# Incineration Kinetic Analysis of Upstream Oily Sludge and Sectionalized Modeling in Differential/Integral Method

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials and Reagents

#### 2.2. Apparatus and Methods

## 3. Results and Discussion

#### 3.1. Sectionalized Rules and Peak-Thermal Kinetic Analysis

#### 3.1.1. Characteristics of the Upstream Oily Sludge

#### 3.1.2. Sectionalized Rules for the Incineration Process of Upstream Oily Sludge

#### 3.1.3. Peak-Thermal Kinetic Analysis of Endothermic/Exothermic Reactions

^{2}) of stages two, three, and four were 64.43 ± 5.34 KJ/mol (0.9798), 90.71 ± 13.35 KJ/mol (0.9389), and 102.11 ± 28.93 KJ/mol (0.8616), respectively.

#### 3.2. The Reasoning Process of the Modeling Method Applied for Oily Sludge Incineration

#### 3.2.1. The Reasoning Process of Differential Methods

#### 3.2.2. The Reasoning Process of Integral Methods

#### 3.3. The Incineration Kinetic Analysis and Model of Stage One

#### 3.4. The Incineration Kinetic Analysis and Model of Stages Two, Three, and Four

^{2}at a variety of heating rates in the KAS method were all higher than that in the Friedman method and FWO method. Therefore, $\overline{{E}_{0}}=78.11\text{}\mathrm{KJ}/\mathrm{mol}$ and $98.82\text{}\mathrm{KJ}/\mathrm{mol}$ were appropriate for the incineration kinetic modeling of Stage 2 and Stage 3, respectively.

^{2}was apparently changed with the heating rates, and relatively high R

^{2}values by Friedman method (Table 8 and Figure 4B) were obtained at ${\alpha}_{10\%}$ (R

^{2}= 0.9693) and ${\alpha}_{30\%}$ (R

^{2}= 0.9774). The intercepts of ${\alpha}_{10\%}$ and ${\alpha}_{30\%}$ linear fitting curves (Figure 4B) plotted by $ln\left({\beta}_{n}\times d\alpha /dT\right)$ versus $\frac{1}{T}$ were 19.33 ± 1.24 and 18.45 ± 1.39, respectively. Thus, two linear equations in two unknowns were simultaneously established and expressed in Equation (19):

^{2}values (Table 8 and Figure 5B) were obtained at ${\alpha}_{10\%}$ and ${\alpha}_{50\%}$ by the Friedman method. The $ln\left({\beta}_{n}\times d\alpha /dT\right)$ intercepts and R

^{2}values of the ${\alpha}_{10\%}$ and ${\alpha}_{50\%}$ linear fitting curves (Figure 5B) were 20.74 ± 0.74, 0.9942 and 19.24 ± 1.32, 0.9602, respectively. The reaction order and the pre-exponential factor were solved from the followed equations:

^{2}of the linear fitting curves in the KAS method were dramatically higher than those in the Friedman method and FWO method. Therefore, $\overline{{E}_{0}}=15.96$ KJ/mol was the optimum parameter for the incineration kinetic modeling of Stage 4. As it was shown in Figure 6B, significant errors appeared in the linear fitting curves of Stage 4 under the Friedman method, and a relatively low R

^{2}value was obtained in each heating rate. Thus, the reaction order and the pre-exponential factor could not be obtained in Equation (13) or Equation (14). We inferred that the probe that was utilized to detect the weight of the reactant was significantly affected by the operating temperatures and caused the apparent errors of $d\alpha /dt$ or $d\alpha /dT$.

#### 3.5. The Judgement of Sectionalized Modeling in Differential/Integral Method

^{2}also demonstrated that the integral method was more suitable than the differential method.

