Introduction

Coal sludge is the by-product of coal washing and selecting process, and its production is about 10–20% of raw coal [1]. With the development of coal industry and the improvement of the coal mechanized mining technology, the quantity of coal sludge has been increasing. And the more coal production, the more coal sludge to be generated. A large amount of coal sludge occupies land and causes serious environmental pollution of air, water and soil. However, coal sludge utilization is inefficient due to its inherent disadvantages such as high ash content, high moisture and so on. Hence, how to dispose coal sludge is still a rigorous problem for coal industry. Coal sludge combustion is one of important ways of its utilization right now. Therefore, research on combustion behavior of coal sludge should be conducted comprehensively for increasing its combustion efficiency and decreasing fuel gas emission.

Thermogravimetric analysis is a traditional and one of the most widespread techniques and has been broadly used for studying the combustion behavior of coal. The advantages of thermogravimetric analysis are its rapid assessment of combustion parameters such as ignition temperature, burnout temperature, maximum rate of mass loss, the general combustion parameter and so on. And thermogravimetric analysis is useful for studying the kinetics of combustion processes. Kok [2] used differential scanning calorimetry (DSC) and thermogravimetry (TG/DTG) to obtained information on the temperature-controlled combustion characteristics of seventeen coals. And the activation energies of the samples were varied in the range of 54–92 kJ mol−1. Elbeyli et al. [3] studied the thermal characteristics and kinetic parameters of cleaned Tunçbilek lignite. They concluded that activation energy values of combustion and pyrolysis reactions were 34.53 and 29.24 kJ mol−1, respectively. Özbas and Kök [4] investigated the effect of heating rate of the thermal properties and kinetics of raw and cleaned coal samples basing on thermogravimetry (TG/DTG) at different heating rates (5, 10, 15 and 20 °C min−1). And for all of the coal samples, higher peak and burnout temperatures were measured with an increasing heating rate. The activation energies of all of the samples were affected inversely as the heating rate was increased. Altun et al. [5] investigated the combustion properties of the lignite, and different binders were analyzed by thermogravimetric (TG/DTG) methods. It was observed that molasses and carboxyl methylcellulose may decrease the residue content at the end of the combustion period. Ren et al. [6] studied combustion characteristics of coal gangue under different atmosphere using TG and tube reactor tests. The results showed that ignition temperature, burnout temperature and peak temperature increase, while the maximum and average combustion rates decrease with decreasing O2 concentrations and the activation energy values of coal gangue combustion varied from 117.6 to 137.4 kJ mol−1 under different atmospheres.

Nevertheless, previous studies have been used the application of thermal analysis to evaluate combustion properties and kinetic of lignite, bituminous, anthracite, coal gangue and their blends [7–12], there are very little studies in the literature on coal sludge combustion characteristics.

In this study, three different types of coal sludge with various volatile contents, ash contents and fixed carbon were chosen to perform TG experiments. And combustion characteristic parameters like ignition temperature, burnout temperature and maximum mass loss rate were deduced from the TG–DTG curves. Furthermore, by performing TG analysis at different heating rates, a kinetic estimate of the coal sludge combustion process using Ozawa–Flynn–Wall (OFW) and distributed activation energy model (DAEM) iso-conversional methods was carried out to calculate the activation energy of the coal sludge. The results can provide a useful basis for further utilizing coal sludge with high efficiency.

Materials and methods

Coal sludge samples

Three kinds of coal sludge from different places were selected for this study, including Taiyuan coal sludge (TY), Jincheng coal sludge (JC) and Shuozhou coal sludge (SZ). All these coals are typical in Shanxi in North China. The coal sludge samples were dried in air, then were grinded and sieved to obtain particle with size smaller than 74 µm for experiments. The data for the corresponding proximate and ultimate analysis are listed in Table 1. The ash composition analysis of the coal sludge samples is shown in Table 2.

