An accurate modelling of the water–rock interactions takes into account all minerals present, even at trace levels, and requires a complete mineralogical analysis of the samples. Because several minerals can control the aqueous speciation of an element, it was also necessary to determine some crystallinity criteria. Indeed, any mineral having alteration figures or an unbalanced structural formula is not considered at equilibrium in the model. Table 1 lists all of the minerals found in the Callovian–Oxfordian formation with their relative abundance, distribution, and information on their crystallinity. Table 1 also indicates whether the phase must be taken into account in the thermodynamic model.

The TRC is an index of the redox potential of the rock. It represents its ‘oxidizability’ and is expressed in term of mole of available electrons. The mean value for the formation is 4.7±1.3meqg−1. These values are similar to those measured in the Opalinus Clay Formation, 4.8±0.9mequivg−1 [30]. TRC values do not vary a lot in the clay formation. The lower values are mainly due to calcareous beds (1.6 mequiv g⁻¹). TRC is linked to the organic matter content and mainly to sulphide minerals and to a lesser extent to siderite. Conditions in the formation are clearly reducing. In the model, the redox potential can be imposed by pyrite.

The Callovian–Oxfordian formation has a very low water content. Water content ranges from 6% to 9% (mass water content dry base). Low contents (1.5%) correspond to levels rich in fine-grained carbonate cement. There is a very good correlation between high carbonate content (>65%) and very low water content (<4%). At the regional scale, variations in water content seem to be insignificant (Table 2).

The water in the clay is of four different types [18]:

• • interlayer water within the sheet structure of clay minerals. This water is strongly adsorbed;
• • another strongly adsorbed water at the clay mineral surface is the (structured) water participating in the hydration shells of the cations (which locally balance the mineral surface charges);
• • loosely held water in the diffuse-layer;
• • free water.

For geochemical purposes, it is convenient to distinguish only between ‘bound’ water (which includes interlayer, strongly adsorbed and some diffuse layer waters) and ‘free’ water (which includes, not only Horseman's free water [18], but also some of the diffuse layer and surface-sorbed waters as well) [23]. Note that the concept of geochemical porosity has been developed for clay to take into account anionic repulsion due to the negatively charged surface of the clay. Anionic repulsion limits the access of anions to part of the porosity. Geochemical porosity is the porosity that is accessible to mobile anions (such as Cl or Br, for example). In a carbonaceous rock, anionic repulsion is limited and anions have access to all of the porosity. This distinction between geochemical porosity and total porosity for argillaceous rock is approximate, however practical. Thus, it is possible to quantify the two types of water by measuring the specific wetted surface using water sorption isotherms (SBETH2O) [10]. For the argillite, the ‘bound’ water is estimated to be about 2 to 3 water layers thick. Knowing the SBETH2O and the thickness of the water layer, the volume of ‘bound’ water is estimated to be about 50% of the total water volume (Table 3). The ionic concentrations can be calculated either with the total water content (TW) or only with the ‘geochemical porosity’ (GP). The advantages of the ‘geochemical porosity’ concept will be demonstrated in the next paragraph.

Leaching of ions is a classic technique to obtain Cl⁻ and Br⁻ (and, in some cases, I⁻ and SO42−) contents in clay porewater. Information concerning cations, aqueous silica, carbonates and fluorides is generally disturbed by the dissolution of minerals. When plotted, concentrations of leached conservative anions give straight lines as a function of the solid/liquid ratio of the batch systems. The dissolution of a mineral gives a hyperbole (Fig. 2), and the oxidation of rock samples produces scattered values.

The behaviour of SO42− during the leaching experiments with a regression coefficient (r2) of 0.997 shows a perfect conservative character. The experiments seem to be undisturbed by pyrite oxidation. The Sr concentration value indicates that celestite is not significantly dissolved during leaching. The SO42− concentrations obtained by leaching represent probably the maximum values present in the porewater. Examples of concentrations of Cl⁻, Br⁻, SO42− in the total water (TW) and in the geochemical porosity (GP) are given in Table 4 for borehole EST205 (external part of the samples immediately cut after drilling to avoid contamination).

