a kinetic

rate expression based on two synthesis routes. The

first term in their kinetic rate expression describes

methanol formation from CO and H,. Furthermore

they assumed that the active sites can be reduced to

inactive sites by a redox equ ilibrium involving CO a nd

CO,. The second term in their kinetic rate expression

describes methanol formation from C02.

The kinetic rate expression proposed by Dybkjaer

(1985) (see Table 2) is based on a dual-site

Langmuir-Hinshelwood mechanism in which H, is

believed to adsorb dissociatively and reacts with ad-

sorbed CO,. Dybk jaer also reported the results of

studies on the chemisorption of H,, H,O, CO and

CO2 on Cu-Zn


2/11

3186

G.

H.

GRAAF

et al.

Table I.

Role of CO, in methanol synthesis as reported by several authors

Authors

Carbon source

for methanol

Adsorption

of CO*? Catalyst

Natta (1955)

Bakemeier et al. (1970)

Leonov et al. (1973)

Schermuly and Luft (1977)

Denise and Sneeden (1982)

Klier et al. (1982)

Monnier

et

a l .

(1984)

Chinchen et al. (1984)

Villa et a l . (1985)

Liu eC al. (1985)

Seyfert and Luft (1985)

Dybkjaer (1985)

co

co

co

co

co +co,

co + co,

co

co*

co

co + co,

co

co2

Yes

No

Yes

Yes

Yes

es

es

Yes

Yes

Yes

Zn-Cr

Zn-Cr

Cu-Zn-Al

cu-?

Cu-Zn-Al

Cu-Zn

Cu-Cr

Cu-E--AI

Cu-Zn-Al

Cu-Zn

Cu-Zn

Cu- -Al,

Cu-Zn-Cr

Table 2. Kinetic rate expressions for the methanol formation on Cu-containing

catalysts as found in recent literature

Authors

Kinetic rate expression

rCH,oH =

Seyfert and Luft (1985)

Villa et al. (1985)

& of i SCH,OHI~;,

(~,+~,f,,+~3~2+~4fCHJOH+~5fCOfH~+~6fC0~~2

(p=80-140 bar, T=235-265C)

. of ;, --fcn,o~IK;,

(Al+Azfco+A,f,oz+A,~~fH,)3

(p=3 95 bar, r=215-245C)

~,~:(p,mJPccd3 A,A:(PcoPH~ -PPCHK ,HIK ~,)

Klier et al. (1982)

Dybkiaer (1985)

anism is more likely than a single-site mechanism. He

also concluded that no distinction can be made be-

tween molecular H, adsorption and dissociative H,

adsorption. Liu et al. (1984) reported an inhibiting

effect of water on the methanol production. The

results of Dybkjaer (1985) are in agreem ent with this

observation.

From the authors mentioned in Table 2 only Villa et

al. and Dybk jaer presented kinetic rate expressions for

the water-gas -shift reaction. Th ese rate expressions

are listed in Table 3.

From the literature survey presented here it follows

that still no agreem ent exists in the open literature on

the kinetics of methanol synthesis. We are of the

opinion that this lack of agreement is mainly caused

by the complicating effects of the simultaneously

proceeding reactions. Due to the presence of the

water-gas-shift reaction it is in no way a simple m atter

to conclude unambiguously whether methanol is

formed from CO, CO, or both. This paper will

quantify the relative importance of CO and CO, in the

synthesis of methanol. Additionally, new kinetic rate

expressions are presented for the reactions involved in

methanol syntheis. Finally, these new rate expressions

will be compared with those listed in Tables 2 and 3.

THEORY

Reaction schemes a nd k i ne t i c r a t e expression s

Without knowing whether methanol is formed from

CO, C O, or both, the safest way of writing down a

reaction scheme is to include both routes. Because the

Cu-Zn-Al catalysts are known to catalyse the water-

gas-shift reaction as well, this reaction should be

modelled too.

Therefore the following three reactions are the basis

for the derivation of the kinetic rate expressions:

(A) CON-+ 2H, = CH,OH

(1)

(B) CO, + H2 = CO +H,O

(2)

(C) CO, + 3H, = CH,OH + H,O.

(3)


3/11

Kinetics of low-pressure methanol synthesis

3187

Table 3. Kinetic rate expressions for the water-gas-shift reaction on

Cu-Zn-Al catalysts as found in recent literature

Authors

Kinetic rate expression

r 410=

Villa et al. (1985)

f co , -fHzo f co IG

A5

(p=3 95 bar, T=215-245C)

From the results of

Dybkjaer (1985), Herman et al.

(1979) and Matulew icz (1984) all reactions are as-

sumed to be based on a dual-site Langmuir-

Hinshelwood mechanism. On site 1 CO and CO,

adsorb com petitively, while on site 2 H, and H,O

adsorb comp etitively. The adsorption of meth anol is

assum ed to be negligible. H, is believed to adsorb

dissociatively. How ever, it is quite straightforw ard to

derive alternative kinetic rate expressions that are

based on molecu lar adsorption of H,. It is now

possible to write down the elementary reactions

necessa ry for the overall reactions (AHC).

