Kinetic Modeling of Paraffins Hydrocracking based upon Elementary Steps and the Single Event Concept.

Reaction Kinetics and the Development of Catalytic Processes G.F. Froment and K.C. Waugh (Editors) 1999 Elsevier Science B.V.

Kinetic Modeling Elementary Steps

333

of Paraffins Hydrocracking based and the Single Event Concept.

G. Martens and G.F. Froment* Laboratorium voor Petrochemische Universiteit Gent, Belgium

upon

Techniek

Abstract

The kinetics of paraffins hydrocracking are developed in terms of elementary steps and single events,thus substantially reducing the number op parameters with respect to an adequate lumping or molecular approach. Plausible assumptions and thermodynamic constraints further reduce the number of independent rate coefficients to i0. These were determined from an experimental program with judiciously chosen Cs-paraffins.

i.

INTRODUCTION

So far the kinetic modeling of catalytic processes involving complex feedstocks and a large number of reactions between the various species has been based upon drastic simplifications yielding a small number of lumps and a limited number of reactions between them. Generally a lump consists of a large number of components belonging to a certain class of hydrocarbons. It is further defined by a physical property, like the boiling range or the density. Lumping is practiced in the modeling of the hydrocracking of vacuum gas oil or of wax produced by the Fischer-Tropsch synthesis. The reactions of the various lumps are described in terms of those of key components, thus inevitably leading to a biased product distribution and to rate coefficients which depend upon the composition of the lump, i.e., which are not invariant neither with respect to the feedstock composition nor to the operating conditions. Consequently a continuous experimental effort is required to support the kinetic model and its application. Froment and co-workers [1..3], on the other hand, excluded all lumping from the reaction network generation. Lumps are only introduced to account for the feedstock compositions, which is not very detailed with today's analytical tools and to set the partial pressures entering into the rate equations for the initial reaction steps. The lumps contain all possible components corresponding to their definition. In a judiciously selected lump the components should be at equilibrium. If the reaction network and the rate equation were based upon molecular structures the kinetic model would clearly comprise a gigantic number of rate coefficients since the rate coefficient for the h y d r o i s o m e r i z a t i o n of paraffins varies with the number of C-atoms in the molecule. To avoid this a more pronounced mechanistic description of the reaction scheme in terms of elementary steps is required. Hydrocracking catalysts contain a metal component (Pt, Pd,NiMo,CoMo,NiW) and an acid component, generally zeolite Y or alumina. The metal loading is sufficient to ensure that the rate determining step is located on the acid sites. The elementary steps on these sites are written in terms of carbenium ion chemistry. 2. O C T A N E

HYDROISOMERIZATIONAND

HYDROCRACKING

The various types of elementary carbenium ion steps o c c u r i n g in paraffins h y d r o i s o m e r i z a t i o n and hydrocracking are shown in Figure 1 for noctane. The elementary steps are protonation and d e p r o t o n a t i o n , h y d r i d e shifts,alkyl shifts,branching isomerization through a protonated c y c l o p r o p a n e intermediate and cracking through ~-scission. ,Present address: Department University, College Station, Texas

of Chemical 77843-3122,USA

Engeneering,Texas

A&M

334

+

§

i li +

!i-!

Craddng

§

11o 11_..

Figure i. Elementary and hydrocracking.

carbenium

3. R A T E

THE

EQUATIONS

FOR

ion

steps

ELEMENTARY

STEPS

in

paraffins

hydroisomerization

In hydrocracking at low temperatures and on a Pt-USY zeolite necessary to explicitly account for the physisorption of the feed nents [4]. This is preferably done through a Langmuir-isotherm:

it is compo-

Ku Pi CPi - Csae I + ~ KLI Pl

(i)

1

Dehydrogenation

into olefins

takes place on the metal:

Co~j .px~ Pi(ads)

The olefins

are protonated

= Oij + H 2

with

on Bronstedt Oij(ads)

KDH'iJ"

acid sites,

+ H § . RII §

(2)

Cp~

yielding

carbenium

ions (3)

335

which isomerize through on the a c i d sites:

hydride-

, methyl-shifts

and

PCP-branchings,

still

Ril ~ - Rno §

Cracking

also

occurs

on these

sites,through

(4) ~-scission:

