Introduction

Global warming caused by the presence of greenhouse gases in the atmosphere is a worldwide issue. Carbon dioxide (CO2) is the primary greenhouse gas emitted from the combustion of fossil fuels [1]. CO2 capture and storage (CCS) is widely recognized as a feasible method to control CO2 emissions, and there are three main CO2 capture approaches: post-combustion, pre-combustion and oxy-fuel combustion. Oxy-fuel combustion is considered as a promising technology for CO2 capture, because it can feasibly produce a high CO2 concentration in the exhaust gas (greater than 90 % by volume) that is almost sequestration-ready and has a low technical risk [2]. So, oxy-fuel combustion has attracted considerable attention in recent years [3, 4].

In 2007, the Canadian Centre for Mineral and Energy Technology (CANMET) proposed a new oxy-fuel system, namely oxy-steam combustion [5]. In this combustion mode, fuels burn in pure oxygen, and the high temperature is moderated by either water or steam. CANMET has recently developed a novel oxy-steam burner for zero emission power plants. The computational fluid dynamics (CFD) simulation and pilot-scale experimental results indicated that oxy-steam combustion led to high CO2 concentrations (~90 %), low CO, moderate NOx and typical SOx levels [6]. Seepana and Jayanti proposed a power generating system based on oxy-steam combustion called steam-moderated oxy-fuel combustion (SMOC) [7]. Those authors suggested that oxy-steam combustion had many advantages over O2/CO2 recycle combustion, such as a compact system, easy operation, small geometry size and energy savings.

Many studies have focused on the O2/CO2 combustion process, and the results indicated the physicochemical properties of dilute gas had a great influence on the combustion characteristics of coal/char [8, 9]. The physical properties of H2O are different from N2 and CO2, and the chemical properties of H2O are more active, so the combustion characteristics of coal/char under an oxy-steam atmosphere are expected to be different from conventional air combustion and O2/CO2 combustion.

Because of the special properties of H2O, the studies of the effect of H2O on the combustion process have received more and more attention. Many published works found adding H2O had certain effects on the burning velocity and flame temperature during the combustion process of gaseous fuels [10–15]. Besides, the oxy-coal combustion process was also changed when substituting part CO2 with H2O [16–19].

Although some works have focused on the effect of adding steam on the combustion characteristics of gaseous fuels in different atmospheres, the combustion characteristics of coal/char in O2/H2O atmosphere have rarely been studied. Recently, we have carried out related studies about coal combustion in O2/H2O atmosphere. Thermogravimetric analysis (TG) results found the coal burning process in O2/H2O mixtures was delayed compared with that in O2/N2 mixtures [20]. The research on the ignition behaviors of pulverized coal particles in O2/N2 and O2/H2O mixtures in a drop tube furnace using flame monitoring techniques indicated the ignition of pulverized coal particles in O2/H2O mixtures was earlier than that in O2/N2 mixtures at same oxygen concentration, and the numerical simulation showed the ignition mechanism of coal particles in O2/H2O atmosphere was homogeneous [21, 22].

Char combustion is a most important process during coal combustion, and the study of combustion characteristics of coal chars under O2/H2O environment is essential to the development of large-scale test platforms. Thermogravimetric analysis is a simple and practicable approach, and it has been widely used to investigate the pyrolysis, combustion and kinetic characteristics of various fuels [23–27].

The aim of the present work is to study the oxy-steam combustion characteristics and kinetic behaviors of two coal chars obtained in argon atmosphere. In this study, the non-isothermal thermogravimetric analysis method was used to investigate the combustion characteristics of char. The activation energy values of the char samples were calculated using three model-free methods, Flynn–Wall–Ozawa (FWO), Starink and Kissinger–Akahira–Sunose (KAS), and the combustion mechanism function was ascertained by the combination of the Popescu method and the Coats–Redfern integral method.

