Abstract
We consider a linear poroelastic material filled with a linear viscoelastic solvent like wet heavy oils (oil as opposed to water or brines is wetting the surfaces of the pores). We extend the electrokinetic theory in the frequency domain accounting for the relaxation effects associated with resonance of the viscoelastic fluid. The fluid is described by a generalized Maxwell rheology with a distribution of relaxation times given by a Cole–Cole distribution. We use the assumption that the charges of the diffuse layer are uniformly distributed in the pore space (Donnan model). The macroscopic constitutive equations of transport for the seepage velocity and the current density have the form of coupled Darcy and Ohm equations with frequency-dependent material properties. These equations are combined with an extended Frenkel–Biot model describing the deformation of the poroelastic material filled with the viscoelastic fluid. In the mechanical constitutive equations, the effective shear modulus is frequency dependent. An amplification of the seismoelectric conversion is expected in the frequency band where resonance of the generalized Maxwell fluid occurs. The seismic and seismoelectric equations are modelled using a finite element code with PML boundary conditions. We found that the DC-value of the streaming potential coupling coefficient is also very high. These results have applications regarding the development of new non-intrusive methods to characterize shallow heavy oil reservoirs in tar sands and DNAPL contaminant plumes in shallow aquifers.
Highlights
In the last 70 yr, a number of laboratory, field, and theoretical investigations have established seismoelectric and electroseismic conversions associated with the charged nature of natural and synthetic porous materials filled with a solvent
Preliminary investigations have attempted to image the subsurface and to locate potential oil and gas reservoirs and ore bodies using these properties (Martner & Spark 1959; Migunov & Kokorev 1977; Kepic et al 1995; Russell et al 1997). These methods were used more recently in hydrogeophysics to detect wet ice in glaciers (Kulessa et al 2006), to localize fractures in a fractured aquifer (Fourie 2003), to image interfaces within the vadose zone (Dupuis et al 2007), and to monitor electromagnetic disturbances associated with earthquakes
We derived below the coupled constitutive equations between the Darcy velocity (Section 3.1) and the total current density (Section 3.2) for a linear poroelastic material saturated by a polar oil (Fig. 2)
Summary
In the last 70 yr, a number of laboratory, field, and theoretical investigations have established seismoelectric (seismic-to-electric) and electroseismic (electric-to-seismic) conversions associated with the charged nature of natural and synthetic porous materials filled with a solvent (usually a Newtonian electrolyte). Pride (1994) completed the theory for a charged porous material filled with water by upscaling the local Navier–Stokes and Nernst–Planck equations using a volume-averaging method to obtain the macroscopic equations His theory connects the Frenkel–Biot poroelastic equations (Frenkel 1944; Biot 1962a,b) and the Maxwell-Lorentz equations (Maxwell 1885; Lorentz 1904) through the electrokinetic coupling occurring in the constitutive equations for the fluxes of water and current density (see Garambois & Dietrich 2001, 2002). We will show that the theory developed in this paper is consistent with recent developments in the theory of streaming current/streaming potential associated with the flow of the pore water in a deformable porous material (see Revil & Linde 2006; Crespy et al 2008)
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