a delayed coking model built using the structure-oriented

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A Delayed Coking Model Built Using the Structure-OrientedLumping MethodLida Tian, Benxian Shen,* and Jichang Liu

State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237,People’s Republic of China

ABSTRACT: A total of 7004 types of molecular lumps and 92 types of reaction rules were proposed to characterize the feedstock and describe the reaction behaviors of delayed coking. The reaction rate constants were estimated as equations of structure vectors.

A reaction kinetic model has been built to predict the products distribution of delayed coking. The good prediction accuracy of themodel has been proven by the comparison of calculation results and experimental results of delayed coking.

1. INTRODUCTION

In 1992, Quann and Jaffe proposed the concept of structure-oriented lumping (SOL).1 ,2 This concept made the kineticlumping method extend to the molecular level and made itpossible to describe the reaction behaviors of complex reactionsystems. In recent decades, the SOL method has been appliedin some fields. In addition, some SOL models have been builtcontinually .3 ,4 In 2005, Jaffe extended this concept to residuedescribing.5 However, building kinetic models of delayedcoking still had two problems: the feedstock residue isdifficult to characterize, and the reaction rate constants aredifficult to calculate. This paper solved the two problemsand built a kinetic model of delayed coking using the SOLmethod.

2. CHARACTERIZATION OF THE FEEDSTOCK

2.1. Structure Vectors To Characterize Feedstock. InSOL, 22 structure vectors were proposed to characterize thefeedstock.1,2 To characterize the residue, Jaffe proposed twomore structure vectors to represent nickel and vanadium.5 Forthe specific delayed coking process, this work changed somestructure vectors slightly. The RS, RN, and NO vectors wereneglected and a vector called “cc” was considered to representthe strength and carbon numbers between cores and cores. The22 new structure vectors and their stoichiometric matrices areshown in Table 1.

2.2. Molecular Lumps and Their Contents Calculation. According to the SOL method, this paper proposed 92 types of

single-core seed molecules and 46 types of multicore seedmolecules to characterize the residue. After adding differentnumbers of −CH2− to seed molecules, a total of 7004 types of molecular lumps were generated to characterize the molecularcomposition of residues. Figures 1 and 2 show single-core seedmolecules and metal compound multicore seed molecules,respectively.

To calculate the contents of the proposed molecularlumps, a cut of feedstock, such as that described in Figure 3 ,is needed.

After doing this, a simulated annealing algorithm (SA) could be used to search the suitable contents.

3. SIMULATE THE MOLECULAR REACTION

BEHAVIORS3.1. Reaction Rules. Reaction rules were used to describe

the molecular behaviors. They were the standard to judgethat how the material molecular matrix turned to a productmolecular matrix. Each reaction rule included reactantselection rule and product generation rule.6 Reactantselection rule selected the molecules (structure vectorgroups), whether this type of reaction will occur. Productgeneration rule generated the product molecules (structure

vector groups) from reactant molecules of this type of reaction.

Delayed coking is a thermal cracking process that obeysthe free-radical mechanism.7 The reactions of delayedcoking are complex. But overall, all the reactions could bedivided into cracking and condensation. According to thereaction types in delayed coking, 92 types of reaction rules

were established to descr ibe the reaction behaviors of heavy oil delayed coking. Some typical reaction rules are asfollows:

(1) Side Chain Breaking of Single-Core Molecules (All)

Reactant selection rule:

> ∨ > ∨ >

∧ > + ∧ < ∧ <

[(A6 0) (N6 0) (N5 0)]

(R me KO) (A6 10) (N6 10)

Product 1:

= − −

= − × >

R R me KO,

br (br 1) (br 0); the rest: 0

1

1

Product 2:

= + =R me KO, br 0; the rest: invariant2 2

Received: October 14, 2011Revised: November 21, 2011Published: December 16, 2011

Article

pubs.acs.org/EF

© 2011 American Chemical Society 1715 dx.doi.org/10.1021/ef201570s | Energy Fuels 2012, 26, 1715−1724

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e.g.,

Reactant:

A6 A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc1 0 0 0 0 1 0 0 0 6 1 1 0 0 0 0 0 0 0 0 0 0Product 1:


A6 A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0

Table 1. Structure Vectors and Stoichiometric Matrices

a

A6 A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc

C 6 4 2 6 5 4 3 2 1 1 0 0 0 0 −1 −1 −1 0 0 0 0 0

H 6 2 0 12 10 6 4 2 0 2 0 0 2 −2 −2 −1 −1 0 −2 −2 0 0

S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0

O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0

Ni 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

V 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0aThe meanings of the 22 structure vectors are as defined in Chart 1.

