P- and S-Wave Velocity Calculation Using X-Ray CT Images for Shaly Tight Sandstone
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摘要: 基于三维X射线CT图像重构的数字岩心模型，是目前计算岩石纵横波速度的重要方法，但由于CT图像难以准确区分致密砂岩中泥质和岩石碎屑颗粒，利用X射线CT图像研究泥质致密砂岩纵横波速度难度较大.本研究通过建立二维数字岩心模型，开展有限元模拟，讨论泥质含量、分布形式以及微孔隙的发育程度对岩石弹性参数的影响，基于影响岩石弹性参数的主控因素，探索利用三维数字岩心模拟泥质砂岩纵横波速度的可行性.研究表明：分散泥质以及骨架结构泥质对岩石体积模量影响较小，颗粒-颗粒接触面结构泥质对体积模量影响较大，三种泥质分布形式对剪切模量影响相当；泥质含量对岩石体积模量的影响小于泥质分布形式，而泥质含量对剪切模量的影响大于泥质的分布形式；与分散泥质相关的微孔隙对岩石弹性参数影响较小，而岩石弹性参数对与骨架结构泥质和颗粒-颗粒接触面泥质相关的微孔隙敏感，且微孔隙增加对剪切模量的减小大于体积模量.根据上述模拟结果，针对泥质砂岩建立了基于三维分水岭算法的颗粒-颗粒接触面泥质模型，模拟结果与实测值吻合较好.Abstract: It is an important method to simulate P- and S-wave velocities using digital core obtained from X-ray CT images. However, since it is impossible to differentiate clay and grains, and abundant micro-pores exist in shaly tight sandstones, simulating P- and S-wave velocities using digital core is a challenge. In this study, 2D digital core models are constructed and simulated using finite element method to understand the effect of clay content and distribution, amount of micro-pores on the rock elastic properties. The results will be used to assist the construction of a 3D model that can be used to simulated P- and S-wave velocities of shaly sandstones. The results show that dispersed clay and framework clay have minor effects on the bulk modulus, while interstitial clay shows large effect on bulk modulus. Effects of the different clay distributions on shear modulus are similar. Clay distribution has larger effect on bulk modulus than clay content, whereas clay content has larger effect on shear modulus than clay distribution. Micro-pores related to dispersed clay have minor effect on rock elastic properties, however micro-pores related to framework clay and grain-grain contact clay are sensitive to rock elastic properties. In addition, micro-pores have larger effect on shear modulus than bulk modulus. Based on the above results, a 3D digital core model using 3D watershed method on the X-ray images has been built and the results show good match with the measured velocities.
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图 2 砂岩CT图像二维切片（a）及相应的二值化图像（b）
Fig. 2. A slice of CT image (a) and the corresponding binary image (b) of sandstone
图 3 三种泥质分布形式不同泥质含量的二维图像
A1~A8为孔隙分布模型；B1~B8为颗粒包壳模型；C1~C8为喉道分布模型
Fig. 3. 2D images of three clay distribution patterns with different clay contents
图 4 基于三维分水岭算法的颗粒‒颗粒接触面泥质模型
Fig. 4. Grain-grain contact clay model based on the 3D watershed method
图 6 不同泥质分布模式的体积模量和剪切模量与孔隙度的关系
Fig. 6. Bulk and shear modulus versus porosity for different clay cement patterns
图 7 不同泥质分布模式、不同泥质弹性参数的体积模量和剪切模量与孔隙度的关系
Fig. 7. Bulk and shear modulus versus porosity for different clay cement patterns and clay elastic properties
图 8 样品D20（a），样品D105（b）和样品D6（c）对应的铸体薄片、CT图像以及表征单元体分析
Fig. 8. Casting thin sections, CT image and representative elementary volume analysis of sample D20 (a), D105 (b) and D6 (c)
图 9 基于分水岭算法的致密砂岩颗粒‒颗粒接触面泥质建模流程
Fig. 9. Grain-grain contact clay model of tight sandstone based on watershed method
图 10 样品D20（a），样品D105（b）和样品D6（c）三维数字岩心模型
Fig. 10. 3D digital core model of samples D20(a), D105(b) and D6(c)
图 11 D20样品三维数字岩心挤压（a）和剪切（b）条件下米塞斯应力分布
Fig. 11. 3D von-mises stress distribution of compression (a) and shear condition (b) of D20
图 12 致密砂岩纵横波速度实测值与预测值对比
Fig. 12. Comparison of measured and predicted P- and S-wave velocities of tight sandstone samples
表 1 不同矿物的弹性参数
Table 1. Bulk (K) and shear (G) moduli of the minerals used in the modeling
石英 泥质0% 泥质2.5% 泥质5% 泥质10% 泥质Xu and White 泥质Mavko 体积模量（GPa） 36.6 34 25.6 22 13.9 26.6 21 剪切模量（GPa） 45 15.2 8.2 5.1 2.3 16.8 7 
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