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Physics and Chemistry of the Earth 32 (2007) 434–440

Osmotic interpretation of overpressures from monovalent basedtriple layer model, in the Callovo-Oxfordian at the Bure site

P. Gueutin a,b,*, S. Altmann b, J. Goncalves a, P. Cosenza a, S. Violette a

a UMR. 7619-Sisyphe, Universite Pierre et Marie Curie, case 125, 4 pl. Jussieu, 75252 Paris, Cedex 05, Franceb ANDRA, 1/7 rue Jean Monnet, 92298 Chatenay-Malabry, Cedex, France

Received 1 July 2005; received in revised form 1 November 2005; accepted 30 December 2005Available online 16 November 2006

Abstract

Overpressures in the range 0.2–0.6 MPa are measured in the Callovo-Oxfordian at the Bure site. An understanding of the origin ofthese pressures is needed in order to justify the hydrogeologic and transport model within this formation. A prior modeling work on thistopic [Goncalves, J., Violette, S., Wendling, J., 2004. Analytical and numerical solutions for alternative overpressuring processes: Appli-cation to the Callovo-Oxfordian sedimentary sequence in the Paris basin, France. J. Geophy. Research 109, B02110, doi:10.1029/2002JB002278.] concluded that an osmotic process could explain at least partly these overpressures. Indeed, in these previous calcula-tions, the presence of a maximum salinity within the clay-rock layer together with a membrane property results in a ‘‘build up’’ in pres-sure. In this paper, the pore space concentration of water activity determining solutes is analyzed taking into consideration thecontribution of ions compensating the structural charge of clay minerals and the fraction of clay minerals in the total lithology accordingto their vertical distribution. The calculations presented here show that taking into account the fraction of the CEC compensating cationspresent in the diffuse layer calculated using a recent model coupling transport and a triple layer model for sorption in clayey porousmedia allows a reasonable representation of observed vertical over-pressure profile.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Overpressures; Clay minerals; Coupled processes; Cation exchange capacity

1. Introduction

Geological formation sequences in sedimentary basinscan have layers, generally confined by over and underlyingvery low permeability formations, which exhibit pressuresgreater than the hydrostatic ones expected at a given depth.Such so-called ‘overpressures’ have also been measured in alow permeability clay-rock formation, the Callovo-Oxfor-dian, at the site in the East Paris Basin (Bure) being inves-tigated by the ANDRA (French National Agency forNuclear Waste Management) to study its suitability forhosting a potential nuclear waste repository. The measuredoverpressures, shown in Fig. 1, are of the order of 0.2–0.6 MPa (i.e., 20–60 m of excess head relative to the

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doi:10.1016/j.pce.2005.12.002

* Corresponding author.E-mail address: gueutin@ccr.jussieu.fr (P. Gueutin).

surrounding aquifers, Figs. 1 and 2). The most commonlyinvoked geological process related to causes of over pres-suring are compaction disequilibrium, diagenesis andtopography changes, but certain thermodynamic andhydrodynamic processes have also recently been put for-ward including osmostic processes and fluid density con-trasts (Neuzil, 1995; Neuzil, 2000; Goncalves et al., 2004).In the specific case of the Callovo-Oxfordian, Goncalveset al. (2004) have shown that an osmotic effect would gen-erate excess pressure within the formation during the per-iod of out-diffusion of initial high porewater NaClconcentrations (seawater), i.e. the first several tens of mil-lions of years. The model however predicts overpressuresmuch lower than those observed presently when pore-water salinities approach the present day, near steadystate profiles, in this � 100 million years old formation.A recent reappraisal of the specific characteristics of the

Fig. 1. Excess head (h*) measured as function of depth in the Callovo-Oxfordian formation.

Fig. 3. Idealized distribution of ion in the vinicity of negative chargedsurface according to the diffuse-layer model (Gouy-Chapman) and thetriple-layer model (Stern and Grahame) (according to Warren and Haack,2001).

P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440 435

Callovo-Oxfordian clay-rock porewater composition whichmight influence water activity (Altmann and Coelho, 2004)shows however that an osmotic phenomenon is still likelyto be the source of the measured pressures (see Fig. 3).