Experimental

Char preparation

Two parent coals of a bituminous coal (FG) and a meager coal (XS) were used to prepare the char samples. The parent coals were crushed, ground with a ball mill and sieved to a particle size fraction of 45–75 μm. The char samples were prepared in a horizontal tube furnace at 1073 K in an argon atmosphere. The char samples were produced by the procedures as follows: Firstly, approximately 1 g of each coal sample was placed on a ceramic boat, and the ceramic boat was placed into the heating zone of the tube furnace. Then, the reactor was heated at a constant rate from room temperature to 1073 K, and the coal sample was kept in the reactor for 30 min at 1073 K under argon atmosphere. The argon was provided from a gas cylinder. Finally, heating was stopped, and the char sample was cooled to room temperature under argon atmosphere. The proximate and ultimate analyses of parent coals and char samples are presented in Table 1.

Table 1 Proximate analysis and ultimate analysis of the coal and char samples
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Oxy-steam combustion tests of coal chars

The char combustion tests were performed in a Netzsch STA449F3 thermobalance with a water vapor generator. The water control precision of the steam generator was 0.02 g h−1. Approximately 5 mg of char sample was used for each experiment. The char samples were heated from room temperature to 1273 K in the mixtures of O2/H2O or O2/N2 with various oxygen concentrations (21, 30 and 40 %) at a heating rate of 20 K min−1. In order to investigate the oxy-steam combustion kinetic, the non-isothermal thermogravimetric experiments were also conducted at different heating rates (10, 15, 20 and 25 K min−1) in 21 % O2/79 % H2O mixtures. The total gas flow rate was 100 mL min−1.

Determination of combustion characteristic parameters

The combustion characteristic parameters can be determined from the combustion profile, including ignition temperature (T i), peak temperature (T max), burnout temperature (T h), maximum rate of mass loss (dW/dt)max and average of mass loss (dW/dt)mean. T i is determined by using TG–DTG extrapolation method, and the T h is defined as the temperature at which the rate of mass loss diminishes to 1 mass% min−1. T max is the temperature which maximum rate of mass loss occurs. The coal reactivity index R is used to evaluate the combustion performance of char sample, defined as [23]:

$$R = \frac{1}{{W_{0} }}\frac{{{\text{d}}W}}{{{\text{d}}t}}$$
(1)

where W 0 is the initial dry mass of the char sample and \({\text{d}}W/{\text{d}}t\) is the mass lose rate of char due to combustion. The greater its value, higher the combustion reactivity.

The combustion characteristic is also evaluated by a comprehensive combustion index S, which is defined as follows [24]:

$$S = \frac{{\left( {{\text{d}}W/{\text{d}}t} \right)_{\hbox{max} } \left( {{\text{d}}W/{\text{d}}t} \right)_{\text{mean}} }}{{T_{\text{i}}^{2} T_{\text{h}} }}$$
(2)

The higher the S, the better the combustion performance of the char.

Kinetic analysis method

The procedure to determine the kinetic parameters is summarized as:

  1. 1.

    The activation energy is obtained through the FWO, Starink and KAS methods;

  2. 2.

    The most suitable kinetic mechanism function G(α) is deduced based on the Popescu method;

  3. 3.

    According to the most suitable kinetic mechanism function G(α), the activation energy E is determined by Coats–Redfern integral method;

  4. 4.

    By comparing the activation energies obtained through the Coats–Redfern integral method with those obtained through the FWO, Starink and KAS methods, the combustion kinetic mechanism function is determined.

Determination of the activation energy

For non-isothermal thermogravimetric experiments with constant heating rate, the reaction rate can be expressed as:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = \frac{A}{\beta }\exp \left( { - \frac{E}{RT}} \right)f\left( \alpha \right)$$
(3)

where α is the degree of conversion, α = (W 0 − W t)/(W 0 − W ∞) (W 0 and W ∞ are the mass at the beginning and at the end of reaction, respectively, and W t is the mass at temperature T). β is the heating rate, A is the pre-exponential factor, E is the activation energy, R is the universal gas constant and f(α) represents the reaction mechanism function. The integration of Eq. (3) yields:

$$G\left( \alpha \right) = \int\limits_{0}^{\alpha } {\frac{{{\text{d}}\alpha }}{f\left( \alpha \right)}} = \frac{A}{\beta }\int\limits_{0}^{T} {\exp \left( { - \frac{E}{RT}} \right)} {\text{d}}T = \frac{AE}{\beta R}P\left( u \right)$$
(4)

where u = E/(RT) and P(u) is the temperature integral:

$$P\left( u \right) = \int\limits_{u}^{\infty}\frac{\exp\left(-u\right)}{u^{2}}du$$
(5)

Actually, the model-free methods differ depending on the approximation of temperature integral P(u).

