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\begin{document}

\title{Oil-Water Transport in Clay-Hosted Nanopores: Effects of Long-Range
Electrostatic Forces}



\author[1]{Hao Xiong}%
\author[2]{Deepak  Devegowda}%
\author[2]{Liangliang Huang}%
\affil[1]{University of Oklahoma Norman Campus}%
\affil[2]{University of Oklahoma}%


\vspace{-1em}



  
  \date{June 11, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
Charged clay surfaces can impact the storage and mobility of hydrocarbon
and water mixtures. Here, we use equilibrium molecular dynamics (MD) and
nonequilibrium MD simulations to investigate hydrocarbon-water mixtures
and their transport in slit-shaped illite nanopores. We construct two
illite pore models with different surface chemistries:
potassium-hydroxyl (PH) and hydroxyl-hydroxyl (HH) structures. In HH
nanopore, we observe water adsorption on the clay surfaces. In PH
nanopores, however, we observe the formation of water bridges because of
the existence of a local, long-range electric field. Our NEMD
simulations demonstrate that the velocity profiles across the pore
depends strongly on water concentration, pore width and the presence or
absence of the water bridge. This fundamental study provides a
theoretical basis for understanding nanofluidics with charged surfaces
and can be applied in such as biological processes, chemical and
physical fields, and the oil and gas extraction in clay-rich formations.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

The behavior of fluids confined in nanopores is significant for
understanding and resolving a suite of challenging problems such as
nanofluidic technology\textsuperscript{1}, biochemical
flows\textsuperscript{2} and membrane separation\textsuperscript{3}. The
structure and dynamics of confined fluids differ drastically from those
in bulk condition\textsuperscript{4--9} as a result of interactions with
the nanopore walls\textsuperscript{10--12}. With charged surfaces, this
effect can be more pronounced through the creation of electric double
layer (EDL) structures \textsuperscript{13,14} and the behavior of water
in the EDL\textsuperscript{15,16}. These phenomena merit a deeper look
in to liquid transport through nanoporous structures with charged
surfaces.

There have been several studies focusing on nano-confined fluid
structures adjacent to charged surfaces. Urashima et al. discuss the
structure of water at a negatively charge silica surface and demonstrate
that the closest water molecules form hydrogen bonds with the negatively
charged silica surface\textsuperscript{17}. Dobrynin et al. investigate
adsorption between a polyampholyte chain and a charged
surface\textsuperscript{18} while Zhang et al. demonstrate that the
charged surface can regulate molecular orientation and
interaction\textsuperscript{19}. Tasca et al indicate that a positively
charged surface can enhance electron transfer\textsuperscript{20} and
Dreier et al. state that the alignment and transport of water molecules
are influenced by charged surfaces\textsuperscript{21}. Ehre et al.
conclude that water molecules freeze differently on positively and
negatively charged surfaces\textsuperscript{22} and Lahann et al.
demonstrate that charged surfaces can switch interfacial properties,
such as wettability in response to an electrical
potential\textsuperscript{23}. Lis et al. state that in addition to
causing water alignment at the surface, the charged surface can lead to
surface-charge screening\textsuperscript{24}.

These contributions enhance our understanding of fluid confinement
within charged nanopore surfaces; however, a more complete picture
should encompass a discussion of transport. Clay minerals are one of the
most fundamental and abundant substances on earth
\textsuperscript{25}and can be used as adsorbents\textsuperscript{26},
carbon dioxide storage and sequestration\textsuperscript{27,28} as well
as water purification\textsuperscript{29}. Generally, clay minerals have
negative surface charges and nonbonded cations\textsuperscript{30,31}
creating negative and positively charged surfaces that make fluid
transport quite complex\textsuperscript{32}. There is also strong
evidence that the cations in the fluid show impacts both on the
structure and storage of fluid\textsuperscript{15,33--36}.

Mixture flow in nanopores, such as flow of red blood
cells\textsuperscript{37}, drug delivery\textsuperscript{38} and oil and
gas production from shales\textsuperscript{39} are quite common. In our
work, a dodecane and ethane mixture form the non-wetting hydrocarbon
phase and water the wetting fluid phase\textsuperscript{40--42}. We use
equilibrium molecular dynamics (EMD) and nonequilibrium MD (NEMD) to
investigate the structure and transport of hydrocarbon-water mixtures in
clay-hosted nanopores with different charged surface chemistries.

