Article
pubs.acs.org/Langmuir
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 East University Avenue, Laramie, Wyoming 82071, United
States
S Supporting Information
*
ABSTRACT: Unconventional reservoirs such as hydrocarbon-bearing shale formations
and ultratight 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 nanometersize pores and ultralow porosities and permeabilities. In a
recent study by Saraji et al.,1 the average pore radii of several
reservoir samples from Bakken formation was reported to be
within 5 to 100 nm range. Better assessment of hydrocarbon
recovery from these ultratight 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
© 2016 American Chemical Society
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 porescale 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 Mayer-Stowe-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
Pcthow =
γow[Low,t + Los,t cos(θow )]
Ao,t
(1)
Received: December 24, 2015
Revised: March 19, 2016
Published: March 24, 2016
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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 generated using the MSP method. This is then
followed by an explanation of the differences we observe.
Section 4 lists the conclusions.
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, γow is the interfacial tension (IFT) between oil and
water, and θow 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 well-known Young−Laplace equation
Pcthow =
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 LennardJones potentials with a cutoff distance of 1.4 nm. Long-range
electrostatic (columbic) interactions beyond the cutoff 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 4.5 × 10−05 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 (γ) value was then
calculated using the following equation29
2γow cos(θow )
r
(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 nanoconfinements. 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 coarse-grained 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 nonpolar 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 nonzero 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/
γ=
Lz ⎡
⎤
1
⎢⟨Pzz⟩ − (⟨Pxx⟩ + ⟨Pyy⟩)⎥⎦
2⎣
2
(3)
where Lz is the simulation box size in the Z direction and ⟨Pαα⟩ is the
ensemble average of normal pressure in the α direction during the
simulation.
2.2. Contact Angle. 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 half-cylinder 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 Nose-Hoover thermostat
may create a 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
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Figure 1. Simulation setup for the capillary pressure measurements (left) and the top view of the calcite mesopore (right).
Table 1. Molecular Structure of Polar Organic Components of the Crude Oil Used in This Study
Figure S1 of the Supporting Information). Visualization and image
processing were performed using VMD34 and ImageJ35 software,
respectively.
⎛ 2ab ⎞
⎟
θ = sin−1⎜ 2
⎝ a + b2 ⎠
D Ewald calculations was about 10%. 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 cutoff distance,
which are unaffected by the choice of Ewald summation. Therefore, we
considered using a 3-D Ewald summation technique, as it was more
stable during the simulations.
(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.
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-
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 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).
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disturb their network of H-bonds. The average number of Hbonds between water molecules decreases from 12.5 × 103 at
ambient conditions to 11.1 × 103 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 8.15 × 103 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
To create the polar fraction, the most abundant functional
groups in crude oils were considered; sulfur is mostly found in
thiophene, thiol, sulfide, and disulfide structures. Carboxylic
acids, phenols, and ketones are the most abundant oxygenbearing functional groups while nitrogen atoms are typically
found in aromatic structures.47 Table 1 lists the 12 polar
molecules considered in this work (the abbreviation we used
for the name of each molecule is shown inside the parentheses).
A mixture with equal molar concentrations of these molecules
was chosen to represent the polar fraction of crude oil.
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
experimentally measured 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/mol, 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
Table 3. Relative Density of Oil Polar Molecules at the Oil/
Water Interface at Reservoir Conditions
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
reservoir conditions
46.4 ± 0.18
Oil-B − water
42.8 ± 0.35
Oil-B − water
51.1 ± 0.46
Oil-B − brine
ambient conditions
reservoir conditions
reservoir conditions
24.7 ± 0.5
22.7 ± 0.5
29.1 ± 0.85
component
relative density
Carbazole
Quinoline
Indole
Benzoic acid
Naphthenic acid
Nonanoic acid
Nonanone
Propylphenol
Benzothiophene
Nonanethiol
Methyloctyl-sulfide
Methyloctyl-disulfide
18.22
2.58
2.23
1.85
1.90
1.56
1.38
1.68
1.86
0.41
0.33
0.30
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 selfassociate 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
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
It is well-known 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. By
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.
The decrease of the electrostatic interactions at higher T and
P is related to the higher kinetic energy of water molecules that
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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 1.0 × 106 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°, 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 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 {101̅4} 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 the SPC/E water model. Replacing the SPC-FW with the
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°; however, the contact angle of water and oil A
was found to be between 0° and 5°. 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
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).
