Velocity-Log Interpretation: The Effect of Rock Bulk Compressibility

Abstract

Abstract Tbe relationsbip between porosity and the speed of propagation of acoustic waves in fluid-saturated porous rocks as measured by the Sonic log and by ultrasonic techniques is analyzed. Biot's continuum theory is used to explain the difference in acoustic wave propagation between a dry and a liquid-saturated porous material. The porosity is a variable in this theory. However, the acoustic wave propagation in the dry rock depends too on porosity, and this dependence is not predicted by the theory. Frequently in dry sandstones, a nearly linear relationsbip between reciprocal acoustic wave velocity and porosity is observed in the low-porosity range. The physics behind this behavior is outlined. An empirical relationship of the form, 1/V ~ A + B ø, applies accordingly for many porous dry rocks, provided the porosity is the only variable. The presence of a liquid in the pores changes the value of B, and this change is found to be in agreement with the Biot theory. The time-average relation introduced some years ago results in an equation of the same type 1/V = ø/Vf + (1 - ø)/Vr - but is not based on a sound physical picture. Still, this relation sometimes predicts approximately correct A and B values. Carbonate rocks with their complicated pore structures sometimes show a different relationship between wave velocity and porosity, unfavorable for log interpretation. Examples are presented. The simultaneous presence of calcite, dolomite and anhydrite, with their different grain densities and matrix compressibilities, complicates acoustic-log interpretation in carbonate rocks still further. Other complicating effects of acoustic-log interpretation are discussed. They are related to the influence of shale streaks and natural fractures on the average wave velocity observed by the logging tool and to the effect of adsorption phenomena on wave propagation in unstressed rocks particularly in sandstones.