Chart 1. Structures and Definitions Used in Table 1

Energy & Fuels Article

dx.doi.org/10.1021/ef201570s | Energy Fuels 2012, 26, 1715−17241716



(2) Multicore Molecules Cracking (First Joint)

Reactant selection rule:

= ∨ = fix rem fix rem[ ( (cc, 100)/10) 3] [ ( (cc, 100)/10) 2]

Product 1:

= + = + = =rem rem rem X rem X R (R, 100) (cc, 10), me (me, 10) 1, cc 0; the rest: ( , 10)1 1 1

Product 2:

= = + = = fix fix fix X fix X R (R/100), IH (IH/10) 1, cc (cc/100); the rest: ( /10)2 2 2 2

e.g.,

Here, the symbol “∨” means “or

”; the symbol “∧

” means “and

”;the subscript “1” means “product 1”; the subscript “2” means

“product 2”; without subscript means “reactant”; “invariant”means equal to reactant; “rem” means “remainder” and “ f ix”

means “eliminate the decimal to recent integer”. According to the method proposed by the authors’ previous

paper,4 simultaneous differential equations could be generated. Inaddition, the product molecular matrix could be calculated fromthe reactant molecular matrix, using the fourth- and fifth-orderRunge−Kutta methods.

3.2. Estimate of Reaction Rate Constants. To solve theabove differential equations, the reaction rate constant of eachreaction should be known. However, the number of equations would

be huge. Some reaction rate constants could be obtained from theliterature,8,9 but far from the standard to solve such differentialequations. It is also inappropriate to obtain these rate constants by experiment. Based on transition-state theory, rate constants could becalculated by formula. Molecular simulating software was used tosearch the transition state and calculate some kinetic parameters.However, for delayed coking, this method was limited by two factors:

(1) There are so many reactions in delayed coking, it is very time-consuming to calculate the rate constant one by one

with this method; and(2) Only simple molecules with a small number of atoms

were available for the transition-state search. For thereactions involving complex molecules, it is difficult to

Figure 2. Metal compounds multicore seed molecules.

Reactant: A6 A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc101 100 0 10 0 243 0 0 0 10301 0 101 0 0 0 0 0 0 0 0 0 2231Product 1:


A6 A4 A2 N6 N5 N4 N3 N2 N1 R br me IH AA NS AN NN RO KO Ni V cc10 10 0 1 0 24 0 0 0 103 0 10 1 0 0 0 0 0 0 0 0 22

Figure 1. Single-core seed molecules.





search its transition state with molecular simulatedsoftware such as Materials Studio.

Since it is hard to calculate every reaction rate constant exactly,it is necessary to estimate the value of rate constants. Theconcept that molecular kinetic properties and structure vectorscould be associated with molecular structure provides the basisfor estimating a large number of reaction rate constants.

The first approximation to estimate the rate constants wasthat all reactions in a class had the same reaction rate constant,

because they underwent the same reaction pathway. However, thisapproximation was insufficient, because, within each reaction class,the molecular structure of reactant and product could influencethe rate constants. So the second approximation was that aperturbation to the reaction rate constants arose, considering theinfluence of different molecular structures on the reaction rateconstants. The structure−activity relationship in kinetics was not

a new concept. Such studies were done by Hammet, Taft, andSwain.10,11 Structure vectors were used to describe the molecularstructure in the SOL method. Therefore, this perturbation could beassociated with structure vectors.

