Reciprocal velocity-porosity general linear form provides consistent and systematic industry-wide applications

Abstract

Velocity is an important rock property that is required and used in different applications in petrophysics, rock physics, and seismic. The published literature shows a plethora of equations and models that relate velocity and porosity, a critical reservoir property. Attempts to account for the presence of shale in the formation invariably lead to more complicated relations. The inability of the industry to streamline these relations handicaps advancements in rock physics and formation evaluation, complicates the application of best practices in time-lapse seismic and fluid substitutions, and jeopardizes the integration of petrophysical, geologic, and seismic characteristics of oil and gas reservoirs. I have considered the following criteria to grade some of the different velocity-porosity relations in use today: (1) the significance of effective stress, (2) usefulness for interpreting geology, (3) predictive capability, and (4) universal applicability. Judging by these criteria, the general linear form, first prescribed by the late George R. Pickett, is the clear winner. The general linear form is a linear relationship between the reciprocal velocity and porosity. It passes theoretical and empirical justification. It is also valid for P- and S-wave velocities, yields easily to mathematical manipulation, and satisfies carbonate as well as clastic rocks for porosities encountered in everyday subsurface investigations. I evaluate practical examples in which the general linear form is the basis for multiple rock-typing criteria, comparative formation evaluation, and interpretive use of the [Formula: see text] ratio. Appropriate integration of the general linear form with other rock property relations provides avenues to redefine the [Formula: see text] ratio and acoustic impedance, and it expands the understanding and applications of reservoir elastic properties, as well as it constrains and streamlines rock physics models and applications.