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

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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. Gonc¸alve`s
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, France
b
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 srcin of these pressures is needed in order to justify the hydrogeologic and transport model within this formation. A prior modeling work on thistopic [Gonc¸alve`s, 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 thesurrounding 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; Gonc¸alve
`s et al., 2004).In the speciﬁc case of the Callovo-Oxfordian, Gonc¸alve`set 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
1474-7065/$ - see front matter
2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.pce.2005.12.002
*
Corresponding author.
E-mail address:
gueutin@ccr.jussieu.fr (P. Gueutin).
www.elsevier.com/locate/pce
Physics and Chemistry of the Earth 32 (2007) 434–440
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-c¸alve`s 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-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, inGonc¸alve`s et al., 2004). The salinity is otherwise dominatedby NaCl. The simulated overpressures are of the order of
Fig. 2. NW-SE cross section showing the head data (m) for ﬁve boreholes EST103, EST104, EST107, HTM102 and MSE101.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
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 (Gonc¸alve`s 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 Gonc¸alve`set 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: possibleimplications 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 Si
4+
is replaced by Al
3+
, and in the octa-hedral-Al sheet, the Al
3+
is replaced by Fe
2+
and/or Mg
2+
.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 of the 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:
Q
v
¼
q
s
1
//
CEC
ð
1
Þ
in which
Q
v
is the excess of charge in C m
3
of pore water,
q
s
is the density of the solid (kg m
3
),
/
is the porosity of the 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,
Q
v
:
Q
v
¼ð
1
f
q
Þ
Q
v
ð
2
Þ
The
f
q
coeﬃcient is deﬁned (Leroy et al., in press) as thefraction of the charge located in the Stern layer. Hence,1
f
q
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; Revil
and Leroy, 2004; Leroy et al., in press), which is character-ized by its own equilibrium pressure and concentration,
C
f
,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:
D
p
¼
RT V
w
ln
a
1w
a
2w
ð
3
Þ
in which
a
1w
and
a
2w
are the activity of water in reservoirs 1and 2 respectively (equivalent mole fractions),
R
is the gasconstant (8.31
·
10
3
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 previoussimulations 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
436
P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440
(Eq. (3)). According to Fritz (1986), for concentrations
lower than 1 mol L
1
, the osmotic pressure can be approx-imated by the Van’t Hoﬀ expression, with an error lowerthan 1%:
D
p
¼
RT
m
D
C
ð
4
Þ
in which
m
is the number of constituent ions of the dissoci-ating solute and
D
C
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, Gonc¸alve`s et al. (2004) givethe generalized forms of the Darcy’s law in 1-D:
q
z
¼
K
z
o
h
o
z
þ
r
K
z
q
g
o
p
o
z
ð
5
Þ
in which
K
z
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.
r
K
z
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
D
P
D
p
q
¼
0
ð
6
Þ
in which
D
P
is the observed diﬀerence in pressure acrossthe membrane and
D
p
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 of water:
q
z
¼
K
z
o
h
o
z
þ
K
c
o
C
o
z
ð
7
Þ
with
K
c
¼
r
RT
m
K
z
q
g
.
3.2. Prior excess head simulations
Gonc¸alve`s et al. (2004) calculated the osmotic eﬀect bysimple analytical or numerical solutions. They suppose that
T
,
q
,
r
and
K
z
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 numerical
solution. 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):
K
z
o
2
h
o
z
2
K
c
o
2
C
o
z
2
¼
S
S
o
h
o
t
ð
8
Þ
D
o
2
C
o
z
2
¼
R
d
o
C
o
t
in which
R
d
is the retardation factor,
D
is the Fick’s diﬀu-sion coeﬃcient (m
2
s
1
) and
S
S
is the speciﬁc storage coef-ﬁcient (m
1
). They take for the parameter values
K
z
=10
13
m s
1
,
S
S
= 10
5
m
1
and
D
= 10
11
m
2
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
=
C
0
,
h
*
= 0 at
t
= 0. The initial concentration,
C
0
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 Gonc¸alve`s 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 excessconcentration 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
P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440
437
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 of
u
d
, the zeta potential and the set of six equations are com-bined to obtain an equation of the form:
F
(
u
d
) = 0 which issolved for
u
d
by a Newton–Raphson iterative method.With the solution of the TLM, it possibles to computethe value of the partition coeﬃcient
f
q
. 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 m
2
/g and a
q
s
= 2600 kg m
3
for the clay contentas measured on the ﬁner granulometric fraction of the Cal-lovo-Oxfordian and 7 m
2
/g and
q
c
= 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
f
q
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),
f
q
is diﬃcult to con-straint. Calculated value of the
f
q
parameter are only validfor 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):
C
ðÞ
¼
Q
v
2
eN
A
2
þ
C
2f
" #
1
=
2
Q
v
2
eN
A
ð
9
Þ
where
Q
v
is the excess charge in the diﬀuse layer (C m
3
),
C
f
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
N
A
is the Avogadro number(6.02
·
10
23
mol
1
). At the boundary of the system, thisequilibrium solution is the aquifers pore water, with
C
f
= 0.017 mol L
1
in the Oxfordian and
C
f
= 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
C
f
is considered between the top and the bottom of the 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-
Table 1Mineralogical composition of the Callovo-Oxfordian’s claysMineral Relative proportionSmectite 49%Illite 49%Chlorite 1%Kaolinite <1%Table 2Parameters values for the calculation of the triple layer modelCallovo-OxfordianVolumetric proportion of clay 30 40 50Surfacic proportion of clay 0.81 0.87 0.91
C
03
¼
C
02
ð
insites
=
nm
2
Þ
5.0 5.4 5.7
Q
i
(C m
2
)
0.21
0.24
0.25Fig. 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 of 0.04 ml.g
1
.438
P. Gueutin et al. / Physics and Chemistry of the Earth 32 (2007) 434–440

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