-
Capillary Condensation of Binary and Ternary Mixtures
ofn‑Pentane−Isopentane−CO2 in Nanopores: An Experimental Studyon
the Effects of Composition and EquilibriumElizabeth Barsotti,*
Soheil Saraji, Sugata P. Tan, and Mohammad Piri
Department of Petroleum Engineering, University of Wyoming,
Laramie, Wyoming 82071, United States
*S Supporting Information
ABSTRACT: Confinement in nanopores can significantly impact
thechemical and physical behavior of fluids. While some
quantitative under-standing is available for how pure fluids behave
in nanopores, there is littlesuch insight for mixtures. This study
aims to shed light on how nanoporosityimpacts the phase behavior
and composition of confined mixtures throughcomparison of the
effects of static and dynamic equilibrium on experimentallymeasured
isotherms and chromatographic analysis of the experimental
fluids.To this end, a novel gravimetric apparatus is introduced and
validated. Unlikeapparatuses that have been previously used to
study the confinement-inducedphase behavior of fluids, this
apparatus employs a gravimetric techniquecapable of discerning
phase transitions in a wide variety of nanoporous mediaunder both
static and dynamic conditions. The apparatus was
successfullyvalidated against data in the literature for pure
carbon dioxide and n-pentane.Then, isotherms were generated for
binary mixtures of carbon dioxide and n-pentane using static and
flow-through methods. Finally, two ternary mixtures of carbon
dioxide, n-pentane, and isopentane weremeasured using the static
method. While the equilibrium time was found important for
determination of confined phasetransitions, flow rate in the
dynamic method was not found to affect the confined phase behavior.
For all measurements, theresults indicate qualitative
transferability of the bulk phase behavior to the confined
fluid.
1. INTRODUCTIONAlthough the study of pure, single-component
fluids innanopores has been broadly undertaken, there is very
littleknowledge as to how mixtures in nanopores behave.
Aquantitative realization of nanoconfinement-induced
mixturebehavior is prerequisite to breakthroughs in many fields
frommedicine and biology to materials science and
electrochemistry.An example of how significantly a comprehensive
under-standing of the effects of nanoporosity on fluid mixtures
canimpact each of these scientific endeavors can be found
inpetroleum engineering, where the ability to accurately
predictconfined mixture behavior could significantly influence
theeconomic valuation of shale and tight gas reservoirs.Within the
next few decades, natural gas consumption is
projected to increase more than that of any other
energyresource.1 Much of this growth in demand will be satiated
byvastly increasing production from shale and tight gasreservoirs.1
In spite of this, very little is known about thephysics of fluid
flow, transport, and storage in these reservoirs.In particular,
there is virtually no understanding of fluid phasebehavior in such
systems. Shale gas reservoirs are typified bynanopores, which
constitute a significant fraction of their totalporosity.2 The
scale of these pores, alone, regardless of theirchemistry or
geometry, may alter the phase behavior of theconfined fluids from
their bulk counterparts. Specifically, thevapor-to-liquid phase
transition may occur earlierthat is, at
lower pressures in an isothermal system or at highertemperatures
in an isobaric systemin confinement than inthe bulk. This
confinement-induced phase change, calledcapillary condensation, has
been reported in the literature, seeBarsotti et al.3 for a
comprehensive review, yet most of theassociated studies involve
single-component fluids in simplepore systems far removed from
those encountered in thereservoir setting.3 Those studies that have
been carried out onmulticomponent fluids are scarce, providing
little overall insightinto the phase behavior of confined fluid
mixtures. The majorityof the experimental studies have been carried
out under isobaricconditions to probe the confinement-induced
bubble point. Alimited number of studies have observed the
confinement-induced dew point, while a few others have focused more
onthe structure of the confined fluid during the phase
transitionwith emphasis on phase separation. To the best of
ourknowledge, none have witnessed the confined critical point
ofmixtures.Studies on the confined bubble point include the work
of
Cho et al.,4 Luo et al.,5 Jones and Fretwell,6,7 and Yun et
al.8
While all the studies, except for that of Luo et al.,5
witnesseddepression of the confined bubble point with respect to
that of
Received: December 4, 2017Revised: January 9, 2018Published:
January 23, 2018
Article
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© 2018 American Chemical Society 1967 DOI:
10.1021/acs.langmuir.7b04134Langmuir 2018, 34, 1967−1980
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the bulk, the results must be viewed in the context of
theexperimental path. The two paths available for studies
ofconfined phase phenomena are adsorption and desorption.
