Prediction of Lignite Ash Melting Behavior from Northwest Greece Based on Its Mineralogical Composition

Abstract

The aim of this study is to predict the ash fusion temperatures of the lignite ash produced in Western Macedonia, Greece, by their composition. The lignite mined in northwest Greece feeds the power plants of Agios Dimitrios, Kardia, Ptolemais, Amyntaio, and Meliti. An extensive number of samples, which were collected by the feeders of power plants during a 10-year period, were investigated. All lignite ashes were mineralogical and chemically quantitatively analyzed by XRD and XRF, respectively. Using a heating microscope, the ash fusion temperatures of the ashes were identified. According to their chemical composition, ashes can be characterized as calcareous. Indices based on the chemical composition showed that, qualitatively, the tendencies of slagging and/or fouling were found to vary mainly between medium to high. For a quantitative estimation, correlations were identified between the quantitative mineralogical composition and the ash fusion temperatures using regression analysis. The whole study focused on creating a model for the prediction of lignite behavior during combustion in power plants. The finest models achieved a mean adjusted regression coefficient of around 0.87, while the accuracy, according to root mean square errors, was less than 40 °C.

1. Introduction

During the last decade, coal has played a vital role in energy production worldwide. Lignite, a low-rank coal that is mined in Greece, constitutes the major domestic energy source, but its use has decreased in the last few years due to European regulations promoting a transition to a post-lignite era. Although coal (lignite for Greece and some other countries worldwide) is a low-cost energy source, the way it is used for energy production creates environmental problems. For these problems, mainly pollution, there have been attempts made to reduce its use by improving exhaust emissions techniques and installing sophisticated filters. Lignite featured in over 40% of the power generation in 2015, but, currently, it has seen a significant decrease in Greece’s energy mix. The main energy production resources are now renewable energy (solar, wind, and waterfall) and natural gas. Meanwhile, though lignite was used up to 12% in 2023, it was mostly used as a backup system with a contribution between 1 to 8% depending on the demands and the production cost of renewable energy resources. Despite the reduction in coal production in Greece, worldwide coal use remains a crucial strategic energy source due to its reliable supply and manageable cost [1,2,3].

The lignite mined in the Ptolemais–Amyntaio area is used to supply five nearby power plant stations with a total installed capacity of 4290 MW (Agios Dimitrios 1595 MW, Kardia 1105 MW, Ptolemais 660 MW, Amyntaio 600 MW, and Meliti 330 MW). Currently, the power plant of Ptolemais is the main power plant station, with Meliti and Agios Dimitrios as backup systems that are operated according to energy production needs. All power plant stations employ pulverized coal-fired boiler combustion technology [1,2]. The lignite that originates from northwest Greece has a low calorific value with a high ash content. There is significant variability in the quality of the fuel, which sometimes fails to meet the specifications required by the power plant. Nevertheless, the utilization of inferior-quality fuels for power plant operations leads to a reduction in cycle efficiency, thereby causing a considerable detrimental impact on CO₂ emissions and the cost of electricity produced. Consequently, the optimal operation of power plants at maximum efficiency serves to mitigate gaseous emissions and enhance environmental performance [4,5,6].

Although coal has been a vital component of energy production, there are always some significant problems that arise due to the generation of substantial quantities of coal combustion products (fly ash) and its composition. The large amount of ash produced has been associated with environmental problems, while the composition related to serious deposition problems causes ash buildup in boilers. The utilization of coal may give rise to technological and environmental issues as a consequence of the minerals present in the coal [7,8,9,10]. Furthermore, the design and mechanism of operation influence the mineral transformations that occur during combustion, as well as the characteristics of combustion byproducts. The vast majority of minerals present in feed coal either decompose or undergo thermal alteration during combustion [11,12,13].

The issues encountered by boilers during the combustion of lignite, such as slagging or fouling, have been recognized as one of the most significant operational problems associated with pulverized coal combustion. Slagging is the deposit formation that occurs on the heat transfer surfaces of energy conversion equipment, while fouling is the deposit formation that occurs on the cooler surfaces of energy conversion equipment. The formation of these deposits (slagging and/or fouling) on the walls and convective pass tubes can cause serious problems in heat transfer and reduce the overall efficiency process [14,15,16]. These problems arise due to varying coal composition. To avoid such issues, a number of power stations utilize blended coal to achieve the desired specifications, thus reducing the occurrence of slagging and fouling [17,18]. However, this practice may not result in reductions in these problems if the theoretically designed coal and the blended one do not behave similarly. The adhesion of ash particles is an important factor of the slagging and fouling processes. The most significant factors influencing the adhesion of ash particles, as identified to date, are their chemical composition and the variability in the constituents responsible for their formation. A considerable number of researchers have investigated the composition of ash and the behavior of minerals in coal ash. However, a significant challenge remains in fully understanding the fusion parameters and the behavior of blended coal ash and mineral matter [11,12,13,14,16,19,20].

