**c.** Reaction-level model

**b.** Process-level model

122 Advances in Petrochemicals

transverse direction [2].

been reported.

A process-level model consists of mass balance equations, momentum balance equation and energy balance equation (eqs. (3-5)) [40, 41]. For the simulation of smooth tubular reactor types, the use of a one-dimensional reactor plug-flow model is generally recognized as providing a sufficient degree of accuracy, as all radical profiles are wiped out due to the high turbulence corresponding to Reynolds numbers of over 250 000. The plug-flow reactor model implicitly assumes that there is no mixing in the axial direction, but rather, perfect mixing in the

*i*

( ) r10

× ×

*o w fm*

<sup>0</sup> ( )

*D H*

 - D ×- = = å

*p m m m*

*m*

coefficient, *Tw* is the outer wall temperature of the tube, *ΔHfm0*

*o*

*r*

*COT T*

l

*r r COT r r*

D = <sup>+</sup> - <sup>+</sup>

of species *m* and *cpm* is the specific heat of species *m*.

*dN <sup>S</sup> r f TPN dL V* , = = <sup>å</sup>n

*i dP <sup>f</sup> f TP EL G <sup>N</sup>*

*<sup>d</sup> k TT dT f TPN dL <sup>c</sup>*

*N*

2 <sup>4</sup> , , 5.07

*m*

*dL D*

p

( )

*m*

*N*

*dL*

In eq. (3), *Nm* is the concentration of species *m* and *L* is the length of the reactor tube. *S* is the flow area, *V* is the volume flow rate, *μim* is the stoichiometric coefficient of reaction *i* and *ri*

the reaction rate of reaction *i*. In eq. (4), *P* is the pressure of the mass flow, *f* is the Fanning friction factor, *E(L)=Le/L*, *Le* is the equivalent length of the reactor tube, *G* is the mass flow rate, *Di* is the internal diameter of the tube and *ρ* is the density of the gas mixture. In eq. (5), *T* is the temperature of the mass flow, *Do* is the outer diameter of the tube, *k* is the overall heat transfer

It should be noted that the measuring point of the COT (coil-outlet temperature) of an industrial furnace is usually on the outer wall of the tube. Thus, the measured COT has a temperature difference from the outlet temperature of the gas mixture. Eq. (6) has been derived from heat balance equations in order to adjust to the temperature difference; the results show that there exists a 15-20K temperature difference, which agrees well with what has previously

*o isolation i coke tube mixture i coke*

ln ( )

*d d r d*

*r*

æ ö ç ÷

è ø

 a

<sup>+</sup> - - (6)

ln <sup>1</sup> ln

l

( ) *<sup>o</sup> isolation isolation o i i*

\_

*P m* ( )

´ ´ <sup>=</sup> <sup>×</sup> = - (4)

( )

<sup>å</sup> (5)

is

is the standard heat of formation

*T m*

, ,

, , (3)

*imi N m*

The reaction model is the most important part of the steam cracking model. Many researchers have conducted in-depth studies on the elementary reaction model. An elementary reaction model can contain thousands of reactions and hundreds of species. The reaction model can be extremely hard to solve due to its stiffness. An accurate and robust elementary reaction model is developed in this chapter, and a Gear algorithm is used to solve the stiff ODEs. Generally, a detailed reaction network is generated by allowing the feedstock components to react according to different reaction families. The reaction families can be summarized as follows: (1) initiation reaction and termination reaction: *R1—R2* ↔ *R1∙+R2∙*; (2) hydrogen abstraction reaction: *R1—H+R<sup>2</sup>* ↔ *R1∙+R2—H*; (3) radical addition and *β*-scission reaction: *R1∙+R2=R3* ↔ *R1—R2—R3∙*.

**Figure 3.** Sub-models in the generation of hydrocarbon steam cracking reaction networks.

The hydrocarbon steam cracking elementary reaction network can be separated into several sub-models. based on the composition of feedstock as shown in Figure 3. The sub-models are generated separately, based on the reaction families described above.