(5)

Ril § - R;x/ + Or~(ads)

The steps on the a c i d sites are rate d e t e r m i n i n g so that the net rate of f o r m a t i o n of the p a r a f f i n s is the s u m m a t i o n of the net rates of f o r m a t i o n of the o l e f i n s :

Rp i - S The o l e f i n s that

are

involved

Roi~

(6)

in p r o t o n a t i o n s , d e p r o t o n a t i o n s

Rol j = E k D e ( 1 ; O i j ) 1

CRil.- E k p r ( 1 ) O o i j C H § j

and

+ ~kcz(Y;a,Oij) y

~-scissions,so

CR ,

(7)

The c a l c u l a t i o n of the c o n c e n t r a t i o n of the c a r b e n i u m ions a p p e a r i n g r e q u i r e s in the first p l a c e an e q u a t i o n for t h e i r rate of f o r m a t i o n :

3

in

(7)

1

i

o

(8)

+ ~ kcr (U; 2 ,o~) c,w- ~ kcr (2; q, o~)c,. u

In the p s e u d o

steady

q

state RaiI. : 0

Eqns acid

(8) and sites

(9),

together

with

a balance

Ct = CH" + $ $

form

a set

of

linear

equations

in

(9)

on the

concentration

of B r o n s t e d t

CRn"

CH., CRi I. .Its s o l u t i o n

(i0)

yields

to be s u b s t i t u t e d into the net rate of f o r m a t i o n of olefins, (7). S v o b o d a et al. [i] h o w e v e r d e r i v e d from t h e i r k i n e t i c s t u d y of c r a c k i n g that (I0) r e d u c e s to Ct=CH+.

4.

REDUCTION

OF THE

NUMBER

OF

the v a l u e s

Cs-hydro-

PARAMETERS

The network of C8 h y d r o i s o m e r i z a t i o n and hydrocracking contains 22 paraffins (17 o c t a n e s and 5 p r o d u c t s of cracking), 75 o l e f i n s (66 o c t e n e s and 9 p r o d u c t s of c r a c k i n g ) , and 57 c a r b e n i u m ions. To r e d u c e the n u m b e r of rate p a r a m e t e r s a n u m b e r of a s s u m p t i o n s has to be i n t r o d u c e d . 1 - O n l y s e c o n d a r y a n d t e r t i a r y c a r b e n i u m ions are c o n s i d e r e d , since m e t h y l and p r i m a r y ions are far less stable. 2-For a g i v e n type of R § (s or t) the rate c o e f f i c i e n t s are i n d e p e n d e n t of the c h a i n length. 3-The v a r i o u s k'isom o n l y d e p e n d on the type of r e a c t a n t ion (s or t) and p r o d u c t ion. 4-The v a r i o u s k'cr~k o n l y d e p e n d on the type of r e a c t a n t and p r o d u c t ion, not

336

on the p r o d u c e d olefin. 5-k'pr o n l y d e p e n d s on the type of R +. 6 - k ' m d e p e n d s on the type of ion and on the p r o d u c e d olefin. 5.

SINGLE

EVENT

RATE

COEFFICIENTS

In the above a s s u m p t i o n s the effect of the s t r u c t u r e of the c a r b e n i u m ions of a g i v e n type is not considered. To a c c o u n t for this effect B a l t a n a s et al. [2] i n t r o d u c e d the "single event" concept. A c c o r d i n g to the t r a n s i t i o n state t h e o r y the rate c o e f f i c i e n t s of the t r a n s f o r m a t i o n of a r e a c t a n t into the t r a n s i t i o n state c o m p l e x can be written:

k8

T

The

rotational

contribution

for the effect of following relation

the

A H 0*

A S o*

k I = ~exp(

R

to

AS ~

structure

on

)exp(-

was

RT

)

considered

k' .Baltanas

et

(ii)

to be al.

representative

[2]

derived

k / - ne.k

with

ne -

a~'z agl, #

the

number

of

single

the (12)

events

in

an

elementary

the rate coeffient of the single event. The global symmetry number

step

and

k

a~, r a n d o~,,

of the r e a c t a n t and the t r a n s i t i o n state also a c c o u n t for chirality. The c a l c u l a t i o n of ~ r e q u i r e s the c o n f i g u r a t i o n of the reactant, but also of the t r a n s i t i o n state. Recent q u a n t u m c h e m i c a l software, in p a r t i c u lar the ab initio versions, a l l o w the c o n f i g u r a t i o n to be d e t e r m i n e d in a r e l i a b l e way. 6.

