Effective Medium Theories for Multicomponent Poroelastic Composites

It is demonstrated that effective medium theories for poroelastic composites such as rocks can be formulated easily by analogy to well-established methods used for elastic composites. An identity analogous to Eshelbyʹs classic result has been derived previously for use in composites containing arbitrary ellipsoidal-shaped inclusions. This result is the starting point for new methods of estimation, including generalizations of the coherent potential approximation, differential effective medium theory, and two explicit schemes. Results are presented for estimating drained shear and bulk modulus, the Biot-Willis parameter, and Skemptonʹs coefficient. Three of the methods considered appear to be quite reliable estimators, while one of the explicit schemes is found to have some undesirable characteristics. Furthermore, the results obtained show that the actual microstructure should be taken carefully into account when trying to decide which of these methods to apply in a given situation.