Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

The Impact of Short-Range Parameters and Temperature Effect On Selective Adsorption of Water and CO2 On Calcite

PHAN VAN CUONG, BJØRN KVAMME, TATIANA KUZNETSOVA*, BJØRNAR JENSEN Institute for Physics and Technology University of Bergen Postboks 7803 NORWAY [email protected] http://www.ift.uib.no

Abstract: - Carbon dioxide can be captured and stored in geological formations. This promising technique of carbon sequestration can contribute both to greenhouse effect reduction and enhanced oil recovery. However, all processes occurring during injection, post-injection, and storage occur in porous rock, making interactions and reactions between CO2, water, and minerals to be of utmost importance. In this work, (MD) simulations were used to study several aqueous interfacial systems involving CO2 focusing on the impact of force field, calcite and temperature variations. Our investigation showed that CO2 transport and interface stability were heavily affected by temperature, calcite, and force field utilized. As temperature increased, the number of CO2 molecule crossing water layer and adsorbing on calcite surface increased while adsorption stability deteriorated. When we applied Buckingham potential between water and calcite, all other interactions were Lennard-Jones (L-J), electrostatic contribution proved to be the deciding factor with the coordination of CO2 oxygen towards the calcium ions in calcite being the most important factor that ensures the stability of calcium-CO2 pairs. When Buckingham potential is applied for both water-calcite and CO2-calcite interactions, with the rest being L-J in form, the coordination of CO2 carbon towards the carbonate oxygen becomes the decisive factor.

Key-Words: - Calcite; Carbon Dioxide; Water; Adsorption; Molecular Simulation

1 Introduction In this work, we used molecular dynamics Carbon dioxide can be captured, transported, and simulations to study several aqueous interfacial permanently stored in geological formations systems involving CO2 and calcite. Our main focus including spent petroleum reservoirs [1]. This was on the impact of calcite and temperature promising technique of carbon sequestration can variations on transport, adsorption, and stability of contribute both to greenhouse effect reduction and CO2 molecules and water as affected by the enhanced oil recovery (EOR). However, all presence of )4110( calcite surface. A special processes occurring during injection, post-injection, attention was paid to role of short-range and storage occur in either porous rock or inside contributions to the intermolecular potentials. rust-covered pipes, making interactions and reactions between CO2, water, and minerals to be of utmost importance. 2 System setup and molecular Calcite is one of the most abundant minerals in simulation details the Earth’s crust, with )4110( plane being the The composite system was built from a 1620-atom most stable [2] and by far the dominant observed slice of calcite crystal [7, 8], two water slabs, a morphology of calcite in situ [3]. Atomistic-scale hydrate crystal, and a carbon dioxide phase with the interactions between )4110( calcite surface and density corresponding to 200 atm and 277 K. The various substances like pure water, aqueous calcite slice was positioned in the middle of the 40 solutions, peptides, etc. have been the subject of Å-thick liquid water block and parallel to the initial several numerical studies already [4-6]; it continue water-CO2 interface. A carbon dioxide hydrate slab to draw interest because of the decisive role they composed of 4x4x2.5 structure I unit cells was play in determining both macroscopic properties and added to probe the potential competition for carbon kinetics of processes. dioxide between hydrate and calcite in reservoirs under conditions where hydrate formation is

ISBN: 978-1-61804-065-7 192 Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

possible. The second water phase consisted only of Our molecular dynamics used the rigid body 500 water molecules meant to cushion the hydrate treatment for all molecules. All calcite crystal atoms crystal from the carbon dioxide. The resulting were fixed in place, as our previous studies found primary simulation cell ranged 48 x 48 x 108 Å in the rearrangement of hydrate calcite surface to be size and is shown in Fig. 1. rather small. Water molecules in hydrate were locked in space but free to rotate around their centers, while the CO2 guests were completely free. We used -based Message-Passing Interface (MPI) to run the MD simulations in parallel on 88 processors of Cray XT4 supercomputing facility at the University of Bergen, Norway.

