versión impresa ISSN 1026-8774
Rev. mex. cienc. geol v.23 n.1 México 2006
Hydration of Camontmorillonite at basin conditions: A Monte Carlo molecular simulation
Hidratación de montmorillonita de calcio en condiciones de cuenca: una simulación molecular Monte Carlo
Raúl Monsalvo1, Liberto de Pablo2 ,*, and M. Lourdes Chávez1
1 Facultad de Química, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Interior, Del. Coyoacán, 04510 México, D. F., México.
2 Instituto de Geología, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior, Del. Coyoacán, 04510 México, D. F., México. * firstname.lastname@example.org
Manuscript received: May 10, 2005
Corrected manuscript received: October 4, 2005
Manuscript accepted: November 18, 2005
Monte Carlo simulations in NPzzT and µVT ensembles of the hydration of Wyomingtype Camontmorillonite have shown the interlayer configurations. Camontmorillonite may hydrate to one, two and threelayer hydrates of d001 spacing 11.83, 13.73, and 15.60 Å at 353 K and 625 bar. At lower temperatures and pressures the spacing increases. Grand canonical simulations show that the onelayer Camontmorillonite hydrate of d001 spacing 12.11 Å is stable at 353 K, 300 bar, 7.21 kcal/mo potential, at a 2.0 km depth of normally compacted sediments. Two and threelayer hydrates do not form. At 353 K, 625 bar, 5.58 kcal/mol potential, the onelayer hydrate is nearly stable. In the clay interlayer, the water molecules are clustered on the midplane, with their protons pointing towards the siloxane surfaces on both sides and on the midplane. The Ca2+ cations are solvated in outersphere coordination, separated 2.77 Å from the water molecules. In sedimentary basins under normal geotherms, onelayer Camontmorillonite is the single hydrate stable at 2 km depth; under overcompacted sediments at 2.7 km depth it becomes unstable.
Key words: montmorillonite, Camontmorillonite, hydration, simulation, Monte Carlo, stability.
Simulaciones Monte Carlo en conjuntos NPzzT y µVT de la hidratación de Camontmorillonita tipo Wyoming muestran la configuración interlaminar. Camontmorillonita puede formar hidratos de una, dos y tres capas, con espaciamiento d001 de 11.83, 13.73,y 15.60 Å respectivamente a 353 Ky 625 bar. A temperaturas menores el espaciamiento es mayor. Simulaciones en conjuntos µVT indican la formación del hidrato de una capa, estable a 333 K, 300 bar, potencial 7.21 kcal/mol, espaciamiento d001 12.11 Å. No se forman los hidratos de dos y tres capas. A 353 K, 625 bar, potencial de 5.58 kcal/mol, el hidrato de una capa no es estable. En el espacio interlaminar, las moléculas de agua se agrupan en el plano intermedio alternativamente orientadas con los protones hacia las superficies de siloxano a ambos lados y en el plano intermedio. Los cationes Ca2+ están totalmente solvatados, fuera del plano intermedio, a distancia de 2.77Å de las moléculas de agua. En sedimentos bajo condiciones normales el monohidrato de Camontmorillonita es estable a 2 km de profundidad, mientras que bajo sedimentos sobrecompactados a 2.7 km de profundidad se vuelve inestable.
Palabras clave: montmorillonita, Camontmorillonita, hidratación, simulación, Monte Carlo, estabilidad.
The adsorption of fluids and chemical species by expandable clay minerals is important to digenetic, metamorphic, petrologic, and geochemical processes (Huggett and Shaw, 1993), soil physics, properties and behavior of soils (Aylmore and Quirk, 1967), stability, retention and transport of contaminants (CotterHowells and Patterson, 2000), waste management (Rutherford et al, 1980) and, in oil exploration and recovery, to borehole stability (Hall et al, 1986; Hall, 1993), adsorption of stabilizing additives and polymers, overpressure and migration of hydrocarbons (Hall, 1993).
The hydration and dehydration of the minerals result in adsorption or separation of fluids and chemical species that affect contamination, rock strength, pore pressure, swelling, and the overall stability of clay systems. The interactions between the clays and fluids are of particular interest to the retention of nutrients and the adsorption, accumulation, decomposition, release, transport, and ultimate fate of contaminants in soils, to soil mechanics, and in petroleumrich basins to the recovery of oil and gas and the quality of the reservoir.