Table 1 Properties of coal sludge
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Table 2 Ash composition of coal sludge samples/mass%
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The ash yield of TY (53.71 mass%) is higher than that of JC (28.9 mass%) and SZ (27.08 mass%). Furthermore, SZ yields higher amount of volatiles (26.98 mass%) than TY (18.93 mass%) and JC (18.78 mass%). However, the fixed carbon of JC (51.31 mass%) is higher than that of SZ (44.87 mass%) and, especially, than that of TY (26.33 mass%).

TG analysis

The combustion characteristics of coal sludge were studied in a thermogravimetric analyzer (Pyris1, PerkinElmer Co). Coal sludge sample was placed in a Pt crucible and was burned under an air atmosphere, with an air flow rate of 60 mL min−1, the furnace temperature was increased from the ambient temperature to 1000 °C. Each coal sludge sample was tested at four different heating rates of 10, 20, 30 and 40 °C min−1. In every test, about (6 ± 0.1) mg sample was loaded into the silver crucible. At these conditions, the residues left in the crucible after combustion were formed by loose particles, which indicate that there was no sign of melting behavior caused by mass and heat transfer limitation [13]. The corresponding thermogravimetric (TG) and the differential thermogravimetric (DTG) combustion curves were recorded continuously as a function of temperature and time during the heating run. The experiments were performed at least three times under identical conditions in order to assure reproducibility of the results for each sample of each heating rate. And the error was acceptable.

Determination of characteristic parameters

Several characteristic parameters were used in this work to evaluate the combustion properties of the coal sludge samples. These characteristic parameters including the ignition temperature (T i); the burnout temperature (T b); the maximum mass loss temperature (T max); and the maximum mass loss rate (DTG max).

The ignition temperature (T i) is described in Fig. 1, and it is identified as following way [14, 15].

Fig. 1
figure 1

Ignition temperature (Ti) definition sketch

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Through the DTG peak point A, a vertical line was made upward to meet the TG curve at point B. Then, a tangent line of TG curve was made at point B, which met the extended TG initial level line at point C. Finally, another vertical line was made downwards through point C, which met the cross axle at point D. And the corresponding temperature of point D was the ignition temperature, T i.

The burnout temperature (T f) was defined as the temperature at which the DTG curve reaches a 1% combustion rate at the end of the curve [16].

The maximum mass loss rate (DTG max) was the mass loss rate of the DTG peak point, and the maximum mass loss temperature (T max) was the corresponding temperature.

Furthermore, there was integration parameter, the general combustion parameter S.

The general combustion parameter S was used to reflect combustion reactivity of the whole combustion process. It was calculated by Eq. (1).

$$S = \frac{{DTG_{\hbox{max} } \times DTG_{\text{mean}} }}{{T_{\rm i}^{2} \times T_{\rm f} }}$$
(1)

where DTG max and DTG mean were the maximum and mean combustion rates, T i was the ignition temperature, and T f was the burnout temperature.

The coal sludge with higher value of S has better combustion performance [17].

Kinetic methods

Coal sludge combustion is greatly complex processes.

The rate of heterogeneous solid- state reaction can be expressed as:

$$\frac{{\text{d}}\alpha}{{\text{d}}t} = k\left( T \right)f\left( \alpha \right)$$
(2)

where α is the conversion degree, t is the time, T is the temperature, k(T) is the temperature dependent constant, and f(α) is a function that depends on the reaction model. α could be calculated from data obtained in the TG analysis, according to Eq. (3)

$$\alpha = \frac{{m_{\rm o} - m}}{{m_{\rm o} - m_{\infty } }}$$
(3)

where m o and m ∞ are the mass at the beginning and at the end of the combustion, respectively. While m is the mass at temperature T.

