• Ash

Figure 12b illustrates that the adsorption isotherm exhibits an obvious negative correlation with ash at all pressures. It is well understood that an increase in ash content tends to decrease the adsorption isotherm on coals, because (i) ash has no a ffinity to methane adsorption [7,18] and (ii) ash-rich samples

are generally associated with lower micro porosities [57] and, therefore, provide less adsorption space to accommodate gas molecules.

• Moisture

Variations in adsorption isotherms caused by inherent and equilibrium moistures are obviously less significant than that by fixed carbon or ash, which is consistent with the ranking of relative importance, as shown in Figure 12c,d. Additionally, it is noticeable that the adsorption capacity does not follow a monotonous decreasing trend with the increase in either inherent or equilibrium moistures. It has been extensively addressed in previous studies [14,58,59] that a coal sample in the moisture-equilibrium state has a significantly lower adsorption capability than in the dry state. This is due to the occupation of some adsorption sites on the coal surface by water molecules because coals have a preferential affinity to water over methane [7]. However, for a coal sample that is already in a moisture-equilibrated state, a further increment in moisture content does not affect the adsorption capacity to gas [14,60]. Besides, as stated in [7,13], the moisture content may be predominated by the coal rank. Thus, the effect of moisture content on the adsorption isotherm may possibly be overridden by the coal rank indicators such as fixed carbon for the coal samples in this study.

• Temperature

Figure 12e shows that there is no significant change in the adsorption isotherm with elevating temperature. Most previous studies [61,62] conclude that the elevation in temperature may result in a noticeable reduction in methane adsorption capacity, because the sorptive surface coverage at a specific gas pressure decreases with increasing temperature, as derived from thermodynamics [7]. However, Crosdale et al.'s [60] experiments on moist coals showed no significant dependence of adsorption capacity on temperatures. More recently, Guan et al. [63] showed that the adsorption capacities for both methane and CO2 remained constant as the temperatures were elevated from 323 to 343 K. Our observations are consistent with [60], which may be attributed to the compensation by water molecule release for the reduction in the sorptive surface coverage caused by temperature elevation [6].

• Vitrinite

To date, there are still controversies regarding the effect of vitrinite content on the methane adsorption capacity. Some studies [1,4,17] showed that vitrinite-rich (bright) coals have a higher methane adsorption capacity than the inertinite-rich (dull) ones with equivalent ranks, which may be attributed to the existence of more micro-pores in vitrinite that is favorable to accommodation of gas molecules [64]. Dutta et al. [18] and Feng et al. [16] stated that methane adsorption capacity follows a "U-shaped" trend with vitrinite content. Other authors [13,65,66] found no obvious correlation between the adsorption capacity and vitrinite content, which holds valid for the coal samples in this study (Figure 12f).

• Vitrinite reflectance

Vitrinite reflectance is a commonly used indicator of the coal rank (maturity), which numerous previous studies [15,16,18] have demonstrated to be closely correlated with the methane adsorption capacities in coals. For the coal samples that were investigated in this study, the vitrinite reflectance exerts a negligible effect on the adsorption isotherm (Figure 12g). This is in line with [67], who argued that the vitrinite reflectance alone cannot control the maximum sorption capacities and simple lithotype analysis is insufficient for evaluating the effects of coal type. One explanation for this observation is that the influence of vitrinite reflectance on methane adsorption capacity is caused by the variations in macromolecular [68] and pore [56] structures during the coalification process as coal maturity increases. Besides, it is again noted that there exists a dependence of vitirnite reflectance on the fixed

carbon for the coals in this study (Figure 11). Thus, the e ffect of vitrinite reflectance may be overridden by that of the fixed carbon from the standpoint of statistical regressions.

The univariate analyses based on the GBDT model are in well accordance with numerous previous studies, which further confirms the validity of the constructed model, as can be seen from the above discussion. It can be also concluded that the GBDT has a remarkably capability of "automatically" identifying the true important features and properly finding the underlying correlations between the output and each input feature, even though both of the features with collinearity and features exerting minor/negligible e ffects on the output were included in the model.

