地震频段部分饱和条件下软孔隙流体饱和度对岩石弹性模量频散衰减的影响

Influence of fluid saturation in soft pores on elastic modulus dispersion and attenuation of rocks under partial saturation condition at seismic frequencies

本文构建软孔隙不同饱和度微-介观双尺度流体流动模型用以揭示地震频段岩石部分饱和时微-介观双尺度流体流动对弹性模量频散和衰减的影响.这一模型经由Betti-Rayleigh互易定理推导软孔隙不同饱和度时频变湿骨架模量,然后将频变湿骨架模量带入White球状斑块饱和模型获得.模型数值计算显示:(1)岩石饱和度一定时,随着软孔隙饱和度增加,岩石弹性模量频散和衰减随之增加;当软孔隙完全饱和时,弹性模量频散和衰减达到最大;另一方面,衰减出现两个衰减峰:较低频段衰减峰与介观流有关,较高频段衰减峰与微观流有关.(2)当介观流、微观流特征频率差异较大时,软孔隙不同饱和度对介观流作用较小,而对微观流作用较大,当软孔隙完全饱和时,对微观流作用达到最大;当介观流、微观流特征频率相近时,软孔隙饱和度对介观流作用增加,且随着饱和度增加而作用增强.(3)新建模型与Li等(2018)微-介观双尺度模型对比可知,Li等(2018)模型可以有效预测部分饱和岩石高频弹性模量变化,但在地震、声波频段可能失效;对此模型进行改进后,其可以有效预测部分饱和岩石不同频段弹性模量变化.最后,本文运用新建模型合理解释部分饱和砂岩地震频段范围衰减数据,验证了新建模型的有效性,并且表明:当岩石处于部分饱和状态时,软孔隙部分饱和更符合实际情况.

A micro-and mesoscopic dual-scale fluid flow model with different soft pore saturations was developed in this paper,so as to reveal the influence of micro-and mesoscopic dual-scale fluid flow on the modulus dispersion and attenuation of partially saturated rocks at seismic frequencies.Based on the Betti-Rayleigh reciprocity theorem,frequency-dependent wet frame moduli with different soft pore saturations were derived,and then the wet frame moduli were incorporated into the White spherical patchy saturation model to obtain the model.The numerical calculation using the model showed that:(1)When the saturation of the rock was constant,the modulus dispersion and attenuation of the partially saturated rock increased as the soft pore saturation increased.When the soft pores were completely saturated,the modulus dispersion and attenuation reached their maximum values.On the other hand,there were two attenuation peaks:one at lower frequencies was related to the mesoscopic flow,and the other at higher frequencies was related to the microscopic flow.(2)When the difference between the characteristic frequencies of the mesoscopic and microscopic fluid flows was large,the different saturations of the soft pores had a small effect on the mesoscopic fluid flow but a larger effect on the microscopic fluid flow.When the soft pores were fully saturated,the effect on the microscopic fluid flow was the largest.As the characteristic frequencies of the mesoscopic and microscopic fluid flows approached each other,the effect of soft pore saturation on the mesoscopic fluid flow increased,and the effect was enhanced with an increase in soft pore saturation.(3)Compared with the micro-and mesoscopic dual-scale model of Li et al.(2018),the model of Li et al.(2018)can effectively predict the variation in the moduli of partially saturated rocks at high frequencies,but may fail at seismic and sonic frequencies.After modification of the model,it could effectively predict the variations in the moduli of partially saturated rocks at different frequencies.Finally,the newly developed model reasonably explained the attenuation data of partially saturated sandstone,and the effectiveness of the model was verified,suggesting that when the rock is partially fluid-saturated,the partial saturation of soft pores is more consistent with reality.