Kinetic study of the effect of thermal hysteresis on pyrolysis of vacuum residue

Abstract

Investigating the thermal hysteresis and its effect on the kinetic behaviors and reaction model of vacuum residue pyrolysis is of significant importance in industry and scientific research. Effects of heating rate and heating transfer resistance on the pyrolysis process were examined with the thermogravimetric analysis. The kinetic characteristics of the vacuum residue pyrolysis were estimated using the iso-conversional method and integral master-plots method based on a three-stage reaction model through the deconvolution of Fraser-Suzuki function. Results showed that the reaction order models for the first and second stages were associated with the evaporation of vapor, while the nucleation and growth models for the third stage were linked to char formation. During the pyrolysis, the thermal hysteresis led to an increase in the reaction order in the first stage, which resulted in a delayed release of generated hydrocarbons due to high heating rate and enhanced heat transfer resistance. The reaction in the last stage primarily involved coking, where the presence of an inert solid acted as a nucleating agent, facilitating char formation and reducing the activation energy. The optimization results suggest that the obtained three-stage reaction model and kinetic triplets have the potential to effectively describe the active pyrolysis behavior of vacuum residue under high thermal hysteresis.

Graphical abstract

Keywords

vacuum residue / pyrolysis / thermogravimetric analysis / thermal hysteresis / kinetic mechanism

1 Introduction

Vacuum residue (VR) is the heaviest product obtained from the distillation of crude oil, with its proportion often exceeding 50% due to the scarcity of light crude oil [1−3]. The inferior properties of VR, including elevated levels of resins, asphaltenes, and heteroatoms (sulfur, nitrogen, oxygen and heavy metals), pose significant challenges due to their increased propensity for coking and adverse impacts on catalysts [4−6]. The rising demand for converting residual oil into cleaner and higher value products, coupled with the necessity of efficiently and economically processing of heavy oils to meet stricter environmental protection requirements, has elevated VR lightening technology as a significant and challenging subject of research in petroleum processing [7,8]. Thermochemical conversion methods, in particular, continue to generate tremendous interest from experts, mainly due to their economic and environmental potential in comparison to alternative processes for the upgrading of heavy oils in petroleum refineries [9].

Thermal conversion processes such as visbreaking [10] and delayed coking [11], being flexibile, simple and economical, accounts for over 65% of total residue processing capacity. VR pyrolysis is widely acknowledged as a complex process that encompasses multiphase reactions, the presence of highly unstable intermediates, and the interplay of mass and heat transfer. The generation of radical fragments occurs through the cleavage of covalent bonds induced by thermal energy, which is noteworthy as it drives the majority of chemical processes known as free radical reactions. Furthermore, the selectivity and yield of the products are influenced by both the chemical properties of the original feedstock and the operating conditions, which regulate the combination or recombination of these radical fragments [12]. For instance, rapid thermal cracking has been proposed and applied to enhance the performance of existing coking technologies, such as Flexicoking, HTL, FTC, and ART process. Evolving thermal cracking technologies, characterized by high temperatures and short contact times, utilize small droplets of heat carriers to achieve high feedstock conversion and maximize the yield of target products, thereby preventing secondary cracking of product vapor [7,13]. These operating conditions enhance the gas-phase cracking reaction ratio, increase the liquid yield and also decrease the coke formation [14,15]. Therefore, the yields and properties of products obtained from heavy feedstock under various cracking conditions, ranging from mild treatment to fast pyrolysis (high-temperature reactions with very short residence times), are dramatically dependent on the heating rate, maximum reactions temperature and resistance time, which are the critical parameters that greatly influence the outcomes of upgrading processes by controlling free radical reactions. Optimum values of these parameters are usually determined based on reaction kinetics obtained experimentally so that a desired conversion and product distribution is achieved. Therefore, successful implementation of any thermal cracking process requires a reasonable knowledge of reaction kinetics for the specific feed at hand [16].

