Modulus—porosity relations, Gassmann’s equations, and the low‐frequency elastic‐wave response to fluids

Publisher Website
Google Scholar
Abstract
Gassmann’s equations relate the low‐frequency drained and undrained elastic‐wave response to fluids. This tutorial explores how different modulus—porosity relationships affect predictions of the low‐frequency elastic‐wave response to fluids based on Gassmann’s equations. I take different modulus—porosity relations and substitute them into Gassmann’s equations through the framework moduli. The results illustrate the range of responses to fluids and can be summarized in a nomograph of the effective fluid coefficient, which quantifies the change in the pore‐space modulus ([Formula: see text]) in response to a change in fluid modulus ([Formula: see text]). Two ratios control the effective fluid coefficient: the ratio of the fluid modulus to the solid‐grain modulus ( [Formula: see text]) and the ratio of the Biot coefficient to porosity ([Formula: see text]). The effective fluid coefficient nomograph is a convenient tool for estimating how low‐frequency elastic‐wave properties will respond to changes in reservoir fluids.