摘要
To simultaneously take into account the Biot-flow mechanism, the squirt-flow mechanism, and the frame-viscoelasticity mechanism, a generalized viscoelastic BISQ （Biot/squirt） model is developed for wave propagation in clay-bearing sandstones based on Dvorkin＇s elastic BISQ model. The present model is extended to a wide range of permeabilities （k 〉 0.05 mD） by introducing a dimensionless correction factor for viscoelastic parameters, defined as a function of the permeability and the clay content. We describe the frame＇s stress-strain relationship of the clay-bearing sandstones by the differential constitutive equations of generalized viscoelasticity and then derive the viscoelastic-wave dynamic equations. With the assumption of a plane-wave solution, we finally yield the phase velocities and the attenuation coefficients by solving the dynamic wave equations in the frequency and wave number domain. The comparison of numerical results and experimental data shows that the generalized viscoelastic BISQ model is applicable for modeling the wave propagation in most of the sandstones mainly bearing kaolinite clay.
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。
基金
supported by the National Science Fund for Distinguished Young Scholars of China (Grant No. 40725012)
the National Hi-tech Research and Development Program of China(863 Program) (Grant No. 2006AA06Z240)
the National Basic Research Program of China (973 program)(Grant No. 2007CB209505).
