Coupled hydromechanical and electromagnetic disturbances in unsaturated porous materials

A theory of cross-coupled flow equations in unsaturated soils is necessary to predict (1) electroosmotic flow with application to electroremediation and agriculture, (2) the electroseismic and the seismoelectric effects to develop new geophysical methods to characterize the vadose zone, and (3) the streaming current, which can be used to investigate remotely ground water flow in unsaturated conditions in the capillary water regime. To develop such a theory, the cross-coupled generalized Darcy and Ohm constitutive equations of transport are extended to unsaturated conditions. This model accounts for inertial effects and for the polarization of porous materials. Rather than using the zeta potential, like in conventional theories for the saturated case, the key parameter used here is the quasi-static volumetric charge density of the pore space, which can be directly computed from the quasi-static permeability. The apparent permeability entering Darcy's law is also frequency dependent with a critical relaxation time that is, in turn, dependent on saturation. A decrease of saturation increases the associated relaxation frequency. The final form of the equations couples the Maxwell equations and a simplified form of two-fluid phases Biot theory accounting for water saturation. A generalized expression of the Richard equation is derived, accounting for the effect of the vibration of the skeleton during the passage of seismic waves and the electrical field. A new expression is obtained for the effective stress tensor. The model is tested against experimental data regarding the saturation and frequency dependence of the streaming potential coupling coefficient. The model is also adapted for two-phase flow conditions and a numerical application is shown for water flooding of a nonaqueous phase liquid (NAPL, oil) contaminated aquifer. Seismoelectric conversions are mostly taking place at the NAPL (oil)/water encroachment front and can be therefore used to remotely track the position of this front. This is not the case for other geophysical methods.

[1]  E. Slob,et al.  Stochastic joint inversion of 2D seismic and seismoelectric signals in linear poroelastic materials: A numerical investigation , 2010 .

[2]  J. Godt,et al.  A closed‐form equation for effective stress in unsaturated soil , 2010 .

[3]  J. Moum,et al.  APPLICATION OF ELECTRO-OSMOSIS TO A FOUNDATION PROBLEM IN A NORWEGIAN QUICK CLAY , 1967 .

[4]  Amyn S. Teja,et al.  Generalized corresponding states method for the viscosities of liquid mixtures , 1981 .

[5]  Ernest L. Majer,et al.  Immiscible two-phase fluid flows in deformable porous media , 2002 .

[6]  Byungill Kim,et al.  Electroosmosis and pore pressure development characteristics in lead contaminated soil during electrokinetic remediation , 2004 .

[7]  Laurence Jouniaux,et al.  Streaming potential of a sand column in partial saturation conditions , 2003 .

[8]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2002, Future Gener. Comput. Syst..

[9]  A. Revil,et al.  CEC‐normalized clay‐water sorption isotherm , 2011 .

[10]  G. E. Archie.  The electrical resistivity log as an aid in determining some reservoir characteristics , 1942 .

[11]  Electrical impedance variation with water saturation in rock , 2000 .

[12]  A. Cheng,et al.  Fundamentals of Poroelasticity , 1993 .

[13]  James W. Mercer,et al.  A review of immiscible fluids in the subsurface: properties, models, characterization and remediation , 1990 .

[14]  M. H. Waxman,et al.  Electrical Conductivities in Oil-Bearing Shaly Sands , 1968 .

[15]  J. Frenkel,et al.  On the Theory of Seismic and Seismoelectric Phenomena in a Moist Soil , 2005 .

[16]  T. Mukerji,et al.  The Rock Physics Handbook: Contents , 2009 .

[17]  A. Revil,et al.  Characterization of transport properties of argillaceous sediments: Application to the Callovo‐Oxfordian argillite , 2005 .

[18]  A. Revil,et al.  Seismoelectric response of heavy oil reservoirs: theory and numerical modelling , 2010 .

[19]  L. A. Richards.  Capillary conduction of liquids through porous mediums , 1931 .

