A Thermal Characteristics Study of Typical Industrial Oil Based on Thermogravimetric-Differential Scanning Calorimetry (TG-DSC)

Abstract

Recent incidents of fire accidents attributed to oil combustion have emerged as a significant threat to both industrial safety and environmental conservation. In this study, the thermal oxidation and thermal analysis kinetics parameters of transformer oil, engine oil, and hydraulic oil in the air atmosphere were explored based on thermogravimetric-differential scanning calorimetry (TG-DSC). Industrial oils showed the same decomposition process in the thermal decomposition process. The peak temperature of the DSC curve was higher than that of the DTG curve, and the peak values of DTG and DSC curves increased with the increase of heating rate. The industrial oils underwent a main mass loss process, with respective ranges of approximately 80–84% for transformer oil, 73–79% for engine oil, and 86–89% for hydraulic oil. Notably, engine oil demonstrated the highest average apparent activation energy, amounting to 110.50 kJ/mol, significantly surpassing hydraulic oil (105.13 kJ/mol) and transformer oil (60.95 kJ/mol). The optimal kinetic model for the evaporative oxidation reaction of the industrial oils in air was identified as the reaction order model (Fn), with the corresponding kinetic mechanism function expressed as f(α) = (1 − α)ⁿ. The use of TG-DSC offers novel perspectives on the thermal stability and safety evaluation of oil products. Meanwhile, the optimal kinetic model and thermal oxidation stability of typical industrial oil evaporation and oxidation reaction in air was determined, possessing a good reference for the safety and the application of industrial oil.

1. Introduction

The proficient exploitation and application of fossil resources has been instrumental in propelling the swift advancement of human society and the economy [1]. The World Energy Outlook 2023 reports that, despite a surge in investments from various nations into clean energy technologies, fossil fuels continue to hold a commanding presence in the current energy landscape, constituting nearly 80% of the total energy supply [2]. Nonetheless, the propensity for industrial oil combustion to ignite fire accidents, attributable to the high flammability inherent in fossil resources, is a matter of growing concern [3,4]. Oil fires not only release an immense amount of thermal energy but also exacerbate the greenhouse effect and generate a plethora of noxious gases, including nitrogen oxides (NOx), sulfur dioxide (SO₂), and carbon monoxide (CO), thereby posing a dire threat to both industrial safety and environmental conservation [5,6]. Therefore, the imperative for fire risk management is to delve into the evaporative oxidation characteristics of diverse industrial oil products under high-temperature conditions.

The application of thermal analysis technology in elucidating the pyrolysis, combustion behavior, and kinetics of oils has garnered widespread recognition among researchers. The cornerstone of thermal analysis technology is the controlled heating of materials to induce physical or chemical transformations. These transformations result in variations of thermodynamic, thermophysical, or electrical properties of the material, detectable as temperature differentials compared to the ambient environment [7,8]. Thermal analysis encompasses techniques such as thermogravimetry (TG), differential thermal analysis (DTA), and differential scanning calorimetry (DSC). Francis et al. discussed the potential of converting waste edible oil into energy and chemicals in the study of pyrolysis using waste edible oil [9]. Katarzyna et al. conducted an experimental evaluation of the engine combustion test of plastic waste pyrolysis oil based on pyrolysis technology [10]. Notably, flaxseed oil exhibited a significant heat release during the DSC test, highlighting its strong propensity for oxidative spontaneous combustion.

At the forefront of modern scientific advancement, the solitary application of thermal analysis technology has been recognized as insufficient to fulfill the evolving research demands, yielding limited insights into material properties and thermal transformation processes, leading to one-dimensional outcomes [11,12]. Consequently, the scientific community has embraced an innovative approach that synergistically combines various thermal analysis techniques. This approach enhances the reliability and comprehensiveness of experimental data, deepening the understanding of intrinsic thermal behavior and the fundamental rules governing material transformations [13]. Among these techniques, TG-DSC stands out as a prevalent method primarily utilized to investigate material thermal behavior, interactions, compatibility, catalytic decomposition, and other pivotal characteristics [14]. The TG-DSC method offers the distinct advantage of concurrently executing TG and DSC analyses on a single sample, thereby procuring concurrent information on mass variations and thermal effects. The dual capability allows for the differentiation between mass changes and energy alterations, providing a lucid elucidation of the thermal analysis process [15]. Pires demonstrated the mass change and heat flow change of these nanoporous materials at different temperatures through TG-DSC experimental results [16]. Similarly, Ostasz et al. employed TG-DSC in the preclinical phase of newly developed potential drugs for thermal research [17]. Osypiuk et al. characterized the synthesis of ZnII complexes of Schiff base using TG-DSC [18]. Thus, the utilization of thermal analysis technology, particularly TG-DSC, proves to be an effective and practical approach for analyzing the pyrolysis and combustion behavior of industrial oils, offering a multifaceted perspective on their thermal stability and reactivity.

The pursuit of thermal analysis kinetics, particularly in elucidating kinetic parameters such as activation energy, pre-exponential factor, and reaction mechanisms during the process, has ascended as a preeminent area of study within the field of thermal analysis [19]. Rattana et al. conducted an in-depth investigation into the thermal stability of engine oil following prolonged thermal degradation, primarily employing TG-DSC analysis [20]. The kinetic parameters were meticulously determined through a robust model-fitting approach, integrating the Coats–Redfern method with model-free methodologies like Friedman, Flynn–Wall–Ozawa (FWO), Kissinger–Akahria–Sunose (KAS), and Vyazovkin methods. The findings delineated that the oxidation process of engine oil follows first-order reaction kinetics, with the KAS method proving the most accurate for oil oxidation studies. Zhang et al. ventured into the realm of Karamay transformer oil pyrolysis, utilizing a triad of techniques via TG, FTIR, and Py-GC/MS to dissect the thermal degradation characteristics [21]. The results revealed that the apparent activation energy changed by less than 10% in the conversion range of 0.05 to 0.95. Additionally, they identified the best-fitting kinetic model for transformer oil pyrolysis, which matched well with the predicted DTG curve. In conclusion, the strategic application of thermal analysis kinetic models enriches our understanding of the thermal decomposition and combustion behavior of industrial oils, laying the foundation for more nuanced and precise research efforts.