The explicit temperature dependence of the rate constant is introduced by replacing k(T) with the Arrhenius equation which gives

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

where A is the pre-exponential factor, E is the activation energy, and they are Arrhenius parameters. R is ideal gas constant, and R = 8.314 J mol−1 K−1. When the heating rate \(\beta (\beta = {\text{d}}T/{\text{d}}t)\) remains constant, the above expression can be transformed into the following equation with a constant β inserted:

$$\frac{{\text{d}}\alpha}{{\text{d}}T} = \frac{A }{\beta }\exp \left( {\frac{ - E}{RT}} \right)f(\alpha )$$
(5)

The integral form of the non-isothermal rate law is produced by integrating the differential non-isothermal rate law:

$$\int_{0}^{\alpha } {\frac{{\text{d}}\alpha}{f(\alpha )}} = g\left( \alpha \right) = \frac{A}{\beta }\int_{{T_{0} }}^{T} {e^{{ - \frac{E}{RT}}} {\text{d}}T}$$
(6)

where g(α) is the integral function of conversion and T o is the initial temperature of the combustion reaction.

The kinetics of combustion reactions can be determined by single-scan methods (model-fitting methods) and multiple-scan methods (iso-conversional methods). Compared to model-fitting methods, using iso-conversional methods, the influence from mass transfer is reduced by using different heating rates, and the mechanism is allowed to be changed during the course of the reaction [18, 19]. The OFW method and the DAEM method are both the representatives of the iso-conversional methods.

According to non-isothermal iso-conversional methods applied by Ozawa [20], Wall and Flynn [21] using the Doyle’s approximation of p(x) [22],the activation energy can be determined by measure the temperature corresponding to fixed values of α from experiments at different heating rates.

The equation for OFW model is showed in following:

$$\ln\beta = \ln \left[ {\frac{AE}{g\left( \alpha \right)R}} \right] - 5.331 - 1.052\frac{E}{RT}$$
(7)

From this equation, we know that the activation energy can be obtained from the slope of the resulting straight line without specifically knowing reaction mechanism by plotting lnβ versus 1/T.

The equation for DAEM model is showed in following [23]:

$$\ln \left( {\frac{\beta }{{T^{2} }}} \right) = \ln \left( {\frac{AR}{E}} \right) + 0.6075 - \frac{E}{RT}$$
(8)

From this equation, both the activation energy can be estimated from the slope of the resulting straight line by plotting \(\ln \left( {\frac{\beta }{{T^{2} }}} \right)\) versus 1/T.

In order to calculate reaction order, Avrami theory [24–26] is employed so as to describe the non-isothermal data where the variation of the degree of conversion with temperature and heating rate can be described as

$$\alpha\left( T \right) = 1 - \exp \left[ { - \frac{k\left( T \right)}{{\beta^{\text{n}} }}} \right].$$
(9)

Taking double logarithm of both sides of Eq. (2) with \({k}\left( {T} \right) = A{\text{e}}^{ - {\text{E/RT}}}\), gives

$$\ln \left[ { - \ln \left( {1 - \alpha\left( T \right)} \right)} \right] = \ln A - \frac{E}{RT} - n\ln \beta$$
(10)

At the same temperature, by plotting \(\ln \left[ { - \ln \left( {1 -\alpha \left( T \right)} \right)} \right]\) versus lnβ at different heating rates, the reaction order can be determined from the slope of the straight line.

Result and discussion

Combustion characteristics of coal sludge

Thermogravimetric analysis of coal sludge

The TG and DTG curves obtained from the temperature-programmed combustion of three kinds of coal sludge at the heating rate of 20 °C min−1 are shown in Fig. 2.

Fig. 2
figure 2

Comparison of the TG–DTG curves of three kinds of coal sludge at the heating rate of 20 °C min−1: TG curve (a); DTG curve (b)

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As shown in Fig. 2a, with the rise of temperature, combustion of coal sludge samples accompany with mass loss. From TG curves given in Fig. 2a, the TG curves are different obviously, there is a small mass loss before 200 °C for each coal sludge, which indicates evaporation process. And after the temperature of 200 °C, as the different nature of different kinds of coal sludge, the mass losses observed from the TG profiles are different. The results showed that the major mass losses for TY, JC and SZ occurred at 320–570, 320–620 and 280–560 °C, respectively. The temperatures of mass started to loss for TY and JC were similar, and it for SZ was a little earlier. That because SZ had higher volatile and lower ash, its devolatilization required lower temperature. So the higher the volatile content in the coal sludge, the lower the devolatilization temperature and vice versa. From Fig. 2a, the residual mass of TY, JC and SZ at the end of the combustion process is 48.04, 28.06 and 26.88%, respectively, which are largely consistent with their ash content.