THERMODYNAMIC

CONSTRAINTS

ON

THE

RATE

COEFFICIENTS

W i t h the a p p r o a c h b r i e f l y p r e s e n t e d here the n u m b e r of rate c o e f f i c i e n t s for p a r a f f i n s is r e l a t i v e l y small: 2 for o l e f i n s p r o t o n a t i o n ( one for sec R +- and one for tert R + - f o r m a t i o n ) , 4 for h y d r i d e shifts (kHs(S;s),kHs(S;t),kHs(t;s),kHs(t;t)),4 for m e t h y l - s h i f t s , 4 for P C P - i s o m e r i z a t i o n and 4 for ~scission. G i v e n the large n u m b e r of o l e f i n s the n u m b e r of i n d e p e n d e n t deprotonation coefficients is v e r y large, but this can be d r a s t i c a l l y r e d u c e d by i n t r o d u c i n g t h e r m o d y n a m i c constraints. For d e p r o t o n a t i o n the f o l l o w i n g r e l a t i o n was d e r i v e d by V y n c k i e r and Froment [3] :

kDe (m; Oij) i kD e (m, O r) fisom (Or"Oij)

(13)

where m stands for sec or tert and Or for a r e f e r e n c e o l e f i n isomer with the double b o u n d in such a p o s i t i o n that b o t h a s- or t-R + can be f o r m e d by protonation. Consequently, for a g i v e n c a r b o n n u m b e r there are o n l y two independent deprotonation rate coefficients: k ~ ( s ; O r) and km(t;Or). For octane h y d r o c r a c k i n g this r e d u c e s the k m from 85 to 7 ( 2 for C 8, 2 for C 5, 2 for C 4 and 1 for C 3 ). A l o n g s i m i l a r lines the f o l l o w i n g c o n s t r a i n t s were d e r i v e d for the k's of the three types of i s o m e r i z a t i o n :

k.s(~;s)

k.s(t;s)

k~cp(t;s) kp~(s)k~e(t;O)

k~zs(S; t)

kMs(S; t)

kpcp(S; t)

kpr( t) kDe(S;O)

(14)

337

This r e l a t i o n r e d u c e s the n u m b e r of i n d e p e n d e n t rate c o e f f i c i e n t s for HS-, MS- and P C P - i s o m e r i z a t i o n from 4 to 3. From the s e c o n d a s s u m p t i o n m e n t i o n e d above it follows that in ( 1 4 ) the ratio k ~ ( t ; O ) / k ~ ( s ; O ) h~s to be i n d e p e n d e n t of the olefin, e v e n w i t h a d i f f e r e n t n u m b e r of C-atoms. In o c t a n e h y d r o c r a c k i n g this f u r t h e r reduces the n u m b e r of k ~ from 7 to 5 (2 for C8, 1 for C 5, 1 for C 4 and 1 for C 3 ions). The c o n c e p t p r e s e n t e d here p e r m i t s the single event rate c o e f f i c i e n t s to be d e t e r m i n e d from h y d r o c r a c k i n g of short paraffins, w h e r e b y the c o m p l e t e p r o d u c t d i s t r i b u t i o n can be m e a s u r e d in a c o n v e n i e n t w a y e.g. by gas c h r o m a t o g r a p h y . To access all rate c o e f f i c i e n t s in an u n a m b i g u o u s way the c o m p o n e n t s to be c r a c k e d have to be j u d i c i o u s l y chosen.

7.