An in-depth comprehension of the kinetics and reaction mechanism of VR pyrolysis could greatly contribute to improving the conversion efficiency, developing appropriate reactors, and controlling product selectivity for the new thermal cracking units currently being developed for heavy feedstock treatment. Thermogravimetric (TG) analysis has been widely applied to estimate thermal characteristic of residual oil during thermochemical conversion and analyze the reaction kinetics by mathematical description of the overall reaction using Arrhenius Eqs [17−19]. These findings indicated that the thermal decomposition temperature of the VR exceeded 350 °C and that as the heating rate was raised, the temperature at which the greatest rate of cracking occurs shifted to a higher temperature [20,21]. The coke yields of petroleum residues could measure the coking tendency accurately using the TG method. It is determined that coke formation is influenced by aromaticity and molecular size. Specifically, asphaltenes fraction contributes the most to the formation of coke among other fractions (asphaltenes > resins > aromatic > saturates) [17,22,23]. The implementation of model-free methods, including Friedman, Flynn-Wall-Ozawa (FWO), and Kissinger-Akahira-Sunose (KAS), etc. has facilitated the accurate determination of kinetic parameters in residual oil pyrolysis [24,25]. It was found that the activity energy in residual oil pyrolysis undergoes significant variation with conversion due to the complexity of the mechanism, which was indicative of a change in the nature of the rate-controlling step. Each fraction in the entire residual oil follows a reaction route independent of the other fractions [20,26]. Therefore, the thermal decomposition process can be categorized into single-step and multi-step reaction processes [27,28]. Each individual pyrolysis stage can be distinguished by observing the TG curves and the evolution of products, to which the Arrhenius type equation can be fitted. This produces one set of kinetic parameters for each component of the residual oil being pyrolyzed. The different sets of parameters thus give specific information on the kinetic behavior of the different compounds during the pyrolysis process [29,30]. Consequently, multi-stage models have been extensively employed for kinetic analysis in residual oil pyrolysis to analyze intricate reactions.

Moreover, traditional TG studies typically employed a relatively low heating rate and sample sizes that were specifically designed to eliminate the influence of heat and mass transfer effects during thermal decomposition. These experimental conditions were chosen to improve the accuracy and repeatability of the measurements. However, it is widely recognized that in most industrial processes, fuel is rapidly introduced into a high-temperature environment. The significant temperature difference between the surface and interior of the particles at high heating rates can create apparent thermal hysteresis effects, which can impact the thermal decomposition processes. Therefore, the extent of the residual oil thermal cracking process depends not only on temperature but also on the conduction-based heat transfer [31,32].

A comprehensive understanding of the heat transfer process is vital in fast pyrolysis due to the heightened reaction rates of primary and secondary cracking at elevated temperatures. Furthermore, the temperature gradient and varying heating rates play a significant role in influencing the pyrolysis kinetics models. However, the current pyrolysis modeling efforts suffer from a lack of incorporation of heat transfer, which results in apparatus-specific kinetic models. There are relatively limited studies dedicated to investigating the kinetics of residual oil pyrolysis under conditions of high heat transfer using multi-stage models.

The heat transfer resistance during fast pyrolysis, which exists between the surface of the sample and heat carriers under high heating rates, has been extensively discussed. This resistance can have a significant impact on the kinetics of thermal decomposition and may even influence the mechanism of decomposition. To accurately describe pyrolysis processes, VR was evenly distributed onto the surface of inert quartz sand. The choice of quartz sand was based on its properties of low specific surface area and high heat capacity. Catalysis was not present during the investigation and efforts were made to minimize any effects on mass transfer caused by the thickness of the oil film. The present study aimed to analyze the influence of high temperature gradients and resistance resulting from high thermal conductivity on the pyrolysis processes and kinetic parameters of the residual oil. Consequently, the following issues require attention: (1) the thermal behavior and pyrolysis processes during the decomposition of VR oil were characterized, both with and without SiO₂ as a carrier; (2) development of a multi-stage kinetic model and calculation of distinct parameters using deconvolution with Fraser-Suzuki (F-S) function; (3) integration of model-free and model-fitting methods for accurate estimation of kinetic parameters and reaction mechanisms; (4) optimization and verification of the acquired kinetic triplets by comparing theoretical and experimental conversion curves.

2 Experimental

2.1 Materials and methods

The VR samples used in this study were obtained from Sinopec Xinjiang Shihezi Petrochemical Co., Ltd. The physicochemical properties of the sample used in this study are listed in Tab.1.

Tab.1 Basic properties of vacuum residue

Density (20 ℃)/(g·cm−3)	Viscosity (80 ℃)/(mm2·s−1)	CCR/wt %	Elemental analysis/wt %						SARA content/wt %					Heavy metal content/(μg·g−1)
			C	H	N	S	O		Sa	Ar	Re	As		Fe	Ni	V
0.9566	545.4	13.11	86.6	11.3	0.6	1	0.5		31.4	39.6	26.4	2.6		13.6	31.8	29.6

Separation of samples into SARA fraction was accomplished using precipitation and column chromatographic methods following ASTM D4124-09. Initially, the oil sample was dissolved in n-heptane to precipitate the asphaltenes, which were left to settle for 24 h. Subsequently, the separated maltenes were passed through a chromatographic column packed with alumina to isolate saturates, with n-heptane serving as the eluant. Aromatics were then separated using a mixture of toluene and methanol, while resins were separated using trichloroethylene.