In this study, the thermal characteristics of transformer oil, engine oil, and hydraulic oil in an air atmosphere are explored based on thermal analysis. TG-DSC analysis was used to investigate the thermal oxidation and mass loss characteristic parameters of industrial oils at different heating rates. Through meticulous kinetic analysis, we determined the kinetic parameters and the kinetic mechanism model for these oils. Additionally, we examined how the heating rate affects the evaporation and oxidation process, kinetic parameters, and kinetic mechanism function. This research offers novel perspectives on the thermal oxidation stability and thermal decomposition kinetics of industrial oils.

2. Experiment Section

2.1. Material Material

In this study, transformer oil (Kunlun KI25X), engine oil (Shell Helix HX85W-40 synthetic oil), and hydraulic oil (Great Wall Zhuoli) were selected as experimental oils for the related research. Transformer oil ((Kunlun KI25X)) was provided by Shenyang Kunlun Tiangong Lubri-cating Oil Co., Ltd., Shenyang, China. Engine oil (Shell Helix HX85W-40 synthetic oil) was purchased from Shell Companies (Royal Dutch Shell), The Hague, The Netherlands. Hydraulic oil (Great Wall Zhuoli) was bought from Shanghai Wuheng Industrial Co., Ltd., Shanghai, China. These selections were made to encompass a diverse range of industrial applications and to provide a comprehensive understanding of the thermal behavior across different oil types. The main parameters of the experimental oils are shown in

Table 1. The main parameters of experimental oils.

Experimental Oils	Density (kg/m3)	Flash Point (°C)	Tilting Point (°C)	Kinematic Viscosity (mm2/s)
Transformer oil	885	143	<−24	9.7
Engine oil	841	232	−36	89.2
Hydraulic fluid	860	240	−15	45.8

.

2.2. Measurement

2.2.1. Measurement Methods

The measurement methods are present in the Supporting Information.

2.2.2. Measurement Equipment

The thermal effects of the experimental oils were meticulously characterized using a thermal analyzer (STA449F5, NETZSCH-Gerätebau GmbH, Selb, Germany).

2.2.3. Measurement Procedure

The measurement procedure is present in the Supporting Information. The specific experimental conditions are shown in

Table 2. Experimental conditions of oil in the TG-DSC test.

Experimental Oils	Temperature Range/°C	Heating Rate/(°C/min)	Atmosphere	Gas Flow /(mL/min)
Transformer oil	30~600	5	air	100
		10
		20
Engine oil	30~600	5	air	100
		10
		20
Hydraulic fluid	30~600	5	air	100
		10
		20

.

3. Results

The evaporation rate and vapor pressure, pivotal attributes of industrial oils, serve as critical parameters in the comprehensive assessment of the design, operability, and safety of novel process equipment. In this context, thermal analysis emerges as an efficacious methodology for elucidating the evaporative characteristics of oils. The analytical approach aids in the optimization of process devices by offering insights into oil behavior across various thermal conditions.

3.1. TG-DSC Analysis of Oil

Figure 1 shows the TG-DTG profiles of transformer, engine, and hydraulic oil, measured at a heating rate of 5 °C/min. The TG curve delineates the gradual decrease in residual mass of the oils with increasing temperature. The DTG curve, serving as the derivative of the TG curve, quantifies the rate of mass loss, thereby directly reflecting changes in the thermo-gravimetric reaction rate. A comparative analysis of the TG-DTG curves for these industrial oils reveals that transformer oil exhibits the lowest initial decomposition temperature, approximately 100 °C. This finding correlates with the lower bond energy and enhanced reactivity of the C–C bonds in the transformer oil. Furthermore, engine oil is distinguished by a pronounced maximum thermal decomposition rate of 8.9%/min, attributed to the substantial and concentrated decomposition of alkanes, cycloalkanes, and aromatic hydrocarbons within the oil. These industrial oils demonstrated minimal residual mass, indicative of their propensity for intense evaporation and oxidation reactions under elevated temperatures, indicating high reactivity and relatively low thermal oxidation stability inherent in these oils.

3.1.1. Typical TG-DTG Curves and Thermal Weight Loss Characteristic Parameters

In Figure 1, the TG-DTG curves of the three industrial oils exhibit a congruent trend in their thermal decomposition profiles. Initially, within the low-temperature range of 30–100 °C, the residual mass of the samples remains largely unaffected, indicating a period of relative thermal stability. However, as the temperature increases, there is a significant decrease in the residual mass of the oils, which stabilizes at a certain point, signifying complete decomposition. The DTG curve, characterized by a distinct single peak, illustrates the dynamic nature of the evaporation-oxidation reaction rate of the samples. With increasing temperature, the reaction rate escalates, peaks, and then starts to decline, ultimately leading to the cessation of the reaction.

To quantitatively dissect the thermal decomposition behavior of industrial oils under an air atmosphere, a suite of characteristic temperature parameters was introduced based on thermogravimetric analysis. T_i denotes the initial decomposition temperature, signifying the onset of the thermal decomposition reaction. T_p is identified as the temperature at which the thermal decomposition rate peaks. T_f, the final decomposition temperature, represents the end of the thermal decomposition process. Furthermore, T_on and T_off are defined as the extrapolated onset and termination temperatures, respectively. These are identified by the intersection of the tangent at the maximum slope of the TG curve with the baseline at T_i and T_f, respectively.

Employing the extrapolated onset temperature (T_on) and extrapolated termination temperature (T_f), the thermal decomposition process of industrial oils can be delineated into three distinct stages: Stage I, Stage II, and Stage III. Stage I is further divided into two sub-stages. Stage I-1, ranging from ambient temperature to the initial decomposition temperature (T_i), is characterized by minimal variation in the residual mass of the oil, indicating a period of thermal inertia. Stage I-2 spans from T_i to T_on, where thermal decomposition becomes noticeable, although the mass loss and its rate remain relatively low. Stage II, from T_on to T_f, consists of three sub-stages: Stage II-1 (T_on to T_p), Stage II-2 (T_p to T_off), and Stage II-3 (T_off to T_f). This Stage witnesses the predominant mass loss during thermal decomposition. Specifically, in Stage II-1, the rate of mass loss for industrial oils escalates with the temperature, while in Stage II-2, it decreases as the temperature rises. Stage II-3 exhibits a lower mass loss compared to the previous sub-stages. Lastly, Stage III, from T_f to 600 °C, within which the residual mass of the industrial oil maintains an equilibrium state as the temperature continues to rise, signifying the conclusion of major thermal decomposition activities.