Adsorption equilibria:

co + sl = COsl

(4)

co, + sl = co+1

(5)

H, + 2~2 = 2Hs2

(6)

H,O +s2 = H,Os2.

(7)

(C4) H,C02sl + Hs2 =

H,COsl +

H,Os2

(17)

(C5) H,COs1+Hs2=H,COsl +s2

(18)

(C6) H,COsl +Hs2 =CH,OH + sl +s2.

(19)

Although these schemes contain some reactions with

equal stoichiome try [e.g. eqs (10) and (18)], these

reactions are regarded as being different. Assum ing

the total number of sites 1 and 2 is constant per weight

of catalyst and neglecting terms originating from

interme diate products, the following equations are

obtained:

c,1,,0t

= c,, + ccor1 + cco2s1 (20)

cs2.,01

= 2 + cHs2 + CHzOa2.

(21)

Kinetic rate expressions can be obtained by choosing

rate-controlling steps for each overall rea ction

[(AHC)] and assuming that all the other elementary

reactions are at equilibrium. For instan ce, if reactions

(A2), (B2) and (C2) are chosen to be the rate-con-

trolling steps, the following kinetic rate expressions

are obtained.

J

vA2 OK,, CfCOfH, -. +3H/(fHz K;, 11

CHoH.A2 = (1 +&of,, f Kc,,_&o,)(l + J$W J2 + KHIoS*O )

J

G, Kcoz

KHz(fco+ fHz -fH ,o fco lKk 1

H0 B2=(1+K~Of~o+.~~2fC0~)(~+K~~f j ; l : /2+~~~ofH~~)

,O, cz =

k J k o zKHz [fco , f H , -fCHIOHf 20 / t f H*KDp l )]

( l+K,o fco+Kco,~~~)( l+K~~f f , j~+K, ,o fH,o)

(22)

(23)

(24)

(= 4h0, c2 1

Reaction (A)

(Al) COsl +Hs2=HCOsl +s2

(A2)

HCOsl

+ Hs2 = H,COsl + s2

(A3) H,COsl + Hs2 = H,COsl +s2

(A4) H,COsl +Hs2=CH,OH +sl +s2.

Reaction (B):

(Bl) CO& +Hs2 =HCO,sl +s2

(B2) HCO,sl + Hs2 = COsl + H,Os2.

Reaction (C):

(Cl) CO,sl +Hs2=HCO,sl+s2

(C2) HCO,sl + Hs2 =

H,CO,sl +

s2

(C3) H2C02sl +Hs2 =H,CO,sl +s2

(8)

(9)

(10)

(11)

U2)

(13)

(14)

(15)

(16)

Since all the elementary reactions involve sites 1 and 2,

the denom inators of all the resulting rate expressions

are identical. The kinetic con stants kiZr k , and k

are in fact compounded. For example kX2 is calculated

as follows:

k - k:,,AzK A,%.to ts.

2 -

(25)

In eq. (25) k;,. A2

is the surface reaction rate constant

based on the elementary reaction (A2), K,, is the

equilibrium constan t of the eleme ntary reaction (Al),

c,r, (,,r is the total num ber of sites 1 per weigh t of

catalyst, and s is the number of neighbouring sites 1

and 2, which is of relevance because reaction can only

occur be tween species adsorbed at adjacent sites 1 and

2 (Frome nt and Bischoff, 1979).


4/11

3188

G.

H. GRAAF et al.

Based on the reaction schemes given above and

assuming that adsorption or desorption steps are not

rate-controlling there are 48 possible comb inations of

kinetic rate expressions. Such a comb ination is called

a kinetic model. The only differences between the

kinetic rate expressions are the driving-force groups.

These driving-force groups are given in Table 4.

Parameter estimati on and model discrimi nation

Each kinetic model given in the previous section

contains seven kinetic constants, which have to be

estimated from experime ntal results. These exper-

imen tal results are sets of the following data:

I

I

rcHaOn 9 rHrO )

K P? Yco 1 Yco2 > YH2. YCH+3H, YHzO.

From the temperature, the total pressure and the mole

fraction fugacities of each comp onent are calculated

by the Soave-Redlich-Kwong equation of state

(Soave, 1972). For a chosen kinetic m odel the reaction

rates for methanol and water can be calculated using

these fugacities in combination with the estimated

values of the parameters (kinetic constants). The

equilibrium constants Kg, and K& in the kinetic rate

expressions are taken from Graaf et al. (1986). Because

reaction (C) is the stoichiome tric

sum of reactions

(A)

and

(B), K&

can be written as follows:

K;, = K;, ICOp=.