Inadsorption, the initial phase of the bulk fluid is
gaseous.Adsorption experiments are exemplified in the literature by
theworks of Jones and Fretwell7 and Yun et al.,8 who used
positronannihilation spectroscopy and a volumetric
flow-throughapproach, respectively. In desorption, the initial
phase of thebulk fluid is liquid. Desorption experiments are
represented inthe literature by studies employing density scanning
calorimetrymeasurements, such as that of Luo et al.5
Although the adsorption and desorption experiments bothresult in
confinement-induced shifts of the fluid phasetransitions, the
results are quantitatively different. Alam et al.explained this
difference in their positron annihilation spec-troscopy study of
the confined dew points of binary mixtures ofnitrogen and argon.9
They found inequalities between theconfined dew points measured
using adsorption and desorptionto result from enrichment of the
confined fluid by the bulk fluidduring desorption.9 Thus, although
adsorption and desorptionboth qualitatively indicate
confinement-induced shifts of thephase transition, the degree to
which those shifts occur is highlydependent on whether desorption
or adsorption is taking place.Furthermore, the studies can be made
either statically or
using a flow-through method, such as that used by Yun et
al.8
Whereas the other studies involving gas mixtures used a
staticapproach in which the fluid within the pores was stationary
atequilibrium, the study of Yun et al. involved fluids that
werealways flowing and therefore experienced dynamic
equilibrium.8
Putting this into the context of natural gas production,
thestatic and dynamic experiments approximately representdifferent
yet complimentary situations throughout the life of areservoir. For
example, the static experiments best approximateunproduced
reservoirs in which fluids are stationary, thesituation of which is
relevant to the original gas in placecalculations. Conversely,
dynamic experiments best approx-imate reservoir processes in which
fluids are flowing, such asproduction and injection, but with a
constant flow rate.Experimentally, the two methods differ in that
during staticexperiments, the overall (confined plus bulk)
composition ofthe fluid is constant while during the flow-through
experiments,only the bulk composition of the fluid is maintained
constantby the flow. Except for this methodological difference,
there isno evidence for any difference in the underlying concept
asboth can provide the desired capillary condensation.
However,comparison between them would support decision making
inchoosing the experimental setup if one decides to
applygravimetric measurements.Nonetheless, in evaluating the data
generated by these
experiments, knowledge of the structure of the fluidthenumber
and location of the molecules of each componentwithin the pores is
also necessary. Although, often nopreferential adsorption is
observed, such as in the work ofAlam et al.,9 there are cases in
which it may significantly alterthe structure of the confined
mixture beyond what is expected,that is, confinement-induced phase
transitions may bedisproportionately skewed by the more selectively
adsorbedcomponent. In measuring the capillary condensation of
binarymixtures of n-hexane and perfluoro-n-hexane, Kohonen
andChristenson observed co-condensation between muscovitemica
surfaces using a surface force apparatus.10 Essentially,both an
n-hexane-rich phase and a perfluoro-n-hexane-richphase condensed,
but they occurred separately, albeit at the
same pressure and temperature, so that the confined fluid didnot
comprise a homogenous mixture.10 Thus, confinementcould not only
affect the phase transitions of fluids, such asnatural gas, but
also their compositions, including the pore fluidoccupancy in the
event of confinement-induced phaseseparation. This could prove
important to the ultimate recoveryof shale gas, because the pore
fluid occupancy dictates themechanisms by which various phases will
be produced.In an effort to better understand the effect of
confinement on
both the phase transitions and compositions of fluids
innanopores, a novel gravimetric apparatus11 is introduced for
thestudy of both pure fluids and mixtures in a variety of
porousmedia using both static and dynamic processes. Unlike
theapparatuses used in previous studies of confined fluid
mixtures,such as the isobaric differential scanning calorimetry5
andpositron annihilation spectroscopy measurements9 or
theisothermal volumetric measurements of Yun et al.,8 ourapparatus
uses changes in mass to directly measure the amountof fluid
adsorbed. This allows for isothermal measurements thatare more
relevant to shale gas recovery than isobaricmeasurements, that is,
temperature can generally be consideredconstant in gas reservoirs,
and more accurate12 than volumetricmeasurements, which cannot
measure the adsorbed amountdirectly but rather depend on equations
of state to calculate it.Similarly, this apparatus has the ability
to facilitate largequantities of adsorbents, including core plugs
housed in high-pressure core holders. Such a high capacity
gravimetricapparatus has not been previously reported in the
literature.Although the evaluation of the confined phase behavior
ofreservoir fluids in core plugs was beyond the scope of thisstudy,
the ability of the apparatus to support a core holder andits
associated plumbing was tested and validated throughoutthis study
by utilizing a titanium core holder packed withMCM-41 for all
experiments herein.In this work, the apparatus was first validated
using
isothermal capillary condensation data in the literature forpure
carbon dioxide and pure n-pentane and with bulkcondensation data
for both compounds from the NationalInstitute of Standards and
Technology (NIST).13 Next,building upon the data for the pure
component isotherms,binary isotherms of carbon dioxide and
n-pentane weremeasured for the first time using a static method and
then adynamic, flow-through method. Finally, two ternary
mixtureisotherms for CO2, n-pentane, and isopentane were
measured.To the best of our knowledge, these are the first
isothermsdisplaying the confinement-induced vapor-to-condensed
phasetransitions of gas mixtures with more than two components.With
respect to the findings of Alam et al.,9 only adsorptionpaths were
used for all measurements to negate the effect of theenrichment of
the confined fluid by the bulk liquid when theyare in direct
contact prior to the desorption. In this work, theobserved abrupt
increase of adsorption in the isotherms ofmixtures is termed
mixture capillary condensation.
