Determination of Cocombustion Kinetic Parameters for Bituminous Coal and Pinus Sawdust Blends.

Cocombustion of bituminous coal (HC) and Pinus sawdust (PS) was investigated in this paper with the aim of determining the kinetic parameters relevant to cocombustion reactions of their fuel blends. PS was used because it is a waste biomass product capable of generating energy. Motivated by the need to partly substitute HC used in existing boilers with PS, the optimum kinetic parameters at different blending ratios were thus investigated with the ultimate goal of diversifying the energy portfolio for these boilers. Blended samples were prepared with a PS substitution by mass ranging from 0 to 30%, thus producing five samples, namely:100HC, 90HC10PS, 80HC20PS, 70HC30PS, and 100PS. A simultaneous thermogravimetric analyzer was used to investigate the degradation of the fuel samples under a synthetic air atmosphere using 5, 12.5, and 20 °C/min heating rates. The kinetic parameters were evaluated using the distributed activation energy model (DAEM) due to its ability to evaluate complex parallel chemical mechanisms. The influential homogenous volatile combustion and heterogenous combustion stages produced an increasing trend for activation energy (E a) with increased PS (100HC to 70HC30PS) from an average of 61.80-104.34 kJ/mol while the pre-exponential factor increased from 1.31 × 105 to 6.52 × 108. Generally, blending of HC with PS did not produce a linear variation of the kinetic parameters; thus, by using various plots, an optimum blending ratio of 80HC20PS was deduced.

Introduction

Cocombustion of coal and biomass provides an alternative for biomass waste management as well as combustion efficiency improvement for boilers if correctly implemented and monitored during the combustion process.[1] Optimization of cocombustion is necessary since introduction of biomass does not result in a linear variation of thermal parameters but is dependent on a plethora of variables that range from fuel physical and chemical properties to combustion operating conditions.[2,3] Unfortunately, coming up with optimized parameters necessary for the cocombustion process on an experimental basis is expensive and considered confidential by most companies.[4] As such computational fluid dynamics (CFD) offers great potential in terms of addressing the gap related to specific regions not capable of running experimental facilities due to resource constraints. Deliberate policies by developed countries on the use of biomass and coal in some of their existing boilers has already produced some positive feedback.[5] However, since developing countries can now use cost effective CFD, the major hurdle is on the initial boundary conditions which are based on unique experimental data to produce good cocombustion models. Due to the sheer vastness of biomass species, a combination of appropriate modeling and experimental techniques are needed to address the gap that exists with respect to certain species that are employed in the cocombustion process. Since combustion involves chemical reactions, predicting good kinetic parameters forms the basis of good mechanisms that can be used to predict the progression of chemical reactions with improved accuracy.[2]

Combustion of solid fuels is based on the fact that a fuel particle goes through distinct stages when it enters the combustion zone, namely: drying, devolatilization, char combustion, volatile combustion, and ash formation.[6] Drying entails the removal of moisture (surface and inherent) when the particle is heated up to around 105 °C in the absence of oxygen while devolatilization involves removal of light volatiles and heavy volatiles when the heating continues further in the absence of oxygen. The quantitative (mass of volatiles released and the rate of release) and qualitative (chemical composition of volatiles) analysis of volatiles is rather complicated making this stage one of the most important ones in the combustion experimental process. As for CFD, volatile combustion submodels use mechanisms that are mainly based on the results of the devolatilization stage.[7] Char combustion requires knowledge of the reactions that occur within the boundary layer and those occurring within the free stream. Fortunately, the experimental analysis of this stage is less cumbersome when information about the fuel is adequate.[6] However, CFD requires specific input parameters which tend to be overlooked by most of the researchers. Similarly, because of the vast biomass species, it tends to be rather impossible to exhaust all the possible fuel blend compositions between coal and biomass while testing various operating conditions.[8] As a result, this study is going to produce kinetic parameters for the chosen fuel species that can be later extended to other compatible useful species.