(25)

For the parameter estimation a direct-search al-

gorithm was developed in which the parameters are

adjusted towards optimum values. The adjustment

steps were taken as fractions of the parameter values

ranging from 0.5 to 0.01. The objective functions were

chosen as follows:

+ WF (Go - Go 1;1

(27)

OF

SARR =

F

H,OH - OH

r H,OH

j

P

Hz0 -kO

+WF

I 1. (28)

I Go lj

In these equations WF is a weighting factor; for

WF = 0 only the methanol production rate

is

con-

sidered in fitting the parameters, for WF = 1 both

methanol and water production rates with equal

weights are considered, and for WF = cc only the

water production rate is considered.

OF,,,

was used because the statistical methods

applied in this paper are based on variances and thus

on sums of squares of residuals. However, a well-

known disadvantage of the sum-of-squares regression

is that large reaction rates and large residuals have the

greatest contribution in the fitting procedure. This

problem vanishes using OF,,,, in which the sums of

absolute values of the relative residuals are minim ized.

For the final results of the chosen kinetic model

OF

SARRwas used.

Table 4 . Driving -force groups of kinetic rate expressions

for reactions (A), (B) and (C)

Rate-controlling

step

Corresponding driving-force

group

(Al)

(A21

643)

6441

031)

(B2)

(Cl)

(C2)

(C3)

(C4)

(C5)

tC6)

Once a

set of optimal constan ts was found for a

given model, the variances of this model for the

methanol production rate and the water production

rate were calculated:

5 H~OH - r OH 13

p=j=1

N-m

(29)

(30)

The values of these variances

are due to experimental

inaccuracies and to a lack of fit of the kinetic model

used.

The variances of all models were tested for their

equality with Bartletts X2-test (Bartlett, 1937). As has

been pointed out by Dumez et al.

(1977) this test is not

a true adequacy test: models that are retained may not

be adequate but simply the best of a series of in-

adequate models. For this reason a model that passed

the X2-test was subsequently tested by two other

methods:

(a)

Physico-chemical constraints.

(b) Residual analysis.

(a)

The estimates of the kinetic parameters must

have physico-chemical meanings. This led to

certain

rules for the estimates of kinetic parameters which are

summ arized below (Boudart, 1972; Vannice

et al.,

1979; Kapteyn, 1980).

Reaction rate constants:

k =

Aexp[-EE,/(RT)J

(31)

rule 1:

k>O

(32)

ruie 2:

E, > 0.

(33)

Adsorption equilibrium constants:

K = exp (A%:,,IR) exp C - AHLJ(R

W (34)

rule 3: K > 0

(35)


5/11


3189

rule 4:

- AH& > 0

(36)

rule 5: 0 < - AS&,, -z S&,.

(37)

(b) The residuals &oH -

r , ,H

and i;120-rnao

should be normally distributed with zero mean. Also,

the residuals should have no trend effects as a function

of any of the independent variablesf,, f& ,fH2, fCHsOH

and hilo.

Equ i pmen t

EXPERIMENTAL

The kinetic study was carried out with a spinning

basket re actor as described by Tjabl

et a l .

(1966). A

commercial catalyst was used (Haldor Topsoe Mk

101). Properties of this catalyst were reported by

Dybk jaer (1981). A simplified flow scheme of the

equipment is given in Fig. 1. The reactant feeds

(prefabricated mixtures of CO, CO, and Hz) were

drawn from gas cylinders (1). The pressure in the

reactor (3) was adjusted with a pressure reducer (2).

The spinning basket reactor was heated electrically

and thermostatted by a proportional thermal con-

troller (4). A small part of the product stream was led

to an on-line GLC (1 I). The flow rate of this part w as

measured with a soap bubble meter (10) and regulated

with two needle valves placed in series (9). The remain-

ing part of the product stream w as passed through a

conden ser of -40C (7) and a gas-liquid separator (6).

The m ethanol and the water formed in the reactor

were condensed almost completely and stored in a

cooled vessel (8). The ga s flow th rough the reactor was

adjusted with a needle va lve (13) which was placed

between a pressure reducer (12) and a back pressure

regulator (14). The gas flow w as measured with a wet

gas mete r (15). The produ ct lines were heate d electri-

cally where necessary in order to avoid unwanted

condensation of methanol and water (see Fig. 1). The

reactan t feed could be sampled for analysis throu gh a

reactor bypass (16) using a needle valve (17 ).

Ana lys is

A schematic drawing of the GLC apparatus is given

in Fig. 2. Gas samples of 1 ml w ere injected. The

column temperature as well as the sampling valve

temperature were maintained at 100C. Helium was

used as a carrier gas. The column (2 mm i.d., 6 m long,

packed with Porapak Q) was connected to a thermal

condu ctivity detector an d a flame ionization detector

placed in series. Calibrations of the detectors were

carried out each day in order to assure accurate

analysis. Hydrogen was not determined directly in the

analysis, but from the material balance:

Y

- 1-_Cy, GZH, .

z -

(38)

I

Measurements

The kinetic experiments were always carried out

under steady-state conditions. External m ass- and

heat-tran sfer limitations were negligible during the

experimental conditions chosen. This was both calcu-

lated and experimentally verified. At temperatures

above 245C intra-particle diffusion limitations were

observed. Therefore, these experimen tal results will

not be dealt with in this paper. A subsequent paper on

the subject of the intra-particle diffusion limitations in

methanol synthesis will be presented in the near

future.

