kinetic-transport models of bimodal reaction sequences. homogeneous and heterogeneous

KINETIC-TRANSPORT MODELS OF BIMODAL REACTION SEQUENCES-L HOMOGENEOUS AND H@TEROGENEOUS

PATHWAYS IN 0XIDATIVE COUPLING OF METHANE

SEBASTIAN C. REYES, ENRIQUE IGLESIA and C. P. KELKAR Corporate Rc&carch Laboratodes, Exxon R-arch and E&tiring Co., Route 22 East, Annandale,

NJ 08801, USA.

AWract-A reaction-transport model that combines gas-phase reactions mcurting within interstitial and intrapellet voids with surface reactions occurring on catalytic sites was used to descritm the oxidative coupling or methane in packed-bed reactors, a typical example or bimodal (h~ogeneous-heterogeneous) reactjon systcma. A kinetic model for gas-phase reactions was a-bled from available literature data; it describes well experimental results in empty reactors. Simtilationa suggest rhat C, yields greater than B-9% are unattainable with CH,/02 mixtures in homogeneous reactors. Staging the introduction of the oxygen reactant along the reactor length minimi= secondary oxidation reactions by lowering the local O1 pressures, and leads to a &ht increase in maximum yield (12% for 200 injection points) but also to much larger required reactor volumes. The introduction of an ideal catalytic function (methyl arid ethyl radical formation without full oxidation) al= increa&es maximum C, yields by ituzeasing rhe coneenlrd- tion of methyl radicals involved in bimolecular coupling step. However, C, yields greater than 30% require seleaivc catalysts with very hi@ turnova rates ( > 100 s - ’ ); higher rates bewme ultimately limited by intrapellet diffusion rates. Again, ,staging oxygen by mulriple injmion schemes increases attainable yields but requires larger reactor volumes and catalytic sites with low reaction order 4 < 1) in oxygen. For optimum conditions, staged oxygen injection taEhniques lead to C, yIelda as high BS 50%.

1. INTRODUCTION

Oxidative coupling offers a potential route for the direct conversion of light alkanes (C,X,) to more useful products. Such reactions often proceed via bimodal pathways that require formation of alkgl rad- icaIs at surfaces and subsequent coupiing and oxidation reactions of these radicals in gas-phase reactions. The increased reactivity of the higher alkanes formed in this reaction limits the maximum attainable yields in bimodal catalytic schemes for oxidative coupling of methane to C,’ hydrocarbons.

High-temperature heterogmeous catalytic processes such as alkane cracking and naphtha reforming often occur in parallel with corresponding homogeneous pathways. More interestingly, surfaces can also form intermediates required in free-radical and

thermal reactions. For example, catalytic dehydro- gettation oCa1kane.s leads to triene intermediates that undergo cyclization to aromatic products in gas- phase electrocyclic addition reactions [l]. In catalytically stabilized thermal (CST) combustion, gas- phase reactions are sustained by the formation of OH and 0 radicals at a solid surface [a].

Partial oxidation [3] and oxidative coupling [4-67 of albanes are alsa examples of bimodal reaction sequertces. In catalytic oxidative methane couptin& methyl radicals formed on metal oxide surfaces undergo thermal recombination reactions to give ethane as the initial product, and ethylene and carbon oxides as secondary products [4-67. Oxidative coup-

ling overcomeS the thermodynamic barriers in methane dehydrodimertition (pyrolysis) reactions by kinetic coupling of .the dehydrogenation and water formation step. The latter lowers thermal eficiency compared to methane pyrolysis and consumes valu- able HZ but allows CHL reactions to -UC at lower temperatures and with greater control of secondary polymerization reactions and much lower tar and coke yields.

Here, we develop a general framework for the description of bimodal reactions in convection-controlled reactors and apply it to the oxidative coupling reactions. A later paper will address the role of diffusive transport on the rate and selectivity of the oxidative coupling chemistry 171. Such a report ex- pands our previous description of transport eF fects ES] and offers a much more detailed analysis

than a recent study of transport restrictions which is based on a four-species kinetic model [9]_ Our diffusional model also allows us to explain the s&&ivity gains observed experimentally [ 101 as catalysis

become limited by intrapellet diffusion of the oxygen reactant.

1.2. Oxidative couphag of methmw

Keller and Bhasin Cl11 first showed that Eatalysts can convert methane to .a mixture of Ci hydrocarbons and carbon oxides (CO,) with much higher rate and selectivity than free-rad&l thermal pathways. Later studies identified several preferred catalysts consisting of promoted basic metal oxides [12-i6J. Kinetic studies later suggested that methyl radicals

2643

are generated at surface [ 173 :

CH, + 0 _ (5) [or 0’ - {s)] - CH;

+ OH(s) [or OzH(s)], (s) = surface site (1)

desorb, and then recombine in the gas phase:

CH;+CH,+M - C,H, + Prig 01

in a step *hat becomes limited by relaxation of excited intermediates atid energy transfer at low pressures. Spectroscopic evidence has confirmed the presence and the reactive nature of gas-phase CH; species in homogeneous and catalytic oxidativo coupling of methane C3-6, Is-Zt].

Homogeneous reactions of methane are initiated by thermal dissociation:

. . CH4-CHS + H

or by oxygen-assisted dissociation:

(3)

CH, + 0,-----s CH; + OIH*. (4)

Rates are higher for CIH6 than for CH4 because of the lower dissociation energy of their C-H bonds [22]. The presence of a catalyst leads to higher initiation rates, to subtle salsctivity changes, and to the preferred formation of COz instead of CO [23].

In oxidative coupling of methane, Cz mleztivity decreases as CH4 conversion increasaq an obstacle to the &ciont use of this conversion chemistry. This inherent dif?iculty in reactions of very stable species, such as methane, arises because titermediate products (e.g. CaH6, C2Hd, and CIH2) am often more reactive than the reactants (U-I,) and continue to convert to thermodynamically favored products (CO,). This in- direct thermodynamic eRect of the weaker C-H bond energy in intermediate products is ditXcuIt to circum- vent by either catalytic or homogenmus prwes. The sequential nature of the reaction scheme, whether proceeding entirely via homogeaeaus pathways or with heterogeneous radical generation:

t

-4 ’ CH4 h2H, (C H ) 2 2 (5)

inherently limits the yields (i.e. the exit concentration) of unstable {reactive) intermediate products. In the kinetic scheme described in eq. (5). only CO, species are truly stable products that cannot reenter the available reaction paths. All other spies (C,H,, &HA, C2H,) are intermediate pmdmts that can react further to more stable CO, spDcies through reaction pathways not significantly different from those used in the activation of methane and which lead to the formation of these intermediate products.

The competitive consumption of C2 products to CO, [24] leads to the decrease in CS selectivity

observed as the level of methane conversion inmases; yields above 25% have not been reported [3,24-267, even ati exhaustive testing of many catalytic materials. Rwnt reports [27,281 clearly suggest the crucial role of secondary reaction6 in controlling Ca yields during oxidative methane coupling. It appears that alternate chemistry occurring at much lower temperatures, significant increases in catalytic methyl formation rates, or novel reactor designs, will be required in drder to increase C1 yields above presently achievable VaIUCS.

Structural propcrties of catalytic materials also af- feet selectivity and yields in bimadal chemical reactions. Heterogenmus steps depend on surface area and site density; homogeneous steps, in contrast. depend ori intrapeIlet and interpellet porosity. Mars over, the intermediate natute of the desired products and the high surface areas and turnover rata required for high heterogeneous radical generation rates oRen lead to intrapellet transport restrictions. Therefore, the pore size and tortuosity of catalyst pellets, and the d&tive diffusivities that these properties control, bewme crucial parameters in the design of novel cata- Lgtic materials.

Here, we present a detail& mdde1 that includes both homogeneous and heterogeneous kinetics. This model describes the effezts of reactor configuration and of the chemical and structural propertics of catalytic materials an Cl selectivity and yieId. Our reae tion-transport model consists of: (I) a homogeneous kinetic model consisting of 145 reversibte reaction steps, which describes available @s-phase reaction data without adjustable parameters, (2) heuristic kinetic models for surface-catalyzed reactions, and (3) pellet and reactor equations that describe the concentrations of 28 reactive sees involved in homogeneous-heterogeneous reactions.

This reactor model is used to explore the underly- ing basis for inherent yield [imitations, the role of heterogeneous radical generation steps, and the ef& of controlled oxygen injection and of surface kinetics on C, yields and selectivity. To the second paper in this series [i’J we exp1ot-e in detail the role ofintrapel- let diffusion constraints, which not only inhibit heterogeneous radical generation but can also lower oxygen concentrations within catalyst pellets.

z 0xiDArIvE COCPLING I~EACTION NETWORKS

2.1. Homogeneous kinetic modd

The homogeneous kinetic mtiel was asmbled from elementary steps reported previously for gas- phase reactions OC light alkanes [29-341, The model includes 145 reversible steps involving 28 reactive species. Elementary kinetics were used for most reactions, except those involving collisional activation or relaxation with third bodies (Appendix A)_ The stoichiomctry and rate constartts for each step are shown in Table 1, Reverse rates were calculated from equilibrium data [34] whenever reverse rate constants were not directly available. Reactions of C; hydrocarbons were excluded from the kinetic network be-

Kinetic-transport m&Is af bimddal reaetian scquenee-I 2645

cause Cjs are minor reaction products at typical oxidative coupling conditions. Reported rate and equilibrium constants were not adjusted in any way in order to improve the agreement between simulations and experimental data.