Osmosis is the movement of water under a chemicalpotential gradient that can be related to the solute concen-tration gradient across a semi-permeable membrane (Fritz,1986). The osmotic effect can be described using coupledequations since solute transport and water movement sharethe same driving forces (Katchalsky and Curran, 1967;Bolt, 1979). The parameters describing these coupled pro-cesses depend on certain properties of clay minerals relatedto the electric interactions between pore solution and min-eral surface associated with the clay minerals interfaceexcess negative charge. In their modeling approach, Gon-calves et al. (2004) assumed that the osmotic effect resultedfrom salinity differences between the Callovo-Oxfordianporewater and that of adjacent formations, and on themembrane properties of the clay-rock. They interpretedthe salinity profiles as resulting from long-term and tran-

Fig. 2. NW-SE cross section showing the head data (m) for five b

sient diffusion-dominated process (Remenda et al., 1996;Hendry and Wassenaar, 1999) starting with a homoge-neous concentration (seawater salinity) within the clay-rock and subjected at its boundaries to lower and constantsalinities. In accordance with these authors, they assumedthe low salinities in the surrounding aquifers to be gov-erned by aquifer recharge and subsequent leaching causedby the uplift and erosion (65–40 Myr). The higher salinitieswithin the Callovo-Oxfordian cause a build-up in pressureby osmotic effect, followed by a decrease in the salinity gra-dient and accompanying excess head. The authors obtain afinal salinity gradient close to the steady-state and similarto the measured salinity profile. The salinities measuredin the surrounding aquifers are higher in the Dogger(5 g L�1) than in the Oxfordian (<1 g L�1) (cf. Fig. 4a, inGoncalves et al., 2004). The salinity is otherwise dominatedby NaCl. The simulated overpressures are of the order of

oreholes EST103, EST104, EST107, HTM102 and MSE101.

436 P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440

several tens of meters near the top of the formation (nearthe Oxfordian), and therefore of the same order as mea-sured values, but go to very low values at the bottom, nearthe more saline Dogger (Goncalves et al., 2004). This latterresult is inconsistent with observed 40 m or so overpres-sures at the bottom of the formation.

The purpose of the present study is to demonstrate thatthe salinity data used in the previous work by Goncalveset al. (2004) are certainly underestimated when consideringmore accurately the composition of solutes in the porespaces, in particular using the recent models developedby Leroy and Revil (2004) and Revil and Leroy (2004) inorder to improve the estimations made by Altmann andCoelho (2004).

First, a short background on clay surface properties(and possible consequences in terms of pressure) is pre-sented, and then the mathematical model for osmotic pres-sure generation and previous calculations are presented.Finally, new simulations of the excess head in the Cal-lovo-Oxfordian based on the estimation of the pore spaceconcentration from the Cation Exchange Capacity (CEC)are discussed.

2. Short background on clay surface properties: possible

implications for pressures

2.1. Double layer theory

Clays are formed by tetrahedral-Si and octahedral-Alsheets. Isomorphic substitutions occur, i.e. in the tetrahe-dral-Si sheet the Si4+ is replaced by Al3+, and in the octa-hedral-Al sheet, the Al3+ is replaced by Fe2+ and/or Mg2+.These isomorphic substitutions together with the ionizationof the silanol groups produce a net negative charge at thesurface. This charge deficiency is counterbalanced by anaccumulation of ions close to the surface, and a diffusedouble layer is developed (Horseman et al., 1996). Severalmodels exist to explain the structure of the diffuse doublelayer, e.g. the Gouy-Chapman model and the Stern model(Rieger, 1994).

The Gouy-Chapman model considers that the ions arenot immobilized on the surface. The counter-ions spreadout into the solution (Horseman et al., 1996). Stern (1924)and Grahame (1947) consider that a substantial part ofthe negative surface charge is balanced by ions adsorbedon the surface (hydrated or not) but strongly fixed (Vial-lis-Terrisse, 2000, Fig. 3). This layer is the well-known Sternlayer. The remaining unbalanced surface charge is balancedby the ions in the diffuse double layer. Hence, in the Sternmodel, there are two layers, the Stern layer containing ionsfixed close to the surface, and the Gouy-Chapman layermade of ions weakly attracted by the surface (Rieger, 1994).