For each experiment the material balances over the

reactor for hydrogen, carbon and oxygen were calcu-

lated. The deviations in these material balances were

always very small, usually less than 5% .

A broad range of experimental conditions was

examined in order to gain a good insight into the

Fig. 1. Flow scheme of the

equipment

used for the kinetic experiments: 1 =gas-cylinder, 2=pressure

reducer, 3 = spinning basket reactor, 4 = thermostat, 5 = manometer, 6 = gas-liquid separator, 7 = cooler,

8 = storage vessel, 9 = needle valves, 10 = soap bubble meter, 11= GLC, 12 = pressure reducer, 13 = needle

valve, 14 = back pressure

regulator, 15 = wet gas meter,

16 = bypass, 17 = needle valve.


6/11

3190 G. H. GRAA F et al.

Pig.

2.

GLC

2 = Porapak Q

apparatus used: I= sampling valve,

column, 3 = TCD, 4 = FID, 5 = integrator,

6 = recorder.

kinetics. These conditions are briefly summarized in

Table 5. It was assumed that the spinning basket

reactor behave d as a perfect mixer. Ju stification of this

assum ption is given by Tjabl et al. (1966).

Reaction rates for water and methanol were calcu-

lated from simple mixed-flow mate rial balances over

the reactor:

,

4 P

PCH,OH

=

YCH,OHWR

(39)

In eqs (39) and (40), p and

T

correspond

to

the

conditions at which 4, is measured, being atmospheric

pressure and room temperature.

RESULTS

Wa ter f orm a t i o n i n me th ano l sy n t h esi s

The am ount of water formed in the methanol

synthesis as a function of the gas flow rate shows some

peculiar features (see Fig. 3). Here, th e quan tity put at

the vertical axis is a dimen sionless measu re for the

amou nt of water related to the water-ga s-shift equilib-

rium. If the water-ga s-shift reaction is at equilibrium,

its num erical value will be one. Under certain con -

ditions more water is formed than is predicted thermo-

dynam ically. We see only one possible explanation for

this phenomenon: in addition to the water-gas-shift

reaction a second water-yielding reaction proceeds.

Since no by-products in detectable amounts were

formed in these experiments, the surplus of water m ust

fC0 fHzO

K P;

fco,fcl,

00

0

10

20 3.0 L.0 50 sc

1030/W

md kg

Fig. 3. Water formation in methanol synthesis: (0)

p = 50 bar, (0) p = 30 bar; (a) p = 15 bar. Symbols = results

of feed 7 (see Table 5). Lines = calculated with model A3B2C 3

after correcting for the difference in activity of the catalyst

used in feed 7 (with respect to m ethanol).

result from the direct synthesis of methanol from CO,,

which indeed yields water.

Still another interesting feature can be detected

from Fig. 3. In some experiments (marked with an

arrow in Fig. 3) the water content is about the same as

predicted from the chemical equilibrium of the water-

gas-shift reaction . In this situation no driving force is

left for this reaction. Furthermore, it should be empha-

sized that the water-gas -shift reaction is not a fast

reaction compared with the methanol formation reac-

tions. Otherwise, the water content would be close to

equilibrium under all conditions. For these reasons,

the contribution of the water-gas-shift reaction to the

amount of water formed will be negligible for the

experiments marked with an arrow in Fig. 3: all the

water formed will be the result of the methanol

formation from CO,. Since hydrogenation of CO

yields only methanol, we can now calculate the

amounts of methanol formed from CO and CO,,

respective ly. The results of these calculations are listed

in Table 6. They prove unambiguously that methanol

is produced from both C O and CO,. It also follows

that none of the two independent synthesis routes is

relatively negligible.

Table 5. E xperimental conditions in the present study (catalyst Cu-Zn-Al)

Feed

1

2

3

4

5

6

7

Feed composition

P 1039%lW

Yco YCO,

YH,

(bar)

(&

(m3s-lkg-)

0.065 0.26 1 0.674 15, 30, 50 483.5, 499.3, 516.7 1-6

0.053 0.047 0.900 15, 30, 50 483.5, 499.3, 516.7 16

0.220 0.155 0.625 15, 30, 50 483.5, 499.3, 516.7 16

0.120 0.02 1 0.859 15, 30, 50 483.5, 499.3, 516.7 l-6

0.179 0.067 0.754 15, 30, 50 483.5, 499.3, 516.7 l-6

0 0.115 0.885 15, 30, 50 483.5 0.3-7

0.092 0.105 0.803 15, 30, 50 499.3 0.14


7/11


Table 6. Relative amounts of methanol formed from CO and from CO, for experiments with feed 7

(see Table 5)

