A Fast Screening Method of Key Parameters from Coal for Carbon Emission Enterprises

Abstract

During the process of determining carbon emissions from coal using the emission factor method, third-party organizations in China are responsible for verifying the accuracy of the carbon emission data. However, these verifiers face challenges in efficiently handling large quantities of data. Therefore, this study proposed a fast screening method that utilizes multiple linear regression (MLR), in combination with the stepwise backward regression method, to identify problematic carbon emission data for the lower calorific value (LCV) and carbon content (C) of coal. The results demonstrated the effectiveness of the proposed method. The regression models for LCV and C exhibited high R-squared (R²) values of 0.9784 and 0.9762, respectively, and the root mean square error (RMSE) values of the validation set were 0.32 MJ/kg and 0.80% for LCV and C, respectively, indicating strong predictive capabilities. By analyzing the obtained results, the study established the optional error threshold interval for the LCV and C of coal as 2RMSE–3RMSE. This interval can be utilized as a reliable criterion for judging the quality and reliability of carbon emission data during the verification process. Overall, the proposed screening method can serve as a valuable tool for verifiers in assessing the quality and reliability of carbon emission data in various regions.

1. Introduction

With the rapid development of the carbon trading market in China, the accurate determination of carbon dioxide emissions has become crucial [1,2]. The widely used emission factor method, also known as the standard calculation-based method, is utilized for calculating carbon emissions from coal combustion [3,4]. Key parameters, such as lower calorific value (LCV) and carbon content (C) per unit of calorific value, are measured to determine the carbon emissions of fossil fuels [5]. In China, these parameters are provided by carbon emission enterprises and may be inspected by third-party verifiers to ensure accuracy. Currently, verifiers rely on tracking the historical carbon emissions of enterprises as evidence for assessing their reports. However, due to the vast amount of data involved in evaluating carbon emissions, it is essential to establish an efficient screening method that can facilitate the identification of potential problematic data, particularly in coal burning processes that often require more extensive data analysis. By establishing a set of predetermined thresholds for the key parameters, it will be easier for verifiers to quickly identify whether the reported data falls within an acceptable range.

Extensive research has been conducted on the correlation between the calorific value of coal and other parameters, due to its significant impact on combustion performance and coal quality assessment. Linear regression models have been developed using proximate analysis [6,7,8,9,10,11,12,13], ultimate analysis [14], or a combination of both [11,15], as shown in

Table 1. Survey of published correlations the between calorific value and carbon content of coal.

Parameter	Reference	Model	Model Evaluation Indicators
Calorific value	Chen et al. (1999) [6]	LCV = 35,860 − 73.7V − 395.7A − 702M	n.g.
	Kucukbayrak et al. (1991) [7]	GCV = 76.56 − 1.30(V + A) + 7.03 × 10−3(V + A)2	R2 = 0.91
	Parikh et al. (2005) [8]	GCV = 0.3536FC + 0.1559V − 0.0078A	MAE = 3.74%
	Majumder et al. (2008) [9]	GCV = −0.03A − 0.11M + 0.33V + 0.35FC	MAE = 1.49%
	Akkaya (2009) [10]	GCV = 0.836M−8.155A−3.559V0.35FC0.626 GCV = 0.561M−6.137V0.381FC0.666 GCV = 33.078 − 0.72M + 0.012M2 − 1.163M3 − 0.324A2	R2 = 0.97
	Mesroghli et al. (2009) [11]	GCV = 37.777 − 0.647M − 0.387A − 0.089V GCV = −26.29 + 0.275A + 0.605C + 1.352H + 0.840N + 0.321S	R2 = 0.97
	Kavsek et al. (2013) [12]	GCV = −3.57 + 0.31V + 0.34FC	R2 = 0.971
	Chelgani et al. (2013) [13]	GCV = 35.391 − 0.47M − 0.364A − 0.028V GCV = −0.408 + 1.243H + 0.348C−0.1N − 0.111O + 0.112S	R2 = 0.998
	Given et al. (1986) [14]	GCV = 0.3278C +1.419H + 0.09257S − 0.1379O + 0.637	n.g.
	Channiwala et al. (2002) [15]	GCV = 0.3491C + 1.1783H + 0.1005S − 0.1034O − 0.0151N − 0.0211A	MAE = 1.45%
Carbon content	Saptoro et al. (2006) [24]	C = a0 + a1A + a2V + a3M + a4FC	n.g.
	Yi et al. (2017) [25]	C = x1 + x2A + x3A2 + x4V + x5V2 + x6FC + x7FC2 (1) Anthracite: C = 306,540 − 3066.61A + 0.0229439A2 − 3066.31V + 0.0435868V2 − 3063.36FC − 0.0106054FC2 (2) High-rank bituminous: C = −143,398 + 1434.61A − 0.0138486A2 + 1435.78V − 0.0125349V2 + 1433.88FC + 0.0106647FC2 (3) Subbituminous: C = 40,521.2 − 403.482A − 0.085603A2 − 403.029V − 0.0193969V2 − 405.885FC + 0.0168029FC2 (4) Lignite: C = 5855.8 − 57.3735A − 0.0220361A2 − 58.4226V + 0.0131499V2 − 58.9345FC + 0.0195368FC2	(1) Anthracite: R2 = 0.95, MAE = 0.53% (2) High-rank bituminous: R2 = 0.93, MAE = 0.51% (3) Subbituminous: R2 = 0.86, MAE = 0.93% (4) Lignite: R2 = 0.92, MAE = 1.87%
	Liu (2022) [26]	C = 50.7368 − 0.5799FC − 0.7066V + 2.8301GCV	MAE = 1.97%
	Zhu (2018) [27]	C = 35.411 − 0.341A − 0.199V − 0.412S + 1.632GCV	n.g.
	Wang et al. (2016) [28]	(1) C = LCV/356 (LCV: 5026–19,040 kJ/kg) (2) C = LCV/383 (LCV: 19,040–29,850 kJ/kg)	RE = −0.6~1.14%

