Article
pubs.acs.org/JPCC
Molecular Dynamics Simulations of Retrograde Condensation in
Narrow Oil-Wet Nanopores.
William R. W. Welch* and Mohammad Piri
University of Wyoming, Department of Chemical and Petroleum Engineering, 1000 University Avenue, Department 3295, Laramie,
Wyoming 82071, United States
S Supporting Information
*
ABSTRACT: Molecular dynamics (MD) simulations were performed for a 70/30 wt % ethane/heptane mixture unconfined and
confined to 60 nm oil-wet nanocapillaries with square cross sectional
widths of 4 nm. Large pressure ranges along both prograde (310 K)
and retrograde (365 K) isotherms were examined. For the unconfined
fluid at 310 K, compression resulted in steady increases in density of
both ethane and heptane up to the predicted condensation point
where a sudden phase transition was observed. At 365 K, pressure
increases caused increased density in ethane but reduced density in
condensed heptane droplets and retrograde phase behavior was
observed as a gradual collapse of the denser phase with increased
pressure above 60 bar. In nanopores, surfaces with strictly repulsive
walls greatly favored association with ethane at all pressures and
promoted exclusion of heptane from the narrow pore at pressures inside the saturation curve. At the oil-wet surface, preferential
adsorption of heptane was seen, the extent of which depended on both temperature and pressure. At 310 K, capillary
condensation, primarily of heptane, was observed at all pressures spanning the saturation curve, maximizing at low pressures. At
365 K, heptane accumulation in the pore peaked at intermediate pressures. At lower pressures, two distinct phases were
observed: an adsorbed phase composed largely of the heavier molecule and a fluid phase composed mainly of the lighter
component. While both equilibrium adsorption and accumulation of fluid inside the pore was significantly reduced at pressures
below 30 bar along the retrograde isotherm, when pressure gradients were induced across the narrow pore, significant clogging
was observed at the low pressure end for pressures as low as 10 bar.
■
INTRODUCTION
In recent years, demand for domestic petroleum feedstock in
North America and the depletion of conventional reservoirs
worldwide has prompted increased global interest in unconventional petroleum reservoirs. Tight oil formations previously
considered to be too impractical and expensive for large-scale
production are now considered important fuel sources. Some of
the most formidable challenges in procuring petroleum from
these reservoirs stem from their low permeability, and, in shale
rocks, the affinity of hydrocarbons to the organic medium in
which it is generated.1 It has been shown that these types of
nanochannels, which can approach molecular dimensions,
constitute significant proportions of the material’s porosity;
accordingly, such pore networks are the key components of
hydrocarbon storage and mediation of fluid flow in shale
formations.2 As demand for hydrocarbon production from shale
formations increases, so does the demand for understanding
phase behavior and dynamics of petroleum compounds in
carbonaceous nanoconfined spaces.3−8
Kerogen in shale oil formations is a compressed amalgamation of large organic molecular networks which decompose
over time rendering free hydrocarbons confined to nanoscale
pore systems defined by the remaining organic solid.9,10 While
© 2015 American Chemical Society
production from shales is typically associated with low
molecular weight gases, shale rocks can also contain
considerable amounts of heavier species and, in general,
complex mixtures that may include water and brine coexist as
vapor, liquid, and surface-adsorbed phases.2,11 Among other
things, condensation and size exclusion are known factors that
complicate fluid behavior in shale pore networks, nonetheless,
current understanding of the behavior of petroleum mixtures in
shale nanonetworks is mostly speculative.12−14
Of particular interest for petroleum community are
retrograde fluids, which exhibit anomalous phase transitions
and solubility properties under high pressures and temperatures
that fall inside the saturation curve of the PV phase
diagram.15−17 Fluid mixtures exhibiting these properties have
been known for over a century, but recently interest has
increased as condensation of larger hydrocarbons in shale gas
formations has generated optimism with respect to increasing
production of heavier hydrocarbons as well as consternation
about the proclivity for condensates to seal pores and inhibit
Received: November 6, 2014
Revised: April 14, 2015
Published: April 15, 2015
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Scheme 1
gas production.15,16 Retrograde condensation is highly sensitive
to the concentration of fluid components and oil-wet networks
with high surface area to volume ratios can drastically alter fluid
compositions; consequently, adsorption and fluid phase
behavior of retrograde mixtures, which depend on the
migration history of the fluid, is complex.17
Given the obscure nature of deep subterranean pore
networks, especially at the nanoscale, computational modeling
is a naturally attractive way to examine physics involved in these
types of systems. For nanochannels with significant solid
surface area involving fluid particles with high Knudsen
numbers, accounting for molecular interactions at interfaces is
crucial. Consequently, molecular dynamics (MD) simulations
suitable for examining nanoscale systems are increasingly
practicable as computational resources become more readily
available. Fluid dynamics and phase phenomena of nanoconfined Lennard-Jones (L-J) fluids, united atom molecular
models, and to a larger extent, water, have been examined by
MD,18−23,24 and more so by Monte Carlo methods.25 Surface
interactions of confined methane, CO2, and some other
hydrocarbons have seen some treatment by MD,26−29 however,
similarly confined multicomponent petroleum fluids in nonmineral organic media still remain relatively unexplored by
molecular simulation.
