Estimation of Carbon Content in High-Ash Coal Using Mid-Infrared Fourier-Transform Infrared Spectroscopy

: The carbon content of different types of coal determines its utility in industries and thermal power generation. The most popular and widely used is the conventional method (ultimate analysis) to determine coal’s carbon content (C, wt.%), along with H, N, and S. In the present study, the authors attempted to analyze the carbon content (C in %) in coals via data from Fourier-transform infrared (FTIR) spectroscopy, which can be a promising alternative. As a reference, the carbon content in the coal samples, referred to as C CHNS (in wt. %), was determined from the ultimate analysis. The mid-infrared FTIR spectroscopic data were used to investigate the response of functional groups associated with carbon or its compounds, which were used to model and estimate the carbon content in coal samples (referred to as C FTIR , in wt %). FTIR spectral signatures were utilized in specific zones (between wavenumbers 4000 and 400 cm −1 ) from a total of 18 coal samples from the Jo-hilla coalfield, Umaria district, Madhya Pradesh, India. These 18 coal samples were used to produce 126 Coal+KBr pellets (at seven known dilution factors for each coal sample), and the spectral response (absorbance) from each pellet was recorded. For model development and validation, the training set and test set were formed using a 17:1 split (K-fold cross validation). The carbon content in the coal samples was modeled using the training set data by applying the piecewise linear regression method employing quasi-Newton (QN) with a breakpoint and least squares loss function. The model was validated using an independent test set. A pairwise comparison of estimates of carbon in the laboratory from the CHNS analyzer (C CHNS ) and modeled carbon from FTIR data (C FTIR ) exhibited a good correlation, relatively low error, and bias (coefficient of determination (R 2 ) up to 0.93, RMSE of 23.71 %, and MBE of −0.52 %). Further, the significance tests for the mean and variance using the two-tailed t-test and F-test showed that no significant difference occurred between the pair of observed C CHNS and the model’s estimated C FTIR . For high-ash coals from the Johilla coalfield, the model presented here using mid-infrared FTIR spectroscopy data performs well. Thus, FTIR can potentially serve as an important method for quickly determining the carbon content of high-ash coals from various basins and can potentially be extended to soil and shale samples.


