Experimental Determination of the Biot Elastic Constant: Applications in Formation Evaluation (Sonic Porosity, Rock Strength, Earth Stresses, and Sanding Predictions)

We developed an experimental method to obtain the Biot elastic constant of rocks from laboratory dynamic and static measurements. The Biot constant often has been calculated with various empirical equations. The experimental determination of the Biot elastic constant is very important to engineering problems associated with sand control, hydraulic fracturing, wellbore stability, earth stresses, sonic porosity, and estimation of compressional-, P, and shear-, S, wave velocity. Both the dynamic and static moduli of actual reservoir sandstone core samples, jacketed and mounted in a triaxial cell under vacuum, were measured at various confining and overburden stresses. The results obtained show that the Biot constant is a complex function of porosity, permeability, pore-size distribution, and overburden and confining stress, which means that it is not really a constant. Also, the static Biot constant is greater than the dynamic one and their difference increases with increasing overburden stress according to the equation a_static = [1+0.05*(σ_z)_ef]*αdynamic (where σ_z is in K_Si). Moreover, both the experimental static and dynamic Biot constants may be significantly different from values calculated with empirical equations. This study suggests that quantifying the Biot constant in the laboratory may enhance the determination of rock-strength/fracturing, earth stresses, rock subsidence, sanding predictions, P- and S-wave velocities, porosity, and pore fluid from sonic and seismic data.