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Atomistic Molecular Dynamics Simulations of Crude Oil/Brine Displacement in Calcite Mesopores Mohammad Sedghi, Mohammad Piri, and Lamia Goual Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b04713 • Publication Date (Web): 24 Mar 2016 Downloaded from http://pubs.acs.org on March 29, 2016

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Atomistic Molecular Dynamics Simulations of Crude Oil/Brine Displacement in Calcite Mesopores Mohammad Sedghi,* Mohammad Piri, and Lamia Goual Department of Petroleum Engineering, University of Wyoming, 1000 E. University Avenue, Laramie, Wyoming 82071, United States

ABSTRACT Unconventional reservoirs such as hydrocarbon-bearing shale formations and ultra-tight carbonates generate a large fraction of oil and gas production in North America. The characteristic feature of these reservoirs is their nanoscale porosity that provides significant surface areas between the pore walls and the occupying fluids. To better assess hydrocarbon recovery from these formations, it is crucial to develop an improved insight into the effects of wall-fluid interactions on the interfacial phenomena in these nanoscale confinements. One of the important properties that controls the displacement of fluids inside the pores, is the threshold capillary pressure. In this study, we present the results of an integrated series of large-scale molecular dynamics (MD) simulations performed to investigate the effects of wall-fluid interactions on the threshold capillary pressures of oil – water/brine displacements in a calcite nanopore with a square cross-section. Fully atomistic models are utilized to represent crude oil, brine, and calcite in order to accommodate electrostatic interactions and H-bonding between the polar molecules and the calcite surface. To this end, we create mixtures of various polar and nonpolar organic molecules to better represent the crude oil. The interfacial tension between oil and water/brine and their contact angle on calcite surface are simulated. We study the effects of oil composition, water salinity, and temperature and pressure conditions on these properties. The threshold capillary pressure values are also obtained from the MD simulations for the calcite nanopore. We then compare the MD results against those generated using the Mayer-Stowe-Princen (MSP) method and explain the differences.

1. INTRODUCTION Oil and gas production from organic-rich shale formations has experienced significant growth in recent years. Rock samples from these formations are often characterized with nanometer size pores and ultralow porosities and permeabilities. In a recent study by Saraji et al.1, the average pore radii of several

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reservoir samples from Bakken formation was reported to be within 5 to 100 nm range. Better assessment of hydrocarbon recovery from these ultra-tight formations depends on our understanding of the relevant interfacial phenomena under nanoscale confinement. It is imperative to develop an improved insight into the impact of confinement on key displacement properties such as the threshold capillary pressure between, for instance, crude oil and water in nanoscale (2 – 50 nm) pores, hereinafter referred to as “mesopores” according to the IUPAC (International Union of Pure and Applied Chemistry) definition.2 The analytical models that are developed to compute threshold capillary pressures for displacements in macropores (larger than 50 nm) ignore the atomic details of molecular interactions by considering fluids and solids as continuous phases. However, for mesopores where the pore radius becomes comparable to the molecular size, the specifics of molecular interactions cannot be overlooked and applying the continuous phase simplification could result in underestimation/overestimation of the pressure drop. In spite of the lack of understanding of threshold capillary pressure in mesopores, very few studies have been performed to provide insight in this area. Threshold capillary pressure (Pcth) is the pressure difference needed for a fluid to displace another fluid in a pore with a given geometry and wettability.3 In the network modeling of oil reservoirs, at low capillary numbers, the flow of fluids in the medium is controlled by the magnitude of Pcth of various pore-scale displacements.3,4 Therefore, accurate calculations of Pcth for different pore sizes and geometries are essential in predicting the correct pattern of fluid displacement in the reservoir rocks. For macropores, a thermodynamic model, based on minimization of Helmholtz free energy, was developed by MayerStowe-Princen3,4 (MSP method) and used to compute Pcth in pores with different cross-sectional shapes.5 For the case of oil and water in a pore with an angular cross section, the threshold capillary pressure is given by, =

, , ,

(1)

where subscripts w, o, and s denote water, oil, and solid, respectively, Low,t is the total length of contact line between oil and water, Los,t is the total length of contact line between oil and solid, Ao,t is the total area of the pore cross section that oil occupies, is the interfacial tension (IFT) between oil and water, and is the contact angle (CA) their interface makes with the pore wall. Parameters Low,t, Los,t, and Ao,t can be calculated from the IFT and CA. For the complete formulations of MSP method, interested readers are referred to refs. 3-5. For a circular cross-section with the radius r, the MSP method becomes the wellknown Young-Laplace equation,


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=

(2)