Investigations into cocombustion of coal and biomass have been carried out before on an experimental basis as summarized in Table . Guo et al.[9] experiments showed a decreasing trend on the overall activation energy (Ea) as the biomass proportion was increased to about 30% which was also supported by Chen et al.[10] When the biomass proportion was increased beyond 30%, its effect on Ea heavily became dependent on the biomass species under study hence the increasing trend at specific conversion percentages. This is explained by the notion that different temperature ranges are responsible for devolatilization, volatile combustion, and char combustion for biomass vs coal samples. However, from a general perspective, a higher Ea is representative of a lower reactivity as more energy is required to initiate a reaction.[10] To avoid this confusion, Zhou et al.[11] analyzed the Ea representative of the volatile combustion regime separately from the one representative of the char combustion regime. Results showed an increase in Ea as biomass proportion increased from 44.5 to 64.5 kJ/mol for the volatile combustion regime while the Ea representative of the char combustion regime decreased from 94.8 to 35.2 kJ/mol. Even though Mureddu et al.[12] did not investigate coal biomass blends, their findings on individual coal and biomass species suggested Pinus woodchips exhibit better combustion activity than coal. This is evidenced by the Ea difference between bituminous coal and Pinus woodchips corresponding to the volatile combustion regime as well as the char combustion regime. An extensive comparison of the different coal biomass blends for different municipal solid wastes and woody biomass residues was performed by Boumanchar et al.[13] By using the Coats–Redfern[14] (C-R) method, the authors generally found the diffusion and power (nucleation) mechanisms giving the best fit between the model and experimental results. In contrast to other researchers, Florentino-Madiedo et al.[15] showed an increased Ea for both the volatile combustion regime and the char combustion regime, though the synergistic effect was not particularly positive. As such, the complex nature of coal-biomass cocombustion is made apparent by the absence of a generalized trend toward the determination of Ea. Wang et al.[16] performed experiments on coal blended with polyurethane and demonstrated that ignition temperature is inversely proportional to Ea. In as much as different models were employed by the authors to analyze their results, the order of Ea for the coal biomass blends was generally consistent obtaining values between 10 and 200 kJ/mol for the different blending ratios.

Table 1

Examples of Coal and Biomass Cocombustion Analysis by Use of Thermogravimetry

	experimental method					kinetic method
fuel	biomass blending ratios (% biomass substitution)	max temperature (°C)	heating rate (°C/min)	sample mass (mg)	purge gas
bituminous coal, lignite, sawdust, rice straw, and catkins[9]	10, 30, 50, 70	900	20	10	air, 80 mL/min	Coats–Redfern
coal and corn stalks biomass[10]	25, 50, 75	850	10, 20, 30, 40, 60	20	80% pure argon and 20% pure nitrogen, 100 mL/min	distributed activation energy model
bituminous coal, corn stalk, and sawdust biomass[11]	10, 20, 30, 50	1000	15, 60	20	air, 100 mL/min	Coats–Redfern
coal and cellulose biomass[1]	25, 50, 75	850	10, 20, 40	10	argon, 60 mL/min	Kissinger–Akahira–Sunose
coal and wood chips[12]	various	1000	10, 20, 30, 40, 50	9	air, 100 mL/min	Flynn–Wall–Ozawa and Kissinger–Akahira–Sunose
coal, biochar, municipal solid waste, and sawdust[13]	various	800	5	7	air, 100 mL/min	Coats–Redfern
coal, torrefied sawdust, paraffin[15]	various	1000	3, 10, 20, 40	10	nitrogen, 100 mL/min	Friedman, Flynn–Wall–Ozawa, and Kissinger–Akahira–Sunose

Table summarizes some of the industrial applications that have tried to model the cocombustion process of biomass with coal. Generally, the validation of the models (if done) is based on temperature profiles within the furnace which are very sensitive toward kinetic parameters. The general agreement among the reviewed authors is for the need to perform good physical and chemical characterization experiments if the cocombustion models are to improve their accuracy. Most common industrial boilers systems within Zimbabwe utilize bituminous coal as a fuel as mirrored by other boiler systems within the region as well. Eventually, the objective of this study is to facilitate the cocombustion of coal and biomass waste within these boilers. Since sawdust (mainly Pinus) is available as a waste product across the region as well, the researchers saw it worthwhile to select sawdust waste rather than compete for wood. Appropriate disposal of sawdust waste offers a lot of environmental positives.[17,18] After extensive literature research, the authors did not encounter any kinetic triplicate parameters applicable to CFD modeling of Sub-Saharan bituminous coal and Pinus sawdust (PS) blends for the devolatilization, volatile combustion, and char combustion separately as required by good CFD modeling software. This is particularly due to the fact that, apart from lagging behind as a region, most authors overlook how combustion occurs in stages. Though some of the authors have managed to provide the overall kinetic triplicate parameters for the whole combustion process,[19] each stage requires pertinent data to perform successful CFD modeling.