Introduction
Coal is an inhomogeneous, naturally occurring, non-renewable energy source and combustible organic rock that contains carbon (C), hydrogen (H), oxygen (O), nitrogen (N), sulfur (S), and various other minor and trace elements. Carbon is a key indicator of coal quality as it constitutes most of the organic matter in coal and is utilized to promptly estimate the coal calorific value [1].
Since the first industrial revolution in the 1800s, coal has been one of the earliest fossil fuels used by humans. The carbon content of coal (organic and inorganic) determines the suitability of its use in different industrial applications. It has been the main source of energy generation because of its abundance and cost. It is used for power and electricity generation and many other industrial uses, like as an essential additive in iron and steel, brickmaking, and the cement industry. Activated carbon, used in filters for water and air purification systems; carbon fiber, used in the construction of automobiles and aircraft; and silicon metal for lubricants are a few products made using coal and coal by-products. Coal accounts for nearly 30% of all global fossil fuel consumption [2].
In India, coal is the sole natural resource and fossil fuel that is readily available throughout the country. Indian coal is mostly found in the Lower Gondwana and Tertiary basins in the central and eastern parts of the country, predominantly with high ash content and low calorific values. Coal remains indispensable worldwide due to the expanding population causing increased demand for electricity and power, especially in emerging nations that lack access to modern, clean energy [3].
The carbon and sulfur content in coal impact the combustion attributes of the coal, pollutant emissions, and also influence coal pricing [4]. The precise determination of the carbon content in coal plays a crucial role in establishing the chemical characterization of fuel commodities. It is essential to substantially improve combustion efficiency and the efficient utilization of equipment, reduce environmental impact, and make informed judgments regarding the appropriateness of coal [4,5]. It also helps to obtain optimal boiler control in the operation of coal-fired thermal power plants. Therefore, it is imperative to create a quick and accurate method for quantifying carbon in coal.
During the combustion process, the generation of carbon dioxide (CO2) poses a significant threat to human health and the global environment [6]. Countries such as China, India, Japan, Russia, the USA, and Australia, which have established coal power industries, consistently report elevated levels of CO2 pollution each year [7]. Coal combustion accounts for about 40% of the world's СО2 emissions, enhancing the greenhouse effect, and is considered one of the major factors causing climate change [8]. The CO2 along with particulate matter (PM 2.5) affect the air quality. It can adversely affect human health, leading to lung and cardiovascular diseases like asthma and a poor life expectancy [9,10].
In recent years, there has been a significant rise in the use of instrumental analytical techniques to analyze coal and coal products. These methods have become widely accepted as standardized test methods for the analysis of coal by national and international organizations. The ultimate analyzer commonly measures the weight percentage of C, H, N, S, and O (by difference) in a coal sample. The instantaneous examination of coal's elemental composition is a major requirement in industrial operations. Different firms and laboratories worldwide have employed several test methods for rapidly estimating the carbon content of coal, but these methods have not been established as standardized test methods. Many research works focused on the ultimate analysis and proximate analysis of coal, targeting the carbon content in coal. The use of non-linear correlations has been suggested for calculating the elemental composition of coal [11]. These correlations were developed based on a large and diverse dataset, which included coals of four different ranks and had a wide range of proximate and ultimate analyses. Correlations were also developed using maximum likelihood estimation (MLE), efficiently predicting the elemental compositions for ultimate analysis [12]. Some of the major estimation methods developed by researchers are as follows: X-ray fluorescence spectrometry (XRF) [13,14]; optical emission spectrometry with inductively coupled plasma (ICP-OES) [15,16]; mass spectrometry with inductively coupled plasma (ICP-MS) [17]; laser-induced breakdown spectroscopy (LIBS) [18][19][20][21][22][23]; thermogravimetric Fourier-transform infrared spectroscopy (TG-FTIR) [24], and Fourier-transform infrared spectroscopy (FTIR) [25][26][27]. All of these methods have advantages and constraints, which were preferred for analyses based on requirements and equipment availability.
In the current study, the authors attempted to build a model using the spectral signatures of coal samples that were captured using FTIR spectroscopy in the mid-infrared range (4000 to 400 cm −1 ). With the help of FTIR data, a prediction model was developed for estimating the carbon content in high-ash Indian coals using the quasi-Newton (QN) method. This FTIR data-based approach is tested for accuracy compared to the traditional ultimate analysis method using the CHNSO analyzer (Make: Elementar, Model: vario MACRO cube, Manufacturer: Elementar Analysensysteme GmbH, Langenselbold, Germany). This technique relies on the concept that carbon compounds absorb specific wavelengths of infrared radiation, thereby enabling the identification and measurement of carbon in coal.
This research article is organized as follows: Section 1 describes the study's objectives and motivation and presents the previously established methods. Section 2 explains the study area and methodology of this study. Model establishment using training and testing data and the comparison between similar methods of carbon content estimation are discussed in Section 3. The study's conclusion, including the recommendations for future work, is given in Section 4. A detailed workflow of this study is visualized in Figure 1.

Geology of the Study Area
The Johilla coalfield is located in the Umaria district of Madhya Pradesh, India. It is a part of the Son-Narmada Basin and is known for its rich coal deposits [28]. The Johilla coalfield is an important source of coal for industries in the region. The coal-bearing strata in the Johilla coalfield are of the Lower Gondwana age and structurally gently folded and faulted [29,30]. The coal samples from Johilla Coalfield are humic (banded) in nature, corresponding to the sub-bituminous coal rank. The grade of Johilla coals varies from G6 to G7. For this study, 18 coal samples were collected from the Johilla bottom seam, Barakar Formation, following the standard method (ASTM D-2234) [31] from the opencast (OCP) and underground (UG) projects, namely, Kanchan OCP, Kudri UG, Pali UG, Pinoura UG, Umaria UG, and Vindhya UG. A location map of the coal sampling sites is shown in Figure 2. The Barakar Formation comprises sandstones, shales, and coal seams. The collected samples were crushed and sieved to ~212 μm size for FTIR and traditional ultimate analyses, as per guidelines of ASTM D-4749 [32].