3.1.2. TG-DSC Analysis of Transformer Oil

The TG-DTG and DSC curves of transformer oil, obtained at heating rates of 5 °C/min, 10 °C/min, and 20 °C/min, are illustrated in Figure 2. Independent of the heating rate, the mass loss rate curve of the transformer oil exhibits a consistent pattern: it increases initially, then decreases as the thermal decomposition temperature rises. Meanwhile, the heat flow curve initially descends, reaching a nadir around 100 °C, and then increases slowly, before ascending to a peak. Subsequently, it experiences a sharp decline and maintains a relatively stable profile between 350 and 500 °C, ultimately continuing its downward trajectory beyond 500 °C. As the heating rate increases, the TG curve shifts to the right, indicating that the time taken to reach the peak mass loss rate occurs at higher temperatures. This phenomenon is ascribed to thermal hysteresis, where a faster heating rate for industrial oil condenses the time required to attain a given temperature. However, due to thermal conductivity effects, the internal temperature of the oil lags, delaying evaporation and oxidation compared to slower heating scenarios. Moreover, peak values on both the DTG and DSC curves of the transformer oil climb with increasing heating rates, suggesting that a faster heating rate not only accelerates thermal decomposition but also intensifies the evaporation-oxidation process.

Transformer oil’s evaporation and oxidation process was analyzed at a heating rate of 5 °C/min. In stage I, the transformer oil revealed a mass loss of about 15.13% from ambient temperature to 192 °C. Concurrently, a minor endothermic peak was discernible in the DSC curve, indicating the release of moisture and pyrolytic byproducts, thus, marking the preliminary stages of thermal decomposition. In stage II, the transformer oil underwent pronounced thermal decomposition, evident from a significant mass loss of around 83.45% within the temperature range of 192–495 °C. During this phase, the DSC curve manifested a striking exothermic peak, attributable to the volatilization of alkanes, cycloalkanes, and aromatic unsaturated hydrocarbons [22]. Furthermore, the char residues generated after the pyrolysis and thermal oxidation reactions of transformer oil did not incur any significant mass loss during Stage III. After the experimental procedure, the transformer oil demonstrated a minimal residual mass of approximately 1.42%. On the DSC curve, the exothermic peak, indicative of the intense thermal reactions, completely vanished at around 515 °C, which is discernibly about 20 °C higher than the temperature corresponding to the mass loss peak in the DTG curve. The heat flow of the transformer oil remained constant throughout the remainder of the test, signifying the conclusion of significant thermal events and the attainment of a new equilibrium state.

To elucidate the influence of the heating rate on the evaporation and oxidation process of transformer oil,

Table 3. Evaporation and oxidation characteristic parameters of transformer oil.

Heating Rates (°C/min)	Ti (°C)	Ton (°C)	Tp (°C)	Toff (°C)	Tf (°C)	Stage I (%)	Stage II (%)	Residual Mass (%)	Tp,DSC (°C)	Peak of Heat Flow (W/g)
5	100	192	237	265	495	15.13	83.45	1.42	260	0.76
10	108	218	260	285	516	16.65	81.52	1.83	288	1.12
20	117	237	285	314	538	17.29	80.59	2.12	336	3.99

summarizes the characteristic temperatures derived from DSC and TG-DSC, along with mass loss data across various stages. A higher heating rate is associated with an increased thermal decomposition temperature in the TG curve and a correspondingly heightened characteristic peak temperature in the DSC curve. This correlation can be attributed to the thermal gradient between the transformer oil and the crucible. Moreover, a higher heating rate translates to a higher crucible temperature, resulting in a pronounced temperature hysteresis effect. This effect is manifested in the gradual increase in Stage I mass loss as the heating rate rises, escalating from 15.13% at 5 °C/min to 16.65% at 10 °C/min, and culminating at 17.29% at 20 °C/min. Conversely, Stage II mass loss exhibits an inverse relationship with the heating rate, with recorded values of 83.45%, 81.52%, and 80.59% at heating rates of 5, 10, and 20 °C/min, respectively. Additionally, the post-reaction residual mass increases with the heating rate, reaching 1.42%, 1.83%, and 2.12% at heating rates of 5, 10, and 20 °C/min, respectively. It is worth noting that the Tp of the DSC curve is higher than that of the DTG curve, suggesting a lag in the thermal response compared to the mass changes during the experiment. The characteristic peak temperature of the DTG curve exhibits a linear increase with the heating rate, mirroring the trend observed in the peak values of the DSC curve.

3.1.3. The TG-DSC Analysis of Engine Oil

The TG-DSC curves of engine oil, depicted in Figure 3, were captured at varying heating rates, revealing distinct thermal behaviors. The DTG curve, indicative of the rate of mass loss, displayed a solitary peak. Meanwhile, the DSC curve, representative of heat flow, exhibited a stable baseline at lower temperatures, followed by a sharp ascent to a pronounced peak at 288 °C. After reaching this peak, the curve experienced a swift decline, with minor undulations throughout the subsequent decomposition phases.

The characteristic peak temperatures in both the TG-DTG and DSC curves shifted to the right as the heating rate increased, a phenomenon attributed to thermal hysteresis. This trend echoes observations from the analysis of transformer oil. For an in-depth understanding of the evaporation and oxidation process of engine oil, a heating rate of 5 °C/min was selected for detailed analysis. Stage I encompassed a mass loss of 25.64% from room temperature to 287 °C, due to the decomposition of the base oil components and the volatilization of pyrolytic gases. Notably, the DSC curve during this stage exhibited minimal heat flux fluctuations. The mass loss was 73.12% for stage II at 287–537 °C, the main evaporation and oxidation stage of engine oil, which contributed to the degradation of the hydrocarbon’s main chain. A noticeable exothermic peak was observed in the DSC curve during stage II. The char residues formed during thermal pyrolysis, a part of the carbonization process, induced a modest mass alteration in the TG curve during Stage III. Upon completion of the test, the engine oil demonstrated a residual mass of 1.24%.