Although many computational studies have been focused on the capillary rise of oil and water, 6–17 far less attention has been directed toward investigating the crude oil-brine displacements in nano-confinements. In a recent study by Chen et al.18, forced displacement of oil by water was probed in a circular nanotube and the amount of remaining oil as well as the threshold external force (presented in reduced units) were determined for different pore wettabilities. Their results indicated that the amount of residual oil and the threshold external force increased as the pore wall became more oil-wet. In our previous study,19 we examined the threshold capillary pressure between dodecane and water in organic pores with different cross-sectional shapes using molecular dynamics simulations. The Martini force field, which is a coarsegrained force field (i.e., zero partial charges for oil and water components), was utilized in the simulations. This meant that all the intermolecular interactions in our simulations were represented by Lennard-Jones (LJ) short-range potentials. The main finding of that work was that Pcth obtained with MD simulations are in close agreement with those from the MSP method. This indicates that the effect of wall-fluid interactions on fluids’ interface was negligible in the pores due to fact that the pore sizes (~14 nm) were much larger than the radius in which LJ interactions were effective (~1.2 nm) and also the fact that there were no long-range electrostatic interactions present in the simulations. Modeling the organic pores and dodecane with coarse-grained LJ particles is an appropriate approximation since they are considered as non-polar materials. However, for a system of inorganic pores (such as calcite, quartz, clays, etc.) containing crude oil and brine (salt water), electrostatic interactions are too significant to be neglected. For instance, the wettability alteration of calcite surfaces by crude oil is attributed to the polar (electrostatic) interactions between carboxylic acids of oil and calcium cations.20,21 Consequently, to obtain reliable estimates of threshold capillary pressure for displacements in inorganic mesopores using MD simulations, it is essential to adopt atomistic models with non-zero partial charges to account for the polar interactions. In this study, we investigate crude oil/brine displacement threshold capillary pressure in angular mineral mesopores using MD simulations that account for polar interactions. Calcite was chosen to represent surfaces in shale reservoirs since it is one of the most abundant minerals found in shale rocks.22 This paper is structured as follows. In Section 2, we present a brief account of the methodology we have used. The main findings of the work are reported in Section 3. We discuss the effects of temperature, pressure, water salinity, and oil composition on the IFT. We then determine the contact angle of the crude oil/brine/calcite system and analyze the interactions between the polar components of oil and calcite surface. Finally, capillary pressures obtained from the MD simulations are compared against those


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generated using the MSP method. This is then followed by an explanation of the differences we observe. Section 4 lists the conclusions.

2. METHODS MD simulations were performed using GROMACS 5.1.0 software.23 The time step was set to 1 fs for all the simulations reported here to enable flexible hydrogen atoms in the organic molecules. Simulations were performed at two temperature (T) and pressure (P) conditions: ambient conditions (298 K and 1 bar) and reservoir conditions (389 K and 472 bar). The CHARMM36 force field24 was used for the organic molecules and water was represented by either SPC/E or SPC-FW models.25,26 For calcite we considered the force fields of Raiteri et al.27 and CHARMM36, which is explained later in this paper. To account for Van der Waals interactions, we applied Buckingham and Lennard-Jones potentials with a cut-off distance of 1.4 nm. Long-range electrostatic (columbic) interactions beyond the cut-off distance were computed using Particle-Mesh-Ewald (PME) algorithm.28 The molecules forming oil and water phases will be introduced in the next section. Below we provide more details regarding the different MD simulations that we performed. 2.1 Interfacial Tension Water and oil were placed in a rectangular simulation box with sides of 6 nm in the X and Y directions and 18 nm in the Z direction normal to the interface. The heights of the oil and water columns were about 12 and 6 nm, respectively. The periodic boundary conditions were applied in all directions and so two interfaces existed between oil and water. During the simulations, the Nose-Hoover thermostat and the Parrinello-Rahman barostat were used to control temperature and pressure, respectively. However, in order to establish a constant area for the oil–water interface (36 nm2), we applied a semi-isotropic pressure coupling technique with a compressibility of 0 bar-1 in the X and Y directions and 4.5E-05 bar-1 in the Z direction. The simulations were run for a minimum of 60 ns after the system had reached the equilibrium temperature and pressure. The IFT () value was then calculated using the following equation,29 =

! ' "〈$$ 〉 − 〈(( 〉 + 〈** 〉 +

(3)

where ,$ is the simulation box size in the Z direction and 〈-- 〉 is the ensemble average of normal pressure in the . direction during the simulation. 2.2 Contact Angle


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A calcite surface with an area of 7.284 × 20.951 nm2 and a thickness of 12 molecular layers (i.e., 3.643 nm) was built. Using a thicker slab of calcite was not necessary as the inclusion of additional layers showed no impact on the structure of water layers adsorbed on the surface.30 We considered a halfcylinder geometry for the water droplet to reduce the nanoscale artifacts in the simulations, as explained in a study by Tenney and Cygan.31 Due to the use of periodic boundary conditions, the water droplet was infinite in the X direction. The oil column surrounding the water droplet on the surface had a height of about 11 nm. The Langevin thermostat was employed to control the temperature since using the NoseHoover thermostat may create flying-ice-cube effect when the center of mass of the system starts to move during the simulation.32 The pressure of the system was controlled by applying external pressures on two pistons placed on top of the oil column and at the bottom of the calcite slab. The pistons were composed of virtual hard sphere particles positioned in a face-centered cubic (FCC) arrangement. The hard sphere particle was modeled using repulsive interactions (i.e., LJ particles with low attraction potential). The size of the simulation box in the Z direction was extended to 3 times the distance between the pistons in order to minimize the periodic effects of PME calculations.33 The contact angle was determined using Eq. 4 where a and b are the height and the base radius of the droplet, respectively (parameters a and b are shown in Figure S1 of the supporting information). Visualization and image processing were performed using VMD34 and ImageJ35 software, respectively. 45