Individual reaction steps in the homogeneous kinetic model are shown in Table 1. Homogeneous methane conversion procmds by free-radical reactions that involve chain initiation, transfer, and termination presses. Primary initiation occurs initially by dissociation of methane in activating collisions with a third body (7; all numbers refer to reaction steps in Table I) or by hydrogen abstraction using O2 (I). As the concentration of radicals increases, faster chain transfer (2-6) and secondary initiation steps (8) become the preferred pathways for methyl radical formation.

Methyl radicals undergo bimolecular coupling reactions (9-l I) to give ethane and oxidative processes with 01, 0, HOz, and OH (19-29, 138, 139) to give methoxy and formaldehyde species that ultimately convert to CO, (30-35). Hydrogen abstraction from formaldehyde leads to formyl radicals (N-56) that react further to form CO (57-61) and CO2 (62-G). Formaldehyde also decomposes very rapidly on mac- tor walls (144). Methylene radicals formed from CH, (81) and ethylene (49) react further in non-oxidative hydrogen transfer reactions (72-74).

Ethyl radicals form in reactions of ethane with the same species that convert methane to methyl radicals (12-18). They also undergo sequential hydrogen abstraction events to form ethylene (36-42, 71). C~HS r%diGals (43-46, 136), and acetylene (127-129, 132). Cl radicals and reactive products lead to CH, (47, 48,75) and to CO and oxy-radicals (49,66.67,76-80, 126, 130-134). Cz oxy-radicals dehydrogenate to HCCO ( lO9- I t 2, t 18-124) and decompose to formaldehyde and CO (107, 108, Ill, 113). Dibydrogen forms in hydrogen atom coupling (84) and in several hydrogen abstraction reactions (e.g. 4, t I, 12, 22. II ). Free-radical reactions of H,O, species are also included in the homogeneous kinetic model (85-106).

A model catalytic function is used to explore the effects OE heterogeneous radical generation on attainable C2 yields. This catalytic function catalyzes (irreversible) hydrogen abstraction reactions with stoichiometry:

CH, + I/4 0, %CHS + l/2 Hz0

praceedjng at a rate given by

rcn, = k,. CH, . CL1 CCH,lC%lB (7)

where k,. CH., is the kinetic constant for methyl radical formation, CL.1 is the density of active sites, and n is the oxygen pr~ure order [ZO, 211. Similarly, ethyl radicals are assumed tti form in similar surface-

catalyzd H-abstraction steps:

C,H, + l/40+=+C,H, + 1/2H,O (8)

at a rate given by

rczn, = &.CzH, CL3 * ICA1 P21”. (9)

These simple kinetics are uxct to explore the effect of site density [L], site reactivity (ki) or selectivity

(k,,clr, !k *, e,u,), and oxygen pressure order on C f at- tamable yields. They describe a hypothetical surface capable of oxidative activation of alkanes to form alkyl radicals, but which does not catalyze undesirable full oxidation reactions of alkanes or alkyd radicals.

The volumetric rates of heterogeneous methyl and ethyl radical generation (rf; i = CH 9, CaHlr) can also be expressed in terms of intrinsic properties of the catalyst:

ri = 1o~~s;p,~[L~~y (10)

where rI is in units of mourn3 s. S, is the BET surface area (m’/g), pp is the particle density (&c), [L] is the density of active sites (sites/m’), and uy is the site turnover rate (molecules/sites). For illustration purposes, we choose typical values of site density (CL]- 1019 sites/m 7), surface area (S, _ 10 m’/gs). and particle density ( p r - 2 g/cc) to express r i solely in terms of site turnover rates:

r, = 3.32. 1Os* y (11)

where r,s are given by eqs (7) and (9). The site mat_ tivity of catalysts are compared on the basis of a standard turnover rate (uO):

Q, = b, [at 1073 K, 0.667 bar CHA, 0.333 bar O,]

(12)

deGrtcd as the turnover rate for methyl radical generation at a specified value of operating conditions. Such a procedure completely defines the value of kJ,Cnp in

eq+ 17). Ethyl radical generatioti tat+?.d are described by re-

Iating its rate constant (ka.C2H,) to that for methyl radical formation (ks+,+ ):

k &ClHl = Y ~ k,, cHx (13)

where y is a constant. The effects of a catalytic &UC- tion on maximum Cz yidds will be examined by varying ug from OLll to I00 [molecules/sit~), n from 0 to I, and y from 0 to 4. Typical experimental catalytic turnover rates are less than 10 (molecules/sites), reflecting expected limits imposed by slow diffusive arrival of reactants at more reactive sites.

3. REACTOR-PELLET EQUATIONS

Hen, we develop a genera1 mathemati~l framework that couples diffusion and (gas-phase and surface) reactions within catalyst pellets with (gas-phase) reactions and convection within interpellet voida In isothermal plug-flow reactors with aegligibte change in the total uumbr of moles, the mass conservatiort of

SEBASTIAN C. REYES et d.

2647

-

Tab

le 1

. (C

ontd

.)

Rea

ctio

n

For

war

d ra

te

Equ

ilib

riu

m co

llsi

arit

R

&T

el-I

ce

'XO,+OH~HO,+O

92 H,O,+HaH,tHO,

93 H,O,tOHe HOLtH,O

94 HLO,+O$OH+HO1

95 H,O,+M*OH+OHtM

%H

$+H

~H

,+O

H

97 H

,O+

O#O

H+

OH

98

OH

+H

+M

F!H

@tM

99

OH

+ HO,aH,OtO,

100H0,tH~H30t0

iOlHO,+HsOH+OH

102 H,O,+ O,aHO,+ HO,

103 H,+02#OHtOH

l@4H10,+H$HzO+DH

lCGOtHtM$OH+M

106

HO

,+M

~O

+O

H+

M

107c

H,C

0tM

Etc

H,t

CO

+M

10

8 C

HIC

O +

OH

e C

H,O

t

HC

O

109

CH

,CO

+ O

H 3

C,H

O

+ H

,O

110

CH

,CO

t 0 # C,HO t O

H

111 CHICO+O#CH,OtCO

112CH,COtHaC,HO+H,

113 CH

,CO

tHF

tCH

,tC

O

114

C,H

V+

O,s

CO

+C

VtO

H

115C

,HO

+O

~C

O+

CO

tH

116 C,HOtH#CH,tCO

117C,HOtOHrtHCOtH+CO

118 CH,CHOF!CH,~HCO

119 CH,CHOtO,eCH,CO+HO,

1m CH,CHOtH#CH,CO+

H,

121

CH

,CH

O

+ O

H #

CH

,CO

t H,O

122 CH,CHO#CH,CO+

OH

123 CH

,CH

O

+ C

H,

G C

:w,C

O +

CH

, 124 CH

,CH

O

+ H

O,

# C

H,C

V

t iI

@,

125

CH

,CO

+M

zCH

,+C

OtM

12

6 C

#,

+ H

O,

ti C

H,C

HO

+

OH

12

7 C

,H,+

M$C

,H,+

H+

M

128

C2H

, t

H #

C

,H,

+ H

, 12

9 C

,H,

+ V

, #

C,H

, +

HO

, 13

0C,H

,tO

,sH

CO

+C

H,O

13

1 C

,H, t 0 # C

HIC

O t

H

13

2 C

2H,

+ O

H #

C,HL + H,O

133

C,H

, f

OH

# C

HJH

O

-..

---.

__

-_

_ __

_

22-3

exp

( -

&5o

o/T

) 48

.2ex

p(-4

000,

‘T)

1.75

expl

- lW

J,fT

J 9-

6 x

lo-$

T’

exp

( -

ZC

Q/T

) 12

8 x 1

0zl T

-G6

exp(

-

26,7

95/T

) i2

x

ws

vexp

( -

926

5/T

) 4.

6 x

10-3

T’~

3exp

( -

8805

/T)

0*02

2T-’

14,4

55;T

30

.0

168.

6 exp

( -

44&

T)

54.2

“;p

( - 2

o*oo

o/T

~

t7.0

e.X

u i -

23s

wT

~

U,lC

$-

2&Q

/k).

4.

7x W

6T-’

5

x JO

-B ex

p ( -

34

254/

T +

31.

82)

3.63

x 1

03 ex

p ( -

29$

50/T

) 28

.2

7hex

p(-

Iwo/

T)

SO

.!1 ex

p( -

a/T

) 19

.95

75.9

exp

( -

4000

/i)

10.9

6exg

{-

1700

/T)

1.5 e

xp(

- 12

50/T

) 1.

2 N

W.4

10

.0

2 x

10’~

exp

{ -

39,S

WT

) 19

.9 T

0,s

exp

(-

21,1

00/T

) 39

.8 e

xp (

- 21

00/T

) 10

.0

5eX

Pi-

WU

O

.O85

exp(

- 3O

Wl/T

) lJ

exp(

-

5350

/T)

1.2

x IO

3 exp

(-

6303

rT)

6.02

2 IO

-acx

p(

-4w

/T)

18 x

i02

9T-‘.