Flynn–Wall–Ozawa (FWO) method

FWO equation relies on Doyle’s approximation which gives [28–30]:

$$P\left( u \right) \cong \exp \left( { - 1.0518u - 5.3308} \right)$$
(6)

This approximation leads to

$$\ln \beta = - 1.0518\frac{E}{RT} + C_{1}$$
(7)

Thus, for a constant conversion ratio α, ln β versus 1/T obtained at several heating rates yields a straight line, and the activation energy E can be determined from the slope.

Starink method

In this method, the approximation of P(u) can be written as [31–33]:

$$P\left( u \right) \cong \frac{{\exp \left( { - 1.0008u - 0.312} \right)}}{{u^{1.92} }}$$
(8)

Equations (4) and (8) lead to:

$$\ln \frac{\beta }{{T^{1.92} }} = - 1.0008\frac{E}{RT} + C_{2}$$
(9)

The activation energy E is determined from the slope of plots of ln(β/T 1.92) versus 1/T.

Kissinger–Akahira–Sunose (KAS) method

The expression of P(u) is expressed using Murray and White approximation [34]:

$$P\left( u \right) \cong \frac{{\exp \left( { - u} \right)}}{{u^{2} }}$$
(10)

Based on this approximation, we obtain KAS equation:

$$\ln \ {\frac{\beta }{{T^{2} }}} = - \frac{E}{RT}+C_{3}$$
(11)

For the same conversion ratio at different heating rates from plots of ln(β/T 2) versus 1/T, the activation energy E can be determined by the slope.

Determination of the kinetic mechanism function

Popescu method

The Popescu method [35] is used to determine the kinetic mechanism function of char combustion. This method can be expressed as:

$$G\left( a \right)_{\text{mn}}\,=\, \int\limits_{{\alpha_{\text{m}} }}^{{\alpha_{\text{n}} }} {\frac{{{\text{d}}\alpha }}{f\left( \alpha \right)}}=\frac{1}{\beta }\int\limits_{{T_{\text{m}} }}^{{T_{\text{n}} }} {k\left( T \right)} {\text{d}}T\,=\,\frac{1}{\beta }I\left( T \right)_{\text{mn}}\,=\,\frac{A}{\beta }H\left( T \right)_{\text{mn}}$$
(12)
$$I\left( T \right)_{\text{mn}}\,=\,\int\limits_{{T_{\text{m}} }}^{{T_{\text{n}} }} {k\left( T \right)} {\text{d}}T$$
(13)
$$H\left( T \right)_{\text{mn}}\,=\,\left( {T_{\text{n}} - T_{\text{m}} } \right)\exp \left( { - \frac{E}{{RT_{\upxi} }}} \right)$$
(14)
$$T_{\upxi} = \frac{{T_{\text{m}} + T_{\text{n}} }}{2}$$
(15)

where X m and X n are two different degrees of the conversion ratio at temperatures T m and T n, respectively. If the experimental data and G(a) are selected properly, a plot of G(a) versus 1/β yields a straight line with an intercept of zero. This G(a) is then a proper mechanism that describes the true chemical reaction process.

Coats–Redfern integral method

According to Eq. (4), the Coats–Redfern integral method can be written as:

$$\ln \left[ {\frac{G\left( a \right)}{{T^{2} }}} \right] = \ln \left[ {\frac{AR}{\beta E}\left( {1 - \frac{2RT}{E}} \right)} \right] - \frac{E}{RT}$$
(16)

At certain temperatures, the plots of ln [G(a)/T 2] versus 1/T obtained from the thermogravimetric data should be a straight line, and the activation energy E can be determined by the slope of the line.

Results and discussion

Combustion characteristics of coal char in O2/H2O atmosphere

Figure 1 shows the TG and DTG curves of FG and XS char combustion under different atmospheres. From the combustion profiles, it can be found that the char combustion process in the O2/H2O atmosphere is obviously different from that in O2/N2 atmosphere with the identical oxygen concentration. Replacing N2 by H2O has a significant influence on the char combustion under the conditions of the experiments. The combustion process of FG and XS char in O2/H2O atmosphere takes place sooner than that in O2/N2 atmosphere with the identical oxygen concentration, and the combustion performance is improved by increasing oxygen concentration. The DTG curves shift to lower-temperature zone along with oxygen concentration increasing.

