Introduction

As a magnificent analytical tool, molecular dynamics (MD) technique has found its applicability in a diverse spectrum of research. An example of this kind is the study the interaction of carbon dioxide and clay minerals, a matter of potential usage for underground carbon sequestration purposes (Chen et al. 2015a, b, c; Javanbakht et al. 2015; Makaremi et al. 2015; Tenney and Cygan 2014). Another example of the kind is the study of interactions between mineral surfaces (representative of reservoir rocks) and mixture of hydrocarbon/water/acid gases (representing typical reservoir fluids), to put petroleum production industry in target (Chun et al. 2015; Fazelabdolabadi and Alizadeh-Mojarad 2016; Underwood et al. 2015; Wu et al. 2012) or analysis of mobilization and recovery of fluids/asphaltene from nanopores using MD (Oughanem et al. 2015; Youssef et al. 2015; Stukan et al. 2012). More recently, Xie et al. (2016) studied oil contamination removal process at microscales, using the molecular dynamics technique.

Calcite is composed of carbonate mineral and categorized as mineral materials. Calcite differs from kaolinite (which is known as clay mineral). Clay mineral is a jargon amongst pedologists and it should be distinguished from clay materials. Clay materials exist in nature as fine-grained materials which their size is below 4 μm. Phyllosilicates are only fundamental constituents of clay materials. However, clay mineral materials are both synthetic and natural materials which may contain non-phyllosilicates as their principal component. Clay minerals such as kaolinite have a layered structure, including nanometer-thick layers. Modification of the surface of clay minerals can be done by synthesis methods such as adsorption and grafting (Bergaya et al. 2013).

A plethora of experimental and computational works is available on wetting behavior of reservoir fluids over mineral surfaces, such as quartz (Hou et al. 2015; Saraji et al. 2013; Wu et al. 2013; Xuefen et al. 2009), calcite (Benlia et al. 2012; Cebecia and Sönmezb 2004; Guiwu et al. 2009; Khusainova et al. 2015; Sakuma et al. 2014; Rezaei Gomari et al. 2006), and kaolinite (Lage et al. 2015; Lebedeva and Fogden 2011; Murgich and Rodríguez 1998; Tabrizy et al. 2011a, b), to ease the conception of the phenomena. Nevertheless, those researches pinpoint to the complexity of wetting behavior existent in different types of minerals. For instance, octahedral and tetrahedral surfaces of {001} kaolinite are discovered with hydrophilic and hydrophobic characteristics, respectively (Ni and Choi 2012; Šolc et al. 2011; Tunega et al. 2004). In addition, hydroxylated surfaces of mineral surfaces can reportedly be different in wetting properties (Chai et al. 2009; Liascukiene et al. 2014). The findings also conclude the wettability and dynamical properties, to be affected by confinement size of pores of reservoir rocks (Al-Quraishi and Khairy 2005; Cui et al. 2003; Standnes and Austad 2000; Yuan et al. 2015). A few investigations were also directed towards analysis of adsorption of organic molecules over clay (Hu et al. 2014; Pernyeszi et al. 1998; Wang et al. 2013) (mainly kaolinite), as well as non-clay (Cooke et al. 2010; de Leeuw and Parker 1998; Freeman et al. 2009; Guiwu et al. 2009; Keller et al. 2015; Sakuma et al. 2014) (mainly calcite) surfaces. In this regards, the main focus has been devoted to the {001} kaolinite or {1014} calcite structures, on the premise of holding the primary cleavage planes (Miller et al. 2007; Sekkal and Zaoui 2013; Titiloye et al. 1993; Zielke et al. 2015).

The present article attempts to address the issue through a comparative framework, to include a mixture of hydrocarbon/acid gas/water in both clay and non-clay environments. The authors, however, are unaware of any available experimental adsorption data with exact correspondence to the simulation systems considered (i.e., fluid composition and type of slit wall); therefore, such comparisons are not attainable at the moment.

Methodology

MD simulations were performed using the LAMMPS simulation package (Plimpton 1995). The simulation considered system was composed of two parts, namely, an immobile (solid) part of mineral structure and a mobile (fluid) part (of hydrocarbon/acid gas/water mixture). OPLS-AA (Optimized Potentials for Liquid Simulations-All Atoms) force field, developed by Jorgensen et al. (1996), was used to describe the interactions among atoms in the hydrocarbon phase. In this work, carbon dioxide (CO2) and hydrogen sulfide (H2S) were regarded as acid gas phase. Nath-Escobedo-de Pablo (NERD) (Nath 2003) revised force field and EPM2 potential model (Harris and Yung 1995) was utilized to model H2S and CO2, respectively. Extended simple point charge (SPC/E) model of Berendsen et al. (1987) was also used to simulate water molecules. According to SPC/E model, the SHAKE algorithm (Ryckaert et al. 1977) was used to preserve bond and angle geometry constraints for water molecules in the course of MD simulations.

