A Study of the Speed of Sound in Porous Granular Media

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Abstract
A theory is developed to explain the influence of pressure, porosity, and liquid saturation on the speed of sound through a porous granular medium. An aggregate of randomly stacked spherical particles of four different sizes is used as a model for the porous medium. The volume-pressure relationship of the aggregate is determined by means of the Hertz theory for the deformation of elastic and isotropic spheres in contact. This relationship is extended to embrace the case of liquid saturation of the aggregate. The bulk modulus is derived from the volume-pressure relationship and the speed of sound is determined from the bulk modulus. It is shown how the theory can be extended to apply to the speed of sound through an aggregate comprised of nonspherical granules and finally, in an approximate form, through a consolidated granular medium. As an example of the application of the latter the speed of sound through sandstone under various conditions of pressure and saturation is predicted, and agreement is noted between the predicted results and those derived experimentally.

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