4P

exp(

-

22,9

17/T

} 96

.4

0.12

4~P

wY

T)

33.1

1 3i

kl2

3Q2O

exp

( -

26,6

16/T

t 0

.09j

ex

p (9

063/

T +

0.5

9)

exp[

lh7,

lg7/

T -

0.99

) ex

p[80

68!T

t

1.39

) ex

p( -

26

,186

/T t

33

.21)

ex

p ( -

772

4/T

t

1.59

) ex

p( -

87

19/T

+

2.39

) ex

p(61

,319

/T-

31.5

8)

exp{

35,3

36/T

- 24

8)

exp

[27$

65/T

t

0.24

) ex

p(l8

J46/

T+

2.

M)

exp(

-

18,5

49/T

+

1.49

) O

Sex

p( -

14

,6W

/Tjr

ex

p(35

,133

iT t

1.

64)

yM+

;iW-

29.1

81

1.17

X 1

0-“e

xp(8

35O

~T

)*

16.2

exp(

- K

IN/T

) l.Oexp(-

7850

/T)*

0.

62 e

xp ( -

165

0/T

)t

XlZ

exp[

-

51,7

50/T

):

Lo4

exp

( -

26sO

/T)f

0*

89ex

p(-

1&50

0/T

)’ 3.

16 x

lO

“‘en

p(

- 45

,@X

I/T

y 3.

9 X

W”e

xp(-

55

600/

T)

51.3

exp

( -

15,5

00/T

)*

1.5xW"cxp(- 8

950/

T?

19ex

p (2

EqT

)t

204e

XpI

- 25

w/T

)*

18.2

exp(

- 11

,70O

/T)~

22

.4 ex

p ( -

17

,3oO

/T)f

1 a

xp (

- 94

50jT

)r

L4c

xpI

- 13

+I5

O/T

)’ 1.

5 exp

( -

72&

J/T

):

exp(

- 55

48/T

+

31.2

4)

2.95

x W

3exp

( -

27,5

50/T

)*

exp

(-

20,6

19/T

+ 2

9.70

) ex

p (3

2,97

6/T

- 0.

28)

exp(

536S

P

t 0.

61)

9.5

exp(

- 4L

XK

yT)t

2o

R9 e

xp (

- 42

,600

/T)t

ex

p(40

,700

]T-

1.87

) 7.

4 x

10’6

exp

( -

5730

0/T

)’

Kinetic-transport mcdels of bimdal reaction sequent- I 2649

reactive species i = 1, _._, N is described by

with initial conditions:

C,(z -o)-c~o. (I51

The right-hand side of eq. (I4) accounts for the rate of reaction of component i within bed interstices and within pellets, respectively. C,(z) is the molar concentration of species i at position .z in the f9actor, R ,,fR o, z) is the rate of reaction of speci- i in reaction j within bed voids at position z, and D1 and &,/&are the effective diffusion coefficient and the concentration gradient of species i, resprztively. WI), E, au and R. are the interstitial gas velocity, bed void fraction, bed surface area to volume ratio, and pellet radius, resl%Wvely. The above definition of gas velocity makes the bed r-&den= time equal to L/UO, where L is the reactor length.

The steady-slarc mass conservation equations and associated boundary conditions for the ith species within the pellets are

where Ci(~, z) is the molar concentration of component i at radial position r within a pellet and axial position z in the reactor, and R, and Lti are the rates

of reaction of component i in reactions j and k within pellet voids and at catalyst surfaces, resFtively. G and S are the number of homogeneous and surface- catalyzed steps, and @ is the pellet porosity. Aqua- tion (17) requires that concentrations at the pellet surface [Cr(R O, t)] be the same as those within bed interstices [Cl(z)] at all axial positions in the reactor. Equation (18) ensures that concentration profiles are symmetric with respect to the center of the pellet.

Equations ( 14)-(t 8) provide a general model that describes concentration gradients in both the pellet and the reactor characteristic dimensions. Computer simulations for this geuer;ll case will be described elsewhere [7J. Here, we explore cakes in which the reactor ia either empty (i.e. no catalyst pellets) or contains pellets that catalyze homogeueous-hetere geneous reactions without diKusiona1 inhibition.

If we neglect intraparticle diffusional constraints, eqs (14) and (16) can be combined using Green’s theorem to give

+(1-&E)@ (

5 RI,+ ; L, >

(19) 3= 1 k=1

2650 $~B&~TI.AN C. REYES er al.

WI = Go GOI

for spherical pellets: its solution describes the kbav- ior of reactors where homogeneous-heterogenmus reactions occur in kinetic-limited pellets (&c&u 5). Tha equations describe changes in the oou- ozntration of reactive species as reaction proceeds along the reactor length. They include homogeneous reactions within the interpellet and intrapellet void volume [s + (1 -6)&J and surface-catalyzed step, expressed per unit of intrapllet ralume [(i - ~)a]+ Equations (19) and (20) form a set of coupled nonlin- ear ordii differential equations that can IX solved using standard numerical methods.

The above system of equations for homogeneous-heterogeneous conditions reduces to the homogeneous case by simply requiring that the interpellet volume fraction (e) become unity. This leads to

Gl(O) = Cl0 (221

an equation whose solution describes the Mwwiour of homogeneous reactors (Section 4). The models described in this section extend previous descriptions that couple the gas-phase reactions with wrface- catalyzed steps [35].

4. HOMCGENIEOUS REACTOR SIMULATIONS

4.1. Comparisons w&k experimmml data

Solutions of the homogeneous reactor equations [(Zl) and (2211 are oomparcd in Fig. 1 with previously reported experimental data for methane/oxygen reactions in empty vessels [23, 361. Pre- dicted C2 selectivities are in excellent agreement with data by Droege et al. [36] at 1073 K, and CH,/O, ratios of 3 LFig. l(a)] and 5 rig. l(b)], and I bar total reactant pressure. At lower temperatures (1023 K) and reactant pressures (U.7 bar), the model also describes experimental selectivities vrtod by Lane and Wolf [23] [Fig. I(c)].

Simulations are also mnsistent with experimental results obtained in our laboratory at 923 K, 0,145 bar CH4, 0.07 bar 01, and 0.78S bar He (Fig. 2) in a gradientless recirculating batch reactor [37]. The model overe$timatcs the C, selectivity slightly, especially at low conversion, but describes ethylene con- tent and qualitative conversion trends quite aozur- ately [Fig. 2(a)J. Detailed selectivity comparisons [Fig. 2(b)] show that the homogeneous kinetic model underpredicts the rate of Ca conversion to CO, especially at low conversions. The poorer ag-nt at lower reaction temperatures is expected because reported holnopneous kinetics are usually obtained at temperatures well above loo0 K.

Fig. 1. Comparison of model predictions and experimental homogeneous seleztivities: (a) kd residence time effect on Cl eelexivity: (- ) model predimionr; (+) data from r&r- - [36] (1073 K, 0.75 bar CH, 0.25 bar O,k @) bed r&den= time e[fezt PII Ct selectivity; (- -). model pm- dictions; (&I data from relerence [36] (1073 K, a833 bar CQ 0.167 bar 0,); and (c) bed residence time &zctr on Ca selectivity: ( -) model pralictions; {a) data from refer- ence [23] (1023 K, 0.467 bar CH,. 0.233 bar O,, 0.30 bar

diluent).

react with molecular oxygen to form CO,. At longer residence times, ethane w&ctivity decreases, while ethylene and carbon monoxide selectivities increase [Fig. 2(b)]_ Ethylene selectivity reaches a maximum and then decreases suggestbg its intermediate role in a consecutive reaction sequence that ultimately leads to stable CO, products [eq. (511. In the mnt example, ethylene nkver disappears from the exit stream because oxygen reactants are depleted before their complete conversion to CO [Fie 2(b)].

Ai short residence times and low methane conversions, methyl radicals are produd primarily by reactions of methane with oxy-radicals and ethane is the predominant initial product pig. z(b)]. Methyl radicals combine with each other to prduce ethane or

Even at very low methane conversion, Cz s&&v- ities are less than ioO%, suggesting that CO formation can also occur by die oxidation of CH, or

CH, radicals [Fig. 2(b)]. C2 electivity decreases as conversion increases, leading to a maximum C3 yield (moles of mrbon in Cl/moles Cl-l, converted) at

Kiectiwranspert mo&ls of bimodal reactivn sequences-1 2651

1wt a.6

5 ID 16 w w W

(aI --ml

w,

w

40

w

5 10 16 W w w

Fig. 2. Comparison of m&l predictions and experimental homogeneous wkctivitiw: (a) bed residence time effects on CT selectivity and ethylene/ethane ratio: (-, -) model predictions; (m n ) data from this study (923 K, 0.145 bar CH,, 0.070 bar O,, 0.75 bar diluent) and (b) bed residence time cjTc& 09 &as.+ ethylene, CO, and CO, selectivities:

(- ) model predictions; (I + + A) data from this study (923 K, &I45 bar CH,. 0.070 bar O,, 0.75 bar diluent).

intermediate CH.+ conversions (and axial positions) in the reactor. This behavior is consistent with consecutive rea&ons involving Cz as an intermediate reactive product; it sugg=ts that reactor backmixing. which increases the effective concentration of reactive Cz products, would also markedly tower C, seleetiv- ity. Yield is defined as the product of selectivity and conversion; yields increase initially with incressing conversion, but reach a maximum and then decrease as conversion iwreases further because of secondary oxidation of Cz species.