Note: C, H, O, N, S, M, A, V, FC, GCV, and LCV represent contents of carbon, hydrogen, oxygen, nitrogen, sulphur, moisture, ash, volatile matter, fixed carbon, gross calorific value, and lower calorific value, respectively; n.g. represents not given.

. These calorific value models exhibit good predictive accuracy, with R² values ranging from 0.97 to 0.998 and mean absolute error (MAE) values ranging from 1.45% to 3.74%. Additionally, it was observed that the combination of both analyses usually yields better results [16]. Nonlinear methods—such as artificial neural networks (ANN) [12,17,18,19], adaptive neuro-fuzzy inference systems (ANFIS) [20], support vector regression (SVR) [16,21,22], random forest (RF) [23], and so on—have also been utilized for prediction. While nonlinear methods require more data and complex training processes, linear regression remains a simple and practical approach, especially when the predictions fall within an acceptable range. Hence, linear regression is used in this study for ease of application in screening carbon emission data.

Fewer studies have specifically focused on predicting carbon content (C) in coal, potentially due to its limited correlation with coal prices. However, some regression equations for C have been developed [24,25,26,27,28], as shown in Table 1. These C models exhibit moderate predictive accuracy, with R² values ranging from 0.86 to 0.95 and MAE values ranging from 0.51% to 1.97%. Additionally, nonlinear methods, such as partial least squares (PLS) [24,29], back-propagation neural networks (BP-ANN) [24], and support vector machines (SVM) [30,31], have also been gradually applied to predict C.

The existing models in the literature cover a wide range of fuel types and calorific values. For instance, Parikh et al.’s model covers different types of solid fuels, with dry basis gross calorific value (GCV) ranging from 14.772 to 34.388 MJ/kg [8]. Channiwala et al.’s model includes various types of solid, liquid, and gaseous fuels, with fuel dry basis GCV ranging from 4.745 to 55.345 MJ/kg [15]. Majumder et al. focused on coal samples, with received basis GCV ranging from 12.75 to 28.37 MJ/kg [9]. Consequently, existing models generally predict LCV with relatively high uncertainty, limiting their applicability as a screening method.

This study proposed a screening method based on multiple linear regression models, specifically utilizing coal samples from China. The optimal multivariate linear regression models of LCV and C were established by evaluating the significance of various coal parameters obtained from both proximate analysis and ultimate analysis. Using these models, verifiers can quickly compare the reported carbon emission data with the model’s predictions to identify any discrepancies. This method provides a reliable and efficient approach for verifiers to quickly screen carbon emission data.