SELECTION

OF

REPRESENTATIVE

FEED

COMPONENTS

The f o l l o w i n g c o n s i d e r a t i o n s led to the final s e l e c t i o n of c o m p o n e n t s to be c r a c k e d : Previous w o r k did not s u c c e e d in d e t e r m i n i n g kMs(t;t) and ~r(t;t) [i]. In these e x p e r i m e n t s u s i n g n-octane, 2-Me-heptane and 2 , 5 - d i M e - h e x a n e the amount of t r i b r a n c h e d p a r a f f i n s was too low to be d e t e c t e d b e c a u s e of the fast (t;t) cracking. To d e t e r m i n e the above m e n t i o n e d rate c o e f f i c i e n t s 2,3,4 t r i M e - p e n t a n e was chosen. A m b i g u i t i e s were e n c o u n t e r e d for k~p(t;t). This single event rate coefficient is i n v o l v e d in the v a r i o u s e l e m e n t a r y steps t r a n s f o r m i n g di- into t r i b r a n c h e d R + and mono- into d i b r a n c h e d R +. Each of the t r a n s f o r m a t i o n s mentioned above contains next to PCP(t;t) also parallel PCP(t;s) or PCP(s;t) steps, so that the a s s o c i a t e d rate c o e f f i c i e n t s c o u l d not be i n d e p e n d e n t l y d e t e r m i n e d . There is no such a p r o b l e m w i t h the f o l l o w i n g four (t;t) P C P - s t e p s w h i c h t r a n s f o r m 2,4 d i M E - h e x a n e into 2,2,3- and 2,3,3triME-pentane :

W i t h a Cs-feed k~p(t;t) can o n l y be o b t a i n e d from the b e h a v i o u r of 2,4diMehexane, 2,2,3- and 2 , 3 , 3 - t r i M e p e n t a n e . F i n a l l y 2 , 3 , 4 - t r i M e p e n t a n e was s e l e c t e d since this c o m p o n e n t is not r a p i d l y t r a n s f o m e d b y (t;t) c r a c k i n g and thus also y i e l d s i n f o r m a t i o n on (t;t) a l k y l s h i f t s w i t h i n t r i b r a n c h e d paraffins.

8.

EXPERIMENTAL

PROGRAM

AND

RESULTS

The c a t a l y s t u s e d was a U S - Y zeolite c o n t a i n i n g 0.5 wt% Pt. The r e a c t o r was a B e r t y r e a c t o r for gas p h a s e operation. The t e m p e r a t u r e r a n g e d from 200 to 260 ~ the p r e s s u r e s from I0 to 50 bar, the r a t i o ~/HC from 30 to I00 and the space time from i0 to 420 gcat.s/mol. The e f f l u e n t c o m p o s i t i o n was a n a l y z e d by m e a n s of an o n - l i n e GC. The e x p e r i m e n t a l p r o g r a m c o n s i s t e d of : 201 e x p e r i m e n t s w i t h p u r e n-octane, 35 e x p e r i m e n t s w i t h a m i x t u r e of 90 mol% n - o c t a n e and i0 mol% 2 - m e t h y l p e n t a n e , 33 e x p e r i m e n t s w i t h a m i x t u r e of 90 mol% n - o c t a n e and i0 mol% 2,5 d i m e t h y l h e x a n e and 57 e x p e r i m e n t s w i t h a m i x t u r e of 90 mol% n - o c t a n e and i0 mol% 2,3,4 t r i m e t h y l p e n t a n e . The product distributions at various conversions confirm previous o b s e r v a t i o n s : e q u i l i b r i u m is r e a c h e d b e t w e e n the v a r i o u s i s o m e r s w i t h i n the mono- and d i b r a n c h e d families. This is not the case w i t h i n the t r i b r a n c h e d family because of the rapid (t;t) ~-scission [5]. An example of a c o n v e r s i o n v e r s u s space time curve is g i v e n in Figure 2 for n-octane.

338

K

T=S33

T=513

5o

c:

40

"-

3o

K

o 20

Io

o

I so

I

I

10o

15o

Space

Figure

2.

Conversion

9. P A R A M E T E R

of n - o c t a n e

I

I

I

200

~5o

Soo

t l me ( O c a t .

versus

space

850

sl tool )

time.

