# Unsteady-State Mathematical Modeling of Hydrocarbon Feedstock Pyrolysis

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- study the mechanism of the pyrolysis process itself and the mechanism of coke deposition;
- (2)
- perform a thermodynamic analysis of the pyrolysis process;
- (3)
- develop a formalized reaction network according to the known mechanism considering the thermodynamic analysis of the pyrolysis process;
- (4)
- develop a kinetic model of the pyrolysis process;
- (5)
- develop an unsteady mathematical model of a pyrolysis reaction furnace with due consideration of the coke deposition on the inner surface of the coil;
- (6)
- complement the system of equations with differential equations for changing the thickness of the coke layer and the pressure of the reaction medium along the length of the coil with the astronomical time;
- (7)
- solve the inverse kinetic problem;
- (8)
- verify the mathematical model;
- (9)
- perform predictive calculations for the duration of the cycle of the pyrolysis furnace;
- (10)
- perform optimization calculations to obtaining the maximum degree of conversion, selectivity, and duration of the cycle of the pyrolysis reaction furnace.

## 2. Materials and Methods

- C
^{2}H^{6}→0.47C_{2}H_{4}+ 0.53CH_{4} - C
_{3}H_{8}→0.32C_{2}H_{4}+ 0.34C_{2}H_{6}+ 0.16C_{3}H_{6}+ 0.18CH_{4} - C
_{4}H_{10}→0.10C_{4}H_{6}+ 0.32C_{2}H_{4}+ 0.27C_{3}H_{6}+ 0.15C_{2}H_{6}+ 0.16CH_{4} - C
_{5}H_{12}→0.16C_{3}H_{6}+ 0.37C_{2}H_{6}+ 0.35C_{2}H_{4}+ 0.12CH_{4} - C
_{2}H_{4}→0.15C_{2}H_{2}+ 0.85H_{2} - C
_{2}H_{4}→polymers - C
_{3}H_{6}→polymers - polymers→coke

_{i}is the rate constant of the i-th reaction, s

^{−1}; K

_{0i}is the preexponential coefficient, s

^{−1}; P

_{0}is the pressure, atm.; E

_{i}is the activation energy of the i-th reaction, J/mol; and T is the process temperature, K.

_{i}, C

_{k}are the concentrations of i-th and k-th components, mol/L; τ is the contact time, s; and a

_{i,j}is the stoichiometric coefficient of the i-th component in the j-th reaction.

_{e}is the effective diameter of the coil, m; ω is the flow rate of the hydrocarbon mixture, m/s; and ρ is the density of the mixture, kg/m

^{3}.

^{2}. However, this is the total value for four parallel coils, so with a coil inner diameter of 100 mm:

_{heat}is the heat exchange area, m

^{2}; and d is the coil inner diameter, m.

## 3. Results and Discussion

_{24}H

_{12}+ 27O

_{2}= 24CO

_{2}+ 6H

_{2}O

^{3}, the volume of deposits is:

^{3}, the weight of coke accumulated over 42 days is:

## 4. Conclusions

- (1)
- The unsteady-state mathematical modeling of hydrocarbon feedstock pyrolysis was developed. It considers the process of coke deposition along the length of the coil showing that the thickness of the coke layer increases towards the end of the coil. This proves the uneven distribution of coke inside the coil, which is consistent with theoretical concepts of coke deposition processes.
- (2)
- The rates of coke deposition along the length of the coil were determined, considering the technological parameters and the composition of the supplied raw materials (the calculated value of coke deposition rate equaled 0.01 mm/day).
- (3)
- The influence of the propane/butane ratio in the feedstock on the quality of the products was determined. With an increase in the propane/butane ratio from 4/1 to 1/4 mol/mol, the ethylene concentration decreased from 3.45 mol/L to 3.35 mol/L.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Coke layer thickness depending on the coil length at the end of the pyrolysis furnace coil.

**Figure 9.**Influence of propane/butane ratio in the feedstock on the yield of propylene and ethylene.

Duration, Hours | Air Flowrate, kg/h |
---|---|

9.25 | 50 |

0.5 | 100 |

0.25 | 150 |

0.25 | 200 |

0.25 | 250 |

0.875 | 315 |

5.75 | 100 |

5.25 | 315 |

3.625 | 90 |

Total air supply for burning, kg | 3493.125 |

Hydrocarbon Feedstock Composition, wt% | Temperature, °K | ||||||
---|---|---|---|---|---|---|---|

Methane | Ethane | Ethylene | Propane | Propylene | Butane | Butylene | |

10.1 | 9.6 | 17.2 | 18.2 | 11.5 | 30.4 | 3 | 825 |

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**MDPI and ACS Style**

Dolganov, I.; Bunaev, A.; Dolganova, I.
Unsteady-State Mathematical Modeling of Hydrocarbon Feedstock Pyrolysis. *Processes* **2020**, *8*, 1394.
https://doi.org/10.3390/pr8111394

**AMA Style**

Dolganov I, Bunaev A, Dolganova I.
Unsteady-State Mathematical Modeling of Hydrocarbon Feedstock Pyrolysis. *Processes*. 2020; 8(11):1394.
https://doi.org/10.3390/pr8111394

**Chicago/Turabian Style**

Dolganov, Igor, Ajur Bunaev, and Irena Dolganova.
2020. "Unsteady-State Mathematical Modeling of Hydrocarbon Feedstock Pyrolysis" *Processes* 8, no. 11: 1394.
https://doi.org/10.3390/pr8111394