A NEW VELOCITY MODEL FOR CLAY-SAND MIXTURES

None of the standard porosity-velocity models (e.g. the time-average equation, Raymer's equations) is satisfactory for interpreting well-logging data over a broad depth range. Clays in the section are the usual source of the difficulty through the bias and scatter that they introduce into the relationship between porosity and P-wave transit time. Because clays are composed of fine sheet-like particles, they normally form pores with much smaller aspect ratios than those associated with sand grains. This difference in pore geometry provides the key to obtaining more consistent resistivity and sonic log interpretations. A velocity model for clay-sand mixtures has been developed in terms of the Kuster and Toksoz, effective medium and Gassmann theories. In this model, the total pore space is assumed to consist of two parts: (1) pores associated with sand grains and (2) pores associated with clays (including bound water). The essential feature of the model is the assumption that the geometry of pores associated with sand grains is significantly different from that associated with clays. Because of this, porosity in shales affects elastic compliance differently from porosity in sandstones. The predictive power of the model is demonstrated by the agreement between its predictions and laboratory measurements and by its ability to predict sonic logs from other logs over large depth intervals where formations vary from unconsolidated to consolidated sandstones and shales.