These counter-ions must exactly balance the excesscharge on the clay mineral surfaces represented by the so-called cation exchange capacity CEC (meq g�1), which cor-responds to the excess of positive charges needed to balancethe negative charge of clay interfaces. Revil and Leroy

(2004) give the following formulation to relate the CEC tothe excess of charge per unit pore volume:

Qv ¼ qs

1� //

� �CEC ð1Þ

in which Qv is the excess of charge in C m�3 of pore water,qs is the density of the solid (kg m�3), / is the porosity ofthe clay-rock and the CEC is expressed in C kg�1. This ex-cess charge can be related to the concentration of counter-ions in the diffuse layer, Qv:

Qv ¼ ð1� fqÞQv ð2Þ

The fq coefficient is defined (Leroy et al., in press) as thefraction of the charge located in the Stern layer. Hence,1 � fq provides an estimation of the fraction of counterions present in the diffuse layer, that modifies the chemicalpotential of water.

2.2. Implications for pressure gradients

We consider here a system at thermodynamic equilib-rium made of a layer of clay-rock and surrounded bytwo reservoirs that can be made of sand or carbonate(representing aquifers). The pore water or free water inthe reservoirs is described as the ‘‘equilibrium solution’’(Sherwood, 1992; Horseman et al., 1996; Revil, 1999; Reviland Leroy, 2004; Leroy et al., in press), which is character-ized by its own equilibrium pressure and concentration, Cf,with the shales. As shown initially by Altmann and Coelho(2004), the concentration should be permanently higher inthe clay-rock (due to the presence of the immobilized coun-ter ions) than in the reservoirs, with concentration differ-ences as high as one order of magnitude if all of thecounter ions are considered. These authors have shownthat, by using the conditions for thermodynamic equilib-rium (i.e., the equality of chemical potential) for water inthe pore space of reservoirs and clay-rock at the bound-aries, the pressure within the pore space of the clay-rock(calculated using the classic equation for osmotic pressuregiven below) should be higher than in the reservoirs:

Dp ¼ �RT

V w

lna1

w

a2w

ð3Þ

in which a1w and a2

w are the activity of water in reservoirs 1and 2 respectively (equivalent mole fractions), R is the gasconstant (8.31 · 103 Pa L mol�1 K�1), T the absolute tem-perature (K), V w is the partial volume of water (L mol�1).

3. Mathematical model for osmosis and previous

simulations on the Callovo-Oxfordian

3.1. Mathematical model

The chemical potential of water is currently expressed interms of the osmotic pressure [see e.g. Katchalsky and Cur-ran, 1967] that is related itself to the solutes concentration

P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440 437

(Eq. (3)). According to Fritz (1986), for concentrationslower than 1 mol L�1, the osmotic pressure can be approx-imated by the Van’t Hoff expression, with an error lowerthan 1%:

Dp ¼ RT mDC ð4Þ

in which m is the number of constituent ions of the dissoci-ating solute and DC is the difference in solute concentration(mol L�1).

Several authors have shown that compacted clays havethe capacity to act as a semi-permeable membrane, i.e.,to allow the movement of the water but to prevent at leastpartly the transport of ions (Olsen, 1969; Marine and Fritz,1981; Keijzer et al., 1999; Neuzil, 2000). The semi-perme-ability of the membrane is its capacity to allow the move-ment of water and to prevent the transport of all or partof the solutes. A perfect, or ideal, membrane, totally pre-vents the transport of ions.

Hence, in such argillaceous media, the flux of water, to afirst approximation, can be considered as driven by twopotentials, the pressure potential (Darcy’s law) and thechemical potential (osmosis). The full coupling requiresthe introduction of pressure, chemical potential and electri-cal potential gradients (Bolt, 1979; Revil and Leroy, 2004).Provided this simplification, Goncalves et al. (2004) givethe generalized forms of the Darcy’s law in 1-D:

qz ¼ �Kzoh�

ozþ rKz

qgopoz

ð5Þ

in which Kz is the Darcy’s permeability (m s�1), q is thedensity of water (kg m�3), g is the acceleration due to thegravity (m s�2), h* is the excess head (i.e., the difference be-tween the hydraulic head and a reference elevation, topo-graphic level or the hydraulic head in the surroundingaquifers, here the reference is taken to be the head in theDogger) and r is the reflection coefficient. rKz is calledthe osmotic permeability. The coefficient r characterizes theideality of the membrane, i.e., for an ideal membrane thereflection coefficient value is 1, no solute transport can takeplace. If the layer has no membrane properties, this coeffi-cient equals 0. The reflection coefficient is defined as Stav-erman (1952); Marine and Fritz (1981):

r ¼ DPDpq¼0

ð6Þ

in which DP is the observed difference in pressure acrossthe membrane and Dp is the theoretical osmotic pressurethat can be evaluated knowing the difference in concentra-tion across the membrane.