In transition-state theory, eq 1 could be used to calculate thereaction rate constant:4

= Δ − Δ

⎜ ⎟⎛

⎝

⎞

⎠k T

k T

h

T S E

RT ( ) expB

(1)

Here, k B is the Boltzmann constant, h the Planck constant, T thetemperature, R the ideal gas constant, ΔS the entropy changes

before and after reaction, and Δ E the reaction energy barrier.Therefore, if ΔS and Δ E were known, the reaction rate constant

under certain temperatures could be calculated.For simple reactions, ΔS and Δ E could be calculated usingMaterials Studio software directly. For complex reactions, ΔSand Δ E could be estimated by functions with structure vectors.

A common function type was

= × + × + ··· + × + y a x a x a x cb bn n

b1 1 2 2

n1 2 (2)

After calculating ΔS and Δ E of simple reactions as a regressionaggregate with Materials Studio software and using “lsqcurvefit”function and the Matlab optimization toolbox, equations to calculateΔS and Δ E could be obtained. These equations are shown inTables 2 and 3.

Figure 4 shows the residual error distributions of theseequations for extrapolated prediction.

It could be found that the residual errors were slightly farfrom the zero point. To revise them, the reaction rate constantsshould be treated as follows:

′ = + δk k(1 ) (3)

Here, k ′ represents the reaction rate constant after revision, k isthe reaction rate constant before revision, and δ denotes the raterevision index. The influence of each reaction class on productdistribution of delayed coking is considered to be the same.Therefore, each reaction class has the same δ value. Sixteen groupsof results from delayed coking experiments of different feedstock under different operating conditions were taken as objectives.Moreover, these δ values could also be calculated using the SA

method. One thing we want to explain is that these functionsare only valid for the temperature range of 460−500 °C.Table 4 includes these δ values.

4. SIMULATE THE DELAYED COKING PROCESS

4.1. Simplification and Assumption. The delayed cokingprocess includes several components, such as coking, fractionation,gas recovery, coking processing, and venting system. The predic-tion of the SOL model is directed only at the reaction system.Therefore, the delayed coking process could be simplified similarto the process depicted in Figure 5.

There were simplifications and assumptions for the model:

(1) The delayed coking process was composed of many short

batch processes.(2) The coking drum inlet amount and its molecular

composition were unchanged every time.(3) All the reactions occurred in a coking drum.(4) The reactant molecules could be vaporized, immediately,

in the coking drum.(5) There were no reactions during the input of materials

and the output of products, and the output of products was completed immediately.

(6) The molecular compositions of gas products leaving andremaining in the coking drum were the same.

(7) The coking drum was an ideal reactor, and the gas in thecoking drum behaved as an ideal gas.

Figure 3. Method of the residue feedstock cutting.





(8) The temperature and pressure of the coking drum in thereaction process was kept constant, and cooling occurred

when the reactions were totally finished.

(9) Molecules of recycled oil were wax oil molecules, and themolecular compositions of each part of the recycled oil

were the same.

Table 2. Equations Used To Calculate Δ E

reaction classes equation

carbon chain cracking

Δ = − − − ×

− +

E 0.3139R 0.2096br 0.0845(R R )

0.0614IH 95.8311

0.8043 0.51371 2

0.0197

side chain breakingΔ = −

− +

+ +

+

− −

+

− −

− −

+

− −

| |

− −

( )( )

( ) ( )

( )

E 0.2074 0.334

0.1495 0.1199

0.0172 92.781

A6 A4

Cores Ni V

N6 N4

Cores Ni V

R

Cores Ni V

0.7023 br me

Cores Ni V

0.3974

IH

Cores Ni V

dehydrogenation

Δ = − −

+ − ×

+ × +

+

− − − −

− − − −

− −

( )

( ) ( )

( )

( )

E 0.0774 0.2927

0.0072 0.3585

0.0018 99.7853me

Cores Ni V

N6 N4

Cores Ni V

R

Cores Ni V

0.3977

IH

Cores Ni V

br

Cores Ni V

0.1599

0.1039

molecular cracking

Δ = − + ×

+ +

− × +

+ +

− − − −( ) ( )

E 0 .5472cc1 0.2772(Cores Cores )