= /012' 346 56 7

(4)

2.3 Threshold Capillary Pressure A calcite mesopore was created by placing slabs of calcite with a thickness of 8 molecular layers perpendicular to each other, so the pore had a square cross section with a side of 5.1 nm. All interactions between the neighboring calcite walls were set to zero to avoid any artificial high-energy interactions that would distort their crystal structure. Oil to water displacements were performed by applying different pressures on the pistons placed at the boundaries of the system in the Z direction. Figure 1 illustrates the simulation setup (left) as well as the cross-sectional view of the pore (right). Similar to contact angle simulations, the temperature was controlled using the Langevin thermostat and the size of simulation box in the Z direction was approximately 3 times larger than the distance between the pistons.


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Figure 1. The simulation set-up for the capillary pressure measurements (left) and the top view of the calcite mesopore (right).

For all of our simulations, we applied the 3-D Ewald summation technique to account for long-range electrostatic interactions. This choice was based on preliminary simulations showing that the magnitude of electrostatic interactions in reciprocal space calculated by 3-D Ewald summation converged asymptotically to the correct value obtained by pseudo 2-D Ewald summation, as we increased the vacuum space. By implementing the vacuum spaces in our MD setups as mentioned above, the difference between pseudo 2-D Ewald and 3-D Ewald calculations was about 10 percent. However, this difference did not have any considerable impact on our simulations since these electrostatic interactions were 4 orders of magnitude smaller than the electrostatic interactions calculated within the cut off distance, which are unaffected by the choice of Ewald summation. Therefore, we considered using 3-D Ewald summation technique, as it was more stable during the simulations.

3. RESULTS AND DISCUSSION 3.1 Interfacial Tension In previous MD studies of oil/water systems, pure organic solvents were usually considered as the oil phase.36,37 In particular, heptane, octane, dodecane, and coarse-grained “oil-like” particles were often used to represent oil.19,36–43 A more realistic oil phase consisting of alkanes, cycloalkanes, and aromatic molecules was recently proposed to model light oils.44,45 In this study, however, we considered the crude


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oil as a mixture of nonpolar (saturate and aromatic fractions) and polar molecules (resin and asphaltene fractions). To construct the nonpolar fraction, 14 molecules were built to include different structures of normal and branched alkanes, cycloalkanes, and aromatics with various molecular sizes. The concentration of molecules in the mixture were loosely correlated to the SARA fractions and the gas chromatography analysis of crude oil B used in a previous study.46 The structure and concentration of these molecules are shown in Tables S1 and S2 of the supporting information (SI). To create the polar fraction, the most abundant functional groups in crude oils were considered; sulfur is mostly found in thiophene, thiols, sulfides, and disulfides structures. Carboxylic acids, phenols, and ketones are the most abundant oxygen-bearing functional groups while nitrogen atoms are typically found in aromatic structures.47 Table 1 lists the twelve polar molecules considered in this work (the abbreviation we used for the name of each molecule is shown inside the parenthesis). A mixture with equal molar concentrations of these molecules was chosen to represent the polar fraction of crude oil. Table 1. Molecular structure of polar organic components of the crude oil used in this study O-bearing functional groups Nonanoic acid (NNAC)

Naphthenic acid (NPAC)

Benzoic acid (BZAC)

Nonanone (NNON)

Propylphenol (PRPH)

N-bearing functional groups Carbazole (CRBZ)

Indole (INDL)

Quinoline (QINL)

S-bearing functional groups Methyloctylsulfide (NNSL)

Methyloctyldisulfide (NNDS)

Nonanethiol (NTHL)


Benzothiophene (ZTHP)

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The polar mixture was then added to the nonpolar one at various concentrations. The IFT values decreased almost monotonically as we increased the concentration of polar fraction. At 52 wt% of polar fraction and ambient conditions, the IFT reduced to 24.7 mN/m, which is in the range of experimentallymeasured IFT values reported by Mirchi et al.46 for their crude oil–water system at the same P and T conditions. Subsequently, we considered two crude oil models, called, oil A and oil B. Oil A contains only nonpolar components and represents light-oils, while oil B contains both polar and nonpolar components in the proportion mentioned earlier and represents typical black crude oils. Densities of crude oils A and B at ambient conditions were calculated to be 816.4 and 894.9 g/mole, respectively. In early IFT simulation runs, to ensure that the system had reached equilibrium, the IFT value was computed every 10 ns until it reached a plateau (usually after 50 ns). Thus, the rest of the simulations were run for at least 60 ns (the profile of the IFT versus simulation time for oil B – water system at ambient conditions is plotted in Figure S2 of the supporting information). The IFT data are tabulated in Table 2 for different oil and water fluid systems. The results indicate that IFT decreases at higher T and P and increases with the increase in water salinity (the brine composition is reported in Table S3 of the supporting information). These trends are in line with the experimental results reported by Mirchi et al.46 Table 2. Interfacial tension (mN/m) between crude oils A and B and water/brine obtained from MD simulations Oil-A – water