There have been indices found based on ash chemical composition [15,16,21], indicating the tendency for slagging and/or fouling problems. The most widely used indices with their formulas and slagging or fouling propensity are shown in

Table 1. Slagging/fouling indices, formulas, and propensity values for coal ashes.

Index	Formula	Slagging/Fouling Propensity
		Low	Medium	High	Severe
Base to acid oxide ratio (Β/A)	${\displaystyle \frac{\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3+\mathrm{C}\mathrm{a}\mathrm{O}+\mathrm{M}\mathrm{g}\mathrm{O}+\mathrm{N}{\mathrm{a}}_2\mathrm{O}+{\mathrm{K}}_2\mathrm{O}}{\mathrm{S}\mathrm{i}{\mathrm{O}}_2+\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3+\mathrm{T}\mathrm{i}{\mathrm{O}}_2}}$	<0.5	0.5–1.0	1.0–1.75	>1.75
Silica ratio (SR)	${\displaystyle \frac{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}{\mathrm{S}i{\mathrm{O}}_2+\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3+\mathrm{C}\mathrm{a}\mathrm{O}+\mathrm{M}\mathrm{g}\mathrm{O}}}$	>0.72	0.65–0.72		<0.65
Ratio SiO2/Al2O3	SiO2/Al2O3	<1.4	1.4–2.8	>2.8
Ratio Fe2O3/CaO	Fe2O3/CaO	<0.30 or >3.00	0.31–3.00
Slagging factor (SF)	Β/A × Sdry	<0.6	0.6–2.0	2.0–2.6	>2.6
Fouling factor (FF)	B/A × Na2O	<0.2	0.2–0.5	0.5–1.0	>1.0
Alkalinity index (A)	Na2O + 0.659 K2O	<2.0	2.0–6.0	6.0–8.0	>8.0
Slagging index	${\displaystyle \frac{\left[\right(\max \mathrm{HT})+4\times (\min \mathrm{IDT}\left)\right]}{5}}$	>1343 °C	1232–1343 °C	1149–1232 °C	<1149 °C

. These indices have been empirically identified in brown coal and sub-anthracite from a worldwide range of coal samples. In addition to these indices, efforts have been made to find relationships that can be used to estimate slagging and/or fouling tendencies. Multiple linear regression analysis and neural and neuro-fuzzy systems have been proposed based on ash chemical composition [22,23,24,25,26,27,28,29,30,31,32].

While the indices presented in Table 1 offer valuable indicators of the slagging and fouling tendencies of ash, they are unable to provide an accurate description of the melting behavior. Ash fusion temperatures can be determined by laboratory ash fusion tests. During these tests, specially formed specimens of coal ash were heated, and four characteristic temperatures, known as ash fusion temperatures, were identified. These four temperatures are the initial deformation temperature (IDT), the softening temperature (ST), the hemispherical temperature (HT), and the fluid temperature (FT).

The technique of multiple linear regression analysis has been employed by many researchers to obtain estimations of ash fusion temperatures. The proposed models were based on the composition of ash and/or on slagging/fouling indices [22,23,24,25,31]. Other more sophisticated models have also been proposed based on neural and neuro-fuzzy inference systems [26,27,28,29,30]. The accuracy of regression models used for the prediction of ash fusion temperatures is dependent on the datasets employed in the regression analysis. When the proposed models were tested on samples of other coals from disparate sources, their accuracy was limited [22,27]. The chemical composition of the ash from Greek lignite, mined in the area of Ptolemais–Amyntaio, is characterized by a high calcium content (up to 75%), which is considerably different from the ash composition of coals investigated in the aforementioned studies. Therefore, the use of mineralogy composition would be more accurate due to the minerals that are transformed during combustion. Chemical elements can be found in more minerals following transformations. Consequently, the development of new regression models to predict the ash melting temperatures for Greek lignites is essential, using mineralogy composition [32].