The characteristic temperature, mass loss, and other pertinent parameters related to the thermal decomposition of engine oil are summarized in

Table 4. Evaporation and oxidation characteristic parameters of engine oil.

Heating Rates (°C/min)	Ti (°C)	Ton (°C)	Tp (°C)	Toff (°C)	Tf (°C)	Stage I (%)	Stage II (%)	Residual Mass (%)	Tp,DSC (°C)	Peak of Heat Flow (W/g)
5	164	287	300	316	537	25.64	73.12	1.24	294	8.52
10	182	296	307	319	554	21.04	77.57	1.39	312	15.90
20	214	302	323	344	569	19.90	79.03	1.07	318	18.37

. It is observed that an increased heating rate correlates with an elevation in both the thermal decomposition characteristic temperature, evident in the DTG curve, and the reaction heat temperature, reflected in the DSC curve. As the heating rate escalates, the mass loss of engine oil during Stage I gradually decreases, whereas during Stage II, it progressively increases. The heat exchange between the surface and the interior of the oil takes a certain amount of time. When the heating rate is high, a certain temperature difference is produced between the two, which increases the decomposition temperature and shifts the curve to the right when the weight loss rate is the same. Moreover, the residual mass of engine oil exhibits a declining trend with an increase in heating rate, which is ascribed to the generation and volatilization of the pyrolysis production at high temperatures. The T_p in the DSC curve surpasses that in the DTG curve, signifying that the thermal response, in terms of heat flow, lags behind the mass change during the thermal decomposition of engine oil.

3.1.4. The TG-DSC Analysis of Hydraulic Oil

As depicted in Figure 4, the TG-DSC curves of hydraulic oil at varying heating rates exhibit a striking resemblance to those of engine oil. The DTG curve for hydraulic oil initially decreases, then rises, and finally stabilizes as the temperature increases. Upon further temperature elevation, the DSC curve rises sharply to reach a peak, reflecting the onset of significant thermal events. Post-peak, minor fluctuations in the DSC curve of hydraulic oil at higher temperatures suggest a complex interplay of exothermic and endothermic reactions during decomposition. Consistent with the results of engine and transformer oils, the characteristic peak temperatures identified in the TG-DTG and DSC curves of hydraulic oil shift to higher temperatures with an increase in heating rate.

In the meticulous analysis of the evaporation and oxidation process of hydraulic oil at a heating rate of 5 °C/min, Stage I, spanning from room temperature to 252 °C, a mass loss of 10.88% was recorded for the hydraulic oil. This initial mass loss is attributed to the evaporation of moisture and the release of light volatile components, marking the onset of the thermal decomposition sequence. In stage II, ranging from 252 to 564 °C, the hydraulic oil experienced a mass loss of 88.94%, which corresponds to the fracture of the hydrocarbon’s main chain and release of pyrolysis products [23]. Additionally, the exothermic peak appears in the DSC curve during stage II, while the residual mass and heat flow stabilize during the subsequent oxidative pyrolysis process.

Table 5. Evaporation and oxidation characteristic parameters of hydraulic oil.

Heating Rates (°C/min)	Ti (°C)	Ton (°C)	Tp (°C)	Toff (°C)	Tf (°C)	Stage I (%)	Stage II (%)	Residual Mass (%)	Tp,DSC (°C)	Peak of Heat Flow (W/g)
5	147	252	287	322	564	10.88	88.94	0.18	302	3.66
10	177	282	310	335	577	11.98	87.48	0.54	305	11.50
20	206	304	320	342	593	12.91	86.54	0.55	310	21.29

encapsulates the characteristic temperatures, mass loss percentages, and related parameters that define the thermal decomposition properties of hydraulic oil.

Similar to the observed behavior in transformer and engine oils, hydraulic oil under a higher heating rate is associated with higher characteristic temperatures in the DTG curve, indicating thermal decomposition, and elevated reaction heat temperatures in the DSC curve. As the heating rate escalates, the mass loss during Stage I of the decomposition process for hydraulic oil progressively rises. Referring to Figure 3 and Figure 4, both the mass loss rate peak and the heat flow peak in the TG-DSC curves of hydraulic oil intensify with an incremented heating rate. Notably, the temperature corresponding to the mass loss rate peak is lower than that of the heat flow peak. A detailed characterization of the thermal decomposition process, with a focus on the effects of heating rate, is crucial for understanding the thermal stability and performance of hydraulic oils.

3.2. Dynamic Analysis and Mechanism Model Establishment

3.2.1. Basis of Dynamics Analysis

In this study, the dynamic parameters extracted from the TG-DSC curves are meticulously employed for a quantitative analysis of the oxidation kinetics of representative industrial oils. The total reaction rate constant was described by the Arrhenius equation [24]:

$$\mathrm{k}\left(T\right)=A\exp \left(-{\displaystyle \frac{E_{\mathrm{a}}}{RT}}\right)$$

(1)

T is the experimental temperature, K; R is the gas constant, R = 8.314 J/mol·K; E_a is the apparent activation energy, kJ/mol; A is the pre-exponential factors, min⁻¹. The apparent activation energy and pre-exponential factors are paramount in the kinetic analysis of thermal processes. The apparent activation energy is a measure of the minimum energy required for a significant fraction of the molecules to undergo a chemical reaction. It essentially reflects the proportion of molecules within a system that possesses sufficient energy to overcome the energy barrier associated with the reaction. The energy barrier is a critical threshold that must be surmounted for the reaction to proceed at a noticeable rate. In the TG-DSC test, the oxidation reaction rate was expressed as:

$${\displaystyle \frac{\mathrm{d}\alpha }{\mathrm{d}t}}=\beta {\displaystyle \frac{\mathrm{d}\alpha }{\mathrm{d}T}}=\mathrm{k}\left(T\right)\mathrm{f}\left(\alpha \right)=A\exp \left(-{\displaystyle \frac{E_{\mathrm{a}}}{RT}}\right)\mathrm{f}\left(\alpha \right)$$

