Derivation of a microstructural poroelastic model

The standard description of wave propagation in fluid-saturated porous media is given by the Biot-Gassmann theory of poroelasticity. The theory enjoys strong experimental support, except for specific and systematic failings. These failings may be addressed by the introduction of the concept of squirt flow. A wide range of squirt flow models exist, but the predictions of these models contradict each other and those of poroelasticity. We argue that a valid squirt flow model should be consistent with the evidence in favour of poroelasticity and with the rigorous results of effective medium theory. We then proceed to derive such a model for a simple pore space consisting of a randomly oriented collection of small aspect ratio cracks and spherical pores. However, compliance with our constraints is not a sufficient condition for the model to be a valid representation of rock. We build confidence in the approach by showing that a range of geometries can be handled without complicating the mathematical form of the model. Indeed, the model can be expressed through macroscopic parameters having physical interpretations that are independent of the specific microstructural geometry. We estimate these parameters for a typical sandstone and demonstrate the predictions of the model.