Seismic wave equations in tight oil/gas sandstone media

Tight oil/gas medium is a special porous medium,which plays a significant role in oil and gas exploration.This paper is devoted to the derivation of wave equations in such a media,which take a much simpler form compared to the general equations in the poroelasticity theory and can be employed for parameter inversion from seismic data.We start with the fluid and solid motion equations at a pore scale,and deduce the complete Biot’s equations by applying the volume averaging technique.The underlying assumptions are carefully clarified.Moreover,time dependence of the permeability in tight oil/gas media is discussed based on available results from rock physical experiments.Leveraging the Kozeny-Carman equation,time dependence of the porosity is theoretically investigated.We derive the wave equations in tight oil/gas media based on the complete Biot’s equations under some reasonable assumptions on the media.The derived wave equations have the similar form as the diffusiveviscous wave equations.A comparison of the two sets of wave equations reveals explicit relations between the coefficients in diffusive-viscous wave equations and the measurable parameters for the tight oil/gas media.The derived equations are validated by numerical results.Based on the derived equations,reflection and transmission properties for a single tight interlayer are investigated.The numerical results demonstrate that the reflection and transmission of the seismic waves are affected by the thickness and attenuation of the interlayer,which is of great significance for the exploration of oil and gas.