We conclude that the gas-phase model describes experimental measurements well, especially at higher temperatures, where the kinetic constants used in the simulations were obtained (Table I). These constants were obtained from compilations of gasification, combustion and partial oxidation literature data ( > loo0 K); thtir extrapolated values at lower temperatures are undoubtedly less accurate.

4.2. Rmctant concentration eficts on Cz yirlds Homogeneous reactor model simulations were

used to explore maximum Ca yields as the temperature and the reactant mncentratians were varied. For mmpleteness, we are studying mixtures with wide ranges of CH4/Oz ratios. Operation under certain oxygen-rich compositions cannot he attained in practi.z lrecausc they lie within the explosion limits.

Methane and oxygen conversions increase with increasing reactor residence time [Fig. 3(a)]. An initial induction period is observed; it reflects the onsei of faster secondary initiation and chain transfer reactions and the initial build-up in the concentration of HOI, OH. 0. and H radicals formed by slower primary titiation steps (using Cl2 and M). The sig- moidal shape of the cuw~ is typical of autoignition processes, which involve fast chain transfer steps after slow and highly endothermic f-radical initiation reactions.

Reactor residence times required for a given oxygen conversion are inversely proporticmal to oxygen partial pressure [Fig. 3(a), 1073 K, 0.5 bar CH4 J, wg- gesting that primary initiation processes controlling the induction period are approximately first-order in oxygen concentration. The induction period is very sensitive to the rate of heterogeneous radical generation and radical quenching reactions, as we shall discuss in more detail later in Section 5.

‘OS

161

(cl ---l-W

Fig. 3. Oxygen concentration effects on methane conversion rate and selectivity (1073 K, 0.5 bar CH,, O.lGI.5 bar 0,): (a) oxygen consumption rate vs bed residence time; (b) C, yields vs oxygen mnuetiom; and (c)C, yields w methane

conversion.

2652 SEBASITAN C. REYF.S et d.

The effwts of oxygen. and methane concentrations on the yield of Cz hydrocarbons are shown in Fig. 3(b) and (c). At low oxygen concentrations, Cz yields continue to increase as conversion incce-. The slope of this curve (proportional to the C1 selectivity) $sc==ZS with inmasing conversion bscauti C2 products convert to more stable CO, molemles in

secondary reactions. At &her oxygen concentrations [e.g. CH+/On = I, Fig 3(b) and (c)], such secondary reactions occur more rapidly and C2 yields ultimately decrease at high methane conversion levels. Thus, maximum yields are obtained at intermediate valuea of oxygen conversion. At low oxygen concentrations, the maximum yield occurs at the reactor exit after almost complete conversion 0C the oxygen reactant [Fig. 3(c)].

Surprisingly, the maximum Cz yields that can be achieved from C&/O2 mixtures depend only weakly OTI inlet oxygen concentration (1073 K. 0.5 bar CH4, 0.1-0.5 bar 0,) [Fig. 3(c)]. These maximum yields reflect the steady-state concentration of reactive intermediates (C,) that exists when the formation and conversion rates of these Cz intermediati become equal. Because homogeneous formation and convet- sion rates of C, molecules depend similarly on oxygen .pressure, steady-state concentrations of these intermediates are nearly independent of oxygen pressure [Fig. 3(c)].

Very low oxygen concentrations (CH,/OO, p 5) inhibit secondary oxidation ma&&s but also limit the level of methane conversion that can be achieved within the reactor. Therefore, staging the introduction of oxygen could maintain reasonable high Cz selectivities while avoiding unreacted methane in the reactor effluent; however, Ct selectivities actually decrease sIightly as the oxygen concentration decreases, as shown by the decreasing value of the initial slopea in Fig. 3(c). As oxygen levels decrease, the rate of bimolecular methyl radical recombination reaction is more strongly influenced by the decrease in methyl radical generation rates than the corresponding rate of hydrogen abstraction from ethane to give ethylene and CO. Thus, ethane formation rates decrease fater than the rate of conrersibn or dthane to CO products, as oxygen levels decrease, leading to lower values of Cz yields.

As oxygen disappears from the reactant stream, much slower non-oxidative homogeneous (pyrolysis) reactions continue to occur and contribute to the observd methane conversion products. This leads to the slight upturn observed in Cz yield-conversion curves as oxygen is depleted [Fig. 3(c)] ; this occurs at lower methane conversion as the inlet oxygen levels decrease. Such pyrolysis reactions are very slow at oxidative coupling conditions and generally become sign&ant only at much higher temperatures and longer-m residence times. These pyrolysis reactions make it difficult to estimate maximum attainable C2 yields from yield-conversion plots because they ELUX a continuous but very slow increase in C1 yields with increasing bed residence time, even after oxygen

is depleted, This increase requires extremely long KW idence times at normal oxidative coupling conditions and it is not of practical interest, in our estimates of maximum yields, we have chosen a true maximum in yield-conversion curves or, in the absence of one, the yield obtained at 85% oxygen conversion, in or+ to avoid conditions that favor selective but extremely slow methane pyrolysis reactions.

The maximum Cz yields that can he achieved in a homogeneous plug-flow reactor depend on temperature and on the inlet concentration of reactants. The effects of temperature and of CH4/OL ratio are shown in Fig. 4 (at a constant CH, pressure of OS bar). Maximum yields occur at different methane conversion levels and reactor residence times as temperature and reactant concentrations change. This figure shows that maximum C2 yields increase (-3-W&) with increasing temperattire (873-1123 K) but become nearly independent of CHd/02 ratios for values up to 10; higher ratios Iead to complete oxygen depletion bdore any significant methane conversion occurs and, therefore, to tower C1 yields [see Fig. xc)]. The temperature effects reflect methyl radical generation rates that increase faster with increasing temperature than oxidation reaction rates, an effect that leads to higher steady-state methyl radical concentrations and favor bimolecular coupling steps as temperature increas-es. The weak dependence of Ca yields on CH,jOz ratio is consistent with the simiiar O2 pressure dependence of the C2 production and consumption steps.

The individual effects of methane and oxygen partial pressures on maximum Cl yields are shown in Fig. 5(a) (1073 K). This figure again shows that maximum yields are nearly independent of oxygen ~IYXS- sure except at very low pressures, when oxygen is depleted before &&cant methane conversion occurs. The net effect of total pressure of reactants ix, therefore., not very pronounced and is further illus-

Fig. 4. Temperature and methane/oxygen ratio eflecls on maximum C, yields [O.S bar CA4, IKI diluent].

Kinetictransport madels of bimcdal reaction sequences --I 2653

equal to that in a cofezd process. Under these coondi- lions, the oxygen pressure at each of N, injection points l~comes

Pi = Pflz/[l + (N, - 1)gl (23)

where Fe, is the total oxygen pressure equivalent to a cofeed process and E is- the oxygen conversion achieved in each stage More additiclna1 oxygen is _ introduced into the reactor; 01 = O.g5 is used in all simulations, in order to minimize conditions that favor slow methane pyrolysis reatiioti. In effect, staging the introduction of oxygen minimizes its local concentration but continues to provide a steady supply of a critical reactant and chemical potential to drive the conversion of methane.

Fig. 5. Merhaw aad okyghl concentration ekts on maximum Cz yields [IO73 K, no diluent]: (a) methane and oxygen concentration efkts; and (b) total pressure effects

(CHJO, = 2).

traced in Fig. 5(b) at a fixed CH,/O, ratio,. This figure shows that maximum Cz yields go through a maximum (-8%) for an intermediate value of total pressure (_ 1.5 bar). The rising portion of this curve occurs because the rate of methyl radical generation increases as pressure increases; the subsequent grad- ual decrease arises because full oxidation is slightly Favored over coupling reactions as total pressure in-

creases at constant C&/O1 ratio. Overall, the resulta presented in Figs 4 and 5 are consistent with available homogeneous oxidative coupling data [Z3, 36, and this study]. which suggest that yields greater than about 10% cannot be achieved throughout a wide range of temperatures and pressures in the absence of heterogeneous methyl radical generation sites.

Somewhat surprisingly, the ititroduction of oxygen at five points along the reactor length actually decreases the maximum C, yields that can be achieved [Fig. 6(a), CH.+/OZ = 11. As we discussed previously, a moderate decrease in O2 concentration injtially lowers the rate of methyl radical generation to a greater extent than the rate of CL consumption (ethyl radical generation), leading to a lower steady- state C, concentration, However, as we continue to increase the number of injection points along the reactor (NP = 100) and, consequently, lower the local oxygen concentration level, maximum attainable C2 yields become greater than those in mfeed homogeneous reactors. At such low oxygen concentrations, Cz selsctivities remain relatively high (slope of Cz yield vs conversion) up to higher CH, conversion levels and the continuous introduction of O1 allows successive increments in methane conversion without the rapid loss of selectivity typical of cofeed reactors. Overall, we find that increasing the number of 0, injection points along the reactor initially decreases& yitlds,slightly [FiB 6(b), 1073 K,0.667 bar CH,, 0.333 bar O,], but ultimately leads IO modest yield improvements (from 8 to 12%) as the number of injection points becomes very large and the reactor begins to resemble an Q-permeable wall reactor.