Our work is prepared as following: Section 2 shows the construction of
different clay models with varying surface chemistries and clay-hosted
pores containing hydrocarbon-water mixtures in a molecular dynamics
simulation setup. In total, this section discusses 42 MD simulations
with varying pore size (5 nm, 10 nm and 15 nm), water concentration
(0-100\%) and surface charges. Section 3 provides a thorough analysis on
fluid structure based on results from Section 2 and Section 4 discusses
transport of the hydrocarbon-water mixture based on the results from
Section 2 and 3. In Section 5, we show how the single-phase velocity
profiles are different for PH and HH pores and finally, we present our
conclusions in Section 6.

\section*{2. Models and Methodology}

{\label{models-and-methodology}}

\subsection*{2.1 Structure of illite and charged surface
chemistry}

{\label{structure-of-illite-and-charged-surface-chemistry}}

Kaolinite, illite, chlorite and smectite are the most commonly occurring
clay minerals\textsuperscript{43} with illite being the most common
diagenetic product in shales\textsuperscript{44}. Generally, clay-hosted
pores in shales are slit-shaped or cylindrical, with few occurrences of
oval- and cone- shaped pores\textsuperscript{45,46}. Because slit pores
are the most prevalent\textsuperscript{47}, we focus on investigating
fluid transport in illite-hosted slit-shaped pores. We refer the readers
to our previous work and those of others\textsuperscript{42,48} for a
more detailed description of the illite unit cell with chemical formula,
K{[}Si\textsubscript{7}Al{]}(Al\textsubscript{4})O\textsubscript{20}(OH)\textsubscript{4}.
In Fig.1, we show one illite layer comprising 20-unit cells. 2 illite
layers form the top pore surface and the other two illite layers form
the bottom. Each illite pore model has three different basal spacings
(5nm, 10nm, and 15nm).

There are generally four illite slit pore structures discussed in
literature based on charged clay surface chemistry: potassium-hydroxyl
(PH)\textsuperscript{49}, hydroxyl-hydroxyl (HH)\textsuperscript{50},
potassium-potassium (PP)\textsuperscript{51}, and a
structure\textsuperscript{52} between the PH and HH pore systems. The
corresponding illustrations are shown in the Fig.S-1 in Supporting
Information. This work considers only the PH and HH pore systems and a
schematic of both are shown in Figs. 2a-b.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Fig. 1} Structure of one illite layer from top (a) and side(b)
views

Color codes: O, green; Al, grey; H, white; Si, orange;
K\textsuperscript{+}, light grey.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Fig. 2} Configurations of PH and HH pore systems at 5nm pore
width. Color definitions are same in Fig.1. Pore systems at 10 nm and 15
nm pore width are not presented but are used in this study.

Seven water concentrations (Cw) are constructed for each of the three
slit pore widths (5, 10 and 15 nm). All the simulation models are shown
in Table S-1 in Supporting Information. In the interests of space, we
only show the initial configurations of the PH models with a pore width
of 5nm in Fig. 3. The temperature and pressure are kept constant. In
order to keep pressure conditions similar across all models, an increase
in water concentration is accompanied by a decrease in the number of
hydrocarbon molecules.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Fig. 3} Initial configurations of the seven PH slit pore models
of 5 nm width with varying water concentration. Cw stands for the water
concentration. The color codes of clay are as in Fig. 1. In the first
panel, the direction of the arrows indicates the direction of an imposed
acceleration in subsequent sections of this paper. The fluid-color
regimes: ethane (light green), H\textsubscript{2}O (red) and dodecane
(light blue).

\subsection*{2.2 Simulation Details}

{\label{simulation-details}}

Our modeling relies on the use of the ClayFF and OPLS All-Atom force
field to describe illite\textsuperscript{53,54} and organic
components\textsuperscript{55}respectively, while the flexible SPC model
and the shake algorithm are applied to model water. Lorentz-Berthelot
mixing rules describe the interactions between different atoms. We use
LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator)
\textsuperscript{56} with periodic boundary conditions applied in 3
directions. A more detailed description is available in our previous
work\textsuperscript{42,48}.

Our workflow is as follows: In the initial set-up, fluid molecules are
placed randomly between the slit pore using the Packmol
package\textsuperscript{57}. We then run equilibrium MD (EMD)
simulations using an NPT ensemble for 5 ns. After equilibrium of
isothermal--isobaric (NPT) ensemble, we further run the simulations for
another 5 ns with a canonical (NVT) ensemble. Temperature and pressure
are maintained at 400 atm and 350 K using Parrinello-Rahman
barostat\textsuperscript{58} and Nose Hoover
thermostat\textsuperscript{59} respectively.

