Effects of squirt-flowin cracks on drained bulk modulus of porous media

Sedimentary rocks are typical porous media which usually contain both cracks and pores. Liquid in rocks will be squeezed out of flat cracks and then flow into spherical pores when rocks are under pressure because cracks are much softer than pores. This kind of flow between cracks and pores is squirt-flow which usually induces elastic modulus dispersion and wave attenuation. This paper studies the effects of squirt-flow as well as the liquid compressibility on the deformation of pore space and derives the expression of drained bulk modulus under dynamic loads. There exists a crack compliance in the expression of drained bulk modulus. The crack compliance contains both the contribution of squirt-flow which is caused by pressure difference between cracks and pores and the contribution of the compressibility of the liquid in cracks. The additional compliance brings about dispersion on drained bulk modulus. The real part of drained bulk modulus increases as frequency increases which means that at high frequency rock becomes stiffer, the imaginary part of drained bulk modulus represents the energy loss in the squirt-flow. Crack density mainly decides the modulus dispersion amplitude and the squirt-flow intensity. The crack aspect ratio mainly decides the characteristic frequency of squirt-flow. The expression of drained modulus in this paper reduces to Biot expression when crack density equals zero.