The creation of reliable prediction models requires the establishment of a suitable and sufficient measurement set. The present study proposes a prediction model of ash fusion temperatures based on the mineralogical composition. For this purpose, an extensive number of samples of lignite from Northwest Greece was collected, and their chemical and mineralogical compositions, as well as ash fusion temperatures, were investigated. The correlation of lignite mineralogical composition with ash fusion temperatures was assessed to predict slagging and/or fouling problems in the boilers.

2. Materials and Methods

Lignite samples were collected over a period of 10 years from the mill feeders of the power plants in the Western Macedonia Lignite Centre (Ptolemais–Amyntaio area). Sampling procedures were carried out during various periods. A systematic sampling procedure was conducted over 12 months, mainly in unit I in the Agios Dimitrios power plant station. Specifically, samples were collected every day for a month, as well as the representative monthly sample for a year, from three units (I, II, and IV), from the power plant station in Agios Dimitrios. Also, we collected representative samples over a week or a month at various times over 10 years from the feeders of power plants in Kardia, Ptolemais, Amyntaio, and Meliti.

The lignite samples were collected from mill feeders before entering the power plant burners at the Agios Dimitrios, Kardia, Ptolemais, and Amyntaio power plants. The lignite used to feed these power plant stations was excavated primarily from the South field mine, which is located close to the Agios Dimitrios power plant, the largest lignite power plant in Greece. The same mine was also used to supply the power plant in Kardia and, to a limited extent, the power plant in Ptolemais. Additionally, the Ptolemais power plant was fed from the Main field, while the Kardia power plant was also fed from the Kardia field and the Amyntaio power plant was fed from the Amyntaio field mine. The Meliti power plant was supplied by the Achlada and Vevi lignite mines in the Florina region. Through this sampling procedure, 258 samples of lignite were collected. The ash fusion temperatures, as well as the ash chemical and mineralogical compositions, were determined for all lignite samples.

The sampling procedure was performed to obtain the differentiation of the lignite layers and positions of the feed power plants as mining exploitation is occurring in several different benches and mine faces, so the examined samples can be considered representative of the overall lignite deposit.

For the determination of lignite composition and the ash fusion temperatures, it is necessary to produce the high-temperature ash of lignite in the laboratory. The lignite samples were heated in air in a laboratory kiln from room temperature to 550 °C for 60 min at a uniform heating rate and held at this temperature for 60 min. The samples were then burned to 815 °C ± 10 °C at a rate of 5 °C/min and maintained at this temperature for about 90 min or until reaching constant weight [33,34].

All ashes were chemically analyzed using an X-Ray Fluorescence Energy Dispersive Spectrometer (ED-XRF), BrukerAXS S2-Ranger (Bruker corporation, Karlsruhe, Germany). The measuring conditions were 40 kV, an Al filter (500 μm) for heavy elements (Fe, Mn, Ti, Ca, and K) and 20 kV, and no filter for light elements (P, Si, Al, Mg, and Na). The loss of ignition (LOI) was determined by burning samples up to 1050 °C for two hours or until reaching constant weight. The mineralogical composition was identified using an automated BrukerAXS D8-Advance diffractometer (XRD), (Bruker corporation, Karlsruhe, Germany). The radiation was Cu, while scanning ranged from 4 to 70° 2θ, with a step size 0.02° and a 4 s/step measuring time. The qualitative analysis was performed with BrukerAXS Diffrac.EVA version 4.2 software (Bruker corporation, Karlsruhe, Germany) and the Crystallographic Open Database (COD database), while the quantification of the mineralogical composition was performed using Autoquan Seifert software version 2.7 (GE Sensing & Inspection Technologies GmbH, Ahrensburg, Germany). Ash fusion temperatures were determined using a Leitz Wetzlar axial horizontal heating microscope (Ernst Leitz GmbH, Wetzlar, Germany) with a constant rate of 10 °C/min, in oxidizing conditions.

The ash fusion test provided an indication of the softening and melting behavior of coal ash at high temperatures within the boiler. Ash fusion temperatures were determined by heating a specially formed specimen of coal ash in a high-temperature furnace to temperatures up to 1600 °C, in oxidizing conditions. The specimen was formed as a cylinder with a 3 mm height and 3mm diameter. The formed specimen was placed in an electric oven and it was observed by a microscope monitor (Figure 1a) as the temperature increased at a constant rate (~10 °C/min). The separate stages (critical temperatures) can be determined by observing the change in the shape of the specimen, according to DIN51730 [35]. The ash fusion test provides a valuable tool for estimating and controlling the slagging potential of coal.