Calcite and kaolinite surfaces were considered as representative of clay and non-clay materials, to form nano-slit walls. In case of calcite surface, \(\{ 10\bar{1}4\}\) calcite structure was utilized, as for being the most stable and neutral surface, to build the 4-nm confined geometry. Neutral octahedral {001} surface of kaolinite was used, as well. To model calcite surfaces, rigid ion model of a force field presented by Pavese et al. (1992, 1996) was employed. The CLAYFF force field (Cygan et al. 2004) was adopted to define all bonded and non-bonded interaction parameters of kaolinite surface. A bread usage of the Pavese and CLAYFF forcefields can be found in recent literature adoptions (Fazelabdolabadi and Alizadeh-Mojarad 2016; Ghatee et al. 2015; Greathouse et al. 2015; Keller et al. 2015; Zielke et al. 2015).

In case of \(\{ 10\bar{1}4\}\) calcite, the methodology suggested by Headen and Boek (2011) was used to describe the van der Waals interaction parameters (to model fluid–solid interface). The van der Waals non-bonded interaction parameters between fluid–solid species in systems, including {001} kaolinite surface, were estimated using the Lorentz–Berthelot mixing rule.

MD simulations were performed under canonical (NVT) ensemble using the Nosé–Hoover thermostat (Hoover 1985; Nosé 1984) with 1 ps relaxation time. Integration of the equations of motion was done every 1 fs. Ewald summation technique was used to calculate electrostatic interactions. The long-range/short-range potentials were truncated at 11 Å distance. Orthorhombic simulation cells were considered with Periodic Boundary Condition (PBC) in xy directions. The Packmol package (Martínez et al. 2009) was used to construct the initial configuration of molecules in the simulation cell.

The nano-slit simulation cell constructed was composed of two parallel surfaces, with a 4-nm separation distance (Fig. 1). Two types of surfaces were considered in those regards: the \(\{ 10\bar{1}4\}\) calcite and the {001} kaolinite. The \(\{ 10\bar{1}4\}\) calcite surface contained seven atomic layers (perpendicular to the z-direction) in a dimension of 82 Å × 45 Å × 19.30 Å. The {001} octahedral kaolinite surface was composed of 6120 atoms in a dimension of 51.42 Å × 80.40 Å × 5 Å, with its xy plane being perpendicular to z-direction. For the case of kaolinite walls, two gaps of 10 Å were introduced to the top/bottom ends of the simulation cell, to avoid any unphysical interactions amongst species in the mineral surfaces (Fig. 1b).

Fig. 1
figure 1

Rectangular pore configurations for a 40 Ǻ calcite pore and b 40 Ǻ kaolinite pore. The calcium/carbon/oxygen/hydrogen/aluminum/silicon atoms are shown by green/blue/red/white/purple/yellow spheres, respectively

Two main systems, namely, S1 and S2, were considered as for the MD simulations. In S1 case, pure molecules are confined between mineral surfaces. In S2 case, mixtures of molecules are placed inside the nano-slit geometry. In addition, molecular dynamics simulations of pure hydrocarbons were performed at bulk conditions over a temperature of 340 K, for further comparison. All MD simulations were attempted under the canonical ensemble.

The time span of MD simulations has been 1 ns (S1 system)/1.5 ns (S2 system). The radius of gyration, \(R_{\text{g}}\), and end-to-end distance were calculated for hydrocarbon chains to explain the confinement effect on them. For a given molecule, the radius of gyration was calculated by Eqs. (1) and (2):

$$\vec{r}_{\text{cm}} = \frac{{\sum\nolimits_{i = 1}^{{n_{\text{segments}} }} {\vec{r}_{i} } }}{{n_{\text{segments}} }}$$
(1)
$$R_{\text{g}} = \left[ {\frac{{\sum\nolimits_{i = 1}^{{n_{\text{segments}} }} {m_{i} \left\| {\vec{r}_{i} - \vec{r}_{\text{cm}} } \right\|^{2} } }}{{\sum\nolimits_{ii = 1}^{{n_{\text{segments}} }} {m_{i} } }}} \right]^{1/2}$$
(2)