In this study, we examine liquid/vapor and adsorption
behavior of a simple model system, a mixture of 70/30 wt %
ethane/heptane, the retrograde phase behavior of which was
first thoroughly demonstrated by Kay in 1938.15 First, large
simulations of the mixture (154 494 ethane molecules and
19 683 heptane molecules) were performed for prograde (310
K) and retrograde (365 K) isotherms in order to gain insight
into the molecular behavior involved in retrograde phase
transitions. Subsequently, the same fluid confined to solid, oilwet nanotubes 60 nm long with a square cross sectional width
of 4 nm was examined under variable pressures induced by
accelerating pistons on either side of the simulation cell as
illustrated in Scheme 1. Finally the same type of system was
used to simulate pressure gradients through shorter (40 nm)
tubes in order to examine condensation processes relevant to
extraction from organic shale.
simulations performed the Andersen thermostat (which
produced comparable results). Statistics were taken from the
final 9 ns of the production runs.
Solid walls for the pore with 4 nm square cross sections were
constructed as L-J spheres with radius of 0.5 nm in a face
centered cubic (fcc) lattice 4 particles thick. To mimic a
strongly oil-wet surface, interaction parameters were derived
such that the 2 nm thick layer of the coarse grained surface
particles produced a force field comparable to that produced by
stacks of associated dodecane molecules in the OPLS-UA force
field. This resulted in LJ spheres with σ of 0.47 nm having an ε
of 3.2 kJ/mol which corresponds well with parameters used in
similar coarse grained hydrocarbon models for dodecane.34−36
Solid particles were held in place using harmonic constraints in
all directions.
For simulations of the ethane/heptane fluid inside nanochannels, stochastic temperature control was employed through
the Langevine dynamics integrator, which is necessary for
nonequilibrium simulations, particularly when center-of-mass
motion is an important factor.37−39 While this can result in
nonconservation of momentum, we believe this is not an issue
in our study because we do not examine extremely nonequilibrium simulations, but in the case of pressure gradients,
quasi-static systems. Consequently, weak stochastic temperature coupling was used in these cases, with the inverse friction
constant set at 50 ps to minimize dampening of dynamics while
maintaining the desired temperature. In order to modulate
pressure, which could vary from one end of a channel to
another, pistons composed of 2 nm thick layers of L-J spheres
in an fcc lattice were placed on two ends of the pore/fluid
system, moving in the positive and negative z directions. Piston
particles were restrained in the x and y directions and assigned
high association energies with each other, forcing fcc layers to
remain intact and allowing for acceleration in the z direction to
create pressure in the system. Association energies between
piston and fluid particles were set to approximate hard-sphere
interactions as were energies between pistons and solid pore
walls. The piston induced pressure system was used for both
equilibrium and quasi-equilibrium simulations involving nanochannels.
In principle, grand canonical Monte Carlo simulations are
best suited to examine adsorption behavior of fluids, nevertheless, for the purposes of this study, relevant information
about the effects of pressure on phase phenomena of the
confined fluid could be adequately obtained by MD using a
large enough fluid volume. Because a highly parallelized MD
code is readily available in GROMACS, we were able to
examine a large number of simulations over large ranges of
pressures for long time periods using MD. Accordingly, data
presented here are for confined fluids, technically calculated in
the NVT ensemble, but effectively, under mobile piston
pressures, in the NPT ensemble.
