Comparison of Fluid Pressure Wave between Biot Theory and Storativity Equation

Abstract EN

Compressibilities of pore fluid and rock skeleton affect pressure profile and flow velocity of fluid in aquifers.

Storativity equation is often used to characterize such effects.

The equation suffers from a disadvantage that at infinite large frequency, the predicted velocity of fluid pressure wave is infinitely large, which is unrealistic because any physical processes need certain amounts of time.

In this paper, Biot theory is employed to investigate the problem.

It is shown that the key equations of Biot theory can be simplified to storativity equation, based on low-frequency assumption.

Using Berea sandstone as an example, we compare phase velocity and the quality factor between Biot theory and storativity equation.

The results reveal that Biot theory is more accurate in yielding a bounded wave velocity.

At frequency lower than 100 kHz, Biot theory yields a wave velocity 8 percent higher than storativity equation does.

Apparent permeability measured by fluid pressure wave (such as Oscillatory Hydraulic Tomography) may be 14 percent higher than real permeability measured by steady flow experiments.

If skeleton is rigid, Biot theory at very high frequencies or with very high permeabilities will yield the same velocity as sound wave in pure water.

The findings help us for better understanding of the physical processes of pore fluid and the limitations of storativity equation.