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摘要:
孔隙纵横比是描述多孔岩石微观孔隙结构特征的重要参数，目前用于获取岩石完整孔隙纵横比分布的经典模型为David-Zimmerman (D-Z)孔隙结构模型，该模型假设岩石由固体矿物基质、一组纵横比相等的硬孔隙以及多组纵横比不等的微裂隙构成，并认为固体矿物基质和硬孔隙均不受压力影响，在此基础上，利用超声纵横波速度的压力依赖性反演岩石硬孔隙和各组微裂隙的孔隙纵横比及孔隙度.该方法的关键点在于以累积裂隙密度为桥梁，借助等效介质理论建立了岩石弹性模量和孔隙纵横比之间的内在联系.但在D-Z模型中，多重孔隙岩石累积裂隙密度的计算直接由单重孔隙裂隙密度公式实现，这种近似导致该模型在许多情况下难以获得良好的反演精度.为了完善经典D-Z模型，本文提出了一种基于虚拟降压的孔隙纵横比分布反演策略，通过多个假想降压过程实现累积裂隙密度的准确计算，并将基于DEM和MT的经典D-Z模型推广到KT和SCA中，结合四种等效介质理论建立了一套完整的反演流程.采用一系列砂岩和碳酸盐岩样品，测试了反演流程在实际岩芯孔隙纵横比提取中的应用效果，研究结果表明：与D-Z模型相比，本文方法的模拟结果与实际数据吻合更好，并同时适用于砂岩和碳酸盐岩；此外，通过分析四种等效介质理论的模拟结果发现，本文方法并不十分依赖于等效介质理论的选择，这些理论获得的孔隙结构参数随压力的变化趋势基本一致，数值上仅存在略微差异，且这种差异随着压力的增大逐渐消失.本文方法是经典D-Z孔隙结构模型的重要补充，对岩石孔隙结构表征、流体饱和岩石速度预测以及孔间喷射流效应的模拟具有十分重要的意义.
Abstract:The pore aspect ratio is an important parameter to describe pore structure characteristics of porous rocks. At present,the most classical model used to obtain complete pore aspect ratio distribution of rocks is the David-Zimmerman (D-Z) pore structure model. The model assumes that the rock is composed of solid mineral matrix,a group of stiff pores having the same aspect ratio and a distribution of micro-cracks with different aspect ratios,in which the material matrix and stiff pores are pressure-independent. Based on the assumptions,the pore aspect ratio and porosity of stiff pores and micro-cracks are extracted from the pressure dependence of ultrasonic velocities. The key point of this method is that the cumulative crack density is taken as a bridge to establish the intrinsic relationship between rock elastic modulus and pore aspect ratio through effective medium theory. However,in the D-Z model,the cumulative fracture density of multi-porosity rock is directly calculated using the formula of crack density theoretically only applicable for rock with a single pore type,which makes it difficult to achieve good inversion accuracy in many cases. In order to improve the classical D-Z model,this paper proposes an inversion method for calculating pore aspect ratio distribution using thought experiment. In this method,the cumulative crack density is accurately computed through a fictitious unloading path,and the classical D-Z model based on DEM and MT is extended to the case of KT and SCA. As a result,a detailed inversion workflow combining with four effective medium theories is established. This workflow is applied in the aspect ratio distribution extraction for a set of sandstones and carbonate samples to illustrate the capability of the method. The results show that the proposed method is in better agreement with the actual data as compared to the D-Z model,and can be applied to both sandstone and carbonate samples. In addition,the proposed method is almost independent of the selection of the effective medium theories. The pore structure parameter obtained from the four theories changes with pressure in a similar way. Although there is a slight difference in these results,it gradually disappears with increasing pressure. Our method is an important supplement to the classical D-Z pore structure model. It is of great significance in the characterization of rock pore structure,prediction of fluid saturated rock velocity and simulation of pore-scale squirt flow.
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图 2
受压后岩石内部硬孔隙和微裂隙的形态变化示意图
Figure 2.
Schematic diagram of stiff pores and micro-cracks in rock at different hydrostatic pressures
图 3
增压过程中岩石内各组微裂隙的形态变化示意图
Figure 3.
The change of each group of micro-cracks in rock during pressure increasing
图 4
基于虚拟降压的孔隙纵横比反演流程图
Figure 4.
Inversion workflow of aspect ratio distribution based on a thought unloading method
图 6
砂岩样品(a-b)和碳酸盐岩样品(c-f)的孔隙结构特征
Figure 6.
Pore structure characteristics of the sandstone (a-b) and carbonate (c-f) samples
图 7
干燥岩芯样品的纵横波速度-压力曲线
Figure 7.
Velocity versus confining pressure for dry rock samples
图 8
基于4种等效介质理论反演的不同有效压力下砂岩(a-b)和碳酸盐岩(c-d)样品的累积裂隙密度分布
Figure 8.
Cumulative crack density distribution as a function of the aspect ratio calculated by different effective medium theories at different pressures for sandstone (a-b) and carbonate samples (c-d)
图 9
基于4种等效介质理论反演的不同有效压力下砂岩(a-b)和碳酸盐岩(c-d)样品的微裂隙孔隙度
Figure 9.
Crack porosity as a function of the aspect ratio calculated by different effective medium theories at different pressures for sandstone (a-b) and carbonate samples (c-d)
图 10
基于不同等效介质理论的模型反演结果与实际测量结果对比
Figure 10.
Comparison of the measured velocities and the results inverted using different effective medium theories
图 11
本文方法和D-Z方法基于DEM理论反演的干燥岩石弹性模量对比
Figure 11.
Elastic Moduli of dry rock calculated with DEM by using our method and D-Z method
表 1
砂岩和碳酸盐岩样品的基本参数
Table 1.
Physical properties of the sandstone and carbonate samples
编号 岩石类型 孔隙度 干燥密度 矿物成分 S1 纯净砂岩 4% 2.54 g·cm-3 石英(100%) S2 泥质砂岩 23.9% 2.02 g·cm-3 石英(66%)，
长石(17%)，
粘土(15%)，
黄铁矿(1%)，
菱铁矿(1%)C1 孔洞型碳酸盐岩 3% 2.59 g·cm-3 方解石(100%) C2 裂缝型碳酸盐岩 0.6% 2.66 g·cm-3 方解石(100%) 
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表 2
基于不同等效介质理论反演的硬孔隙纵横比
Table 2.
Inversion results of the characteristic aspect ratio for the stiff pore obtained from different effective medium theories
岩芯样品 KT SCA MT DEM S1 硬孔纵横比αs 0.39 0.37 0.38 0.42 平均误差ε 0.18% 0.34% 0.18% 0.19% S2 硬孔纵横比αs 0.14 0.29 0.10 0.15 平均误差ε 4.31% 3.36% 2.74% 2.05% C1 硬孔纵横比αs 0.17 0.18 0.17 0.18 平均误差ε 0.17% 0.27% 0.19% 0.21% C2 硬孔纵横比αs 0.95 1.00 0.96 0.95 平均误差ε 4.96% 4.60% 4.96% 4.97%
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