A mathematical model to characterize the degree of coalification based on the low-angle region of the X-ray diffractogram.

Based on X-ray diffraction (XRD) pattern of coal, an empirical model for judging the coalification degree is used to calculate the ratio of the 002 peak height to the Full width at half maximum (FWHM). However, the existing models are often simpler and more suitable for judgment of the medium and low rank coal, while are not feasible in determination of high rank coal. In order to address this issue, the objective of this study is to establish a new modified mathematical model based on optimization of the existing empirical models. Through the calculation of Bragg equation, it demonstrates that the low-angle region (2θ= 3-10°) in the XRD pattern reflects the information of micropore in coal with a diameter of (0.884-2.94) nm. Accordingly, its diffraction intensity corresponds to the porosity rate in coal. As a result, the modified mathematical model has been established for characterizing the coalification degree by introducing the variation of porosity rate with the coal ranks creatively. The synergistic effects of the change regulation of organic matter peak and the porosity rate with coal rank ensure the accuracy of the model. Furthermore, the good stability and high reliability of new model are verified through the recalculation of a total of 14 coal samples. Study results demonstrated that the new method enabled to determine coal rank more conveniently and accurately in the industrial production.