The thermal behaviors of VR, S-VR (VR with Quartz sand grains) and SARA fractions were investigated in a TG analyzer (HITACHI, SII TG/DTA 7300, Japan) with heating rates of 5, 10, and 20 K·min^–1. Each sample, approximately 10 mg in mass weight, was introduced in an alumina crucible. High purity nitrogen (100 mL·min^–1) was employed as the purge gas for all testing.

2.2 Kinetic analysis theory

During the TG experiments, a comprehensive kinetic expression was employed to characterize the pyrolysis process:

(1)$\frac{\mathrm{d}\alpha }{\mathrm{d}t}=k(T)f(\alpha ),$

where α is the degree of conversion, the conversion function ƒ(α) is dependent on the specific reaction mechanism, which is detailed in Tab.2 [33].

Tab.2 The common reaction model of solid-state pyrolysis

Mechanism description	Symbol	ƒ(α)	G(α)
Reaction order model	F1	1 – α	–ln(1 – α)
	F1.5	(1 – α)3/2	2[(1 – α)– 1/2 – 1]
	F2	(1 – α)2	(1 – α)–1 – 1
	F3	(1 – α)3	1/2[(1 – α)–2 – 1]
Diffusion model	D1	α2	1/2α
	D2	(1 – α)ln(1 – α) + α	[–ln(1 – α)]–1
	D3	[1 – (1 – α)1/3]2	3/2(1 – α)2/3[(1 – (1 – α)1/3)]–1
	D4	1 – 2/3α – (1 – α)2/3	3/2[(1 – α)–1/3 – 1]–1
Nucleation growth 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
	A4/5	4/5(1 – α)[–ln(1 – α)]–1/4	[–ln(1 – α)]5/4
	A5/6	5/6(1 – α)[–ln(1 – α)]–1/5	[–ln(1 – α)]6/5
Shrinking core model	R1	1	α
	R2	2(1 – α)1/2	1 – (1 – α)1/2
	R3	3(1 – α)1/3	1 – (1 – α)1/3
Power law	P1.5	3/2α1/3	α2/3
	P2	2α1/2	α1/2
	P3	3α2/3	α1/3

The reaction rate constant k(T) follows the Arrhenius law and the expression is:

(2)$k(T)=A\exp \left(-\frac{E}{RT}\right),$

where A is the pre-exponential factor (s^–1), E is the apparent activation energy (kJ·mol^–1) and R is the universal gas constant (8.314 J·K^–1·mol^–1). Equation (2) is brought into Eq. (1) and it gives:

(3)$\frac{\mathrm{d}\alpha }{\mathrm{d}t}=A\exp \left(-\frac{E}{RT}\right)f(\alpha ).$

Taking constant heating rate β into Eq. (3) (β = dT/dt), the non-isothermal kinetic expression can then be transformed into:

(4)$\frac{\mathrm{d}\alpha }{\mathrm{d}t}=\frac{A}{\beta }\exp \left(-\frac{E}{RT}\right)f(\alpha ).$

The integral form of Eq. (4) can be acquired as follow:

(5)$G(\alpha )={\int }_0^{\alpha }\frac{\mathrm{d}\alpha }{f(\alpha )}={\int }_{T_0}^T\frac{A}{\beta }\exp \left(-\frac{E}{RT}\right)\mathrm{d}T.$

2.2.1 Iso-conversional methods

The iso-conversional approach is widely accepted for extracting the kinetic triplets from TG results under different heating rates, as it eliminates the need for assuming the reaction mechanism. In this study, the equations for the Friedman, FWO, and KAS iso-conversional methods were derived to estimate the activation energies [28,34,35].

Friedman method:

(6)$\ln \left(\beta \frac{\mathrm{d}\alpha }{\mathrm{d}T}\right)=\ln (A)+\ln (f(\alpha ))-\frac{E}{RT},$

FWO method:

(7)$\ln (\beta )=\ln \left(\frac{AE}{RG(\alpha )}\right)-5.331-1.052\frac{E}{RT},$

KAS method:

(8)$\ln \left(\frac{\beta }{T^2}\right)=\ln \left(\frac{AE}{RG(\alpha )}\right)-\frac{E}{RT},$

The value of E is estimated from the slope of lines by plotting ln(β${\displaystyle \frac{\mathrm{d}\alpha }{\mathrm{d}T}}$), ln(β), ln(β/T²) against 1/T. In this work, the range of α is 0.10–0.90 with a step of 0.1.