4.4. Concr0lM oxygen injecdon in hom0geneow reuctors

Our simulations show that oxidation of C2 products occurs primarily by reaction with molecular oxygen and with oxygen-containing species. Therefore, controlling the amount of oxyger~ in the gas phase and, consequently, the oxy-radical concentration, should improve the yields. Tbc concept of controlled injection is not new but has not ken explored systematically in the literature. Here, we explore the case in which the oxygen reactant is introduced sequentially along the reactor length, while keeping the total amount of oxygen added throughout the reactbr

An unavoidable and costly consequence of oxygen staging is an almast proportional increase in the residence time (and reactor vatumt) required to achieve a given methane conversion and C, yield as the num- her of injection points (NJ increases [Fig. 6(c}]. This occurs because the kinetic driving Foroe for the overatr conversion reaction decreases markedly as we decrease local oxygen concentrations by increasing the number of Or injection points along the reactor. A lOO-fold reactor volume increase is required to implement staging schetnes that lead to even minor improvements in homogeneous Cz yields (9.6%. N, = 40) [Fig. 6(b) and (c)l, Thus, ic appears that oxygen staging Tar yield improvements is an impractical approach in homogeneous rectors. Reactor designs such as noncatalytic oxygen-permeable wall reactors and high conversion backmix& reactors ap- pear to be equally impractical. Applications of staging and of these related typs of reactors, however, may become feasible in the presence of. a high-activity

2654 SBBAST~AN C. RWES et aI.

Fig. 6. The effect ol gttaged oxygen injection ofl homogeneous C, yields (1073 K, 0.5 bar CH,, 0.5 bar 0,): (a) coreed vs staged oxygen injwtion (H, = 5, IV, = SO); (b) rmximurn C, yield vs i/N,; and (c) required tid- time

w I/N,.

catalytic function that decreases the residence times

required to achieve a given methane conversion level in oxidative coupling reactors_ In the sections that

follow, we explore the benefits of a catalytic Function in oxidative coupling processes&

I HOMOGENEOUS-HETEBOGEINEDUS REACIFOB

!SlMCJLATIONs

In this saction, we de&be yield and selectivity trends in piug-flow reactors that combine gas-phase reactions with surface-catalyzed steps. We assume that active surface sites catalyze the formation of methyl and ethyl radicals only [reactions (6) and (7)]. Therefore, this analysis offers an optimistic view of the oxidative methane coupling process because &let&-

ous oxidation reactions at surf- are excluded; this optimistic model aHows us to explore an ideal catalytic function that establish& an absolute upper limit on attainable yields. The present analysis k,Jso re- stricted to kinetic-limiti conditions without intrapellet diffusional inhibition,’ whti mass conservation of species are described by eqs (19) and (201 this restriction will lo relaxed in a later report v]. The absence of diffusional inhibition leads to uniform reactant and product concentrations across a catalyst pellet. In such cases, the characteristic time scale for reactant diffusion is much shorter than that for chemical reaction.

5.1. Eflects of catalyst properties on maximum C2 yields

The C2 yield of combined homogeneous and heterogeneous reactions is controlled by three kinetic parameters that describe the catalyst: the turnover rate (u), the ratio of kinetic constants for ethyl and methyl radical generation (y), and the oxygen pressure order (n). Our simulations explore how these parameters affect product yields in r@hane coupling; they also suggest catalyst properties/&at lead to maximum C2 yields.

Figure 7 shows maximum Cz yields as a function of site turnover rate, a property that reflects the intrinsic activity of surface sites (curve A). These calculations assume no ethyl radical generation (y = 0) and first- order kinetics for oxygen pressure (n = 1) at catalytic surfaces. At low turnuver rates (v -c 0.1 s-l), the presence of a catalyst increases the maximum C2 yields obtained in homogeneous reactors only slightly. Sig- nificant yield improvements occur onty for turnover rates greater than about 10 s - 1 even on ideal s&cc- tive catalysts, which generate only methyl radicals without catalyzing detrimental full oxidation reactions or even ethyl radical formation. Figure 7 illus- trates that, even for this selective catalytic function, high yields ( z 30%) squire very high turnover rates ( > 30 s- 1 ), presently unattainable at reasonable temperatures on available catalytic materials+ Also, high turnover rates are likely to introduce diffusional limitations because pore structures in which

loo1

Fig. 7. The effect of an ideal methyl generation catalytic surface on maximum cz yields: (curve A) maximum yields; (curve B) catalyst effectiveness factor (1073 K, 0.667 bar

CH,, 0.333 bar O,, R = 1, y = Ci).

sites are contained limit our ability to transport react- sots into pellets where they are rapidly consumed by very active sites. This renders most active sites within pellets unavailable for reaction and leads to average reaction rates much lower than within kin&c-limited pelIets_ A simple analysis of diffusion/reaction (Ap pdix B) gives an effectiveness factor (percentage of kinetic rate attained) shown as curve B in Fi& 7 in which we assume oxygen to lo !he diffusion-limited component. It shows that as turnover rati-increase_ oxygen has a lower probability of reaching interior sites before reaction occurs (and u < lQO%k kinetic turnover rates greater than SO s - t are unlikely to be practically exp1oitc.d because of iutrapellct diffusion limitations.

Heterogeneous methyl radical generation incrcascs the local steady-state concentration of methyl radicals involved in bimolecular coupling reactions. An ideal catalyst function that selectively generates methyl radicals from methane (but not ethyl radicals from ethane) has only a -ndary effect in the rate of ethane consumption to CO, precursors. It increases secondary conversion of CI only through pathways or radicals that benefit from a higher conoentration of methyl radicals in the reactor. IIowcver, it seems unhkdy that a catalytic function that activates methane will not also activate ethane because of the similar activation pathways required and of the lower energy of C-II bonds in ethane compared with methane. Catalytic sites that also form ethyl radicals from ethane reduce the benefit of a catalytic function OIL Cz yields by providing pathways for the activation of desired C, molecuIes to more reactive precursors to full oxidation products.

In Fig 8, we illustrate the effect of ethyl radical generation on maximum yields. Curve A is for methyl radical generation only (y = 0) and curves B and C correspond to two levels of ethyl radical formation described by the parameters y = 2 and y = 4, respectively; the latter value retleers the relative reactivity of CaHs aud CHL in homogeneous hydrogen abstraction reactions. This figure shows that maximum yields decrease as the value of y increases &cause ethane converts more rapidly to more reactive ethylene,

acetylene, and oxygen-containing intermedia- ef- fective precurso r-s to CO,. Curves B and C rep-t more reahstic situations that, however, still neglezt direct oxidation of auy species at catalytic surfrlca Even without direct oxidation, very high turnover rates are required to achieve yields above 25% when y = 2 or 4. These results arc consistent with cxpcri- mental measurements obtained for a wide range of catalysts and conditions; yields greater than about 25% have not been experimentally observed [3, 24-261. Our simulations confirm that gas-phase reactions are a major obstacle to higher Cz yields; homogeneous pathways limit attainable CI yields in oxidative coupling processes even on idea1 selective catalysts.

Figure 9 illustrate the effect of oxygen pressure order of heterogeneous methyl radical generation rates on maximum Cz yields. The curves A, C, and D wcrc obtained for a surface reaction order of 0.5 and y-values of 0, 2, and 4, respectively. Curve B for first-order methyl radical generation rates is shown for comparison purposes (7 - 0, n - I). The increased yields with lower oxygen pressure order reflect the increasing ability of the catalyst to maintain a high rate of formation of methyl radicals as the oxygen pressure decreases with increasing conversion. TIICSC results suwt that low kinetic orders in oxygen concentration for heterogeneous methy radical formation Icad to higher Cz yields; preferably, they should be much smaher than the order of gas-phase reactions of reactive C1 products to CO, in order to maximize the benefit of the heterogeneous function as methane (and oxygen) conversion increase along the reactor length. As we will show later, such low reaction orders also maximize the benefits of staged oxygen injection in catalytic reactors.

It is well known that peroxy-radicals, formed by slow initiation from reactants (l), arc primary chaio- branching centers in methane coupling processes. Once formed, proxy-radicals participate in degencr- ate branching reactions that lead to intermediate products (e.g. Hz0 and HaCO) and take part in sub-

Fig. 8. Tht effect of an ideal methyl and ethyl gener&ion catalytic surface DP maximum C, ykIds: (curve A) n=l,y=O;(cwveB)n=1.~=2;(curveC)n~1,~=4

(1073 K_ 0.667 bar CH,, 0.333 bar O,L

Fig. 9. The cffazt of an ideal methyl generation catalytic surface L)” maximum C, yields: (curve A) PI = 0.5, y = 0; (curveB)n=l.y=O;(curveC)n-R5,ya2;(-I))

n = OS,7 = 4.

2656 ~EBAWlAt4 c. REYES @t d.

sequent chain transfer and propagation reactions. The initial increase in the concentration of prtiucts lead to the induction period and self-accelerating behavior ,shown in Fi& 3(a) because of a build-up in the concentration of chain-branching precursors. In par- ticula~, the formation of H,Oz is an imwrtant step, kuse this species decomposes in activated collisions with a third body (95) giving rise to hydroxyl groups that are very effective methy radical initiators (3). However, this decomposition step can be readily intercepted by H,O, collisions with .basic or inert surfaces that promote chain termination of these active centers, These radical quenching reactions cause the overall conversion to decrease and lengthen the induction period required in methane conversion [3841].

In this section, we sbow how a dimerent type of catalytic function, one that destroys chain transfer gas-phase centers, can be introduced into the reactor in order to control the rare and selectivity of homogeneous reactions. In some sense, this catalytic function acts as a staging mechanism that decreases the apparent O1 cotiamration within the reactor by scavenging oxy-radicals and. thus, reversing some of the homogeneous radical generation and transfer steps. In the process, however, it also decreases markedly the rate of homogeneous’mcthane conversion and the local concentrations of methyl radicals required in bimolecular coupling reactions.

