Abstract
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.
Highlights
Fluid in the subsurface is very important for hydrogeologists and petroleum engineers, as significant portions of fresh water and hydrocarbon are stored in rock pores
(1) Under the assumption of low frequency, the constitutional relation of rock skeleton, the fluid mass conservation, and the fluid momentum equation in Biot theory can be simplified to storativity equation
For water-saturated Berea sandstone, at frequency lower than 100 kHz, both phase velocity and the quality factor of fluid pressure wave are close between the equation and Biot theory
Summary
Fluid in the subsurface is very important for hydrogeologists and petroleum engineers, as significant portions of fresh water and hydrocarbon are stored in rock pores. The equation yields a finite velocity of fluid pressure wave. At infinite high frequency, the equation yields infinite large velocity of fluid pressure wave, which is unrealistic. In this regard, the storativity equation is not accurate enough. The second approach has the assets that both velocity and attenuation of fluid pressure wave are got as functions of frequency but has the liabilities that flow velocity and pressure profile are dependent on the specific boundary condition and initial condition. As Biot [11, 12] theory involves a set of partial differential equations (that are difficult to directly solve), the second approach is simpler and significantly facilities comparing fluid pressure wave between Biot theory and storativity equation.
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