Petroleum Radiation Processing

1

1

Theory of

Radiation-Induced

Cracking Reactions

in Hydrocarbons

Practical application of the chain reaction theory for the interpretation of data on

thermal and radiation cracking of hydrocarbons and calculations of the basic crack-

ing parameters faces certain difculties associated with the following problems of

the theory:

1. The kinetic description of the chain cracking reactions often comes into

contradiction with the process of thermodynamics. In the case of thermal

cracking (TC), it does not allow a distinct determination of the cracking

start temperature, while in the case of radiation-thermal cracking (RTC),

it does not allow the determination of the dependence of the cracking start

temperature on the irradiation dose rate.

2. The methods for the calculation of the reaction chain length on the base of

the process kinetic characteristics are not sufciently developed. In the case

of radiation cracking, dependence of the chain length on temperature and

dose rate remains practically unknown.

3. A correct description of the dependence of the cracking rate on temperature

and dose rate (in the case of radiation cracking) requires a special theoreti-

cal consideration.

4. The nature of the reactions and molecular states, as well as mechanisms

of chain propagation in low-temperature radiation cracking (LTRC), still

remains unclear.

This chapter deals with the consideration of these problems as applicable to TC,

RTC, and LTRC of hydrocarbons.

1.1 THERMAL CRACKING: NUMBER OF PROPAGATION STEPS,

CRACKING START TEMPERATURE, REACTION RATE

By denition, the chain length is the number of elementary events in a chain reac-

tion initiated by a single chain carrier. The chain length is often interpreted as the

2 Petroleum Radiation Processing

ratio of the chain reaction propagation rate to its termination rate (or the rate of chain

initiation to the rate of chain termination).

The commonly used equations for chain initiation, propagation, and termination are

Kke

ii

EkT

iB

=

−

/

(1.1)

Kke

pp

Ep kT

B

=

−

/

(1.2)

Kke

tt

EkT

t

=

−

/

(1.3)

To calculate the chain length, the number of elementary reactions initiated by all

chain carriers in the unit of time should be divided by the number of carriers gener-

ated per unit of time. In the case of the radical mechanism (Talrose 1974),

ν

==

−

KR

K

kR

k

e

p

i

p

i

EE kT

ip

()

/

(1.4)

where R is concentration of the chain-initiating radicals.

Let us consider the case of a quadratic chain termination that prevails in the reac-

tions of hydrocarbon cracking.

In the dynamical equilibrium,

ke kR

i

EkT

t

iB

−

=

/2

(1.5)

This implies a well-known equation for the radical concentration:

R

k

k

e

i

t

Ek

T

i

=













−

12

2

/

/

(1.6)

The number of propagation steps (chain length) can be evaluated as

ν

==

−

−

−

W

K

kkeke

ke

p

i

it

EkT

p

EkT

i

EkT

i

p

i

/

/

/

2

/

or

ν

=

−

k

kk

e

p

it

EEkT

ip

(/ )

2/

(1.7)

Here, E

i

/ 2 − E

p

≈ 20 kcal/mol.

Thus we come to an absurd expression inapplicable to a chain endothermic

reaction.

3Theory of Radiation-Induced Cracking Reactions in Hydrocarbons

Wu et al. (1997b) suggested that the reaction mechanism and rate constants of vari-

ous reactions in the case of RTC should be the same as those for pure TC. They repre-

sented a summary of the reaction mechanisms for liquid-phase cracking of long-chain

parafns proposed by many authors (Voge and Good 1949, Ford 1986, Khorashev and

Gray 1993, Song et al. 1994, Wu et al. 1997a) to account for the product distributions.

It was noted that liquid-phase cracking obeys a one-step mechanism, while gas-

phase cracking follows a two-step or multistep decomposition model. The following

basic reactions were proposed for hydrocarbon cracking in the liquid phase:

Initiation

MRR

ki

jj

→+

*

thermalinitiation

(1.8)

MRRR HR

P

jj

∼∼→→++*

**

*andradiationinitiation (1.9)

Propagation

′

+→+

′

RM HM

k

H

*

(1.10a)

MR alkene

k

p

* →

′

+−1

(1.10b)

Radical addition

MalkeneC

k

ad

*

+− →

′

•+

1

18

(1.11)

Termination

MM product

k

t

**

+→

ρ

1

(1.12a)

′

+→RM product

k

t

*

ρ

2

(1.12b)

′

+

′

→RR product

k

t

ρ

3

(1.12c)

R′ =

•

C

1

−

•

C

15

in the case of hexadecane.

In Equations 1.8 through 1.12, M indicates the n-hexadecane molecule and R*

the parent radical; ρ

1

− ρ

3

denotes the probabilities of different terminations in the

liquid phase and gas phase, respectively. Isomerization of primary to secondary

radicals was not included in this scheme. The authors (Wu et al. 1997b) explained

it referring to the assumption in the paper (Kossiakoff and Rice 1943) that, prior

to H abstraction and β-scission, larger radicals isomerize instantaneously through

internal hydrogen abstractions with ring formation. It should be pointed out that this

statement is not applicable to alkane isomerization. Isomerization is not an instanta-

neous process and not necessarily resulting in ring formation.