Table 2

Industrial Applications of Coal and Biomass Cocombustion That Have Been Modeled

	combustion parameters	CFD modeling parameters
fuel	boiler capacity and type, location, and biomass blending ratios	devolatilization, char combustion, volatile combustion, drag, radiation, and turbulence submodels	observations
pinewood and bituminous coal[22]	1 MW wall-fired pulverized furnace, United Kingdom, 10% by mass biomass substitution	FG-DVC devolatilization, Smith intrinsic char combustion, EDM volatile combustion, Haider and Levenspiel drag, P-1 radiation and, RNG k-ε turbulence submodels	determination of particle diameters and trajectories within the furnace were the main priority
			they overlooked experiments useful in obtaining kinetic parameters
PS and bituminous coal[5]	150 MW commercial boiler, Chile, 10% by mass biomass substitution, tangential fired pulverized fuel furnace	two competing rates of devolatilization, kinetic/diffusion surface reaction char combustion, EDM volatile combustion, Morsi and Alexander drag, discrete ordinates radiation and, standard and realizable k-ε turbulence submodels	burnout and temperature-related parameters were successfully modeled,
			most kinetic parameters were generally obtained from the literature
municipal solid waste (sludge) and coal[23]	100 MW commercial boiler, China, 10% by mass biomass max substitution, tangential fired pulverized fuel furnace	single kinetic rate devolatilization, multiple-surface-reaction char combustion, two-step reaction and finite-rate/EDM volatile combustion, P-1 radiation, realizable k-ε turbulence submodels	emphasis was placed on the NOx emissions obtained coupled with the economic benefits of cocombusting sludge
			typically obtained generalized parameters from the literature as no specific experiments on sludge characterization were presented
Cynara cardunculus (biomass) and bituminous coal[19]	350 MW commercial boiler, Spain, no substitution, wall-fired pulverized fuel furnace	single rate kinetic devolatilization, single film boundary layer char combustion, mixed-is-reacted volatile combustion, P-1 radiation, standard k-ε turbulence submodels.	focused on gas species distribution within the furnace and burnout parameters
			performed necessary TGA experiments to obtain kinetic parameters
biomass and lignite[24]	40 kW test facility, Germany, no substitution, vertical pulverized fuel furnace	single rate kinetic devolatilization, multiple-surface-reaction char combustion, Eddy dissipation-concept volatile combustion, discrete ordinate/WSGGM radiation, Reynolds stress model (RSM) turbulence submodels	validated model using velocity profiles
			acknowledged limitations caused by particle shape and using assumptions for kinetic parameters
wood and coal[25]	500 MW, United Kingdom, no substitution, wall-fired pulverized fuel furnace	FG-DVC devolatilization, multiple-surface-reaction char combustion, Eddy dissipation volatile combustion, Haider and Levenspiel drag, discrete ordinate radiation, realizable k-ε turbulence submodels	temperature-related parameters were successfully modeled
			generally, most of the boundary conditions were obtained from the literature

This research will help address the gap that exists with regards to Sub-Saharan coal and biomass cocombustion, thus becoming useful technical data for power plant retrofitting and optimization. To address these gaps, this research focused on investigating the kinetic parameters that are used within the cocombustion of bituminous coal and PS blends by implementing the distributed activation energy model (DAEM).[10]

Methodology

Sample Preparation, Proximate, and Elementary Analysis

The bituminous coal used in this research was of thermal grade obtained from Hwange, Zimbabwe, a high exploration region.[20] The sawdust was obtained from local sawmills around the Eastern Highlands which use Pinus taeda and Pinus patula species as their main timber raw material.[21] The ISO18283:2006 standard was used to prepare the coal and PS samples for further analysis. Grinding of the fuel samples was done using an IKA MF 10 cutting mill and a lab-scale closed ball mill. The samples were then oven-dried at 105 °C for 24 h before being placed on a vibrating shaker for the sieving process. To ensure homogeneity, a particle diameter group between 180 and 250 μm was chosen for subsequent analysis.

The fuel blends were prepared on a mass basis and labeled appropriately with HC representing the bituminous coal and PS representing the Pinus sawdust. The notation that was adopted for the sample labeling hence analysis was, for example, “90HC10PS” representing 90% coal and 10% PS on a mass basis. In total five samples were prepared for further analysis which were: 100HC, 90HC10PS, 80HC20PS, 70HC30PS, and 100PS. A Barnstead Thermolyne 6000 muffle furnace was used to carry out the proximate analysis of the fuel samples. The ISO 562:2010 and ISO 1171:2010 standards were followed throughout the proximate analysis, thus obtaining the volatile matter, ash, and fixed carbon content.[26] Approximately weights of 1 g were used for the proximate analysis, and to ensure result validity, each fuel sample was tested in triplicate. A Thermo Fisher Scientific Flash analyzer (EA 1112) was used to perform the ultimate analysis (CHNS) of the prepared samples using weights of approximately 1.8 mg for each run. The oxygen and fixed carbon content were determined using the difference method.