Fig. 1
figure 1

TG and DTG curves of FG char (a) and XS char (b) combustion under different atmospheres

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Figures 2 and 3 show the comparison of char reactivity R and peak reactivity R max of FG and XS char under different atmospheres. Figure 2 indicates the substitution of H2O for N2 in the bulk gas has apparent effect on the char reactivity. The char reactivity in O2/H2O atmosphere is higher than that in O2/N2 atmosphere with the identical oxygen concentration for both FG and XS char. Figure 3 also shows the R max of FG char is higher than that of XS char. The effect of oxygen concentration on the char reactivity in both atmospheres is also clear. The char reactivity increases with increasing oxygen concentration in both O2/H2O and O2/N2 mixtures, and it is found to be proportional to the oxygen concentration.

Fig. 2
figure 2

Comparison of FG char (a) and XS char (b) reactivity versus temperature under different atmospheres

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Fig. 3
figure 3

Comparison of FG and XS char peak reactivity under different atmospheres

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Figure 4 shows the combustion characteristic temperatures and the comprehensive combustibility index S of FG and XS char in different atmospheres with various oxygen concentrations (21, 30, 40 %). Figure 4 shows that the ignition temperature, peak temperature and burnout temperature in O2/H2O atmosphere are lower than those in O2/N2 atmosphere with the identical oxygen concentration, which indicates the combustion rate of char in O2/H2O atmosphere is faster compared with that in O2/N2 atmosphere. Figure 4 also shows that the comprehensive combustibility indexes in O2/H2O atmosphere are higher than those in O2/N2 atmosphere under the same oxygen concentration. The combustion performance of FG and XS char is improved when the diluent gas is changed from N2 to H2O.

Fig. 4
figure 4

Combustion characteristic temperatures and the comprehensive combustibility index S of FG char (a) and XS char (b) under different atmospheres

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The higher char reactivity and combustibility index in O2/H2O atmosphere may be due to the high reactivity and diffusivity of steam. The mole fractions of some active radicals, such as O and OH, in O2/H2O atmosphere are larger than those in O2/N2 atmosphere with the identical O2 concentration due to high reactivity of H2O [36]. These active radicals can be conducive to the oxidation of char. In addition, as the char combustion reaction progresses, the influence of diffusion on the char combustion becomes more pronounced [37]. The diffusion coefficient of O2 in H2O is 8.6E−5 m2 s−1 (773 K, 0.1 MPa) and almost 25 % higher than that of O2 in N2 (6.4E−5 m2 s−1, 773 K, 0.1 MPa). Consequently, the probability of collision of O2 to the surface of char in O2/H2O atmosphere is much higher than that in O2/N2 atmosphere, and it also contributes to the acceleration of the char combustion rate.

Activation energy of char combustion in 21 % O2/79 % H2O atmosphere

Activation energy is the most important kinetic parameter of char combustion and can be calculated from the experimental data of non-isothermal thermogravimetric tests. Model-fitting and model-free methods are two commonly used methods to calculate the activation energy. The advantages and limitations of the two methods have been discussed in numerous reports [29, 38]. Model-free methods are regarded as the most reliable methods for the determination of activation energy. Hence, three model-free methods are used in this study to determine the activation energies of char combustion.

In the model-free methods, a set of conversion values at different heating rates should be chosen from the thermogravimetric experimental data to determine the activation energy. Because most solid-state reactions are not stable at the beginning and the end of the reaction, which result in the deviation of experimental values from the theoretical data [39, 40], the range of conversion from 0.1 to 0.9 is chosen in our study.

According to Eqs. (7), (9) and (11), the plots of (1) ln β versus 1/T; (2) ln(β/T 1.92) versus 1/T; (3) ln(β/T 2) versus 1/T at each chosen α and the corresponding linear fitting by the least-squares method are shown in Fig. 5. The kinetic parameters and the correlation coefficients of linear fitting for each method are listed in Tables 2 and 3.