2. Materials and Methods

2.1. Sample Collection and Preparation

In this research, we collected 95 coal samples from enterprises located across certain province, China. The selection of these samples was carried out in a random manner to ensure their representativeness. These parameters encompassed total moisture; moisture content; ash content; volatile matter content; and fixed carbon content, among others, all of which were determined using standardized prescribed methodologies. All measurements were executed under air-dry conditions. Additionally, the values of LCV and C were appropriately adjusted to a received basis.

The experimental findings for the coal samples are presented in

Table 2. Descriptive statistics of coal sample data.

Coal Property	Minimum	Maximum	Mean	Standard Deviation
Mad (%)	2.48	19.92	7.24	4.04
Aad (%)	3.69	34.06	18.48	6.91
Vad (%)	25.52	42.41	31.14	4.57
FCad (%)	34.07	60.74	43.38	4.04
St,ad (%)	0.12	1.98	0.77	0.31
Had (%)	3.23	4.41	3.71	0.24
Car (%)	39.90	61.14	50.72	4.69
LCVar (MJ/kg)	14.85	22.78	19.05	2.02

Note: M_ad: moisture content on an air-dried basis; A_ad: ash content on an air-dried basis; V_ad: volatile matter content on an air-dried basis; FC_ad: fixed carbon content on an air-dried basis; H_ad: hydrogen content on an air-dried basis; C_ar: carbon content on an as-received basis; LCV_ar: lower calorific value content on an as-received basis.

. The moisture content exhibited a range from 2.48% to 19.92%, while ash content ranged from 3.69% to 34.06%. Volatile matter content spanned from 25.52% to 42.41%, while fixed carbon content varied between 34.07% and 60.74%. Total sulfur content ranged from 0.12% to 1.98%; hydrogen content from 3.23% to 4.41%; carbon content from 39.90% to 61.14%; and LCV from 14.85 MJ/kg to 22.78 MJ/kg. The predominant coal types in the region were identified as bituminous coal and lignite, characterized by generally higher volatile matter and LCV. To facilitate the analysis, the dataset of 95 coal samples was randomly split into two subsets: a calibration set and a validation set. The calibration set, comprising 85 sets of data, was employed to develop multiple linear regression models for both C and LCV. The validation set, consisting of 10 data sets, was utilized to assess the performance of the regression models.

2.2. Methodology

2.2.1. Multiple Linear Regression

Multiple linear regression is a statistical method used to explore the quantitative relationship between a dependent variable (y) and multiple independent variables (x₁, x₂, …, x_n). This method assumes a linear relationship between the dependent variable and the independent variables. The multiple linear regression model can be expressed as follows [32]:

$$\mathrm{y}={\mathrm{a}}_0+{\mathrm{a}}_1{\mathrm{x}}_1+{\mathrm{a}}_2{\mathrm{x}}_2+ \dots +{\mathrm{a}}_{\mathrm{n}}{\mathrm{x}}_{\mathrm{n}}+\mathsf{\epsilon }.$$

(1)

In this equation, a₀, a₁, a₂, …, a_n are the regression coefficients that represent the impact of each independent variable on the dependent variable. The term ε represents the random error term, which captures the unexplained variability in the relationship.

2.2.2. Stepwise Backward Regression Method

The stepwise backward regression method is a useful statistical analysis method which can assist researchers in excluding independent variables that have minimal contribution to the dependent variable from the model, thereby improving the predictive accuracy of the regression model [33]. Its specific procedure is as follows: Firstly, a regression equation is established by using all m variables, and then the least significant variable among these m variables—referring to the one with the largest p-value (denoted as sig(t)) in the regression coefficient test—is selected and eliminated from the equation. A t-test is then performed on the m regression coefficients, yielding p-values denoted as {P₁, P₂, …, P_m}. The variable with the largest p-value is identified and denoted as:

$$P_j=max \left\{P_{1, }{P}_{2, }{\dots , P}_{m }\right\}.$$

(2)

Given a significance level of α, if P_j ≥ α, the variable x_j is first eliminated from the regression equation. Then, a regression equation is established again with the remaining m-1 independent variables, and a significance test is conducted on the regression coefficients. This process continues sequentially, until the t-test values of all remaining variables in the regression equation are less than the significance level α, indicating that no more variables can be removed. At that time, the obtained regression equation is the final determined equation.

