Double Porosity Biot Theory Extension

Reservoir stones are generally a porous medium, heterogeneous, fractured and saturated with oil, gas or water. The analysis of wave propagation on these media is carried out using the Biot-Gassman theory for porous media and an extended Biot's theory for fractured porous medium. One way to model fractures is using the concept of double porosity, understanding it as a system of three phases: solid, fluid in the pores and fluid in the fractures. This work shows a macroscopical or phenomena-logical description of seismic wave propagation on fractured porous media. From the movement and constitutive equations of the double porosity system and as a natural generalization of Biot's Theory we obtain the dispersion relations as analytical expressions of the three P waves and an S wave by the way of a six order polynomial for the P waves and a second order polynomial for the S wave. In this research the stress-particle velocity scheme is used, writing it as a first order system of differential equations with the advantage of higher precision in its numerical implementation.