The DTG curves of coal sludge are shown in Fig. 2b. As can be seen from Fig. 2b, the three kinds of coal sludge exhibit unique DTG profiles. However, three kinds of coal sludge are all displayed only one prominent peak over a wide temperature distribution, respectively. And that means there was no obvious boundary for the combustion of volatile and carbon, which was the same to the literature [12].

The peak temperature which shows the maximum combustion rate has been reached at 455.75 °C for SZ, 489.97 °C for TY and 512.81 °C for JC, respectively. The temperature of maximum combustion rate is the lowest for SZ, and this maybe attributed by the higher volatile content in SZ which is shown in Table 1.

The values of the maximum combustion rate for TY, JC and SZ were 8.33, 11.32 and 10.29% min−1, respectively. The value for JC was the highest, for TY was the lowest, for SZ was a litter lower than that for JC and higher than that for TY. Peak temperature and its corresponding rate can be used as the measure of combustibility and reactivity, respectively [27]. SZ had higher combustibility, and JC had higher reactivity.

Characteristic parameters of coal sludge combustion

Several characteristic parameters deduced from TG–DTG curves are listed in Table 3. These parameters could evaluate the coal sludge combustion properties.

Table 3 Characteristics parameters of three kinds of coal sludge
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As can be seen from Table 3, at the heating rate of 20 °C min−1, the most easily ignited coal sludge is SZ, and the ignition temperature of SZ is 388.92 °C. The next easily ignited coal sludge is TY and then comes JC with ignition temperature is 434.80 and 443.33 °C, respectively. This order was consistent with that of content of volatile in three kinds of coal sludge. And the same time, the orders of burning temperature and the maximum mass loss temperature for the three kinds of coal sludge were same to the order of ignition temperature. The general combustion parameters (S) also are listed in Table 3. It can be found from Table 3 that value of S for TY coal sludge is the lowest, for SZ is the highest and for JC is in middle. For TY coal sludge, its lowest value of S may largely attribute to its too high content of ash to impact heat and mass transfer in combustion process.

What is more, it can be seen from Table 3 that the change trends of these characteristic parameters of this three kinds of coal sludge at other different heating rates were the same as what happened at the heating rate of 20 °C min−1.

The effect of heating rate on combustion process

The thermogravimetric (TG) and the differential thermogravimetric (DTG) results of TY, JC and SZ coal sludge samples of different heating rates (10, 20, 30 and 40 °C min−1) are shown in Fig. 3. Because the change trends of TG and DTG profiles with the heating rates of three different kinds of coal sludge were similar, we take TY coal sludge as example to analysis. As can be seen in Fig. 3a, although the different heating rates are, the curves of TG are similar. However, the combustion process is found in a wider temperature range with the heating rate increase. The percentage of mass loss is all about 52% at heating rate 10 °C min−1 and at heating rate 40 °C min−1. It can be known that the residue yield could not been affected by heating rate obviously. Their onset temperature for volatile release and mass loss is about 350 °C, and final combustion temperature detects as mass stabilization is about 650 °C.

Fig. 3
figure 3

TG and DTG curves for TY at different heating rates: TG curves (a); DTG curves (b)

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As can be seen in Fig. 3b, the temperature of maximum mass loss rate of TY is 480.05 °C at a heating rate of 10 °C min−1, while it is 489.97 °C at 20 °C min−1, 505.67 °C at 30 °C min−1, 515.23 °C at 40 °C min−1. As the heating rate increases, the DTG curves are translated to higher temperatures, which means that coal sludge combustion happens in a higher temperature zone, but the heating rate could not affect the temperature of maximum mass loss rate obviously. However, the maximum mass loss rate of TY coal sludge increases from 4.56 to 12.41% min−1; therefore, the heating rate could affect the maximum mass loss rate obviously. It shows that the coal sludge has higher reactivity with increasing the heating rate. That may be because it was difficult for the difficult-flammable component in the coal sludge sample to be ignited only using the heat released from the reactivity, and much more heat from external environment was needed to supply for continued combustion. So, a higher heating rate provides the advantageous condition for coal sludge to continue to combust.