Clay minerals of the smectite type are common. In soils and sediments usually occur Na, Ca, and Mgmontmorillonite or their combinations. In clay deposits, in Mexico are found Ca, Na, and Mgmontmorillonite in the underclays of the Mexican Basin, subjected to hydrationdehydration, contaminants, and occasional multiplying seismic effects; in Durango the dominant specie is Namontmorillonite, lowcalcic and highswelling, whereas in other localities, namely Tlaxcala and Guerrero, predominate Ca and Mgmontmorillonite.
In industrial processes, smectites are normally used in their protonic form or with different adsorbed metallic and organic species to impart distinct properties. Their characteristics and behavior vary, usually associated with their silicic framework and surface properties; structural replacements modify the structural framework to change the surface properties and ultimate behavior of the clay. Reactions on the clay surface define their properties. Naand Camontmorillonite are the most abundant on which other chemical species, fluids, metallic and organic ions or molecules build.
Smectites are relatively stable but prone to transform and modify their properties. Their fine particle size and disordered structure are not easily amenable to some analytical techniques but they are characterized by proper mineralogical procedures. Their surface properties are highly sensitive to the surrounding environment and more complex to characterize, essentially on account of their in situ behavior. As in many geochemical and mineralogical processes, i.e., mineral deposition from hydrothermal fluids or mineral stability at high temperatures, pressures or depths under brines and oil fluids, require complex interpretations and explanations, often distinct from those available from experimental data or extrapolated from different environments and conditions.
In the present paper is discussed the behavior of Camontmorillonite under surface and lowdepth environments, as determined from molecular simulations. Reactions on the clay surface are fundamental to establish interrelations with parent minerals and understanding related processes. Molecular simulations allow characterization of the clay interlamellar space at the atomic and molecular levels, identifying fundamental properties, reaction mechanisms, thermodynamics, and kinetics of reactions, mimicking in situ conditions not easily reproduced experimentally or where direct observation is not simple.
Camontmorillonite is a 2:1 expandable clay mineral that swells upon contact with water. Experimental studies (Posner and Quirk, 1964; Pezerat and Mering, 1967; Keren and Shainberg, 1975; Suquet et al., 1975; McEwan and Wilson, 1980; Slade et al, 1991; Sato et al, 1992; Cases et al, 1997; Bray et al, 1998; Bray and Redfern, 1999, 2000) have shown that at the ambient conditions of 300 K and 1 bar the anhydrous phase of d001 spacing 9.55 9.96 Å hydrates to 11.19 12.45 Å onelayer hydrate, 15.00 15.50 Å twolayer hydrate, and 18.0 19.1 Å threelayer hydrate. Monte Carlo simulations (ChávezPáez et al, 2001a) have shown that in the same ambient environment of 300 K and 1 bar are formed stable 9.82 Å, 12.20, 14.70, and 18.419.0 Å anhydrous, one, two, and threelayer hydrates. However, the characteristics and stability of Camontmorillonite at conditions other than atmospheric have been scarcely described (Stone and Rowland, 1955; Koster von Groos and Guggenheim, 1987, 1989; Khitarov and Pugin, 1996; Siqueira et al, 1997, 1999; Wu et al, 1997; de Pablo et al, 2005).
Parent Namontmorillonite has been shown from simulation studies to form the stable monolayer hydrate at 353 K and 625 bar whereas Kmontmorillonite does not (de Pablo et al., 2004; Chavez et al., 2004; de Pablo et al., 2005). The condition of 353 K and 625 bar is particularly significant. It prevails at a 2.7 km depth of overcompacted sediments, where clay minerals may transform by adsorbing or releasing components or from reaction with circulating brines, oil and gas flows.
The behavior of the clay sediments, shales, will depend on their mineralogy, and on the temperature, pressure, and composition of the surrounding environment. Simulations studies are particularly adept considering their applicability to mimic in situ environments which otherwise are difficult to reproduce experimentally.
The characteristics and behavior of Camontmorillonite at low depths have not been described. In the present study, the stability and swelling of Wyomingtype Camontmorillonite are investigated by Monte Carlo simulations at constant stress in the isobaricisothermal NPzzT ensemble and at constant chemical potential in the grand canonical µT ensemble, at the basin conditions of 333353 K and 300625 bar.