Oil-A – water

Oil-A – brine

Ambient conditions

Reservoir conditions


46.4 ± 0.18

42.8 ± 0.35

51.1 ± 0.46

Oil-B – water

Oil-B – water

Oil-B – brine

Ambient conditions



24.7 ± 0.5

22.7 ± 0.5

29.1 ± 0.85

It is well-know that the strong electrostatic interactions between water molecules (due to their H-bonds) are responsible for the interfacial tension between oil and water. Therefore, for a binary system of oil and water/brine where the oil composition is fixed, the change in IFT should be related to the change of electrostatic interactions in the aqueous phase. Therefore, we calculated the electrostatic (coulomb) energy of water/brine at different T and P, as reported in Table S5 of SI. The results show that electrostatic interactions decreased at higher T and P conditions and increased with water salinity. Comparing Table 2 and Table S5, it is clear that the IFT between oil and water/brine is directly affected by the magnitude of electrostatic interactions in the aqueous phase.


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The decrease of the electrostatic interactions at higher T and P is related to the higher kinetic energy of water molecules that disturb their network of H-bonds. The average number of H-bonds between water molecules decreases from 12.5E3 at ambient conditions to 11.1E3 at reservoir conditions. Correspondingly, water density decreased from 997 to 952 g/l. For the brine simulation, the average number of H-bonds reduced to 8.15E3 due to the fact that ions occupied spaces between water molecules and separated them from each other. However, the significant electrostatic attractions between water and ions and between ions with opposite charges easily overcome the decrease in the H-bonds. The coulomb energies between water molecules and ions in the brine are reported in Table S6 of the SI. To determine which functional groups are more active at the oil/water interface, we calculated the relative density of the organic molecules at the interface compared to their average densities in the bulk based on their density profiles in the Z direction. Each interface region had a thickness of almost 2 nm and was determined based on the density profiles of water/brine, as shown in Figure S4 in the SI. The density profiles were generated over 40 frames during the last 20 ns of IFT simulations. The relative density of the polar organic molecules at reservoir conditions is reported in Table 3 (the density profiles are provided in Figure S3 of the supporting information). The relative density was calculated by dividing the average density of molecules in the interface region over their average densities in the rest of the oil phase (bulk phase). With this definition, the relative density does not depend on the bin size used for the density profile construction. The results indicate that the accumulation of carbazole at the interface is considerably greater than other molecules. This is due to the fact that carbazole has a high tendency to self-associate and form stack-shaped aggregates through aromatic interactions. Among other polar molecules, N and O functional groups showed a comparable tendency to accumulate at the interface; however, quinolone and indole, which are polar aromatic molecules with plane geometries, have a slightly stronger affinity to the aqueous phase. This can be attributed to their ability to establish stronger Van der Waals interactions with water molecules because of their aromatic rings. Benzothiophene, which is a polar aromatic molecule with no H-bonding ability, certainly shows an accumulation comparable to the O-containing molecules that do form H-bonds with water molecules. The rest of the sulfur-bearing molecules however have relative densities lower than 1 since they are neither aromatic nor able to form H-bonds. Similarly, nonpolar molecules have almost zero presence at the interface. The density analysis was repeated for simulations at ambient conditions, and with high brine salinity (using brine instead of water) and similar results were observed for all cases (the relative density results are shown in Tables S4 and S5 of the supporting information).


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Table 3. Relative density of oil polar molecules at the oil/water interface at reservoir conditions Component