Figure 4 shows the effect of heating rate on the ignition temperature, burnout temperature of the three kinds of coal sludge. It can be seen from Fig. 4 that the ignition temperature and the burnout temperature tend to increase with increasing the heating rates. Furthermore, the ignition temperature is affected slightly by the heating rate, while the burnout temperature is affected strongly. That may be because the increasing heating rate induced the large temperature gradient between internal and external surfaces of the coal sludge particle, which was adversed to the release of volatile. And the ignition temperature and burnout temperature were further affected [8].

Fig. 4
figure 4

Effect of heating rate on the combustion characteristic temperatures

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Figure 5 shows the effect of heating rate on general combustion parameter S of the three kinds of coal sludge. And it can be found from Fig. 5 that the general combustion parameter S of three kinds of coal sludge increases with the increase of the heating rate from 10 to 40 °C min−1, and the effect of heating rate on S of SZ is the greatest. The experimental results indicate that a higher heating rate is useful for the combustion performance of coal sludge under the experimental conditions in this study.

Fig. 5
figure 5

Effect of heating rate on the general combustion parameter S

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Kinetic analysis

The iso-conversional method is considered as a good approach for the study of combustion kinetics of carbonaceous material. In this study, the combustion activation energy values were obtained by Ozawa–Flynn–Wall (OFW) method and distributed activation energy model (DAEM) method. According to Eqs. (7) and (8), activation energy values were calculated adopting heating rates of 10, 20, 30, 40 °C min−1. The curves of fitting to kinetic model proposed by OFW and DAEM to various conversion degrees (α) corresponding to the combustion of TY, JC and SZ at different heating rates are shown in Figs. 6 and 7, respectively. From the slope of line, the apparent activation energy (E) of the dynamic combustion at various conversion degrees (α) could be estimated. And the activation energy values obtained by the OFW method and the DAEM method are listed in Table 4. It can be seen from Table 4 that the activation energy values have good correlation coefficients (R 2) in the range of 0.8730–0.9999, and most of them are larger than 0.9500, showing acceptable accuracy of results. As the data outside the range of 20–80% had poor correlation coefficient, only the conversion values in this range were considered. Table 4 shows the activation energy values corresponding to each conversion value, and the average value of E was obtained as arithmetic mean of several values. Furthermore, there were significant variations of activation energy with conversion values, as conversion values increase, the values of activation energy reduce, which indicated that the combustion processes of three kinds of coal sludge were all kinetically complex, and should be considered as multi-step processes. And the change trends were similar to the literature for lignite coal [28].

Fig. 6
figure 6

Curves of fitting to kinetic model proposed by Ozawa–Flynn–Wall to various conversion degrees (α) corresponding to the combustion of TY, JC and SZ at different heating rates

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Fig. 7
figure 7

Curves of fitting to kinetic model proposed by DAEM to various conversion degrees (α) corresponding to the combustion of TY, JC and SZ at different heating rates