The hydration of Casaturated montmorillonite is studied by Monte Carlo simulation in the NPzzT and µVT ensembles (Allen and Tildesley, 1987), at environments of 333 K and 300 bar existing at 2 km depth in normally compacted sediments, and of 353 K and 625 barprevailing at 2.7 km depth of overcompacted sediments (geotherms at the Gulf of Mexico, geothermal gradient of 30 °C/km, geostatic gradient 150 bar/km, Hower et al, 1976).
The simulations employ the model and approach described by ChávezPáez et al. (2001a, 2001b). The clay considered is the Casaturated Wyomingtype montmorillonite Of unit cell (Si7.75Al0.25)(Al3.50Mg0.50)O20(OH)4Ca0.375• nH2O and charge of 0.75, 33% of which is in the tetrahedral sheet. Eight unit cells form the 320atoms simulation cell, measuring 21.12 Å in the x dimension, 18.28 Å in the y dimension, and 6.56 Å in the z dimension. The positions and charges of the atoms in the unit cell are those of pyrophyllite (Skipper et al., 1995a), with substitution in the simulation cell of octahedral Al3+ in positions (3.52,3.05,0), (7.04,3.05,0), (3.52,6.09,0), and (7.04,6.09,0) by Mg2+ and tetrahedral Si4+ in positions (2.64,1.52,2.73) and (0.88,1.52,2.73) by Al3+.
The total interaction energy between atoms is defined by Equation 1, which includes the Coulomb attractionrepulsion energy and the LennardJones and van der Waals dispersion energy. ChávezPáez et al. (2001a) simulated the interaction energy from Equation 2, which combines the model of Skipper et al. (1995a, 1995b) for the claywater system and the TIP4P water model of Jorgensen et al. (1983). In Equation 2, the first term of the summation represents the Coulomb attractionrepulsion contribution to the total energy of interaction whereas the remaining terms correspond to the LennardJones dispersion contribution, mi and mj are the number of sites in molecules i and j, qia is the charge at site a of molecule i, qjb is the charge at site b of molecule j, riajb is the distance between atom a in molecule / and atom b in molecule./. The parameters A, B, C, D, E, F, and G are site specific parameters developed for the interaction between calcium and TIP4P water. In the present case the parameters of Bounds (1985) (Table 1) are used.
In constant stress simulation, NPzzT, the stress Pzz normal to the clay surface, the temperature T, and the number of molecules N are kept constant. The system is allowed to sample the configuration space through molecular displacements and volume fluctuations. Volume fluctuations are allowed only in the direction normal to the clay surface. The acceptance probability of a new configuration n generated from a configuration m by displacing an atom orby changing the volume of the simulation box is given by Equation 3.
Unm is the difference in energy between the two configurations, Vnm is the difference in volume, and Vn and Vm are the corresponding volumes, β1 = kbT is the inverse temperature, kb is Boltzmann's constant and T is the absolute temperature.
In the grand canonical ensemble, µVT, chemical potential, volume, and temperature are kept constant. The system samples the configuration space through molecular displacements and concentration fluctuations. However, due to the high densities that water can reach in the clay interlayer, sampling can be inefficient and a biasing technique has to be implemented to improve sampling. It is achieved by implementing a rotationalbias insertion method, were a water molecule is inserted randomly in the system and the selection of its orientation is biased. Trial insertions are accepted with probability
and deletion of water molecules is accepted with probability
δUnm is, like Unm in Equation 3, the energy difference between the two configurations, Pj is the probability of selecting jth orientation from k randomly generated orientations; z =exp (βµ) / Λ3 is the activity, Λ is the thermal length of the molecule, and µ is the chemical potential of bulk water (Allen and Tildesley, 1987; ChávezPáez et al., 2001a, 2001b).
We simulate the watercalcium interaction applying the TIP4P water model of Jorgensen et al. (1983) and the parameters of Bounds (1985) (Table 1). At 300 K and 333 bar and at 353 K and 625 bar, we prefer the TIP4P model because its influence on the density or the energy does not appear significant, and by doing so our results can be compared with those known previously on Casaturated montmorillonite under the surface ambient environment (Boek et al., 1995; ChávezPáez et al., 2001a). The waterclay and claycalcium interactions are neglected. The simulations required 2 x 106 Monte Carlo steps for equilibration and, after the equilibration period, simulations proceeded for additional 2 x 106 Monte Carlo steps, until the statistics was satisfactory and smooth calculated functions developed.