2.2.1 Force fields and the impact of short-range interactions The force field used the conventional approach Fig 1. Side view snapshot of the initial system. describing potential energy as a sum of individual

non-bonded energy terms with two contributions, 2.1 Fractional charges in calcite the electrostatics and the van der Waals. Maestro/Jaguar quantum chemistry package [9, 10] PS Conventional Lorentz-Berthelot mixing rules were utilizing B3LYP with LACVP basis set and with used to calculate the cross interactions. The short- force convergence flag set was used to estimate the range potential energy between CO2 and water was partial charges in vacuum for a 210-atom calcite represented by the Lennard-Jones potential of [13] slab cleaved along the dominant )4110( plane. and modified F3C [4, 14] models, respectively. Except for the edges of the crystal, vacuum charges The inclusion of carbon dioxide in the system proved to be quite uniform. These values are listed resulted in the additional challenge concerning the in Table 1; they agree quite well with those of Fisler description of interaction between calcite and CO2. et al. [11] where the calcium ion charge were kept In the absence of available experimental results fixed at +2, and the focus was on the carbonate characterizing the behavior of carbon dioxide close group, allowing carbon and oxygen charges to vary to calcite or similar minerals, we found it necessary but constraining their sum to -2. In our approach to test a series of short-range potentials that ranged that used Maestro/Jaguar, all atomic charges in from pure Lennard-Jones, a combination of calcite were free to vary while their sum was Lennard-Jones and Buckingham potentials, and pure constrained to zero. The charges were then mapped Buckingham interactions between calcite and CO2, onto a 1620-atom calcite slab cleaved out of a larger with the Buckingham CO2 model fitted to reproduce calcite crystal along the )4110( plane. bulk properties [15] (see Table 2). Table 1. Fractional atomic charge in calcite Table 2. Lennard-Jones and Buckingham force field parameters for carbon dioxide ([13] and [15]) and Atom Fractional charge (e) water ([2] and [14])

This work Fisler et al. [13] O in H in C O in CO2 Calcium 1.881 2.000 H2O H2O Charge Carbon 1.482 1.344 [e] 0.6512 -0.3256 -0.8476 0.4238 Oxygen -1.118 -1.115 σ [Å] 2.7570 3.0330 3.1666 0.8021 ε 0.2339 0.6657 0.7732 0.04184 2.2 MD details [kJ/mol] Molecular dynamics MDynaMix package [12] was A [kJ 1491.6 1629.9 2889.7 106.2 employed, with temperature kept constant at three Å6/mol] different temperatures (277, 388, and 500 K). The B 909.23 1483300.0 293206.3 11537.16 time step was 0.5 fs, with periodic boundary [kJ/mol] conditions applied in all three directions. The cut-off C [1/Å] 2.27 4.4 3.659 3.875 radius for the Lennard-Jones potential was set to 10 Å.

ISBN: 978-1-61804-065-7 193 Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

The Lennard-Jones parameters used for calcite were Table 5. Location and depth of minima for taken from [16] which featured a rather deep and Buckingham interaction between calcite and water narrow well in case of the calcium ion. The goal of Depth Calcite-H O r [Å] this unusual force field was apparently to emphasize 2 min [kJ/mol] the role of short-range contributions to override the normally dominant electrostatic forces [5, 17, 18]. C (calcite) - H (H2O) 3.54 -0.140 Table 3. Lennard-Jones and Buckingham force field C (calcite) - O (H O) 3.73 -0.551 parameters for calcite 2 +2 Ca C O Ca (calcite) - H (H2O) 3.87 -0.339 1.482 -1.118 Charge, q [e] 1.881 Ca (calcite) - O (H2O) 4.11 -1.280 σ [Å] 0.899 3.742 2.851 O (calcite) - H (H O) 3.31 -0.142 ε [kJ/mol] 113.819 0.5021 0.6657 2 A [kJ Å6/mol] 55686.7 2432.71 1123.56 O (calcite) - O (H2O) 3.48 -0.556 B [kJ/mol] 82942.86 369822.7 230230.1