#### *4.2. Influence of Input Features on the Model Accuracy*

The constructed model includes not only features with convincing control on the adsorption capacity (equilibrium pressure, ash content, fixed carbon content, and vitrinite reflectance), but also features showing minor or negligible relevance with the output (vitrinite content, inherent moisture, equilibrium moisture, and temperature), as mentioned earlier in Section 2.4.1. To demonstrate the influence of input feature selection on the model accuracy, several estimation models with di fferent scenarios of input features (Table 4) were separately constructed, following the same procedure described in Section 2.4.2.


**Table 4.** Input feature scenarios for analyzing the estimation accuracy.

\* Abbreviations: P—equilibrium pressure; A—ash; FC—fixed carbon; IM—inherent moisture; *R*o—vitrinite reflectance; EM—equilibrium moisture; V—vitrinite; T—temperature.

We began the analysis by including only equilibrium pressure and three coal property parameters (fixed carbon, ash and vitrinite reflectance) that show relatively strong correlations with adsorption capacity (Figure 4) in order to estimate the adsorption isotherm (Scenario#1 in Table 4). It can be seen from Figure 13 that this scenario produces an estimation result with the lowest accuracy in terms of all the evaluation matrices, suggesting that using only these four key features are not su fficient for accurate estimation of the isotherm. With these four parameters held in the model, we then added one of the remaining less significant features (inherent moisture, equilibrium moisture, vitrinite, temperature) at a time into the model. It is shown (Figure 13) that the inclusion of equilibrium moisture in the model (Scenarios#2) results in a most noticeable reduction in the estimation error than that of any of the other features (Scenarios#3, #4, and #5). In order to honor the contribution of equilibrium moisture to estimation accuracy improvement, we fixed equilibrium moisture together with the aforementioned four key parameters in the input feature bank; the feature bank was then expanded by adding one (Scenarios#6, #7, and #8) or two (Scenarios#9, #10, and #11) out of the remaining features sequentially in order to further examine the e ffect of input feature scenarios on the estimation results. It is depicted in Figure 13 that the estimation accuracy exhibits a general decreasing trend with more input features being included in the model. The model that incorporates all available input features (the one addressed

in Section 3.1, which is assigned as Scenario#12 in this section) demonstrates the highest estimation accuracy among all of the scenarios investigated.

**Figure 13.** Error matrices of (**a**) average absolute error (AAE), (**b**) average relative error (ARE), (**c**) root mean squared error (RMSE) and (**d**) R<sup>2</sup> for different input feature scenarios.

All available features that may potentially affect the isotherm should be incorporated in the construction of the estimation model for the adsorption isotherm, as indicated from the above results. The exclusion of insignificant features identified with correlation coefficient is highly questionable and tends to decrease the estimation accuracy. This finding is well supported by Beker et al. [33]. It is reiterated that the GBDT is highly robust to interferences from insignificant features and it has a strong capability to properly find the underlying correlations between the input features and the adsorption amount.

It should be noted that feeding more input features into the estimation model requires more efforts to obtain the associated feature information. Generally, the proximate analysis parameters (ash, fixed carbon, and inherent moisture contents) are less expensive and easier to be experimentally measured than the maceral analysis parameters (e.g., vitrinite content). Therefore, it should be of practical significance to use as less maceral features as possible while ensuring relatively high modeling accuracies. Scenarios#7, #8, # 9, and #11 result in high modeling accuracies when compared with Scenario #12, as can be seen from Figure 13. Among these four scenarios, only Scenario#8 does not include the vitrinite, which is a required input feature for all of the remaining scenarios (Table 4). As such, Scenario#8 may be the most "cost-effective" ones when considering the less input features and reasonably high modeling accuracy.