0.0057 0.0042

0.0027 Cores 98.0873

R

1.51021 2

0.0039

A2 A6 A4

Cores Ni V

0.0081

Cores Ni V

0.0024

0.0031

1 1 1

ring opening

Δ = +

+ +

+

− − − −

| |

− −( )

( ) ( ) E 0.1742 0.0137

0.3248 100.7336

A6 A4

Cores Ni V

R

Cores Ni V

0.0649

IH

Cores Ni V

polycondensation

Δ = − + −

+ + +

+

− −

− −

⎛⎝⎜ ⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

E 0.1885(A6 A4 ) 0.1876

0.0312R 0.0321 106.4872

1 10.5089 A6 A4

Cores Ni V

0.4953

10.1719 R

Cores Ni V

0.1833

2 2

2 2 2

2

2 2 2

Diels− Alder

Δ = −

+ +

+

− −

− −

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

E 0.1737R 0.5179

0.2842 95.7364

10.2178 N6 N4

Cores Ni V

0.3113

R

Cores Ni V

0.2106

2 2

2 2 2

2

2 2 2

desulfuration

Δ = +

+ +

+ +

− − − −

− −

( ) ( )( )

E 0.2284 0.4805

0.0057 96.1871

N6 N4 N1

Cores Ni V

0.7471R

Cores Ni V

0.5244

me

Cores Ni V

0.0078

decarboxylation

Δ = +

+ +

+

− −

−

− −

+

− −( )

( ) ( ) E 0.0199 0.0099

0.0073 102.7983

N6 N4

Cores Ni V

0.8033 R 1

Cores Ni V

0.1386

br me

Cores Ni V

0.0061





4.2. Routinization of the Reaction Process. Only the batchprocess could be disposed with the SOL method; therefore, it wasnecessary to assume that the delayed coking process was composed

of many short batch processes. At the same time, an imaginary coking drum was needed. This coking drum was an operating unitthat had two valves (for the inlet and outlet, respectively).

Table 3. Equations Used To Calculate ΔS

reaction classes equation

carbon chain cracking

= − − − ×

− +

Δ0.0369R 0.0087br 0.6745(R R )

0.0049IH 25.8387

S

R

0.8942 0.13941 2

0.0289

side chain breaking= −

− +

+ +

Δ +

− −

+

− −

− −

+

− −

| |

− −( )

( ) ( )

( )

0.0218 0.0299

0.0151 0.0123

0.0018 24.5755

S

R

A6 A4

Cores Ni V

N6 N4

Cores Ni V

R

Cores Ni V

0.8072 br me

Cores Ni V

0.4011

IH

Cores Ni V

dehydrogenation

= − −

+ −

+ +

Δ +

− − − −

− − − −

− −

( )

( ) ( )

( )

( )

0.0164 0.0602

0.0019 0.0798

0.0004 26.0377

S

R

N6 N4

Cores Ni V

R

Cores Ni V

0.4122

IH

Cores Ni V

br

Cores Ni V

0.1604

me

Cores Ni V

0.1113

molecular cracking

= −

− +

Δ + +

− −

− −

( )

( )

0.0015Cores 0.1311

0.0772 27.2086

S

R

0.0019 A2 A6 A4

Cores Ni V

0.3917

R

Cores Ni V

0.2299

1 1 1

ring opening

= − −

− +

Δ +

− − − −

| |

− −( )( ) ( )0.0369 0.0049

0.0429 26.9285

S

R

A6 A4

Cores Ni V

R

Cores Ni V

0.0517

IH

Cores Ni V

polycondensation

= + +

− − +

Δ +

− −

− −

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜

⎞

⎠⎟

0.0318 A6 A4 0.0303

0.0052R 0.005 29.1078

S

R 1 1

0.4873 A6 A4

Cores Ni V

0.5015

10.1476 R

Cores Ni V

0.1604

2 2

2 2 2

2

2 2 2

Diels− Alder

= − +

− +

Δ +

− −

− −

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

0.0399R 0.1195

0.0668 25.3282

S

R 10.2977 N6 N4

Cores Ni V

0.3075

R

Cores Ni V

0.2073

2 2

2 2 2

2

2 2 2

desulfurization

= − −

− +

Δ + +

− − − −

− −

( ) ( )( )