Combustion Kinetic Parameter Modeling

The most common experimental method used in conjunction with modeling techniques for combustion kinetic parameter determination is based on finding the mass loss when the sample is under a controlled heating environment. Specifically, this method is referred to as thermogravimetric analysis which requires an instrument capable of capturing the heating temperature range, heating rate, heating atmosphere, and sample mass with accuracy.[27] Basically, the fuel sample degrades within the instrument with α being used to denote the degree of degradation as given by eq . M0 represents the initial weight, M represents the sample weight at time t, and Mf represents the final weight over the specific time range.

Thermal degradation being a kinetic process can then be written based on the Arrhenius equation, eq , and the rate of thermal degradation, eq , to produce a reaction mechanism equation that can be analyzed using experimental data.where f(α) refers to the reaction mechanism model, k(T) represents the reaction rate constant, A represents the pre-exponential factor (s–1), Ea represents the activation energy (kJ/mol), R represents the universal gas constant (J/mol·K), T represents the temperature (K), and β refers to the heating rate β = dT/dt (K/s).[28,29]

Several models have been developed that can be used to link experimental data to combustion reaction mechanisms for kinetic parameter determination. It is important to note that the reaction mechanism model f(α) is unknown at the beginning of any data analysis. Generally, these models used to link experimental data to combustion reaction mechanisms are thus classified as either model fitting methods or isoconversional (model-free) methods.[1]Table summarizes the different models commonly used to analyze experimental data.

Table 3

Model Fitting Methods and Isoconversional Methods

method	description
Coats–Redfern[13,14]	model fitting requires previous knowledge of the reaction mechanism
modified Coats–Redfern[27,30]	isoconversional: an integral method which depends on the temperature integral approximation
Friedman[15]	isoconversional: a differential method that uses determination of the reaction rate at an equivalent stage for various heating rates
Flynn–Wall–Ozawa[15,31]	isoconversional: an integral method which depends on the temperature integral approximation
Vyazovkin[27]	isoconversional: solutions can only be obtained by use of computer algorithms due to complexity and nonlinearity
Kissinger–Akahira–Sunose[15,32]	isoconversional: an integral method which depends on the temperature integral approximation
distributed activation energy[10]	isoconversional: an integral method that acknowledges chemical reactions occurring in parallel

Mathematical integration of eq does not produce an exact solution since integration of exp(−E/RT) is not exact because of the variables involved. Thus, after rearranging, eq can be rewritten as eq . G(α) is used to represent the integrated form of the reaction mechanism model f(α).

Isoconversional methods are best used when determining kinetic reaction parameters, particularly the Ea without necessarily considering the reaction mechanism model f(α). On the other hand, for model fitting models, eq is integrated to obtain eq , though rearranging is still necessary to obtain eq .

Fitting experimental data to eq then becomes possible especially after considering certain assumptions. One of these assumptions is that combustion analysis acknowledges that (1 – 2RT/E) ≈ 1, thus producing a linear equation. As such the experimental data is traced in such a way that y = ln[G(α)/T2] is plotted against x = 1/T. From a mathematical point of view, the plot of y vs x is supposed to be linear with a gradient of −E/R and a y-axis intercept of ln(AR/βE).[16] The linear trace is then analyzed to determine the reaction model function with the least error.[28,33] To determine the value of G(α), each reaction model function has a characteristic equation as presented in Table .

Table 4

Reaction Model Functions for Combustion[13,16]

reaction model	G(α)=	f(α)=
reaction order models
zero order	α	1
first order	– ln (1 – α)	1−α
nth order (tested n = 2)		(1−α)n
nucleation models
power law (n ≠ 1) (tested n = 1/2 and n = 2)	α1/n	nα(n–1)/n
Avrami–Erofeev (tested n = 1/2 and n = 2)	[(−ln(1 – α)]1/n	n(1 – α)[(−ln(1 – α)](n – 1)/n
geometrical contraction models
two dimensional (contracting area)	1 – (1 – α)1/2	2(1– α)1/2
three dimensional (contracting volume)	1 – (1 – α)1/3	3(1−α)2/3
diffusion models
1D diffusion	α2
2D diffusion	[(1 – α)(ln(1 – α)] + α	[ – ln (1 – α)]−1
3D diffusion

The method implemented within this study, the DAEM,[10] which is a model-free method, is represented by eq . The method is derived from the Kissinger–Akahira–Sunose[15] model, which is an isoconversional model with the only difference between the two being inclusion of the stabilizing constant, 0.6075. The constant 0.6075 is obtained through simplification of eq based on the first order reaction model. Naturally, it means other reaction models from Table are eligible to be employed, but research has proved how a balance between accuracy and complexity is obtained by using the first order reaction mechanism[34]

The DAEM has been known to produce good results especially with complex reactions such as biomass pyrolysis as well as low temperature degradation.[34] The strength of this model is within its ability to acknowledge how parallel reactions occur during the combustion process. Mathematically, plotting of ln (β/T2) against 1/T at a given degree of degradation is supposed to give a linear graph.[35,36]The y-intercept will then be employed to evaluate the pre-exponential factor.