where \(\vec{r}_{\text{cm}}\) and \(n_{\text{segments}}\) indicate the (vector) of center-of-mass of a given molecule and the number of (atomic) segments in a molecular chain, respectively. \(\vec{r}_{i}\) and \(m{}_{i}\) denote, respectively, the (vector) of coordinates and the mass of the iith segment of a given molecule, and ∥ ∥ represents the vector norm. The mean-squared displacement (MSD) was computed, and the self-diffusion coefficient, D, in different systems studied. Calculation of the self-diffusion coefficient (for a given molecule type) was performed using the Einstein relation (Frenkel and Smit 2011) [Eqs. (3), (4)]:

$$D = \frac{1}{2d}\mathop {\lim }\limits_{t \to \infty } \frac{{{\text{d}}\langle \left\| {\Delta \vec{r}_{\text{cm}} (t)} \right\|^{2} \rangle }}{{{\text{d}}t}}$$
(3)
$$\Delta \vec{r}_{\text{cm}} (t) = \frac{{\sum\nolimits_{k = 1}^{N} {[\vec{r}_{{{\text{cm}}_{k} }} (t) - \vec{r}_{{{\text{cm}}_{k} }} (t = 0)]} }}{N}.$$
(4)

Here, \(\vec{r}_{{{\text{cm}}_{k} }}\) refers to the vector of center-of-mass of the kth molecule of a given species, for which a total of N molecules exists. In addition, d denotes the dimensionality of the system (d = 3), and \(\langle \rangle\) indicates the ensemble average of the quantity.

Results and discussion

The naming convention for the (slit) simulations is introduced in Table 1. The information on the composition of molecules considered in mixture states (S2 systems) is also listed in Table 2.

Table 1 Naming convention for the MD simulations
Table 2 Density of molecules for different MD simulations

z-Density profiles

Atomic z-density profiles of the MD simulations of S1/S2 systems are presented in Figs. 1 and 2. The position of the calcite and kaolinite walls in each profile has been embedded in the figures, to visually aid the comparison on relative positioning of z-density profiles over the mineral surfaces. S1 system simulations were attempted for propane, hexane, heptanes, and decane molecules. However, for the sake of brevity, only the z-density results for decane are reported herein. The other z-density results can be found in Figs. S-1 and S-2 in the Supplementary Information to this article.

Fig. 2
figure 2

Atomic z-density profiles for A S1-calcite-C10, B S1-calcite-H2O, C S1-calcite-H2S, and D S1-calcite-CO2, a S1-kaolinite-C10, b S1-kaolinite-H2O, c S1-kaolinite-H2S, and d S1-kaolinite-CO2 simulations at 340 K

According to z-density profiles of decane and water in calcite nano-slit, two major peaks are appeared. The final configuration of molecules in S1-calcite-C10 and S1-kaolinite-C10 simulation systems is depicted in Fig. 3. Given the type of molecule under confinement being the same (decane), the adsorption layer over the calcite surface is more ordered state (Fig. 3a) than the kaolinite case (Fig. 3b). The results for confined CO2 in nano-slit calcite (Fig. 2d) are in perfect agreement with the previous results (Fazelabdolabadi and Alizadeh-Mojarad 2016). The adsorption results for CO2 (Fig. 2d, D) indicate carbon dioxide to have stronger tendency towards hydrophilic {001} octahedral kaolinite surface than \(\{ 10\bar{1}4\}\) calcite surface, with the same value of CO2 density. A similar trend is for H2S, with the density of hydrogen sulfide being kept equal in both the systems (Fig. 2C, c). The trend is somehow reversed for the water case; and H2O has more tendency for adsorption onto the calcite surface than {001} octahedral kaolinite (Fig. 2B, b). The results for z-density of oxygen atoms over {001} octahedral kaolinite surface are in good agreement with previous computational reports (Feibelman 2013; Tunega et al. 2004).