Relative density

Carbazole

18.22

Quinoline

2.58

Indole

2.23

Benzoic acid

1.85

Naphthenic acid

1.90

Nonanoic acid

1.56

Nonanone

1.38

Propylphenol

1.68

Benzothiophene

1.86

Nonanethiol

0.41

Methyloctyl-sulfide

0.33

Methyloctyl-disulfide

0.30

The relative densities of carbazole at oil-water/brine interfaces were similar at reservoir conditions (Tables 3 and S7) and 3-fold larger than those at ambient conditions (Table S8). As mentioned earlier, the large accumulation of carbazole at the interface is related to their aggregation tendency. Therefore, to explain the difference in the relative densities, we examined the aggregation behavior of carbazole in the bulk phase of oil B at ambient and reservoir conditions. To this aim, we performed NPT simulations of oil B at these T and P conditions for 60 ns using 4 times greater number of molecules than in the IFT simulations. The analysis on carbazole aggregation was carried out by the g_cluster utility of GROMACS software over the last 20 ns of the simulations. The calculations revealed that the average aggregation number and the maximum size of carbazole aggregates increased from 8 and 28 at ambient conditions to 11 and 56 at reservoir conditions, respectively. This suggests that the higher accumulation of carbazole at oil-water/brine interfaces is attributed to the increase in their aggregation propensity at higher T and P. The extent of aggregation of carbazole is related to the strength of molecular interactions in the oil phase. As the molecular interactions become weaker, association of carbazole becomes more enthalpically favored, resulting in a higher aggregation amount. The energy calculations of oil B during the bulk simulations indicate that as T and P increase from ambient to reservoir conditions, the magnitude of the Lennard-Jones energy of the system decreases from -3.18E5 to -2.89E5 kJ/mol. Similarly, the nonbonding potential energy changes from -3.40E5 to 3.01E5 kJ/mol and the oil density decreases from 895 to 848 g/l. As the result, the weaker interactions between oil molecules at higher T and P leads to greater


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aggregation of carbazole molecules. The end-snapshots of carbazole aggregates in bulk oil-B at ambient and reservoir conditions are displayed in Figure S5 of SI for visual comparison.

3.2 Contact Angle Calcite mineral is the most stable polymorph of calcium carbonate (CaCO3) at ambient conditions. The structure of the {101:4} calcite surface has been extensively studied through MD simulations and several force fields have been developed accordingly.27,48–50 Among those, the force field developed by Raiteri et al.27,48 is fitted to the thermodynamic properties of calcite surface instead of its mechanical properties. In this force field, Buckingham potentials are used to describe intermolecular interactions between calcium and carbonate atoms. These potentials have a softer repulsion term than Lennard-Jones potentials and therefore are more suitable to simulate the ionic structure of calcite. However, using LJ potentials exclusively is significantly faster than applying a mixture of LJ (for water and organic molecules) and Buckingham potentials (for calcite) in MD simulations. Hence, to test whether we could employ LJ parameters from the CHARMM36 force field for calcite, we performed MD simulations to measure the contact angle of water/oil/calcite system by using two different calcite models: 1) Raiteri et al. model which is a fully flexible calcite model that we will refer to as the “flexible model”; 2) a combination of CHARMM36 LJ parameters and Raiteri et al. partial charges, which we refer to as the “rigid model”, since the positions of carbon atoms and calcium cations are restrained with a harmonic force constant equal to 1.0E6 kJ/mol nm2. To simulate a system containing a combination of organic and mineral phases represented by different force fields, as in the flexible model, it is recommended to refit the cross-term potential parameters for the specific system of study. Freeman et al.51,52 proposed a systematic fitting of these parameters and we followed their methodology to determine the potentials between calcite and the polar components of crude oil. In particular, the potentials between calcium cation and the heteroatoms (such as nitrogen and oxygen) are important due to their strong electrostatic attractions. Table S6 of the supporting information lists the Buckingham potentials we used between calcium and heteroatoms with the A parameter fitted to the structural parameters of calcite or calcium nitride, according to Freemen and co-workers

51,52

The

fittings were performed using the General Utility Lattice Program (GULP).53,54 To compare contact angles obtained with different calcite models, we used SPC-FW water to be consistent with Raiteri et al. force field. The contact angle at ambient conditions with the flexible and the rigid model was 27 and 29 degrees, respectively. In both cases, calcite is strongly water-wet and shows similar qualitative behavior. In addition, no deformation or dissolution of the calcite surface was observed


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when the flexible model was used, meaning that restraining the position of particles is not creating unrealistic artifacts in the MD simulations. The fact that no dissolution/deformation was occurred is not surprising considering that we are simulating the {101:4} flat surface which is by far the most stable configuration of calcite. It is well-known that surface defects such as kinks and steps represent the potential nucleation sites for the crystal growth and dissolution.55,56 Therefore, we adopted the CHARMM36 force field with Raiteri et al. partial charges to model calcite for the rest of the simulations presented in this paper. Furthermore, to be consistent with the IFT simulations, we used SPC/E water model. Replacing SPC-FW with SPC/E model did not have a considerable effect on the simulated contact angle. The contact angles were obtained at reservoir conditions for different oil and water fluid systems. For the fluid systems of water - oil B and brine - oil B the contact angles were similar and equal to 23 degrees; however, the contact angle of water and oil A was found between 0-5 degrees. The results indicate that calcite is strongly water-wet even in the presence of polar molecules of crude oil. Nevertheless, due to the adsorption of polar components, the contact angle is higher for the water - oil B fluid system compared to the one with oil A. Moreover, our results suggest that the contact angle is not sensitive to brine salinity. In the experimental work of Mirchi et al.46, it was shown that the correlation between contact angle and salinity is not straightforward and perhaps could depend on rock mineralogy: for a rock sample with a dominant clay mineralogy (shale A), the contact angle increased with brine salinity, while for another sample consisting of mainly calcite and dolomite (shale B), the contact angle remained constant, similar to the results of our MD simulations. To investigate the tendency of polar molecules to adsorb on calcite, we placed oil B on the calcite surface and carried out MD simulations for 60 ns at ambient and reservoir conditions. The simulations were repeated with a different initial configuration to ensure reproducibility of the results. Similar to the previous section, we obtained the density profile of polar molecules in the Z direction, as shown in Figure S4 of the supporting information. The relative density of the molecules at the interface compared to their average densities is also reported in Table 4. We considered 1 nm distance from the calcite surface as the interface region based on the density profiles of oil molecules. The relative densities reported in Table 4 are the average of results of two simulations at each condition. For the calcite surface opposite to the water interface, carbazole has the lowest relative density at the surface, which is again related to its high tendency for self-aggregation. When a polar oil molecule adsorbs on calcite surface, it will be pinned to the surface from the adsorption site and hence the entropy will be reduced. The loss of entropy must be overcome by the enthalpy of adsorption in order for adsorption to occur. However, it is obvious that the loss of entropy for an aggregate of molecules pinned


