3D digital core applied to numerically predict elastic response caused by mesoscopic flow
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摘要:
复杂介质油气藏的地震波频散和衰减是地球物理勘探中油气特征反演与解释的重要属性.介观尺度处于微观孔隙尺度与宏观地震波场尺度之间，地震波穿过饱和流体岩石时激励流体发生频散和衰减，导致地震波能量损耗，被称为介观波致流.其形成机理、特征和规律一直是勘探地球物理学和岩石物理学等领域共同关心的科学问题，也是研究的前沿和难点之一.本文首先选取印第安纳灰岩（Indiana）作为研究对象，通过排水方式饱和样品，使用CT方法研究介观流体分布特征和规律；为研究其机理，引入Biot孔弹性理论构建三维（3D）数值模型，模拟部分饱和岩石的纵波速度频散和衰减特征.经对比，数值模拟结果与实验结果匹配，表明Biot孔弹性理论可以用来描述介观波致流的物理机理.本文发展的岩石物理实验结合数值模拟的研究手段为今后研究介观流衰减和频散的特征和规律提供了理论和方法借鉴.
Abstract:Seismic wave dispersion and attenuation are important seismic attributes for characterizing oil and gas in geophysical exploration. When the seismic wave passes through the porous sedimentary rocks, the induced fluid oscillation between the rock-pore and wavelength scale exhibits significant seismic dispersion and attenuation, i.e., mesoscopic dispersion and attenuation. The corresponding mechanism and characteristics have always been a scientific issue of common concern in the fields of exploration geophysics and rock physics. It is also one of the frontiers and difficulties regarding the mesoscopic flow. In the paper, a numerical model is developed to investigate the effect of fluid distribution on mesoscopic dispersion and attenuation of partially saturated Indiana limestone using the drainage method. The fluid distributions in the sample are characterized by the CT scanning method, being the input of the numerical model under the framework of Biot's pore-elasticity theory to predict dispersion and attenuation. The consistency between the prediction and measurement suggests the feasibility of introducing digital petrophysics to analyze the porous fluid distribution quantitively as well as to predict the corresponding dispersion and attenuation characteristics.
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Key words:
- 3D digital core /
- Mesoscopic flow /
- Seismic wave /
- Dispersion /
- Attenuation
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图 1
带有红色矩形扫描区域的印第安纳灰岩
Figure 1.
Indiana limestone with a scanning area of the red rectangle
图 2
使用蒸发排水法饱和样品的过程
Figure 2.
The process of saturating the sample using the drainage method
图 3
CT扫描图像去噪及空间位置校正
Figure 3.
CT scanning results in denoising and the corresponding space registration
图 4
(a) 三维孔隙度分布；(b) 采用排水方法饱和，含水饱和度88%样品内的三维流体分布；(c) 图(a)的YZ剖面；(d) 图(b)的YZ剖面；(e) 孔隙度随着XY平面的变化(沿着Z轴)
Figure 4.
(a) 3D porosity distribution; (b) 3D fluid distribution for water saturation of 88% using drainage method; (c) YZ section of figure (a); (d) YZ section of figure (b); (e) Porosity versus XY slice (along Z-axial)
图 5
(a) 网格粗化; (b) 自适应细化网格; (c) 纵波边界条件位置; (d) 应力位置
Figure 5.
(a) Mesh coarsening; (b) Adaptive mesh refinement; (c) Location for P-wave modulus boundary condition; (d) Location for stress loading
图 6
纵波模量平均方差随测试样品数量NR的变化
Figure 6.
Average variance of P-wave modulus as a function of the total number of realizations NR
图 7
纵波模量平均方差随体积比的变化
Figure 7.
Average variance of P-wave modulus versus different volume ratios
图 9
三维归一化流体压力分布的YZ方向横截面
Figure 9.
YZ section of the 3D normalized fluid-pressure distribution
图 10
3D样品中心横截面的归一化流体分布
Figure 10.
Normalized fluid distribution for the center cross-section of the 3D sample
图 11
(a) 纵波模量和(b)纵波衰减随频率变化的曲线
Figure 11.
Variation of (a) P-wave modulus and (b) P-wave′s attenuation with frequency
表 1
Indiana石灰岩、水和空气的特性
Table 1.
Properties of the Indiana limestone, water, and air
属性 Indiana灰岩 水 空气 孔隙度ϕ(%) 10.8 - - 长度L(mm) 81.0 - - 直径D(mm) 39.7 - - 渗透率κ(m2) 2×10-17 - - 排水体积模量Kd(GPa) 24 2.25 1×10-4 排水剪切模量μ(GPa) 15.2 0 0 密度ρ(kg·m-3) 2369.2 1000 1 黏度η(Pa·s) - 10-3 2×10-5 注：干燥纵波模量为5 MPa差压(即围压减去孔压)下所测.
Note：The dry P-wave modulus is measured under 5 MPa differential pressure (i.e., confining pressure minus pore pressure).
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表 2
岩石物理参数符号定义
Table 2.
Definitions of symbols used for the petrophysical parameters
符号 物理意义 取值 κ 渗透率 约0~1000×10-14 m2 η 流体黏度 约10-3cP~2000 cP ϕ 孔隙度 ＜60% μ 干燥样品剪切模量 ＜300 GPa Kd 干燥样品体积模量 ＜Ks Ks 基质颗粒体积模量 5~300 GPa ρb 饱和流体的岩石密度 (1-ϕ)ρs+ϕρf ρs 基质密度 1000~3700 kg·m-3 ρf 流体密度 0~2000 kg·m-3 Kf 流体体积模量 10-5~5 GPa ρc 复密度 
τ 孔隙迂曲度 0~1 λm Lamé常数 
α Biot-Willis系数 
M 流体模量 
Sg 含气饱和度 0~1 Sw 含水饱和度 0~1 注：表中取值范围参考了《岩石物理手册》中常见储层岩石及流体的取值范围(Mavko et al., 2009)， 
Note：The range of values refers to the values of the reservoir rocks and fluids in the Rock Physics Handbook (Mavko et al., 2009), -
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