(2)

β is the heating rate, °C/min; k(T) is the constant of the reaction rate; f(α) is a kinetic mechanism function; α is the conversion rate. The kinetic analysis of the TG curve is expressed as:

$$\alpha ={\displaystyle \frac{m_0-m_{\mathrm{t}}}{m_0-m_{\mathrm{f}}}}$$

(3)

m₀ is the initial mass of the sample, g; m_t is the mass of the sample that varies with time, g; m_f is the residual mass after the test, g. The kinetic analysis of the DTG curve is expressed as:

$$\alpha ={\displaystyle \frac{H_{\mathrm{t}}}{H_{\infty }}}$$

(4)

The variables H_t and H_∞ represent the total heat absorption at a given time t and over the entire thermal decomposition process, J/g. Under linear heating conditions, Equation (1) was expressed as:

$${\displaystyle \frac{\mathrm{d}\alpha }{\mathrm{d}T}}={\displaystyle \frac{A}{\beta }}\exp \left(-{\displaystyle \frac{E_{\mathrm{a}}}{RT}}\right)\mathrm{f}\left(\alpha \right)$$

(5)

The integral kinetic mechanism function g(α) is the integral form of f(α), which was expressed as:

$$\begin{array}{l}\mathrm{g}\left(\alpha \right)={\displaystyle {\int }_0^{\alpha }\frac{\mathrm{d}\alpha }{\mathrm{f}\left(\alpha \right)}}={\displaystyle \frac{A}{\beta }}{\displaystyle {\int }_{T_0}^T\exp }\left(-{\displaystyle \frac{E_{\mathrm{a}}}{RT}}\right)\mathrm{d}T\end{array}$$

(6)

T₀ is the initial temperature of the test, K. The kinetic parameters were determined using Equation (6). The thermal characteristics of typical industrial oils in the TG-DSC test were quantified by kinetic analysis.

3.2.2. Kinetic Parameters

In the realm of thermal analysis, determining kinetic parameters is crucial for understanding the thermal degradation behavior of materials. Two predominant approaches are commonly employed: model-free methods and model-based methods [25]. The model-free method evaluates kinetic parameters without relying on a predefined reaction model, thus, avoiding potential compensation effects inherent in assuming a specific reaction model. This method provides valuable insights into kinetic parameters across various conversion rates, aiding in the deciphering of complex reaction mechanisms [26,27]. Notably, it enables the derivation of reliable kinetic parameters, such as activation energy, through the iso-conversion method, eliminating the need to understand the underlying reaction mechanism. Commonly utilized model-free methods include the Friedman, Malek methods, FWO [28], KAS, Starink, and others. Among them, the Friedman method requires data with ultra-high accuracy, while the Malek methods are only suitable for analyzing specific reaction mechanisms. Therefore, the two methods are not suitable for the thermal reaction kinetics analysis of industrial oils. FWO uses an approximation for the temperature integral and assumes a constant value for the activation energy during the reaction process. Similar to FWO, KAS is an integral method that uses a different approximation for the temperature integral. The Starink method optimizes the FWO and KAS methods, providing a more accurate temperature integral approximation without the need for assumptions. In summary, while the FWO and KAS methods are more established in the literature, the Starink method offers improvements in accuracy by optimizing the temperature integral approximation. In this study, the FWO, KAS, and Starink methods were selected to calculate the apparent activation energy. The apparent activation energy calculated by the FWO method was expressed as:

$$\ln \beta =\ln \left[{\displaystyle \frac{AE}{R\mathrm{g}\left(\alpha \right)}}\right]-5.331-1.052{\displaystyle \frac{E}{RT}}$$

(7)

The apparent activation energy calculated by the KAS method was expressed as:

$$\ln \left({\displaystyle \frac{\beta }{T^2}}\right)=\ln \left[{\displaystyle \frac{AE}{R\mathrm{g}\left(\alpha \right)}}\right]-{\displaystyle \frac{E}{RT}}$$

(8)

The apparent activation energy calculated by the Starink method was expressed as:

$$\ln \left({\displaystyle \frac{\beta }{T^{1.92}}}\right)=C\mathrm{s}-1.0008{\displaystyle \frac{E}{RT}}$$

(9)

In the thermal analysis, particularly when examining the TG curves at various heating rates β, a common approach involves selecting a constant conversion rate α, assuming that the kinetic mechanism function f(α) is equivalent to an integral kinetic mechanism function g(α). C_s is a constant related to the reaction.

The left side of the kinetic equation is related linearly to the inverse of the temperature, 1/T. The linearity allows for the determination of apparent activation energy at a given conversion rate from the slope of the plot. The average activation energy is then used to calculate the pre-exponential factor. Based on Equation (4), the -KAS method is used to solve the pre-exponential factor, mainly considering the temperature and conversion rate at the maximum reaction rate [29].

$${\displaystyle \frac{{\mathrm{d}}^2\alpha }{\mathrm{d}{t}^2}}=\left[{\displaystyle \frac{\beta E}{R{T}_{\max }^2}}+A{f}^{\prime }\left({\alpha }_{\max }\right)\exp \left(-{\displaystyle \frac{E}{R{T}_{\max }}}\right)\right]{\left({\displaystyle \frac{\mathrm{d}\alpha }{\mathrm{d}t}}\right)}_{\max }=0$$

(10)

Considering the first-order reaction f’(α) = −1, the above equation can be expressed as:

$${\displaystyle \frac{\beta E}{R{T}_{\max }^2}}-A\exp \left(-{\displaystyle \frac{E}{R{T}_{\max }}}\right)=0$$

(11)

Therefore, the pre-exponential factor A was expressed as:

$$A={\displaystyle \frac{\beta E}{R{T}_{\max }^2}}\exp \left({\displaystyle \frac{E}{R{T}_{\max }}}\right)$$

(12)

The average activation energy of the above three methods was replaced by E to determine the pre-exponential factors at different heating rates.