An elementary reaction model for light hydrocarbon can be found in much of the literature and databases, and it is more accurate than the automatic generated elementary reaction model. Thus, the elementary model for steam cracking is separated into two parts: a light hydrocarbon and heavy hydrocarbon reaction model (carbon number greater than five). The light hydrocarbon reaction model is generated using RMG [24]. RMG considers each species as unique and comprising a set of molecular structural isomers. When a reaction network is generated using RMG, it need not consider all the isomers in the real steam cracking process; instead, only a set of representative species are considered during the generation of a reaction network. The heavy reaction model is combined using different reaction models of pure compound feedstock and each reaction model is generated from the reaction families. The reaction coefficients can be obtained from the summary of experimental data (Table 1) in the

work of Dente et al. [26]. The heavy hydrocarbon reaction model was generated using our own code.

The automatic generated reaction network may contain a large number of unimportant reactions and species. These reactions can increase the complexity of the model and make the model hard to solve. Thus, reaction model reduction is needed following the automatic model generation. The QSSA method is introduced first to remove the *μ* radicals in the reaction network [33]. As eq. (6) shows, the reaction rate of *μ* radicals can be treated as zero, based on the assumption.


**Table 1.** Reference kinetic parameters of pyrolysis reactions [26].

$$\frac{d\begin{bmatrix} c \\ \end{bmatrix}}{dt} = r\_{\text{formation}} - r\_{\text{consumption}} \approx 0 \tag{7}$$

Thus, eq. (8) can be derived from eq. (7):

**Figure 4.** Flowchart of automatic generation and reduction of reaction network.

work of Dente et al. [26]. The heavy hydrocarbon reaction model was generated using our own

The automatic generated reaction network may contain a large number of unimportant reactions and species. These reactions can increase the complexity of the model and make the model hard to solve. Thus, reaction model reduction is needed following the automatic model generation. The QSSA method is introduced first to remove the *μ* radicals in the reaction network [33]. As eq. (6) shows, the reaction rate of *μ* radicals can be treated as zero, based on

*CH3-Csec Csec-Csec Csec-Cter Csec-Cquat*

exp(-13,500/RT) 108

exp(-14,500/RT) 108

exp(-15,000/RT) 108

Primary radical 1011exp(-20,600/RT) 1.58×1010exp(-14,500/RT) 3.16×109

Secondary radical 1011exp(-21,600/RT) 1.58×1010exp(-15,500/RT) 3.16×109

Tertiary radical 1011exp(-22,100/RT) 1.58×1010exp(-16,000/RT) 3.16×109

Methyl radical Secondary radical Tertiary radical Alkyl radical

exp(-2,500/RT) exp(1,500/RT) exp(2,500/RT) 0.316×exp(8,000/RT)

*formation consumption*

*r r*

5×1016exp(-83,500/RT) 5×1016exp(-81,000/RT) 5×1016exp(-80,000/RT) 5×1016exp(-78,000/RT)

Primary H-atom Secondary H-atom Tertiary H-atom

1-4 H-transfer 1-5 H-transfer 1-6 H-transfer

Primary radical Secondary radical Tertiary radical 1014exp(-30,000/RT) 1014exp(-31,000/RT) 1014exp(-31,500/RT)

0

ë û =- » (7)

exp(-11,200/RT) 108

exp(-12,200/RT) 108

exp(-12,700/RT) 108

exp(-9,000/RT)

exp(-10,000/RT)

exp(-10,500/RT)

exp(-19,500/RT)

exp(-20,500/RT)

exp(-21,000/RT)

code.

the assumption.

124 Advances in Petrochemicals

**Initiation reactions: unimolecular decomposition of C-C bonds**

**Isomerization reactions (Transfer of a primary H-atom)**

**Alkyl radical decomposition reactions (to form primary radicals)**

**Table 1.** Reference kinetic parameters of pyrolysis reactions [26].

Thus, eq. (8) can be derived from eq. (7):

*d c*

é ù

*dt*

**Corrections of decomposition rates to form**

**H-abstraction reactions of alkyl radicals**

Primary radical 108

Secondary radical 108

Tertiary radical 108

$$\left| r\_j + \sum\_{i \neq j} k\_{i,j} \mathcal{R}\_i - \left| \sum\_{i \neq j} k\_{j,i} + k\_{d\_i} \right| \mathcal{R}\_j = 0 \right. \tag{8}$$

In eq. (8), *rj* is the rate of direct formation of *j*-radical, *ki,j* is the rate constant for the isomerization reaction (*Ri* → *Rj* ) and *kdj* is the total rate constant for the decomposition reactions of *Rj* ; *μ* radicals are reduced using eq. (8). The number of species included in the model is decreased.