Fig. 5
figure 5

Arrhenius plots proposed by different models at various conversion degrees of FG char (a) and XS char (b)

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Table 2 Kinetic parameters and correlation coefficients of FG char calculated by different methods
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Table 3 Kinetic parameters and correlation coefficients of XS char calculated by different methods
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Tables 2 and 3 show that the correlation coefficients are all higher than 0.98, which indicates that the linear correlation is quite good. In Tables 2 and 3, the activation energies calculated from FWO, Starink and KAS decrease with the increase in the conversion level. The reasons for this behavior may be associated with the combustion control mechanism [37, 41]. The char combustion is under kinetic control at low temperatures (low conversion level). As the reaction proceeds, the reaction rate of the char increases, and the amount of ash accumulating at the particle surfaces increases, resulting in the inhibition of O2 diffusion to the surface of the char particle. Consequently, the control mechanism is changed from kinetic control at low temperatures to the combined control of the kinetics and diffusion at high temperatures. Moreover, the catalysis of minerals and the change in the pore structure may result in the increase in the char reactivity [42–45]. Liu [37] and Wang et al. [46] also reached similar conclusions in their experiments on char combustion in oxy-fuel atmospheres.

In Tables 2 and 3, at a given conversion ratio, the activation energy of FG char is less than that of XS char. This difference may be attributed to the different compositions of char sample and the evolution of the pore structure during devolatilization. The char reactivity decreases with increasing ash content due to the presence of ash on the surface [45]. As given in Table 1, the ash content of the FG char sample is lower than that of the XS char sample, resulting in the lower activation energy of the FG char sample compared with the XS char sample. Table 4 shows the pore parameters of the FG and XS char samples. The Brunauer–Emmett–Teller (BET) surface area of FG char (25.13 m2 g−1) is higher than that of XS char (12.61 m2 g−1). Because the higher specific surface area of the char results in a higher reactivity [47], the combustion reactivity of FG char is higher than that of XS char.

Table 4 BET surface area and average pore size of FG and XS char
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Kinetic mechanism function of char combustion in 21 % O2/79 % H2O atmosphere

According to the Popescu method, 41 typical mechanisms are analyzed [48]. The calculated values of correlation coefficients R 2 and standard deviations SD are used as criteria for all candidate reaction models (R 2 > 0.996 and SD < 0.02). The seven reaction mechanism models meeting the criteria are listed in Table 5 for FG char. Based on the mechanism functions listed in Table 5, the Coats–Redfern integral method is used to determine the active activation energy.

Table 5 Correlation coefficients (R 2) and standard deviations (SD) of the possible reaction models determined by the Popescu method
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Table 6 shows the kinetic parameters of FG char obtained by the Coats–Redfern integral method at 25 K min−1. The kinetic parameters are found to strongly depend on the reaction model. According to R 2 and SD, the No. 16 chemical reaction (first-order) model is the most suitable for FG char and the corresponding activation energy is 122.08 kJ mol−1. The activation energy of FG char is in the range of activation energy values (91.04–127.56 kJ mol−1) obtained by the FWO method. Consequently, the combustion mechanism function of FG char in O2/H2O is −ln(1 − a). This result demonstrates that the combustion of FG char in O2/H2O atmosphere follows the first-order chemical reaction kinetic.

Table 6 Results from the application of the Coats–Redfern integral method for the possible kinetic models
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Conclusions

The combustion and kinetic behaviors of two coal char samples (FG and XS) in O2/H2O atmosphere were investigated using non-isothermal thermogravimetric analysis. According to the TG–DTG curves, replacing N2 by H2O had a significant influence on the char combustion under the conditions of the experiment. The combustion reactivity and performance of FG and XS char were improved in O2/H2O atmosphere compared with O2/N2 atmosphere with the identical oxygen concentration due to the high reactivity and diffusivity of H2O. Meanwhile, the ignition temperature, peak temperature and burnout temperature in O2/H2O atmosphere were lower than those in O2/N2 atmosphere with the identical oxygen concentration. The activation energies of FG and XS char obtained by the FWO, Starink and KAS methods decreased with the increasing conversion level because of the change in the combustion control mechanism, and the activation energy of FG char was less than that of XS char. The combustion of FG char in O2/H2O atmosphere was found to follow the first-order chemical reaction kinetic.