The flow chart of the methodology of this study is shown in Figure 1. For this study, we utilized SPSS statistical analysis software to establish multiple linear regression models for C and LCV based on the 85 data sets. Then, the stepwise backward regression method was used for the selection of independent variables, including the significance test of the regression model (F-test) and the significance test of the regression coefficient (t-test). The aim was to identify the most relevant independent variables that contribute to the prediction of C and LCV. Finally, the predicted values of the model (LCV and C) can be compared with the data reported by the enterprise. If the error of the above two is greater than the preset threshold (2RMSE–3RMSE), the data is doubtful, and further analysis is required. This method is helpful for verifiers to quickly identify whether the reported data falls within an acceptable range.

2.2.3. Model Evaluation Indicators

The obtained multiple linear regression models for C and LCV were evaluated using several indicators to assess the accuracy and reliability of the models. These indicators included the R-squared (R²), the root mean square error (RMSE), the mean absolute error (MAE), and the mean relative error (MRE). The coefficient of determination (R²) indicates the proportion of variance in the dependent variable that can be explained by the independent variables. The root mean square error (RMSE) measures the average magnitude of the residuals between the predicted and actual values, providing an overall assessment of the model’s prediction accuracy. The mean absolute error (MAE) calculates the average absolute difference between the predicted and actual values, representing the average magnitude of the errors. The mean relative error (MRE) measures the average percentage difference between the predicted and actual values, indicating the average relative deviation.

Generally, smaller values of RMSE, MAE, and MRE indicate higher prediction accuracy of the model [34,35]. The values of R², RMSE, MAE, and MRE are calculated using Formulas (3)–(6).

$$R^2=1-\frac{\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{\sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}$$

(3)

$$RMSE=\sqrt{\frac{\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{n}}$$

(4)

$$MAE=\frac{\sum _{i=1}^n\left|y_i-{\widehat{y}}_i\right|}{n}$$

(5)

$$MRE=\frac{\sum _{i=1}^n\frac{\left|y_i-{\widehat{y}}_i\right|}{y_i}}{n}$$

(6)

In the equation, y_i and ${\widehat{y}}_i$ represent the reference values and model predictions, respectively; $\overline{y}$ represents the mean of reference values; n represents the number of coal samples; and k is the number of independent variables.

3. Results

3.1. Model Building

3.1.1. Low Calorific Value

To develop a multiple linear regression model (Model 1 as listed in

Table 3. Variance results for the low calorific value model.

Model		Coefficient	Sig.(t)	Sig.(F)	R2
1	Intercept	−2.116	0.446	3.53 × 10−62	0.9775
	Mad	−0.025	0.384
	St,ad	0.394	0.033
	Car	0.393	4.91 × 10−41
	Had	0.151	0.565
	FCad	0.01	0.647
	Aad	0.004	0.882
	Vad	0.00032	0.993
2	Intercept	−2.097	0.2	1.36 × 10−63	0.9778
	Mad	−0.025	0.325
	St,ad	0.395	0.027
	Car	0.393	2.21 × 10−47
	Had	0.152	0.504
	FCad	0.01	0.564
	Aad	0.004	0.797
3	Intercept	−1.726	0.024	4.85 × 10−65	0.9781
	Mad	−0.03	0.06
	St,ad	0.408	0.017
	Car	0.393	5.64 × 10−48
	Had	0.107	0.454
	FCad	0.008	0.601
4	Intercept	−1.604	0.027	1.69 × 10−66	0.9783
	Mad	−0.034	0.016
	St,ad	0.371	0.016
	Car	0.397	9.91 × 10−59
	Had	0.12	0.392
5	Intercept	−1.202	0.027	6.32 × 10−68	0.9784
	Mad	−0.032	0.021
	St,ad	0.359	0.019
	Car	0.398	1.77 × 10−59

) for LCV, all parameters from proximate analysis and ultimate analysis (C, H, S, M, A, V, FC) were used as independent variables. The performance of the model was assessed through analysis of variance (ANOVA), including metrics such as R², F-test, and t-test [36].

R-squared (R²) for Model 1 was found to be 0.9775. This value indicates a strong linear fit between the independent variables and the low calorific value. The F-test, which assesses the overall significance of the regression model, yielded a significance level (Sig.(F)) of 3.53 × 10^-62, which is considerably lower than the significance threshold of 0.05, indicating that the model has a significant linear relationship with LCV. However, the t-test results indicated that the variables V_ad, A_ad, FC_ad, and H_ad were not statistically significant (Sig.(t) > 0.05) in relation to LCV. This suggests that these parameters have an insignificant linear relationship with LCV and may not contribute significantly to the prediction of LCV within this model.