3.2.3. The Model of the Kinetic Mechanism

The model-based method provides a structured approach to comprehend the kinetic mechanism of reactions, considering the underlying reaction model. In cases where model-free methods fail to offer sufficient insight into the reaction mechanism, the model-based method can be employed for elucidating the evaporation and oxidation kinetics of typical industrial oils. Utilizing the average activation energy E, derived from three iso-conventional model-free methods across different conversion rates, we determined the kinetic mechanism model through the Master-plot method [30]. Within this methodology, the integral form of Equation (5) is expressed as:

$$\mathrm{g}\left(\alpha \right)={\displaystyle \frac{A{E}_{\mathrm{a}}}{\beta R}}\mathrm{P}\left(u\right)$$

(13)

P(u) denotes the temperature integral, formulated as:

$$\mathrm{P}\left(u\right)=0.00484\exp \left(-1.0516u\right)$$

(14)

μ = E_a/(RT). When selecting α = 0.5 as the reference point, the integral Master-plots are expressed as:

$${\displaystyle \frac{\mathrm{g}\left(\alpha \right)}{\mathrm{g}\left(0.5\right)}}={\displaystyle \frac{\mathrm{P}\left(u\right)}{\mathrm{P}\left(u_{0.5}\right)}}$$

(15)

Ensuring the reliability of kinetic analysis is paramount, particularly in complex processes such as the evaporation, oxidation, and combustion of industrial oils. For our kinetic analysis, we considered reaction mechanism models that align with the experimental observations from the oil evaporation and oxidation experiment. As delineated in Table 2, the kinetic models in the study include the reaction order model, diffusion model, power function law, and nucleation model. The methodology involves substituting different conversion rates α into the kinetic Formula (15). The relationship curve between g(α)/g(0.5) and α serves as the theoretical curve. The optimal kinetic model is then determined by aligning this theoretical curve with the experimental curve.

3.3. Determination of Kinetic Parameters and Mechanism Model

3.3.1. Preliminary Determination of Kinetic Parameters

As depicted in Figure 5, the apparent activation energy, E_a, for various experimental oils was determined using three distinct iso-conventional methods: FWO, KAS, and Starink. These methods were applied to calculate E_a across a range of conversion rates α, from 0.1 to 0.9, incrementing by 0.1. This process involved utilizing the slope of linear fits. For illustration, Figure 5a presents the computation for transformer oil using the FWO method. Specifically, at a conversion rate of 0.1, temperature data collected at various heating rates underwent linear regression analysis. The slope derived from this linear fit at a 0.1 conversion rate was then utilized to calculate the apparent activation energy. This procedure was repeated for other conversion rates, yielding a set of values for transformer oil as determined using the FWO method. The calculation of the apparent activation energy and the determination of the correlation coefficient (R²) are pivotal steps. The calculated values of E_a and R² for each conversion rate and method are summarized in

Table 6. Typical kinetic mechanism model.

Reaction Mechanism Model	Sign	f(α)	g(α)
Reaction order model	F0	1	α
	F1	1 − α	−ln (1 − α)
	F2	(1 − α)2	(1 − α)−1 − 1
	F3	(1 − α)3	[(1 − α)−1 − 1]/2
Diffusion model	D1	α/2	α2
	D2	[−ln (1 − α)]−1	[(1 − α) ln (1 − α)] + α
	D3	3 (1 − α)2/3/[2 (1 − (1 − α)1/3)]	[1 − (1 − α)1/3]2
Power function	P2	2α1/2	α1/2
	P3	3α2/3	α1/3
	P4	4α3/4	α1/4
Nucleation model	A1.5	3/2 (1 − α) [−ln (1 − α)]1/3	[−ln (1 − α)]2/3
	A2	2 (1 − α) [−ln (1 − α)]1/2	[−ln (1 − α)]1/2
	A3	3 (1 − α) [−ln (1 − α)]2/3	[−ln (1 − α)]1/3
	A4	4 (1 − α) [−ln (1 − α)]3/4	[−ln (1 − α)]1/4

.

As presented in

Table 7. Apparent activation energy of oils based on the iso-conversion method.

Industrial Oils	α	FWO		KAS		Starink		Average Value
		Ea	R2	Ea	R2	Ea	R2	Ea
transformer oil	0.1	62.97	0.98	59.65	0.97	58.76	0.98	60.46
	0.2	63.02	0.99	58.26	0.99	59.44	0.99	60.24
	0.3	62.80	0.99	57.65	0.99	58.83	0.99	59.76
	0.4	62.65	0.99	57.32	0.99	58.32	0.99	59.43
	0.5	62.74	0.99	58.82	0.99	58.63	0.99	60.07
	0.6	64.22	0.99	58.71	0.99	59.02	0.99	60.65
	0.7	65.03	0.98	59.44	0.99	59.75	0.99	61.40
	0.8	66.16	0.98	61.86	0.98	60.83	0.97	62.95
	0.9	67.28	0.97	61.56	0.97	61.87	0.97	63.57
	Average value	64.10	0.98	59.25	0.98	59.49	0.98	60.95
engine oil	0.1	102.77	0.99	100.90	0.98	84.57	0.99	96.08
	0.2	105.06	0.99	104.96	0.99	93.27	0.99	101.10
	0.3	113.01	0.98	111.30	0.98	110.08	0.99	111.46
	0.4	121.07	0.99	117.78	0.99	116.61	0.99	118.49
	0.5	124.23	0.98	123.65	0.99	127.68	0.98	125.19
	0.6	123.05	0.97	121.13	0.92	125.59	0.94	123.26
	0.7	117.38	0.93	113.90	0.95	113.10	0.94	114.79
	0.8	115.38	0.91	112.11	0.92	108.27	0.92	111.92
	0.9	106.96	0.94	105.88	0.92	95.13	0.95	102.66
	Average value	114.32	0.96	112.40	0.96	108.26	0.97	110.50
hydraulic oil	0.1	86.65	0.99	79.95	0.99	86.06	0.99	84.22
	0.2	86.21	0.99	79.71	0.99	81.68	0.99	82.53
	0.3	88.45	0.98	85.33	0.97	84.08	0.99	85.95
	0.4	94.54	0.98	89.14	0.96	89.35	0.97	91.01
	0.5	102.34	0.96	103.04	0.96	98.81	0.96	101.40
	0.6	110.64	0.97	102.07	0.96	104.59	0.97	105.77
	0.7	125.18	0.97	114.00	0.92	116.57	0.96	118.58
	0.8	142.53	0.99	134.48	0.99	134.85	0.99	137.29
	0.9	143.15	0.99	140.46	0.99	134.75	0.99	139.42
	Average value	108.85	0.98	103.12	0.97	103.42	0.98	105.13