RESULTS AND DISCUSSION
Simulations in the NPzzT ensemble at constant mass, pressure, and temperature indicate that at the basin conditions of 353 K and 625 bar the adsorption of 32 water molecules per layer of Camontmorillonite (98 mg/g of clay) results in the formation of the onelayer hydrate of d001 , spacing 11.83 Å (Table 2). The water molecules are clustered on the interlayer midplane, tilted with their hydrogen atoms oriented towards the siloxane surfaces on both sides and to the midplane (Table 2, Figure 1a). The Ca2+ ions are on the interlayer midplane solvated in outersphere complexes, but some are closer to the clay surface. A distance of 1.624 Å separates the outmost proton layers. The configuration is illustrated in the snapshot of Figure 2a.
The adsorption of 64 molecules (196 mg/g) increases the d001 , spacing to 13.73 Å, placing the water molecules in two welldefined layers, one to each side of the interlayer midplane, 1.899 Å apart (Table 2, Figure 1b). The water protons are distributed over four layers, two outmost ones, 3.449 Å apart, and two closer to the central plane. Ca2+ ions are solvated in both layers of water, slightly off the oxygen atoms; none are midway between the two layers of water, nor are they closer to the clay surface or in innersphere coordination with the siloxane oxygens (Figure 2b). At higher contents of water, namely 96 molecules (294 mg/g), the spacing increases to 15.60 Å, preserving the 2layer configuration with the water molecules separated 3.524 Å, the outmost protons 5.399 Å apart, and minor excess water molecules located about the interlayer midplane (Table 2, Figure 1c). The Ca2+ ions are on the interlayer midplane and inbetween the two water layers, with few atoms closer to the siloxane surface.
The results indicate that, at 353 K and 625 bar, the adsorption of 32, 64, and 96 water molecules places the molecules respectively at 0.012, 0.9120.987, and 1.7871.737 Å from the interlayer midplane. The interlayer configuration changes from onelayer when adsorption is between 32 and near 64 water molecules to twolayer when increased to 64 96 molecules. The Ca2+ ions are essentially in outersphere complexes in the water layers, symmetrical to the protons and slightly off the oxygen atoms.
At 333 K and 300 bar, prevailing at 2 km depth, the adsorption of 50 water molecules develops a onelayer hydrate of d001 , spacing 12.11 Å, higher than that formed at 353 K and 625 bar. It has water molecules off the interlayer midplane, closer to the clay surface (Table 2). Its snapshot (Figure 2c) illustrates a bulkier interlayer relative to that at 353 K when 32 molecules were adsorbed (Figure 2a).
Our simulated d001 spacing of 11.83 and 12.11 Å for the onelayer hydrates at 353 K and 625 bar and at 333 K and 300 bar are within the range of 11.1912.45 Å known from experimental studies (McEwan and Wilson, 1980; Bray and Redfern, 1999, 2000) and are shorter than the 12.20 Å simulated for Camontmorillonite under surface conditions of 300 K and 1 bar (Laird et al., 1995; Laird, 1996; ChávezPáez et al, 2001a) (Table 3). The simulated 15.60 Å spacing limiting the twolayer hydrate, with 96 adsorbed molecules of water, compares with the experimental 15.015.8 Å (Posner and Quirk, 1964; Keren and Shainberg, 1975; Sato et al., 1992; Bray et al., 1998), the 15.0 Å measured at 260300 K and 487075 bar (Wu et al, 1997), and the 14.7 Å (ChávezPáez et al, 2001a) known from simulations at 300 K and 1 bar. The reported threelayer hydrates of 18.5019.10 Å spacing (Posner and Quirk, 1964; Suquet et al, 1975; Sato et al, 1992; Wu et al, 1997; ChávezPáez et al, 2001a) were not simulated in the present work.
The radial distribution functiong(r) shows for the onelayer Camontmorillonite hydrate a coordination probability of 10.026 molecules of water per cation, at a Ca0 separation of 2.775 Å (Table 2, Figures 3a and 3b). Increasing the adsorption to the twolayer hydrate state raises the separation to 2.815 Å and reduces the probability to 7.441. When temperature and pressure are decreased to 333 K and 300 bar, the probability is 7.906 with the rCaO distance remaining at 2.775 Å. Integration of g(r) as per Equation 6 (Allen and Tildesley, 1987) indicates solvationof the cation by 10 water molecules, which is within the 910 range known for the calciumwater system (Bounds, 1985).