The effect that radical qluenching has on C2 yields can be simulated by simply adding to the network of gas-phase reactions the following surface reaction:

HIOJ -40, + Hz0 (W

which can occur at reactive sites on the reactor wak or at solid surfaces within catalyst pelkts or solid inert materials [38, 391. FoIlowing our previous description of surface-catalyzed reactions (Section 2.2h we use the following kinetic expression:

rHlo = 55422- wzoa. [HA&] (qol/m3 s) (25)

which des&bes the rate of radical quenching in terms of a turnover rate for chain termination at surfaces (y~,~,). Figure 10 shows Cz yields vs r&dence time for various chain termination rates. This figure clearly shows the retarding effect of radical quenching on

Fig. 10. The effect of radical quenching an induction periods and maximum C, yields.

methane eonversion and its consequent etim on maximum Cz yields. These trends are cxlnsistent with experimental observations [38, 39,413. In particular, we have verified that by simply increasing the aspect ratio of an empty tub while maintaining total reactor volume, leads to lower methane cOnversion due to the increased frequency of reactive collisions of H,O, with the reactor walls. Similar conclusions apply to reactors containing increasing amounts of inert solids.

5.3. Controlled oxygrn injection in catalytic reacsors In the previous section, we showed that yields

greater than abut 25% require extremely high a&v- ity and selectivity of active sites, levels that are diEi- cult fo reach on porous materials becau~ of diffusional constraints. We also concIuded that the control of secondary gas-phase oxidation reactions is a critical requirement for higher C2 yields. These results suggested that further improvements in catalyst activity or selectivity alone are unlikely to increase Cz yieIds significantly above levels already reported [4-6, 261. Therefore, as we previously explored in homogeneous re;tctors, we consider the ef- fe&s of staging the introduction of oxygen into a bimodal catalytic reactor.

Figure 1 l(a) and (b) shows Cz yields as a function of methane conversion for cofeed (N, = 1) and staged oxygen injection (NP = 10 and N, = 50) on catalysts with heterogeneous oxygen pressure orders of 1 and 0.5, respectively. These simulations were carried out at 0.667 bar CH,, 0.333 bar 03, and T = 1073 K for a homogeneous-heterogeneous system with a tum- over rate of 1 s -‘, no ethyl radical generation (r = 01 and no diffusional constraints. Figure II(a) shows that, for high values of oxygen p-sure orders (n = I), staging the introduction of the oxygen feed along IO injection points does not improve C2 @Ais attained in the cofeed mode (N, = 1). Tncreassd yields are. obtained, however, whtn oxygen concentrations are lowered further by continuing to increase NP_ Fig- ure 1 l(b) shows that, for lower oxygen pressure orders (PI = OS), the maximum yield increases as we move from a cofeed mtie (&, = 1) to a staged oxygen injection process. even for few injection points (N, = 10). This occurs because lower oxygen pressures do not significantly decrease the catalyst ability to produce methyl radicals and maintain high methyl radical concenlrations, conditions that favor coupling reactions, even at low oxygen concentrations. Methyl radical generation at surface sites with weak dependence on oxygen concentration decreases more slowly than homogeneous ethyl radical formation and mn- version to CO, as oxygen concentration decreases.

Maximum C7 yields obtain4 as we increase the number of injection points are shown in Fig. Ia@. Curve A is for gas-phase reactions only and, as already shown in Fig. 6(b), shows only modest yield improvements over a cofeed process. Curves I3 and C describe the results for an ideal catalytic function for methyl radical formation only and oxygen pros- sure orders of 1 and 0.5, respectively. Clearly, the

Fig. 11. The eket of staged oxygen injection on homo- gcncous-heterogeneous C, yields (1073 K, 0.667 bar CH,, 0.333 bar 0,): (a) c~fead YS staged oxygen injection IN, = 10, Np,= 50. R = 1.0) and (b) coreed vt staged oxygen

rnjection (N# = 10, Np = 50, s = 0.5).

coupled homogeneous-heterogeneous systems show significant yield improvements, specially for catalysts with low oxygen pressure orders (curve C).

Because of the low oxygen concentrations that pre- vail in controlled injection reactors, the requimd bed residence time (or reactor volume) increases markedly with Nr A very large increase in residence time ( >lC@-fold) is required to cause significant yield irn- provements over a coked process. The least favorable case is for homogeneous reactors; the catalyst with the lowest oxygen pressure dependence is least affected by increased reaction times as oxygen introduction is staged along the reactor.

In the limit of a very large numk of injection points, the reactor behaves as a permeable membrane, except that the oxygen concentration profile actually changes as Oa is consumed between injection points (in our simulations, a new oxygen addition is done only after the previous amount has reacted to 85% conversion). An alternate but closely related proEBd- urc for achieving high +elds is to maintain a lixed, low oxygen, level throughout the reactor length. a process that could he achieved with an oxygen-permeable membrane or with a gradientless backmixed reactor. The results of a simuIation of this system [433 m presented in Fig. 13. Here, we plot maximum C, yields as a function of oxygen concsntration, eX-

pressed per unit at-methane pressure (0.667 bar) at the reactor inlet. As expected, this figure closely resemble Fig. 11(a) (curves A-C) but also shows that maximum C2 yields go through a maximum at intermediate. but

I I oml OAl 0.1 1

Fig. 12. The effect of rstaged oxygen @z&ion cm maximum C, yields and required bed rcsidtn62 times; (curti A) horn*- paecus reactiona u = 0; (curve B) IrctffDgatwr u&D_ 1.0 s-1, n=l.&y=O; (curve C) heferoge~eouq u=l.O g-1,

n = 0.5, y = 0 {IO73 K, 0.667 bar CH,, 0.333 bar 0,): (a) maximum C, yields vx l/hrP and (b) required residence time

vs I/N,.

P

Fig. 13, The etTect of a fixed oxygen concentration on mm- imum C, yields (curve A) homogcnwus reactions, v = 0 s-‘; (curve B) hcrerogeneous, u= 1.0 s-‘,n= 1.&r-0; (CUM C) het~~gene~~~, u = 1.0 s - I, n = 0.5. z = 0; (curw

I)) heterogeneous, v- 1.0 s -‘> d = 0, p = 0.

very low (10 - 3 -10 -‘h oxygen ooncenti-ations. In addition to curves A-C, which correspond to the con&- tions of those in Fig. 1 l(a), curve D for P zero oxygen pressure order is also included. Overall, this figure summarizes the benefits of low oxygen canccntratian for ideal catalytic functions. In practice, the required bed residence timea would bz very large and the maximum yields much lower because of the less selective nature of many catalytic materials.

In this section, we discuss how some of the apparent Cz yield limitations arc not necessarily inherent in the homogeneous-heterogeneous nature of the. reaction pathways and can be overcome by the selection of appropriate catalytic functions and reactor -ation, albeit with a great difficulty.

The kinetic scheme of cq. (5) can also be described 3s a sequential reaction:

A I,B LC

tCH,/O,) tc,) ICOX) (26)

where the objective is to increase yields of B, the intermediate product in this sequence. Clearly, this requires that we selectivety increase the rate of fmna- tion of B (rl) or that we selectively inhibit its subsequent conversion to C (Q). A selective catalytic function achieves the &rst and, with certain restrictions, the controlled injection of oxygen achieves the #&ond.

Clearly, the truly intrinsic C2 yield limits imposed by the presents of homobeous pathways have not been reached in practice, as shown by Cz yields well above 50% attainable in controlled injection [Fig. laa]] and permeable wall (Fig. 13) reactors. The apparent experimental limits are not intrinsic consequences of the required involvement of homogeneous pathways in oxidative coupling and can be overcome with the use of selective catalysts.

Spe.cifically, catalysts with high methyl radical generation turnover rates must not catalyze rapid SE+ ondaty full oxidation or Ca activation reactions. Also, heterogeneous kinetics must differ in their kinetic oxygen order from car-pnding homogeneous pathways spacifi~lly, heterogeneous methyl radic4 generation rates must be less sensitive to changes in oxygen concentration than homogeneous oxidative processes than catalytic activation of Ca products. These are rather strict requirements, certainly difficult to achieve in practice; they cannot, however, IX classi- fied as intrinsic with our cupTent knowLedge of the surface chemistry of methyl radical formation pathways.

Undoubtedly, the best catalytic performance (7 = 0, n = 0) till remain unattainable given the similar surface pathways and kinetics for methane and ethane reactions and the fact that all reactions ap proach first-order kinetics at sufficiently low reactant concentrations. Clearly, the practi= of controlled oxygen injection will require much more active and selective catalysts with heterogeneous oxygen pressure orders near zero. Yet, overcoming theEe limitations is not precluded by theory. The limitations may be dificult to overcome, perhaps even impossible, reactor designs may be complex and expensive to operate, and the catalysts may be unattainabIe with materials currently known, but the limitations are not intrinsic. The burden falls once again on catalysis to

ptuvide the required solutions to control the rather unselective nature of homogeneous reaction pathways,

7. CONCLUSIONS

In this work, we have developed a comprehensive reactionjdi~usion/~nv~i~n model that couples de+ tailed gas-phase reaction networks within interstitial and intrapellet voids with surface_Fatalpd steps in packed-bed reactors. This model is applied to the analysis of the onidative coupling of methane, a rypi- cal and important example of a bimodal reaction involving strongly coupled homogeneous and heterogeneous reaction pathways.