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Table 4 Activation energy values obtained from OFW and DAEM method for TY, JC and SZ coal sludge
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The slopes of linear fittings, the value of E calculated by the OFW method and DAEM method are shown in Table 4. The activation energy values during combustion process of TY are 150.23 and 144.88 kJ mol−1, estimated through OFW and DAEM methods, respectively. The activation energy values of JC are 119.62 and 113.63 kJ mol−1, and the corresponding values are 151.23 and 146.78 kJ mol−1 for SZ. The activation energy values obtained from the DAEM method are lower than that obtained from the OFW method. However, the change trends are similar between values calculated by OFW method and DAEM method. From Table 4, it is obvious that TY possessed relatively similar activation energy values to that of SZ, and the values of them both are higher than the corresponding values of JC coal sludge. This may be related to the different amounts of alkaline metal (Na and K), alkaline earth metals (Ca and Mg), Fe and Ti in each kind of coal sludge. As seen in Table 2, JC contains significantly higher amounts of alkaline metal, alkaline earth metals, Fe and Ti compared with TY and SZ, and these metal may play a catalytic role during combustion of coal sludge, which resulted in lower activation energy value. However, the interactions of coal sludge component may be a reason, too.

Anyway, the activation energy values of the three kinds of coal sludge were higher than values of coal, when compared to the data in the literature [29, 30].

Figure 8 shows the curves of activation energy versus the conversion rate of coal sludge combustion. It can be seen that within the α = 20–80% range, the curves corresponding to the different coal sludge from OFW and DAEM method are similar. So, we choose the activation energy versus the conversion rate by OFW method to analysis. The activation energy value on each conversion is lowest for JC coal sludge. And the values for SZ coal sludge are higher than that of TY when the conversation rate α ≤ 40, while the results are opposite for α ≥ 50. Furthermore, the activation energy values are almost the same for TY and SZ coal sludge when the conversation rate is 80%. Moreover, the activation energy values decrease with the increasing conversation rates. This result agreed with the results reported in previous research on coal [29].

Fig. 8
figure 8

Activation energy versus the conversion rate of coal sludge combustion a by OFW method; b by DAEM method

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The relationship between the apparent activation energy E and the pre-exponential factor A can be written in the following formula [31, 32]:

$$\ln A = \, aE + b,$$

where a and b are the compensation coefficients.

Figure 9 shows the compensation effect analysis curves of TY, JC and SZ coal sludge combustion. The linear fitting of lnA and E was carried out based on the calculated kinetic parameters through DAEM method. It can be observed from Fig. 9 that the pre-exponential factor A increases with increasing values of E, the three kinds of coal sludge show linearity, which indicates that the linear correlation between lnA and E is quite good.

Fig. 9
figure 9

Compensation effect analysis curves of TY, JC and SZ coal sludge combustion

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Reaction order is also a kinetic parameter to describe combustion mechanism. It is calculated based on Eq. (10) by plotting \(\ln \left[ { - \ln \left( {1 -\alpha \left( {T} \right)} \right)} \right]\) versus lnβ. The reaction order (n) as a function of temperature for TY, JC and SZ coal sludge combustion is shown in Table 5. Reaction orders were evaluated at three different values of temperature (430, 480 and 530 °C). The values are in the range of 0.39–0.68 and are dependent on the extent of the reaction and on the type of the coal sludge. It is not constant during the combustion, which also indicates that the complexity of the multiple step process. TY and JC coal sludge had comparable reaction order values and higher than that of SZ coal sludge.

Table 5 Reaction order versus temperature
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Conclusions

This research provided the thermal and kinetic behavior of TY, JC and SZ coal sludge from Shanxi in northwestern China, and the following conclusion was obtained:

  1. 1.

    The value of general combustion parameters (S) for TY coal sludge is the lowest, for SZ is the highest, and for JC is in middle at any heating rate. It was observed that the residue yield and the ignition temperature could not been affected by heating rate obviously. However, the heating rate could affect the maximum mass loss rate and the burnout temperature obviously and strongly. Furthermore, the value of general combustion parameters (S) of three kinds of coal sludge increases with increased heating rate. The experimental results indicate that a higher heating rate is useful for the combustion performance of coal sludge in this study.

  2. 2.

    The activation energy values obtained from the DAEM method are a little lower than the ones obtained from the OFW method for every kind of coal sludge. OFW and DAEM methods showed that the activation energy values of JC coal sludge are minimum, with the value of 119.62 kJ mol−1 using OFW method and 113.63 kJ mol−1 using DAEM method.