Within this research, goodness of fit was evaluated by calculating the coefficient of determination, R2, which is a statistical parameter. This is basically a ratio between the total sum of squares of vertical deviations from each data point to the fitted line and the total sum of squares about the mean as given by eq .[37] When the value of R2 was close to 1, it indicated a good fit with regards to the reaction model function chosen.

Thermogravimetric Analysis

A Hitachi STA7200RV simultaneous thermogravimetric analyzer was employed as the instrument for the thermogravimetric experimental analysis as represented in Figure .

Figure 1

Thermogravimetric analyzer workbench schematic.

Since the thermal degradation had to resemble combustion, synthetic air was chosen as the purge gas with a constituent by volume of 79% N2 and 21% O2. The purge gas flow rate was set at 20 mL/min, which meant under the oxidative environment, excess oxygen was being supplied to assure complete combustion. The ramp setting was chosen meaning the heating rate could be entered such that the researchers could investigate three heating rates of 5, 12.5, and 20 °C/min. The dynamic temperature range of the instrument was set between 25 and 915 °C meaning no isothermal conditions were investigated. Samples of approximately 10 mg were prepared and fed into an autosampler and a ceramic pan was used for the experiments. The data logger was programmed to record data after every 0.5 s producing the thermogravimetric and differential thermal analysis data automatically. To assure validity of results, some of the fuel samples were tested thrice during the run of the experiments. Data analysis was carried out using Origin Pro 2021 analytical software for better visualization of raw and derived data for further analysis.

Results and Discussion

Proximate and Ultimate Analysis

Proximate and ultimate analysis results of the fuel samples are summarized in Table . The trends relate quite well with previous studies done by other authors showing higher volatile matter for biomass.

Table 5

Chemical Properties of Coal, Pine Sawdust, and Fuel Blends

	proximate analysisa (weight %)			ultimate analysisa (weight %)
	fixed carbonb	volatile matter	ash	C	H	Ob	N	S
100HC	53.97	23.10	22.93	58.671	2.946	13.245	1.613	0.593
90HC 10PS	48.21	29.91	21.88	58.489	3.367	14.246	1.448	0.570
80HC 20PS	46.35	31.82	21.83	56.954	3.734	15.632	1.296	0.555
70HC 30PS	46.02	33.74	20.24	56.885	4.093	17.100	1.143	0.535
100PS	15.62	80.68	3.70	49.504	6.035	40.404	0.358	0

On a dry basis.

By difference.

The fixed carbon, which is generally higher for coal than biomass, decreases as blending increases, which is the same trend shared for ash. There is no linear variation between the volatile content, ash, and fixed carbon with the blending ratio for the whole range. Generally, substances with high volatile content have a higher ignition tendency while those with high fixed carbon have better combustion stability.[38] Mishra and Mohanty[34] also highlighted how reduced ash content in the fuel/blend results in better combustion properties and reduced fuel preparation costs. Marangwanda et al.[39] further supported the notion by demonstrating how combustion stability decreases as the biomass blending ratio increases due to the increased volatile matter. As noted by Guo et al.,[9] a higher ignition tendency is associated with a lower Ea for the prohomogenous volatile combustion zone, which means the fuel/blend will require less energy to ignite (igniting at lower temperatures).

Kinetic Parameter Analysis

TG-DTG Curves of Blended Samples

Using data obtained from the experiments, TG-DTG curves were traced for the fuel samples under test. The curves have been presented in detail in a previous study by the same authors[39] while a data file also accompanies this publication with all the graphs employed by the authors. The instrument had a sensitivity of 0.1 μg for TG mass readings, which equated to a minimum uncertainty of 0.001% and a maximum value of 0.036% for the values recorded throughout the experiment. Also, since the values were recorded continuously (in case there is some repeated error), it became justifiable to overlook analysis of uncertainty throughout analysis of TG results. An illustrative graph is presented in Figure on how the different points were obtained within this research.

Figure 2

TG-DTG curve for 80HC20PS at a 12.5 °C/min heating rate under an air atmosphere.