3191

l~3LXJL,ol(&0*fH,)

lOSKi

YCHlOH YH.0

6.9 7.54 0.0109 0.0061

8.2 7.54 0.0122 0.0074

7.5 7.54 0.0110 0.0067

% CH,OH % CH,OH

from CO from CO,

44 56

39 61

39 61

Parameter estimati on and model discrimi nation

Table 7. Kinetic models that passed the X*-test

In a first series of compu tations the results of feeds

l-5 of Table 5 were used, because replicated exper-

iments showed a constant catalyst activity. At each

temperature the data of about 30 experiments were

collected. The parameter estimation was carried out at

each temperature for all 48 kinetic models

given

in

Table 4. How ever, the results of these calculations

were very dependent on the initial guess values of the

parameters. A careful1 analysis of this phenomenon

showed that ill-guessed initial param eter values led to

solutions in which one of reactions (A) and (C) [eqs (1)

and (3)] was completely neglected. As was shown

above, this is essentially wrong. For this reason the

data were screened for experiments in which the

water-gas -shift reaction was approximately at equilib-

rium (within 10%). As explained above the amounts of

methanol produced from CO and from CO, were

calculated from these experiments. The ratio of the

kinetic factors cou ld be calculated from these results

for all kinetic models. For instanc e, the kinetic m odels

A2BlC2 and A2B2C2 yield the following equation:

P&,0,)

(r&J)+

Kinetic model

(~1

(%)

A3BlC2 7.9 28.7

A3BlC3

6.4 26.8

A3B2C3 6.4

24.2

These deviations are defined by the objective

function, OFsARR [eq.

(28)].

Table 8. Relative catalyst activities w ith respect to methanol

and water

Kinetic

model

Activity for

methanol

Activity for

water

A3BlC2 1.45 + 0.27 1.75 +0.30

A3BlC3

1.34+0.05

1.38 kO.07

A3B2C3

1.36 +0.04

1.35kO.05

k&z Kc,, GL, y,,oDF,,

t(=

kA2 &OK,, = (YCH,OH - y,,o)DFc, .

(41)

The parameter estimation was carried out again, with

k& Kcoz

K,, = akaz K,,K,, while a was not involved

in the fitting p rocedure but calculated from the exper-

iments for which the water-gas-shift reaction was

approximately at equilibrium. WF was chosen to be

0.5. It should be noted that the fitting results were

almost independent of values of the WF ranging from

0.1 to 2. This revised approach gave co nsiderably

better results: based on the X2-test at a 95% confidence

level six models were retained from the original 48

models. For these six models the parameter estimation

was repeated for all three temperatures simul-

taneously. Here it was assumed that all parameters

follow an Arrhen ius tem perature depend ency. Initial

guess values of the parameters were based on the

results of the parameter estimation at each tempera-

ture. The data consisted of the results of 89 exper-

iments. Now, a was no longer excluded from the fitting

procedure. Based on the X2-test three models were

retained at a 95% confidence level. These m odels are

given in Table 7.

with the catalyst activity during experiments with

feeds l-5). For each experiment of feed 6 (18 exper-

iments) and each kinetic model of Table 7 the relative

methanol activity and water activity were calculated.

The activity of methanol or water is defined as being

the ratio of the observed rate of formation and the

calculated rate of formation using one of the kinetic

models in combination with the estimated values of

the param eters. The results of these calculations are

listed in Table 8.

For the correct kinetic mode l equ al catalyst ac-

tivities might be expected for both methanol and

wate r. Based on the results listed in Table 8 in

combination with those listed in Table 7 we conclude

that the best kinetic model is A3B2C3.

In Fig. 4 rates of methanol and water production as

predicted by model A 3B2C3 are compared with the

experimental results of feed 6. As can be seen there is a

good agreemen t between the model calculations and

the experimental data. The same agreement can be

seen in Fig. 3: the solid lines were calculated with

model A3BZC3 in combination with a correction for

catalyst activity (with regard to methanol).

In order to discriminate between these three rival

models, the results of the experiments with feed 6 (see

Table 5) were used. These results were not used for the

parameter estimation, because the catalyst activity

was different during these experiments (compared

A thorough residual analysis on model A3B2C3,

which is not given here, showed that trending effects of

the residuals as a function of any of the independent

variables were absent. The residuals were also nor-

mally distributed with zero mean.

It

turns out that the kinetic model can be simplified,

because the number of free sites 2 is negligible, which


8/11

3192

G. H. GRAAF et al

IO3

mol

S

kg-'

OO

10

2.0

30

L-0

I

.0

6.0

103~,IW

n?

Kco=(7.99f 1.28) x lo-

58,100 f 600

x exp

RT

>

K,,=(1.02+0.16)x lo-

(

67,400 f 600

x exp

RT

>

K,,o/K~~=(4.13f1.s1)x lo--

104,500+ 1100

x exp

>

T

(48)

(49)

(50)

(51)

The Arrhenius diagrams are given in Figs 5 and 6. The

results of the parameter estimation per temperature

are also plotted in Figs 5 and 6. The differences

between these results and the results obtained from th e

param eter estimation for all temp eratures are justified

by the confidence intervals.

