Modelling the effect of fluid communication on velocities in anisotropic porous rocks

An inclusion!based anisotropic poroelasticity model "IBAPM# has been developed from the J[ D[ Eshelby "0846\ Proceedin`s of the Royal Society of London Series A\ 130\ 265 285# and T[ Mura "0876\ Micromechanics of Defects in Solids\ Martinus Nijho}\ Dordrecht# theories[ Eshelby|s interaction energy approach is employed to calculate the e}ective elastic constants of a solid containing dilute pores\ since it o}ers two approximations ] one corresponding to the condition of constant load and the other to the condition of constant displacement[ The e}ect of pore ~uid communication on the poroelasticity of a porous rock is modelled via pore connectivity[ A totally isolated pore system implies that pore pressure is equilibrated within each individual pore only and may vary from pore to pore\ depending on the shape and orientation of each pore[ In terms of the local ~ow mechanism\ this gives us a high!frequency estimate of the e}ective elastic moduli[ The low!frequency estimate\ on the other hand\ is modelled by a communicating pore system[ In this case all pores are assumed to be connected and\ consequentlypore pressure is equilibrated within the whole pore system[ Other related problems discussed in the paper include ] "0# extension of the model to the case of pores having arbitrary orientations\ "1# extension of the non!interacting model to higher pore concentrations and "2# consistency checks of IBAPM with previous models[ In particular the low! frequency version of the model is compared with the anisotropic version of the Gassmann model "R[ J[ S[ Brown and J[ Korringa\ 0864\ Geophysics\ 39\ 597 505#[ Finally the model is applied to the laboratory measurements reported by J[ S[ Rathore\ E[ Ejaer\ R[ M[ Holt and L[ Renlie "0884Geophys[ Prosp[\ 32\ 600 617#[ 0887 Published by Elsevier Science Ltd[ All rights reserved[