On the propagation of a disturbance in a heterogeneous, deformable, porous medium saturated with two fluid phases

Vasco, D. W.; Minkoff, Susan E.

doi:10.1190/geo2011-0131.1

Cited by 3 publications

(24 citation statements)

References 62 publications

(167 reference statements)

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“…Because ε ≪ 1, only the lowest-order terms are retained. This procedure was presented in detail in Vasco (2009) and Vasco and Minkoff (2012) for propagation in a porous medium containing one and two fluid phases, respectively. Because the approach has been described in detail in these two studies, I shall only present the results of the asymptotic analysis.…”

Section: Asymptotic Expressions For the Displacementsmentioning

confidence: 99%

“…Following the procedure applied to that matrix, or the procedure described in Vasco and Minkoff (2012), I can show that the condition for equation 44 to have a nontrivial solution is the vanishing of the determinant of the matrix…”

Section: The Longitudinal Modes Of Propagationmentioning

confidence: 99%

“…This can be seen by factoring out the identity matrices and the vectors l ⊥ 1 and writing the system 38 as four equations for the four unknowns t s , t 1 , t 2 , and t 3 . Alternatively, one can adopt the formal approach in Vasco and Minkoff (2012) and use the rule for the determinant of a matrix composed of block matrices (Silvester, 2000).…”

Section: The Transverse Mode Of Propagationmentioning

confidence: 99%

“…Therefore, I point out some representative studies that treated single phase flow (Garg, 1971;Pride et al, 1992), and two-phase flow (Berryman et al, 1988;Santos, 1990;Tuncay, 1995;Tuncay andCorapcioglu, 1996, 1997;Lo et al, 2005Lo et al, , 2009) for a homogeneous medium. Recently, the two-phase work was extended to a medium containing smoothly varying heterogeneity in Vasco and Minkoff (2012). These papers dealt with large-scale, wave-induced flow, the so-called macroscopic flow.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, I extend the two-phase work of Vasco and Minkoff (2012) to the case in which there are three fluid phases. Specifically, I consider the zeroth-order terms of an asymptotic analysis of the equations governing the coupled deformation and flow in a heterogeneous porous medium containing three fluids.…”

Section: Introductionmentioning

confidence: 99%

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On the propagation of a disturbance in a smoothly varying heterogeneous porous medium saturated with three fluid phases

Vasco

2013

GEOPHYSICS

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From the equations governing the deformation of a porous medium containing three fluid phases, I derive expressions for the phase velocity of the various modes of displacement. These expressions are valid for a medium with smoothly varying heterogeneity. There is a single mode of transverse displacement, similar in nature to an elastic shear wave. The four-phase velocities of the longitudinal modes of displacement are derived from the solutions of a quartic equation. The coefficients of the polynomial equation are written as linear sums of the determinants of 4 × 4 matrices. The matrices contain various combinations of the parameters from the governing equations. The three-phase expressions are compared to two-phase estimates for the case in which one of the fluid saturations vanishes. Also, in a numerical illustration, velocity variations of around 10% are associated with the cyclic injection of carbon dioxide and water into an oil-saturated reservoir.

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Section: Asymptotic Expressions For the Displacementsmentioning

confidence: 99%

Section: The Longitudinal Modes Of Propagationmentioning

confidence: 99%

Section: The Transverse Mode Of Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the propagation of a disturbance in a smoothly varying heterogeneous porous medium saturated with three fluid phases

Vasco

2013

GEOPHYSICS

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Seismoelectric theory in partially saturated conditions

Revil

Jardani

Sava

et al. 2015

The Seismoelectric Method

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Seismoelectric couplings in a poroelastic material containing two immiscible fluid phases

Jardani¹,

Revil

2015

Geophysical Journal International

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A new approach of seismoelectric imaging has been recently proposed to detect saturation fronts in which seismic waves are focused in the subsurface to scan its heterogeneous nature and determine saturation fronts. Such type of imaging requires however a complete modelling of the seismoelectric properties of porous media saturated by two immiscible fluid phases, one being usually electrically insulating (for instance water and oil). We combine an extension of Biot dynamic theory, valid for porous media containing two immiscible Newtonian fluids, with an extension of the electrokinetic theory based on the notion of effective volumetric charge densities dragged by the flow of each fluid phase. These effective charge densities can be related directly to the permeability and saturation of each fluid phase. The coupled partial differential equations are solved with the finite element method. We also derive analytically the transfer function connecting the macroscopic electrical field to the acceleration of the fast P wave (coseismic electrical field) and we study the influence of the water content on this coupling. We observe that the amplitude of the co-seismic electrical disturbance is very sensitive to the water content with an increase in amplitude with water saturation. We also investigate the seismoelectric conversions (interface effect) occurring at the water table. We show that the conversion response at the water table can be identifiable only when the saturation contrasts between the vadose and saturated zones are sharp enough. A relatively dry vadose zone represents the best condition to identify the water table through seismoelectric measurements. Indeed, in this case, the coseismic electrical disturbances are vanishingly small compared to the seismoelectric interface response.

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On the propagation of a disturbance in a heterogeneous, deformable, porous medium saturated with two fluid phases

Cited by 3 publications

References 62 publications

On the propagation of a disturbance in a smoothly varying heterogeneous porous medium saturated with three fluid phases

On the propagation of a disturbance in a smoothly varying heterogeneous porous medium saturated with three fluid phases

Seismoelectric theory in partially saturated conditions

Seismoelectric couplings in a poroelastic material containing two immiscible fluid phases

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