Article pubs.acs.org/EF
Kinetic Model for the Deep-Severity Thermal Reaction in the Coke Drum of Delayed Coking Junwei Yang, Guoping Shen, Peilin Li, Wei Wei, Chuxin Zhang, and Jiazhi Xiao* State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao, Shandong 266580, People’s Republic of China S Supporting Information *
ABSTRACT: The coke drum is the main reactor of the delayed coking process, in which the deep-severity thermal reaction of heavy oil takes place. To simulate the product distribution in this reactor, a kinetic model for the deep-severity thermal reaction was developed on the basis of the experimental data of a vacuum residuum in a microbatch reactor at 430−490 °C. The modelpredicted results agree well with the experimental values. The ratio of the cracking gas/light distillate rate constant increases with the reaction temperature. Both the primary condensation/cracking rate constant and the secondary condensation/cracking rate constant increase with the reaction temperature. It means that the lower reaction temperature is advantageous to increase the distillate yield at the same reaction severity. Furthermore, a practical transformation method was presented to improve the suitability of this model. The comparison results indicated that this transformation method is available for the kinetic model in this research. Moreover, it can also be used for other lumping models similarly. well with experimental data. Takatsuka et al.14 developed a practical model to describe the cracking and condensation of the residue. The cracking product was divided into four lumps, obtained from the first-order parallel reaction. However, the secondary reaction of the heavy fraction product was not considered. Zhou et al.22 proposed an 11-lumped model with six feed lumps and five product lumps; however, the feed lumps were obtained by solvent sedimentation and Al2O3 column separation, which is neither a standard nor an extensively used method. Therefore, this model was not extensively applied. Yan et al.23 developed a six-lumped model, which include the primary reactions for gas, distillate, and coke formation and the secondary reactions for light gas oil (LGO) and heavy gas oil (HGO) to coke. The apparent activation energy of the cracking reaction was less than that of the condensation reaction. However, the secondary reactions for heavy gas oil to gas and light distillate were ignored. Therefore, the aim of the present work was to develop a kinetic model for the deep-severity thermal reaction in the coke drum of delayed coking, which included the secondary cracking and condensation reactions of heavy gas oil. The ratio of condensation to cracking reaction was discussed. Furthermore, a practical transformation method was proposed to improve the suitability of this model.
1. INTRODUCTION Delayed coking is an economical and practical process for conversion of heavy oil into more valuable light-end products. This process does not require a catalyst; therefore, the feedstock of the delayed coking unit can be any inferior heavy oil that contains high asphaltene, resin, sulfur, and metals.1,2 The most common feedstock is a vacuum residue; however, it can also accept fluid catalytic cracking slurry and pitch. The products are gas, distillate, and coke. In this processing, the feedstock is heated to 490−510 °C in a coking furnace, and then the deep-severity cracking and condensation reactions in the coke drum take place, which is the main reactor of the delayed coking process. At most delayed coking units, it is more profitable to decrease the coke yield because the market value of the coke is lower than that of the other light-end products.3 Therefore, it is necessary to study the thermal reaction kinetics and product distribution of heavy oil in this process. There are many kinetic models developed for the thermal reaction of heavy oil,4−9 which could probably be divided into two categories on the basis of the reaction severity. One is the low-severity or mild reaction lumped model, which is mainly used for the simulation of the low-severity cracking reaction in the coking furnace10−13 or the mild reaction in the soaker process.14−17 In these processes, the overall cracking conversion was usually less than 30−50% and the thermal condensation reaction was ignored. Many of the reported models18−20 are of this category. The other is the deep-severity reaction model,21−23 mainly used for the thermal reaction in the coke drum of the delayed coking process. For the deep-severity thermal reaction, the condensation reaction and secondary reaction of the product must be taken into account. Del Bianco et al.21 presented a simple three-lumped model based on the parallel-consecutive reactions of the distillate, coke, and intermediate, which agrees © 2017 American Chemical Society
2. EXPERIMENTAL SECTION Thermal reaction experiments were carried out in a microbatch reactor apparatus, including a microbatch reactor (20 mL), a temperature monitoring and control system, and a product collection system. The material of the microbatch reactor is stainless-steel, which can be heated using a metal bath and quenched in ice water. To ensure the temperature uniformity of the reaction mass in the reactor, the inner Received: December 15, 2016 Revised: February 3, 2017 Published: February 6, 2017 2681
DOI: 10.1021/acs.energyfuels.6b03340 Energy Fuels 2017, 31, 2681−2686
Article
Energy & Fuels diameter of this reactor was customized as 15 mm. The experimental condition was in the temperature range of 430−490 °C and at a pressure of 0.1 MPa (g), which is similar to the reaction condition of industrial coke drum. The feedstock used in the thermal reaction experiments was LYVR, and the properties of LYVR were listed in Table 1.