## 4. Conclusions

^{2}values that appeared in the linear fitting curves of Stage 4, the reaction order and the pre-exponential factor could not be obtained under the Friedman method.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The DSC/TGA analysis of upstream oily sludge at ${\beta}_{n}$ (n = a, b, c, d, and e); ${\beta}_{a}=$ 5 K/min (

**A**), ${\beta}_{b}=$ 10 K/min (

**B**), ${\beta}_{c}=$ 15 K/min (

**C**), ${\beta}_{c}=$ 20 K/min (

**D**) and ${\beta}_{d}=$ 25 K/min (

**E**), endothermic/exothermic peak analysis (

**F**).

**Figure 2.**Four sectionalized stages in TGA. TGA test carried out in different heating rates (

**A**); TGA test of stage 1 (

**B**); TGA test of stage 2 (

**C**); TGA test of stage 3 (

**D**); TGA test of stage 4 (

**E**).

**Figure 3.**The linear fitting results for Stage 1 under the KAS, Friedman, and FWO methods ((

**A**)—KAS method, (

**B**)—Friedman method, and (

**C**)—FWO method).

**Figure 4.**The linear fitting results for Stage 2 under the KAS, Friedman, and FWO methods ((

**A**)—KAS method, (

**B**)—Friedman method, and (

**C**)—FWO method).

**Figure 5.**The linear fitting results for Stage 3 under the KAS, Friedman, and FWO methods ((

**A**)—KAS method, (

**B**)—Friedman method, and (

**C**)—FWO method).

**Figure 6.**The linear fitting results for Stage 4 under the KAS, Friedman, and FWO methods ((

**A**)—KAS method, (

**B**)—Friedman method, and (

**C**)—FWO method).

Materials | Atmosphere | Thermal Test Method | Modeling Method | Basic Three Elements | Reference |
---|---|---|---|---|---|

Oil sludge, Phenolic plastic | Nitrogen | TGA/DTG | Integral | ${E}_{a}$ | [11,34] |

Oil sludge | Nitrogen | TGA | Differential | ${E}_{a}$, A and n | [12] |

Polyurethane Foams | Nitrogen | TGA | Differential | ${E}_{a}$ | [30,31] |

Chalcogenide Ge_{2}Sb_{2}Te_{5} | Nitrogen | DSC | Integral | ${E}_{a}$ | [36] |

Polyurethane | Nitrogen | TGA | Differential | ${E}_{a}$, A and n | [37] |

Rice husk | Nitrogen | TGA | Integral | ${E}_{a}$ | [39] |

Parameters | Heating Values (MJ/Kg, dry basis) | Ash Content (wt.%, dry basis) | Moisture (wt.%) | Bulk Density (kg/m³) |
---|---|---|---|---|

Values | 35.45 ± 3.64 | 57.56 ± 1.23 | 3.24 ± 1.08 | 1366.25 ± 46.73 |

Parameters | Stage 1 | Stage 2 | Stage 3 | Stage 4 | |
---|---|---|---|---|---|

DSC | Endo/Exo ^{1} | ND ^{2} | Exo | Exo | Endo |

TGA | Weight Loss | 10% | 10% | 20% | 5% |

Peak temperature at ${\beta}_{n}$ (K) | ${\beta}_{a}=5\mathrm{K}/\mathrm{min}$ | ND | 562.974 | 695.604 | ND |

${\beta}_{b}=10\mathrm{K}/\mathrm{min}$ | ND | 584.081 | 726.649 | 939.433 | |

${\beta}_{c}=15\mathrm{K}/\mathrm{min}$ | ND | 598.507 | 740.092 | 965.624 | |

${\beta}_{d}=20\mathrm{K}/\mathrm{min}$ | ND | 618.030 | 742.590 | 993.691 | |

${\beta}_{e}=25\mathrm{K}/\mathrm{min}$ | ND | 623.446 | 768.950 | 987.380 | |

E_{p} (KJ/mol) | $ln\left({\beta}_{n}/{T}_{p}{}^{2}\right)\u20131/{T}_{p}$ | ND | 64.43 ± 5.34 | 90.71 ± 13.35 | 102.11 ± 28.93 |

R^{2} | ND | 0.9798 | 0.9389 | 0.8616 |

${\mathit{\alpha}}_{\mathit{n}}$ | ${\mathit{\beta}}_{\mathit{a}}=5\mathbf{K}/\mathbf{min}$ | ${\mathit{\beta}}_{\mathit{b}}=10\mathbf{K}/\mathbf{min}$ | ${\mathit{\beta}}_{\mathit{c}}=15\mathbf{K}/\mathbf{min}$ | ${\mathit{\beta}}_{\mathit{d}}=20\mathbf{K}/\mathbf{min}$ | ${\mathit{\beta}}_{\mathit{e}}=25\mathbf{K}/\mathbf{min}$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

$\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | $\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | $\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | $\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | $\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | |

${\alpha}_{10\%}$ | 3.26 | 349.781 | 3.33 | 350.605 | 2.16 | 358.763 | 2.65 | 365.125 | 2.29 | 369.640 |

${\alpha}_{30\%}$ | 4.51 | 394.986 | 4.35 | 409.822 | 5.24 | 406.490 | 3.64 | 416.323 | 4.22 | 421.908 |

${\alpha}_{50\%}$ | 5.59 | 435.879 | 5.19 | 448.973 | 3.63 | 458.567 | 4.09 | 470.557 | 3.66 | 477.807 |

${\alpha}_{70\%}$ | 6.90 | 467.820 | 6.75 | 481.817 | 5.78 | 501.161 | 5.77 | 511.133 | 5.51 | 521.753 |

${\alpha}_{90\%}$ | 7.97 | 495.421 | 7.99 | 509.078 | 7.42 | 531.442 | 7.73 | 541.839 | 7.19 | 553.763 |

${\mathit{\alpha}}_{\mathit{n}}$ $({\mathit{\beta}}_{\mathit{a}}\u2013{\mathit{\beta}}_{\mathit{e}})$ | KAS Method $\mathit{ln}\left({\mathit{\beta}}_{\mathit{n}}/{\mathit{T}}^{2}\right)\u20131/\mathit{T}$ | FWO Method $\mathit{ln}\left({\mathit{\beta}}_{\mathit{n}}\right)\u20131/\mathit{T}$ | Firedman Method $\mathit{ln}\left({\mathit{\beta}}_{\mathit{n}}\times \mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}\right)\u20131/\mathit{T}$ | |||
---|---|---|---|---|---|---|

${\mathit{E}}_{0-\mathit{\alpha}\mathit{n}}(\mathbf{KJ}/\mathbf{mol})$ | R^{2} | ${\mathit{E}}_{0-\mathit{\alpha}\mathit{n}}(\mathbf{KJ}/\mathbf{mol})$ | R^{2} | ${\mathit{E}}_{0-\mathit{\alpha}\mathit{n}}(\mathbf{KJ}/\mathbf{mol})$ | R^{2} | |

${\alpha}_{10\%}$ | 59.26 ± 15.62 | 0.8453 | 65.84 ± 14.79 | 0.8676 | 53.56 ± 17.26 | 0.7572 |

${\alpha}_{30\%}$ | 56.83 ± 17.05 | 0.8622 | 63.51 ± 16.13 | 0.8818 | 45.41 ± 23.09 | 0.7633 |

${\alpha}_{50\%}$ | 54.53 ± 5.44 | 0.9738 | 61.93 ± 5.11 | 0.9798 | 47.32 ± 5.83 | 0.9571 |

${\alpha}_{70\%}$ | 54.04 ± 5.15 | 0.9691 | 60.45 ± 4.83 | 0.9774 | 49.06 ± 9.38 | 0.9558 |

${\alpha}_{90\%}$ | 53.78 ± 6.24 | 0.9565 | 60.24 ± 5.87 | 0.9685 | 55.80 ± 7.08 | 0.9555 |

Parameters | Reaction Order (n) | Pre-Exponential Factor (ln A) | Coefficient of Determination (R^{2}) |
---|---|---|---|

$\beta =5\text{}\mathrm{K}/\mathrm{min}$ | 0.97 ± 0.28 | 13.72 ± 0.44 | 0.9236 |

$\beta =10\text{}\mathrm{K}/\mathrm{min}$ | 0.87 ± 0.25 | 13.79 ± 0.40 | 0.9202 |

$\beta =15\text{}\mathrm{K}/\mathrm{min}$ | 0.85 ± 0.29 | 13.46 ± 0.45 | 0.9012 |

$\beta =20\text{}\mathrm{K}/\mathrm{min}$ | 0.81 ± 0.30 | 13.42 ± 0.47 | 0.8766 |

$\beta =25\text{}\mathrm{K}/\mathrm{min}$ | 0.82 ± 0.30 | 13.32 ± 0.45 | 0.8868 |