An interesting observation was made during the calculation of Cl⁻ concentrations in TW and GP. If we know the Cl⁻ concentration in mg kg⁻¹ of rock, we can calculate the Cl⁻ concentration in the porewater. For the samples from the auxiliary shaft, the mean concentration of Cl⁻ in the total porosity is 2.37×10−2±1.22×10−2moll−1. If a distinction is made between the argillaceous layers and the carbonaceous layers (water content <4%), two mean TW concentration values are observed (Table 5). The Cl⁻ concentration in the carbonaceous layers is about twice as great as in the argillaceous layers. If we consider that the concept of geochemical porosity is applicable only to the argillaceous layers, the Cl⁻ concentration values in the two media are very similar. The Cl⁻ content in the formation is rather homogeneous at the URL site and a value of 3×10−2moll−1 can be used in the model.

The Cl⁻ contents were determined for all of the boreholes (Fig. 3). Cl⁻ concentrations were calculated in the geochemical porosity for the argillaceous layers and in the total porosity for the calcareous layers. Dogger porewater was sampled in the regional boreholes and the Cl⁻ concentrations are given in Fig. 3, which shows the strong influence of this formation on the Cl⁻ content in the Callovian formation. The Cl⁻ content varies with depth in borehole EST312. A straight line can be drawn from the Dogger at 110 mmol l⁻¹ to the top of the formation at 40 mmol l⁻¹. For borehole MSE101 and at the URL site, there is less vertical variation between 50–60 and 30 mmol l⁻¹. Although MSE101 is located northeast of the URL, no Cl⁻ variations can be detected between the two locations. For the two boreholes located southwest of the site, the vertical variation is negligible (EST 322: 17±10mmoll−1, EST342: 26±23mmoll−1). There is, therefore, a regional variation with a decreasing concentration of Cl⁻ from northeast to southwest.

One possible explanation for this might be that saline water migrates from the Triassic formation via a fault system located northeast of borehole EST312. Since there is a Cl⁻ concentration gradient in the Dogger formation, diffusion or a very slow advection might explain the horizontal migration of Cl⁻. The Dogger clearly influences the chemistry of porewater in the Callovian–Oxfordian formation.

At the URL (EST205/PAX data), the mean CEC of the Callovian–Oxfordian formation is 17.4±6.1meq/100g. The lowest values are measured in the more calcareous beds (2.1 meq/100 g) and the highest values in the I/SR0 zone (25.1 meq/100 g at 463.74 m). The I/SR1 (less rich in smectite) has a very stable average value of 16.1±0.6meq/100g.

As Bradbury and Baeyens [4] pointed out, the adsorbed cation population is a reflection of the solution in equilibrium with the mineral assemblage. Exchange reactions are very rapid and adsorbed cations are immediately in equilibrium with the porewater. The proportion of exchangeable cations is, therefore, very useful information. At the URL site, the distribution of exchangeable cations slowly evolves. In addition to the 4% of exchangeable Sr²⁺, the adsorption sites are taken up mainly by 45.3±1.6% of Ca, 25.0±2.1% of Mg, 17.7±1.9% of Na, and 8.1±1.1% of K.

Exchangeable Sr was not systematically determined at the regional scale. Only the concentrations of exchangeable K, Na, Mg, and Ca will, therefore, be discussed. No significant vertical variations were observed for the different boreholes. This is also true for EST312, which presents the major Cl evolution. From northeast to southwest, there are large variations in the exchangeable-cation distribution (Fig. 4). CaX₂ values are identical in borehole EST312 and in the URL (EST205/PAX), and MgX₂ increases to the detriment of alkaline ions. For example, there is only half as much KX. Southwest of the URL site at borehole EST322, the proportion of MgX₂ is identical to that at the URL, there is a greater proportion of CaX₂ and only one third as much NaX. Borehole EST342, located beyond the Marne and Joinville fault systems, has a greater proportion of NaX, to the detriment of MgX₂.

Considering the ion exchange populations of the regional boreholes, we can conclude that, for the COX porewater:

• • the proportion of Na decreases from northeast to southwest following the decrease of the Cl⁻ content;
• • the proportion of K also decreases, in a lesser extent;
• • Ca and Mg concentrations are stable considering the electroneutrality.

