Отправлено: 08.02.09 10:12. Заголовок: A generalized viscoe..

A generalized viscoelastic Biot/squirt model for clay-bearing sandstones in a wide range of permeabilities
Журнал Applied Geophysics
Chinese Geophysical Society
ISSN 1672-7975 (Print) 1993-0658 (Online)
Volume 5, Number 4 / Декабрь 2008 г.
DOI 10.1007/s11770-008-0038-y
pp 249-260

A generalized viscoelastic Biot/squirt model for clay-bearing sandstones in a wide range of permeabilities
Jianxin Nie1 , Dinghui Yang2 and Huizhu Yang3

(1) State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China
(2) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China
(3) Institute of Seismic Exploration, Tsinghua University, Beijing, 100084, China

Received: 20 September 2008 Revised: 1 November 2008 Published online: 8 January 2009

Abstract 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.
Keywords viscoelasticity - BISQ model - clay-bearing sandstones - phase velocity - attenuation coefficient

This work was 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), and the National Basic Research Program of China (973 program) (Grant No. 2007CB209505).
Nie Jianxin received a PhD degree in Engineering Mechanics from Tsinghua University in 2005. He is currently a lecturer at Beijing Institute of Technology. His research interests include rock physics, wave propagation modeling, and inverse methods in petrophysics.

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Jianxin Nie
Email: niejx@bit.edu.cn



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