2. MATERIALS AND METHODS2.1. Materials. Three MCM-41 samples
were obtained
from Glantreo, Ltd. MCM-41 is a mesoporous silica well-known
throughout the literature for its easily tuned pore sizeand simple
pore geometry, consisting of uniform, unconnectedcylindrical
pores.14 Using nitrogen adsorption isotherms at 77K,
Barrett−Joyner−Halenda (BJH)15 and Dollimore−Heal(D−H)16 analyses
gave average pore sizes of 3.51 and 3.70nm, respectively, for the
first sample, 2.59 and 2.78 nm for the
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second sample, and 6.06 and 6.32 nm for the third sample. Forthe
first sample, small angle X-ray scattering indicated thepresence of
hexagonal unit cells with a lattice parameter of 4.78nm, while
transmission electron microscopy (TEM) showedparticle size to be
approximately 1 μm in diameter. TEMmicrographs of the 3.70 nm
MCM-41 used in this study areshown in Figure 1. The properties of
all of the adsorbentsconsidered in this work are given in Table
1.
For the purposes of this work, three packs of the MCM-41were
used, where each sample of MCM-41 was packed into itsown titanium
core holder using the packing proceduredescribed by Saraji.19
Through geometric calculations, the2.78, 3.70, and 6.32 nm MCM-41
packs were found to haveinterparticle void volumes of 46.7, 46.6,
and 47.0 cm3,respectively. The total volume of each core holder was
56.4cm3, that is, in all three cases, the MCM-41 took
upapproximately 17% of the available volume.For the adsorption
experiments, carbon dioxide (99.9995%,
Airgas, Inc.), n-pentane (99.8%, Alfa Aesar), and
isopentane(99%, Alfa Aesar) were used. For single-component
experi-ments, the n-pentane was first dried with calcium
hydride.Subsequently, the fluid was distilled and then stored
underhelium. Gas mixtures were prepared using a gravimetric
gasmixing system developed in-house for this purpose.
Thecompositions of the mixtures were confirmed through acombination
of fixed gas and detailed hydrocarbon analysis
using a customized Agilent 7890B gas chromatograph
fromSeparation Systems, Inc.
2.2. Experimental Setup and Procedure. Isotherms weremeasured
using a novel gravimetric apparatus11 that allows forboth static
and flow-through measurements of adsorption,desorption, and
capillary condensation in adsorbent packs attemperatures from
173.15 to 503.15 K. An environmentalchamber (Thermotron) with
precise temperature control of±0.1 K was used as a
thermostat.Throughout the experiments, a Rosemount pressure
trans-
ducer (Emerson) and a Leybold TM 101 vacuum gauge wereused to
measure positive and negative (i.e., below atmospheric)pressures,
respectively, at a frequency of once per second. Aswith all
gravimetric apparatuses, the phase of the confined fluidwas
determined by the relationship between its mass andpressure. The
mass of the MCM-41 pack was measuredcontinuously at a frequency of
once per second throughout theexperiments with an accuracy ±0.00001
g using an XPE 505Cmass comparator from Mettler Toledo. A
custom-made dataacquisition box and LabVIEW computer program were
used tolog all data. A schematic of the experimental setup is
presentedin Figure 2.The integrity of the system was maintained by
outgassing it
at 373.15 K for at least 12 h after any exposure to humidity
orair. This was to prevent irregularities in the data due
tophysisorbed water. It was determined that no heat wasnecessary to
achieve appropriate outgassing between consec-utive isotherms where
neither air nor water was present as longas the same vacuum level
could be achieved between theisotherm measurements.
2.2.1. Static Method. In the static method, for
experimentsinvolving both pure gases and mixtures, a variable
dosingvolume was used to incrementally increase the gas
content(mass) to change the pressure of the system under
isothermalconditions, while the system was closed between doses. In
allcases, the dosing volume was simply a combination of valvesand
variable lengths of tubing plumbed directly into the system.For
experiments with pure carbon dioxide, the dosing volumewas fed
directly by the gas cylinder. For the pure n-pentane andthe mixture
experiments, the dosing volume was fed by a dual-cylinder 6000
series Quizix pump (Chandler Engineering). This
Figure 1. TEM micrographs of the MCM-41 employed in this work.