Reaction rate analysis is used to reduce the unimportant reactions in the reaction network. The average reaction rate in the reaction network reflects the importance of the reaction in the network. Thus, we can rank the reactions based on the average reaction rate and reduce the reactions where the reaction rate is less than *Rmin* [44].

The flowchart of the automatic generation and reduction of the reaction network is shown in Figure 4.

**d.** Molecular-level model

The physical properties of some species (radical, non-common substances, etc.) involved in the model are difficult to obtain from databases. The physical properties of these species can be calculated using the group contribution method [42]. RMG also supplies a thermochemistry estimates utility using the group contribution method and was used in our model to auto‐ matically calculate the physical properties of these species.



In eq. (8), *rj*

Figure 4.

**d.** Molecular-level model

reaction (*Ri* → *Rj*

126 Advances in Petrochemicals

reactions where the reaction rate is less than *Rmin* [44].

matically calculate the physical properties of these species.

CH3J+CH3J ↔ C2H6 8.26E+17 -1.4 1 BUT-2+C2H5J ↔ C4H7J

C2H5J+HJ ↔ C2H6 1.00E+14 0 0 BUT-1+C3H7J ↔ C4H7J

C2H4+HJ ↔ C2H5J 1.55E+14 0 2.8 BUT-2+C3H7J ↔ C4H7J

C2H6+HJ ↔ C2H5J+H2 2.27E+08 1.75 7.51 BUT-1+C3H7J ↔ C4H7J

HJ+HJ ↔ H2 1.09E+11 0 1.5 BUT-2+C3H7J ↔ C4H7J

C3H7J+HJ ↔ C3H8 2.00E+13 0 0 BUT-1+C2H3J ↔ C4H7J

CH3J+C3H7J ↔ i-C4H10 6.64E+14 -0.57 0 BUT-2+C2H3J ↔ C4H7J

C3H8+C2H5J ↔ C3H7J+C2H6 3.08E+03 2.66 10.1 BUT-1+C4H7J ↔ C4H7J

C3H8+HJ ↔ C3H7J+H2 1.60E+08 1.69 4.78 BUT-2+C4H7J ↔ C4H7J

**Reaction A n E**

is the rate of direct formation of *j*-radical, *ki,j* is the rate constant for the isomerization

radicals are reduced using eq. (8). The number of species included in the model is decreased.

Reaction rate analysis is used to reduce the unimportant reactions in the reaction network. The average reaction rate in the reaction network reflects the importance of the reaction in the network. Thus, we can rank the reactions based on the average reaction rate and reduce the

The flowchart of the automatic generation and reduction of the reaction network is shown in

The physical properties of some species (radical, non-common substances, etc.) involved in the model are difficult to obtain from databases. The physical properties of these species can be calculated using the group contribution method [42]. RMG also supplies a thermochemistry estimates utility using the group contribution method and was used in our model to auto‐

**(kcal/mol)**

CH3J+C2H5J ↔ C3H8 1.37E+13 0 0 BUT-1+HJ ↔ C4H7J+H2 1.40E+04 2.36 1.11 C2H5J+C2H5J ↔ n-C4H10 1.15E+13 0 0 BUT-2+HJ ↔ C4H7J+H2 2.60E+06 2.38 2.8

+C2H6

+C3H8

+C3H8

+C3H8

+C3H8

+C2H4

+C2H4

+BUT-1

+BUT-1

C3H6+HJ ↔ C3H7J 2.01E+13 0 2.1 C4H7J ↔ C4H7J 2.82E+08 1.28 27.89

**Reaction A n E**

) and *kdj* is the total rate constant for the decomposition reactions of *Rj*

; *μ*

**(kcal/mol)**

3.36E+12 0 12.39

1.94E+02 2.96 6.79

1.72E+12 0 12.29

3.12E-04 4.31 3.39

3.36E+12 0 12.39

5.11E+00 3.59 5.06

4.64E+13 0 7.5

3.12E-04 4.31 3.39

3.36E+12 0 12.39


**Table 2.** Elementary reaction network for light hydrocarbon steam cracking.