Ultimate Analysis
The ultimate analysis is a traditional method for the determination (in weight percentage) of the elemental composition of coal, mainly the carbon (C), hydrogen (H), nitrogen (N), sulfur (S), and oxygen (O) by difference. ASTM (American Society for Testing and Materials) D5373-08 is the standard method used to determine the total carbon, which includes carbon in the volatile matter. This method can be performed on either an ultimate CHNS or carbon-sulfur analyzer. In the present work, crushed coal samples (~212 µm) were utilized to determine the elemental composition of the coal. For that, 10 mg of samples, sealed inside a tin boat (foil), were placed on an automated sample holder of the CHNS analyzer. The ultimate analysis was conducted at the Department of Applied Ge-ology, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India, in the Vario Macro Cube of Elementar, following the guidelines mentioned in ASTM D-4239 and D-5373 [33,34]. It is a piece of benchtop laboratory equipment calibrated for determining CHNS in coal samples with the highest precision and accuracy. The samples were heated at approximately 1150 °C and 850 °C in combustion and reduction tubes, respectively, in the presence of helium gas purging at a rate of approximately 600 mL/min continuously at 1200-1300 mbar pressure and oxygen (O2) dosing of 50 mL/min for 5 min. Using adsorption and desorption, the equipment carries out the determination of nitrogen (N), carbon (C), and hydrogen (H). An infrared detector, included in the equipment, is used to quantify the sulfur (S) content [35].

Fourier-Transform Infrared (FTIR) Spectroscopy
FTIR spectroscopy can be used to identify the functional groups in coal [36]. In this study, FTIR (model and make: INVENIO S, BRUKER OPTIK GmBH, Bremen, Germany) spectral analysis was carried out on the coal+KBr pellets prepared by mixing coal (~212 µm size, powdered) with KBr powder (IR spectroscopy grade, Uvasol, Kallumbromid, Germany). The sample powder was poured, evenly spread into the hydraulic die, and pressed for 5 min under ~6 tons. To diminish the effect of moisture and other gases, nitrogen gas was flushed into the FTIR optical bench for 2 hr at a rate of approximately 200 L/h before the analysis. The prepared pellets were inserted in the standard sample holder with a quick lock base plate and put into the analysis chamber for analysis. These pellets were irradiated with infrared radiation, and the resulting absorption spectrum was measured and analyzed. The measured spectra were clipped to the desired frequency range of 4000 to 400 cm −1 and the resultant FTIR data were plotted as an absorbance vs. frequency plot (Y-X plot). The absorption spectra of coal samples are typically complex and may also contain contributions from other components such as water, minerals, and organic compounds.

Quasi-Newton (QN) Method
A non-linear piecewise linear regression employing the quasi-Newton (QN) method with a breakpoint method and loss function (least squares) was utilized to create a model that can predict the carbon percentage in coal using spectral data from the coal in the training set. The resulting model is then validated using a "test set" and can be further used to make estimations of carbon in new coal samples. This model creation process involves several stages, including identifying an initial model, iteratively refining the model using the "stepping criteria" to reach convergence, and stopping the search once the stepping criteria or the maximum number of allowed iterations have been reached. The QN method is a non-linear multivariate optimization method that works by finding either the highest or lowest points. These methods are an extension of Newton's method, which calculates the curvature of a function using its second derivatives. However, the QN method uses approximations of the Hessian matrix, is updated continuously as the algorithm progresses, and saves enormous computation costs and storage requirements. This approach helps the algorithm converge more quickly to the optimal solution without requiring the full computation of the Hessian matrix [37,38].

Elemental Composition of Coal
In this study, a lab-based method called "ultimate analysis" was used to determine the amount of carbon in the coal as well as the contents of H, N, S, and O (by difference). The total carbon in the ultimate analysis is the measured weight percent of the carbon present in the coal [39]. The weight percent of the elements (C, H, N, and S) present in the coal samples used in this study is given in Table 1. In the present analysis, the carbon content ranges from a minimum of 53.38 wt% in the Johilla_S02 sample to a maximum of 68.95 wt% in the Johilla_S15 coal sample.