3. KINETIC MODEL 3.1. Model Description. The thermal reaction product contains gas, distillate, and coke. To describe the product distribution of the delayed coking process, the product was divided into six lumps based on the product cutting scheme of the delayed coking, namely, gas, gasoline [initial boiling point (IBP)−210 °C], diesel oil (210−360 °C), LGO (360−420 °C), HGO (420−540 °C), and coke. As reported by most researchers,21,24,25 the thermal reaction of hydrocarbon is amenable to the first-order reaction and the secondary reaction of the product mainly occurs in the heavy fraction. The curves between the lump yields and the reaction time at 460 °C were shown in Figure 2. It is indicated that the
Table 1. Properties of the Experimental LYVR property
value
property
value
density at 20 °C (g cm−3) carbon (wt %)
1.01
CCR (wt %)
21.97
83.21
3560
hydrogen (wt %) sulfur (wt %) saturate (wt %) aromatic (wt %) resin (wt %) C7 asphaltene (wt %)
11.16 3.13 7.2 48.5 30.7 13.6
kinetic viscosity at 100 °C (mm2 s−1) molecular weight (g mol−1) Fe (μg g−1) Mg (μg g−1) Na (μg g−1) Ni (μg g−1) V (μg g−1)
1016 5.1 0.2 3.3 46.2 140
As shown in Figure 1, the oil gas generated from the thermal reaction was cooled and separated into gas and distillate and then
Figure 2. Lump yields xi versus reaction time at 460 °C: gasoline (IBP−210 °C), diesel oil (210−360 °C), LGO (360−420 °C), and HGO (420−540 °C).
HGO product occurs in the secondary reaction obviously. The secondary reactions of LGO and diesel oil are not obvious as a result of the light fraction being mostly vaporized under the reaction conditions. Thus, the assumptions of the deep-severity kinetic model are listed as follows: (1) All of the primary and secondary reactions are amenable to irreversible first-order reaction. (2) The secondary reaction of HGO includes the cracking to light products and further condensation to generate coke. Figure 3 shows the reaction network of this kinetic model.
Figure 1. Experimental analysis procedure.
collected in a gas collection bottle and a distillate receiver, respectively. The residue in the reactor contained unconverted feedstock, heavy gas oil, and coke products. The gas components were analyzed by an Agilent 6890N gas chromatograph. The distillate in the receiver was analyzed by the ASTM D2887 procedure using a Bruker 450-GC gas chromatograph. The residue in the reactor was divided into two parts. One part was analyzed by the IP 480B procedure, which covers materials that are not totally eluted from the chromatographic column. The other part was used to measure the coke yield. The coke product, defined as tolueneinsoluble (TI) material, was separated using a centrifugal method. The liquid product that remained in the reactor, containing unconverted vacuum residue, distillate product, and TI material, was dissolved and centrifuged 5 times with 50 mL of toluene each time. The centrifugal condition is 3000 revolutions min−1 for 10 min. Finally, the deposits should be dried in an oven for 3 h to remove residual toluene.
Figure 3. Reaction network of the deep-severity kinetic model: vacuum residue (VR, 540 °C+), gasoline (IBP−210 °C), diesel oil (210−360 °C), LGO (360−420 °C), and HGO (420−540 °C).