The confidence intervals in eqs (46) and (47) were

calculated from

SSR

to.991

= SSR,r + SSR,i, m

N-m

FI m ,N-m .0.99,.

(52)

?J

kbs,,, Kc, C offi~, .Lx,odfA:

K;, )I

CH30HA3(1 + Kcofco + Kco&oz) Cfh;2+ K~,olk~~~K,,ol

(43)

zO.BZ =

k6, B2 Km o,_G, -_A,,o o/K;z 1

(1 +KcoJzo + oJLod CfX2

+(K.r,olk~~2)f.,01

(44)

J

k;S.ca

&o,Cfco ,f%2 - fCu,o&,ol(fH3j2K;~)l

CHsoH*C3= (1 + c0 fco + K

cozfcoz) IX:

+W,,JKAI:)f,,ol

(45)

( = &,o.

c3

1

The reaction rate constants are marked with the

subscript ps (pseudo), because they now contain the

adsorption equilibrium constant of hydrogen. Th e

parameter estimation was carried out again for this

simplified form of model A3B2C3 . It should be noted

that the model predictions as presented in Figs 3 and 4

did not chang e n oticeably after the simplification

mentioned above. The following results were obtained:

&,, A3 =

(2.69kO.14) x IO

- 109,900 f 200

x exp

RT

>

(46)

- 123,400 + 1600

x exp

RT

>

(471

In this equation Ftm.N -,,,0.991 is Fishers F-value with

[m. N-m] degrees of freedom at a 99% significance

level (Fisher, 1958). The confidence intervals were

obtained by varying one parameter at a time and

holding all the other parame ters at their optimal

values.

The results of the parameter estimation were used to

check whether the kinetic model follows the physico-

chemical constraints. It can be seen from eqs (46H51)

that rules 14 [eqs (32)-(36)] are obeyed.

From the pre-exponen tial factors of the adsorption

constants the entropies of adsorption for CO and CO,

were calculated from eq. (34). Together with the

boundary values from eq. (37) these adsorption

entropies are listed in Table 9.

Clearly, the adsorption entropies have reasonable

values. For hydrogen and water, only the ratio of

adsorption constants w as determined: this gives no


9/11

Kinetics of low-pressure methanol synthesis 3193

T

oc

220

L

2LO

230

I

I

I

210 L

I

0.8

0.7

- i

0.6

0.5

i

3

-2

i04 k

- m ot E? k bar

-112

-0.8

- 0.7

- 0.6

- 0.5

Fig. 5. Reaction rate constants vs temperature: (0) k ,,,(n)

kb,.,,, 0) VP,..,.

Symbols =regression per

temperature. Lines = regresslon with all temperatures.

ii

Fig. 6. Adsorption constants vs temperature: (0)

Kc,,, A)

Kc,,, (0) K,,oIK,,

I/*.

ymbols = regression per temperature.

Lines = regression with all temperatures.

Table 9. Adsorption entropies of CO and CO,

Compound

-AS,,,

S (500 K)t

(J mole1 K-

)

(J mol- K-l)

co

116.7

CO,

133.9

tTaken from Stull et al. (1969).

213.2

243.9

useful information about the adsorption entropies,

however. Therefore, we may conclude that the kinetic

model A3B2C3 obeys all the physico-chemical con-

straints.

From the results

of feed 6 the adsorption of

hydrogen, which was assumed to be dissociative, can

be studied to a greater extent. Because feed 6 did not

contain CO, it may be assumed that methanol is

formed almost exclusively from CO*. This was con-

firmed by model calculations, which are not given

here. After rearrangement of eq. (45) the following

equation is obtained:

k ; , , ca Km 2 Cfc,,f,:/ -fc,ofH ,ol(f~~2K;,)1

r O(l + of,, + KC02fC02)fH :/2

Thus on plotting the left-hand side of eq. (53) against

f*O /fix2

a straight line should be obtained. As can be

seen from Fig. 7, the results are in complete agreemen t

with our expectations, thus supporting the assum p-

tion that hydrogen is adsorbed dissociatively.

Compa r i s on w i t h l i t er a t u r e

Parameter estimation was also carried out with the

models taken from the literature given in Tables 2 and

3 using the experimental data of feeds 1-5. Because

Seyfert and Luft (1985) and K lier

et a l .

(1982) have not

presented kinetic rate expressions for the water-gas-

shift reaction, these literature models were completed

with the kinetic rate expression for this reaction as

given by Villa et a l . (1985).

The optimal parameters were determined for these

models. U sing these optimal parameters the devi-

ations for the methan ol and water production rates

were calculated. These values are summ arized in

Table 10.


10/11

3194

G. H. GRAAF et al.

5.0

L.H.5 ~1531

1

LO

3.0

1

OO

I

I ,

I 1 I

0.7

0 2 03

fC l o / fC I:2

I2

bar

Fig. 7. Adsorption of hydrogen and water: (0) p = 50 bar,

( 0) p = 30 bar, (A) p = 15 bar. Symbols = resu lts of

feed 6 (see

Table 5). Line = best fit

based on SSR.