Eqs. (5) and (6) are combined to obtain the transport ofwater:

qz ¼ �Kzoh�

ozþ Kc

oCoz

ð7Þ

with Kc ¼ rRT mKzqg .

3.2. Prior excess head simulations

Goncalves et al. (2004) calculated the osmotic effect bysimple analytical or numerical solutions. They suppose thatT, q, r and Kz are constant on z in the analytical solution,and they suppose that r is dependent on the pore radius band the concentration C (Bresler, 1973) in the numericalsolution. They obtain two coupled equations, one for themovement of water and one for the diffusion of ions. Thetransport of ions by advection is neglecting, becausethe major process to transport of ions is the diffusion(ANDRA, 1999):

Kzo2h�

oz2� Kc

o2Coz2¼ SS

oh�

otð8Þ

Do2Coz2¼ Rd

oCot

in which Rd is the retardation factor, D is the Fick’s diffu-sion coefficient (m2 s�1) and SS is the specific storage coef-ficient (m�1). They take for the parameter values Kz =10�13 m s�1, SS = 10�5 m�1 and D = 10�11 m2 s�1obtained from experimental investigations performed byANDRA (ANDRA, 1999).

Their initial and boundary conditions are h* = 0, C = 0at outside Callovo-Oxfordian, and in the Callovo-Oxfor-dian C = C0, h* = 0 at t = 0. The initial concentration, C0

is the salinity of the sea water, i.e., 0.75 mol l�1. At theend of the simulation, they obtain values for the reflectioncoefficient varying between 0.5 and 0.8. The simulatedexcess heads, about 30 m in the centre of the layer, areon the order of the measured values by ANDRA (cf.Fig. 7, in Goncalves et al., 2004) but are still lower thanmeasurements. The salinity, dominated by NaCl in theirsimulations, varies between 0.03 and 0.16 mol L�1.

These concentrations are low, and they are close to theconcentration in the surrounding aquifers, indicating asolution that can be considered in near steady state withregard to mobile ion concentrations, in particular Cl�

and Na+. These concentrations do not include the concen-trations of the immobile counter ions in the diffuse layercompensating the surface charge, and if these ions contrib-ute to reducing the water activity in the clay-rock, the‘osmotically effective’ solute concentration will be underes-timated (Altmann and Coelho, 2004). In the next part, weuse the calculation proposed by Leroy and Revil (2004) toestimate a relevant concentration in the clays accountingfor electrostatic interactions.

4. Simulations of excess of head accounting for the excess

concentration due to clay surface interaction

The theoretical system under consideration in part 2.2 isequivalent to the real system involving the Callovo-Oxfor-dian and the two aquifers (Fig. 2). In what follows, we willestimate the mean pore space concentration but this timetaking into account the presence of counter-ions in the pore

438 P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440

space of the clay-rock following the calculation proposedby Revil and Leroy (2004).

The triple layer model (TLM) equations from Leroy andRevil (2004) are solved. The six variables (three potentialsand three charge densities) are expressed as functions ofud, the zeta potential and the set of six equations are com-bined to obtain an equation of the form: F(ud) = 0 which issolved for ud by a Newton–Raphson iterative method.With the solution of the TLM, it possibles to computethe value of the partition coefficient fq. If we do the calcu-lation for a pure smectite a value of 0.988 is found, compa-rable to that obtained by Revil and Leroy (2004) for a puresmectite. The TLM involves surface properties, such as thesurface density of sites causing a negative charge of clayminerals surface. They are available for pure clay minerals(Leroy and Revil, 2004, and included references). But theCallovo-Oxfordian is a mixed medium associating clayminerals, calcite and quartz. We consider this heteroge-neous medium in an equivalent medium approach withhomogeneous, charged material. The relevant minerals, inthis calculation, are the clay minerals, because of their reac-tive surface. The equivalent surface parameters are thuscalculated using the surface proportion occupied by clayminerals and estimated from their volumetric proportion.The relative proportion of smectite and illite is also consid-ered (Table 1). For this calculation, we take a specific sur-face of 60 m2/g and a qs = 2600 kg m�3 for the clay contentas measured on the finer granulometric fraction of the Cal-lovo-Oxfordian and 7 m2/g and qc = 2300 kg m�3 for thecomplementary grains (Gaucher et al., 2004). We obtain90% of surface occupied by clay for 50% of clay volumetriccontent (Table 2).