[20]  Yalcin B. Acar,et al.  Principles of electrokinetic remediation , 1993 .

[21]  J. Friborg.  Experimental and theoretical investigations into the streaming potential phenomenon with special reference to applications in glaciated terrain , 1997 .

[22]  C. Bruell,et al.  Electroosomotic Removal of Gasoline Hydrocarbons and TCE From Clay , 1993 .

[23]  André Revil,et al.  Streaming potentials of granular media: Influence of the Dukhin and Reynolds numbers , 2007 .

[24]  Karl E. Butler,et al.  Vertical seismoelectric profiling in a borehole penetrating glaciofluvial sediments , 2006 .

[25]  N. C. Lockhart,et al.  Electrical properties and the surface characteristics and structure of clays. II. Kaolinite—a nonswelling clay , 1980 .

[26]  Niklas Linde,et al.  Derivation of Soil‐Specific Streaming Potential Electrical Parameters from Hydrodynamic Characteristics of Partially Saturated Soils , 2012, 1209.6335.

[27]  Zhenya Zhu,et al.  Experimental measurements of the streaming potential and seismoelectric conversion in Berea sandstone , 2013 .

[28]  Ernest L. Majer,et al.  Wave propagation through elastic porous media containing two immiscible fluids , 2005 .

[29]  A. Revil,et al.  In situ mineralogy and permeability logs from downhole measurements: Application to a case study in chlorite‐coated sandstones , 2003 .

[30]  A. Nur,et al.  The squirt-flow mechanism: Macroscopic description , 1994 .

[31]  André Revil,et al.  Permeability of shaly sands , 1999 .

[32]  M. Jackson,et al.  Multiphase streaming potential in sandstones saturated with gas/brine and oil/brine during drainage and imbibition , 2011 .

[33]  A. Revil,et al.  Electrical burst signature of pore‐scale displacements , 2009 .

[34]  Rudolf A. Römer,et al.  On Large-Scale Diagonalization Techniques for the Anderson Model of Localization , 2006, SIAM J. Sci. Comput..

[35]  Warren S. Ross,et al.  Field Tests of Electroseismic Hydrocarbon Detection , 2005 .

[36]  A. Revil,et al.  Detection of preferential infiltration pathways in sinkholes using joint inversion of self‐potential and EM‐34 conductivity data , 2007 .

[37]  R. Keren,et al.  Effect of Magnesium on the Hydraulic Conductivity of Na-Smectite-Sand Mixtures , 1988 .

[38]  Thomas Elboth,et al.  Flow noise reduction from superhydrophobic surfaces , 2012 .

[39]  D. Kulik,et al.  Acid–base surface chemistry and sorption of some lanthanides on K+-saturated Marblehead illite: I. results of an experimental investigation , 2000 .

[40]  Gerard T. Schuster,et al.  Migration methods for imaging different‐order multiples , 2007 .

[41]  Egon Zimmermann,et al.  Coupled Hydrogeophysical Inversion of Streaming Potential Signals for Unsaturated Soil Hydraulic Properties , 2012 .

[42]  O. Schenk,et al.  ON FAST FACTORIZATION PIVOTING METHODS FOR SPARSE SYMMETRI C INDEFINITE SYSTEMS , 2006 .

[43]  Eugenio Aulisa,et al.  Analysis of generalized Forchheimer flows of compressible fluids in porous media , 2009 .

[44]  A. H. Thompson.  Electromagnetic‐to‐seismic conversion: successful developments suggest viable applications in exploration and production , 2005 .

[45]  J. Bear,et al.  Modeling groundwater flow and pollution , 1987 .

[46]  Gary A. Pope,et al.  DNAPL Removal from a Heterogeneous Alluvial Aquifer by Surfactant‐ Enhanced Aquifer Remediation , 2001 .

[47]  C. Doussan,et al.  Streaming current generation in two‐phase flow conditions , 2007 .

