Contribution of Stern layer and membrane polarization to spectral induced polarization of variably saturated sandy soils

2 Pages·2012·0.482 MB·English

by  A. Brovelli and G. Cassiani

GeophysicalResearchAbstracts
Vol.14,EGU2012-7345,2012
EGUGeneralAssembly2012
©Author(s)2012
Contribution of Stern layer and membrane polarization to spectral
induced polarization of variably saturated sandy soils
A.Brovelli(1)andG.Cassiani(2)
(1)EcologicalEngineeringLaboratory,Institutd’ingénieriedel’environnement,EcolepolytechniquefédéraledeLausanne
(EPFL),1015Lausanne,Switzerland,http://ecol.epfl.ch.(alessandro.brovelli@epfl.ch),(2)UniversitàdiPadova,
DipartimentodiGeoscienze,Padova,Italy([email protected])
Spectral induced polarization is receiving increasing attention as a tool to map subsurface properties in a
non-invasivemanner.Althoughempiricalcorrelationshavebeendevisedtolinkmeasurementstoporousmedium
properties,suchasthetimeconstantoftheCole-Colemodeltograinsizedistributionandhydraulicconductivity,a
comprehensiveprocess-basedmodelisstillmissing.Twofundamentallydifferentmechanismshavebeenproposed
sofar,(i)electricaldoublelayerpolarization,inparticularoftheSternlayerand(ii)membranepolarization.This
lattermechanismisduetotheaccumulationofionsattheoppositesidesofnarrowpore-throats,whicheffectively
act as ion-selective channels and lead to the formation of a membrane potential. Both mechanisms have so far
shown the ability to explain to some degree experimental observations, although not in a completely convincing
manner.
The goal of this work was to test whether the two process concur to the observed polarization of the porous
mediumorratheraremutuallyexclusive.TheHashin-ShtrickmanAverage(HSA)modelofBrovelliandCassiani
(2010, 2011) was extended to compute the complex bulk conductivity of variably saturated porous media.
Complex surface conductance was computed from EDL polarization theory, whereas membrane polarization
affectspore-waterconductivity.
Thefrequency-dependentHSAmodelwascomparedwiththemeasuredspectralinducedpolarizationofvariably-
saturatedsandysoils.Asatisfactorycomparisonwasfoundformostsamples,inparticularwithwatersaturation
above0.8.Itwasobservedthatthetwopolarizationmechanismsleadtoseparatephasepeaks,whicharerelated
tothecharacteristicdiffusionlengthandtortuosityofgrainsandpore-throats.Whensaturationisdecreased,Stern
layerpolarizationbecomesthedominantmechanism,asthewaterphaseisprogressivelylessabundantandmore
disconnected. In addition, the measured polarization becomes more difficult to explain with the model, perhaps
becauseadditionalmechanisms–suchasthepolarizationoftheair-waterinterface–comeintoplay.
Contribution of Stern layer and membrane polarization to spectral
induced polarization of variably saturated sandy soils
Alessandro Brovelli(1)and Giorgio Cassiani(2)
Abstract EGU2012-7345 (1) EcologicalEngineeringLaboratory,EnvironmentalEngineeringInstitute,EcolePolytechniqueFédéraledeLausanne,Lausanne,Switzerland,http://ecol.epfl.ch.Emails:[email protected].
(2) DipartimentodiGeoscienze,UniversitàdiPadova,Padova,Italy,http://www.geoscienze.unipd.it.Email:[email protected].
1. Introduction and motivations 2. Methodology 3. Polarization mechanisms
• Mostexistingprocess-basedmodelsofinducedpolarization(IP)considereither • The (frequency-dependendent) bulk conductivity in variably saturated • Membrane polarization is modelled using a modified form the SNP model (Titov et
membrane (e.g. Titov et al., 2002) or grain (EDL) polarization (e.g. Revil and conditions is computed using the Hashin-Shtrikman Average (HSA) model of al., 2002), with a convolution integral over the pore-throat distribution fp(L,a)
• FElxopresrcihm,e2n0t1s0)h,abvuetnhootwbeovtehrmsheocwhannitshmasttboogtehthtehre.grainsizedistributionandthe σBb*r(oωve)l=liHanSdA(Cσaw*ss(ωia)n,iσ(2s*(0ω10),,φ2,0s1w,1m),(nth)e=*d3e−2nφoteφsmco−1mσp*eHxSvUar+iaφble2−s)3,φm−1σ*HSL, σw*(ω)=σw01−∞∫0∞∫0fp(L,a)η0(L,a)1−1−ex2p(−iω2τpiω(Lτ)p(L))dLda−1
characteristics of the pore space influence SIP (spectral induced polarization)
rpeoslparoinzasteionofplagyraanurloalre.materials. Possibly this suggests that both types of σH*SU(σ*p,σs*,φ)=σs*+(σ*−σ1*−)φ−1+ φ σH*SL(σ*p,σs*,φ)=σ*p+(σ*−σ*φ)−1+1−φ Chargeabilityη0=2π(a2+4aα2L)(2L∆−t1±+ξ−1L−1) ,and time constant τp
p s 3σ* s p 3σ* 1 2 1 2 2
• Furthermore, theoretical and experimental works on micro/nanofluidic devices • σ and σ are the upper and lowser H-S bounds, σ is the conductivity of thep • Stern layer polarization is modelled following Revil and Florsch, (2010),
