将真实孔隙简化抽象为长椭球孔、扁椭球孔和球形孔3种类型,基于细观力学理论建立数字岩心的三维抽象孔隙模型;结合Eshelby等效介质理论考虑不同类型孔隙微观结构变形的本构关系,在单孔、多孔和混合孔隙弹性变形条件下研究孔隙结构特征对孔隙体积压缩系数的影响。研究表明,数字岩心的孔隙体积压缩系数与孔隙度、孔隙纵横比以及不同类型孔隙体积占比有关：①长椭球孔孔隙压缩系数与孔隙纵横比正相关,扁椭球孔孔隙压缩系数与孔隙纵横比负相关。②孔隙纵横比满足高斯分布且纵横比均值相同,长椭球孔、扁椭球孔纵横比分布越集中孔隙压缩系数越大,相同应力条件下变形量越大。③孔隙压缩系数随孔隙度增大而增大。④孔隙度一定,扁椭球孔、球形孔越多岩石越容易发生变形,孔隙压缩系数越大;长椭球孔越多岩石越不容易变形,孔隙压缩系数越小。通过10种典型数字岩心样品孔隙体积压缩系数计算结果检验,数字岩心真实孔隙体积压缩系数解析计算方法可用于数字岩心样品的孔隙体积压缩系数计算。图12表1参23
The real pores in digital cores were simplified into three abstractive types, including prolate ellipsoids, oblate ellipsoids and spheroids. The three-dimensional elliptical-pore model of digital core was established based on mesoscopic mechanical theory. The constitutive relationship of different types of pore microstructure deformation was studied with Eshelby equivalent medium theory, and the effects of pore microstructure on pore volume compressibility under elastic deformation conditions of one type, multiple types and mixed types of pores were investigated. The results showed that the pore volume compressibility coefficient of digital core is closely related with porosity, pore aspect ratio and volumetric proportions of different types of pores. (1) The compressibility coefficient of prolate ellipsoidal pore is positively correlated with the pore aspect ratio, while that of oblate ellipsoidal pore is negatively correlated with the pore aspect ratio. (2) At the same average value of pore aspect ratio satisfying Gaussian distribution, the more concentrated the range of pore aspect ratio, the higher the compressibility coefficient of both prolate and oblate ellipsoidal pores will be, and the larger the deformation under the same stress condition. (3) The pore compressibility coefficient increases with porosity. (4) At a constant porosity value, the higher the proportion of oblate ellipsoidal and spherical pores in the rock, the more easier for the rock to deform, and the higher the compressibility coefficient of the rock is, while the higher the proportion of prolate ellipsoidal pores in the rock, the more difficult it is for rock to deform, and the lower the compressibility coefficient of the rock is. By calculating pore compressibility coefficient of ten classical digital rock samples, the presented analytical elliptical-pore model based on real pore structure of digital rocks can be applied to calculation of pore volume compressibility coefficient of digital rock sample.
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