C [1/Å] 2.198 3.6019 3.9602 3 Results and discussion

3.1 "Hybrid" Lennard-Jones -- Buckingham As seen from Table 2, the Lennard-Jones radii and system well depths of water and carbon dioxide oxygen are This system was characterized by the unusually not too dissimilar, which would make the short- strong Lennard-Jones interaction between calcium range interactions of water and carbon dioxide with in calcite and carbon dioxide [19] and regular calcite comparable in strength. In this case one Buckingham potential for water and calcite [2]. would expect the electrostatics to determine the At all three temperatures (277, 388, and 500 K), relative affinities between various substances and CO molecules managed to cross the aqueous layer the mineral surfaces. 2 to reach the calcite slab surface where they were The Buckingham potential between calcite and able to successfully displace the original water water was adapted from [2]. The comparison of molecules from the vicinity of calcium ions. The Buckingham interactions between the different sites simulation results have also showed that CO of water and carbon dioxide required a graphical 2 transport and adsorption stability were heavily treatment summarized in Tables 4 and 5. As in case affected by the presence of calcite and temperature of L-J potential, locations and depths of the cross variation. interaction are quite similar for water and CO . Both 2 The inset in Fig. 2b shows the number of calcium and carbon in carbon dioxide bear significant positive charges, making the purely adsorbed CO2 molecule on )4110( calcite surface as attractive nature of their short-range interaction a function of simulation time. At the lowest much problematic as proven by simulations. temperature (277 K), water-CO2 interface of MD simulation system was relatively non-volatile. The Table 4. Location and depth of minima for number of CO2 molecules that successfully crossed Buckingham interaction between calcite and CO2 the water layer and adsorbed onto the )4110( calcite Depth surface was enough to cover only a fraction of the Calcite-CO r [Å] 2 min [kJ/mol] calcite surface during 7.5 ns of the simulation time. At a higher temperature (388 K), CO2 molecules had C (calcite) - C (CO2) 3.80 -0.282 enough kinetic energy to easily cross the water layer and adsorb on the calcite surface, with the water- C (calcite) - O (CO2) 3.67 -0.480 CO2 interface mostly retaining its original flat shape. This was in stark contrast with the situation Ca (calcite) - C (CO2) N/A N/A at 500 K, where the water-CO2 interface was highly

Ca (calcite) - O (CO2) 4.15 -0.994 volatile with vigorous intermixing of water and CO2. A large number of CO2 molecules crossed the O (calcite) - C (CO2) 3.50 -0.303 aqueous layer and were adsorbed onto )4110( calcite surface. O(calcite) - O (CO2) 3.44 -0.477 When CO2 molecules approached the calcite surface, they tended to coordinate to the calcium ion

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so as to maximize the electrostatic attraction by temperatures. The values are average over 500 pointing one of their oxygen atoms towards the trajectory frames obtained after 7.4 ns of simulation. calcium ion, as shown in Fig. 2 (a- side view, b- top As seen from the figure, the adsorption energy of view). The adsorption process appeared to reach water was significantly higher than that of carbon saturation at 500 K when each calcium ion of dioxide at all three temperatures, indicating the

)4110( calcite surface had adsorbed a CO2 preference for carbon dioxide over water on calcite surface, and explaining why water molecules were molecule. When two CO2 molecules were competing for the same calcium, only one achieves replaced by the CO2. the energetically favorable position, while the other The adsorption energy of CO2 molecules also either left the surface and re-entered the water bulk appeared to become smaller with increasing or found another calcium ion. temperature, accounting for the somewhat lower The demonstrated affinity of carbon dioxide for stability and subsequent number fluctuations of the calcite surface and its ability to displace the adsorbed carbon dioxide at 500 K (-75.5 kJ/mol at previously adsorbed water molecules was quantified 277 K versus -63.6 kJ/mol at 500 K). The adsorption energy amounted to -71.1 kJ/mol at 388 further by comparing the energies of water and CO2 in different environments. We have used Visual K, falling in between 277 K and 500 K. We have Molecular Dynamics (VMD) [19] with NAMD also run separate MD simulations to estimate the Energy Plugin version 1.3 [20] to estimate energies energies of CO2 in bulk (same density and temperature as the CO slab used in the composite calcite surface and 2 characteristic for )4110( system) and dissolved in water at 2.9 mole fraction. adsorbed CO2 molecules, and water molecules The potential energy amounted to -10.16(6)±2 adsorbed on the other side of calcite where they did kJ/mol and -25.(5)±5 kJ/mol, respectively, proving not have to compete with carbon dioxide. The to be significantly smaller than the adsorption energies were obtained by summing all non-bonded energy. Even when one takes into consideration interactions between water and CO2 molecules significant motion constraints imposed on adsorbed within 5 Å of calcite. These values were heavily molecules, especially at surface saturation, the dominated by electrostatic contributions, making the incurred entropy penalty will be more than offset by error of using the Lennard-Jones instead of the energetic benefits of adsorption on calcite. Buckingham potential for water rather negligible.