3.2. Mathematical Model. The rate equations of the deepseverity kinetic model in Figure 3 can be written as follows: 4
−
dx = (kc + ks)x = (∑ kLi + k w + ks)x dt i=1
dx Li = kLix + k wLix w , dt
i = 1, 2, 3, and 4
(1)
(2)
4
dx w = k wx − (∑ k wLi + k ws)x w dt i=1 2682
(3) DOI: 10.1021/acs.energyfuels.6b03340 Energy Fuels 2017, 31, 2681−2686
Article
Energy & Fuels dxs = ksx + k wsx w dt
Table 2. Estimated Kinetic Parameters of the Deep-Severity Kinetic Model
(4)
Here, x is the mass fraction of the vacuum residue (540 °C+). xLi is the mass fraction of the i lump (gas, gasoline, diesel oil, and LGO). xw and xs are the mass fractions of the HGO and coke, respectively. k refers to the total cracking rate constant. kLi, kw, and ks are the primary reaction rate constants to generate the light fraction lumps, HGO, and coke, respectively. kwLi and kws are the secondary reaction rate constants to generate the light fraction lumps and coke. t is the reaction time. The initial conditions of these ordinary differential equations are as follows: t = 0,
x = x0 ,
reaction kc ks kL1 kL2 kL3 kL4 kw kwL1 kwL2 kwL3 kwL4 kws
x Li = x Li0 ,
i = 1, 2, 3, and 4,
x w = x w0 ,
xs = 0
where x0 is the initial mass fraction of the VR lump and xw0 and xLi0 are the initial mass fractions of HGO and the i lump, respectively. 3.3. Kinetic Parameter Estimation. A total of 11 rate constants of this kinetic model were estimated by solving the differential equations (eqs 1−4). The differential equations were solved using the Runge−Kutta method. Equation 5 shows the objective function. The nonlinear least squares method was employed to estimate the rate constants. The Levenberg− Marquardt algorithm was used to accelerate the convergence of the objective function. Fobj =
∑ (ycalculate − yobserve )2
−E/R ⎛1 ⎡ ln⎜ N ∑ ⎢exp ⎣ ⎝
−E RTi
(±18) (±23) (±25) (±16) (±17) (±19) (±20) (±16) (±20) (±19) (±20) (±21)
correlation coefficient, R2
× × × × × × × × × × × ×
0.94 0.92 0.84 0.95 0.94 0.89 0.92 0.81 0.85 0.87 0.82 0.92
4.60 4.22 2.86 2.44 3.57 1.24 1.61 2.90 5.80 2.20 5.15 1.37
107 107 107 106 105 106 108 109 105 105 107 107
F statistic
99% F
103.54 52.40 60.24 75.55 31.50 43.76 34.04
8.53 8.53 8.53 8.53 8.53 8.53 8.53
4. RESULTS AND DISCUSSION 4.1. Model Verification. To test the reliability of this model, the estimated kinetic parameters of this model were used to calculate the lump yields. A comparison of predicted and experimental yields of coke (xs) and total cracking (gas + liquid) products was presented in Figure 4. A comparison of
(5)
Figure 4. Predicted versus experimental yields of coke and total cracking product (gas + liquid) lumps.
⎞
( )⎤⎥⎦⎠
147.25 154.21 161.96 142.49 127.48 139.42 163.80 190.23 133.14 124.36 163.13 153.93
frequency factor (s−1)
cracking ranges from 120 to 250 kJ mol−1 and the apparent activation energy of condensation ranges from 130 to 268 kJ mol−1. In this present study, the estimated activation energies of cracking are also in the range from 127 to 163 kJ mol−1. However, the estimated activation energy of condensation is 154.21 kJ mol−1, which is greater than that of total cracking of 147.25 kJ mol−1. That is consistent with the literature-reported results.23,30
To simplify the solution of the complex model and decrease the number of parameters to be estimated simultaneously, a sequential method presented by Ancheyta et al.26,27 was employed. The frequency factors and apparent activation energies were calculated according to the Arrhenius equation by the linear least squares method. Moreover, there was a non-isothermal reaction at heating and cooling stages of the thermal reaction experiment. It took about 1−2 min from the temperature of 350 °C to the reaction control temperature of 430−490 °C. However, the heavy oil begins to crack at 350 °C.28 Therefore, the influence of the non-isothermal reaction at heating and cooling stages on reaction results cannot be ignored. Therefore, an equivalent reaction temperature (ERT) was used to equivalently transfer the actual non-isothermal reaction into the isothermal reaction. Then, the kinetic parameters of this model can be estimated by the isothermal method. The detailed information on this method can be found in the literature.29 T̅ =
apparent activation energy (kJ mol−1)
predicted and experimental yields for cracking lumps (xLi and xw) was shown in Figure 5. Results demonstrated that the predicted yields agree well with the experimental values, which indicates that this model is capable of describing the experimental results. Moreover, the F test for predicted and experimental values was also carried out. Table 2 showed the critical value at the 1% significance level and F statistic values. It is indicated that this deep-severity kinetic model gives a good fit to the experimental data. 4.2. Cracking Reaction Behavior. To analysis the cracking product distribution, the kinetic parameters in Table 2 were employed to calculate the primary cracking rate
⎟
(6)