After EMD simulations, non-equilibrium MD (NEMD) simulations are
performed for another 10 ns to mimic hydrocarbon-water transport.
Several methods exist for inducing flow in molecular dynamics, such as
forced\textsuperscript{60--62}, surface-induced, pressure
difference\textsuperscript{63}, osmotic pressure\textsuperscript{64} and
gravitational approaches\textsuperscript{65--67}. In our simulations, we
adopt the gravitational technique because other methods have been known
to cause a distortion of the velocity-field and density profile along
the flow direction\textsuperscript{67--69}. A uniform external force
(along the x-direction as shown in Fig. 3), is imposed on all molecules
inside the illite nanopores\textsuperscript{70,71}. Published literature
suggests using small accelerations on the order of
10\textsuperscript{-4} to 10\textsuperscript{-3} nm/ps\textsuperscript{2
72,73} to avoid velocity jumps in the system and therefore, in our
study, the acceleration ranges from 0.0005 to 0.002
nm/ps\textsuperscript{2}.

It should be noted that in MD simulations, fluid temperature is
calculated from the kinetic energy\textsuperscript{74}. However, in NEMD
simulations, the molecule velocities in the direction of the driving
force consists of both thermal velocities and the imposed center-of-mass
velocity. To ensure the temperature is maintained, our fluid temperature
calculations do not include the center-of-mass
velocity\textsuperscript{69}. The temperature and pressure during the
NEMD simulations are shown in Fig. S2 in the Supporting Information.

\section*{3. Equilibrium Configurations of Fluid in PH and HH Pore
Systems}

{\label{equilibrium-configurations-of-fluid-in-ph-and-hh-pore-systems}}

Fig. 4 presents the equilibrium configurations of water and hydrocarbon
and number density profiles (along z-direction) in 5 nm HH (Fig.4a-b)
and PH (Fig. 4c-d) nanopores. We do not show the illite structure for
clarity.

Fig. 4a shows a water film adjacent to the clay surfaces in the HH pore
system. Water preferentially adsorbs on the surfaces because of the
significant electrostatic force and hydrogen bond between water
molecules and the surfaces\textsuperscript{75}. This observation is
analogous to water adsorption in silica-based pore
structures\textsuperscript{69,76}. Increasing the water concentration to
58.82\% as shown in Fig.4b leads to an increase in the adsorbed film
thickness. The number density of water (shown in the blue line) and
hydrocarbon (black solid line) are relatively constant across the pore.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Fig. 4} Distribution of water (in blue) and hydrocarbon (in
black) in hydroxyl-hydroxyl (HH) and potassium-hydroxyl (PH) in 5nm.
Illite is not shown for clearance. The figure shows that water-bridges
are prevalent in PH pore systems, while adsorption is dominant in HH.

The distribution of water in PH pores is in marked contrast to the HH
nanopores. Fig. 4c shows the water-bridge phenomenon (corresponding to
the peak in the number density of water shown in a blue line) at Cw of
18.87\%. Increasing the Cw to 58.82\% as shown in Fig.4d leads to the
two water bridges demonstrated by the existence of two peaks in the
water density profile. This effect has been attributed to `capillary
condensation'\textsuperscript{76--78}, but we present another argument
in this paper for the existence of water bridges. If this were purely
capillary condensation, the water bridge should vanish as pore width
increases. However, even at 10nm and 15nm pore widths, the water bridges
remain intact (See Fig.S-3 in Supporting Information).

It is important to note that the water-bridge phenomenon can also exist
in an HH clay-hosted pore under specific conditions, typically at higher
water concentrations and for smaller pore widths. Table 1 shows the
conditions under which a water bridge occurs.