Ensuring that large simulations of adsorption in narrow pores
have converged to true equilibrium states proved tedious
especially for systems with significant phase separation. For
■
METHODS
All MD simulations were performed in parallel using the OPLSUA force field30 as implemented in GROMACS 4.6.3
software.31 Interaction cutoffs were set to be 1.5 nm with the
function switched to begin continuously decaying to zero at 1.2
nm. In preliminary investigations, an integration time step of 3
fs, while producing higher bond energies (see Supporting
Information, Figure S1), produced vapor/liquid phase behavior
nearly identical to what was observed using shorter time steps,
and the long time step was used for all simulations. Equilibrium
simulations of bulk fluids were performed in the NPT ensemble
using the velocity-Verlet integrator, the MTTK barostat,32 and
the Nose−Hoover thermostat under strong coupling conditions for 45 ns.33 Initial configurations were obtained from
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example, initial rapid expulsion due to starting too far from
equilibrium may be followed by condensation of droplets
outside the pore, prohibiting the proper amount of heptane
from re-entering the pore on any reasonable time scale. We
were generally able to avoid said problem using the stepwise
equilibration from high to low pressure and most simulations
converged, such that average numbers of adsorbed particles did
not change for the final 25 ns after a total of 250 ns. For the
lower pressures at 310 K, equilibration times of 500 ns were
required.
■
In Figure 1a, contours for heptane illustrate how a single
component fluid should behave; for a pure fluid with strict
phase transitions, there are two main regions, a broad region of
lower densities and a narrower region, well separated, at higher
density. The probability profiles are unimodal and approximately Gaussian in shape, indicating only one phase at each
pressure. The gradual shift in the distribution centers between
2.5 and 10 bar is followed by a sudden increase at 12.5 bar.
Accordingly, a clear distinction between vapor and liquid
phases is predicted for pure heptane between 10 and 12.5 bar at
505 K. This is below the experimental value of 16 bar,15 which
is not surprising considering the OPLS-UA force field was not
parametrized for hydrocarbons at high pressures.
In Figure 1b, profiles of ln(ρ) vs density probability for the
binary ethane/heptane system exhibit some marked differences
between the two isotherms. At 310 K, distributions are
narrower. The high density tail above 20 bar increases slightly
in both area and density as pressure increases, but the two
phases are never distinct in the density plot under coexistence
conditions. There is a sharp transition to the liquid state at 30
bar, similar to what is seen in the single component system. At
365 K, the range of pressures in which phases coexist is
broader, consistent with experimental observation for isotherms
closer to the critical temperature. Interestingly, at the higher
temperature, the high density portion of the profiles, while
increasing in area, decreases in density as the system is
compressed. Along the 365 K isotherm, at lower pressures, the
two phases cover distinct regions of density which merge with
increasing pressure, eventually coalescing into a single phase at
72.5 bar. Again, phase transition pressures predicted for both
isotherms are underestimated, in both cases by approximately
10 bar.15
Ethane and heptane density profiles are examined separately
for each isotherm in Figure 2. At 310 K (Figure 2a), density
distributions for ethane generally follow the same trends as
those of entire fluid (Figure 1b), the main difference being that
the high density tails do not overlap with the liquid phase. In
the heptane distributions at 310 K, a sudden phase separation is
evidenced by the leftward shift of the low density portion of the
contour above 20 bar accompanied by an increase in the area of
the high density region of the curve. For heptane, the high
density portion does span the liquid density region. These data
indicate that condensation in the saturation envelope is almost
exclusively due to the larger molecule. Importantly, at 310 K, in
both components, regions of highest density increase upon
compression, in both volume and density, until the phase
transition point.
In contrast, at 365 K (Figure 2b), distributions for the ethane
component are bimodal and for pressures above 45 bar, the
high density components coincide with the uniform distribution seen at the highest pressures. Both low and high density
regions in the ethane component increase in density upon
compression, while for heptane, the density of the most
compact regions decreases, as observed in the entire fluid
(Figure 1b). At 365 K, while the densest regions appear to be
composed primarily of heptane at lower pressures, as pressure
is increased, condensed regions increase in ethane concentration, with a concomitant reduction in heptane density.