The Callovo-Oxfordian surface parameters calculatedare indicated in the Table 2. The TLM is solved for thishomogeneous medium and a value of fq is computed,according to the relation proposed by Leroy and Revil(2004). Values of 0.981 for 30% of clay content, of 0.982for 40% and of 0.983 for 50% are found. However, asquoted by Revil and Leroy (2004), fq is difficult to con-straint. Calculated value of the fq parameter are only valid

Table 1Mineralogical composition of the Callovo-Oxfordian’s clays

Mineral Relative proportion

Smectite 49%Illite 49%Chlorite 1%Kaolinite <1%

Table 2Parameters values for the calculation of the triple layer model

Callovo-Oxfordian

Volumetric proportion of clay 30 40 50Surfacic proportion of clay 0.81 0.87 0.91C0

3 ¼ C02 ðinsites=nm2Þ 5.0 5.4 5.7

Qi (C m�2) �0.21 �0.24 �0.25

for a single binary monovalent (1:1) electrolyte such asNaCl.

From this estimate we calculated the theorical porewater concentration in mol L�1 following Revil and Leroy(2004):

Cð�Þ ¼Qv

2eN A

� �2

þ C2f

" #1=2

� Qv

2eN A

ð9Þ

where Qv is the excess charge in the diffuse layer (C m�3),Cf is defined by Leroy and Revil (2004) and Leroy et al.(in press) as the salinity of the pore water in the fictious res-ervoir locally in thermodynamic equilibrium with the shale,it can also be seen as the ‘‘free solution’’ in the shale if itexists, (in mol m�3) and NA is the Avogadro number(6.02 · 1023 mol�1). At the boundary of the system, thisequilibrium solution is the aquifers pore water, withCf = 0.017 mol L�1 in the Oxfordian and Cf = 0.085 mol/Lin the Dogger.

This calculation is made for two water contents0.08 mL g�1 and 0.04 mL g�1 and for an equivalent mono-valent system (i.e., NaCl). In a first approach a mean CECvalue (i.e., 15 meq. 100 g�1) is considered (Fig. 4). In sec-ond approach the variation of the CEC with depth as mea-sured by Gaucher et al. (2004) is introduced in thesimulations. For this purpose the available data for theCEC is interpolated through the Callovo-Oxfordian(Fig. 5). In these two approaches, a steady state linear gra-dient of Cf is considered between the top and the bottom ofthe Callovo-Oxfordian. This gradient is the result to trans-port of a salt between the Dogger and the Oxfordian.

The excess head calculations are performed consideringa steady state for the solute concentration. The counter-

Fig. 4. Excess head profiles simulated as function of depth for a constantconcentration in the Callovo-Oxfordian. The black line is for the watercontent of 0.08 ml.g�1 and the grey line is for the water content of0.04 ml.g�1.

Fig. 6. Excess head profiles simulated as function of depth from theconcentration calculated by the TLM.

Fig. 5. Interpolated values of the CEC on the total depth of the Callovo-Oxfordian from the data to Gaucher et al. (2004).

P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440 439

ions are by definition immobile, implying r = 1. Thisparameter is also equal to one for ions for which the solu-tion activity is controlled locally by water/mineral dissolu-tion/growth equilibrium reactions (for example Ca2+ andcarbonate minerals, Altmann and Coelho, 2004). Thesteady state is justified by the shape of the salinity curvemeasured in the Callovo-Oxfordian and previously simu-lated by a quasi-steady state attained at the end of the cal-culation by Goncalves et al. (2004).