The progressive hydration of Camontmorillonite increases the d001 , spacing and the separation of the water layers from the interlayer midplane (Table 2, Figure 4a). The energy of interaction between atoms increases in the order 24.245, 19.664, and 17.714 kcal/mol as the adsorbed H2O changes from 32 to 96 molecules (Table 2, Figure 4b).
The Coulomb energy decreases from 1.415 to 6.679 and 10.137 kcal/mol, inverse to the LennardJones energy that increases to 26.369, 13.167, and7.648 kcal/mol. The total interaction energy is lower for Camontmorillonite in the 333 K, 300 bar environment.
Grand canonical µVT simulations
To ascertain the thermodynamic stability of hydrated Camontmorillonite, simulations were conducted in the grand canonical µVT constant mass, volume and temperature ensemble. The simulations started by calculating the chemical potentials of bulk water for a system of 216 water molecules (ChávezPáez et al., 2001a, 2001b) at 353 K and 625 bar and at 333 K and 300 bar. For the former, the simulated chemical potential was of5.58 kcal/mol and for the latter 7.21 kcal/mol.
Simulations in the grand canonical ensemble define the stability of the clay mineral when the chemical potentials in the mineral interlayer and of the bulk supernatant fluid are equal. The thermodynamic stability of the Camontmorillonite hydrates is determined from the minima in the swelling free energy as a function of the interlayer separation (ChávezPáez et al, 2001a, 2001b). The free energy is calculated from Equation 7 where Pzz is the interlayer pressure tensor and (Pzz)npp is the normal external bulk pressure. The derivative of this expression defines the stable d001spacing when the calculated pressure tensor Pzz equals the bulk pressure on the clay. Values of Pzz distinct from the bulk pressure do not represent real solutions and lack any physical meaning; opposite assumptions would lead to collapse or blow the clay structure. A simple graphical solution is a plot depicting the dependence of Pzz on the d001 spacing.
Simulations using the TIP4P water model (Jorgensen et al, 1983) show that for d001 spacings between 11.5 and 18 Å, the adsorbed water increases from 39.27 to 140.40 molecules per layer or 120.36 to 430.33 mg/g (Table 4, Figure 5a), the total energy changes from 22.871 kcal/mol to 16.383 kcal/mol, the LennardJones energy varies from 22.116 to 3.970 kcal/mol, and the Coulomb energy from 0.601 to 12.538 kcal/mol (Figure 5b). Simulations at 333 K and 300 bar (Table 5, Figure 5c) indicate adsorption of 150.86316.53 mg water/g, d001 spacing of 12.016.0 Å, energy of interaction 23.549 19.110 kcal/mol, LennardJones energy 18.118 11.396, Coulomb energy 5.647 7.564 kcal/mol, and pressure tensor from 10654.69 2532.54 bar. The LennardJones and Coulomb energies add to the total energy of interaction; the values presented in Tables 2 and 4 do not do exactly add, due to some mishandling of the data outputs.
The variation of the pressure tensor Pzz with the adsorbed water depicts the path shown in Figure 6. At 353 K and 625 bar, the data in Figure 6a show that within the statistical uncertainty associated with Monte Carlo simulations, the onelayer hydrate Camontmorillonite approaches stability, without attain it. In the less deep environment of 333 K and 300 bar, the onelayer hydrate is stable (Figure 6b), characterized by a d001 spacing of 12.11 Å. Two and threelayer hydrates do not form.
At 353 K and 625 bar, the nearly stable onelayer Camontmorillonite hydrate has a d001 spacing of 12.50 Å, formed by the adsorption of 55.21 water molecules (169.22 mg H2O/g clay), total interaction energy 21.107 kcal/mol, and interlayer density 0.342 g/mL. At 333 K and 300 bar, the stable onelayer hydrate has d001 12.11 Å, adsorbs 54.50 molecules of water, interaction energy 22.803 kcal/mol, LennardJones dispersion 6.345 kcal/mol, Coulomb attractionrepulsion 16.449 kcal/mol, density 0.337 g/mL. The density profiles (Figure 7) show that at 353 K and 625 bar the water molecules cluster in a broad band 0.087 Å off the interlayer midplane, with protons on the midplane and 1.087 Å and 1.137 Å to each side, and the calcium cations off the midplane, solvated in outersphere complexes within the water layer. At 333 K and 300 bar, the density profiles indicate that the water molecules are on the interlayer midplane, oriented to both siloxane surfaces, with the protons 1.112 and 1.137 Å to both sides, slightly farther apart than at 353 K and 625 bar; the calcium atoms are solvated off the interlayer midplane. Snapshots of both hydrates (Figures 8a and 8b) show a broad layer of water molecules with the cations coordinated in the water layer, away from the siloxane surface.