The different behavior seen in the density distributions for
the system at 310 and 365 K can be easily understood from
visualizations of the MD trajectories. In Figure 3, snapshots of
the simulations at the two different temperatures over relevant
pressure ranges are illustrated. At 310 K, as pressure is
RESULTS
Simulations of Unconfined Fluids. In order to
quantitatively examine phase separation in NPT simulations
of bulk fluids, each simulation cell was divided into a number of
smaller cubes, 3375 (153) for the simulations of the ethane/
heptane mixture and 525 (53) for smaller simulations of pure
heptane. The populations and particle densities in each small
cube were calculated for 200 frames over 9 ns trajectories at
equilibrium for each pressure and corresponding frequency
histograms were constructed (see Supporting Information
Figure S2). Figure 1 shows selections from density histograms
for pure heptane (Figure 1a) and for the 70/30 wt % ethane/
heptane mixture (Figure1b) at 310 K (upper panel) and 365 K
(lower panel).
Figure 1. Profiles of ln(ρ) vs probability where ρ is particle density in
OPLS united atoms/nm3 at selected pressures for (a) pure heptane at
505 K and (b) the 70/30 wt % ethane/heptane mixture at 310 K (top
panel) and at 365 K (bottom panel).
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Figure 3. Representative snapshots of NPT simulation cells depicting
condensation in the 70/30 wt % ethane(green)/heptane(blue)
mixture at variable pressures along isotherms at (a) 310 and (b)
365 K. Snapshots are scaled to facilitate visualization and the length of
one dimension for each cubic cell is indicated at the bottom of each
snapshot.
indicate an obvious phase transition at 310 K, show gradual
changes between 55 and 72.5 bar at 365 K, followed by a
change in the curvature of the function at 72.5 bar. These data
are consistent with the information presented in Figures 2 and
3, indicating the transition to purely supercritical fluid at 72.5
bar, underestimating the experimental value of 83 bar.15 In
principle, the simulated volumes of liquid and vapor could be
calculated from areas under the corresponding portions of
density profiles, however because the two parts are often not
distinct, and overlapping extensively in the retrograde region, it
is difficult to tell exactly at which pressure these simulations
predict the maximum condensation to occur at 365 K.
Heptane−heptane radial distribution functions indicate maximum structure of associated heptane at 55 bar (Supporting
Information, Figure S4). On the other hand, simple visualization of trajectories strongly indicates the maximum liquid
volume to be at 60 bar.
Equilibrium Simulations in Oil-Wet Pores. In equilibrium adsorption studies, single capillary tubes 60 nm long
having square cross sections of 4 nm were initially given hard
sphere potentials (no lipophilicity) and flooded with the
retrograde fluid pushed by pistons with a force corresponding
to 800 bar. The solid spheres of the packed tubes were then
given the strongly oil-wet lipophilicity parameter (ε = 3.2 kJ/
mol), and the fluid was allowed to expand at both 310 and 365
K under pressures encompassing the saturation envelope of the
bulk fluid for both temperatures. Expansion was controlled in a
stepwise fashion such that simulations for each pressure were
started from equilibrated conformations at the pressure
immediately above in the series. For quasi-equilibrium
simulations of confined fluids under pressure gradients,
simulations were started from final configurations of equilibrated simulations under 90 bar of pressure on either side and
then pistons at each end were given different accelerations.
The initial simulated ethane and heptane distribution in
pores having repulsive walls were surprising, especially in
Figure 2. Profiles of ln(ρ) vs probability of the 70/30 wt % ethane/
heptane mixture with partial densities for ethane and heptane plotted
separately. Simulations were performed at (a) 310 and (b) 365 K, over
the pressures indicated.
increased, total heptane association also increases up to 27.5
bar, as indicated by the increase in the area of the liquid portion
of the density distributions in Figure 2, and then all at once, the
droplets collapse resulting in a uniformly distributed liquid. In
contrast, at 365 K, inclusion of hotter ethane into condensed
droplets results in gradual expanding of the heptane droplets.