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 −3.18 × 105 to −2.89 ×
105 kJ/mol. Similarly, the nonbonding potential energy changes
from −3.40 × 105 to 3.01 × 105 kJ/mol and the oil density
decreases from 895 to 848 g/L. As a result, the weaker
interactions between oil molecules at higher T and P lead to
greater 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 {101̅4} 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
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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
Table 5. Interaction Energy (kJ/mol) between Calcite
Components and Oil Polar Molecules at Ambient
Conditions
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Table 4. Relative Density of Oil Polar Molecules on Calcite
at Different T and P Conditions
component
ambient conditions
reservoir conditions
Carbazole
Quinoline
Indole
Benzoic acid
Naphthenic acid
Nonanoic acid
Nonanone
Propylphenol
Benzothiophene
Nonanethiol
Methyloctyl-sulfide
Methyloctyl-disulfide
Benzene
0.14
0.81
1.17
1.06
1.11
1.17
1.32
1.04
1.91
3.24
0.96
0.80
0.14
0.40
2.75
4.48
3.01
3.47
3.27
3.01
3.81
2.10
0.74
0.24
0.11
0.37
CO32−)
CO32−)
CO32−)
CO32−)
Indole
Indole
Indole
Naphthenic acid
Naphthenic acid
Naphthenic acid
Nonanethiol
Nonanethiol
Nonanethiol
Benzene
Benzene
Benzene
Coulomb
LJ
Coulomb +
LJ
1824
−3370
−1546
−2253
−729
−2982
−203
−1146
−1350
465
−960
−495
−58
−236
−294
296
−163
134
−71
−1417
−1488
−114
−570
−685
1766
−3606
−1840
−1957
−892
−2849
−274
−2563
−2838
351
−1530
−1180
Table 6. Interaction Energy (kJ/mol) between Calcite
Components and Oil Polar Molecules at Reservoir
Conditions
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
Ca2+
CO32−
(Ca2+ +
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 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 the 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
CO32−)
CO32−)
CO32−)
CO32−)
CO32−)
CO32−)
CO32−)
CO32−)
Quinolone
Quinolone
Quinolone
Indole
Indole
Indole
Naphthenic acid
Naphthenic acid
Naphthenic acid
Nonaic acid
Nonaic acid
Nonaic acid
Benzoic acid
Benzoic acid
Benzoic acid
Nonanone
Nonanone
Nonanone
Propylphenol
Propylphenol
Propylphenol
Nonanethiol
Nonanethiol
Nonanethiol
Coulomb
LJ
Coulomb +
LJ
−5945
3049
−2896
6846
−11492
−4646
−7007
−1109
−8115
−6185
−863
−7048
−5758
−2305
−8063
−15222
10441
−4782
−2069
−3733
−5802
−35
−120
−155
−15
−657
−672
−177
−626
−804
869
−223
646
742
−162
580
754
−265
489
868
−1187
−319
490
−306
184
−7
−155
−162
−5960
2391
−3568
6669
−12118
−5450
−6138
−1331
−7470
−5443
−1025
−6468
−5003
−2570
−7573
−14355
9254
−5100
−1579
−4039
−5618
−42
−276
−318
that LJ and columbic potentials are proportional to
1
r6
and 1 ,
r
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
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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).
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 interaction between NPAC and calcite is almost 3 times
greater at reservoir conditions compared to ambient conditions
due to its higher adsorption propensity.
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 −30.4 × 103 to −26.3 × 103
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
oil−water interface was found to decrease by 40% when 0.1
mol % of benzenesulfonic acid was added to the oil.
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 and 300 bar.
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 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
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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 displacement 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.
Figure 3. Total number of organic atoms during the MD simulations
with various pressure differences imposed on the system.
Table 7. Comparison between the Threshold Capillary
Pressures Obtained from MD Simulations and MSP
Calculations
Oil B−Water
Oil B−Brine
Oil A−Water
MD simulations
MSP method
250−300
300−350
400−450
159
204
314
■
from MD simulations were considerably greater than those
obtained from the MSP calculations. We attribute the
discrepancy to the following: 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
the 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.
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 23°, 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).
ASSOCIATED CONTENT
S Supporting Information
*
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.langmuir.5b04713.
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 (PDF)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
4. CONCLUSIONS
In this study we conducted an integrated series of MD
simulations to investigate the effects of wall−fluid interactions
(i.e., nanoconfinement effects) on the threshold capillary
pressures of crude oil−water/brine displacements in an angular
ACKNOWLEDGMENTS
We gratefully acknowledge financial support of Hess Corporation and the School of Energy Resources at the University of
Wyoming.
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■
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