Table 10. Accuracies of the kinetic models taken from recent

literature compared with the

model proposed in this study

Kinetic model from

Seyfert and Luft (1985) 10.8 100

Villa et al. (1985) 12.3 100

Klier et

a l . (1982) 10.0 57

Dybkjaer (1985) 14.7 167

This study 6.4 24

These deviations are defined by the objective function

OFSARR [es- WI.

Comparing these results with the results of mode1

A3B2C 3 it is obvious that

the

latter describes the

kinetics

in methanol synthesis much better. This was

confirmed by the X2-test: using this criterion the four

models from the literature were rejected, thus

favouring model A3B2C3.

CONCLUSIONS

Experimental evidence shows that methanol can be

formed simu ltaneously from both CO and CO2 in

low-pressure methanol synthesis.

The experimental results on the methanol syn-

thesis kinetics can b e explained by a dual-site

Langmuir-Hinshelwood mechanism, based on dis-

sociative hydrogen adsorption and three independent

reactions: methanol formation from CO, methanol

formation from CO, and the water-gas-shift reaction.

Depending on which elementary reaction step is

rate-controlling in each of these three parallel reac-

tions, 48 different kinetic m odels are possible. Based

on X2-statistics and consistency tests a final model was

selected.

The kinetic parameters could be determined as

functions of temperature between 210 and 245C. The

values of these parameters are

not

in conflict with the

physico-chemical constraints.

The experiments

further support the assumption of

dissociative hydrogen adsorption.

At least for the commercial

catalyst applied in this

study, the kinetic mod el proposed here explains th e

experimental results with a significantly improved

accuracy as compared with the kinetic models pro-

posed by Seyfert and Lu ft (1985), Villa et al. (f985),

Klier et al. (1982) and Dybkjaer (1985).

Acknowledgements -We

thank Haldor Topsoe A/S, Lyngby,

Copenhagen, Denmark for delivering their methanol syn-

thesis catalyst Mk 101 and the N.V. Nederlandse Gasunie,

Groningen, Netherlands, for delivering gas mixtures for

calibration purposes.

A

A

I ...6

c

DF

:

j

k

Ki

K

Al .. .

K

A4

K

B 1 . . .

K

82

K

K

c l - C6

K ,

m

N

OF

P i

p

r

R

S

S

S

T

W

WF

Y

:

AH

AS

$

Supe rsc r ip t s

0

NOTATION

pre-exponential factor

kinetic constants in literature ex-

pressions

concentration,

mol kg-

driving force

energ y of activation, J mol-

partial fugacity, bar

experiment index

reaction rate constant

adsorption equilibrium constant,

bar- ;

e.g. for CO:

K

f

OG1

co= __

I I

COSl EP

elementary reaction equilibrium

constant

e.g.

chemical equilibrium constant based

on partial pressures

number of parameters

number of experiments

objective function

partial pressure, bar

total pressure, bar

reaction rate per weigh t of catalyst,

mols-kg-

gas constan t (8.314), Jmolm KP

number of neighbouring sites

variance

entropy, J mol 1K -

temperature, K

weight of catalyst, kg

weighing factor

mole fraction

ratio of kinetic constan ts

relative error

enthalpy change, J mol-

entropy chan ge, Jmol- K-

gas flowrate at standard temperature

and pressu re (25C, 1.013 bar), m3 s-

indicates standard pressure (1 ,013 bar)

indicates calculated value


11/11


3195

butene dehydrogenation.

I nd. Engng Chem. Fundam. 16,

adsorption

298-301.

indicates

rate-controlling

step of

Dybkjaer, I., 1981, Topsoe methanol technology. Chem.

methanol from CO reaction

Econ. Engng Rev. 13(6), 17-25.

Dybkjaer, I., 1985, Design of ammonia and methanol syn-

indicates ra te-controlling step of the

thesis reactors. Paper presented at the NATO conference

water-gas-shift reaction

on chemical reactor design and technology, Canada.

indicates

rate-con trolling step of

Fisher, R. A., 1958, Statistical Methodsfor Research Workers,

methanol from

CO,

reaction

13th edition. Hafner, New York.

indicates component CO

Froment, G. F. and Bischoff, K. B., 1979, Chemical Reactor

Analysis and Design, p. 98. J. Wiley, New York.

indicates comnonent

CO,

Graaf, G. H., Siitsema, P. J. J. M., Stamh uis, E. J. and Joosten,

Subscripts

ads

Al . ..A4

Bl...B2

Cl...C6

co

CO,

CH,OH

EQ

gas

HZ

Hz0

i

max

min

Ps

SARR

sr

SSR

Sl

s2

tot

1

2

3

indicates component CH;OH

at,equilibrium

gaseous component

indicates component H,

G. g. H., 1986, Chemical equilibria in methanol synthesis.

Chem. Engng Sci. 41, 2883-2890.