Fig. 3
figure 3

Final snapshots of molecular distributions for a S1-calcite-C10 and b S1-kaolinite-C10. The calcium/carbon/oxygen/hydrogen/aluminum/silicon atoms are shown by green/blue/red/white/purple/yellow spheres, respectively

The adsorption profiles (Fig. 4), obtained by MD simulations, were calculated for the S2 systems (with mixture of molecules being under slit confinement). For the sake of comparison, the density of molecules is kept the same, between the systems of different wall types. Visual inspection of the final configuration of molecules in systems (Fig. 5) may lead us to an important finding that adsorption layer of water molecules over calcite surface (in S2 systems) looks more ordered than its adsorption layer counterpart over the kaolinite surface, albeit kaolinite’s hydrophilicity. The accumulation of hydrocarbon molecules in the middle of simulation box can be a result of hydrophilicity of {001} octahedral kaolinite surface and this behavior is in agreement with previous results (Ni and Choi 2012). To obtain accurate results, the system should have reached equilibrium prior to sampling the simulation box. For the sake, we followed the standard protocol, and monitored the system`s temperature and energy versus simulation time, to ensure equilibrium. The data are presented in the Supplementary Information to this article.

Fig. 4
figure 4

Atomic z-density profiles for A S2-calcite-C10, B S2-calcite-H2O, C S2-calcite-H2S, and D S2-calcite-CO2, a S2-kaolinite-C10, b S2-kaolinite-H2O, c S2-kaolinite-H2S, and d S2-kaolinite-CO2 simulations at 340 K

Fig. 5
figure 5

Final snapshots of molecular distributions for a S2-calcite and b S2-kaolinite. The calcium/carbon/oxygen/hydrogen/sulfur/aluminum/silicon atoms are shown by green/blue/red/white/magenta/purple/yellow spheres, respectively

In case of acid gases, the change in type of the slit wall (S2 systems) seems to alter the arrangement of H atoms in vicinity of the surfaces by comparing the z-density profiles of hydrogen atoms in Fig. 4C, c and D, d. The simulation findings on the tendency of hydrocarbon, acid gases, and water towards the calcite surface are also in agreement with published experimental reports (Broseta et al. 2012; Karoussi and Hamouda 2008; Tabrizy et al. 2011a, b).

Radius of gyration and end-to-end distance

The radius of gyration \((\langle R_{\text{g}} \rangle )\) and end-to-end distance of molecules were computed under canonical ensemble, and are reported in Tables 3 and 4. The results are in good agreement to previous reports on pure hydrocarbons (modeled using United-Atom or All-Atom force fields) (Feng et al. 2013; Ferguson et al. 2009; Thomas et al. 2006). Comparison against the bulk-configuration results shows reduction in these properties, which is more conspicuous for longer chain hydrocarbons. This change in conformation of molecules should be regarded as an apparent effect of nano-slit confinement.

Table 3 Average radius of gyration, \(\langle R_{\text{g}} \rangle\) (Å), for different MD simulations
Table 4 Average end-to-end distance (Å) for different MD simulations

Self-diffusion

Calculation of the ensemble average of the mean square displacement (MSD) of center-of-mass of each molecule type was attempted every 4 ps. The data were subsequently used to establish the two-dimensional self-diffusion coefficient of molecules, using Eqs. (3) and (4). Table 5 lists the computed self-diffusion values under each wall type. A huge reduction in diffusion coefficient is seen, for example, for H2O, in shifting to mixture state (S2 system). This can be described by strong adsorption of water molecules over S2-calcite/S2-kaolinite than S1-calcite/S1-kaolinite. However, in comparison, less water molecules are adsorbed over the kaolinite surface, giving the molecules more freedom of movement, and hence, a larger value for diffusion coefficient is obtained for kaolinite case with water. The phenomenon is somehow reversed for acid gases in mixture state, with less acid gases being adsorbed onto calcite surface, resulting to a more freedom of movement and increased value in self-diffusion of acid gases in S2-calcite systems. A similar argument may be put forward, to describe the change-in-value for hydrocarbons.

Table 5 Self-diffusion coefficient \(D_{H2O}\)(10−9 m2s−1) for different MD simulations at 340 K

Conclusions

MD simulation results of pure molecules (S1-calcite/S1-kaolinite systems) indicate water to have higher tendency to be adsorbed over the {1014} calcite surface than {001} octahedral kaolinite surface and supported by two distinct layers of adsorption. Acid gases follow the opposite trend of having more tendency of being adsorbed over the kaolinite surface than calcite. The existence of a middle-region water phase was also ruled out in a 40-Å calcite slit-pore in (S2 systems). The change in the radius of gyration and end-to-end distance of hydrocarbon molecules should be attributed to a conformational change induced by confinement in nano-slit environment. The change-in-value of diffusion coefficients can be attributed to different levels of molecular adsorptions, with higher freedom of movement from less adsorption onto system walls, which results in a higher value diffusion coefficient.