2.2.2 Master-plots method for optimized kinetic model

The integral master-plots methods were employed to investigate the optimized kinetic model of different stages for VR with or without carriers [28]. The thermal analysis kinetic equation can be expressed as follows:

(9)$G(\alpha )=\frac{AE}{\beta R}\left[p(\mu )-p\left({\mu }_0\right)\right]\cong \frac{AE}{\beta R}p(\mu ),$

where p($\mu$) is temperature integral, and p($\mu$) = ${\int }_{\mathrm{\infty }}^{\mu }-\left({\mathrm{e}}^{-\mu }/{\mu }^2\right)\mathrm{d}\mu$, $\mu$ = E/RT.

To resolve approximative value of p($\mu$), one can employ empirical equations, as it has no exact analytical solution [28,34].

(10)$p(\mu )={\mathrm{e}}^{-\mu }/\mu (1.00198882\mu +1.87392298),$

and the final integral master-plots equation for estimating optimized kinetic model is:

(11)$\frac{G(\alpha )}{G(0.5)}=\frac{p(\mu )}{p\left({\mu }_{0.5}\right)}.$

Equation (11) demonstrates that when an appropriate kinetic model is applied, the experimental value of p($\mu$)/p($\mu$_0.5) is consistent with the theoretical value of G(α)/G(0.5) for a given α. Consequently, the mechanism function corresponding to the theoretical plots that best fits the experimental plots can be regarded as the most probable mechanism function for VR pyrolysis by comparing theoretical and experimental curves [36,37].

2.2.3 Deconvolution method

The pyrolysis of VR is a complex process that encompasses interconnected reaction pathways. It is crucial to comprehend the distinct stages of the pyrolysis process and subsequently verify the optimized kinetic modeling of each stage independently. In this study, the deconvolution method utilizing the F-S function in Origin software is employed to distinguish the overlapping stages of VR [33,38].

3 Results and discussion

3.1 Thermal cracking of VR and its SARA fractions

The TG and derivative thermogravimetry (DTG) curves capturing the thermal cracking process of vacuum VR and S-VR were acquired using three different heating rates (5, 10, and 20 K·min^–1) under a nitrogen atmosphere. The curves depicted in Fig.1 display significant thermal hysteresis, specifically in relation to the impact of high heating rates and heat transfer resistance from inert carriers. Additionally, Tab.3 presents a summary of the characteristic parameters associated with pyrolysis processes.

Fig.1 The TG and DTG curves with the heating rate of 5, 10, and 20 K·min–1. (a, b) TG and DTG of VR; (c, d) TG and DTG of S-VR.

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Tab.3 Pyrolysis chracteristic parameters for VR and S-VR at 5, 10 and 20 K·min–1

	β/(K·min−1)	Ti /K	Tmax /K	Tf /K	DTGmax /(wt %·min−1)	Mr /wt %
VR	5	520.4	720.6	773.0	3.59	10.28
	10	534.3	723.3	785.5	6.76	10.60
	20	562.9	742.2	804.1	20.65	11.50
S−VR	5	535.4	718.5	750.2	4.6	19.5
	10	566.6	733.8	777.4	10.5	20.0
	20	582.8	749.3	794.5	20.8	20.3

Ti, the initial decomposition temperature; Tmax, the temperature corresponding to the maximum weight loss rate; Tf, the terminal decomposition temperature; DTGmax, the maximum weight loss rate; Mr, the residual weight after pyrolysis experiment.

The thermal decomposition of VR commences at around 500 K and persists until it reaches 800 K. Analysis of the DTG curves reveals a single-stage pattern for global decomposition. According to widely accepted understanding, the initial volatilization of VR primarily attributed to the evaporation of light alkanes, which continues until approximately 620 K. In the temperature range of 620 to 770 K, there is a noteworthy increase in volatilization, indicating the cracking of heavier fractions like resins and asphaltenes. Beyond 770 up to 850 K, the volatilization becomes negligible, remaining relatively constant. It was found that the coke yield for VR was approximately 10.0 wt %. The above results indicated that the pyrolysis process of VR can be assumed to consist of three sequential reaction stages.