The equation to be solved is:

Kzo2h�

oz2� Kc

o2Coz2¼ 0 ð10Þ

The salinity profile is considered as known and given by aconcentration equivalent to the CEC within the pores ofthe clay-rock calculated using the concentration Cf (Eq.(9)), and much lower concentration in the surroundingaquifers. This last point yields a substantial and permanentcontrast in concentration at the boundaries of the systemdue to the presence of counter-ions in the clay-rock butnot in the reservoirs.

Parameters values are kept the same as in Goncalveset al. (2004). The results of this simulation are shown inFig. 4 for a constant CEC and in Fig. 6 for a variableCEC corresponding to the measurements. Fig. 6 shows thatthe simulated pressures in the order of 15–40 m, lower thanthe measured ones, for the two porosity values. But the glo-bal profile of pressure is in a good agreement with the data.The large variations of the excess head are explained by thecontrasted values of the CEC through the vertical profile,as shown in Fig. 5. Simulated values at the top and the bot-tom of the Callovo-Oxfordian does not match as well themeasurements, this difference could be explained by thelack of CEC values in these zones. The excess head build

up by osmotic effect is higher at the Callovo-Oxfordianupper boundary, corresponding to a higher difference inconcentration. This build-up is lower at the contact withthe Dogger.

It is important to note that the fq used here has been cal-culated for a monovalent ion, NaCl system.

5. Discussion and conclusions

In this article, we analyse, the possibility of an osmoticinterpretation of overpressures in the Callovo-Oxfordianclay-rock. On the basis of a previous modelling approach,the estimates of excess head are discussed. For this pur-pose, we used a triple layer model (TLM) to calculate thedistribution of counter-ions in the pores space of clay min-erals. From the estimation of the CEC and using the calcu-lation proposed by Revil and Leroy (2004) that gives themean concentrations in the pore space (Eq. (8)), we obtainexcess head build-up.

The excess head calculation is updated here at steadystate with a theoretical concentration within the clay-rockderived from the CEC and the concentration Cf. Hence,the concentration contrast is substancial at the boundariesof the system since the concentration is 0.085 mol L�1 inthe Dogger and 0.017 mol L�1 in the Oxfordian. The pres-ent simulations give excess head values that varies between8 and 45 m. These values lower than measures ones couldbe explained by two features, a very difficult estimationof the parameter fq (Revil and Leroy, 2004) and a simplifi-cation of the system, using only a NaCl equivalent system,although the system contains also divalent cations.

These simulations show that the introduction of the claycontent variation (i.e., CEC) with depth allows a betteragreement between measured and simulated values.

440 P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440

The calculated TLM applies for a monovalent solutionwhen the pore fluid solution in the Callovo-Oxfordianhas been shown to be predominantly divalent. A differentset of equations for the TLM should be treated yieldingcertainly different values for the partition coefficient fq,probably more representative for the Callovo-Oxfordian.

The model used here is simplified, we have to test a morecomplex and fully coupled model as for instance those pro-posed by Revil and Leroy (2004). It is moreover importantto solve the transport equations when transport isneglected here. Three measurements appear very impor-tant: the measurement of the coupling parameters (e.g.the reflection coefficient), the measurement of the equilib-rium solution concentration and the measurement of theCEC on the top and the bottom of the Callovo-Oxfordian.The coupling parameters for the solute transport and watermovement has to be established experimentally to arrive toa set of equations that allow the best understanding andprediction of the transport properties of the Callovo-Oxfordian in a complementary approach to that ofRosanne et al. (2004).

Acknowledgement

The financial support by CNRS-INSU through theECCO-PNRH program (AM/MR/456) is gratefullyacknowledged.

References

Altmann, S., Coelho, D., 2004. Model of flow and solute transport in theCallovo-Oxfordian, undisturbed and disturbed states, ANDRA report.

ANDRA, 1999. Referentiel Geologique du site Meuxe/Haute-Marne, vol.4, Le Callovo-Oxfordien.

Bolt, G.H., 1979. Soil Chemistry, B. Physico-Chemical Models. Elsevier,Amsterdam, 479 pp.

Bresler, Eshel., 1973. Anion Exclusion and Coupling Effects in NonsteadyTransport Unsatured Soils : I. Theory. Soil Science Society of AmericaProceedings 37 (5), 663–669.

Fritz, S.J., 1986. Ideality of clay membranes in osmotic processes: AReview. Clay. Clay Miner. 34 (2), 214–223.

