考虑微观孔隙几何的砂岩自发渗吸理论模型

Theoretical model of water spontaneous imbibition of sandstone considering microscopic pore geometry

为研究砂岩微观孔隙结构几何对其吸水特性的影响机理,应用Hagen-Poiseuille方程、Laplace-Young方程、分形几何理论,考虑孔隙的截面形态、大小分布和通道迂曲3种几何特性,建立了平均几何与分形几何表征的毛细管吸水模型,并对模型的适用性、有效性进行了验证。对比已有模型,分析了各几何参数影响孔隙结构吸水特征的敏感性。研究结果表明:①吸水性特征参量与孔隙几何、迂曲度、孔隙率、最大孔隙尺寸有关,孔隙几何形状越不规整、连通孔隙通道越迂曲、孔隙结构非均质性与各向异性越强,孔隙结构吸水性相对较弱;②平均几何表征的模型中等效平均孔隙直径的物理意义不明确,代入空间平均孔隙尺寸的计算结果大于实测值,而分形几何表征的模型各参数物理意义明确,得到与实测值相近的结果;③对于三维孔隙连通性以及孔吼特征性较弱的孔隙结构,模型适用性较强,相比程序复杂的IFU(Pia)模型、BEA模型,能得到相近甚至更精确的理论预测结果。

In order to study the influence mechanism of micro pore geometry of sedimentary rock on its water absorption characteristics,based on Hagen-Poiseuille equation,Laplace-Young equation and fractal geometry theory,the capillary water absorption models which is respectively represented by average and fractal geometry are established by taking into account three geometric characteristics of pore section shape,pore size distribution and tortuous pore space.Compared with the existing model,the applicability and validity of representative model are verified by using existing experimental data.Finally,the sensitivity of geometric parameters influencing water absorption characteristics of pore structure is analyzed in detail.The results show that the parameters of water absorption characteristics are related to the pore geometry shape,tortuous fluid channel,free porosity and maximum pore size,whereas the more irregular the pore geometry and the more tortuous the connected pore channel,the stronger the heterogeneity and anisotropy of pore structure,and the weaker the water absorption.The physical meaning of equivalent average pore diameter is not clear in the model represented by average geometry,and the calculation result is larger than the measured values when average space pore size is directly brought into the model,while the physical meaning of parameters is clear in the model represented by fractal geometry,and the results close to measured values can be obtained;the proposed models have strong applicability for the pore structure with weak 3D pore connectivity and pore roar characteristics,and compared with the complicated IFU model and BEA model,similar or even more accurate theoretical predicted results can be obtained based on the simplified models.