As noted by Zhou et al.,[11] thermal degradation of coal makes apparent four stages on the TG-DTG curves which are: low temperature decomposition stage (closely related to inherent moisture release through evaporation), oxygen adsorption stage, homogeneous and heterogeneous combustion stage, and burnout stage. The authors further highlighted that when biomass is blended, the homogenous and heterogenous combustion stage can be split into two distinct stages: the prohomogeneous combustion stage and the proheterogeneous combustion stage. However, they did not manage to determine kinetic parameters for both stages explicitly which this research addressed as well. Within this research, kinetic parameters during the low temperature decomposition were not determined (T < T1). This was supported by the fact that few chemical reactions occurred during this initial stage thus no significant mass loss was experienced.

Tinit represents the temperature at the start of the experiment thus the release of moisture begins accompanied by a slight decrease in mass. Subsequently, Stage 2 is noted by the region with an almost constant or slight mass increase. This corresponds to the physical and chemical adsorption of the oxygen stage (region between T1 and Tig). As highlighted by Wang et al.,[16] the reason why the sample mass remains almost constant or increases at first during Stage 2 is because after oxygen adsorption, oxygen-containing complexes are formed on the fuel particle surface. This process is also accompanied by release of light volatiles (decrease in mass) thus a contradicting phenomenon existing during Stage 2. If the release of light volatiles is more significant than the mass gain due to oxygen adsorption, an overall mass loss will be experienced during Stage 2 thus a decrease of mass in Stage 2 for the 80HC20PS fuel blend.[40]

Of tremendous importance is the point at which ignition occurs symbolized by the region where rapid mass loss commences the TG curves. Within this research, ignition was judged to occur when the mass loss rate was at 1% weight/min as employed by some other authors in their corresponding studies.[27,32] The other method of locating the ignition point which uses tracing of tangents on the TG-DTG curves is too subjective especially when the effect of blending comes into play since some points of inflection became intertwined. The temperature at the ignition point is symbolized by Tig, while the time by tig. The fuel continued to lose weight until the burnout point when volatile and char combustion were judged to have been completed. The burnout point is also denoted by the point at which the mass loss rate is 1% weight/min after the fuel has lost most of its mass. Tb is used to denote the burnout temperature, while tb for the time at burnout.

The prohomogeneous volatile and proheterogeneous combustion zones can be made apparent as distinct stages. During the prohomogeneous volatile combustion zone, Stage 3, hydrocarbon active structures on the fuel surface increase exponentially leading to an increased oxygen adsorption and sample degradation rate. The products, tars, volatiles, CO, and CO2 were then produced in large quantities leading to an increased mass loss rate. Passing into the proheterogeneous combustion zone, volatiles continue to burn while the fixed carbon or char is ignited and combusted. As such, more CO and CO2 gases are produced leading to an increased mass loss rate.[16]Tmax is used to show the temperature at which maximum mass loss rate occurs visualized by a peak on the DTG curve, tmax the time at that point and DTGmax the corresponding mass loss rate. Stages 3 and 4 encompass the most influential reactions related to combustion as most of the mass loss occurs within these regions because of the prohomogeneous and heterogenous combustion reactions. For example, the 80HC20PS sample loses on average 74.6% of its initial weight within this stage. Eventually, as alluded to in the introductory section, the kinetic parameters for each stage were determined exclusively without averaging the parameters for the whole process.[40,41]

Kinetic Analysis by the DAEM

The DAEM method was first used to determine the Ea for the different stages in the combustion process. For a given degree of degradation (α), ln(β/T2) was traced against 1/T to give a linear plot. Using a viable approach proposed by Wang et al.,[32] more emphasis was placed on Stages 3 and 4 with regards to this method. The chosen degrees of degradation of 0.1 up to 0.9 where all within the prohomogeneous and proheterogeneous combustion stage. For example, at a heating rate of 20 °C/min, the prohomogeneous volatile combustion stage began at a degree of degradation of 0.04249 for the 70HC30PS sample, 0.03458 for the 80HC20PS sample, and 0.02843 for the 90HC10PS sample. The proheterogeneous char combustion stage terminated at a degree of degradation of 0.9785 for the 70HC30PS sample, 0.9798 for the 80HC20PS sample, and 0.9821 for the 90HC10PS sample. These lower and upper limits where almost similar for the other heating rates of 12.5 and 5 °C/min. The prohomogeneous combustion stage for the various heating rates had an average degree of degradation upper limit of 0.1877 which led the authors to suggest that the Ea values obtained at degrees of degradation of 0.1 and 0.2 where related to the prohomogeneous combustion stage. The rest of the values where then linked to the proheterogeneous combustion stage.

