**1. Introduction**

Upstream oily sludge is the most significant solid waste generated in the oil production industry, and is mainly discharged from the crude oil storage process [1,2]. Ordinarily, crude oil is housed in oil tanks prior to being refined to petroleum products, and the heavier species are separated and settled at the bottom of the storage tanks [3–5]. The solid sediments are the major components of upstream oily sludge, which contains a high concentration of complex petroleum hydrocarbons (PHCs, e.g., asphaltenes, resins, and tar), fine solids, and heavy metals [6,7]. On account of the toxicity and ignitability characteristics, which represented a significant adverse effect to ecosystem and human health, both upstream and downstream oily sludge have been regarded as hazardous waste in China since 2008 [8–10]. A variety of oil recovery and/or sludge disposal methods have been studied for the treatment of upstream oily sludge, such as thermal treatment (incineration or pyrolysis) [11–13], solidification [14], solvent extraction [15,16], photocatalysis [17], ultrasonic treatment [18], and biodegradation [18–21]. In China, the incineration process was identified as the most efficient method for the disposal of upstream oily sludge, and has been successfully designed, established, and commercialized in the last few years. However, the other mentioned methods have been rarely applied in practice for failing to reach a compromised balance between satisfying the strict environmental regulations and maintaining a reasonable operating cost [22,23]. Various incinerators such as circulating fluidized bed combustion, rotary kiln, and chain boiler combustion were adopted in the industrial application and operated with a combustion temperature between 730–1200 ◦C [1,12,23]. Furthermore, excess air and auxiliary fuels were indispensable for the incineration process. The incineration product was directly affected by a variety of factors, including the pretreatment method, operating temperature, residence time, feedstock quality, and addition of auxiliary fuels [24].

Most of the current studies focused on the thermal co-treatment of upstream oily sludge with auxiliary solid waste and/or the by-products that exist in gaseous phases and solid residue [22,25,26]. Generally, thermal analysis occupied the pivotal position throughout the thermal treatment of solid waste, and was frequently studied in the dehydration, carbonization, and incineration of industrial waste such as red mud, sewage sludge, and antibiotic residues [27–29]. The thermogravimetric analysis (TGA) test was a representative non-isothermal method for thermal kinetics analysis that was sensitive enough to exhibit the weight loss of the reactant with the operating temperature/time. It was usually applied for the thermal decomposition of certain reactants in air or nitrogen conditions. Ordinarily, the reaction kinetics of thermal decomposition was represented by the nth-order reaction rate equation [30–33] (see Equations (1)–(3)). Furthermore, the Arrhenius equation (Equation (4)) was commonly utilized to describe the reaction rate constant.

$$d\alpha/dt = \mathcal{K}(T)f(\alpha) \tag{1}$$

$$\mathfrak{a} = (\mathcal{W}\_i - \mathcal{W}\_t / \mathcal{W}\_i - \mathcal{W}\_\mathfrak{e}) \times 100\%, \mathfrak{a} \in (0\% - 100\%) \tag{2}$$

$$f(a) = (1 - a)^n \tag{3}$$

$$K(T) = A \exp(-E\_a/RT) \tag{4}$$

where *t* and *T* are the operating time and temperature; *α* is the conversion ratios of the reactant; and *dα*/*dt* is the relationship between the instantaneous conversion ratio and the operating time. In Equation (2), *Wi*, *Wn*, and *We* are the initial weight, weight at a certain time, and the final weight of the reaction, respectively. In Equations (1) and (4), *K*(*T*) is the reaction rate constant. In Equation (3), *f*(*α*) is the nth-order reaction rate equation, and n is the reaction order. Meanwhile, in Equation (4), A is the pre-exponential factor; *Ea* is the activation energy; and *R* is the gas constant.