The separate stages were recorded by indicating the following temperatures (Figure 1b–e):

• Initial deformation temperature (IDT): This is reached when the corners of the molded specimen first become rounded (Figure 1b).
• Softening (sphere) temperature (ST): This is achieved when the top of the molded specimen takes on a spherical shape, where the width (R_w) is almost the same as the height (R_h) (Figure 1c).
• Hemisphere temperature (HT): This is identified when the entire molded specimen takes on a hemispherical shape with a height (r) that is almost half of the width (Figure 1d).
• Fluid temperature (FT): This is determined when the molten ash collapses into a flattened button shape on the furnace floor, where the height is almost 1/3 of the height in the hemisphere temperature (Figure 1e).

It is important to note that the initial deformation temperature is often difficult to record with precision due to the difficulty of observing the initial changes that occur. As a result, its identification is more prone to error compared to temperatures in the other three stages (softening, hemisphere, and fluid temperatures), which are more clearly defined and easily observable.

Regression analysis represents a statistical technique for the investigation of the relationship between variables. Regression models are used for a range of purposes, including data description, parameter estimation, or the prediction and estimation of variables. In more detail, regression analysis assists in understanding how the typical value of the dependent variable changes when any of the independent variables are varied. The most widely used of all statistical techniques is linear regression analysis, which simply can be characterized as a correlation between the dependent and one or more independent variables. Model coefficients are estimated using the method of least squares. It is typically assumed that the model’s prediction errors are independently and identically normally distributed.

One of the more important characteristics that are used to check if the variables that have been chosen are the proper ones is the correlation coefficient. A Pearson correlation coefficient, r, is a number between −1 and +1, which measures the strength of the linear relationship between two variables. The closer the correlation is to −1 or +1, the stronger the relationship. When r = 1, there is a perfect correlation. The sign of the correlation indicates the direction of the relationship. A positive value means that the Y variable increases, as the X variable does. A negative value means that, as the Y variable increases, the X variable decreases. A value of 0 indicates that there is no correlation between the two variables, while 0 < r ≤ 0.19 is a very weak correlation, 0.2 ≤ r ≤ 0.39 is a weak correlation, 0.4 ≤ r ≤ 0.59 is a moderate correlation, 0.6 ≤ r ≤ 0.79 is a strong correlation, and 0.8 ≤ r < 1 is a very strong correlation [36,37,38].

The models that are usually used to express linear regression analysis are single or multiple. Multiple linear regression analysis is a correlation of a dependent variable with more than one independent variable (Equation (1)), while single linear regression analysis is simply expressed as the correlation between a dependent variable and an independent variable.

Y = b₀ + b₁X₁ + b₂X₂ + b₃X₃ + … + b_kX_k + ε,

(1)

where the subscript i = 0, 1, …, k represents the i^th observation in the data sample, b_i is an unknown model coefficient, X_i is the i^th predictor variable, and ε is a random deviation.

In this study, the multiple linear regression analysis was used to develop correlations between the chemical or mineralogical compositions of various lignite ashes and their fusion temperatures. The prediction models were created using the multiple regression model selection procedure.

The multiple regression model selection procedure is designed to construct a statistical model presenting the quantitative impact of two or more independent variables, X, on a dependent variable, Y. The procedure includes an option to perform a stepwise regression, where a subset of X variables is selected. The fitted model may be used to make predictions, including confidence limits and/or prediction limits. Residuals may also be plotted and influential observations identified. The stepwise procedure to select the variables was used (regression model selection), taking into account the less-independent variables in combination with the adjusted correlation coefficient (R_adj) (Equation (2)):

$${\mathrm{R}}_{\mathrm{adj}}^2=100\left(1-\left({\displaystyle \frac{\mathrm{n}-1}{\mathrm{n}-\mathrm{p}-1}}\right){\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\widehat{\mathrm{y}}}_{\mathrm{i}}\right)}^2}{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\overline{\mathrm{y}}}_{\mathrm{i}}\right)}^2}}\right)\%,$$

(2)

where y_i is the observed value of Y, ${\overline{\mathrm{y}}}_{\mathrm{i}}$ is the predicted value from the fitted model, n is the number of observations, and p is the number of independent variables included in the model [36].

The accuracy of the predicted values is expressed by the root mean squared error (RMSE) (Equation (3)). This is an estimate of the variance in the deviations from the fitted model, describing the fitting of the model between the observed and predicted values.