Identification of Functional Group
The identification of functional groups related to carbon and their spectral responses is critical for further analysis. In FTIR, infrared radiation is absorbed by the samples, which can help identify and quantify several compounds by closely examining the absorption spectra at specific zones. The known carbon compounds in coal, which have been delineated in this study for modeling, are alkanes, alkenes, aromatic, alcohols, amide, ketones, mercaptans, thioethers, aldehydes, carboxylic acids, ethers, ester, anhydrides, and acyl halides (see Table 2, modified after [40,41]). A total of 42 peaks were identified and used in the present work. The area under the curve was calculated on all 42 peaks using the detailed account of peak assignment relating to their functional groups, as defined in Table 2. To study the nature of absorbance with respect to the carbon content at specific wavelengths, the pellets were prepared for FTIR analysis, as given below. Each coal sample was mixed with a laboratory-grade KBr powder to produce a set of seven Coal+KBr pellets with a specific dilution factor. The KBr amount was fixed at 220 ± 0.20 mg with varying coal content such that the content of the coal in the Coal+KBr mix (pellets) was at nearly 0.10, 0.20, 0.30, 0.40, 0.60, 1.00, and 1.40 percent. The spectral signature (absorbance) from each pellet was recorded, adjusted for baseline, and clipped for the wavenumber 4000-400 cm −1 range (Figure 3). The recorded signatures also include the spectra of KBr, which was added to the coal samples to make pellets. To remove the KBr signature, a spectral signature of only KBr pellets was recorded, and it was used as a baseline spectrum for further analysis. This baseline spectrum was subtracted from each pellet's signature, and the resultant spectrum was used for further calculations. Figure 3. For a series of seven Coal+KBr pellets (for Johilla S07) made at 0.10, 0.20, 0.30, 0.40, 0.60, 1.00, and 1.40 percent of coal, a systematic increase in absorbance is clearly discernible using FTIR spectroscopy. The location of peaks for sensitive/functional groups related to carbon in coal is marked in series from C1, C2, …, C42 (as given in Table 2).

Model Estimation
For model building and validation, the carbon content in the coal samples obtained through the traditional CHNS analyzer (CCHNS) was used as a reference (true value). For model development and validation, the training set and test set were formed using a 17:1 split (K-fold cross validation). The non-linear and linear relationships between the functional groups of carbon compounds ( Table 2) that directly correspond with their amounts in the coal samples were modeled using a numerical iterative method based on the QN method with the breakpoint and loss function. The piecewise linear regression method employing the QN method with breakpoint was used with the objective of minimizing the difference between the predicted and observed values (the least squares loss function) and restricting the errors in the carbon estimation.
The model creates two distinct forms of the coefficient for the given variables (left and right equations, QNbp_L and QNbp_R) while considering the breakpoint and a single form of the coefficient (QNnbp) for the non-breakpoint. It has been found that the C% estimated from the avg equation (QNbp_avg, where bp = with breakpoint and avg = average of left and right equations) may offer the estimated value that is closest to the experimentally observed value.
Occasionally, as compared to experimental data, QNbp_avg estimates C% values that are outside of the expected range. Thus, the valid range, which is 1.5*IQR (interquartile range, IQR) and is derived using the QNbp_avg, was calculated in order to identify and eliminate out-of-range values (if any). As a result, if the anticipated value of the C % from QNbp_avg is out of range, the C % from QNnbp is considered the model's estimated value. The overall efficacy of the FTIR-based estimation of C % is increased by employing a threshold to identify occasional out-of-range values, and it helps to reduce the error in estimating the carbon content in unknown samples. The procedure is demonstrated by the conditions described below: Condition 1: The value from the QNbp_avg model is taken into consideration if the predicted carbon content (CFTIR, wt% from QNbp_avg) is within the range (out min to out max): Value within the range = QNbp_avg  [42].
However, as shown in the boxplot ( Figure 5), the interquartile range and mean demonstrate that the carbon content estimated via the traditional (ultimate analysis) method and the proposed (FTIR spectroscopy) methodology are similar in range. The RMSE (23.71 %), and MBE (−0.520%) are significantly low, which is reflected in the distribution of the mean bias error (Figure 5), and the MBE (in wt.%) ranges from approximately −0.22 to 0.21.
From the t-test, it can be inferred that the null hypothesis H0 is accepted. It is noticeable that the mean of the observed values (CCHNS, wt.%) is significantly similar to the mean of the model-predicted values (CFTIR, wt.%) at the 99% confidence level, where α = 0.01. Similarly, in the F-test, the null hypothesis H0 is accepted. According to this, the variance of the observed (CCHNS, wt.%) values ( 2 ) is significantly similar to the variance of the model-predicted (CFTIR, wt.%) values ( 2 ) at the 99% confidence level (where α= 0.01). The acceptance region (Fstat < Ftable) for the F-test at the 99% confidence level is 0.615 to 1.626.
In Figure 6, the observed carbon content is plotted along with the model-predicted values. Each sample was divided into a set of seven for the analysis. A total of 115 samples were modeled, excluding the cases with negative anomalies in the FTIR values. The validation exercise using the independent test set clearly shows that the estimated modeled (using FTIR) values are nearly similar to their observed experimental (using ultimate analysis) values. Thus, the carbon content in the coal samples has been accurately predicted by the model employing FTIR spectral response. Figure 6. Comparison between the carbon content for observed (ultimate analysis) and model-predicted (FTIR) (coal) samples.