demonstratedthatmembranepolarizationoccursinrealsystems(seeforexample HSU HSU p
Manietal.,2009). aproer et-hsep aecleec (tari cfuanl cctoiondnu ocft iwviatiteesr oefle tchter icwaal tceorn adnudc tsiovliitdy pahnads seast.u ration), σwand σs σ*S(ω)=4E (Σs'+iΣs'') Σs'(ω)=ΣS1−∞∫ g(τ) dτ Σs''(ω)=ΣS∞∫g(τ)ωτdτ
• TheaimofthisworkistodevelopamechanisticmodelforSIPthatincorporates s h  01+ω2τ2  01+ω2τ2
• mis Archie’s cementation exponent, φis porosity and S water saturation.
both grain and membrane polarization and uses a non-linear mixing rule to w • Σis the surface conductance of the Stern layer , g(τ)is the distribution of
describeeffectofthepore-spaceconfigurationofthesolidandfluidphases. • Maxwell-Wagner polarization and high frequency noise are considered using a relaxation times, which is computed from the grain size distribution, E is related
h
Cole-Cole model to the first moment of the grain size distribution.
4. Model application and preliminary results 5. Discussion
• The model fits reasonably well measurements at high water saturation (Sw>0.5),
• Experiments from Binley et al., (2005) and Cassiani et al., whereas in drier conditions the comparison is less satisfactory.
((22000099)) wweerree uusseedd ttoo tteesstt tthhee mmooddeell.. SSww==11..00 SSw==00..8833 • The ability of the model to reproduce the patterns observed in the experimental
• Available data on the grain-and pore-size distributions
data suggests that the observed SIP results from a combination of grain and
were used to constrain model parameters.
membrane polarization.
• Archie’s cementation and saturation exponents were
• Frequently, however, Maxwell-Wagner polarization and noise at high frequency
calibrated on the data in the DC limit
(ω>100Hz) hide the contribution of membrane polarization.
Sample VEC 7-5, • In our model, the relaxation time is controlled by the characteristic length of the
Binley et al., (2005) pores (membrane polarization) and of the grains, the diffusion coefficient and a
tortuosity factor computed from Archie’s cementation factor and water
Sample VEC 7-5, saturation.
Sw=0.42
Binley et al., (2005) • As the grain diameters are normally greater than the characteristic length of
Sw=0.58 pore-throats, Stern (grain) polarization occurs at lower frequencies than
S=0.58 S=0.42
w w membrane polarization.
Sw=0.83
• According to our model, as water saturation decreases, the contribution of
surface conductivity (i.e of Stern layer polarization) increases and becomes
Sw=1.0 dominant, while membrane polarization remains constant.
6. References and acknowledgements
Sw=1.0 Sw=1.0 • Binley,A.M.,L.D.Slater,M.Fukes,andG.Cassiani(2005),Therelationshipbetweenfrequencydependentelectricalresistivityand
hydraulicpropertiesofsaturatedandunsaturatedsandstone.WaterResour.Res.,41(12),W12417.Doi:10.1029/2005WR004202.
• Brovelli,A.andG.Cassiani(2011)Combinedestimationofeffectiveelectricalconductivityandpermittivityforsoilmonitoring.Water
Resour.Res.47,W08510.Doi:10.1029/2011WR010487.
• Brovelli,A.andG.Cassiani(2010).AcombinationoftheHashin-Shtrikmanboundsaimedatmodellingelectricalconductivityand
permittivityofvariablysaturatedporousmedia.GeophysicalJ.Intern.180(1):225:237.Doi:10.1111/j.1365-246X.2009.04415.x.
• Cassiani,G.,A.Kemna,A.VillaandE.Zimmermann(2009).Spectralinducedpolarizationforthecharacterizationoffree-phase
hydrocarboncontaminationofsedimentswithlowclaycontent.NearSurf.Geophys.,7(5-6):547-562.doi:10.3997/1873-0604.2009028.
Parameter Binleyet al., (2005) Cassianiet al., (2009) • Mani,A.,T.A.ZangleandJ.G.Santiago(2009)Onthepropagationofconcentrationpolarizationfrommicrochannel-nanochannel
interfaces.PartI:Analyticalmodelandcharacteristicanalysis.Langmuir,25:3898-3908.
Archie’s mand n 1.5;1.6 1.75; 2.24 • Revil,A.andN.Florsch(2010).Determinationofpermeabilityfromspectralinducedpolarizationingranularmedia.GeophysicalJ.Intern.
181:1480-1498.
Grain size distribution 1.5x10-4 1.4x10-5 m 1.45x10-4 1.0x10-5 m • Titov,K.,K.Komarov,V.TarasovandA.Levitski(2002).Theoreticalandexperimentalstudyoftimedomain-inducedpolarizationinwater-
saturatedsands.J.Appl.Geophysics50:417-433.
Cell #4 of Cassiani et al., (2009) Cell #5 of Cassiani et al., (2009) Pore-throatdistribution 7x10-7 1.25x10-7 m 6.9x10-7 1.25x10-7 m This work was supported by the EU FP7 collaborative project iSOIL“Interactions between soil
related sciences –Linking geophysics, soil science and digital soil mapping”. We thank A.
Surface conductance (ω=0Hz) 3.6x10-8 S 2.1x10-8 S
Binley(Lancaster University, UK) for providing us the experimental data.