Average | 0.82 ± 0.30 | 13.32 ± 0.45 | 0.9023 |

${\mathit{\alpha}}_{\mathit{n}}$ | Stage | ${\mathit{\beta}}_{\mathit{a}}=5\mathbf{K}/\mathbf{min}$ | ${\mathit{\beta}}_{\mathit{b}}=10\mathbf{K}/\mathbf{min}$ | ${\mathit{\beta}}_{\mathit{c}}=15\mathbf{K}/\mathbf{min}$ | ${\mathit{\beta}}_{\mathit{d}}=20\mathbf{K}/\mathbf{min}$ | ${\mathit{\beta}}_{\mathit{e}}=25\mathbf{K}/\mathbf{min}$ | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

$\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | $\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | $\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | $\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | $\mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}$ (×10 ^{−3}) | $\mathit{T}$ (K) | ||

${\alpha}_{10\%}$ | Stage 2 | 10.57 | 516.785 | 10.08 | 531.892 | 10.49 | 554.185 | 8.89 | 565.030 | 9.81 | 572.626 |

Stage 3 | 3.51 | 622.887 | 2.89 | 639.315 | 4.39 | 667.270 | 4.36 | 684.588 | 4.43 | 694.448 | |

Stage 4 | 50.82 | 902.590 | 21.16 | 904.648 | 8.05 | 914.979 | 5.77 | 923.805 | 4.72 | 927.736 | |

${\alpha}_{30\%}$ | Stage 2 | 13.60 | 533.479 | 13.03 | 549.453 | 14.35 | 570.510 | 12.99 | 582.810 | 12.09 | 590.517 |

Stage 3 | 9.25 | 657.685 | 7.96 | 682.952 | 9.50 | 697.241 | 8.41 | 715.626 | 7.60 | 727.265 | |

Stage 4 | 56.23 | 907.129 | 21.91 | 911.520 | 12.60 | 934.999 | 10.61 | 948.819 | 7.82 | 959.173 | |

${\alpha}_{50\%}$ | Stage 2 | 15.53 | 546.946 | 15.83 | 563.042 | 15.21 | 583.725 | 13.97 | 597.489 | 13.73 | 606.171 |

Stage 3 | 13.73 | 674.935 | 13.56 | 701.422 | 10.61 | 716.113 | 10.48 | 737.392 | 9.32 | 750.831 | |

Stage 4 | 45.91 | 911.038 | 30.19 | 917.644 | 14.53 | 949.547 | 11.59 | 965.994 | 7.69 | 983.627 | |

${\alpha}_{70\%}$ | Stage 2 | 14.17 | 560.069 | 15.98 | 575.404 | 11.44 | 598.262 | 11.76 | 612.476 | 10.76 | 622.225 |

Stage 3 | 16.51 | 687.783 | 19.34 | 714.310 | 15.14 | 731.354 | 11.44 | 755.153 | 14.27 | 769.902 | |

Stage 4 | 41.20 | 914.145 | 31.44 | 923.775 | 12.63 | 963.750 | 9.04 | 983.212 | 5.73 | 1015.759 | |

${\alpha}_{90\%}$ | Stage 2 | 8.51 | 577.680 | 10.3 | 590.512 | 6.53 | 621.731 | 6.09 | 635.915 | 5.94 | 646.828 |

Stage 3 | 15.38 | 700.390 | 27.47 | 722.863 | 19.72 | 743.134 | 11.03 | 772.596 | 22.36 | 778.701 | |

Stage 4 | 25.62 | 919.106 | 32.64 | 929.565 | 6.11 | 982.866 | 0.97 | 1076.961 | 2.45 | 1058.503 |

**Table 8.**The activation energies of stages two, three, and four obtained from the KAS, FWO, and Friedman methods.

Stage | ${\mathit{\alpha}}_{\mathit{n}}$ $({\mathit{\beta}}_{\mathit{a}}\u2013{\mathit{\beta}}_{\mathit{e}})$ | KAS Method $\mathit{ln}\left({\mathit{\beta}}_{\mathit{n}}/{\mathit{T}}^{2}\right)\u20131/\mathit{T}$ | Friedman Method $\mathit{ln}\left({\mathit{\beta}}_{\mathit{n}}\times \mathit{d}\mathit{\alpha}/\mathit{d}\mathit{T}\right)\u20131/\mathit{T}$ | FWO Method $\mathit{ln}\left({\mathit{\beta}}_{\mathit{n}}\right)\u20131/\mathit{T}$ | |||
---|---|---|---|---|---|---|---|