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\widehat{\mathrm{y}}}_{\mathrm{i}}\right)}^2}{\mathrm{n}-\mathrm{p}-1}}}.$$

(3)

3. Results and Discussion

For all high-temperature lignite ash samples, we determined the chemical composition, mineralogical composition, and ash fusion temperature. The chemical composition of the lignite ash from North Greece indicated that it is calcareous and can be classified as Class C according to ASTM C618 or calcareous W according to EN 197-1 [39,40]. The mineralogical quantitative composition also identified that ashes are rich in calcareous minerals. Ash fusion temperatures showed the tendency of slagging and/or fouling varied from low to severe, with the majority of samples being medium to high.

3.1. Characterization of Lignite Ashes

The average and the standard deviation of chemical and mineralogical compositions, as well as ash fusion temperatures, of the lignite ash samples are presented in

Table 2. Average and standard deviations of the ash chemical composition, mineralogical composition, and ash fusion temperature of 258 lignite ash samples collected from North Greece.

Ash Chemical Composition (% w/w)		Ash Mineralogical Composition (% w/w)		Ash Fusion Temperatures (°C)
SiO2	29.99 ± 6.65	Amorphous	23.2 ± 6.5	Initial Deformation
Al2O3	12.52 ± 3.24	Anhydrite	8.7 ± 1.6	1223 ± 68
Fe2O3	6.27 ± 1.45	Gehlenite	6.5 ± 3.2	Softening
CaO	34.36 ± 9.43	C2S	8.8 ± 2.3	1278 ± 85
MgO	4.57 ± 1.12	Brownmillerite	8.4 ± 3.5	Hemisphere
SO3	6.28 ± 2.18	Lime/Portlandite	10.6 ± 4.6	1303 ± 94
Na2O	0.64 ± 0.37	Calcite	6.9 ± 4.6	Fluid
K2O	0.78 ± 0.29	Hematite	2.1 ± 0.2	1326 ± 92
TiO2	0.43 ± 0.19	Merwinite	2.1 ± 0.7
MnO	0.06 ± 0.01	Muscovite	5.5 ± 1.1
P2O5	0.38 ± 0.15	Periclase	1.8 ± 0.1
LOI	3.79 ± 2.32	Feldspar	8.9 ± 2.7
		Quartz	8.0 ± 1.2
		Talc	9.3 ± 4.5

. From the results of the chemical composition, we observed a high presence of CaO and SiO₂, while Al₂O₃, Fe₂O₃, SO₃, and MgO were detected in significant percentages. The mineralogical quantitative composition also identified that ashes are rich in calcareous minerals, such as lime/portlandite, calcite, gehlenite, C2S, anhydrite, and brownmillerite, while quartz, feldspar, muscovite, talc, and the amorphous phase are also noteworthy. The ash fusion temperatures varied, having a standard deviation between 68 and 94 °C.

The tendency of slagging and/or fouling according to the chemical composition was examined by the indices presented in Table 1, provided by the literature [6,7,8], while the results are shown in

Table 3. Slagging and fouling indices and resulting tendencies of the 258 examined lignite ash samples.

Index	Mean	Range	Mean Slagging–Fouling Tendency	Range of Slagging-Fouling Propensity
Base to acid oxides ratio (Β/A)	1.30	0.40–4.76	High	Low to severe
Silica ratio (SR)	0.40	0.02–0.66	Severe	Medium to severe
SiO2/Al2O3 ratio	2.53	1.02–11.24	Medium	Medium to high
Fe2O3/CaO ratio	0.20	0.01–0.72	Low	Low to severe
Slagging factor (SF)	3.02	0.09–12.65	Severe	Low to severe
Fouling factor (FF)	0.73	0.01–6.99	High	Low to severe
Alkalinity index (A)	1.15	0.27–3.52	Low	Low to medium
Slagging Index (SI)	1239	1160–1597	Medium	Low to High

.

By using indices reported in the literature based on the chemical composition [15,16,21], similar to the determined ash fusion temperatures, a qualitative prediction of the slagging and/or fouling tendencies is achieved.

From the determined ash fusion temperatures, we showed the tendency of slagging and/or fouling to vary for most samples from medium to high. Many samples show a high to severe tendency of melting behavior. The average tendency is low for the index of the Fe₂O₃/CaO ratio and Alkalinity index (A), while it was medium for theSiO₂/Al₂O₃ ratio and slagging index. The base to acid oxides ratio, similar to the fouling factor, presented a high tendency, while the silica ratio and slagging factor were severe. Similar results were determined by using indices reported in the literature based on the chemical composition [6,7,8], providing a qualitative prediction of the slagging and/or fouling tendencies.