An accurate homogeneous kinetic model assembled from Iiterature data leads to predictions in excellent agreement with exprimental data in homogeneous reactors. This gas-phase reaction network is combined with an ideal heterogeneous reaction model (mcthyf and ethyl radi4 generation without surface oxidation steps) in order to Htablish how tht rate and specificity of the catalytic function affects methane conversion and CI hydrocarbon yields.

Homogeneous reactor simulations over a wide range of temperature and inlet reactant pressures show that maximum Cz yields greater than about S-9% cannot be obtained using CHc/& feeds. These simulations are consistent with experimental findings. These yield values can only be sIightly improved (up to - 12% for 200 injection wints) if instead of eofccd- ing CH, and O2 at the reactor inlet, the oxym reactant is introduced gradually along the reactor length in order to inhibit secondary oxidation rcac- tions of C2 reactive products.

Homogeneous C2 yields can also be improved by the addition or a catalytic function. However, detailed homogen~us-heterogeneous reactor mode.1 simulations over a wide range of catalyst properties (such as activity, selectivity, and kinetics) show that yields greater than about 30% require catalysts with very high turnover rates, highly selective sites for methyl radical generation, and heterogeneuus kinetics with low order in oxygen pressure. Further yield improvements can be obtained by staging the oxygen introduction through multiple injection ports. Hvwevcr, the resulting lower oxygen ~EMIES requiti much longer residence times (hger reactor volumes) in order to achieve a given methane conversion and Cz yield.

Overall, the model preswti here provides a powerful tool for scoping the behavior of chemically reacting systems where homogeneous reactions MZM in parallel with surface-catalyzed chain initiation and propagation steps. In particular, it allowed us to mechanistically interpret existing data on oxidative coupling of methane as well as to systematically explore reaction conditions under which C2 yields w be maximized. Our results will be extended in later reports to descrik irrtrapzllet transpot-t restrictions and to predict the effect of a catalytic function and of

(homo~neous-heterogeneous) reactions. u

Y NOTATION

bed surface area px unit volume molar concentration within iutrapellet voids molar concentration at reactor i&t molar concentration within interpellet voids oxygen molecular diameter effective diRusivity within catalyst pellets molecular diffusivity Knu&n diffusivity effective oxygen diffusivity fugacity of reactive species number of gas-phase reactions rate constant for consumption of corn- ponent A ratt constant for formation of component A rate eonstant for consumption of corn- ponent B kinetic constant for forward reaction kinetic constant for Fverse reaction pseudo first-order kinetic constant kinetic constant for heterogeneous methyl radial generation kinetic constant for heterogeneous ethyl radical generation cquilibdum constant reactor length rate of surface reactjon of component i in reaction k molecular weight of oxygen oxygen pressure order for surface- catalyzed reaction atalyst site density total numbeT of chemical species number of injection points total pressure oxygen pressure at injection point total oxygen pressure at reactor inlet catalyst pellet radial dimension forward rate ot reaction irreversible rate of surface reaction reverse rate of reaction rate of radical quenching at surfaces

rate of methyl radical generation at catalyst surface rate of ethyl radical generation at catalyst surface catalyst pellet radius rate of gas-phase reaction of component i in reaction j number of sutface-catalyzed reactions BET surface arca absolute temperature interstim gas velocity axial reactor dimension

ISI

WI

oxygen conversion bet-n injection points ratio of kinetic constants for ethyl to methyl radical generation at catalytic surfaces bed void fraction effectiveness factor stoichiometric coefgcicnt particle density tortuasity factor turnover rate pellet porosity Thiele modulus

REFERENCES

Derbentsev, Y. I. and Isagulyants, G. Y., 1969, Study of the mechanisms of heterogeneous-catalytic re~~Gons by the mcth& of labelled moleeulm (labelled with ‘%j. Russ. Chem Rev. 38, 714-727. Hung, S. L., Griflin, T. A. and Plcffcrle. L.-D, 1988+ The stability limits of the catalytically stabiilzed thermai combustion of methane md ethane. Jnd. Engng Ch. Res. 27, 1377-1382. Koch+ G. W., Krenzhe, L. D. and Notermann, T. M., 1972, Selective oxidction of propylene. A&. Cural. 2’7, 185-225. Drirsooll, 13. J, Campbell, K. D. and Lunsford, J. II, 1987, Surface-generated gap-phase racli& formation, de&ctiuo. and rote in catalysis. Rdv. C:atnl. 35,139-l 86. Lee, J. S. and Oyama. S. T., 1988, Oxidative wnpling of methane to higher hydrocarbons. Carol. R~u. Sci. ER#~# 30,249-380. Lunsford. J. H.. 1989. The role of surIace-generated gas-phase radicals in caralysis. LMgmlrir 4 12-16. Revcs. S. C.. Id&a. E and Kelkar. C. P.. 1992. Kirtetb tra&& J&&IS bP bimodal reaction s&n-. II. The role of intrapeHlet diffusion inhibitions in oxidative coupling of methane. Cham Enarrg Sci. (to be sub- mitted). Reyes, S. C., Iglcsia, E. and Kelkar, C. P., 1991, Rcac- tion-transport models of bimodal reaction networks. Oxidative coupling of methane, in Proce.&~s of 12th North Am&cart Meti@ of the Catalysis Society, Lexington. Kentucky. Santamaria. J. M.. Mire. E. E. and WolL E E.. 1991.

tlJ7-II65 Follmer, G.. Lehmann, L. and Baerns. M.. 198% Effect of transport limitations on Cs, selectivity in the oxidative methane coupling reaction using a NaOH!CaO ataiyst. CatolyvYis To&y 4, 323-332. Keller, G. E. and Bhasin, M. M., 1982, Synthesis of ethylene via oxidative coupling oI metbane. I. Deter- mination of active catalysts. J. Carol. 73, 9-19. Hinsen, W, Bytyn, W. and Baenrs, M., 1984, Oxidative dehydropnation and couphng of methane. in I%+ ceeditzgs 0f 8th intermuimal Confpm in Cptplygcp, Vol. 3, pp. 581-592. Ito, T., Wang, T. X., Lin, C. H. and Loosford, J. H, 1985, Oxidative dimcriz&m of methane over a lithium-prom&d rnasnesium OX& catalyst. J. Am. Chem. Sm. 107.5062-5068. van Kaat-, H. M. N., Ccerts. I. W. M. l-l. and van der Wiele, K., 1988, Ethylene synthesis by catalytic oxidation of methane over lithium dopad magnesium oxide catalysts: the interaction of catalytic and non- c&alytic tea&on steps, in Froce@dings of 9th I.C.C.

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ct71

ClSl

Cl91

WI

WI

~241

WI

WJI

~271

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WI

WI

C311

C321

c331

c341

(Edited by M. J. Pbilligs and M. Ternan), PP. 930-936. Calgaq. Canada. van Kasttren, J. M. N., Geerts, J. W. M. H. and van der Wiele, K., 1990, The role of heterogeneous reactions during the oxidative couplingofmethane over Li/MgO catalysts. Catalysis Today 6, 497-502. Geetts, J. W. M. H., van Kasteren. H. M. N. and van der Wick, K., 1990, Molten salts in a bubble cohu-nn reactor as catalysts for the oxidatiw cdupliag of methane. J. chrm S&z them Commun. tl,802-803. Campbell, K. D. and ‘Lunsford, J. H, 1988. Contribu- tion of gas-phase radical scrupling in the catalytic oxidation of methane, J. phys. Ckem. 92, 5792-5796. Martir. W. and Lunsford, J. H.. 1981. The lormation ol gas-phase n-ally] radicals from propylene over bismuth oxide and y-bismuth molybdate atalystg 3. Am Cla@m Sue. 103. 3728-3732. Dr&ll, D. I. and Lunsford, J. H., 1983, Kinetic iso- tope efht in the partial oxidation of proppylene over Bi,U,. J. phys. Chem. 87.30-303. Fen& Y., Niiranen. 5. and Gutman, D.. 1991, Kinetic studies of the catalytic oxidation of methane. 1. methane radm production on I % Sr/la,Oa. 1. phys. Chtva 95, 6558-6563. Fen& Y., Niitanen, 1. and Gutman, D., 1991, Kinetic studies of the cataIytic oxidation of methane. 2. Methyl radical mmbination and ethane formation over 1% SrjLa @,. J. phys. Chem. 95,65#-6568. Westbrook, C. K.. Creighton, J, Lund C. and Dryer, F. L., 1977. A numerical model of chemical kinetics of combustion in a turbulent flow reactor. J. phys. Chem 81. 2542-2554, Lane, G. S. and Wolc E E., 1988, Methane utilization by oxidative coupling. I. A study of reactions in the gas phase during tht cofeeding of methane and oxygen. J. Curs/. 113,. 144-163. Ek~t~om, A., Lapwewia, J. A. and Campbell, I., 1989, Ongm of the low limits in the higher hydrocarbon yields in the oxidative coupling reaction ol methane. A&. Catal. 56, LZP-L34. Dubois, J.-L. and Cameron, C. J,. 1990. Common fea- fwes ofoxidative coupling of methane mkfl catalysts. Appl. GuruI. 67, 49-71. McCarty, J. G., McEwcn. k B. and Quinlan. M. A., t 9943, Models of the direct catalytic partial oxidation of Iigbt alkane% in NQW ~.&pmenrs in S&&as Oxi&- riart (Edited by G. Centi and F. Triffiro). Elscvier, Amsterdam. Labinger, J. A. and Ott, K. C., 1987, Mechanistic studies on the &dative coupling of methane. J. pays. Chw 91, 2682-2684. Labinger, J. A., 1988, Oxidative coupling of methane: afi inhetint limit to s&ctivity. Cutal. L&t. 1.371-376. Skinner, G. B.. Ltfshitq A., Scheller, K. and Burcat. A., 1972, Kinetics of methane oxidation. J. &em. Whys. 56, 3853- 3811. Warnatz, J, 1984, lUe coet%zients in the C/H/O system, in Combustion Chemistry (Edited by W. C. Cardiner, Jr), pp. 197-360. Sprinsr, Berlin. Zanthoff, H. and Baerns, M.. 1990, Oxidativecoupling of methane in the gas phase. Kinetic simulation and experimental verification. Jnd. Engng Ctim Res. 29, 2-10. Mackie. J. C,, Smith. J. G,, Nelson. P. F+ and Tyler, R. J., 1990, Inhibition of C, oxidation by methane undw oridative coupling conditions. Energy Frrels 4 277-285. Bahn, G. S., 1965. Reactions involving H,O, HO,, atid 0,. but only fine of thedt specks with H,. O,, OH, H, and 0. FyradyMmics t, 3 15-317. Tsang. W. and Hampton, R. F., 1986, Chemical kinetic data base for combustion chemistry. Part I. Methane and r&ted compounds. J. Whys. Ch. A& Data 15, 1087-1279.