\textbf{Table 1} . The matrix below shows conditions under which a water
bridge will form for the models considered in this study.\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
& & \textbf{HH} & \textbf{HH} & \textbf{HH} & \textbf{PH} & \textbf{PH}
& \textbf{PH}\tabularnewline
\midrule
\endhead
& & \textbf{5nm} & \textbf{10nm} & \textbf{15nm} & \textbf{5nm} &
\textbf{10nm} & \textbf{15nm}\tabularnewline
\textbf{Water concentration} & 0\% & NA & NA & NA & NA & NA &
NA\tabularnewline
& 18\% & & & & x & x & x\tabularnewline
& 56\% & & & & x & x & x\tabularnewline
& 71\% & x & x & & x & x & x\tabularnewline
& 80\% & x & x & x & x & x & x\tabularnewline
& 100\% & NA & NA & NA & NA & NA & NA\tabularnewline
\bottomrule
\end{longtable}

\subsection*{3.1 Analysis of the Electric
Field}

{\label{analysis-of-the-electric-field}}

Inspired by the work of Zhang et al.\textsuperscript{79}, Namin et
al.\textsuperscript{80}, Fuchs et al. \textsuperscript{81,82}, Ponterio
et al. \textsuperscript{83}, and Chen et al. \textsuperscript{84} who
indicate that an electric field can change the OH stretching band and
water distribution, our hypothesis is that the positive potassium
cations and negative surface in clay nanopores might produce an instant
local electric field. This sequentially changes the behavior of confined
fluids leading to the water bridge phenomenon. To validate this
hypothesis, we calculate the electric field of PH and HH pore systems by
computing the electrostatic force on a test atom with charge \emph{e} .

This is done by measuring a cross-section of the pores devoid of any
fluid. Fig.5 shows the calculated electric field in 5 nm, 10 nm and 15
nm PH and HH pores. The average strengths of electric field in 5 nm, 10
nm and 15 nm PH pores, as shown in Fig.5a, are 12.92 V/nm, 8.72 V/nm,
6.56 V/nm with standard deviation of 0.51, 0.39 and 0.44 respectively.
While in theory the electric field should be
uniform\textsuperscript{85}, non-uniformly distributed charges in the
clay minerals cause variations in the electric field near the clay
surface.

Fig. 5b shows the calculated electric field in 5 nm, 10 nm and 15 nm HH
pores which range from -1.5 V/nm and 1.5 V/nm. In Fig.5b, near the upper
surface, the strength of electric field is about 1.5 V/nm. Moving across
the pore, the field strength decreases to zero and its absolute value
increases again (with an accompanying change in direction). Such
electric fields have also been observed to occur naturally in zeolite
cavities\textsuperscript{86--88}. In both pore systems, an increase in
pore width is accompanied by a decrease in electric field strength, an
observation that is consistent with Bueno et al.\textsuperscript{85}.

Skinner et al.\textsuperscript{89}, Cramer et al.\textsuperscript{90}and
Hao et al.\textsuperscript{32} also indicate that electric field
strengths larger than 1 V/nm change the structure of water. A comparison
of the electric fields in Fig.5 suggests that PH pores exhibit stronger
and more long-range fields in comparison to HH pores. In the HH pore,
the effective length of the electric field \textgreater{} 1V/nm is about
0.5 nm as shown in Fig.5b impacting the water distribution only near the
surface. In the PH nanopore, a strong electric field extends across the
entire pore width promoting the formation of water bridges.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Fig. 5} Calculated electric field in different width. Absolute
values of the electric field strengths in PH pores (left) are observed
to be larger than those in HH nanopores (right). Increases in pore width
decreases the strength of the electric field in both pore systems.

In Fig.6, we discuss the orientation of the water molecules at a
concentration of 58.82\% in both pore systems. The water orientational
direction is defined as the angle between V\textsubscript{1} and
V\textsubscript{2} vectors (Fig. 6a), where V\textsubscript{1} is a unit
vector normal to the surface and V\textsubscript{2} is the OH vector.
Fig. 6b shows one sharp peak in the PH pore at 130\selectlanguage{ngerman}° indicating that the
two OH bonds are aligned with the direction of the electric field. These
results are similar to those presented in Skinner et
al.\textsuperscript{89}. The OH bond orientation in HH pores is more
heterogeneous with a relatively weaker peak at 90°, which is consistent
with Cramer et al. \textsuperscript{90}. Figs. 5 and 6 confirm that the
existence of electric field influences the orientation of water
molecules within the pore.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Fig. 6} In (a), V1 is the unit normal vector. V2 is the OH
vector (OH bond angle). \selectlanguage{greek}θ \selectlanguage{english}is the angle between two vectors. In (b), we
show the OH bond angle for all water molecules for different pore widths
in HH and PH pores. In PH pores, a dominant angle of 130\selectlanguage{ngerman}° is observed
while in HH pores, the OH bond angles are largely random with a weaker
peak at 90°. The electric field of \textbf{Fig. 5} influences the
orientation of water molecules in both pore systems.