Our simulations in the NPzzT ensemble show that Camontmorillonite can form one, two and threelayer hydrates. Simulations in the (µVT ensemble confirm that in normally compacted sediments at 2.0 km depth, 333 K and 300 bar, onelayer Camontmorillonite hydrate is stable but two and threelayer hydrates do not form. At 353 K and 625 bar, mimicking overcompacted sediments at 2.7 km depth, the onelayer hydrate is nearly stable, not attaining full stability. In this environment, the unstable clay could transform to other minerals, adsorb from or release species to the surrounding environment to develop a stable configuration. The simulations point that Camontmorillonite could be stable at 353 K and 625 bar and possibly even under more stringent environments, if sediments were normally compacted or potentials more suitable.
Our results extend the stability of the onelayer Camontmorillonite hydrate to 2.0 km depth and probably higher, upwards from previous investigations limiting its stability to burial depths of 1.5 km, with possible conversion to other minerals in deeper environments (Siqueira et al, 1997). The present simulations did not reach the high temperature and pressure of 513 K and 1200 bar (Siqueira et al, 1999) and above (Wu et al, 1997) experimentally determined for the stability of the 1819 Å 3layer hydrate and of 260310 °C and 48260 bar along the 0.7 g/mL isochore (Wu et al, 1997) and of 453 K and 900 bar (Siqueira et al, 1999) determined for its transformation to the 15 Å twolayer hydrate. Recent data from de Pablo et al (2005) have confirmed that onelayer Camontmorillonite is stable down to 8.7 km in normally compacted sediments; twoand possibly threelayer hydrates develop at 6.7 km depth, 473 K and 1000 bar. Na and Kmontmorillonite form in similar environments one and twolayer hydrates of d001 , spacing larger than Camontmorillonite.
Monte Carlo simulations on the hydration of Camontmorillonite under basinlike conditions of 353 K and 625 bar and of 333 K and 300 bar reveal interlayer configurations similar to those known at the surface ambient environment of 300 K and 1 bar. At low states of hydration, the water molecules cluster on the interlayer midplane with their protons alternatively oriented towards the siloxane surfaces and on the interlayer midplane. At higher states of adsorption, the water molecules are distributed in two separate layers close to the clay surfaces, with the molecules tilted so their protons point towards the siloxane surfaces and the interlayer midplane. The calcium ions form outersphere complexes in the water layers, always positioned off the interlay er midplane.
For the force field considered in this work, within the statistical error of Monte Carlo simulations, Camontmorillonite forms a 12.11 Å onelayer hydrate stable at 333 K and 300 bar, at a 2 km depth of normally compacted sediments. Two and threelayer hydrates do not form. At 353 K and 625 bar, prevailing at 2.7 km depth of overcompacted sediments, the onelayer hydrate only approaches stability without quite reaching it. Under equal conditions of temperature, pressure, and chemical potential our previous simulations indicate that Namontmorillonite is clearly stable (de Pablo et al., 2004) but Kmontmorillonite may not (Chavez et al., 2004). A difference is established with clays under the ambient surface setting of 300 K and 1 bar where two and threelayer hydrates are formed. The results imply that Camontmorillonite as well as Na and Kmontmorillonite may, at depth, loose water to their onelayer hydrates.
The present study was supported by DGAPA, UNAM, Project IN106502. The authors thank DGSCA, UNAM, for extended allocation of their supercomputing resources. The Instituto Mexicano del Petróleo offered partial support.