0.0459 0.1307

0.0016 25.8764

S

R

R N6 N4 N1

Cores Ni V

0.7713

Cores Ni V

0.5766

me

Cores Ni V

0.008

decarboxylation

= − −

− +

Δ +

− −

−

− −

+

− −( )

( ) ( )0.0424 0.0031

0.0009 25.7382

S

R

N6 N4

Cores Ni V

0.7979 R 1

Cores Ni V

0.1291

br me

Cores Ni V

0.0011





The simulation of the delayed coking process proceeded asdescribed in Figure 6.

4.3. Product Division. The main products of delayedcoking were gas, gasoline, diesel, wax oil, and coke; the

results of the SOL model gave the molecular compositionof the products. To compare the simulated results andexperimental results efficiently, it is necessary to separatethe molecules. The molecular carbon number, the boilingpoint, the carbon content, and the carbon residue value

were the main factors that were used to separate theproducts. The molecules whose carbon numbers were <4

were defined as gas. In the remaining molecule s, those whos e boil ing poin ts wer e <205 °C were defined asgasoline. In the rest of the molecules, those whose boilingpoints were <365 °C and had carbon numbers of <24 weredefined as diesel. Of the remaining molecules, those whosecarbon content was >90 mass %, had boiling points that

Figure 4. Residual error distributions of extrapolated prediction.

Table 4. Rate Revision Index for Each Reaction Class

reaction class rate revision index, δ carbon chain cracking 0.0632

side chain breaking 0.1364

dehydrogenation 0.0337

molecular cracking 0.1194

ring opening 0.0708

polycondensation 0.039 × (1 + Ni + V)

Diels− Alder 0.0244

desulfurization −0.0102

decarboxylation −0.0469





were >450 °C, or had carbon residue values of >5% weredefined as coke. The rest of the molecules were defined as

wax oil .

5. MODEL PREDICTION RESULTS

5.1. Simulation of Feedstock. The composition andproportion of two types of residue samples from Sinopec asdepicted in Figure 7.

After calculating the contents of the 7004 types of molecularlumps in these two residues respectively, the bulk properties of these two residues could be calculated. Calculation and experi-mental bulk properties are shown in Tables 5 and 6.

Tables 5 and 6 show that the 7004 types of molecularlumps mainly reflected the bulk properties of residue samples;the calculated results were in good agreement with the experi-mental results.

Figure 5. Delayed coking process simplified diagram.

Figure 6. Simulation diagram of the delayed coking SOL model.

Figure 7. Composition of residue samples.

Table 6. Calculation and Experimental Bulk Properties of Residue Sample 2

index calc exp index calc exp

C (wt %) 87.09 86.23 Sa. 21.98 22.90

H (wt %) 10.94 11.54 Ar. 46.22 44.18

S (wt %) 0.61 0.47 fA 0.22 0.21

N (wt %) 0.34 0.42 H/C 1.51 1.61

O (wt %) 1.02 1.34 SG 909 962

V ( μg/g) 5.80 5.10 CCR 14.04 13.87

Ni ( μg/g) 76.30 79.60 MW 917 995

Table 5. Calculation and Experimental Bulk Properties of Residue Sample 1

index calc exp index calc expC (wt %) 87.54 87.36 Sa. 10.80 10.57

H (wt %) 11.14 10.81 Ar. 50.34 50.52

S (wt %) 0.57 0.41 fA 0.28 0.29

N (wt %) 0.49 0.61 H/C 1.53 1.48

O (wt %) 0.26 0.81 SG 994 1004

V ( μg/g) 5.20 7.90 CCR 23.21 26.15

Ni ( μg/g) 6.10 9.10 MW 1109 1197





5.2. Simulation of Delayed Coking. Experiments and modelcalculations of delayed coking for the two aforementioned residueshas been performed. The operating conditions of experiments andmodel calculations are as given in Table 7.

Calculated and experimental results of the delayed cokingproduct distribution are shown in Table 8.

Figure 8 includes the calculated and experimental results of delayed coking for the same residue under different operatingconditions.