The main objective for thermal kinetics analysis was to obtain the basic three elements [33], i.e., the activation energy (*Ea*), the pre-exponential factor (A), and the representation of the nth-order reaction rate equation ( *f*(*α*)). Obviously, it was imprecise to distinguish the mass signal versus time or temperature in a single isothermal or non-isothermal thermogravimetric test. Thus, multiple non-isothermal thermogravimetric analyses were often applied for the thermal kinetic studies. If the relationships between the operating temperature and reaction time were in the form of Equation (5), and meanwhile, the heating rate was constant in a certain TGA test, Equation (1) could be re-written as Equation (6):

$$T = \beta t + T\_o \Rightarrow dT/dt = \beta \tag{5}$$

$$
\hbar \, da \,/d\Gamma = A / \beta \times \exp(-E\_a/RT) f(a) \tag{6}
$$

where *T* and *To* are the operating temperature and initial temperature, respectively; *β* is the heating rate, *dα*/*dT* is the relationships between the instantaneous conversion ratios and the operating temperature.

Equation (6) was the basic differential form for the study of thermal kinetic analysis, which represented the relationships between the instantaneous conversion ratios of the reactant with *T* under certain heating rates (*β*). The Friedman method [34] and Coats–Redfern method [35] were obtained by rearranging Equation (6) and applied to the thermal kinetic analysis in the pyrolysis

### *Int. J. Environ. Res. Public Health* **2019**, *16*, 384

process of oily sludge, effectively [12]. However, limitations for differential methods still existed and were mainly attributed to *dα*/*dT*, which was dramatically affected by the background noise of the TGA test [36–40]. Therefore, the activation energy (*Ea*) obtained in differential methods was imprecise.

Based on Equation (6), the integral method for the study of thermal kinetic analysis could be deduced as follows:

$$
\alpha da/dT = \frac{A}{\beta} \varepsilon \exp\left(-E\_d/RT\right) f(a) \Rightarrow \frac{1}{f(a)} da = \frac{A}{\beta} e^{-E\_d/RT} dT \tag{7}
$$

$$\log G(\mathfrak{a}) = \int\_0^1 \frac{1}{f(\mathfrak{a})} d\mathfrak{a} = \frac{A}{\beta} \int\_{T\_\sigma}^T e^{-E\_\mathfrak{a}/RT} dT \tag{8}$$

where *<sup>G</sup>*(*α*) is the integral Equation of *f*(*α*); and *To* and *T* are the initial and final operating temperature, respectively.

The activation energy (*Ea*) and pre-exponential factor (A) could be obtained by rearranging Equation (8), and the negative effect of background noise could be avoided. However, the solution of the nth-order reaction rate equation *f*(*α*) and the reaction order (n) were hard to obtain. Therefore, both the differential method and integral method have their advantages and limitations during the acquisition of the activation energy, pre-exponential factor, and the nth-order reaction rate equation.

The pyrolysis kinetics analysis of oily sludge or plastic was reported in previous studies and the methods that were used are listed in Table 1, including the utilized thermal test method, the modeling method, and the basic three elements (*Ea*, A, and *f*(*α*) or *n*).

**Table 1.** Thermal kinetics analysis and modeling methods reported in the previous studies.


TGA: thermogravimetric analysis; DTG: derivative thermogravimetric analysis; DSC: differential scanning calorimetry.

The reaction schemes of upstream oily sludge incineration were extremely complex due to the complicated composition; meanwhile, the reaction mechanism and the corresponding kinetic parameters for the incineration of various intermediate products and by-products may differ with the change of heating rate and operating temperature regions. It is difficult to identify or distinguish whether or not the kinetics model is suitable for the different reaction stages during the incineration process only on the basis of TGA curves. However, few studies have been available concerning the incineration reaction kinetics or in both differential and integral modeling methods for upstream oily sludge.

The aims of the present work were as follows. (1) Both the multiple non-isothermal thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) were performed to study the incineration thermal kinetic of oily sludge, simultaneously. (2) The work aimed to provide a new viewpoint to sectionalize the reaction stages in TGA/DSC curves. (3) The work aimed to present and utilize a comprehensive differential integral method to obtain the incineration kinetics model in different reaction stages.