ESTIMATION

T h e n u m b e r of p a r a f f i n r e s p o n s e s p e r e x p e r i m e n t was 18 (4 less t h a n the n u m b e r of p a r a f f i n s in the r e a c t i o n n e t w o r k b e c a u s e of the o v e r l a p p i n g of 3 - M e - C 7 w i t h 3 - E t - C 6 a n d 3-Et-3-Me-Cs; 4 - M e - C 7 w i t h 3,4-diMe-C6; 2,3-diMe-C 6 with 2-Me-3-Et-Cs). Since replicate experiments were performed a weighted least squares objective f u n c t i o n was used. Its m i n i m i z a t i o n i n v o l v e d two techniques i) R o s e n b r o c k in the e a r l y s t a g e s 2) M a r q u a r d t in the final stage. Where well established rules of carbenium ion chemistry were available these were introduced as c o n s t r a i n t s on r a t i o s of r a t e c o e f f i c i e n t s of s o m e e l e m e n t a r y steps. The s t a t i s t i c a l t e s t s on the fit a n d on the p a r a m e t e r s [6] w e r e s a t i s f i e d . P a r i t y p l o t s for some of the r e s p o n e s are s h o w n in F i g u r e s 3 a n d 4. T h e p a r a m e t e r values, a l s o that of the physisorption c o n s t a n t of n - C 8 i s o m e r s are g i v e n in T a b l e I. Table 1 Composite

Arrhenius

and van

't H o f f

parameters

for C 8 h y d r o c r a c k i n g

Parameter

k'0 (mo i / (goath) )

E*0 (kJ/mol)

k'ms(S; S)

0.18

i0 I0

48.7

k*Ms (S ; t ) = k*Ms (t ; S )

0.33

i0 I~

48.1

k*MS(t ;t)

0.43

1011

47.9

k*~:p (s ; s )

0.61

i0 v

48.5

k*~zp (s ; t ) = k*pcp (t ; s )

0.86

108

48.0

k*~p (t ; t )

0.21

108

47.7

k*c~k (s ; s )

0.12

i0 I0

70.9

k*cr~k (S ; t )

0.45

106

17 .i

k'cr~k (t ; S )

0.88

1012

77.3

k*er~k (t ;t )

0.15

109

9.4

Parameter

K 0 (bar I)

AH~s k J / m o l

KL,8

8.3

74.8

10 .8

339

The rate coefficients k + in this table are products of the single event rate coefficient and the equilibrium constant for p r o t o n a t i o n / d e p r o t o n a t i o n [6]. The k+0 are really products of Csm,Ct,A*pr=A'~/A'mp and A'imm or A'cr+k. The prime indicates that the frequency factor of the elementary step does not include the entropy contribution due to the change in global symmetry since this is already accounted for by means of the number of single events, ~. E"0 in Table 1 is the algebraic sum of the p r o t o n a t i O n enthalpy and the activation enthalpy of the elementary step. The k'ms(S;S) and k'Ms(S;t) may contain a minor contribution of (s;s) and (s;t) ethyl shifts because of the overlapping of the GC peaks of ethyl- and methyl paraffins.

0.0of, ,.**i

o o.,,,, o.,,,,

o.o,,, ,.,,,l

o

o

r

,.i,4

,.,,.

,. ,,,a ,.ooo,

,.1,i

~176

o

,,,1,+

,.1,,i i.iii

::::::

o 0.***i

,.,**+

,.1,**

1.,**,

,.,,,

,.,,i

,.,,1+

1.1,+,

,.,,,,

Figure 3. Observed and calculated responses for 2,4-dimethylhexane

i0.

Figure 4. Observed and responses for propane.

calculated

CONCLUSION

A complete set of single event rate coefficients for paraffins hydroisomerization and hydrocracking has been obtained from an experimental program involving a number of judiciously chosen C 8 hydrocarbons. The set of parameters is statistically significant, satisfies the rules of carbenium ion chemistry and leads to an excellent fit of the experimental data. The fundamental modeling adopted in this work ensures that the set of parameters is valid also for the hydroisomerization and hydrocracking of higher paraffins.

ii.