Herman, R. G.,

Klier, K., Simmons, G. W., Finn,

B.

P.,

Bulko,

J. B. and Kobylinsk i, T. P., 1979, Catalytic synthesis of

methanol from CO/H.. J. Catal. 56, 407409.

indicates component H,O

Kapteyn,

F., 1980. The MetatheSis of Alkenes over

indicates component CO, COz, H,,

Rheniumoxi de-Alumini a, p. 77.

Dissertation. Amsterdam.

CH,OH or H,O

Klier, K., Chatikavanij, V., Herman , R. G. and Simmons, G.

maximum value

W., 1982, Catalytic synthesis of methanol from CO/H,. J.

Catnl. 74, 343Lj 60.

minimum value

Leonov, V. E., Karavaev, M. M., Tsybina, E. N. and

pseudo

Petrishcheva, G. S., 1973, Kinetics of methanol synthesis

based on sum of absolute values of

on a low-temperature catalyst. Kinet. Katal . 14, 970-975.

relative residuals

Liu, G., Willcox, D., Garland, M. and Kung, H. H., 1984, The

rate of methanol production on a copper-zincoxide cata-

surface reaction lyst. The dependence on the feed composition.

J. Catal. 90,

based on sum of squares of residuals

site 1

site 2

total

indicates m ethanol from CO reaction

in KS,

indicates water-gas-shift reaction in

G,

indicates methanol from CO, reaction

in Kg,

REFERENCES

Bakemeier, H., Laurer, P. R. and Schroder, W., 1970, Devel-

opment and application of a mathem atical model of the

methanol synthesis. Chem. Engng Prog. Symp. Ser. 66(98),

l-10.

Bartlett, M. S., 1937, Properties of sufficiency and statistical

tests. Proc. R. Sot. A 160, 268-282.

Boudart, M., 1972, Two-step catalytic reactions. A.I.Ch.E. J.

18,

465-478.

Chinch en, G. C., Denn y, P. J., Parker, D. G., Short, G . D.,

Spencer, M. S., Waugh, K. C. and Whan, D. A., 1984, The

activity of copper-zincoxide-aluminiumoxide methanol

synthesis catalyst. Prep. Pap. Am. them. Sot. Div. Fuel

Chem. 2 J(5), 178-188.

Denise. B. and Sneeden, R. P. A., 1982, Hydrocondensation

of c&bondioxide IV. J. Molec. Cat 15, 359-366.

Dumez, F. J.. Hosten, L. H. and Froment, G. F., 1977, The use

of sequential discrimination in the kinetic study of l-

139-146.

Liu, G., Willcox, D., Garland, M. and Kung, H. H., 1985, The

role of CO, in methanol synthesis on Cu-Znoxide: an

isotope labeling study.

J. Catal. 96,

251-260.

Matulewicz, E. R. A., 1984,

Kinetics and Spectroscopic I n-

vestigations of Propene Metathesis and Methanol Synthesis.

Dissertation, Amsterdam.

Monnier, J. R., Apai, G. and Hanrakan, H. J., 1984, Effect of

CO, on the conversion of HZ/CO to methanol over

copper+hromia catalysts.

J. Catol. 88,

523-525.

Natta, G., 1955, Synthesis of methanol, in

Catalysis: Hydro-

genation and Dehvdrogenation (Edited by P. H. Emmett),

pp. 349411. Rheinhoid, New York. _

Schermulv, 0. and Luft, G., 1977, Untcrsuchung der

Niederiruck-Methanolsynthese im Treibstrahlreaktor.

Chemie-Ingr - Techn.

49, 907.

Seyfert, W. and Luft, G., 1985, Untersuchungen zur

Methanolsynthese im Mitteldruckbereich. Chemie-lngr-

Techn. 57, 482-483.

Soave. G.. 1972. Eauilibrium constants from a modified

RedlichLKwong etuation of state. Chem.

Engng

Sci. 27,

1197-1203.

Stull, D. R., Westrum, E. F. and Simke, G. C., 1969,

The

Chemical Thermodynami cs of Organi c Compounds, pp.

219-220. Wiley, New York.

Tjabl, D. G., Simons, 3. B. and C arberry, J. J., 1966, Hetero-

geneous catalysis in a continuous stirred tank reactor. Ind.

Engng

Chem. Fundam. 5, 171-175.

Vannice, M. A., Hyun, S. H., Kalpakci, B. and Liauh, W. C.,

1979, Entropies of adsorption in heterogeneous catalytic

reactions.

J. Catal. 56,

358-362.

Villa, P., Forzatti, P., Buzz i-Ferraris, G., Garone , G. and

Pasquon, I., 1985, Synthesis of alcohols from carbonoxides

and hydrogen,

Ind. Engng

Chem.

Process Des. Dev.

24,

12-19.

Kinetics of Methanol Synthesis 2

Documents

Transcript of Kinetics of Methanol Synthesis 2