The values represented in Table were obtained from the plot of ln(β/T2) against 1/T for the samples at 5, 12.5, and 20 °C/min heating rates as shown in Figures 456. Eq shows the rearranged form that was used to determine the Ea values, while eq shows the corresponding equation used for the pre-exponential factor.

Table 6

DAEM Method for Fuel Blends Heated in Air at 5, 12.5, and 20 °C/min

	degree of degradation	70HC30PS			80HC20PS			90HC10PS			100HC
		R2	E (kJ/mol)	A (s–1)	R2	E (kJ/mol)	A (s–1)	R2	E (kJ/mol)	A (s–1)	R2	E (kJ/mol)	A (s–1)
Stage 3	α = 0.1	0.9980	113.02	5.358 × 109	0.9980	105.99	5.64 × 108	0.9980	214.89	6.51 × 1016	0.9980	100.35	1.12 × 106
	α = 0.2	0.9965	99.09	7.832 × 107	0.9965	103.90	2.48 × 107	0.9965	107.89	5.05 × 106	0.9965	85.61	4.71 × 104
Stage 4	α = 0.3	0.9988	117.06	3.361 × 108	0.9988	106.74	4.86 × 106	0.9988	92.15	1.61 × 105	0.9988	75.86	6.56 × 103
	α = 0.4	0.9963	121.62	8.355 × 107	0.9963	104.36	1.35 × 106	0.9963	83.76	2.67 × 104	0.9963	66.90	1.20 × 103
	α = 0.5	0.9910	113.66	7.333 × 106	0.9910	99.08	3.46 × 105	0.9910	75.94	5.72 × 103	0.9910	58.45	2.53 × 102
	α = 0.6	0.9818	105.19	9.792 × 105	0.9818	92.81	9.06 × 104	0.9818	67.87	1.28 × 103	0.9818	50.14	5.65 × 101
	α = 0.7	0.9675	98.27	2.158 × 105	0.9675	83.79	1.68 × 104	0.9675	60.04	3.04 × 102	0.9675	43.58	1.67 × 10
	α = 0.8	0.9540	90.04	4.215 × 104	0.9540	77.08	4.43 × 103	0.9540	54.20	9.66 × 10	0.9540	39.13	6.84 × 100
	α = 0.9	0.9602	81.09	6.713 × 103	0.9602	69.79	9.87 × 102	0.9602	48.97	3.24 × 10	0.9602	36.21	3.48 × 100
			104.34	6.52 × 108		93.73	6.62 × 107		73.85	6.56 × 105		61.80	1.31 × 105

Figure 3

Plot of ln[β/T2] vs 1/T for 70HC30PS at 5, 12.5, and 20 °C/min under an air atmosphere.

Figure 4

Plot of ln[β/T2] vs 1/T for 80HC20PS at 5, 12.5, and 20 °C/min under an air atmosphere.

Figure 5

Plot of ln[β/T2] vs 1/T for 90HC10PS at 5, 12.5, and 20 °C/min under an air atmosphere.

Figure 6

Plot of ln[β/T2] vs 1/T for 100HC at 5, 12.5, and 20 °C/min under an air atmosphere.

The average Ea values for both Stages 3 and 4 were then consolidated as shown in Table for all the fuel samples based on the ln(β/T2) against 1/T plots.

Table 7

DAEM Activation Energy and Pre-Exponential Factor Values for the Fuel Blends Heated in Air

fuel blend	stage	E (kJ/mol)	A (s–1)
100HC	Stage 3	92.98	5.84 × 105
	Stage 4	52.90	1.16 × 103
90HC10PS	Stage 3	107.89	5.05 × 106
	Stage 4	68.99	2.78 × 104
80HC20PS	Stage 3	104.95	2.94 × 108
	Stage 4	90.52	9.53 × 105
70HC30PS	Stage 3	106.05	2.718 × 109
	Stage 4	103.85	6.118 × 107

Figure does show that Stage 3 (provolatile combustion) tends to require more energy to activate with regards to blends containing high content of coal. However, the difference between the energy required to activate Stage 3 vs Stage 4 tends to decrease as the blending ratio increases. One possible explanation might be due to the higher energy required to activate the degradation of hemicellulose and cellulose within biomass as postulated by Wnorowska et al.[38] The other explanation might be due to the effect of diffusion within the boundary layer as rightly explained by Sarroza et al.[42] Diffusion of oxygen toward the char particle is hindered by a volatile cloud formed during devolatilization. Consequently, the Ea required to combust a char particle becomes higher whenever high volatile substances are involved. However, it is very important to understand that in a volatile free environment, biomass char is considered more reactive than coal char as investigated by Al-Qayim et al.[43] In agreement, the authors recorded an increase of 43.9% from 72.94 to 104.95 kJ/mol (averaged Stages 3 and 4) in Ea as more PS was introduced.