Up to approximately 60 bar, the volume of the condensed
phase grows; above 60 bar, the high pressure vapor phase
effectively breaks apart the liquid and this happens over a broad
pressure range; we take this to be the predicted retrograde
region. Here, animated visualizations (see Supporting Information) show increasingly relaxed regions of heptane association
that persist throughout the simulations up to 72.5 bar.
For the retrograde isotherm, two pressures of interest may be
approximated (within 2.5 bar) from these simulations, the dew
point pressure and the pressure of maximum condensation
although the latter is somewhat more difficult to ascertain.
Density data (Supporting Information, Figure S3) which
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condensation, exclusion of heptane from the pore surface
results in heptane accumulating outside the narrow pore
(Supporting Information, Figure S5). For subcritical pressures,
association with the surface is diminished for both species, but
still more so for heptane.
For the strongly oil-wet surface, the distribution of heptane is
opposite to what is seen for the nonoil-wet surface. At the oilwet surface, there is a higher concentration of heptane at the
surface where the distribution mimics the solid structure. For
the lower temperature, outside of the first adsorption layer,
heptane distribution is fairly uniform and this is generally true
across all pressures. The same is true for ethane and at 310 K,
the fluid exists as a single liquid phase in the narrow, oil-wet
nanotube even at low pressures. At 365 K, however, a different
trend is seen. As the pressure decreases toward the lower region
of the saturation envelope, heptane molecules become
distributed predominantly in the first and second adsorption
layers. In contrast, for ethane, at pressures above 20 bar,
molecules are evenly distributed outside the first adsorption
layer.
Figure 5 illustrates adsorption of each species as a function of
pressure in the first and second adsorption layers of the oil-wet
pore (Figure 5a) as well as total accumulation of each species
inside the pore (Figure 5b). The stoichiometric ratio of ethane
to heptane atoms (OPLS united-atoms) is approximately 2:1 in
the bulk fluid and populations inside the nanopore corresponding to this composition are observed for both temperatures at
high pressures. This is more or less true for the second
adsorption layers, but not the case for the first adsorption layer
where the ethane/heptane ratio is always lower than the fluid
composition, indicating heptane is absorbed preferentially at
comparison to those in oil-wet pores. Figure 4 shows density
profiles obtained from simulations of the ethane/heptane
Figure 4. Simulated density profiles for heptane and ethane at selected
pressures and temperatures in narrow oil-wet and nonoil-wet
nanotubes with 4 nm cross sectional widths.
mixture confined to narrow nonoil-wet pores and oil-wet pores
at the pro-grade and retrograde temperatures. Heptane does
not associate well with the nonoil-wet surface; in fact heptane
molecules prefer to be separated from the wall by a layer of
ethane at all pressures. Under high pressures, ethane molecules
pack tightly such that their distribution indicates the molecular
structure of the pore surface (a lattice in this case) and to some
extent this is even true for the second layer of ethane. In
general, for the nonoil-wet walls, under conditions promoting
Figure 5. Simulated adsorption isotherms for a fixed amount of the 70/30 wt % ethane/heptane mixture inside an oil-wet nanopore with cross
sectional width of 4 nm and length of 60 nm. Average adsorption was measured for the layer directly adsorbed to the solid lattice, within 0.6 nm,
(L1) as well 0.6 nm further (L2) as indicated by the schematic in the upper left corner of panel a. Simulations were performed between 5 and 30 bar
in increments of 5 bar at 310 K with additional points at 40, 50, and 70 bar. For the 365 K isotherm, simulated pressures ranged between 20 and 150
bar in increments of 10 bar with an additional point at 200 bar. Panel b shows plots of the total number of atoms (OPLS united atoms) in the pore
for each species at each pressure.
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the oil-wet surface. At 310 K, simulated heptane adsorption in
the first adsorption layer exceeds ethane adsorption up to 40
bar, and the same is true below approximately 35 bar for
heptane accumulation in the rest of the pore space. In these
simulations, as pressure is decreased, the concomitant volume
expansion is mostly due to ethane, resulting in capillary
condensation primarily of heptane at low pressures. Accordingly, there is significant liquid content in the pore at all
pressures for the prograde isotherm.