\section*{4 Results and Discussion: Fluid
Transport}

{\label{results-and-discussion-fluid-transport}}

\subsection*{4.1 Fluid Transport in HH
Nanopores}

{\label{fluid-transport-in-hh-nanopores}}

In this section, we report on the hydrocarbon and water velocity
profiles with different accelerations (0.0005, 0.001, and 0.002
nm/ps\textsuperscript{2}) at 350 K and 400 atm. This would be analogous
to imposing advective flow on the fluid confined within the pores. The
velocity profile is obtained applying the bin
method\textsuperscript{91}which is shown in Supporting Information.

We present the water (Fig. 7a) and hydrocarbon (Fig. 7b) velocity
profiles at 0.0005 nm/ps\textsuperscript{2} in the 5 nm HH nanopore.
Because the hydrocarbon and water velocity profiles at the acceleration
of 0.001 nm/ps\textsuperscript{2} and 0.002 nm/ps\textsuperscript{2}show
similar trends with that of 0.0005 nm/ps\textsuperscript{2}, they are
not shown here and provided in Fig.S4 in Supporting Information.

Fig. 7a indicates that the water velocity changes with increasing water
concentration directly as a result of the growth in the thickness of the
adsorbed layer of water as shown in Fig. 8. A thicker adsorbed layer
impedes flow. At 100\% water, we observe the classical parabolic
signature of liquid flow in slit-pores.

Fig. 7b indicates that increasing water concentration promotes
hydrocarbon flow up to a point. The initial increase has been attributed
to the creation of smooth surfaces following adsorption of
water\textsuperscript{69}. Subsequent increases decrease the effective
flow radius for hydrocarbon flow as shown in Fig. 8, leading to a
decline of hydrocarbon velocity.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Fig.7} Water and hydrocarbon velocity profiles at 0.0005
nm/ps\textsuperscript{2} in 5 nm HH nanopore. Cw stands for water
concentration. Water concentration is seen to strongly impact both water
and hydrocarbon velocities.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

\textbf{Fig. 8} Distribution of water molecules for various water
concentrations. Hydrocarbon is not shown. On the left, Cw = 18.97\% and
on the right, Cw = 71.43\%. Increases in water concentration increases
the adsorbed layer thickness that in turn influences water and
hydrocarbon velocities.

Fig. 9 shows the water and hydrocarbon velocity profiles at a higher
value of acceleration of 0.002 nm/ps\textsuperscript{2} in a larger 15
nm HH nanopore (velocity profiles for the 10 nm HH nanopore are provided
in Fig. S5 in Supporting Information). The flow profiles are is observed
to be more complex at all values of saturation and is a function of the
location of the respective phases within the pore.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\textbf{Fig. 9} Water and hydrocarbon velocity profiles at 0.002
nm/ps\textsuperscript{2} in 15 nm HH pores. The flow profiles for both
phases appear more complex and simply correspond to the local phase
densities within the pore.

Fig.10 shows the velocity profiles in a 5 nm, 10nm and 15nm HH pore with
a water concentration of 71.43\%. The peaks and the troughs in the
velocity profiles correspond to the local density of the water and
hydrocarbon phases within the pore.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

\textbf{Fig. 10} Distribution of water at 0.002
nm/ps\textsuperscript{2}and Cw = 71.43\% in 5nm, 10nm, 15nm HH pores.
The hydrocarbon molecules are not shown. The result indicates that at
each pore size, the peaks and troughs in the velocity profiles
correspond to the local density of each of the phases.

We also note that the concentration of water and pore size can also
change the distribution of hydrocarbon and water. At specific water
concentrations (Cw = 71.43\% and pore size= 10 nm), we can also observe
water bridges in HH nanopores.

\subsection*{4.2 Fluid Transport in PH
Nanopores}

{\label{fluid-transport-in-ph-nanopores}}

In the previous section, we reviewed transport of water and hydrocarbon
in HH pore systems where water bridges are largely absent except under
some specific conditions. In this section, we present the corresponding
results for PH pores where water bridges are prevalent across multiple
pore sizes and water concentrations.

The water and hydrocarbon velocity profiles for 54 NEMD simulations in
PH nanopore are provided in Figs. S6-7 in Supporting Information. In
this section, we only analyze a few representative hydrocarbon-water
velocity profiles in PH nanopores and address the effects of pore size,
water concentration and electric field (the effects of acceleration are
provided in Supporting Information).