Figure 7

Plot of Ea vs blending ratio.

Figure does demonstrate how Ea varies with degree of conversion for the different fuel samples. Both 100HC and 90HC10PS samples show a clear progression of decreasing Ea as a function of degree of conversion. The 80HC20PS sample then shows a quasi-activation energy between α = 0.1 and 0.3, which is then exaggerated by the 70HC30PS sample at α = 0.2 with a drop in Ea before increasing and later dropping gradually after α = 0.4. Analysis of Figure alongside Figure highlights how the region between α = 0.1 and 0.3 falls within the prohomogeneous combustion zone for the 80HC20PS and 70HC30PS samples. As such it makes sense to note that the type of volatiles released from biomass influence combustion progression heavily for any blending greater than the 80HC20PS mass ratio. This can also be seen by the plot in Figure , which is generally expected to have a linear gradient to demonstrate a kinetic compensation effect as discussed by Chen et al.[10] Kinetic compensation is generally expected for most heterogenous-based chemical reactions as experienced within this research.[44] As such a compromise between blending ratios and benefits can be obtained from the 80HC20PS sample. Figure compares the behavior of previous studies with the current one with respect to Ea and conversion degree for coal samples. Mureddu et al.[12] during their experiments with bituminous South African coal, which has properties very close to the bituminous coal under test, obtained slightly lower Ea. The average Ea of South African coal was 59.47 kJ/mol while that of the coal under test was 61.80 kJ/mol. The slight difference might be due to the heating rates employed by Mureddu et al.[12] (10, 20, 30, 40, and 50 °C/min heating rates) as well as the modeling method used, Kissinger–Akahira–Sunose (KAS). However, as supported by other authors that used the KAS method with respect to coal, the Ea associated with Stages 3 and 4 is around 80–150 kJ/mol while that associated with biomass is around 60–193 kJ/mol.[31,35,36] Wang et al.[27] also demonstrated how coal containing blends have an Ea between 85 and 143 kJ/mol with regards to the combined Stages 3 and 4.

Figure 8

Plot of Ea vs degree of conversion.

Figure 9

Plot of ln(A) vs activation energy.

Figure 10

Plot of activation energy comparison vs degree of conversion of Hwange coal and South African coal.

Conclusions

Through experimental work coupled with modeling techniques, the kinetic parameters of HC and PS blends were determined with success. The research gap existent due to the need of having correct combustion parameters necessary for optimum operation of most boilers that are moving toward greener energy was addressed within this research. Experimental work was necessary so as to generate boundary conditions that can be used for further optimization of combustion boilers. This was mainly because no linear relation could be deduced that could link sample blending proportions to expected kinetic parameters. In conclusion:

The higher volatile composition within PS was responsible for a decrease in ignition temperature from 457.70 to 265.76 °C as the mass proportion was increased from 0 to 30% for a heating rate of 20 °C/min. The biochar obtained from PS was deduced to have catalyzed the decrease in burnout temperature as well by 14.64% from 820.05 to 699.97 °C. The DTG curve developed two peaks as soon as PS was blended with the first peak being linked to homogenous volatile combustion while the second peak was linked to heterogenous char combustion.

The kinetic parameters that were evaluated using the DAEM produced no linear trends as the PS proportion was increased from 0 to 30%. The influential homogenous volatile combustion produced an increasing trend for activation energy (Ea) with an increased PS mass ratio (100HCto 70HC30PS) from 92.98 to 106.05 kJ/mol. The heterogeneous combustion stage also produced an increasing trend from 52.90 to 103.85 kJ/mol. Similarly, the pre-exponential factor increased with blending for both homogenous and heterogenous combustion from 5.84 × 105 to 2.72 × 109 s–1 and 1.16 × 103 to 6.12 × 107 s–1, respectively.

Good kinetic compensation is obtained for the 100HC and 90HC10PS samples guiding the authors to suggest an optimum blending ratio of 80HC20PS when all the appropriate parameters are taken into account. This blending ratio guaranteed a large change in Ea which symbolized maximum influence of PS at reduced blending ratios. This is particularly important for cofiring facilities that do not need to change most of their operating conditions when they cater for biomass substitution.

In summary, the necessary boundary conditions related to cocombustion of HC and PS blends were evaluated at different blending ratios resulting in parameters for each combustion stage, namely, devolatilization, volatile combustion, and char combustion.