基于固体替换模型的有机质含量对页岩弹性性质的影响分析

页岩中的TOC(Total Organic Carbon,总有机碳)含量,对页岩的有效弹性模量以及与之相关的弹性波速度(P波和S波)有重要影响,建立弹性模量与TOC含量关系是页岩气甜点预测的重要手段之一.CS和SM两种固体置换理论主要针对孔隙度较大的砂岩,能否适用于孔隙度低、孔隙形态复杂和非均质性强的页岩目前尚未深入研究.鉴于目前已知的富有机质页岩的TOC赋存形态与裂缝以及孔隙形态类似,有关TOC含量对岩石弹性模量的影响可视为孔隙物质充填问题来研究.本文利用数字岩心技术,构造同一数字岩心不同TOC含量的样本群,基于CS和SM两种固体替换理论模型,通过有限元(FEM)数值模拟交叉验证,详细研究了两种固体替换方程对页岩的适用性和TOC含量对页岩弹性性质的影响.研究表明,由于实际岩心孔隙及TOC分布的非均质性,CS替换方程弹性模量预测值与FEM模拟结果存在差异,而SM替换方程预测值与FEM模拟结果基本一致,两种方程的预测差异揭示页岩非均质强度,利用SM替换方程中的参数α_1,α_2,β_1和β_2可详细分析实际岩心孔隙及TOC分布的非均质特征.

The analysis of the influence of organic content on the elastic properties of shale based on solid substitution model

The elastic moduli and the elastic wave velocities related to the elastic moduli are influenced by the fraction of TOC in shales. Therefore, the relation between the elastic moduli and the fraction of TOC in rocks, in turn, can be served as a method to explore the shale gas sweet spot. C&S and S&M substitution equations are mainly focused on the solid substitution problem for sandstones with large porosity. Whether the C&S and S&M substitution equation can be used to solve the solid substitution problem for shale with low porosity, complex pore structure and high heterogeneity is not researched deeply until now. Because the TOC shape in organic-rich shale is similar to shale pore and crack structure, the influence of the TOC content on the elastic moduli of shale can be regarded as a kind of solid substitution problem. In this research, we constructed a group of digital rock cores with different TOC content, and based on C&S and S&M solid substitution equations and FEM simulation researched the application of the two substitution equations, and the influence of TOC contents on the elastic properties of shale. It is shown that because of the heterogeneity of the distribution of pore and TOC in shales, there is error between the result of C&S equation and FEM simulation. However, the result of S&M equation is consistent with the result of FEM simulation. The difference between the results of C&S and S&M equations indicate the heterogeneity of the shales. The parameters α₁ ,α₂, β₁ and β₂ in S&M equation can be served as the parameters representing the heterogeneity of the distribution of pore and TOC in shales.