REFERENCES

Svoboda G.D.,Vynckier E.,Debrabandere B. and Froment G.F., SingleEvent Rate Parameters for Paraffin Hydrocracking on a Pt/US-Y Zeolite,Ind. Eng. Chem. Res. 1995,34,3793 Baltanas M.A.,Van Raemdonck K.K.,Froment G.F. and Mohedas S.R., Fundamental Kinetic Modeling of H y d r o i s o m e r i z a t i o n and hydrocracking on N o b l e - M e t a l - L o a d e d Faujasites. i. Rate Parameters for Hydroisomerization, Ind. Eng. Chem. Res. 1989, 28, 899 Vynckier E. and froment G.F., Modeling of the kinetics of Complex Processes Based upon Elementary Steps. Kinetics and Thermodynamic Lumping of Multicomponent Mixtures, Astarita G., Sandler S.I., Elseviers Science Publishers, Amsterdam, 1991,p 131. Steijns M. and Froment G. F., H y d r o i s o m e r i z a t i o n and Hydrocracking. 3. Kinetic Analysis of rate data for n-Decane and n-Dodecane. Ind. Eng. Chem. Prod. Res. Dev. 1981,20,660. Martens J.A. ; Jacobs P.A. Conceptual Background for the conversion of hydrocarbons in Heterogeneous Acid Catalysis, Theoretical Aspects of Heterogeneous Catalysis, Moffat J.B. Eds. , Van N o s t r u n d Reinhold,

340

New York ,1998 Froment G.F., Bischoff E d , J o h n W i l e y & Sons,

12 N O M E N C L A T U R E A' = f r e q u e n c y factor contribution, hl

C H.

= concentration

Co~~

= surface

Cp~

= surface

of

of

elementary

free

concentration concentration

CR.

= surface

Csat

= concentration

C t = concentration

concentration of of

K.B., C h e m i c a l NY, 1 9 9 0

total total

active of of

step

reactor

not

acid

Analysis

including

sites,

and

Design,

symmetry

mol/gc~

O U, mol/gca t Pi,mol/gca t

of

Rik+ , mol/gc~

physisorption active

acid

sites, sites,

mol/gca t

mol/gc~

De = deprotonation DH = dehydrogenation ES = e t h y l s h i f t HD = hydrogenation k = single-event rate coefficient, hI k' = r a t e c o e f f i e c i e n t of e l e m e n t a r y step, h I k* = c o m p o s i t e single event rate coefficient, mol/(gc~.h) kcr(ml;m2, O U) = s i n g l e e v e n t r a t e c o e f f i c i e n t for cracking of a c a r b e n i u m i o n of t y p e m I to f o r m a c a r b e n i u m i o n of t y p e m 2 a n d a n o l e f i n Ou, h -I k ~ ( m , O U) = s i n g l e e v e n t r a t e c o e f f i c i e n t for deprotonation of a c a r b e n i u m i o n of t y p e m t o f o r m a n o l e f i n Ou, h -I kisom(ml,m 2) = s i n g l e e v e n t r a t e c o e f f i c i e n t for isomerization of a c a r b e n i u m i o n of t y p e m I to f o r m a c a r b e n i u m i o n of t y p e ~ , h ~ kpr(m) = s i n g l e e v e n t r a t e c o e f f i c i e n t for protonation of a n o l e f i n w i t h formation of a c a r b e n i u m i o n of t y p e m, h I KDH.U = d e h y d r o g e n a t i o n equilibrium c o n s t a n t of Pi to f o r m Oij, b a r KL.i = L a n g m u i r p h y s i s o r p t i o n c o n s t a n t of Pi, bar1 MS = methyl shift = n u m b e r of s i n g l e e v e n t s O U = olefin with index j formed from paraffin with index i Or = r e f e r e n c e olefin Pi = g a s - p h a s e partial pressure of Pi, b a r Pi = p a r a f f i n with index i Pr = protonation PCP = branching via protonated cyclopropane R§ = carbenium ion Rik§ = c a r b e n i u m ion with index k formed from paraffin with index i Rou = n e t r a t e of f o r m a t i o n of O~, mol/(gc~.h) Rpi = n e t f o r m a t i o n of Pi, mol/(gc~-h) RRik+ = n e t r a t e of f o r m a t i o n f o r Rik+, mol/(gc~.h) Acknowledqment The authors are the experimental

greatful data.

to

A.

Collier

and

B.

Debrabandere

for

providing

2