, R² values for the apparent activation energy, calculated using the FWO, KAS, and Starink methods surpass 0.91, indicating the strong reliability of the calculation results. For transformer oil under an air atmosphere, the average apparent activation energy, as calculated by the respective methods, is 64.10 kJ/mol (FWO), 59.25 kJ/mol (KAS), and 59.49 kJ/mol (Starink). The consistency in the trend of activation energies obtained by these three methods reflects a unified pattern in the evaporation and oxidation process of transformer oil. It is worth noting that the average apparent activation energy remains relatively steady at approximately 60 kJ/mol for conversion rates below 0.5. As the conversion rate increases beyond 0.5, the average apparent activation energy gradually increases, peaking at 63.57 kJ/mol at a conversion rate of 0.9.

For engine oil in the air atmosphere, the average apparent activation energy values, as calculated using the FWO, KAS, and Starink methods, are 114.32 kJ/mol, 112.40 kJ/mol, and 108.26 kJ/mol, respectively. The trend for engine oil demonstrates an initial increase followed by a decrease as the conversion rate progresses. At a conversion rate of 0.1, the average apparent activation energy is 96.08 kJ/mol, suggesting a relatively lower energy barrier for the initiation of the decomposition process. The energy requirement hits a maximum at a conversion rate of 0.5, with an average apparent activation energy of 125.19 kJ/mol, indicating a more significant energy demand during the mid-stages of decomposition. As the conversion rate approaches completion (0.9), the average apparent activation energy declines to 102.66 kJ/mol. In the case of hydraulic oil, the average apparent activation energy values obtained using the FWO, KAS, and Starink methods are 108.85 kJ/mol, 103.12 kJ/mol, and 103.42 kJ/mol, respectively. The peak average apparent activation energy for hydraulic oil is achieved at a conversion rate of 0.9, reaching 139.42 kJ/mol.

Although there are minor discrepancies in the apparent activation energy values for industrial oils calculated using different methods, the variations fall within an acceptable error range, thus, providing a dependable foundation for further analysis. Among the analyzed oils, engine oil demonstrated the highest average apparent activation energy, specifically 110.50 kJ/mol. This value significantly exceeds that of hydraulic oil at 105.13 kJ/mol, and transformer oil at 60.95 kJ/mol. A higher apparent activation energy indicates a greater energy requirement for oil decomposition initiation and continuation, reflecting the thermal stability of the oil. For a first-order reaction, the pre-exponential factor, which represents the frequency of effective collisions for reactions under standard conditions, was preliminarily calculated using Formula (12) for oils at different heating rates. For transformer oil, at heating rates of 5 °C/min, 10 °C/min, and 20 °C/min, the calculated pre-exponential factors were 2.46 × 10⁵ min⁻¹, 2.43 × 10⁵ min⁻¹, and 2.39 × 10⁵ min⁻¹, respectively. The pre-exponential factors of engine oil at heating rates of 5 °C/min, 10 °C/min, and 20 °C/min were 2.40 × 10⁹ min⁻¹, 3.54 × 10⁹ min⁻¹, and 3.62 × 10⁹ min⁻¹. For hydraulic oil, the pre-exponential factors at different heating rates were 1.29 × 10⁹ min⁻¹, 9.78 × 10⁸ min⁻¹, and 1.31 × 10⁹ min⁻¹.

3.3.2. Determination of Kinetic Mechanism Model

In the kinetic analysis of thermal decomposition for industrial oils, integrating theoretical and experimental curves is a sophisticated approach to ascertain the most representative kinetic model. By incorporating the initial apparent activation energy and pre-exponential factor into Formula (15), we derived the theoretical curve representing the relationship between g(α)/g(0.5) and α, while the experimental curve represented the relationship between P(u)/P (u0.5) and α. These curves were then compared to identify the kinetic model that best fits the experimental data. In this study, a heating rate of 10 °C/min was chosen for analyzing the apparent activation energy of different industrial oils. Figure 6 illustrates both the theoretical and experimental curves for the dynamic mechanics models of various industrial oils.

Figure 6a presents the theoretical curves for the kinetic models listed in Table 7, encompassing the reaction order model (Fn), diffusion model (Dn), power function rule model (Pn), and nucleation model (An). The comparison between experimental and theoretical curves in Figure 6 indicates that the experimental curves fall between the reaction order models F0 and F1. This observation suggests that a reaction order model of the form f(α) = (1 − α)ⁿ could effectively represent the reaction mechanism of the experimental oils. However, since the kinetic mechanism cannot be fully expressed by an integer value n, and a non-integer value n indicates that the actual kinetic mechanism of evaporation and oxidation deviates from the ideal model after the reaction order, further fitting analysis is warranted to determine the exponent n at different heating rates.

By substituting the reaction order model f(α) = (1 − α)ⁿ into the kinetic mechanism function, Formula (16) was expressed as:

$$\mathrm{g}\left(\alpha \right)={\displaystyle \frac{A{E}_{\mathrm{a}}}{\beta R}}\mathrm{P}\left(u\right)={\displaystyle \frac{1-{\left(1-\alpha \right)}^{1-n}}{1-n}}$$

(16)

Figure 7 shows the relationship between $\left[1-{\left(1-\alpha \right)}^{1-n}\right]/\left(1-n\right)$ and $\left[E_{\mathrm{a}}\mathrm{P}\left(u\right)\right]/\left(\beta R\right)$. The meticulous analysis of the kinetic mechanisms underlying the evaporation and oxidation of industrial oils necessitates adjusting the reaction order index to achieve the highest linear correlation between the theoretical and experimental curves [31]. The pre-exponential factor, indicating the frequency of effective collisions per unit of time and volume, is further refined using the slope of the linear regression curve depicted in Figure 7.

