基于Chapman模型的气水两相饱和岩石速度频散及衰减表征

Characterization of velocity dispersion and attenuation of gas-water two-phase saturated rock based on Chapman model

含裂隙岩石的裂隙系统与其内的流体的分布,很大程度上会影响地震波在其内的传播,导致速度频散和衰减.本文基于Chapman模型,研究润湿相和非润湿相流体随频率的变化.许多学者研究的是单一流体下的频变各向异性理论,本文着重于气水两相流体部分饱和的情况.引入了基于分形理论的相对渗透率模型,并使用无量纲参数q来表征斑块饱和现象.首先研究气水两相的相对渗透率与分形维数的关系,然后考虑了斑块饱和效应对流体混合物的有效迁移率的影响.根据数值算例,在Chapman模型中分别引入相对渗透率模型和斑块饱和效应,观察各自对横波速度和衰减的影响.最后分析耦合的相对渗透率和斑块饱和对横波速度和衰减的影响.根据算例结果可知,在中频时,相对渗透率及斑块饱和效应都比低频和高频的情况对横波速度和衰减影响大.最后考虑分形维数和无量纲参数q的耦合影响,发现无量纲参数q对横波速度和衰减的影响都明显要大于分形维数.同时还引入了横波分裂来分析这种耦合效应对各向异性的影响,结果表明横波分裂与分形维数成反比,与无量纲参数q成正比,这种现象在低频较为明显.

The distribution of the fractured system and the fluids in the fractured rock can greatly affect the propagation of seismic waves within it,resulting in velocity dispersion and attenuation.The commonly used pore fluid theories mainly include poroelastic wave theory based on Biot theory and fluid displacement method based on Gassmann fluid displacement equation.In this paper,based on the Chapman model,we study the variation of the wetting and non-wetting phase fluids with frequency.Many scholars have studied the theory of frequency-dependent anisotropy in a single fluid.This paper focuses on the study of partially saturated gas-water two-phase fluids.A relative permeability model based on fractal geometry is introduced,and a dimensionless parameter q is used to characterize the patch saturation phenomenon.Firstly,the relationship between the relative permeability of gas-water two-phase and fractal dimension is studied,and then the effect of patch saturation on the effective fluidity of fluid mixture is considered.Through numerical examples,two different relative permeability models are introduced into the Chapman model,respectively,to observe their effects on shear wave velocity and attenuation,and then consider the effect of patch saturation on the Chapman model.Finally,the frequency-dependent anisotropic elastic modulus equations of two-phase immiscible fluid-saturated fractured rocks are calculated,and the shear wave velocity and its dispersion are obtained.The calculation example results show that the relative permeability and patch saturation effect have more influence on the shear wave velocity and attenuation at medium frequencies than at lower and higher frequencies.Finally,considering the coupling influence of fractal dimension and dimensionless parameters q,it is found that the influence of dimensionless parameters q on shear wave velocity and shear wave attenuation is significantly greater than that of fractal dimension,and shear wave velocity and attenuation are inversely proportional to dimensionless parameters q and proportional to fractal dimension.At the same time,in order to better reflect the influence of relative permeability and patch saturation on anisotropy,shear wave splitting is also researched.In the Chapman model after introducing the coupled patch saturation effect and relative permeability model,shear wave splitting is related to the fractal dimension is inversely proportional to the dimensionless parameter,and this phenomenon can be more obvious at low frequencies.