Here, T̅ and Ti are the equivalent reaction temperature (ERT) and the reaction temperature at different times, respectively. N refers to the count of data record. R and E are the gas constant and apparent activation energy, respectively. The detailed experimental conditions and lump yields were given in Table S1 of the Supporting Information. The apparent activation energies and frequency factors of all reactions were listed in Table 2. The correlation coefficient R2 for ln k versus 1/T ranges from 0.81 to 0.95. As reported on the deep-severity thermal reaction,5,21,23 the apparent activation energy of 2683
DOI: 10.1021/acs.energyfuels.6b03340 Energy Fuels 2017, 31, 2681−2686
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kwL3, is also the largest and the rate constant of gas, kwL1, is minimal. It is similar to the primary reaction that the ratio of the secondary cracking gas/light distillate (gasoline + diesel + LGO) rate constant, kwL1/kwL2−4, increases with the reaction temperature. 4.3. Condensation Reaction Behavior. The market value of the coke product is lower than that of the other products of the coker; thus, most of the commercial units are limited to generate coke, which is a condensation product. To discuss the effect of the reaction temperature on the coke yield, the primary and secondary condensation rate constants with different reaction temperatures were calculated (Figure 8). Figure 5. Predicted versus experimental yields of cracking product lumps: gasoline (IBP−210 °C), diesel oil (210−360 °C), LGO (360− 450 °C), and HGO (450−540 °C).
constants with different reaction temperatures (Figure 6). Results indicated that the primary reaction rate constant of
Figure 8. Condensation rate constants versus reaction temperature: kws, HGO to coke; ks, VR to coke; kc, VR to gas and distillate; and kwL, HGO to gas and light distillate.
Results showed that the rate constant of primary condensation, ks, is significantly greater than that of secondary condensation, kws. It is indicated that the vacuum residue is easier to generate coke than HGO. Moreover, the ratio of the primary condensation/cracking rate constant, ks/kc, is greater than that of the secondary condensation/cracking rate constant, kws/ kwL. Both ks/kc and kws/kwL increase with the reaction temperature. It means that the lower reaction temperature is advantageous to reduce the coke yield at the same reaction severity. 4.4. Method for Cutting Point Transformation. During the practical application, the cutting points of gasoline, diesel oil, and LGO are often adjusted because of the change of the production plan. For this reason, the lumping scheme of the kinetic model should be changed to be consistent with the cutting scheme. Then, the kinetic parameters must be reestablished, which leads to the application of the model being very inconvenient. It is a common shortcoming of the lumping kinetic models. In view of this, a practical transformation method was proposed to improve the suitability of the model in this research. As shown in Figure 9, the typical true boiling point (TBP) distillation curve of distillate, generated from the thermal reaction, is continuous and smooth. It can be regarded as a continuous function of the boiling point and the distillation yield. Thus, the transformation method was proposed to calculate the product yields with adjusted cutting scheme based on the Lagrange interpolation polynomial. The steps to calculate the product yields with adjusted cutting scheme are as follows: (1) The original cutting points of gasoline, diesel oil, and LGO are T01, T02, and T03, respectively. The corresponding distillation yield on the basis of the weight of reaction feed is y0i = f(T0i ), and
Figure 6. Primary cracking rate constants versus reaction temperature: kL1, gas; kL2, gasoline; kL3, diesel oil; kL4, LGO; and kL2−4, light distillate (gasoline + diesel + LGO).
diesel oil, kL3, is the largest and the primary reaction rate constant of gas, kL1, is minimal. However, the ratio of the primary cracking gas/light distillate (gasoline + diesel oil + LGO) rate constant, kL1/kL2−4, increases with the reaction temperature as a result of the apparent activation energy of the gas being greater than that of the light distillate. That is consistent with the literature reported by Sawarkar et al.5 and Yan et al.23 It means that the gas yield of the primary reaction increases with the reaction temperature. For the secondary cracking reactions of HGO to gas and light distillate (Figure 7), the reaction rate constant of diesel oil,
Figure 7. Secondary cracking rate constants versus reaction temperature: kwL1, gas; kwL2, gasoline; kwL3, diesel oil; kwL4, LGO; and kwL2−4, light distillate (gasoline + diesel + LGO). 2684
DOI: 10.1021/acs.energyfuels.6b03340 Energy Fuels 2017, 31, 2681−2686
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assumed that the products are clearly separated, which is different from the real industrial products.