At 365 K, heptane accumulation at the surfaces and in the
pore in general, is significantly reduced at low pressures, but
reaches a maximum at 60 bar. Directly at the surface, heptane
adsorption is favored over a broad range of pressures, from 40
to 110 bar and maximizes between 50 and 60 bar. The same
general pattern is seen at the second adsorption layer and
throughout the pore, but there is a marked difference between
the first and second layers. In contrast to what is observed at
310 K for low pressures, below 30 bar, fewer heptane atoms are
adsorbed at the first layer, although accounting for
stoichiometry, heptane is still favored. This is not the case
outside the first layer, where ethane and heptane populations
more closely resemble the bulk concentration at low pressures.
It is notable that upon expansion from 60 to 50 bar, at 365 K,
adsorption of heptane in the first layer remains constant, at the
maximum, while the heptane population in the second layer is
significantly reduced. As pressure is reduced further to 30 bar,
the heptane concentration in the pore, as well as in the second
adsorption layer, decreases dramatically while the change in
ethane concentration is much less steep. This illustrates a key
difference for the confined fluid at the two different
temperatures: at 365 K, ethane is not preferentially expelled
from the pore at lower pressures, at least, not to the degree that
it is at 310 K. For the retrograde temperature, at the point of
maximum heptane accumulation, the total amount of fluid in
the pore is significantly less than the maximum observed 310 K
and capillary condensation is not observed for the lower
pressures at 365 K.
Quasi-Equilibrium Simulations in Pores under Pressure Gradients. During extraction in shale reservoirs, induced
pressure gradients can cause condensation to occur as pressure
decreases, and it is this condensation that is of interest.
Unsurprisingly, the data above suggest substantially more liquid
formation in the small nanopore at 310 K than what is seen at
low pressures for the bulk fluid. However, it is less clear,
considering the apparent adsorption and fluid phase separation
of the heavy and light molecules, what amount of condensation
should be expected at the retrograde temperature. In order to
examine condensation due to pressure drops in the retrograde
fluid, simulations were performed on the fluid at 365 K with
different pressures at the two ends of the simulation cell.
The important trends in heptane accumulation could be
readily seen after 18 ns and these are illustrated in Figure 6. For
the oil-wet pore, at pressures as low as 10 bar, a notable
accumulation of heptane occurs at the low pressure end of the
tube and this occurs to a significant extent up to 50 bar.
Similarly to what is seen in the bulk, for pressures in the
retrograde region, the increased disruption of condensation
occurs as pressure increases and for the supercritical pressure
(shown at 110 bar), there appears to be no heptane
condensation at the pore junction.
These clogging effects are examined more quantitatively in
Figure 7, where average numbers of heptane and ethane atoms
in 1 nm cross sections of the simulation cell are plotted for a
Figure 6. Truncated snapshots of simulations of the 70/30 wt %
ethane (green)/heptane (blue) mixture at 365 K pushed through
nanopores by pressure gradients. Rotated images on the left-hand side
are zoomed in slightly so heptane accumulation inside the pores can be
more easily viewed.
Figure 7. Plot of the number of atoms in 1 nm slices along the long
pore axis of 40 nm pores in a selection of the pressure gradient
simulations illustrated in Figure 6. Counts of heptane atoms are
indicated by solid lines and those for ethane by dashed lines. The
enlarged section of the plot at the top of the figure illustrates the
effects of increasing pressure on heptane accumulation at the low
pressure end of the nanotube.
section of the cell containing the pore in the center. The tall
spike on the low pressure end of the pore indicates the density
of heptane atoms at the pore entrance. Peak heptane
accumulation in this selection of pressures occurs at 30 bar
and it is notable, again, that at 10 bar, the pore entrance is
congested to a significant extent.
■
DISCUSSION AND CONCLUSION
The parameter set used here (OPLS-UA) underestimates phase
transition points at the high pressures examined in this study
and in order to more accurately describe the phase diagram
using molecular simulations, a more robust force field would be
required. Indeed, all atom models including explicit hydrogen
atoms and partial charges are known to produce superior
results. Additionally, for a more detailed description of the
phase diagram of the bulk fluids, a Monte Carlo method may be
more appropriate and histogram reweighting might be
employed in order to access information about other
temperatures.
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area to induce condensation at lower pressures than what is
seen in the bulk is apparent at 310 K, but the same is not
predicted at equilibrium for low pressures at 365 K in this pore.