The thermal decomposition of VR exhibited a notable lateral shift in the temperature of the maximum degradation peak as the heating rate increased. This shift was attributed to the combined influences of heat transfer at different heating rates and the thermal conductivity property of VR involved in the pyrolysis process, known as thermal hysteresis [39]. At higher heating rates, the release of volatile matter was delayed due to the significant temperature disparity between the particle’s surface and interior, resulting in a reduction of volatile release at specific temperatures.

The addition of SiO₂ in the TG experiment has clearly shown an enhancement in thermal hysteresis depending on heat transfer by conduction, as shown in Fig.1(c) and 1(d). Consequently, the evaporation of hydrocarbons is delayed, resulting in intensified reactions within a narrower temperature range at higher temperatures, and an increased maximum weight loss rate, as given in Tab.3. Furthermore, pyrolysis with abundant SiO₂ additives has shown a higher coke yield compared to pyrolysis without additives. It may be due to the following reasons for the increase in coke yield. Quartz sand, as the carrier material, exhibits strong adsorption of polar components such as resin and asphaltene, thereby enhancing condensation reactions that facilitate coke formation. Additionally, the thermal hysteresis effect delays the devolatilization of residue oil until higher temperatures, resulting in an increased concentration of radicals in the liquid phase. This elevated concentration of radicals reinforces coke formation through condensation reactions, ultimately leading to a higher coke yield. As a result, the inert carriers act as nucleating agents in char formation.

As shown in Fig.1, thermal hysteresis did not seem to affect the decomposition mechanism as the shape of the peaks remained relatively unchanged while the pyrolytic decomposition rate varied. However, it is essential to examine whether this assumption or viewpoint still holds true under conditions of significant heat transfer resistance. Additionally, given the complex composition of raw materials and reactions involved, a comprehensive investigation into this influence is necessary.

This section describes the thermal decomposition process of SARA fractions from VR under a heating rate of 10 K·min^–1 in a N₂ atmosphere. It is observed from Fig.2(a) that coke formation of the fractions is determined by both aromaticity and molecular size. It follows the order: saturates < aromatics < resins < asphaltenes. By the comparison of the coke yield of VR itself and the sum of weighted coke yields of the SARA fraction, it was suggested that the thermal cracking process of VR exhibited an interactive effect between SARA fractions [40,41]. A comparison of each fraction in Fig.2(b) reveals that aromatics and resins exhibit a wide temperature range in which they are volatilized, pyrolyzed, and capable of participating in condensation reactions during pyrolysis, resulting in the formation of heavier molecules like asphaltenes. Additionally, the conversion rates corresponding to the maximum weight loss rate of aromatics and resins occur at T_max values of 700 and 710 K, respectively. It is noteworthy that there is a substantial overlap in the overall temperature range.

Fig.2 (a) TG and (b) DTG SARA fractions of VR at 10 K·min–1 under N2 atmosphere.

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Among the fractions present in the VR, asphaltenes are regarded as the heaviest. They undergo extremely harsh conditions, leading to condensation reactions that result in the formation of coke as the final residue at temperatures above 710 K. During the thermal process, an interaction occurs between asphaltenes and other fractions in the petroleum residue, causing the blends to exhibit different performance compared to individual fractions [40]. The physical dispersion and chemical interaction, particularly hydrogen transfer, likely play a more significant role in coke formation during the co-pyrolysis of fractions [42,43].

3.2 Kinetic analysis

3.2.1 Determination of apparent activation energy

Iso-conversional methods are widely recognized as one of the most reliable strategies for extracting the activation energy of thermally-induced processes from TG data. In this study, the E of thermal processing was estimated using differential calculations using FWO and KAS methods, as well as integral calculations with Friedman.

Figures S1 and S2 (cf. Electronic Supplementary Material, ESM) show the Arrhenius plots of VR and S-VR obtained by Friedman, FWO and KAS methods, respectively. Based on the slope of regression lines, the E values of reaction process at various conversion degrees were estimated. The correlation between E and conversion degrees is seen in Fig.3. The value of E suggests that at low conversion level (< 30%), only the evaporation of lighter components occurs. However, as the conversions increase, the cracking reactions involve heavier fractions such as aromatics, resins, and asphaltenes, requiring higher activation energy to break more complex molecules. The noticeable discrepancy in activation energies across different temperature ranges implies the existence of distinct reaction mechanisms for specific fractions at different temperature zones [38,44]. Consequently, the pyrolysis process of the VRs should be characterized by varying kinetic expressions [22].

Fig.3 Apparent activation energy versus conversion rate of VR using iso-conversional methods.