Fig. 3. Average adsorption energy per molecule after 7.4 ns of simulation 3.2 Pure Lennard-Jones interaction with calcite

When purely Lennard-Jones force fields were used

for water and carbon dioxide interaction with Fig. 2. Side view (a) and top view (b) snapshots of calcite, it was water that completely dominated the the )4110( calcite surface at 500 K after 7.4 ns. One adsorption on calcite, preventing carbon dioxide from adsorbing. We have applied the Lennard-Jones CO2 molecule adsorbed by calcium ion. The inset in interaction after running the initial system for a (b) shows the number of adsorbed CO2 molecule as a function of simulation time. period sufficient for 2 carbon dioxide molecules to be firmly adsorbed onto the surface at 277 K. When The adsorption energy per molecule between the switch was made to the Lennard-Jones

)4110( calcite surface and bulk H2O or adsorbed interaction between water and calcite, one of the molecules immediately left the surface, while the CO2 molecules is plotted in Fig. 3 for all three

ISBN: 978-1-61804-065-7 195 Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

other remained stuck to the surface, with no new As seen in Fig. 5, the closest distance between CO2 able to approach the surface during 0.9 ns of carbon in carbon dioxide and calcium in calcite is the simulation time. around 4.5 Å; this separation corresponds to an almost-zero Buckingham pair-wise energy,

3.3 Pure Buckingham interaction with calcite eliminating any danger of unphysical sorption. We used the same initial configuration as in the The adsorption affinity of carbon dioxide was previous section to switch the system to purely somewhat higher at the temperature of 500 K. A Buckingham force field for calcite interaction with number of CO molecules could be found in the water and carbon dioxide. In contrast to the case of 2 immediate vicinity of the calcite surface at any point pure L-J interactions, both carbon dioxide molecules initially left the surface at lower temperatures (277 in the simulation, with several of them adsorbed onto the surface itself (see Fig. 6). In contrast to the K and 388 K). behavior exhibited by adsorbed dioxide in other The subsequent simulations showed that while studied systems, the stability of adsorption is much water continued to heavily dominate the adsorption lower. The carbon dioxide molecules can now easily on calcite, several CO2 molecules managed to come into contact with the surface and even adsorb for a leave the surface to be replaced by others, as well as fraction of the run at the lower temperatures. The move along the surface from one adsorption site to another. At least two preferential orientations can be final alignment of adsorbed CO2 molecules at these temperatures was entirely different from that of the observed, one with carbon dioxide oxygen normal to Lennard-Jones case. As seen in the snapshot of Fig. the surface and coordinated against calcium, and the 4 and indicated by the radial distribution functions other identical to the one at 277 K, i.e. the molecule plotted in Fig. 5, the carbon dioxide molecules are lies flat against the surface close to the carbonate now seeking to maximize the electrostatic attraction ion and with RDFs very similar to those in Fig. 5. by positioning itself flat on the surface and coordinating towards the carbonate ion instead of calcium.

Fig 6. Purely Buckingham system at 500 K, 0.4 ns

after the switch. Fig 4. Side view of the Buckingham system at 277 K after 1.08 ns of simulation. Note the drastically 4 Conclusion changed alignment of adsorbed CO molecule. 2 Our investigation showed that CO transport and 2 interface stability were heavily affected by temperature, calcite, and force field utilized. As temperature increased, the number of CO2 molecule crossing water layer and adsorbing on calcite surface increased while adsorption stability deteriorated for all the investigated combinations of short-range potentials. When we applied Buckingham potential between water and calcite, with all the other interactions being Lennard-Jones, the electrostatic contribution proved to be the deciding factor with the coordination of CO2 oxygen towards the calcium Fig 5. Radial distribution function for carbon in ions in calcite being the most important factor that dioxide molecule adsorbed on calcite. ensured the stability of calcium-CO2 pairs. When

ISBN: 978-1-61804-065-7 196 Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