[48]  Nicolas Florsch,et al.  Determination of permeability from spectral induced polarization in granular media , 2010 .

[49]  M. Avena,et al.  Proton Adsorption and Electrokinetics of an Argentinean Montmorillonite , 1998 .

[50]  John A. Hudson,et al.  Comprehensive rock engineering : principles, practice, and projects , 1993 .

[51]  Olaf Schenk,et al.  Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization , 2007, Comput. Optim. Appl..

[52]  Moid U. Ahmad.  A LABORATORY STUDY OF STREAMING POTENTIALS , 1964 .

[53]  N. Linde,et al.  Chemico-electromechanical coupling in microporous media. , 2006, Journal of colloid and interface science.

[54]  Brij Lal,et al.  A textbook of sound , 1995 .

[55]  André Revil,et al.  Spectral induced polarization of shaly sands: Influence of the electrical double layer , 2012 .

[56]  Jeroen Tromp,et al.  Spectral-element simulations of wave propagation in porous media: Finite-frequency sensitivity kernels based upon adjoint methods , 2008 .

[57]  H. Tchelepi,et al.  Effect of electroosmosis on relative permeabilities of sandstones , 1994 .

[58]  A. Revil,et al.  Constitutive equations for ionic transport in porous shales , 2004 .

[59]  M. R. Sheffer,et al.  Forward modelling and inversion of streaming potential for the interpretation of hydraulic conditions from self-potential data , 2007 .

[60]  Steven D. Glaser,et al.  The streaming potential of liquid carbon dioxide in Berea sandstone , 2004 .

[61]  S. Hubbard,et al.  Petrophysical properties of saprolites from the Oak Ridge Integrated Field Research Challenge site, Tennessee , 2013 .

[62]  Po-zen Wong,et al.  Determination of rock properties by low‐frequency AC electrokinetics , 1999 .

[63]  A. Revil,et al.  Waveform joint inversion of seismograms and electrograms for moment tensor characterization of fracking events , 2012 .

[64]  R. H. Brooks,et al.  Hydraulic properties of porous media , 1963 .

[65]  Frequency-dependent electroosmosis. , 2002, Journal of colloid and interface science.

[66]  M. Karaoulis,et al.  Imaging with cross-hole seismoelectric tomography , 2012 .

[67]  A. Puppala,et al.  Quantitative Estimation of Clay Mineralogy in Fine-Grained Soils , 2011 .

[68]  K. Holliger,et al.  Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks , 2012 .

[69]  Karl E. Butler,et al.  Seismoelectric imaging of the vadose zone of a sand aquifer , 2007 .

[70]  Pope Ga,et al.  Lessons from enhanced oil recovery research for surfactant-enhanced aquifer remediation. , 1995 .

[71]  A. Revil,et al.  Effective conductivity and permittivity of unsaturated porous materials in the frequency range 1 mHz–1GHz , 2013, Water resources research.

[72]  Pride,et al.  Governing equations for the coupled electromagnetics and acoustics of porous media. , 1994, Physical review. B, Condensed matter.

[73]  A. Revil,et al.  Constitutive equations for coupled flows in clay materials , 2011 .

[74]  James G. Berryman,et al.  Bulk elastic wave propagation in partially saturated porous solids , 1988 .

[75]  A Fully-Coupled Geomechanics and Flow Model for Hydraulic Fracturing and Reservoir Engineering Applications , 2010 .

[76]  H. Vinegar,et al.  Induced polarization of shaly sands , 1984 .

[77]  Karl E. Butler,et al.  Anatomy of a seismoelectric conversion: Measurements and conceptual modeling in boreholes penetrating a sandy aquifer , 2009 .

[78]  S. Finsterle,et al.  Electrokinetic coupling in unsaturated porous media. , 2007, Journal of colloid and interface science.

[79]  D. J. Marshall,et al.  Induced polarization, a study of its causes , 1959 .

[80]  Chi Ma,et al.  Cation Exchange Capacity of Kaolinite , 1999 .