The quantitative tendency was determined by the ash fusion temperatures, which showed that melting behavior starts at the softening temperature, at about 1270–1300 °C. It should be mentioned that the lignite ashes from the Ptolemais–Amyntaio area have a lower melting temperature (lower ash fusion temperature) due to the presence of a high percentage of calcium (CaO) or calcium minerals compared to the coal ashes containing silicon (SiO₂) or silicate minerals [31,37].

3.2. Correlation of Ash Composition with Ash Fusion Temperatures

The results of the chemical and mineralogical compositions similar to ash fusion temperatures were correlated using a simple regression analysis. In more detail, ash fusion temperatures were correlated with the ash chemical composition (

Table 4. Pearson correlation coefficients (r) for ash fusion temperatures and chemical composition of the 258 lignite ash samples.

	Initial Deformation Temperature	Softening Temperature	Hemisphere Temperature	Fluid Temperature
SiO2	−0.65	−0.77	−0.79	−0.77
Al2O3	−0.26	−0.37	−0.39	−0.42
Fe2O3	−0.25	−0.23	−0.20	−0.19
CaO	0.73	0.82	0.80	0.80
MgO	−0.22	−0.26	−0.24	−0.29
SO3	−0.03	−0.07	−0.04	−0.05
Na2O	−0.28	−0.30	−0.33	−0.29
K2O	−0.40	−0.41	−0.39	−0.39
TiO2	−0.49	−0.49	−0.45	−0.38
P2O5	0.05	−0.07	−0.04	−0.08
LOI	−0.31	−0.09	−0.01	0.08

) as well as the mineralogical composition (

Table 5. Pearson correlation coefficients (r) for ash fusion temperatures and mineralogical compositions of the 258 lignite ash samples.

	Initial Deformation Temperature	Softening Temperature	Hemisphere Temperature	Fluid Temperature
Amorphous	−0.47	−0.58	−0.59	−0.59
Anhydrite	−0.46	−0.54	−0.50	−0.51
Gehlenite	−0.04	−0.14	−0.20	−0.19
C2S	0.73	0.81	0.79	0.78
Brownmillerite	0.72	0.81	0.79	0.78
Lime/portlandite	0.73	0.82	0.80	0.80
Calcite	0.52	0.48	0.48	0.40
Hematite	−0.25	−0.23	−0.20	−0.19
Merwinite	0.60	0.63	0.59	0.58
Muscovite	−0.04	−0.17	−0.21	−0.25
Periclase	−0.20	−0.23	−0.21	−0.25
Feldspar	−0.50	−0.61	−0.62	−0.64
Quartz	−0.65	−0.77	−0.79	−0.77
Talc	−0.33	−0.11	−0.01	0.06

), and the Pearson correlation coefficients were calculated.

The correlation of the chemical composition with the ash fusion temperatures (Table 4) determined a positive strong relation between CaO and the initial deformation temperature, while there was a very strong positive relation between the other three temperatures with CaO (r ≥ 0.80). On the other hand, the correlation of SiO₂ with ash fusion temperatures showed a negative strong relation (r = −0.65 to r = −0.79). Al₂O₃, F₂O₃, and MgO showed a negative weak relation, while Na₂O and K₂O showed a negative moderate correlation. The other elements showed a very weak relation, positive or negative (r ≤ 0.19). From these results, it is obvious that the ash fusion temperatures depend on the CaO content and have a negative dependence on SiO₂ content. Fe₂O₃ andvolatile elements (Na₂O and K₂O), have a weak to moderate relation to the melting behavior of lignite ashes. The results are in agreement with previous studies of lignite samples from Western Macedonia [31,32,41]. Comparing the results with ashes from different regions and different coal qualities, a variation can be observed. The lignite ashes studied in the present work exhibit lower characteristic temperatures, due to the increased presence of calcium oxide. In contrast, the coal from other regions with high silicon and aluminum oxide concentrations displayed higher temperatures [23,42].

From all the simple regression correlations of minerals with ash fusion temperatures (Table 5), we observed that most calcareous minerals (C2S, brownmillerite, lime/portlandite, calcite, and merwinite) have moderate to strong or almost very strong positive relations (r = 0.40 to r = 0.82), especially for the softening temperature, while quartz, feldspar, or amorphous phases have a moderate to strong negative relation (r = −0.50 to r = −0.79). Also, it was observed that anhydrite has a moderate negative relation (r = −0.46 to r = −0.54), while gehlenite, hematite, muscovite, and talc mainly have a very weak relation (r ≤ 0.25). The results obtained from the simple correlations of minerals with ash fusion temperatures show how lignite ashes behave during combustion due to a mixed chemical formula. It is more obvious that calcareous minerals are associated with fusion temperatures, while minerals with volatile elements or silicates and amorphous phases decrease the temperature (negative correlation).

