Modeling velocity dispersion and attenuation using pore structure characteristics of rock
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摘要:
孔隙尺度的喷射流流动是引起地震波速度频散和衰减的重要机制之一. 目前，大多数喷射流模型仅考虑硬孔隙与微裂隙之间的局部流动，而忽略了具有不同孔隙纵横比微裂隙间的喷射流作用. 为了研究各种类型孔隙间的流体流动效应，本文对经典喷射流模型进行了扩展，通过结合等效介质理论和孔隙结构模型，根据从干燥岩石超声速度-压力曲线中提取的微裂隙孔隙纵横比分布，求取出岩石中各种微裂隙的体积压缩系数，并在此基础上，利用孔隙空间的压力松弛效应对微裂隙间的喷射流效应进行了模拟，并运用Biot理论描述了硬孔隙间的宏观流动效应. 扩展后的理论模型不仅考虑了微裂隙与硬孔隙间的局部流动、硬孔隙与硬孔隙间的Biot宏观流，还加入了微裂隙与微裂隙间的喷射流作用，且模型的高、低频极限始终与Mavko-Jizba理论和Gassmann方程保持一致. 模型应用分析发现，对于砂岩和大部分致密灰岩样品，扩展模型均能给出与超声实验测量数据吻合良好的估计结果. 此外，扩展模型预测的速度频散及衰减表明，喷射流机制在地震和测井频段发挥着重要作用，其速度频散曲线由低频至高频呈逐渐增大趋势，不具有明显的快速变化特征，与经典频散曲线形态存在显著差异；在低有效压力下，频散和衰减程度较大，喷射流机制发挥主要作用，而随着有效压力的增加，Biot宏观流机制开始占主导，频散和衰减程度逐渐减小.
Abstract:Pore-scale squirt flow is one major mechanism that results in seismic wave dispersion and attenuation. Most existing squirt models only consider the local fluid flow between stiff pores and micro-cracks, but the squirt effects of micro-cracks with different pore aspect ratios are often being overlooked. Therefore, the classical squirt model is extended to investigate the fluid flow between pores with different aspect ratios. We first calculate the bulk compressibility of micro-cracks by using the aspect ratio distribution extracted from pressure-dependent dry ultrasonic velocities. Then, squirt flow effects between micro-cracks is modeled according to the pressure relaxation in the pore space. The global fluid flow in the stiff pores is described by Biot theory. The extended theoretical model considers the interaction between stiff pores and cracks, the Biot global flow in stiff pores, and also the squirt fluid flow effects among micro-cracks. The high- and low-frequency limits of the extended model are consistent with Mavko-Jizba and Gassmann equation, respectively. Modeling results of the extended model is consistent with the laboratory ultrasonic measurements for sandstones and most of the tight carbonate samples. In addition, velocity dispersion and attenuation predicted by using the extended model indicate that the squirt flow may play an important role at seismic and logging frequencies. The modeled velocities grow from low frequency to high frequency slowly and no obvious fast change is observed, which is significantly different from those predicted by classical models. At low differential pressure, the squirt flow mechanism dominates the dispersion and attenuation. However, Biot global flow mechanism gradually stands out with increasing pressure and, as a result, the dispersion and attenuation decline.
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Key words:
- Squirt effect /
- Velocity dispersion and attenuation /
- Pore structure /
- Pore aspect ratio
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图 1
扩展Gurevich喷射流模型的速度频散和衰减计算流程
Figure 1.
Workflow for calculating velocity dispersion and attenuation using extended Gurevich squirt model
图 2
岩石样品的超声实验数据与孔隙结构参数反演结果
Figure 2.
Measured ultrasonic data and inverted pore structrue parameters for rock samples
图 3
超声频率条件下实验测量数据与模型预测结果比较
Figure 3.
Comparision of measured velocities and predictions obtained from different models at ultrasonic frequency
图 4
饱水条件下所有岩芯样品的模型计算结果与超声实验速度比较
Figure 4.
Ultrasonic velocity measurements and model predictions at water-saturated condition
图 5
代表性砂岩和灰岩样品的柱体薄片
Figure 5.
Thin sections for representative sandstone and limestone samples
图 6
经典Gurevich喷射流速度频散与衰减曲线随微裂隙孔隙纵横比与孔隙度的变化规律
Figure 6.
Squirt velocity dispersion and attenuation predicted by classical Gurevich model as a function of crack aspect ratio and porosity
图 7
0 MPa有效压力下饱水灰岩样品C1的纵波速度频散(a)和衰减(b)
Figure 7.
P-velocity dispersion and attenuation for water-saturated limestone sample C1 at 0 MPa
图 8
不同有效压力灰岩样品C1中微裂隙的孔隙纵横比分布(a)和孔隙度度分布(b)
Figure 8.
Aspect distribution (a) and porosity distribution (b) of limestone sample C1 at different pressure
图 9
砂岩S1的纵横波速度频散(a—b)及衰减(c—d)曲线
Figure 9.
P- and S-velocity dispersion (a—b) and attenuation (c—d) as a function of frequency and pressure for sandstone sample S1
图 10
灰岩C1的纵横波速度频散(a—b)及衰减(c—d)随压力和频率的变化
Figure 10.
P- and S-velocity dispersion and attenuation as a function of frequency and pressure for limestone sample C1
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