Sealing due to condensation under pressure gradients at 365 K
in the narrow oil-wet pore may be alleviated under retrograde
conditions, but probably not at low pressures. The models
presented here offer some valuable insights into retrograde
hydrocarbon fluids in narrow oil-wet pore spaces. For
applications to more realistic systems, such as shale, the
model system should be improved to more accurately predict
phase diagrams and extended to account for more complex
fluids as well as diverse pore shapes, sizes and compositions.
Nonetheless, for the highly lipophilic or systems examined in
this study, in which Columbic influences are minimal, the
simple van der Waals type force field provides valuable insights.
MD simulations using the Lennard-Jones force field do appear
to capture the phenomenon of retrograde phase behavior for
this binary fluid. For compression along the retrograde
isotherm, the gradual phase transition in the retrograde region
is seen as increased disruption of condensed heptane droplets
by the high pressure ethane phase resulting in loosely
associated heptane clouds which persist over long periods of
time between 62.5 and 72.5 bar. The expansion of the heptane
phase under compression at 365 K is in stark contrast to what is
observed for compression of the same fluid at 310 K, in which
liquid density for both components increases with pressure
until the system suddenly transforms to a uniform liquid with a
sharp phase transition. The way in which the liquid phase
collapses in simulations of the retrograde region presented
difficulties in examining liquid content based on local densities.
It should be pointed out, however that the type of collapsing
behavior observed here might not be observed with any
retrograde fluid. For more complex fluids with a broad range of
molecular weights, the density of the heaviest components need
not decrease and a reduction in droplet size might be observed
during compression rather than uniform expansion of the entire
droplet.
Inside the narrow nanopore, nonoil-wet surfaces exhibit a
high preference for the lighter molecule. This was observed at
both temperatures and all pressures and the nature of the effect
is not immediately clear. If the effect is purely entropic, it might
be observed to some extent for adsorption in the oil-wet pore
as well. However, no preference for ethane at the oil-wet
surface greater than what can be predicted based on
stoichiometric composition under any conditions is observed.
In any case, there may be an enthalpic component to the effect:
heptane molecules, having the stronger L-J potential field,
should preferentially associate with ethane rather than the
repulsive wall; consequently, ethane which is lighter and
abundant surrounds heptane molecules or aggregates resulting
in an ethane layer at the solid surface.
In the oil-wet pore, heptane is preferentially adsorbed to the
pore wall under nearly all conditions studied. At 310 K,
accumulation of heptane at the pore wall under low pressures is
accompanied by a significant increase in heptane concentration
throughout the pore and in general capillary condensation of
heptane is observed at pressures well below the bulk
condensation point. It is apparent from the equilibrium
adsorption simulations that heptane accumulation is maximized
at approximately the same pressure as what is seen in the bulk
fluid under retrograde conditions. On the basis of information
obtained from equilibrium isotherms, we may expect reduction
in pressure below 50 bar to open up the interior of the pore at
365 K. On the contrary, simulations of the fluid flowing under
pressure gradients seem to indicate otherwise; fluid entering a
40 nm long pore under supercritical conditions at one end
condenses heptane at the opposite, low pressure end for
pressures as low as 10 bar. In these simulations, the maximum
accumulation appears to occur at 30 bar, but above 70 bar, such
accumulation is significantly reduced.
In summary, molecular level interpretations for the differences between retrograde and prograde phase behavior for
petroleum fluids in bulk and in carbonaceous nanopores are
accessible using simple Lennard-Jones models of a binary
ethane/heptane mixture. The ability for high oil-wet surface
■
ASSOCIATED CONTENT
S Supporting Information
*
Figues showing effects of time step on bond energies, predicted
particle distributions of unconfined fluids in NPT simulations,
predicted densities for the 70/30 wt % ethane/heptane system,
heptane/heptane radial distribution functions, and truncated
snapshots of 70/30 wt % ethane/heptane fluid pressurized in
nanopores with non-oil-wet solid surfaces and a movie showing
MD animation. This material is available free of charge via the
Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*(W.R.W.W.) E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
We gratefully acknowledge financial support of Hess Corporation and the School of Energy Resources and the College of
Engineering and Applied Science at the University of Wyoming.
We also thank the Advanced Research Computing Center at
the University of Wyoming for extensive computational
resources which made this research possible.
■
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