3.3. Multiple Linear Regression Models

The simple regression correlations showed that the chemical composition of calcium (CaO) in calcareous minerals (C2S, brownmillerite, lime/portlandite, calcite, and merwinite) leads to higher ash fusion temperatures, while silica (SiO₂) and silicate minerals (quartz and feldspar) minimize the ash fusion temperature. Based on these results, several multiple linear regression models were developed using these oxides or minerals in conjunction with regression model selection. The steps were to increase gradually the number of independent variables (chemical or mineralogical ash composition) for the prediction of the ash fusion temperature (dependent variable). We assessed various correlations for the chemical or mineralogical composition with ash fusion temperatures, using either simple or multiple linear regression analysis for the chemical composition or quantitative mineralogical composition and the ash fusion temperatures. For all the combinations that were performed, the adjusted regression coefficient and root mean square error were determined. We also developed models that using multiple regression model selection (stepwise regression method). Finally, the best prediction model for each ash fusion temperature was selected based on the value of the minimized root mean squared error (RMSE) and the maximized adjusted regression coefficient (R_adj).

The optimal regression model for the prediction of the softening temperature (ST) from the chemical composition was presented with five independent variables (Figure 2). Similar results were estimated for the other temperatures (initial deformation, hemisphere, and fluid).

The regression equations, adjusted correlation coefficients, and root mean squared errors that were produced by the correlation of ash fusion temperatures as dependent variables with the chemical composition as the independent variable are presented in

Table 6. Prediction models of ash fusion temperatures based on the chemical composition.

Temperature (°C)	Equation	Radj	RMSE (°C)
Initial deformation temperature (IDT)	IDT = 1247 − 2.03 × SiO2 + 2.83 × CaO − 24.61 × Na2O − 44.53 × TiO2 − 7.69 × LOI	0.80	34
Softening temperature (ST)	ST = 1186 − 2.36 × SiO2 + 2.25 × Al2O3 + 5.29 × CaO − 27.66 × Na2O − 74.86 × TiO2	0.86	38
Hemisphere temperature (HT)	HT = 1451 − 5.50 × SiO2 + 3.09 × CaO − 6.62 × MgO − 39.64 × Na2O − 85.31 × TiO2	0.85	44
Fluid temperature (FT)	FT = 1493 − 6.01 × SiO2 + 3.26 × CaO − 12.49 × MgO − 36.07 × Na2O − 47.34 × TiO2	0.83	48

, while the graphical presentation of the correlation between the predicted to the observed values for all the critical temperatures are presented in Figure 3.

It can be observed that the adjusted correlation coefficient is very strong (R_adj ≥ 0.80) for all the critical temperatures. A higher correlation was found for the softening temperature (R_adj = 0.86), while the accuracy was 38 °C.

To detect how the minerals are affected by ash fusion temperatures, we assessed correlations using multiple linear regression analyses for the quantitative mineralogical composition and the ash fusion temperatures. These correlations, assessed using the mineralogical composition, allowed the establishment of quantitative relationships for the determination of ash fusion temperatures, especially for the softening and hemisphere temperatures, as well as of the approximate values of the initial deformation and fluid temperatures of the ashes. Likewise, it was shown that, especially the calcareous phases of gehlenite, brownmillerite, lime/portlandite, and calcite, as well as the quartz and amorphous content are relevant for the determination of ash fusion temperatures.

The best correlation was achieved by the regression model based on maximized adjusted regression coefficients (R_adj) and minimized root mean squared error (RMSE) for the prediction of the softening temperature (ST) from the mineralogical composition contains five independent variables, as shown in Figure 4. Similarly, the regression models with predictor variables were estimated for the other temperatures (initial deformation, hemisphere, and fluid). The predictor variables were mainly calcareous, silicate minerals, and amorphous. The adjusted correlation coefficients of the regression models, which were used for the softening temperature, were around R_adj = 0.87, while the accuracy according to the root mean square error was 34 °C. Following a more detailed investigation of the number of independent variables, it was shown that the number varied from four to six predictor variables. For each temperature, we chose the number of independent variables that increased the adjusted correlation coefficient, while minimizing the root mean square error. If there was little variance, the smaller number of variables was preferred.

