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Title: Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids

Abstract

An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic porous medium containing two immiscible fluids. The theory is based on the Berryman-Thigpen-Chin (BTC) model, in which capillary pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain. These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety of initial and boundary conditions. The stipulation of 'low frequency' underlying the derivation of our equations in the time domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in both unconsolidated and consolidated materials containing water and a nonaqueous phase liquidmore » ranges typically from kHz to MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies (e.g. seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions are imposed.« less

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
Earth Sciences Division
OSTI Identifier:
950854
Report Number(s):
LBNL-1656E
Journal ID: TPMEEI; TRN: US200911%%98
DOE Contract Number:
DE-AC02-05CH11231
Resource Type:
Journal Article
Resource Relation:
Journal Name: Transport in Porous Media; Journal Volume: 68; Related Information: Journal Publication Date: 2007
Country of Publication:
United States
Language:
English
Subject:
54; 58; BOUNDARY CONDITIONS; CRITICAL FREQUENCY; EXCITATION; INTERSTITIALS; PARTIAL DIFFERENTIAL EQUATIONS; PERMEABILITY; PRESSURE DEPENDENCE; SEISMIC WAVES; SHEAR; STIMULATION; VISCOSITY; WATER; WAVE EQUATIONS; WAVE PROPAGATION

Citation Formats

Lo, W.-C., Sposito, G., and Majer, E.. Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids. United States: N. p., 2007. Web. doi:10.1007/s11242-006-9059-2.
Lo, W.-C., Sposito, G., & Majer, E.. Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids. United States. doi:10.1007/s11242-006-9059-2.
Lo, W.-C., Sposito, G., and Majer, E.. Thu . "Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids". United States. doi:10.1007/s11242-006-9059-2. https://www.osti.gov/servlets/purl/950854.
@article{osti_950854,
title = {Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids},
author = {Lo, W.-C. and Sposito, G. and Majer, E.},
abstractNote = {An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic porous medium containing two immiscible fluids. The theory is based on the Berryman-Thigpen-Chin (BTC) model, in which capillary pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain. These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety of initial and boundary conditions. The stipulation of 'low frequency' underlying the derivation of our equations in the time domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in both unconsolidated and consolidated materials containing water and a nonaqueous phase liquid ranges typically from kHz to MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies (e.g. seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions are imposed.},
doi = {10.1007/s11242-006-9059-2},
journal = {Transport in Porous Media},
number = ,
volume = 68,
place = {United States},
year = {Thu Feb 01 00:00:00 EST 2007},
month = {Thu Feb 01 00:00:00 EST 2007}
}
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  • A study was made of the effect of interfacial tension (IFT) on the immisciple displacement of oil by water through water-wet-porous media, commonly found in practice. This was done through the comparison of the displacement efficiencies of 2 binary liquid-systems: oil-water (immiscible) and sucrose solution-water (miscible). The liquids were choosen and prepared such that both systems had identical viscosity ratio and density difference. Results of the study have shown that the displacement efficiency was higher in the immiscible case. This suggests that IFT should be increased to improve the recovery of oil under water-wet-conditions. This conclusion is explained by themore » fact that the capillary force, due to IFT, is in the direction of the driving force, under the waterflooding condition. The results also indicate that the size of the porous bed is an important factor determining the magnitude of the IFT effect. 10 references.« less