Next, the stepwise backward regression method was employed to refine and improve the predictive performance of the regression model. Starting from the independent variables of the previous regression model, the parameter with the largest value of Sig.(t) (indicating insignificance) was identified and eliminated. The remaining independent variables were then used for the subsequent regression. This process was repeated until all remaining independent variables were significant.

In this case, the parameters V_ad, A_ad, FC_ad, and H_ad were eliminated in sequence, as they were determined to be statistically insignificant. With each elimination, the R-squared (R²) value increased, indicating an improved fit of the model. Additionally, the significance level (Sig.(t)) of the remaining parameters decreased, indicating their increased significance in relation to LCV.

By employing the stepwise regression procedure, we generated a refined model (Model 5) that incorporates only the significant independent variables, written as:

$$Q_{net,ar}=-1.202-0.032M_{ad}+0.359S_{t,ad}+0.398C_{ar}.$$

(7)

The R² value of this model is 0.9784, indicating a slight improvement compared to the initial model. The inclusion of the parameters M_ad, S_t,ad, and C_ar in the model is statistically significant, as evidenced by their Sig.(t) values being less than 0.05. This suggests a significant linear relationship between each independent variable and the dependent variable LCV.

3.1.2. Carbon Content

The multiple regression model for C was developed using the same process described above. The initial model included seven coal quality parameters (Q, H, S, M, A, V, FC), and a stepwise backward regression procedure was conducted to refine the model. The refined model for C is presented in

Table 4. Variance results for the carbon content model.

Model		Coefficient	Sig.(t)	Sig.(F)	R2
1	Intercept	13.819	0.037	8.32 × 10−61	0.9756
	Aad	−0.098	0.17
	Vad	−0.141	0.126
	Qnet,ar	2.301	4.91 × 10−41
	St,ad	−0.533	0.238
	FCad	−0.018	0.737
	Mad	0.013	0.853
	Had	0.108	0.866
2	Intercept	13.881	0.035	3.39 × 10−62	0.9759
	Aad	−0.098	0.168
	Vad	−0.134	0.095
	Qnet,ar	2.305	8.81 × 10−43
	St,ad	−0.529	0.238
	FCad	−0.017	0.744
	Mad	0.011	0.873
3	Intercept	14.729	1.35 × 10−4	1.24 × 10−63	0.9762
	Aad	−0.107	0.016
	Vad	−0.142	0.023
	Qnet,ar	2.301	6 × 10−45
	St,ad	−0.533	0.231
	FCad	−0.024	0.483
4	Intercept	13.553	8 × 10−5	5.04 × 10−65	0.9764
	Aad	−0.095	0.02
	Vad	−0.126	0.029
	Qnet,ar	2.273	3.48 × 10−50
	St,ad	−0.549	0.215
5	Intercept	15.649	3.07 × 10−7	2.96 × 10−66	0.9762
	Aad	−0.129	3.40 × 10−5
	Vad	−0.159	0.002
	Qnet,ar	2.228	7.99 × 10−56

and written as:

$$C_{ar}=15.649-0.129A_{ad}-0.159V_{ad}+2.228{LCV}_{ar}.$$

(8)

After conducting a stepwise backward regression, only three parameters were found to have a high level of significance and were retained in the model. The R² value of 0.9762 indicated a good fit. Furthermore, the Sig.(F) value of the model, which is 2.96 × 10⁻⁶⁶ (less than 0.05), indicates that the fitted regression equation is statistically significant and demonstrates a linear relationship between the independent variables and the dependent variable. This suggests that the selected parameters play a crucial role in predicting C accurately.

It is important to note that the models are specific to the analyzed coal samples and may not be generalized to other datasets or coal samples.

3.2. 33.2 Error Thresholds

Based on the developed models, it is possible to obtain predicted values for key carbon emission parameters, such as low calorific value and carbon content. These predicted values can be compared to the actual measured values to analyze the absolute errors. By determining thresholds for these errors, it becomes possible to establish criteria for assessing the reasonableness of carbon emission data during the verification process.

3.2.1. LCV

The calculation results demonstrate that among the 85 calibration samples (as presented in

Table 5. Proportion of acceptable sample data within different error thresholds.