The regression equations that have a higher adjusted correlation coefficient in conjunction with a low root mean square error, which determine the ash fusion temperatures of lignite ashes, are presented in

Table 7. Prediction models of ash fusion temperatures based on the chemical composition.

Temperature (°C)	Equation	Radj	RMSE (°C)
Initial deformation temperature (IDT)	IDT = 1514 + 7.1 × Gehlenite + 3.5 × Calcite + 1.7 × Feldspar − 42.5 × Quartz − 4.3 × Talc	0.84	27
Softening temperature (ST)	ST = 1020 − 42.8 × Brownmillerite + 49.2 × Lime/Portlandite + 3.2 × Calcite + 5.0 × Muscovite + 5.4 × Feldspar	0.87	34
Hemisphere temperature (HT)	HT = 1148 − 2.4 × Amorphous − 41.4 × Brownmillerite + 53.6 × Lime/Portlandite + 3.4 × Calcite − 41.3 × Merwinite + 6.0 × Feldspar	0.86	37
Fluid temperature (FT)	FT = 1565 − 2.4 × Amorphous + 22.1 × Lime/Portlandite + 2.1 × Calcite − 66.8 × Merwinite − 159.5 × Periclase	0.84	40

. Also, the values of the adjusted correlation coefficient (R_adj) and the root mean square error (RMSE) are presented. Graphic presentations of the predicted versus the observed ash fusion temperatures are presented in Figure 5.

The softening temperature (ST) appeared to have the higher adjusted correlation coefficient (R_adj = 0.87) and the hemisphere temperature (HT) was a bit lower (R_adj = 0.86), while the root mean square errors were RMSE = 34 °C and RMSE = 37 °C, respectively. For the initial deformation temperature, as well as the fluid temperature, the adjusted correlation coefficient was determined to be R_adj = 0.84, while the mean square errors (RMSEs) were 27 °C and 40 °C, respectively.

The correlation coefficients for both chemical and mineralogical compositions as independent variables were similar with slightly better results when we used the mineralogical composition. On the other hand, the root mean square error gave better results due to the smaller temperature errors in the prediction models. Although the correlation coefficients differed in the second decimal, the results of the root mean square error were better according to the difference up to 10 °C.

The model that determines the tendency of slagging and/or fouling by mineralogical composition could be more accurate than the chemical composition of the ashes. This could be because it considers the mixture of chemical elements in minerals or in the amorphous phase and not the individual chemical elements expressed as oxides.

The results are in agreement with previous studies in the literature. A distinction is made, as the presence of calcium lowers the characteristic temperatures, in contrast to the silica-rich ashes that show increased temperatures. Volatile elements, such as K, Na, as well as iron do not seem to affect this.

4. Conclusions

The chemical composition of lignite from North Greece was characterized by the high content of calcium, while the mineralogical composition showed that all ashes were rich in calcareous minerals and amorphous phase. The slagging and/or fouling tendency was indicated to be medium to high.

Compared to ash fusion temperatures from other coal ashes, it is observed that the lignite ash from the Ptolemais–Amyntaio area has lower temperatures due to a high presence of calcium, while ashes from other areas rich in silicon and aluminum present higher characteristic temperatures. As for the volatile elements, such as potassium, sodium, as well as iron, they do not seem to be affected.

The correlation of ash lignite chemical and mineralogical compositions with ash fusion temperatures led to quantitatively estimating the tendency of slagging and/or fouling, determining the ash fusion temperatures.

Based on the quantification of the mineralogical composition of the lignite ashes, it is possible, mainly through multiple linear regression models, to determine the critical ash fusion temperatures (initial deformation, softening, hemisphere, and fluid). The adjusted regression coefficients were in the range of 0.84–0.87, while the accuracy according to the root mean square error was around 27 to 40 °C. Likewise, it was shown that, especially the calcareous phases of gehlenite, brownmillerite, lime/portlandite, and calcite, as well as the quartz and amorphous content, are relevant for the determination of ash fusion temperatures.

The correlation of the ash chemical composition also led to estimations of the melting behavior, with a similar degree of correlation, using the mineral composition. The models that were created using the mineralogical composition can be more accurate than those with using chemical compositions or indices using the ash chemical composition.

It can be observed that the prediction error of all models does not exceed 50 °C, which is the maximum acceptable temperature for ash fusion according to the DIN 51730 standard [35].

The optimal model that could predict the melting behavior or the temperature at which the sample start to melt (softening temperature) achieved a mean adjusted regression coefficient (R_adj) of 0.87 and a prediction error up to 34 °C.