多孔介质分形维数的两相渗吸数学模型研究

Study on Two-Phase Permeation Mathematical Model Considering Fractal Dimension of Porous Media

在Poiseuille方程基础上,考虑微观渗吸过程重力、毛管力作用的影响,利用分形维数表征多孔介质微观复杂结构特征,建立了微观两相界面渗吸数学模型。利用压汞实验退汞曲线中退汞压力与退汞量之间的线性关系,可以得到经润湿相和非润湿相表面局部占据后,微观孔隙内部两相可动空间的分形维数,且两相界面运移时间大小等于界面前缘位置对应的曲线积分面积。应用表明:数学模型计算结果与两相渗吸实验数据吻合效果非常好,由此证明该数学模型的建立能够有效模拟两相渗吸过程,为当前多孔介质渗吸研究提供了有效的理论及实验支持,有效降低两相渗吸实验研究周期,提高研究效率。

On the basis of the Poiseuille equation,considering the influence of gravity and capillary force in the microscopic imbibition process,the fractal dimension is used to characterize the microscopic and complex structure of the porous medium,and the mathematic model of microscopic two-phase imbibition is established.The fractal dimension of the two phase movable space in the porous media is obtained by the linear relationship between the mercury removal pressure and the amount of mercury entered by the mercury intrusion curve,and the interfacial moving time is equal to the curve integral area corresponding to the leading edge position of the interface.The results show that the results of the mathematical model are compared with the experimental results of the two-phase imbibition test.The study of mathematic model has provided effective theoretical and experimental support,which can effectively reduce the experimental period of two-phase imbibition and improve the research efficiency.