## 4 Discussion  
### Novel Method for Determining the \(T_{2c}\) Cut-Off  
In previous studies, the \(T_{2c}\) values were determined from the \(T_{2}\) spectra of saturated and centrifugal samples. This method assumed that centrifugation could remove all free water in samples. There are two problems when this method is used to measure the \(T_{2c}\) of clay-quartz mixtures: (1) The strength of the clay-quartz mixtures is much lower than that of coal, sandstone, and shale, so the centrifugal force may damage the samples, and (2) because of the complexity of the structure, the water in mixtures is hardly removed by the centrifugal method. Even at the maximum rotational speeds, little water is extracted from samples by centrifuging. Therefore, a new method needs to be proposed for determining the \(T_{2c}\) of clay-quartz mixtures.  
According to the results of NMR and evaporation tests, the evaporation process can be divided into two stages. The water that evaporated easily corresponded to a larger signal decay rate and the water that evaporated with more difficultly corresponded to a smaller decay rate. Based on this, the water in mixtures can divided into two types: the free water and the bound water. In this study, the water that evaporated during the constant rate stage and falling rate stage was defined as the free water and the bound water, respectively. The \(T_{2c}\) was used to discriminate between the free water and the bound water in the \(T_{2}\) spectrum. The \(T_{2c}\) divides the \(T_{2}\) spectrum of initial saturated mixtures into two parts. The cumulative signal amplitude from \(T_{2 min}\) to \(T_{2c}\) corresponded to bound water. On the contrary, the cumulative signal amplitude from \(T_{2c}\) to \(T_{2 max}\) corresponded to free water. Therefore, the \(T_{2c}\) could be determined from the \(T_{2}\) spectra of mixtures under two saturated states: an initial state and a falling rate state. The mixture under the initial state and falling rate state were the saturated mixture  
Figure 9: Variation of the \(At\) decay rate with respect to the heating time. From top to bottom, curves with different colors and symbols with different shapes indicate variation of M40, M60, M80, M100, K40, K60, K80, and K100, respectively. The scales of the Y axes of the upper and lower parts of the figure are different. Red and olive vertical line indicate 20 and 6 h, respectively. \(T_{f}\) is the time when the decay rate started to fall.  
before evaporation and the mixture at the beginning of the falling rate stage, respectively. Based on the two \(T_{2}\) spectra, the cumulative signal amplitude curves of mixtures under two states could be obtained. A line parallel to the \(T_{2}\) axis can be drawn from the maximum cumulative signal amplitude of the falling rate state, which intersects with the cumulative signal amplitude of the initial state. The \(T_{2i}\) of the intersect point was the \(T_{2}\) cut-off value. Figure 10 shows the \(T_{2c}\) of all eight mixtures.  
Figure 10: Cont.  
The relationships between \(T_{2c}\) and the clay content of mixtures are shown in Figure 11, which reveals that the \(T_{2c}\) decreased as the clay content increased. The relationships between \(T_{2c}\) and the clay content of K-Q mixtures and M-Q mixtures can be expressed by Equations (17) and (18), for which the \(R^{2}\) values were 0.987 and 0.912, respectively.  
\[T_{2c}=-0.012 CC+6.626 \tag{17}\]  
\[T_{2c}=-0.016 CC+3.322 \tag{18}\]