Revisiting the Wyllie time average equation in the case of near‐spherical pores

Abstract

We suggest a generalized form of the Wyllie equation to better describe acoustic velocity variation with porosity in rocks with a mixture of intercrystalline and near‐spherical pores. Introducing a pore shape factor in the Wyllie equation allows different weights to be applied to the solid‐phase P‐wave velocity to account for rock frame stiffness. This is demonstrated in carbonate and igneous rocks having variable amounts of spherical porosity, ranging from 0% to 80% of the bulk porosity. The generalized equation describes a velocity–porosity envelope instead of the simple line given by the Wyllie equation. The lower limit of the velocity envelope is for rocks that have only interparticle or intercrystalline porosity (Wyllie equation behavior), and the upper limit is when all pores are spherical or near spherical. This upper limit corresponds to the Hashin‐Shtrikman upper bound for porosities up to 30%. The realization portrays Wyllie's velocity–porosity relationship as one particular case in which all pores are intercrystalline or interparticle with a pore shape factor equal to unity. An increase in the amount of high‐aspect‐ratio pores leads to higher pore shape factor. We suspect that this factor may be generalized to include fracture porosity with values less than unity. We suggest that this factor represents the acoustic equivalent of the cementation factor in Archie's law for resistivity measurements. The velocity calculated by the modified model correlates well with both the measured velocity and the calculated velocity using the Kuster‐Toksöz theoretical model. Various factors controlling acoustic velocity in carbonates can be quantified, based on this modification.