Table 8. Kinetic parameters and kinetic mechanism function of different oils.

Industrial Oils	Heating Rate (°C/min)	Ea (kJ/mol)	A (min−1)	f(α)	R2
transformer oil	5	60.95	3.12 × 105	(1 − α)0.11	0.9952
	10		3.50 × 105	(1 − α)0.12	0.9996
	20		3.52 × 105	(1 − α)0.14	0.9993
engine oil	5	110.50	2.14 × 109	(1 − α)0.48	0.9882
	10		2.66 × 109	(1 − α)0.50	0.9926
	20		2.24 × 109	(1 − α)0.51	0.9791
hydraulic oil	5	105.13	6.41 × 108	(1 − α)0.35	0.9971
	10		8.12 × 108	(1 − α)0.36	0.9911
	20		7.16 × 108	(1 − α)0.37	0.9759

consolidates the apparent activation energy, pre-exponential factors, kinetic mechanism function, and correlation coefficients for different industrial oils at various heating rates.

As depicted in Figure 7 and detailed in Table 8, the correlation coefficients for the kinetic mechanism function and the pre-exponential factor, as determined by the Master-plots method, exceed 0.97. The high value signifies a strong linear relationship and underscores the high reliability of the calculation results, lending confidence to the kinetic parameters derived from the analysis. The kinetic analysis has identified the reaction order model as the most representative of the evaporation and oxidation reaction of industrial oils in an air atmosphere. This model is characterized by the kinetic mechanism function f(α) = (1 − α)ⁿ, where the variation primarily lies in the reaction order. The apparent activation energies for engine oil, hydraulic oil, and transformer oil are determined to be 110.50 kJ/mol, 105.13 kJ/mol, and 60.95 kJ/mol, respectively. The main reason is that the chemical composition of transformer oil, engine oil, and hydraulic oil is different, and the composition difference has a direct impact on the thermal stability and chemical reaction activation energy of the oil. Transformer oil is mainly composed of cycloalkanes, while engine oil and hydraulic oil may contain more additives and mixtures of different types of hydrocarbons, which may improve their thermal stability and activation energy. Meanwhile, the reaction orders for engine oil, hydraulic oil, and transformer oil fall within the ranges of 0.48–0.51, 0.35–0.37, and 0.11–0.14, respectively. According to the kinetic reaction of the reaction order model, the reaction rate is positively correlated with the concentration of the remaining reactants. Consequently, the evaporation and oxidation reaction rate of engine oil is more significantly influenced by the quantity of remaining oil compared to hydraulic oil and transformer oil. Furthermore, while different heating rates exert a considerable influence on the TG-DSC behavior of the oils, their impact on the pre-exponential factor and the reaction order is relatively minor. The findings from this kinetic analysis are instrumental in understanding the thermal stability and degradation kinetics of industrial oils. They provide valuable insights for the optimization of oil formulations and for the design of thermal management strategies in applications where the thermal properties of oils are crucial for performance, safety, and reliability.

4. Summary

In this comprehensive study of the thermal characteristics of transformer oil, engine oil, and hydraulic oil under an air atmosphere, several key findings have been established through rigorous thermal analysis. The evaporation and oxidation process of these oils was meticulously analyzed, and the mass loss characteristics at varying heating rates were quantified using TG-DSC tests. Kinetic analysis was employed to determine the kinetic parameters and the kinetic mechanism model for these oils. The main conclusions drawn from the research are:

(1)

Thermogravimetric analysis of industrial oils, represented by TG-DTG curves, revealed a singular peak during the thermal decomposition process. The peak signifies an initial increase in the evaporation and oxidation reaction rate, peaking at the maximum and then gradually tapering off. By introducing characteristic temperatures from thermogravimetric analysis, the mass loss process of industrial oils was divided into three main stages. The primary evaporation and oxidation reaction of industrial oils mainly occurred in stage II, where the mass loss for transformer oil, engine oil, and hydraulic oil ranged between approximately 80–84%, 73–79%, and 86–89%, respectively.

(2)

Thermal analysis, evidenced by the TG, DTG, and DSC curves, exhibits a notable shift towards higher temperatures with an increase in the heating rate. The peak temperature of the DSC curve was higher than that of the DTG curve, indicating that the heat changes lagged behind the mass loss during the thermal decomposition of the oils. Moreover, as the heating rate escalated, the peak values of both DTG and DSC curves augmented, highlighting that a higher heating rate not only increased the thermal decomposition but also aggravated the evaporation and oxidation reactions of oils.

(3)

Three model-free iso-conversational methods, FWO, KAS, and Starink methods, were used to calculate the apparent activation energy of the oils. The trend calculated using different methods exhibited a slight difference, with an increase in the conversion rate. The apparent activation energy of engine oil, hydraulic oil, and transformer oil was determined to be 110.50, 105.13, and 60.95 kJ/mol, respectively. Additionally, the Master-plot method aided in identifying the kinetic mechanism model, with the reaction order model (Fn) emerging as the most suitable for describing the evaporative oxidation reaction of these industrial oils in an air atmosphere, corresponding to the kinetic mechanism function f(α) = (1 − α)ⁿ.

This research offers novel perspectives on the thermal oxidation stability and the thermal decomposition kinetics of industrial oils. In addition, this research is helpful in predicting and controlling the thermal oxidation process of oil products more accurately and also has important reference significance for oil selection and safety in industrial applications. Nevertheless, it is important to acknowledge the limitations of the current thermal analysis, which was conducted on a small scale and, thus, did not account for the scale effect on the behavior of these oils. Meanwhile, using numerical simulations to simulate the thermal behavior of large-scale oil at different scales is also an effective strategy for exploring the safety of industrial oils. Therefore, the focus of future work should be on exploring the influence of different scales on the thermal analysis of industrial oil by using the strategy of experiment combined with numerical simulation.