Comparison with Previously Developed Models
A comparison between the previously published estimation methods and the present study for the determination of carbon content in coal samples is summarized in Table 4. In this table, the name of the method used in the estimation model, reference, location, nature, the number of samples, correlation statistics, and measures of error are tabulated for comparison. In general, in terms of single point estimation, it was observed that the models using the LIBS estimation technique provide better correlation coefficients (R 2 ranges from 0.86 to 0.99). LIBS provides a near-accurate value when targeting a single point-based estimation. The efforts to determine the elemental analysis of coal (C, H, N, and S) using data from the proximate analysis yielded a good correlation (R 2 from 0.86 to 0.95) ( Table 4). For bulk sample analysis, the current method using FTIR data gives a good correlation (correlation coefficient R 2 = 0.93 compared to the ultimate analysis) with relatively low RMSE and bias (MBE). So, both the proposed method and the traditional method of ultimate analysis can accurately estimate the amount of carbon in large samples such as those from a specific coal seam (or a specific mine face, etc.).

Conclusions
Estimating the carbon content in coal is essential for determining its usability and the potential impact on health and the environment. The FTIR data-based model for estimating the amount of carbon in coal offers an alternative to traditional ultimate analysis with the CHNSO analyzer. The results of determining the carbon content using the FTIR-based model (CFTIR) are summarized as follows: • A strong linear relationship was found between the observed (CCHNS, wt.%) and model-estimated (CFTIR, wt.%) carbon content, with a high coefficient of determination (R 2 of 0.93), low RMSE (23.71 %), and low MBE (-0.52%). • The mean carbon contents estimated from CCHNS and CFTIR were 0.383 and 0.391, respectively. Similarly, the variance was 0.075 for the observed carbon using the CHNSO analyzer (CCHNS) and 0.077 for the FTIR data-based model (CFTIR). • The t-test and F-test of significance, conducted for mean and variance, respectively, clearly show that there is no significant difference between the CCHNS (wt. %, observed) and CFTIR (wt. %, model-estimated) values.
The authors recommend future research into calculating the carbon content in coal produced from various coal fields and basins using the proposed methodology based on the FTIR data. The FTIR data-based model has the potential to be further tested and employed in the regular determination of carbon in high-ash coal in laboratories and industries. The FTIR data-based model can also be suitably modified and tested to determine the carbon content in other types of natural samples, such as soil, shale, and other organic-rich rocks. Acknowledgments: The authors are thankful to South Eastern Coalfield Limited (SECL) for providing the necessary support related to the mine visit, sample collection, fieldwork, and geological literature. The authors are grateful to the DST, India (http://www.dst.gov.in), for providing financial support to set up the "DST-FIST Level-II Facility" at the Department of Applied Geology (AGL), IIT (ISM), Dhanbad (http://www.iitism.ac.in). For the sample preparation, analyses, and visualization used in this study, the authors are thankful to the AGL, IIT (ISM), Dhanbad, for providing the necessary access to the equipment (particularly the CHNS(O) analyzer and FTIR spectroscopy), technical support, and laboratory facilities through the DST-FIST Level-II Program (No. SR/FST/ESII-014/2012(C)). The authors are thankful to all of their colleagues and individuals who helped them directly or indirectly during the work.

Conflicts of Interest:
The authors declare no conflicts of interest.