用积分法求取岩石孔隙结构特征值

An integral method for calculating pore structure eigenvalue of rock

针对图解法求取孔隙结构特征值使用条件严格,同时误差较大,而矩法饱和度范围又受限于试验。采用积分法求取特征值,即对孔隙半径进行积分求取特征值。积分法必须先获取孔隙半径数学表达式,即毛管压力数学模型。对毛管压力数学模型进行了探究,在双对数坐标系下推导并建立了毛管压力幂函数模型,采用最小二乘法求取模型参数,并通过对比Sami论文数据验证了推导的模型。深入分析矩法与积分法的联系可知,代入孔隙半径数学表达式即可用积分法求取岩石孔隙结构特征值。最后,对3种方法求取结果进行分析讨论,得出积分法算法严谨,更加接近真实值。这一研究加深了对岩石微观孔隙结构认识。

Due to the limitations of both the graphic method and the rectangular method in determining the pore structure eigenvalues of rock, an integral method is proposed, in which the pore radius is integrated to determine the eigenvalues. In applying the integral method, the pore radius is first determined through a capillary pressure model. Then a capillary pressure power function is derived and presented in the double logarithmic coordinate system, and the model parameters are acquired using the least square method. The proposed model is validated through comparing the calculations with the data provided in Sami＇s paper. A connection between rectangular method and integral method is identified, showing that the pore structure eigenvalue can be calculated using the integral method. Finally, comparison of the proposed method with other two methods indicates that the results calculated by the integral method are closer to the real values. This study can help understand the characteristics of rock micro-pore structure.