An experimental study of the dilation factor

Abstract

Dilation factor [Formula: see text] is the ratio of relative change in velocity to relative change in deformation (strain). It has significant implications for 4D seismic studies where it can be used to infer reservoir or overburden thickness changes from seismic changes, but the effect of stress on [Formula: see text] and its components is not well understood. We conduct static strain and ultrasonic velocity measurements to study the effect of stress on [Formula: see text] and its components. Measured absolute [Formula: see text] values (6–91 in sandstones and 6–11 in shale) depend on the deformation mechanisms causing the strain. The dynamic (low-amplitude) Young’s modulus generally is higher than the static (high-amplitude) Young’s modulus. Hence, theoretical models that use the same mechanism to describe wave propagation and macroscopic deformation are invalid. The ratio of dynamic to static modulus depends on the direction of stress applied with respect to the density and placement of cracks. Values of [Formula: see text] differ for P- and S-waves, especially in the presence of fluids. The values also depend strongly on the stress states; hence, using a constant value of [Formula: see text] from the surface to reservoir depth should be avoided. Absolute [Formula: see text] values increase for sandstones and decrease for shales with decreasing confining pressure, which explains the low [Formula: see text] values from 4D seismic data. Our data offer insight into the behavior of [Formula: see text] values with different rock types, stress, and fluid, and they can be used to constrain model calculations.