Absolute Errors	Proportion of Model Calculated Value (%)
	Low Calorific Value (RMSE = 0.29 MJ/kg)	Carbon Content (RMSE = 0.70%)
≤RMSE	70.59	76.47
≤2RMSE	94.12	94.12
≤2.5RMSE	97.65	98.82
≤3RMSE	100	98.82

and Figure 2), there are 60 samples (70.59%) where the absolute errors between the model-calculated low calorific value and the measured value are less than, or equal to, the RMSE of 0.29 MJ/kg. Additionally, there are 80 samples (94.12%) with errors within 2RMSE (0.58 MJ/kg); 83 samples (97.65%) with errors within 2.5RMSE (0.72 MJ/kg); and all 85 samples (100%) have errors within 3RMSE (0.86 MJ/kg).

3.2.2. C

Similarly, among the 85 calibration samples (as depicted in Figure 2), there are 65 samples (76.47%) with absolute errors of the model-calculated carbon content and the measured value ≤RMSE (0.70%); 80 samples (94.12%) with errors ≤2RMSE (1.40%); and 84 samples (98.82%) with errors ≤2.5RMSE (1.75%) and ≤3RMSE (2.10%).

In conclusion, the verifier can independently select thresholds within the range of 2RMSE to 3RMSE to judge the acceptability of low calorific value and carbon content data. Any data exceeding this threshold of absolute errors will be considered abnormal.

3.3. Validation of Regression Model

To validate the accuracy of the established models, 10 sets of data from the validation dataset were used. The results are presented in

Table 6. Results of regression model validation.

Sample	LCVar				Car
	Measured Value (MJ/kg)	Predicted Value (MJ/kg)	Absolute Error (MJ/kg)	Relative Error (%)	Measured Value (%)	Predicted Value (%)	Absolute Error (%)	Relative Error (%)
1	22.44	21.82	−0.62	2.77	57.33	58.55	1.22	2.12
2	21.61	21.18	−0.43	2.00	55.90	56.69	0.79	1.41
3	19.72	19.81	0.09	0.44	52.21	52.20	−0.01	0.01
4	19.40	19.37	−0.03	0.13	51.23	49.92	−1.31	2.56
5	19.06	19.23	0.17	0.90	50.73	50.22	−0.51	1.00
6	17.76	17.53	−0.23	1.31	46.42	47.08	0.66	1.42
7	18.51	18.64	0.13	0.71	49.16	48.91	−0.25	0.50
8	20.80	20.72	−0.08	0.39	54.54	54.73	0.19	0.35
9	15.31	15.20	−0.11	0.69	41.79	42.50	0.71	1.70
10	15.99	15.45	−0.54	3.40	42.92	44.08	1.15	2.69

. In this study, 2.5RMSE is selected as the error threshold.

For the low calorific value, the absolute errors between the predicted values and the measured values of the 10 validation coal samples are within the error threshold of the regression model (2.5RMSE = 0.72 MJ/kg). The overall RMSE, MAE, and MRE for the validation dataset are 0.32 MJ/kg, 0.24 MJ/kg, and 1.27%, respectively.

Regarding the carbon content, the absolute errors between the calculated values and the measured values of the 10 coal samples are within the error threshold of the regression model (2.5RMSE = 1.75%). The overall RMSE, MAE, and MRE for the validation dataset are 0.80%, 0.68%, and 1.38%, respectively.

The results indicate that the established regression models for low calorific value and carbon content have a good fit and, to some extent, can effectively predict LCV and C.

4. Discussion

In order to examine the performance of the established models in screening, a comparison was made with the results obtained from existing empirical formulas, using the aforementioned validation dataset of 10 coal samples.

4.1. Comparison of the LCV Regression Models

Four typical regression models for the calorific value of coal, noted in references [6,7,8,9], were selected to be compared with the LCV model proposed in this study. This study focused on coal for the carbon market, resulting in a narrower coal sample range compared to others. Additionally, it is worth noting that these models express the predictions in different types of calorific values and on various bases, unlike the present model, which utilizes LCV on a received basis. For instance, the model by Chen et al. [6] presents the calorific values as LCV on an air-dried basis, while those by Kucukbayrak et al. [7] and Parikh et al. [8] express them as GCV on a dried basis. On the other hand, the model by Majumder et al. [9] provides the results in GCV on a received basis. To ensure consistency, the results reported in GCV on a dried basis and a received basis were adjusted to GCV on an air-dried basis according to the Chinese national standard (GB/T 35985-2018) [37]. Subsequently, a further conversion to LCV on a received basis was performed using the equation provided below:

$${LCV}_{ar}=({GCV}_{ad}-206H_{ad})\times \frac{100-M_t}{100-M_{ad}}-23M_t$$

(9)

where H_ad is the hydrogen content of the coal on an air-dried basis in %, M_t is the total moisture content of the coal on a received basis in %, and M_ad is the moisture content of the coal on an air-dried basis in %.