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to the surface is much greater than that of a single molecule (as the movement of all the molecules in the aggregate becomes limited upon adsorption). As a result, for carbazole aggregates, the reduction of entropy cannot be compensated by the enthalpy of adsorption. This suggests that large asphaltenous molecules with high aggregation tendency may have more difficulty adsorbing on the calcite surface compared to smaller resinous molecules with less tendency for self-aggregation. Another interesting finding was the difference in the amount of adsorption of polar molecules at different T and P conditions. At ambient conditions, nonanethiol and benzothiophene have the highest relative density at the interface; however, at reservoir conditions, nitrogen- and oxygen-bearing molecules have higher adsorption quantities. Among nonpolar molecules, only benzene at ambient conditions shows a small tendency to adsorb on calcite surface. To better elaborate on the adsorption of oil molecules on calcite, we reported in Tables 5 and 6 the electrostatic (columbic) and LJ interactions between calcite components and some oil molecules at different T and P conditions. The adsorption of nonanethiol at ambient conditions (see Table 5) is primarily driven by the LJ attraction between the molecule and carbonate anion. This is not surprising as sulfur is a larger and more polarizable atom compared to C, N, and O, and thus can have stronger LJ interactions. Considering the fact that LJ and columbic potentials are proportional to

' ;

and

' ,

respectively, where r is the distance, it is evident that LJ interactions are significantly more susceptible to disruption when the kinetic energy of molecules (i.e., temperature) increases. Therefore, at higher temperatures (i.e., reservoir conditions), nonanethiols desorb from the surface. The adsorption of N and O containing oil molecules is governed by columbic interactions and hence they can remain adsorbed on the surface at higher temperatures. Table 6 shows their interaction energies with the calcite components at reservoir conditions. It is clear that ketonic oxygen (C=O) and the nitrogen in quinolone interact with Ca2+ cations while OH and NH functional groups (in propyl phenol and indole) adsorb on the CO32- anions since they form H-bonds with the oxygen atoms of carbonate. Consequently, Carboxylic functional groups (COOH in naphthenic, nonanoic, and benzoic acids), which have both ketonic oxygen and hydroxyl group, interact with both Ca2+ and CO32- ions, however, their interaction with Ca2+ is stronger. Here, we should clarify that the sole purpose of Tables 5 and 6 is to compare LJ and electrostatic energies between the organic molecules and the calcite components in order to understand the nature of their interactions. The reported values are the interaction energies of all organic molecules with the calcite and hence it directly depends on how many of those molecules adsorbed on the surface. For instance, the electrostatic interactions between NPAC and calcite is almost 3 times greater at reservoir conditions compared to ambient conditions due to its higher adsorption propensity.


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To better understand the adsorption tendency of polar molecules such as NPAC at reservoir conditions, one can relate the adsorption amount to the difference between molecular interactions at the interface region and in the bulk phase. As discussed in the previous section, the internal energy of oil B decreases at higher T and P, which implies weaker molecular interactions at these conditions. By calculating the interaction energies between NPAC and the rest of oil molecules during the NPT simulations of oil B, we found that the total interaction energy decreased from -30.4E3 to -26.3 kJ/mol as T and P increased from ambient to reservoir conditions. This means that oil B becomes a less favorable environment at higher T and P leading to a higher adsorption of NPAC. These results suggest that the adsorption behavior of organic molecules at interfaces (water, calcite, etc.) is sensitive to the oil media. Altering oil composition or T and P conditions can have a considerable impact on the adsorption behavior of oil molecules. For instance, in a recent quantum mechanics study by Andersson et al.,57 the adsorption of benzoic acid at oilwater interface was found to decrease by 40% when 0.1 mol% of benzene sulfonic acid was added to the oil.

