We describe a practical velocity model for clastic rocks developed from the Kuster and Toksoz, effective medium and Gassmann theories. In this model, the total pore space is divided into two parts:
pores associated with sand grains and
pores associated with clay minerals (including bounding water).
The essential feature of the model is that the difference in pore geometry implies a difference in elastic compliance. Clay components are made much more compliant with increasing porosity than sands are. The model is able to simulate the combined effect of lithology, clay content, water-saturation and fluid type on P-wave and S-wave velocities. In contrast to common applications of Gassmann's theory to simulate fluid relaxation, we use Kuster and Toks?z and effective medium theories to derive the elastic moduli of the dry rock frame. The predictions are therefore derived from tabulated grain matrix parameters. The model was used to study the relationship between porosity, clay content and P- and S-wave velocities. Numerical results indicate that clays affect the elastic behaviour of clastic rocks in two ways:
by reducing the elastic moduli of the grain matrix, and
by creating pores with small aspect ratios.
The porosity-velocity relationship predicted for shales agrees with Wood's suspension model rather than Wyllie's time average equation or Raymer's model. The model was also used to predict S-wave logs from other logs. An S-wave log can be predicted in three ways: from porosity (?) and shale volume (Vsh). from the P-wave sonic log (DT) and Vsh, or from DT and ?. Comparisons of predictions with log and laboratory measurements demonstrated that prediction from DT and Vsh or ??was more robust than that from ? and Vsh. DT is normally less error-prone than ? or Vsh. Velocity dispersion was studied by considering the effect on the model of the relaxed and unrelaxed extremes of fluid flow. This allows the dependence of velocity dispersion in a clastic rock on porosity, clay content, and elastic properties of the grain matrix and pore fluid to be simulated. The comparisons between our predictions and laboratory and well logging data span a wide range of conditions and rock composition and demonstrate the flexibility, applicability and reliability of the model.