[35] Gbctts, J. W. M. H., Chen, Q., van Kasreren. J. M. N. and van der Wiele. K.. 19w. Thermodvnamlcs and

C361

c371

C381

II391

Cal

c413

~421

c431

kinetic modeling tithe homogeneous gas phase rea+ tione of the oxidativive coupling of methane. Caralysis Todcly 6, 519-526. Droqe, M. W., Hair, L. M, Fitz W. J. and Westbrook, C. K., 1989. Partial oxidation reactions of methane and oxygen. in Procerdings ofSPE Gas Tdmdogy Sympc- swum, SI’E 19081, pp. 247-256. Igksia, E, Baumgartner, J. E., Price, G. L., Rose, K. D. and Robbins. I. L., 1990, Alkane rearrangement pathways on tellurium&a& catalysts. .!. Col01. 12% 95-111. Vardanyan. I. A and Nalhdyan, A. B., 1985, On the mechanism of thermal oxidation of methane. Int. J. Chem. Kinetics 17, 901-924. Hatano, M., Hinsen, P. G,, Vines, K. S. and Lunsford, J. H., 1990, Comments on “Blank reactorconrctions in studies of oxidative dehydrogenation of melhane’” by D. J. C. Yates tid W. E. Zlotin. J. Cocol. IW, 557-561. Yates, D. J. C. and Zlotin, N. E., 1990, Reply to Hatano, Hinsen. Vines, and Lur~slo~d’s Comments on “Blank reactor correctiona in studi= of oxidative de+ hydrogetlntion ol methane”. J. Caral. 124. 562-565. K&r&, Z and Wolf E. E, 1890. Comments on the effect of gas-phase reactions on oxidative coupling of methane. J. Crrrul. 124, 566-564. Reyes, S. C. and Igksia, E., 1991. Efkctive diffu&iti= in catalyst pellets: new model porbus slrwtures and transport simulations tezhniqucs. J. Cud. 129, 457-472. ~rna& K., Aasbimoto, S., Taminaga, H. and Fujimoto, K., 1989, Oxidative coupling of methane using a membrane reactor. App!. Cata!. 52, Ll-L4.

APPENDM A: HOMOGENEOUS RFACTION KINETISS

The homogeneous kinetic m&l consisxs ol a network of revertible elementary steps tb+ account for the Comation and destruction of radicals and of reactive htermediate products; the network describes the consumption of reactants to rarm stable (CO,) and reactive (e.g C,H,, C,H,, H t, CO,‘. .) products. Kinetic parameters were obtained primarily from Tsang E34] and h&l& et 41. [32] wmpila- tions of literature data; but other sources [29-31, 331 were all ud when required steps were not rcportcd in these primary references.

Rate constants for monomolacular, bimolecular, and tri- molecular reactions arc in s-l, m3/mol * m6/j0-nola 8 units, resptively. The forward reaction rates are given by

‘I. I = $. i n cf, I”’ IAl) I

where k,,, is the forward rate conatant,J) is the fugacity or pressure of the reactants in the $h step, and Y is their stoichiomctric dcient in the chcmicxl reaction d eacribing the elementary process. Their values are reported in Table 1. The teeverse raics are given by

r,.i - ki fl CXI’” (.A21 h

with de&kg parameters similar to ahoe in (All but with the reaction step proceeding in the opposite direction. Valuer

or k, # or K, = kj.,/b arc also reported in Table 1. Ki values were calculated from thermodyoarnic data [34].

Rtaedan steps involving mlliaional activation or relaxation with third bodies (M) obey compkx pressure and temperature functions that are not adequately represent& by law or ma88 action kinetics. For example, the steady-state rate of 8. collisionally activatd step:

Kinetic-tran$porl models of bitnodal reaction 6eqwn-1 2661

is given by

(A41

At low pressures ([Ml 4 kc/k -*A collisional activation of A limits the overall reaction rate and eq. (AS) times

rate = kA[A][M]_ (ASI

At higher lures (CM] s k,/k -A), collisiona prmses are quasi-equilibrated and reactions of A* limit the overall rate

rate- = kB $ [A] (A61 A

thus, the reaction becomes pseudo-monomolecular in spite of the bimolecular nature of the initial wliisional activation step. The energy transfer et%ciency ol a third bdy (M) actuaIly depends on its chemical identity. In this study. we assume transfer &&n&s equal to those of the most elfezt- ive colliders in tbc reaction mixture.

All reaction steps containing M in Table I were analyzed using rate expressions similar to (A5j. Most appeared to exhibil bimotecular behavior even at high pressura~ (P & 10 barb Reaction steps {7), (9), (36), (Nl), (125X and (127) were corrected by ussing pressure and temperature functions for ka and k&,/k_, given by Tsang [34] [for (9b (SO), (12711 and Warn&z [30] [for (7), (36) And (12511.

APPENDIX a- PJ?FIXTIVENB3 FACTOR WITHIN CATALY5T PELLETS

Here, we develop a relationship between catalyst e&z- ivcness (II) and turnover rates (0) in order to illustrate how high volumetric activities. needed for improved yields, lead to diffusional inhibition within catalyst particles. High turnover rates lead to reaction time seal- much shorter than time scales for intraparticle diffusion; the resulting radial wncentration padients within pellets affect reaction rates and mltiivity. Both reactants and products may develop gradients within the particle, but we focus on oxygen as the limiting diffusion-hindered component; in effect, the diffusion sieving eflea is more pronounced for 0, than CH, [7]_ l%his. therefore, restricts our analysis to the effect of oxygen depletion within pellets on methane conversion rates. The general - where all species are diffusion-hindered is described e&where [7]+

At high turnover rates, oxygen consumption -rs primarily via reaction (6). The methane concentration is assumed to be uniform throughout the particle; therefore, the kinetic of this reaction, assumed to be an elementary step, becmnes pudo-firs-order in oxygen concentration. The carrcspond- ing ei%liveness factor (q = actual rate of reaction/rate of reaction at particle surface) for spherica particles then becomes

where

‘+‘a = lppp, R;/D’ 01 WI and Y is the Thiele modulus which quantifies the ratio of characteristic diffusion to reaction times; the larger this ratio is, the more diffusion-hindered the reaction becomes. R, is the radius of the catalyst pell&t, k”” is the pseudo-first-order kinetic constant for reaction (6), and D& is the cffactivc oxygen dit%.ivity within the catalyst pellet. According to eq. (7), the appareat kinetitic constant becomes

kpw = k z. cn,. C-LIo @31

where [CHJo is the methane concentration at the pellet surface.

The effective oxygen diffusivity can be estimated from I;421

where

Equations (B4 j(l36) are based on a simple m&l that estimates an effective difFusivity in terms of the propertiee of the pore structure (porosity UJ, rorluority s, BET surf= - S,, and catalyst density p,). and the Bosanquet’s appro&nation that averages contributions ro diffusion from Knudsen (D,) and molecular (Db) transport m-s within a pore 1421. For illustration purpom WC choose the following typical parameters to obtain TV as a function of U:

0 = 0.4; r = 1.8, S, = lOn+/g

p,=2&~Re=Z.5mm, T-1073K

P = 1 bar, [C&J, = 0.667 bar

which upon substitution in eqs (Bl)+6) gives

(B7)

The variation 01 ‘I (expressed ob a percent basis) with u is pmtwl graphically in Fig, 7; $ is always less than one, thereby showing that, for high turnover rates, the rate of methane consumption is always less than the corresponding rate obtained in the absence of oxygen concentration gradients within atalysf ptllets.

kinetic-transport models of bimodal reaction sequences. homogeneous and heterogeneous

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