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The Friedman, FWO, and KAS methods demonstrated average activation energies (E_a) of 158, 131 and 126 kJ·mol^–1, respectively, for VR pyrolysis alone. In contrast, the inclusion of abundant SiO₂ additive as carriers showed slight alteration in E_a values (157, 136 and 127 kJ·mol^–1). However, it is worth mentioning that the apparent activation energy curves for VR pyrolysis with SiO₂ carriers exhibit an inflection when the conversion rate exceeds 70% using three iso-conversional methods. Our findings lead us to conclude that this inflection is composed of two aspects of physics and chemistry, both of which may be closely related to heat transfer. The increase in activation energy during the initial stage of the reaction primarily stems from the energy required for the endothermic process of the carrier. On the other hand, heat transfer resistance increases the radical concentration in the high-temperature range, facilitating the coking reaction and reducing the activation energy of char formation. These results are consistent with observations from TG curves, as shown in Fig.1. Previous research [23] indicated that a higher heating rate led to the occurrence of major reactions at elevated temperatures. Consequently, the observed variation in activation energy reflects a change in the nature of the rate-controlling step. Additionally, this effect can potentially contribute to the emergence of distinct reaction processes within a high-temperature range.

3.2.2 Separation of overlapping peaks by F-S fitting

In the aforementioned analysis and discussions, the variation in activation energy observed through model-free methods implies a change in the intrinsic properties of the rate-controlling step and suggests that the pyrolysis of VR might involve multi-steps reaction models. To determine the most suitable peak fitting for describing the overlapping reactions of pyrolysis, the DTG curves obtained at a heating rate of 10 K·min^–1 were evaluated using the F-S function. This evaluation aimed to determine whether a two-stage or three-stage reaction model would better describe the data. As depicted in Fig.4, the three-stage reaction models exhibit higher correlation coefficients (R² = 0.9985) compared to the two-stage reaction models (R² = 0.9854). This higher level of correlation signifies that the three-stage reaction models more appropriately depict the weight loss rate and provide a better representation of the true pyrolysis process. Consequently, the three-stage peak fitting approach is applied to further separate the peaks and analyze the kinetic models.

Fig.4 Deconvolution results of different reaction models for VR with heating rate of 10 K·min–1.

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Fig.5 illustrates the fitting curves obtained using the three-stage peak fitting approach, which perfectly align with the experimental weight loss rate for VR and S-VR at all reaction conditions. The correlation coefficient R² is nearly equal to 1, indicating a high degree of agreement. Additionally, the analysis allows for the identification of distinct stages (referred to as S1/3, S2/3, and S3/3) and the generation of globally fitted curves. The initial stage (S1/3) encompasses the temperature range of 373–573 K and displays minimal mass losses. This can be attributed to the limited vaporization of compounds, indicating the absence of notable chemical transformations during this stage [45]. In the subsequent stage (S2/3), spanning from 573 to 823 K, significant alterations occur and result in the generation of volatile compounds. Lastly, the third stage (S3/3), spanning 823 to 1023 K, leads to comparatively minor mass losses. The thermal cracking of VRs with SiO₂ additives exhibits a similar pattern.

Fig.5 Deconvolution of reaction rate curves for (a, b, c) VR and (d, e, f) S-VR at the heating rate of 5, 10, and 20 K·min–1.

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Tab.4 lists the typical temperatures of the three discrete peaks and reaction rate for VR and S-VR. The results demonstrate an increase in the peak temperature ($T_{p_i}$) and maximum weight loss rate (dα_i/dT) for all stages with the elevation of heating rates and the the presence of SiO₂ carriers. Furthermore, the high heat transfer resistance leads to a delayed expulsion of hydrocarbons, thereby intensifying reactions within a narrower temperature range. The coefficient ω_i, which represents each stage proportionally, can serve as a reference point for subsequent optimization procedures. Additionally, it can numerically demonstrate the increase in the ratio of hydrocarbon expulsion within a high temperature range.

