TY - JOUR
T1 - Motional modes of dilatational waves in elastic porous media containing two immiscible fluids
AU - Lo, Wei Cheng
AU - Sposito, Garrison
AU - Majer, Ernest
AU - Yeh, Chao Lung
N1 - Funding Information:
Gratitude is expressed to the National Science Council, Taiwan , for financial support under Contract No. NSC98-2628-M-006-008 . Financial support for the research reported in this paper was also provided partially by the Laboratory Directed Research and Development Program at Lawrence Berkeley National Laboratory and partially by National Cheng Kung University Landmark Program ( R046 ).
PY - 2010/3
Y1 - 2010/3
N2 - Numerical simulations of dilatational waves in an elastic porous medium containing two immiscible viscous compressible fluids indicate that three types of wave occur, but the modes of dilatory motion corresponding to the three waves remain uncharacterized as functions of relative saturation. In the present paper, we address this problem by deriving normal coordinates for the three dilatational waves based on the general poroelasticity equations of Lo et al. 2005 [13]. The normal coordinates provide a theoretical foundation with which to characterize the motional modes in terms of six connecting coefficients that depend in a well defined way on inertial drag, viscous drag, and elasticity properties. Using numerical calculations of the connecting coefficients in the seismic frequency range for an unconsolidated sand containing water and air as a representative example relevant to hydrologic applications, we confirm that the dilatational wave whose speed is greatest corresponds to the motional mode in which the solid framework and the two pore fluids always move in phase, regardless of water saturation, in agreement with the classic Biot theory of the fast compressional wave in a water-saturated porous medium. For the wave which propagates second fastest, we show, apparently for the first time, that the solid framework moves in phase with water, but out of phase with air [Mode (III)], if the water saturation is below about 0.8, whereas the solid framework moves out of phase with both pore fluids [Mode (IV)] above this water saturation. The transition from Mode (III) to Mode (IV) corresponds to that between the capillarity-dominated region of the water retention curve and the region reflecting air-entry conditions near full water saturation. The second of the two modes corresponds exactly to the slow compressional wave in classic Biot theory, whereas the first mode is possible only in a two-fluid system undergoing capillary pressure fluctuations. For the wave which has the smallest speed, the dilatational mode is dominated by the motions of the two pore fluids, which are always out of phase, a result that is consistent with the proposition that this wave is caused by capillary pressure fluctuations.
AB - Numerical simulations of dilatational waves in an elastic porous medium containing two immiscible viscous compressible fluids indicate that three types of wave occur, but the modes of dilatory motion corresponding to the three waves remain uncharacterized as functions of relative saturation. In the present paper, we address this problem by deriving normal coordinates for the three dilatational waves based on the general poroelasticity equations of Lo et al. 2005 [13]. The normal coordinates provide a theoretical foundation with which to characterize the motional modes in terms of six connecting coefficients that depend in a well defined way on inertial drag, viscous drag, and elasticity properties. Using numerical calculations of the connecting coefficients in the seismic frequency range for an unconsolidated sand containing water and air as a representative example relevant to hydrologic applications, we confirm that the dilatational wave whose speed is greatest corresponds to the motional mode in which the solid framework and the two pore fluids always move in phase, regardless of water saturation, in agreement with the classic Biot theory of the fast compressional wave in a water-saturated porous medium. For the wave which propagates second fastest, we show, apparently for the first time, that the solid framework moves in phase with water, but out of phase with air [Mode (III)], if the water saturation is below about 0.8, whereas the solid framework moves out of phase with both pore fluids [Mode (IV)] above this water saturation. The transition from Mode (III) to Mode (IV) corresponds to that between the capillarity-dominated region of the water retention curve and the region reflecting air-entry conditions near full water saturation. The second of the two modes corresponds exactly to the slow compressional wave in classic Biot theory, whereas the first mode is possible only in a two-fluid system undergoing capillary pressure fluctuations. For the wave which has the smallest speed, the dilatational mode is dominated by the motions of the two pore fluids, which are always out of phase, a result that is consistent with the proposition that this wave is caused by capillary pressure fluctuations.
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U2 - 10.1016/j.advwatres.2009.12.007
DO - 10.1016/j.advwatres.2009.12.007
M3 - Article
AN - SCOPUS:77955980669
SN - 0309-1708
VL - 33
SP - 304
EP - 311
JO - Advances in Water Resources
JF - Advances in Water Resources
IS - 3
ER -