Table 8 and Figure 8 show that the calculated results agreed with the experimental results well. The proposed model hadgood accuracy for product distribution prediction of thedelayed coking process.

6. CONCLUSIONSome changes of structure vectors were made and theircontents were calculated. A total of 7004 types of molecularlumps were proposed. Based on this, a reaction kinetic modelto predict the product distribution of delayed coking process

was built using the structure oriented lumping (SOL) method.The model used 92 types of reaction rules to describe thereaction behaviors of delayed coking and estimated reactionrate constants as equations of structure vectors. Different fromother SOL works, the proposed model could predict theproduct distribution of delayed coking. From the comparison of calculated results and experimental results of productdistribution, it could be proven that the proposed model had

good accuracy for product distribution prediction of delayedcoking process.

■ AUTHOR INFORMATION

Corresponding Author

*Fax: 0086-21-64252851. E-mail: [email protected].

■ REFERENCES

(1) Quann, R. J.; Jaffe, S. B. Structure-Oriented Lumping: Describingthe Chemistry of Complex Hydrocarbon Mixtures. Ind. Eng. Chem. Res.1992 , 31 , 2483−2497.

(2) Quann, R. J.; Jaffe, S. B. Building useful models of complex reaction systems in petroleum refining. Chem. Eng. Sci. 1996 , 51 (10),

1615−1635.(3) Yang, B.; Zhou, X.; Chen, C.; et al. Molecule Simulation for theSecondary Reactions of Fluid Catalytic Cracking Gasoline by theMethod of Structure Oriented Lumping Combined with Monte Carlo. Ind. Eng. Chem. Res. 2008 , 47 , 4648−4657.

(4) Tian, L.; Wang, J.; Shen, B.; et al. Building a Kinetic Model forSteam Cracking by the Method of Structure-Oriented Lumping. Energy Fuels 2010 , 24 , 4380−4386.

(5) Jaffe, S. B. Extension of Structure Oriented Lumping to VacuumResidua. Ind. Eng. Chem. Res. 2005 , 44 , 9840.

(6) Quann, R. J. Modeling the Chemistry of Complex PetroleumMixtures. Environ. Health Perspect. 1998 , 106 (Supplement 6), 1441−1448.

(7) Liang, C.; Shen, B. Delayed Coking ; Sinopec Press: Beijing, 2007.

Table 7. Operating Conditions of Delayed Coking a

sample temperature (°C) pressure (MPa) recycle ratio feeding flow (g/min) steam flow (g/min) feeding time gas stripping time (min)

1 480 0.181 0.29 15.69 0.21 191 111

2 480 0.177 0.30 16.01 0.40 190 118aNote that the volume of the coking drum in the small test device is 4 L.

Table 8. Calculation and Experimental Results of Delayed Coking Product Distribution

Gaseous Composit ion (mass %) Solids Composit ion (mass %) Liquid Composit ion (mass %)

sample gas coke gasoline diesel wax oil total yield of liquids

1

exp 6.06 32.63 20.13 28.52 12.66 61.31

calc 6.16 32.99 20.00 28.61 12.24 60.85

2

exp 7.13 28.32 21.06 27.83 15.66 64.55

calc 7.31 27.68 19.77 28.02 17.22 65.01

Figure 8. Calculated and experimental results for different operating conditions: (a) different temperatures, (b) different pressures, and (c) differentrecycle ratios.



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(8) Belohlav, Z.; Zamostny, P.; Herink, T. The kinetic model of thermal cracking for olefins production. Chem. Eng. Process. 2003 , 42 ,461−473.

(9) Allara, D. L.; Shaw, R. A compilation of kinetic parameters for thethermal degradation of n-alkane molecules. J. Phys. Chem. Ref. Data1980 , 9 (3), 523−559.

(10) Hammet, L. P. The effect of structure upon the reactions of organic compounds. J. Am. Chem. Soc. 1937 , 59 , 96−103.

(11) Gould, E. S. Mechanism and Structure in Organic Chemistry;Holt, Rinehart, and Winston: New York, 1960.



a delayed coking model built using the structure-oriented

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