Gaucher, E., Robelin, C., Matray, J.M., Negrel, G., Gros, Y., Heitz, J.F.,Vinsot, A., Rebours, H., Cassagnabere, A., Bouchet, A., 2004.ANDRA underground research laboratory: interpretation of themineralogical and geochemical data acquired in the Callovo-Oxfordianformation by investigative drilling. Phys. Chem. Earth 29, 55–77.

Grahame, D.C., 1947. The electrical double layer and the theory ofelectrocapillarity. Chem. Rev. 41, 441–451.

Goncalves, J., Violette, S., Wendling, J., 2004. Analytical and numericalsolutions for alternative overpressuring processes: Application to theCallovo-Oxfordian sedimentary sequence in the Paris basin, France. J.Geophys. Research 109, B02110. doi:10.1029/2002JB002278.

Hendry, M.J., Wassenaar, L., 1999. Impplications of the distribution ofdD in porewaters of groudwater flow and the timing of geologicalevents in a thick aquitard system. Water Resourc. Research 35 (6),1751–1760.

Horseman, S.T., Higgo, J.J.W., Alexander, J., Harrington, J.F., 1996.Water, Gas and Solute Movement Trough Argillaceous Media.Nuclear Energie Agency (NEA), 290 pp.

Katchalsky, A., Curran, P.F., 1967. Nonequilibrium Thermodynamics inBiophysics. Harvard University Press, Cambridge, Massachusetts, 284pp.

Keijzer, T.J.S., Kleingeld, P.J., Loch, J.P.G., 1999. Chemical osmosis incompacted clayey material and the prediction of water transport. Eng.Geol. 53, 151–159.

Leroy, P., Revil, A., 2004. A triple-layer of the surface electrochemicalproperties of clay minerals. J. Colloid Interf. Sci. 270, 371–380.

Leroy, P., Revil, A., Coelho, D., in press. Diffusion of ionic species inbentonite. J. Colloid Interf. Sci.

Marine, I.W., Fritz, S.J., 1981. Osmotic model to explain anomaloushydraulic heads. Water Resourc. Research 17 (1), 73–82.

Neuzil, C.E., 1995. Abnormal pressures as hydrodynamic phenomena.Am. j. Sci. 295, 742–786.

Neuzil, C.E., 2000. Osmotic generation of ‘anomalous’ fluid pressures ingeological environments. Nature 403, 182–184.

Olsen, H.W., 1969. Simultaneous fluxes of liquid and charge in saturatedkaolinite. Proc. – Soil Sci. Soci. Am. 33, 338–344.

Remenda, V., Van der Kamp, G., Cherry, J., 1996. Use of vertical profilesof d18O to constrain estimates of hydraulic conductivity in thickunfractured aquitards. Water Resourc. Research 32 (10), 2979–2987.

Revil, A., 1999. Ionic diffusivity, electrical conductivity, membrane andthermoelectric potentials in colloids and granular porous media: aunified model. J. Colloid Interf. Sci. 212, 503–522.

Revil, A., Leroy, P., 2004. Constitutive equations for ionic transport inporous shales. J. Geophys. Research 109, B03208. doi:10.1029/2003JB00275.

Rieger, P.H., 1994. Electrochemistry. Chapman & Hall, New York, 483pp.

Rosanne, M., Paszkuta, M., Thovert, J.-F., Adler, P.M., 2004. Electro-osmotic coupling in compact clays. Geophys. Research Lett. 31,L18614, doi:10.1029/2004GL02077.

Sherwood, J.D., 1992. Ionic motion in a compacting filtercake. Proc.Royal Soci. London 437, 607–627.

Staverman, A.J., 1952. Non-equilibrium thermodynamics of membraneprocesses. Trans. Faraday Soci. 48, 176–185.

Stern, O., 1924. Zur Theorie des Elektrolystichen Doppelschriht. Z.Elektrochem. 30, 508–516.

Viallis-Terrisse, H. 2000. Interaction des silicates de calcium hydrates,principaux constituants du ciment, avec les chlorures d’alcallins –Analogie avec les argiles., These, Universite de Bourgogne, 256 pp.

Warren, L.A., Haack, E.A., 2001. Biogeochemical controls on metalbehaviour in freshwater environments. Earth-Sci. Rev. 54, 261–320.