The well-known “Biot-Gassmann” formula for the difference between “undrained” and “frame” compressibilities of rocks is in error. The error was introduced by Gassmann (implicitly revising earlier work by Biot), and results in an expression which is simpler than Biot’s equivalent expression, containing only one material parameter (KS) in place of Biot’s two (H and R). The error occurred when Gassmann applied a hydraulically-open theorem to a hydraulically-closed system, violating the assumptions of the undrained compressibility. The inconsistency between Gassmann and Biot (and equivalent results of Brown/Korringa, and Rice/Cleary) is caused by Gassmann’s logical error, rather than by the issue of solid micro-homogeneity. The additional parameter may be experimentally determined via the “Skempton B-coefficient” (the ratio of fluid pressure to external pressure in an undrained quasi-static compression test). The additional parameter enables the resolution of a long-known inconsistency between Gassmann’s result and effective medium theory. The correct expression, with its additional parameter, is required to analyze the fluid-dependence of rock incompressibility for all macro-isotropic rocks with uniform fluid pressure, with or without solid microhomogeneity. A new generation of experimentation is required to determine the systematics of the magnitude of the correction to the Gassmann formula.
Presentation Date: Tuesday, October 13, 2020
Session Start Time: 1:50 PM
Presentation Time: 4:20 PM
Presentation Type: Oral