Table 4. Relative density of oil polar molecules on calcite at different T and P conditions Component

Ambient conditions


Carbazole

0.14

0.40

Quinoline

0.81

2.75

Indole

1.17

4.48

Benzoic acid

1.06

3.01

Naphthenic acid

1.11

3.47

Nonanoic acid

1.17

3.27

Nonanone

1.32

3.01

Propylphenol

1.04

3.81

Benzothiophene

1.91

2.10

Nonanethiol

3.24

0.74

Methyloctyl-sulfide

0.96

0.24

Methyloctyl-disulfide

0.80

0.11

Benzene

0.14

0.37


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Table 5. Interaction energy (kJ/mol) between calcite components and oil polar molecules at ambient conditions Coulomb

LJ

Coulomb + LJ

Ca2+

Indole

1824

-58

1766

CO32-

Indole

-3370

-236

-3606

(Ca2+ + CO32-)

Indole

-1546

-294

-1840

Ca2+

Naphthenic acid

-2253

296

-1957

CO32-

Naphthenic acid

-729

-163

-892

(Ca2+ + CO32-)

Naphthenic acid

-2982

134

-2849

Ca2+

Nonanethiol

-203

-71

-274

CO32-

Nonanethiol

-1146

-1417

-2563

(Ca2+ + CO32-)

Nonanethiol

-1350

-1488

-2838

Ca2+

Benzene

465

-114

351

CO32-

Benzene

-960

-570

-1530

(Ca2+ + CO32-)

Benzene

-495

-685

-1180


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Table 6. Interaction energy (kJ/mol) between calcite components and oil polar molecules at reservoir conditions Coulomb

LJ

Coulomb + LJ

Quinolone

-5945

-15

-5960

Quinolone

3049

-657

2391

(Ca + CO3 )

Quinolone

-2896

-672

-3568

Ca2+

Indole

6846

-177

6669

Indole

-11492

-626

-12118

(Ca + CO3 )

Indole

-4646

-804

-5450

Ca2+

Naphthenic acid

-7007

869

-6138

Naphthenic acid

-1109

-223

-1331

(Ca + CO3 )

Naphthenic acid

-8115

646

-7470

Ca2+

Nonaic acid

-6185

742

-5443

Nonaic acid

-863

-162

-1025

(Ca + CO3 )

Nonaic acid

-7048

580

-6468

Ca2+

Benzoic acid

-5758

754

-5003

Benzoic acid

-2305

-265

-2570

Benzoic acid

-8063

489

-7573

Nonanone

-15222

868

-14355

Nonanone

10441

-1187

9254

Nonanone

-4782

-319

-5100

Propylphenol

-2069

490

-1579

Propylphenol

-3733

-306

-4039

Propylphenol

-5802

184

-5618

Nonanethiol

-35

-7

-42

Nonanethiol

-120

-155

-276

Nonanethiol

-155

-162

-318

Ca2+ CO3

2-

2+

CO3

2-

2+

CO3

2-

2-

2+

CO3

2-

2-

2+

CO3

2-

2-

2-

2+

2-

(Ca + CO3 ) Ca

2+

CO3

2-

2+

2-

(Ca + CO3 ) Ca

2+

CO3

2-

2+

2-

(Ca + CO3 ) Ca

2+

CO3

2-

2+

2-

(Ca + CO3 )


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3.3 Threshold Capillary Pressure To determine oil/water displacement threshold capillary pressure, oil was pushed into a calcite pore that was initially filled with water. This was possible by applying a greater pressure on the piston adjacent to oil (oil piston) than the one adjacent to water (water piston). We applied external pressures of 1072 and 472 bar on the oil and water pistons, respectively, in order to inject oil into the pore (with a pressure difference of 600 bar) while maintaining the downstream fluid (i.e. water/brine) at reservoir conditions (389 K and 472 bar). After the oil meniscus reached distances greater than 5 nm from both ends of the pore, we removed the external pressure and froze the pistons for 100 ns so that the composition of the oil inside and outside the pore reached equilibrium. The IFT between oil and water was monitored during the simulations to test whether the system was at steady-state conditions. To this end, oil and water molecules in the vicinity of the meniscus were placed in a separate simulation box, as shown in Figure 2 (molecules inside the white dotted rectangle). The size of the IFT simulation box was 3 × 3 × 7 nm3 and was almost equally divided between oil and water in the Z direction. IFT simulations were then carried out at reservoir conditions as explained in the previous section. The IFT values obtained at the end of 100 ns for oil B/water, oil B/brine, and oil A/water fluid systems were 23.1, 30.7, and 43.5 mN/m, respectively. They closely matched the IFT data reported in Table 2, indicating that our systems had reached equilibrium. Subsequently, we unfroze the pistons and started to decrease the pressure on the oil piston from 1072 bar (in 50 bar increments) to reduce the pressure difference across the oil - water interface in the pore. At each pressure difference, simulations were carried out for at least 4 ns during which the total number of organic atoms inside the pore was monitored to obtain the threshold capillary pressure (that is, the pressure difference at which oil starts to retract from the pore). As an example, we have plotted in Figure 3 the total number of organic particles inside the pore during the simulations of oil B/water fluid system. In this case, the threshold capillary pressure was between 250 – 300 bar.