5. CONCLUSION A kinetic model for the deep-severity thermal reaction in the coke drum of delayed coking was developed on the basis of the thermal reaction experiments. The main conclusions on the results and implications of this model are as follows: (1) The ratio of the cracking gas/light distillate (gasoline + diesel oil + LGO) rate constant increases with the reaction temperature. (2) Both the primary condensation/cracking rate constant and the secondary condensation/cracking rate constant increase with the reaction temperature. It means that the lower reaction temperature is advantageous to reduce the coke yield at the same reaction severity. (3) A practical transformation method was presented to improve the suitability of the lumping kinetic model. The comparison results indicated that this transformation method is available for the kinetic model in this research. Moreover, it can also be used for other lumping models similarly.
Figure 9. Typical TBP distillation curve of the distillate generated from the thermal reaction: T01, 210 °C; T02, 360 °C; and T03, 420 °C. i
yi0 = f (Ti0) =
∑ xLi+ 1,
i = 1, 2, and 3 (7)
1
(2) The adjusted cutting points of gasoline, diesel oil, and LGO are T1, T2, and T3, respectively. The corresponding distillation yield on the basis of the weight of reaction feed is yi = f(Ti), which can be calculated by Lagrange interpolation polynomial. yi =
l1(Ti )f (T10)
Here, l j(T ) =
+
l 2(Ti )f (T20)
(T − T 0) ∏3i = 1 0 i 0 , (T j − Ti ) i≠j
+
l3(Ti )f (T30)
■
* Supporting Information
(8)
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.6b03340. Detailed experimental conditions and lump yields (Table S1) and original data of the TBP distillation curve (Table S2) (PDF)
j = 1, 2, and 3.
(3) Then, the product yields with adjusted cutting scheme can be calculated as follows: Gasoline yield, x′L2 = y1. Diesel oil and LGO yields, x′Li = yi − 1 − yi − 2, i = 3 and 4. 4 4 HGO yield, x w′ = (∑2 x Li + x w ) − ∑2 x Li . To prove the validity of this transformation method, it was employed to predict the product yields with the original cutting point plus 10 °C and minus 10 °C, respectively. The original data of the TBP distillation curve was given in Table S2 of the Supporting Information. Table 3 showed the comparison of Table 3. Measured versus Calculated Product Yields item original cutting point + 10 °C
original cutting point − 10 °C
a
measured yield (wt %) predicted yield (wt %) absolute error (wt %) measured yield (wt %) predicted yield (wt %) absolute error (wt %)
ASSOCIATED CONTENT
S
■
AUTHOR INFORMATION
Corresponding Author
*Telephone: +86-532-8698-1812. Fax: +86-532-8698-1787. Email:
[email protected]. ORCID
Jiazhi Xiao: 0000-0002-6048-3417
a
Notes
The authors declare no competing financial interest.
gasoline
diesel oil
LGO
HGO
13.28
21.90
11.70
10.83
13.65
21.40
12.30
10.40
0.37
−0.50
0.55
−0.42
11.38
20.24
11.46
14.65
11.70
19.75
11.55
14.73
0.32
−0.49
0.09
0.08
■ ■
ACKNOWLEDGMENTS The authors are thankful for the financial support by the “Fundamental Research Funds for the Central Universities”. REFERENCES
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measured and calculated product yields to reaction conditions of 473 °C and 20 min. Results demonstrated that all of the predicted absolute errors are less than 1%. It is indicated that this transformation method is available to improve the suitability of the model in this research. Moreover, it can also be used for other lumping models similarly. It should be noticed that there is also a disadvantage to use a polynomial to interpolate the distillation yields. The interpolation method 2685
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