Tab.4 Thermal characteristic for the three isolated peaks at different heating rates for VR and S-VR

	β/(K·min−1)	S1/3			S2/3			S3/3
		$T_{p_1}$/K	dα1/dT		$T_{p_2}$/K	dα2/dT		$T_{p_3}$/K	dα3/dT
VR	5	621.21	2.96		679.32	4.03		721.93	5.03
	10	651.30	3.00		699.96	4.47		728.48	6.91
	20	667.27	2.69		718.05	4.49		746.93	7.07
	ωi	0.38			0.32			0.30
S-VR	5	633.74	2.84		692.31	4.54		723.13	7.85
	10	648.49	2.50		703.39	4.57		736.73	9.17
	20	654.38	2.29		715.19	5.47		746.32	8.45
	ωi	0.31			0.32			0.37

3.2.3 Determination of activation energy E by iso-conversion methods

Based on the deconvolved data, the activation energies of each sub-stage reaction were also analyzed using three iso-conversional kinetic methods. The conversion range varied from 0.1 to 0.9 with increments of 0.1. Figures S3–S8 (cf. ESM) show the Arrhenius plots of VR and S-VR for the three stages, respectively. The activation energies calculated for three stages using different models are summarized in Fig.6 and Fig.7 for comparison. The figures illustrate a similar dependency in the distribution of activation energy for each stage. The significant deviations in the values of E for each sub-stage suggest the existence of unique reaction kinetic model within the overall pyrolysis processes.

Fig.6 Variation of the activation energy of VR for the three stages. (a) First stage (S1/3), (b) second stage (S2/3) and (c) third stage (S3/3).

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Fig.7 Variation of the activation energy of S-VR for the three stages. (a) First stage (S1/3), (b) second stage (S2/3) and (c) third stage (S3/3).

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In terms of VR pyrolysis, the activation energy values for the first stage (S1/3) in Fig.6(a) consistently maintained a constant shape. These values (about 80 kJ·mol^–1) were observed to be lower compared to other processes for all methods, which can be explained by the evaporization of lighter hydrocarbons [21]. The activation energy values for the second stage (S2/3) in Fig.6(b) exhibit an increasing trend with conversion level, indicating an escalation in the energy demand for this reaction stage, and leading to a heightened complexity of the reaction. This increase can be related to the dissolution of relatively weak chemical bonds that occur during the breakdown of components with aliphatic structures [40]. Additionally, the high E observed at the third stage (S3/3) in Fig.6(c) can be ascribed to the decomposition of asphaltene as well as the formation of coke resulting from the condensation reactions. As previously mentioned, the presence of SiO₂ not only increases the energy required for the devolatilization of organic matter, mainly due to its high heat transfer resistance and endothermic nature, but also promotes the occurrence of significant decomposition reactions at higher temperatures. This, in turn, impacts the variation in activation energy observed for the second and third stages and may suggest a change in the reaction mechanism.

Based on the findings of this research, it is hypothesized that the volatilization and cracking reactions across different stages are interconnected, leading to a synergistic phenomenon due to high thermal hysteresis [46]. Specifically, at lower conversion range, the volatilization and partial cracking of light components are delayed, resulting in an overall increase in activation energy. Additionally, the activation energy exhibits a decreasing trend in the high conversion stage, which serves as key evidence for the presence of beneficial effects. It is believed that the inert solid acts as a nucleating agent in char formation.

3.3 Kinetic model determination

The mean activation energy values estimated using the KAS method were utilized to determine the appropriate kinetic model for each discrete stage via the integral master-plots method. The optimal model was determined by comparing the experimental plots of p(μ)/p(μ_0.5) of three different stages in VR and S-VR pyrolysis at a heating rate of 10 K·min^–1 with the theoretical plots of g(α)/g(0.5) based on the reaction model outlined in Tab.2.

As depicted in Fig.8, a notable concurrence is observed between the predicted theoretical reaction order models (Fn) for the first and second stages, as well as the nucleation and growth models (An) for the third stage, irrespective of the presence or absence of carriers. Specifically, for the VR pyrolysis process, the initial and second stages corresponded to the theoretical plots F1.5 (Fig.8(a)) and F1 (Fig.8(b)), respectively. In the case of the final stage (Fig.8(c)), the kinetic model transitioned to A4/5. Therefore, these calculations allow us to establish the reaction models for residual oil to follow a distributed reactivity model. According to the Fn reaction model, an increase in heat transfer resistance caused by carriers leads to delays in the release of produced hydrocarbons and the occurrence of secondary cracking reactions, ultimately resulting in an increase in the reaction order at the first stage (n = 3). As a nucleation model, the last reaction stage could be attributed to a coking event that produces char, where the presence of inert solid acts as a nucleating agent, positively influencing char formation [36].

Fig.8 G(α)/G(0.5) versus α for various reaction models and p(μ)/p(μ0.5) versus α for various phases [(a, d) S1/3, (b, e) S2/3, (c, f) S3/3] of VR and S-VR at 10 K·min–1.