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Figure 2. Longitudinal section view of crude oil B and water molecules inside the calcite pore (top left); snapshot of IFT simulation to determine the IFT across oil/water meniscus (top right); Orientation of water molecules near the calcite wall (bottom)

19500 250 bar

Number of organic atoms

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300 bar

19000

350 bar

18500

18000

17500

17000 0

1

2

3

4

Time (ns) Figure 3. Total number of organic atoms during the MD simulations with various pressure differences imposed on the system. The capillary pressure was determined at reservoir conditions for oil/water fluid systems inside the pore and compared against those generated using the MSP method, as listed in Table 7. For the MSP


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calculations, we used IFT and contact angle values reported in sections 3.1 and 3.2. The greater capillary pressure between oil B – brine compared to oil B – water mixture is the result of greater IFT values between oil B and brine compared to water (29.1 compared to 22.7 or 24.7 mN/m). The results show that capillary pressures obtained from MD simulations were considerably greater than those obtained from the MSP calculations. We attribute the discrepancy to the followings: First, as oil invades the pore, an adsorbed layer of water with a thickness of about 0.5 nm remains on the wall, which reduces the effective radius of the pore and consequently increases the capillary pressure across oil/water interface.58 If we take into account this adsorbed layer in the MSP calculations by assigning the pore width of 4.0 nm instead of 5.1 nm, the MSP threshold values increase from 159, 204, and 313 bar (as shown in Table 7) to 214, 274, and 404 bar, respectively. In the case of oil A (nonpolar oil), the capillary pressure of 404 bar is in fact in agreement with the MD simulation results. Table 7. Comparison between the threshold capillary pressures obtained from MD simulations and MSP calculations MD simulations

MSP method

Oil B – Water

250 – 300

159

Oil B – Brine

300 – 350

204

Oil A – Water

400 – 450

314

The second possible explanation for this discrepancy is that the IFT between oil and water inside the pore could be slightly influenced by calcite/water interactions. As illustrated in Figure 2, we observed that the calcite surface affects the orientation of the two water layers nearest to it. The first layer of water molecules is positioned so that the oxygen in water can have electrostatic interactions with Ca2+ while the second layer arranges itself so that one of the hydrogens in water can form H-bonds with oxygens in carbonate. It is possible that the strong ordering of water molecules in the adsorbed layers could prevent them from having optimal electrostatic interactions (i.e., polar interactions and H-bonding) with the oil polar molecules and as a result, the IFT increases to some extent. For a 4.0 nm pore and a contact angle of 23o, IFT should be greater than 28.1 and 33.7 mN/m in order for Pcth from the MSP method to be greater than 250 and 300 bar, respectively. These back-calculated IFT values are about 13 – 25 % larger than those obtained from the MD simulations (see Table 2).


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4. CONCLUSIONS In this study we conducted an integrated series of MD simulations to investigate the effects of wall-fluid interactions (i.e., nano-confinement effects) on the threshold capillary pressures of crude oil - water/brine displacements in an angular calcite mesopore. We utilized detailed atomistic models to represent the fluids and calcite surface in order to account for the electrostatic interactions (including H-bonding) between polar components and the calcite. Accordingly, mixtures of various polar and nonpolar oil molecules were considered to create more realistic models of typical black crude oils. The interfacial tension and contact angle values were determined for different oil compositions and brine salinities, and various T and P conditions. The trends observed in the simulations of IFT and CA indicated that the addition of polar components in the crude oil decreases the IFT while increasing the CA, although calcite remains strongly water-wet. Increase in water salinity, on the other hand, increases the IFT while it has negligible effect on the CA. The adsorption of oil molecules at water and calcite interfaces were also examined and the results were interpreted according to the specific interactions between the oil and water and calcite surfaces. The threshold capillary pressures of oil-water/brine displacements in a calcite mesopore with a square cross-section, were then obtained from MD simulations and compared against those generated using the MSP method. It was observed that MD simulations produce greater pressures compared to the MSP counterparts. This discrepancy was attributed to the adsorption of water layers on the pore walls and the strong ordering of water molecules in the adsorbed layers.

ASSOCIATED CONTENT Supporting Information Snapshot of a water droplet on calcite surface surrounded by oil, structure of nonpolar oil molecules, composition of nonpolar fraction of crude oil, number of water and oil molecules used for the IFT simulations, change of IFT with simulation time, total Coulomb energy of water and brine at ambient and reservoir conditions, composition of the brine used in the MD simulations, Coulomb energies between water molecules and ions in brine, density profiles of oil polar molecules in contact with water, density profiles of water and brine during the IFT simulations at ambient and reservoir conditions, relative densities of oil polar molecules at oil and water-brine interface at ambient and reservoir conditions, snapshot of carbazole aggregates in oil-B at ambient (top) and reservoir (bottom) conditions, Buckingham parameters between Ca2+ and heteroatoms (O and N) found in the polar molecules of crude oil, density profiles of oil polar molecules in contact with calcite.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ACKNOWLEDGEMENTS We gratefully acknowledge financial support of Hess Corporation and the School of Energy Resources at the University of Wyoming.

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