The work of many authors [1,4,16,21,24,25,28,31] shows that there is a large consensus that ion-exchange reactions are essential if we wish to model the porewater chemistry of clay-rich formations. We therefore determined a complete set of ion-exchange constants (KGTH/Na, KGTK/Na, KGTNH4/Na, KGTCa/Na, KGTMg/Na, KGTSr/Na) on the <2-μm clay fractions using the Gaines–Thomas [11] approach. As opposed to [19,21], which use H⁺, our reference cation is Na⁺. This gives constants that can be compared to data presented in the other studies after formalism adaptation [9,27].

For a detailed description of the following experimental method, see [12].

Batch experiments were done using the purified clay fraction (<2μm) from a sample (K119 at 476 m) from borehole EST205. The clay (0.5 g) was equilibrated (72 h) with a solution (25 ml) of Na_xA_1−xCl 5×10−3moll−1 (A = K or NH4+) or Na_xB_0.5−xCl 5×10−3moll−1 (B = Ca, Mg, Sr). The discrete variations of x enabled a progression of the ion-exchange reactions. After separation (centrifuging and filtration), this first solution was analyzed and the equivalent fractions of aqueous species were determined. The clay was re-dispersed (24 h) in a concentrated solution of cobaltihexamine (4 g l⁻¹). After separation (centrifuging and filtration), this second solution was analyzed and the equivalent fractions of adsorbed species were calculated. During this calculation, the molar quantity of aqueous species remaining in the residual porewater (after the first centrifugation) was corrected. The equivalent fractions of aqueous and adsorbed Na and A (or B) were used to construct isotherms (Fig. 5).

Using the Gaines–Thomas approach [11], it is possible to calculate for the exchange sites Xi−, the selectivity coefficient KGTM/Ni (Eq. (1)) for an exchange between two cations M and N of charges m+ and n+, respectively. EM and EN (Eq. (2)) are the equivalent fractions of the adsorbed species. In Eq. (2), ECi is the exchange capacity of the Xi− sites.

Isotherm data are processed from Eq. (1) using a non-linear regression [20]. By modelling the Na/K isotherm, we were able to identify illite-type and smectite-type sites. For the Opalinus Clay, a similar fit was done with two types of sites [12]. However, in this study, the global approach considering the ion exchange sites as a whole was tested for the modelling of porewater in neutral conditions. Therefore, in this paper, only the global constants are given in Table 6.

The most original component of the THERMOAR project is the direct analysis of CO₂ partial pressure on core samples [14]. The core samples were placed in a rigid container immediately after they had been drilled and the edges sawed off. Then the container was filled with an inert gas (N₂, He, or Ar). The results are slightly different, depending on the inert gas used. The best results were obtained when the initial total pressure in the container was sufficiently high (Ptot>800mbar). The temperature and pressure in the cell were monitored continuously. The container was placed in a ventilated cupboard thermostated at a temperature of 25 °C. The gases released from the container were analyzed by gas chromatography until the pCO2 stabilized. At this point, analyses of CO₂ isotopes were done [15].

The mean pCO2 values for the reference borehole EST205 are between 3.10 and 7.17 mbar (logpCO2:−2.51/−2.15). These results are in the range of data compiled by Coudrain-Ribstein et al. [5] for sedimentary confined aquifers (1 to 100 mbar at 25 °C). Fig. 6 presents the data obtained at a regional scale in the best analytical conditions (Ptot>800mbar). Values range between 1.4 and 4.1 mbar (logpCO2:−2.9/−2.4). No variation as a function of depth or at the regional scale can be observed. This can be a good indication of an internal control of this parameter by the mineralogy, the nature of which is constant throughout the formation. The isotopic composition of the gas confirms this. It shows (Fig. 7) that the CO₂ has an original isotopic composition independent of the mantle, the atmosphere, organic matter or bacterial activity. Considering the gas δ13C values, we were able to determine the isotopic composition of the bicarbonate ions at equilibrium with the gas. The values are between −2 and +2‰. The δ13C signatures of the bicarbonates and of the carbonate cements of the clay rocks (mainly calcite and some dolomite and siderite) are similar. This proves that the pCO2 is controlled by the mineralogical assemblage (carbonates) and not by degradation of organic matter or diffusion of gas coming from other geological formations.

