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在Dvorkin弹性 BISQ(Biot/Squirt)模型的基础上,本文提出能同时考虑“Biot流动机制-喷射流动机制-骨架粘弹性机制”的广义粘弹性 BISQ模型;并定义了一个由渗透率和泥质含量控制的粘弹性参数修正因子,使得该模型适用于更广渗透率范围(k>0.05mD)的含泥质砂岩。本文应用微分型广义粘弹性本构关系描述含泥质砂岩固体骨架的应力应变关系,推导出粘弹性波传播的动力学控制方程,通过假设一组平面谐波解,给出频率-波数域波动方程的相速度和衰减系数表达式。数值结果与实验数据的对比研究表明,本文所提出的适用于更广渗透率范围含泥质砂岩的广义粘弹性BISQ模型是有效和正确的。
Based on the Dvorkin elastic BISQ (Biot / Squirt) model, a generalized viscoelastic BISQ model which can simultaneously consider the “Biot flow mechanism - jet flow mechanism - skeleton viscoelasticity mechanism” is proposed. The viscoelastic parameter correction factor controlled by shale content makes this model suitable for muddy sandstone with a wider permeability range (k> 0.05mD). In this paper, the differential-type generalized visco-elastic constitutive relation is used to describe the stress-strain relationship of viscous-elastic sandstone skeleton. The governing equation of viscoelastic wave propagation is deduced. By assuming a set of plane harmonic solutions, the frequency- Equation of phase velocity and attenuation coefficient expression. The numerical results and experimental data show that the generalized viscoelastic BISQ model proposed in this paper is effective and correct for the muddy sandstone with a wider range of permeability.