${\mathit{E}}_{0-\mathit{\alpha}\mathit{n}}\text{}(\mathbf{KJ}/\mathbf{mol})$ | R^{2} | ${\mathit{E}}_{0-\mathit{\alpha}\mathit{n}}\text{}(\mathbf{KJ}/\mathbf{mol})$ | R^{2} | ${\mathit{E}}_{0-\mathit{\alpha}\mathit{n}}\text{}(\mathbf{KJ}/\mathbf{mol})$ | R^{2} | ||

Stage 2 | ${\alpha}_{10\%}$ | 75.40 ± 5.81 | 0.9825 | 61.80 ± 6.34 | 0.9693 | 62.84 ± 5.53 | 0.9772 |

${\alpha}_{30\%}$ | 79.10 ± 5.56 | 0.9854 | 66.58 ± 5.84 | 0.9774 | 69.77 ± 5.31 | 0.9810 | |

${\alpha}_{50\%}$ | 80.59 ± 5.88 | 0.9843 | 64.64 ± 7.59 | 0.9602 | 67.25 ± 5.62 | 0.9795 | |

${\alpha}_{70\%}$ | 80.29 ± 6.81 | 0.9789 | 54.68 ± 11.97 | 0.8743 | 66.74 ± 6.50 | 0.9723 | |

${\alpha}_{90\%}$ | 75.16 ± 8.69 | 0.9614 | 42.63 ± 15.31 | 0.7210 | 61.57 ± 8.26 | 0.9487 | |

Stage 3 | ${\alpha}_{10\%}$ | 94.42 ± 8.09 | 0.9738 | 92.41 ± 4.07 | 0.9942 | 70.83 ± 7.71 | 0.9654 |

${\alpha}_{30\%}$ | 103.31 ± 5.03 | 0.9930 | 84.01 ± 10.33 | 0.9565 | 87.32 ± 4.85 | 0.9908 | |

${\alpha}_{50\%}$ | 100.83 ± 6.18 | 0.9888 | 66.66 ± 7.83 | 0.9602 | 84.63 ± 5.94 | 0.9853 | |

${\alpha}_{70\%}$ | 97.26 ± 6.77 | 0.9857 | 67.74 ± 15.01 | 0.8703 | 80.98 ± 6.52 | 0.9808 | |

${\alpha}_{90\%}$ | 98.28 ± 9.40 | 0.9732 | 77.59 ± 35.79 | 0.6103 | 81.76 ± 8.99 | 0.9647 | |

Stage 4 | ${\alpha}_{10\%}$ | 15.68 ± 0.074 | 0.9999 | −34.35 ± 6.88 | 0.8925 | 89.05 ± 56.65 | 0.4516 |

${\alpha}_{30\%}$ | 15.71 ± 0.073 | 0.9999 | 179.03 ± 45.85 | 0.8355 | 78.65 ± 66.51 | 0.3179 | |

${\alpha}_{50\%}$ | 15.40 ± 0.068 | 0.9999 | 92.93 ± 60.19 | 0.4687 | 103.69 ± 127.91 | 0.1797 | |

${\alpha}_{70\%}$ | 16.54 ± 0.197 | 0.9996 | 95.77 ± 170.19 | 0.0955 | 50.20 ± 33.35 | 0.4303 | |

${\alpha}_{90\%}$ | 16.46 ± 0.195 | 0.9996 | −43.57±31.13 | 0.3949 | 94.35 ± 14.70 | 0.9321 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Wang, X.; Qi, Y.; Xi, F.
Incineration Kinetic Analysis of Upstream Oily Sludge and Sectionalized Modeling in Differential/Integral Method. *Int. J. Environ. Res. Public Health* **2019**, *16*, 384.
https://doi.org/10.3390/ijerph16030384

**AMA Style**

Zhang Y, Wang X, Qi Y, Xi F.
Incineration Kinetic Analysis of Upstream Oily Sludge and Sectionalized Modeling in Differential/Integral Method. *International Journal of Environmental Research and Public Health*. 2019; 16(3):384.
https://doi.org/10.3390/ijerph16030384

**Chicago/Turabian Style**

Zhang, Yanqing, Xiaohui Wang, Yuanfeng Qi, and Fei Xi.
2019. "Incineration Kinetic Analysis of Upstream Oily Sludge and Sectionalized Modeling in Differential/Integral Method" *International Journal of Environmental Research and Public Health* 16, no. 3: 384.
https://doi.org/10.3390/ijerph16030384