In the Callovian–Oxfordian formation, the nature of the mineralogy and the pCO2 regulation mechanisms can be considered as invariable at a regional scale. As the nature of the clay is also stable, the exchange selectivity coefficients can be used for the entire formation. The regional variation of the porewater chemistry was observed for Cl⁻ and the ion exchange population. The model was initially constructed to define the porewater chemistry at the URL and, in a second step, was adapted to regional variations.

Due to the stability of the mineralogy and the geochemical data, the porewater chemistry was considered to be constant in the clay formation at the URL location. All calculations were done at thermodynamic equilibrium. Due to the very low permeability of the clay formation and the probable residence time of the water, it is realistic to suppose that thermodynamic equilibrium can be reached in these geological media. The numerical model of the porewater chemistry involves two steps. First, seawater is diluted by pure water, and then the resulting water is equilibrated with the mineralogical assemblage and the exchange sites (X) of the clay. The dilution is defined so as to obtain the Cl⁻ concentration determined in Section 4.1.4. The entire mineral assemblage (Section 4.1.1) controls the following elements: e⁻, S, C, Si, Ca, Mg, Na, K, Sr, Fe, Al. Concerning the mineralogy, some simplifications have been considered: pure phases (dolomite and siderite) and end-members for chlorite solid solution (daphnite [Fe] and clinochlore [Mg]) have been introduced in the modelling, in place of the observed minerals. Some geochemical subsystems can be distinguished in the model. Na is only determined by ion exchange (NaX). A subsystem Fe, S, e⁻, Sr, accounts for daphnite (Fe-chlorite), celestite, pyrite, and ion exchange (SrX₂). A subsystem Si, Al, K is determined by quartz, illite, and ion exchange (KX). A subsystem C, Ca, Mg, is controlled by pCO2, calcite, and dolomite. The ion exchange equations for Ca and Mg are considered in the equation system. However, they are not the determining factors for the water chemistry. They can only adjust the distribution of cations on the exchanger. The pH is calculated by iteration to obtain the electroneutrality of the solution.

The calculations are performed with the PHREEQC code [22] using the llnl.dat database [33]. Three cases are presented in Table 7. The simulations use the Cl⁻ concentrations determined in the geochemical porosity. ‘A’ simulation uses the maximum measured pCO2 value and ‘B’ simulation a value in the best analytical range (Section 4.1.7). ‘Chlo’ corresponds to test cases where pCO2 is not fixed. Mg-chlorite was added to the phase assemblage as in the model of Coudrain-Ribstein et al. [5]. In this model, pCO2 is not controlled externally and is determined by the equilibrium between calcite, dolomite, and the Mg-chlorite.

Fig. 8 shows that the solutions are relatively concentrated, with an ionic strength of 10−1moll−1. The pH values are between 7.00 and 7.28. The Eh values are low (−176mV<EhSHE<−156mV). The waters have a Cl/SO₄ facies. Na is twice as concentrated as Ca and Mg and four times as concentrated as K. The alkalinity is moderate, between 1 and 3 mmol kg⁻¹_w. The Al and Si contents agree with a system controlled by silicates and aluminosilicates. The Fe contents (determined by the equilibrium with daphnite) are quite high. However, the model calculates a quasi-equilibrium with siderite, which has been found in places in the formation. The logpCO2 value calculated with the ‘Chlo’ model (−1.96) is similar to the maximum measured logpCO2 values (−2.15). This is a good indication that the model converges toward a representative chemistry. Another possible verification is the proportion of adsorbed cations that are accounted for by model. Table 7 shows that the results are close to the measured values. On the contrary, if microcline is tested in the model instead of illite, the percentage of adsorbed cations is significantly different. This indicates that this phase does not participate in the regulation of the porewater chemistry.

To model the porewater at a regional scale, the ‘B’ model described in Section 4.2.2 was adjusted using the Cl⁻ concentrations obtained for boreholes EST312 and EST322 (Section 4.1.4). The corresponding adsorbed ion concentrations are considered in the model (Section 4.1.5). Fig. 8 shows the evolution of the porewater chemistry, which is related mainly to a decrease in salinity (NaCl) from northeast to southwest in the structural block in which the URL is located. The decrease is of about one order of magnitude for the Cl and Na concentrations. The other concentrations are determined by the mineralogy and do not evolved significantly.