The Biot (or Biot-Willis) coefficient is an important parameter for geomechanical models. It dictates the effective stress for rock compressibility. This parameter can be measured in the laboratory with careful geomechanical experiments, which can give accurate results. However, the laboratory tests are relatively expensive because it demands sampling and time. Moreover, especially in oil exploration, rock sampling can be relatively scarce and biased. In this paper we describe a case study where we measured the Biot coefficients of selected rock samples from a Santos Bazin Pre-salt oil field. We observed good and useful correlations between the Biot coefficient and some petrophysical and geophysical properties as well. For instance, the Biot coefficient increases with the porosity according to an approximately linear relation. It is also well correlated with the acoustic impedance, with the Biot coefficient decreasing with increasing acoustic impedance. The observed correlations suggest several possible ways of deriving the Biot coefficient. We also propose a method for estimating this parameter from sonic logs or, alternatively, from sonic, density and compositional logs. The estimated Biot coefficient is virtually "continuous" through the logged interval and can be used to populate geomechanical models.
The Biot's coefficient, or Biot-Willis coefficient, (Biot, 1941; Biot and Willis, 1957) can be defined in terms of the drained rock bulk modulus, Kd, and the solid matrix bulk modulus, Km, as:
(equation)
This is an important parameter for geomechanical models because it will define the effective stress σef acting on the rocks and influencing the rock elastic moduli: σef = σ − αPp. Where σ is the total stress and p the pore pressure. Note that the preceding definition are considering isotropic stress conditions, but we can write similar versions in case of triaxial stress conditions. The main point in the effective stress concept is that any increase or decrease in fluid pressure is equivalent to an increase or decrease in the total stress divided by the Biot coefficient.
In soil mechanics, the effective stress is simply the difference between external stress and pore pressure (σef = σ − Pp). Thus, any increase or decrease in fluid pressure is equivalent to an equal increase or decrease in external or confining stress.