高阶煤煤岩毛管压力曲线新数学模型及关键参数

毛管压力是影响煤层气赋存和开发的重要参数，为建立能够有效表征高阶煤煤岩毛管压力曲线的数学模型，以高阶煤为研究对象，开展了高压压汞实验，系统评价了目前常用的典型毛管压力曲线数学模型的适应性，建立拟合程度更高的数学模型。结果表明，6块高阶煤煤样毛管压力曲线基本没有中间平缓段，整体表现为向左上方凸出的形态，与常规砂岩、低阶煤差异明显；BC模型、贺承祖模型和Li模型均不能很好地拟合高阶煤的毛管压力曲线；建立的新毛管压力曲线数学模型，能够很好地拟合高煤阶煤样毛管压力实验数据，拟合程度达到97%以上；在双对数坐标中，毛管压力和最小毛管压力的对数差与进汞饱和度与最小毛管压力的对数差呈线性关系，可利用该线性关系直接求取毛管压力模型的斜率a和幂指数b，求解步骤较为简单；在其他条件相同时，毛管压力与斜率a和幂指数b均成反比。

New mathematical model and key parameters of capillary pressure curves of high-rank coal samples

Capillary pressure is an important parameter that affects the occurrence and development of coalbed methane. In order to establish an effective mathematical model to characterize capillary pressure curves of high-rank coalbed methane reservoirs, coal samples from No.3 coal seam in southern Qinshui Basin was taken as the research object, high-pressure mercury intrusion experiments were carried out, and the adaptability of the typical mathematical models of the capillary pressure curve currently in common use are systematically evaluated. Then a new mathematical model with higher fitting degree for high-rank coal is established. The results show that capillary pressure curves of 6 coal samples have no middle flat section, and the overall performance showed the protruding to upper left, which is obviously different from those of the conventional sandstone or low-rank coal reservoirs. BC model, He Chengzu’s model and Li’s model could not fit the capillary pressure curves of high-rank coal samples well. A new empirical model of capillary pressure curve, is established by processing capillary pressure data. The fitting degree of this model and capillary pressure curve data reaches over 97%, and the fitting effect is better than the existing models. In the log-log coordinates, the logarithmic difference between capillary pressure and the minimum capillary pressure is linear with the logarithmic difference between mercury saturation and the minimum capillary pressure, and the linear relationship can be used to directly obtain the slope a and power exponent b of the new capillary pressure model. The values of slope a and power exponent b are inversely proportional to the capillary pressure, when other conditions are equal.