Allen, M.P., Tildesley, D.J., 1987, Computer Simulation of Liquids: London, U.K., Clarendon Press, 404 p. [ Links ]
Anderson, M.A., Trouw, F.R., Tam, C.N., 1999, Properties of water in calcium and hexadecyltrimethylammoniumexchanged bentonite: Clays and Clay Minerals, 47, 2835. [ Links ]
Aylmore, L.A.G., Quirk, J.P., 1967, The micropore size distribution of clay mineral systems: Journal of Soil Science, 18, 117. [ Links ]
Boek, E.S., Coveney, P.V., Skipper, N.T., 1995, A study of hysteresis in the swelling curves of sodium montmorillonite: Langmuir, 11, 46294631. [ Links ]
Bounds, D.G., 1985, A molecular dynamics study of the structure of water around the ions Li+, Na+, K+, Ca2+, Ni2+, and Cl-: Molecular Physics, 54, 13351355. [ Links ]
Bray, H.J., Redfern, S.A.T., 1999, Kinetics of dehydration of Camontmorillonite: Physics and Chemistry of Minerals, 26, 591600. [ Links ]
Bray, H.J., Redfern, S.A.T., 2000, Influence of counterion species on the dehydroxylation of Ca2+, Mg2+, Na+ and K+ exchanged Wyoming montmorillonite: Mineralogical Magazine, 64, 337346. [ Links ]
Bray, H.J., Redfern, S.A.T., Clark, S.M., 1998, The kinetics of dehydration in Camontmorillonite; An insitu xray synchrotron study: Mineralogical Magazine, 62, 647656. [ Links ]
Cases, M., Berend, I., Francois, M., Uriot, J.P., Michot, L.J., Thomas, F., 1997, Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite. 3. The Mg2+, Ca2+, Sr2+, and Ba2+ exchanged forms: Clays and Clay Minerals, 45, 822. [ Links ]
ChávezPáez, M., de Pablo, L., de Pablo, J.J., 2001a, Monte Carlo simulations of Camontmorillonite hydrates: Journal of Chemical Physics, 114, 1094810953. [ Links ]
ChávezPáez, M., van Workum, K., de Pablo, L., de Pablo, J.J., 2001b, Monte Carlo simulations of sodium montmorillonite hydrates: Journal of Chemical Physics, 114, 14051413. [ Links ]
Chávez, M.L., de Pablo, L., de Pablo, J.J., 2004, Monte Carlo molecular simulation of the hydration of Kmontmorillonite at 353 K and 625 bar: Langmuir, 20, 1076410770. [ Links ]
CotterHowells, J.D., Patterson, E., 2000, Minerals and soil development, in Vaughan, D.J., Wogelius, R.A. (eds.), Environmental Mineralogy: Budapest, Eótvós University Press, 91 124. [ Links ]
De Pablo, L., Chávez, M.L., Sum, A.K., de Pablo, J. J., 2004, Monte Carlo molecular simulation of the hydration of Namontmorillonite at reservoir conditions: Journal of Chemical Physics, 120, 939946. [ Links ]
De Pablo, L., Chavez, M.L., de Pablo, J.J., 2005, Stability of Na, K, and Camontmorillonite at high temperatures and pressures; A Monte Carlo simulation: Langmuir, 21, 1087410884. [ Links ]
Glaeser, R., Mering, J., 1968, Domaines d'hydratation homogene des smectites: Comptes Rendus de l'Academie des Sciences (Paris), 267, Serie D, 463466. [ Links ]
Hall, P. L., 1993, Mechanism of overpressuring; an overview, in Manning, D.A.C., Hall, P.L., Hughes, C.R. (eds.), Geochemistry of ClayPore Interactions: London, U.K.,Chapman and Hall, 265315. [ Links ]
Hall, P. L., Astill, D. M., McConnell, J. D. C, 1986, Thermodynamic and structural aspects of the dehydration of smectites in sedimentary rocks, 21, 633648. [ Links ]
Hower, J.E., Hower, M.E., Perry, E.A., 1976, Mechanism of burial metamorphism of argrillaceous sediment; 1. Mineralogical and chemical evidence: Geological Society of America Bulletin, 86, 725737. [ Links ]
Huggett, J.M., Shaw, H.F., 1993, Diagenesis of Jurassic mudrocks of the North Sea, in Manning, D.A.C., Hall, PL., Hughes, C.R. (eds.), Geochemistry of ClayPore Interactions: London, U.K., Chapman and Hall, 107126. [ Links ]
Jorgensen, W.L., Chandrasekhar, J., Madura, J.D., Impey, R.W., Klein, M.L., 1983, Comparison of simple potential functions for simulating liquid water: Journal Chemical Physics, 79, 926935. [ Links ]