Full size|PPT slide

To ensure the accuracy and reliability of the reaction order in each stage, the calculation of the n and A can be performed by integrating multi-stage kinetic models into Eq. (9).

(12)$G(\alpha )=\frac{(1-\alpha {)}^{1-n}-1}{n-1},$

(13)$G(\alpha )=[-\ln (1-\alpha ){]}^n.$

By applying the least-squares fit on G(α)~[(Ep(μ)/βR], the A and n were calculated for various stages (S1/3, S2/3, and S3/3) of VR and S-VR decomposition at a heating rate of 10 K·min^–1. The calculations were based on the closest zero intercept and the highest correlation coefficient (R²), as illustrated in Figs. S9 and S10 (cf. ESM). The resulting kinetic parameters (E, A, and ƒ(α)) for VR cracking at different stages and four various heating rates are presented in Tab.5.

Tab.5 Kinetic triplets (E, A, and G(α)) for various phases of VR and S-VR pyrolysis at 10 K·min−1

Stage	E/(kJ·mol−1)			A/min−1			G(α)			Mechanism
	VR	S-VR		VR	S-VR		VR	S-VR		VR	S-VR
S1	83.2	102.25		1.22 × 109	2.30 × 1011		2[(1−α)−1/2−1]	1/2[(1−α)−2−1]		F1.5	F3
S2	156.3	178.99		1.50 × 1011	6.30 × 1012		−ln(1−α)	−ln(1−α)		F1	F1
S3	171.1	187.00		4.72 × 1012	7.93 × 1015		[−ln(1−α)]5/4	[−ln(1−α)]2/3		A4/5	A1.5

3.4 Evaluation of reaction mechanism of VR pyrolysis

As previously stated, the three-stage reaction model is provided using the model-free method and the multi-step model-fitting method. However, the accuracy and application of the acquired kinetic parameters and the three-stage reaction model in predicting thermal behavior under various reaction conditions and comprehending the thermal hysteresis effect during processing have to be determined. The determination of response reaction processes is typically resulting from a comparison of calculated results with measuring data obtained in active-world settings. As shown in Fig.9, the calculated curve and measuring results were nearly identical, suggesting that the E, A, and ƒ(α) might serve as a significant theoretical foundation for investigating VR thermal decomposition. The reproduced curves for each individual process at various heating rates are shown in Figs. S11 and S12 (cf. ESM), demonstrating a significant agreement between the predicted and measuring data.

Fig.9 Comparison of calculated and experimental conversion of pyrolysis of (a) VR and (b) S-VR at 5, 10 and 20 K·min–1.

Full size|PPT slide

The findings presented in this study demonstrate the utility of TG analysis for investigating the pyrolysis kinetics of VR. To gain further insights into the structure and properties of residual oil, the integration of TG with complementary techniques such as gas chromatography/mass spectrometry and Fourier transform infrared spectroscopy can offer a comprehensive understanding of the reaction process and resultant products.

4 Conclusions

The pyrolysis characteristics and kinetics parameters of VR were investigated at a series of heating rates, within inert carriers, to understand the thermal hysteresis resulting in heat transfer resistance during thermal decomposition processes. The complex and overlapping reactions of pyrolysis were deconvoluted into three distinct stages using the F-S function to estimate the kinetic parameters. A multi-stage reaction model and corresponding kinetic parameters were established using the iso-conversional method and integral master-plots method to accurately describe the pyrolysis processes of VR. The primary findings of this investigation are summarized below.

(1) The active pyrolysis process of VR encompasses several decomposition stages. The evaporation of vapor from devolatilization and thermal decomposition was attributed to the reaction order models (Fn) for the first and second stages, whereas the nucleation and growth models (An) were linked to char formation in the third stage.

(2) The presence of thermal hysteresis resulted in an increased reaction order during the first stage, leading to increased reactant concentration of generated hydrocarbons due to enhanced heat transfer resistance. In the last stage, the reaction primarily involved coking, which produced char. The presence of inert solid acted as a nucleating agent, facilitating the formation of char.

(3) The three-stage reaction model and corresponding kinetic triplets obtained in this study have the potential to accurately describe the active pyrolysis behavior of VR under conditions of high heat transfer resistance.

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Competing interests

The authors declare that they have no competing interests.

Acknowledgements

The authors acknowledge the support from the National Key Research and Development Program of China (Grant No. 2021YFB3801300) and the National Natural Science Foundation of China (Grant Nos. U22B20149, 22021004).

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11705-024-2496-z and is accessible for authorized users.

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