\textbf{Effect of Pore size}

Fig.11 shows the water (Fig.11a) and hydrocarbon (Fig.11b) velocity
profiles at an acceleration and water concentration of 0.002
nm/ps\textsuperscript{2} and 71.43\% respectively in different PH
nanopore sizes. Water and hydrocarbon velocities increase with an
increase of pore size which is in agreement with Liu et
al.\textsuperscript{41}. Additionally, water and hydrocarbon velocity
profiles are parabolic in the 5 nm PH nanopore and show flatter profiles
for the 10nm and 15nm pores with increasing distance from the pore walls
and the accompanying decrease in fluid-pore wall interactions.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

\textbf{Fig. 11} Water and hydrocarbon velocity profiles at the
acceleration and water concentration of 0.002
nm/ps\textsuperscript{2}and 71.43\% respectively in different PH
nanopore sizes. The result indicates that pore size impacts the velocity
patterns. At 5nm, we observe a parabolic shape for the flow profiles
which get progressively flatter as the pore size increases.

In Fig. 12, we take a closer look at the water bridges present in the PH
pores at a water concentration of 71.43. Hydrocarbon molecules are not
shown for clarity. The red-colored water molecules are those adjacent to
the pore surface and the yellow-colored water molecules are those
present in the water bridge. Fig. 12a shows the distribution of water in
a 5nm PH pore obtained from our equilibrium MD (EMD simulations) on top
and under 0.002 nm/ps\textsuperscript{2} on the bottom. The water bridge
in Fig. 12a is a sheet extending across the entire x-direction in the
5nm PH nanopore.

Figs. 12b-c show the corresponding information for 10nm and 15nm pore
widths. Water molecules move freely between the water bridge and
adsorbed layer resulting in the velocity profile in Fig. 12a (shown in a
blue line). However, when pore sizes increase to 10 nm or 15 nm, there
is limited or no exchange of water molecules between the film and the
bridge. The combination of a constant acceleration and no exchange
contributes to the flat velocity profiles observed in Figs. 12b-c.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

\textbf{Fig. 12} Molecular distribution and velocity profiles of water
in PH pores of different widths at a water concentration of 71.43\%. The
acceleration is 0.002 nm/ps\textsuperscript{2}. Hydrocarbon is not shown
for clarity. The red dots represent adsorbed water and the yellow dots
are those in the water bridge. In a 5 nm PH nanopore, acceleration
causes the adsorbed layer to exchange both mass and velocity with water
at the pore center. Increasing the pore size to 10 nm or 15 nm, as
revealed by the flatter velocity profile, no mass or velocity exchange
occurs between the adsorbed layer and water in the bridge or pore
center.

\textbf{Effect of Water Concentration}

Fig.13 shows the water (Fig.13a) and hydrocarbon (Fig.13b) velocity
profiles at 0.002 nm/ps\textsuperscript{2} in a 10 nm PH nanopore for
different values of water concentration. The velocity of water decreases
with increasing water concentration (Fig. 13a) because of the increased
thickness of the water bridge. The thickness of the water bridge at
water concentrations of 18.87\%, 58.82\%, 71.43\% and 80.00\% is 0.94
nm, 1.24 nm, 1.60 nm and 1.96 nm respectively. This is shown in Fig. S9
in Supporting Information.

Fig. 13b shows an increased hydrocarbon velocity for an initial increase
in the water concentration which has been attributed to the creation of
smoother surfaces for hydrocarbon flow\textsuperscript{69}. However,
when the water concentration is increased, the width of the water bridge
progressively increases (shown in Fig S10), thereby hampering
hydrocarbon flow.

Fig. 13 also indicates flat velocity profiles exist for both the oil and
water phases. Because of the hydrophilic surface, hydrocarbon molecules
are responding to the acceleration and are not strongly influenced by
the pore surfaces, leading to a flatter velocity profile.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

\textbf{Fig. 13} Water and hydrocarbon velocity profiles at the
acceleration of 0.002 nm/ps\textsuperscript{2} in 10 nm PH nanopore. The
result indicates that water concentration can impact the flow pattern.