Buckingham potential is applied for both water- [10] Jaguar, version 7.5, Schrödinger, LLC, New calcite and CO2-calcite interactions, with the rest York, NY, 2009. being Lennard-Jones in form, the coordination of [11] D. K. Fisler, J. D. Gale and R. T. Cygan, A CO2 carbon towards the carbonate oxygen becomes shell model for the simulation of rhombohedral the decisive factor. carbonate minerals and their point defects, Our investigation has also highlighted the crucial American Mineralogist, Vol.85, 2000, pp. 217- importance of reliable force fields suitable for 224. describing the interactions between carbon dioxide [12] A. P. Lyubartsev and A. Laaksonen, and calcite. In our opinion, the best way to M.DynaMix - a scalable portable parallel MD parameterize the potential would through be fitting simulation package for arbitrary molecular them against experimental data for carbon dioxide. mixtures, Computer Physics Communications, Vol.128, No.3, 2000, pp. 565-589. References: [13] J. G. Harris and K. H. Yung, Carbon Dioxide's [1] R. Korbøl and A. Kaddour, Sleipner vest CO2 Liquid-Vapor Coexistence Curve And Critical disposal - injection of removed CO2 into the Properties as Predicted by a Simple Molecular Utsira formation, Energy Converion and Model, The Journal of Physical Chemistry, Management, Vol.36, No.6-9, 1995, pp. 509- Vol.99, No.31, 1995, pp. 12021-12024. 512. [14] M. Levitt, M. Hirshberg, R. Sharon, K. E. [2] S. Hwang, M. Blanco and W. A. Goddard, Laidig and V. Daggett, Calibration and Testing Atomistic Simulations of Corrosion Inhibitors of a for Simulation of the Adsorbed on Calcite Surfaces I. Force field Molecular Dynamics of Proteins and Nucleic Parameters for Calcite, The Journal of Physical Acids in Solution, The Journal of Physical Chemistry B, Vol.105, 2001, pp. 10746-10752. Chemistry B, Vol.101, 1997, pp. 5051-5061. [3] J. M. Didymus, P. Oliver, S. Mann, A. L. [15] S. Tsuzuki, T. Uchimaru, M. Mikami, DeVries, P. V. Hauschka and P. Westbroek, K. Tanabe, T. Sako and S. Kuwajima, Influence of low-molecular-weight and Molecular dynamics simulation of supercritical macromolecular organic additives on the carbon dioxide fluid with the model potential morphology of calcium carbonate, Journal of from ab initio molecular orbital calculations, Chemical Society, Faraday Transactions, Chemical Physics Letters, Vol.255, No.4-6, Vol.89, No.15, 1993, pp. 2891-2900. 1996, pp. 347-349. [4] B. Kvamme, T. Kuznetsova and D. Uppstad, [16] Ø. B. Sunnarvik, The effect of calcite mineral Modelling excess surface energy in dry and on hydrate stability and CO2 adsorption, MSc wetted calcite systems, Journal of Thesis, University of Bergen, 2011, Norway. Mathematical Chemistry, Vol.46, No.3, 2009, [17] R. Eriksson, J. Merta, and J.B. Rosenholm, The pp. 756-762. calcite/water interface II. Effect of added lattice [5] M. J. Yang, P. M. Rodger, J. H. Harding and S. ions on the charge properties and adsorption of L. S. Stipp, Molecular dynamics simulations of sodium polyacrylate, Journal of Colloid and peptides on calcite surface, Molecular Interface Science, Vol.326, 2008, pp. 396-402. Simulation, Vol.35, No.7, 2009, pp. 547-553. [18] P. Somasundaran, Adsorption of Starch and [6] K. Wright, R. T. Cygan and B. Slater, Structure Oleate and Interaction between Them on of the (1014) surfaces of calcite, dolomite and Calcite in Aqueous Solutions, Journal of magnesite under wet and dry conditions, Colloid and Interface Science, Vol.31, No.4, Physical Chemistry Chemical Physics, Vol.3, 1969, pp. 557-565. No.5, 2001, pp. 839-844. [19] W. Humphrey, A. Dalke and K. Schulten, [7] R. T. Downs and M. Hall-Wallace, The VMD: Visual molecular dynamics, Journal American Mineralogist Crystal Structure of Molecular Graphics, Vol.14, No.1, 1996, pp. Database, American Mineralogist, Vol.88, 33-38. No.1, 2003, pp. 247-250. [20] J. C. Phillips, R. Braun, W. Wang, J. Gumbart, [8] S. A. Markgraf and R. J. Reeder, High- E. Tajkhorshid, E. Villa, C. Chipot, R. D. temperature structure refinements of calcite and Skeel, L. Kalé and K. Schulten, Scalable magnesite, American Mineralogist, Vol.70, molecular dynamics with NAMD, Journal of No.5-6, 1985, pp. 590-600. Computaional Chemistry, Vol.26, No.16, 2005, [9] Maestro, version 9.0, Schrödinger, LLC, New pp. 1781-1802. York, NY, 2009.

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