The comparison between the present model and the reference models in predicting the validation set is depicted in Figure 3. The present model demonstrates the lowest MAE of 0.24 MJ/kg, which is 2~10 times lower than that of the reference models. This suggests that the present model exhibits a significantly better fit to the validation of coal samples. Setting the threshold at 2.5RMSE = 0.72 MJ/kg, all ten sample data points fall within the acceptable region.

In contrast, the use of the reference models may not be effective as a screening method. Employing the same threshold of 0.72 MJ/kg, the models proposed by Chen et al. [6] and Majumder et al. [9] report 2 and 1 data points, respectively, out of the 10 data points falling outside the acceptable region. This observation aligns with the slightly larger MAEs reported by these models. Furthermore, the predictions made by Kucukbayrak et al. and Parikh et al. exhibit a relatively large discrepancy, with most data points falling outside the acceptable region; this may be attributed to the diverse fuel sample types and wider range of coal samples used for their model establishment, or possibly the parameter basis conversions.

In conclusion, the proposed LCV model in this study demonstrated a high level of suitability for effectively screening coal emission data, surpassing the performance of reference models.

4.2. Comparison of Carbon Content Regression Models

As the LCV and C of coal are mostly studied separately, three other typical regression models for estimating the carbon content of coal were chosen for comparison with the model developed in this study: models by Liu [26], Zhu [27], and Wang et al. [28]. To ensure a consistent basis for comparison, the reference models expressed at a different basis were converted to a received basis, in line with the present model. The outcomes of the carbon content regression model comparisons are illustrated in Figure 4.

The present model and the model proposed by Zhu exhibit the lowest MAE values for the validation samples—0.68% and 0.73%, respectively. One possible reason for such an agreement may be that the data sources used by both models were from coal-burning power plants. Additionally, the parameters used in both models, including LCV, V, and A, are quite similar, except for an additional parameter of S involved in Zhu’s model. When the acceptance threshold is set at 1.75%, all 10 data points are within the acceptance region according to both models.

However, the models of Liu and Wang et al. show higher MAEs of 1.92% and 3.32%, respectively. These models identified 5 and 9 questionable data points, respectively, out of the 10 validation samples. Notably, Wang’s model utilizes only one LCV parameter, to predict the carbon content. The significant discrepancy observed in their model highlights the criticality of careful parameter selection during model establishment. Additionally, the noticeable discrepancy in the model of Liu could be attributed to the utilization of different types of coal samples compared to the ones used in our study.

Overall, when compared with the reference models, the carbon content model proposed in the present study exhibits a higher level of suitability for screening the quality of coal data in the carbon market.

5. Conclusions

In this work, a fast screening method for the LCV and C of coal, based on MLR models used to assess the quality of coal data in the carbon market, was proposed. By employing MLR combined with the stepwise backward regression method, non-significant variables were gradually eliminated, resulting in highly accurate regression models for LCV and C. The major variables in the LCV regression model were identified as M_ad, S_tad, and C_ar, resulting in an R² value of 0.9784, and RMSE, MAE, and MRE values of 0.32 MJ/kg, 0.24 MJ/kg, and 1.27%, respectively. The major variables in the C regression model were identified as A_ad, V_ad, and LCV_ar, with an R² value of 0.9762, and RMSE, MAE, and MRE values of 0.80%, 0.68%, and 1.38%, respectively. The results of the LCV and C models demonstrated strong predictive capabilities. Additionally, this study determined that the optional error threshold interval of the LCV and C of coal is 2RMSE–3RMSE, which can serve as a reasonable judgment basis for carbon emission data during the verification process. The LCV and C models proposed in the present study exhibit a higher level of suitability for screening the quality of coal data in the carbon market in comparison with the reference models.

The screening method proposed in this study can serve as a valuable tool for verification agencies in evaluating the quality and reliability of carbon emission data in various regions, which can contribute to the promotion of standardized and orderly operation, as well as the sustainable development of the carbon emission trading market.