Keren, R., Shainberg, I., 1975, Water vapor isotherms and heat of immersion of Na/Camontmorillonite systemsI. Homoionic clay: Clays and Clay Minerals, 23, 193200. [ Links ]
Khitarov, N.L., Pugin, V.A., 1996, Behavior of montmorillonite under elevated temperatures and pressures: Geochemistry International, 3, 621626. [ Links ]
Koster von Groos, A.F., Guggenheim, S., 1987, Dehydration of a CaMgexchanged montmorillonite (SWy1) at elevated pressures: Clays and Clay Minerals, 72, 292298. [ Links ]
Koster von Groos, A.F., Guggenheim, S., 1989, Dehydroxilation of a Ca and Mgexchanged montmorillonite: American Mineralogist, 74, 627636. [ Links ]
Laird, D.A., 1996, Model for the crystalline swelling of 2:1 layer phyllosilicates: Clays and Clay Minerals, 44, 553559. [ Links ]
Laird, D.A., Shang, C., Thompson, M.L., 1995, Hysteresis in crystalline swelling of smectites: Journal Colloid Interface Science, 171, 240245. [ Links ]
McEwan, D.M.C., Wilson, M.J., 1980, Interlayer and intercalation complexes of clay minerals, in Brindley, G.W., Brown, G. (eds.), Crystal Structures of Clay Minerals and their XRay Identification: London, U. K., Mineralogical Society, 197248. [ Links ]
Pezerat, H., Mering, J., 1967, Recherches sur la position des cations exchangeable et de l'eau dans les montmorillonite: Comptes Rendus de l'Académie des Sciences (Paris), Serie D, 265, 529532. [ Links ]
Posner, A.M., Quirk, J.P., 1964, Changes in basal spacing of montmorillonite in electrode solution: Journal of Colloidal Science, 19, 798812. [ Links ]
Rutherford, D.W., Chiou, C.T., Eberl, D.D., 1980, Effects of exchanged cation on the microporosity of montmorillonite: Clays and Clay Minerals, 45, 534543. [ Links ]
Sato, T., Watanabe, T., Osuka, R., 1992, Effect of layer charge, charge location, and energy change on expansion properties of dioctahedral montmorillonites: Clays and Clay Minerals, 40, 103113. [ Links ]
Siqueira, A.V.C. de, Skipper, N.T., Coveney, P.V., Boek, E.S., 1997, Computer simulation evidence for enthalpy driven dehydration of smectite clays at elevated pressures and temperatures: Molecular Physics, 92, 16. [ Links ]
Siqueira, A.V. de, Lobban, C., Skipper, N.T., Williams, G.D., Soper, A.K., Done, E., Dreyer, J.W., Humpreys, R.J.O., Bones, J.A.R., 1999, The structure of pore fluids in swelling clays at elevated pressures and temperatures: Journal of Physical Condensed Matter, 11, 91799188. [ Links ]
Skipper, N.T., Sposito, G., Chang, F.R.C., 1995a, Monte Carlo simulation of interlayer molecular structure in swelling clay minerals. 2. Mondayer hydrates: Clays and Clay Minerals, 43, 294303. [ Links ]
Skipper, N.T., Chang, F.R.C., Sposito, G., 1995b, Monte Carlo simulation of interlayer molecular structure in swelling clay minerals. 1. Methodology: Clays and Clay Minerals, 43, 285293. [ Links ]
Slade, P.G., Quirk, J.P., Norrish, K., 1991, Crystalline swelling of smectite samples in concentrated NaCl solutions in relation to layer charge: Clays and Clay Minerals, 39, 234238. [ Links ]
Stone, R.L., Rowland, R.A., 1955, DTA of kaolinite and montmorillonite under H2O vapor pressure up to six atmospheres, in Third National Clay Conference of the Clay Minerals Society: Houston, Texas, National Academy of Sciences and National Research Council, 39, 103116. [ Links ]
Suquet, H., de la Calle, C., Pezerat, H., 1975, Swelling and structural properties of saponite: Clay and Clay Minerals, 23, 19. [ Links ]
Wu, T.C., Bassett, W.A., Huang, H.L., Guggenheim, S., Koster van Groos, A.F., 1997, Montmorillonite under high H2O pressures: Stability of hydrated phases, dehydration hysteresis, and the effect of interlayer cations: American Mineralogist, 82, 6978. [ Links ]