\section*{5. Single-Phase Velocity Profile Comparison between HH and PH
Pores}

{\label{single-phase-velocity-profile-comparison-between-hh-and-ph-pores}}

This section focuses on the effect of the electric field single-phase
velocities for different pore sizes for a fixed acceleration of 0.002
nm/ps\textsuperscript{2} in PH and HH pores, we compare. The results are
shown in Fig. 14 indicating that the PH nanopore exhibits flatter flow
profiles at the pore center due to the presence of the electric field as
shown in Fig.5.

Normally, adsorption is the result of van der Waals forces, covalent
bonding and electrostatic attraction\textsuperscript{92}. In this work,
we do not consider covalent bonding\textsuperscript{93}. Therefore, in
our study, adsorption is solely due to the van der Waals force and
electrostatic attraction. Adjacent to the surface, these forces impact
fluid transport. However, van der Waals force quickly diminish for
increasing distances from the pore surface \textsuperscript{94}, while
the electrostatic interaction force can expand more than 10
nanometers\textsuperscript{32}.

Therefore, in the PH pore, fluid transport is controlled by the electric
field and imposed acceleration, leading to a flat pattern as shown in
Figs.14a-b. Increasing pore sizes for PH pores increases the width of
flat pattern as shown in Figs.14c-d because of the increase in the width
of the zone dominated by the electric field. However, in HH nanopore,
there is a negligible electric field at the nanopore center. Therefore,
classical parabolic shaped patterns are observed in HH nanopores as
shown in Fig.14.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}

\textbf{Fig. 14} Comparison of single phase (water and hydrocarbon)
velocities between HH and PH nanopores of different widths. The
self-generated electric field in PH pores and the imposed acceleration
dictate fluid transport in the center of the pore. For the same
acceleration, the fluid velocity profile is flat in PH pores and
parabolic in HH pores.

Fig. 15 shows the distribution of water in 5 nm PH and HH pores.
Hydrocarbon is not shown for clarity. During transport, a water bridge
persists in PH pores as shown in Fig.15a. This is because of the
stronger electric field. Fig.12 also confirm the persistence of water
bridges in PH pores irrespective of pore size. However, the water bridge
of the HH nanopore breaks down as shown in Fig.15b. We can infer that
the strength of the hydrogen bond in the water bridge in the HH nanopore
is weaker compared to the forces holding the water bridge intact in the
PH nanopores.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}

\end{center}
\end{figure}

\textbf{Fig. 15} Water distribution in EMD and NEMD simulations in 5 nm
PH (left) and HH (right) nanopore. Hydrocarbons are not presented for
clearance. It indicates that the water bridge breaks down during flow in
the NEMD simulation in the HH nanopore, demonstrating that the strength
of hydrogen bond is weak to persist the water bridge. However, in PH
nanopore, with the assistance of electric field, the water bridge
persists in NEMD simulations.

\section*{5. Conclusions}

{\label{conclusions}}

This study focuses on the use of Equilibrium Molecular Dynamics (EMD)
and Non-equilibrium MD (NEMD) simulations to investigate
hydrocarbon-water interactions, structure and transport in clay-hosted
nanopores with two different charged clay surface chemistries (HH and PH
nanopores). The following conclusions can be drawn from this work:

\begin{enumerate}
\tightlist
\item
  Under different water concentrations and pore sizes, PH clay pores
  support the formation of water bridges. In HH pore systems, water is
  largely present adjacent to the pore surface in an adsorbed layer.
  There are limited instances where a water bridge forms in an HH pore,
  however.
\item
  The strength of the self-generated electric field is stronger in PH
  pores in comparison to HH pores for all pore widths. This favors the
  water bridge phenomenon and strong alignment of the water molecules
  with the electric field.
\item
  With an imposed acceleration, the velocity profiles in HH and PH clay
  pores are different. Water preferentially flows adjacent to the pore
  surface for HH pores with hydrocarbon occupying the center of the
  pore. With PH pores, the water bridge persists under acceleration and
  a different velocity profile is observed irrespective of pore width.
\item
  As mentioned earlier, in HH pores, water bridges can form under
  specific conditions, but dissipate during flow. However, in PH
  nanopores, with the assistance of the electric field, water bridges
  exist under flowing conditions.
\end{enumerate}

\section*{Acknowledgements}

{\label{acknowledgements}}

The computing for this project was performed at the OU Supercomputing
Center for Education \& Research (OSCER) at the University of Oklahoma.
We thank Drs. Carl Sondergeld, Chandra Rai, Ali Tinni and Felipe Perez
for the discussions that helped shape this work.

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