A Theoretical Study On The Attenuation Of Elastic Waves In Porous Media Containing Cracks

The dynamic poroelastic theory proposed by Biot is widely used to describe thebehavior of elastic waves propagating in fluid saturated porous media. Meanwhile, it iswell known that the Biot theory predicts much weaker attenuations than measuredvalues. One accepted reason is that in the Biot theory energy dissipates only due toviscous friction cauded by the average fluid motion relative to the framework of solidgrains. The porous rock, however, usually contains cracks. This paper focuses on theeffect of local squirt flow from cracks to the pores on the dispersion and attenuation ofelastic waves in a porous medium containing cracks.Firstly, we introduce Biot theory and fast P wave, S wave and slow P wavedispersion and attenuation formulas are in brief. After these we analyze the Biotcorrection model due to squirt mechanism under closure condition, in other words,Tangmodel, which introduce an additional compliance on Biot module.Then differentadditional compliance factors varying as frequency changing are contrasted andanalyzed in this paper.Secondly, Biot model is corrected by considering the squirt flow under drainagecondition. We compare the closed-correction model and drainage correction model anddisscuss the physical mechanism leading to the differences between the two models.Finally, by integrating closed-correction model and drainage correction model,weestablish this unified correction model including the Biot mechanism and squirtmechanism. Two energy loss mechanisms to waves attenuation are discussed andcompared, the dynamic compatibility phenomeno predicted by Biot is studied in thisunified model. Crack shapes these may have effects on wave properties are also studied.The drainage squirt correction model in this paper predicts much more attenuationand velocity dispersion than closure squirt correction model, because fluid in porosunder drainage conditon can move much more easily than that in poros under closedcondition, so drainage condition would provide smaller impediments on squirt flow.Because of this new unified model has both the advantages of Biot’s model and Tang’smodel, it may be used in wave fields among geophysics.