From the images, the MCM-41 was found to have an average particle
size of 1μm, while the particles were found to have a thin,
elliptical geometry.
Table 1. Comparison of the Adsorbent CharacteristicsReferenced
in This Work to Those Used in This Study
adsorbentBET surfacearea [m2/g]
D−H poresize [nm]
BJH poresize [nm]
NLDFT poresize [nm]
this work:2.78 nm
1043 2.78 2.59
this work:3.70 nm
832 3.70 3.51
this work:6.32 nm
586 6.32 6.06
Morishige &Nakamura17
865 4.4
Russo et al.18 934 4.57
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minimized air contamination of the n-pentane, which was liquidat
standard conditions, and allowed for precise pressure controlof the
bulk mixtures to prevent liquid dropout. During thestatic
measurements, each new dose of gas introduced into thesystem was
allowed to equilibrate until the pressure of thesystem became
constant.Equilibrium time for both the adsorption and capillary
condensation regions of isotherms has been discussed in
theliterature by Naumov,20 who found that for cyclohexane at 297K
in Vycor glass with pores of approximately 6 nm diameter,adsorption
equilibrium occurred within 1 h, while capillarycondensation
equilibrium could not be achieved even after 4h.20 Therefore,
according to the findings of Naumov, if time isdivided equally
among all data points, those for adsorption maybe at equilibrium,
while those for capillary condensation maynot. To determine the
effects of nonequilibrium on the shapeand condensation pressures of
the pure component isotherms,an isotherm for carbon dioxide at
234.35 K was measured inwhich doses of gas at different pressures
for both adsorptionand capillary condensation were left to
equilibrate for 4 h.
During those time periods, pressure and mass data wererecorded
at 5, 10, 30, 60, 120, 180, and 240 min. The resultingisotherms are
shown in Figure 3.In the case of Figure 3, the capillary
condensation pressure at
30 min was estimated to be 2.8% higher than the
capillarycondensation pressure at 120 min. Although beyond the
scopeof this study, this may also have implications for
determinationof the hysteresis critical temperature, as hysteresis
may beartificially induced through variations in the equilibrium
time.Similarly, it may affect the method used to locate the
porecritical temperature. Using a method proposed by Morishigeand
Nakamura, locating the pore critical temperature is reliantupon the
slope of the isotherm,17 which may also be affected byincreasing or
decreasing the time allowed for equilibrium, asshown in Figure 3.It
is important to note that our apparatus is fundamentally
different from the more traditional gravimetric
apparatusespresented in the literature, as shown in Figure 4.
Mosttraditional gravimetric apparatuses utilize a weighing
pansuspended in a gaseous atmosphere of the adsorbate, where
Figure 2. Schematic of the experimental setup: (a) balance, (b)
antivibration table, (c) core holder, (d) draft shield, (e)
environmental chamber, (f)frame, (g) thermocouple power supply and
data logger, (h) dual cylinder Quizix pump, (i) turbomolecular
pump, (j) pressure transducer, (k)vacuum gauge, (l) gas cylinders,
(m) gas chromatograph, (n) computers, and (o) data acquisition
box.11
Figure 3. Effect of equilibrium time on the capillary
condensation pressure and the structure of the isotherm for CO2 at
234.35 K. Data points weretaken at 5, 10, 30, 60, 120, 180, and 240
min after each dose. At 120 min and onward, the change in pressure
due to nonequilibrium was found to benegligible.
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any phase change within the adsorbent on the weighing pancauses
depletion (in the case of adsorption) of the adsorbateatmosphere as
the gas molecules are drawn into the pore space.This allows for the
measurement of mass uptake curves, butalso necessitates corrections
for buoyancy as the density andpressure of the adsorbate atmosphere
change. In our apparatus,both the adsorbent and the bulk adsorbate
are housed withinthe core holder, so that for each dose of
adsorbate, the mass ofthe dose is constant, although the phase may
change. Theinjected dose initially causes an abrupt increase in the
detectedpressure that then decreases as the system equilibrates as
shownin Figure 5. The more gas that is adsorbed, the more
thepressure of the bulk adsorbate will decrease after each
dose.Because of this pressure behavior, the equilibrium during
the
static method was defined as the point at which the data
pointsfor the pressure averaged over 1 min became constant.As it is
discussed in section 3.1, the absolute mass measured
can be converted to the mass of the confined phase bysubtracting
out the mass of the bulk fluid based on thegeometries of the core
holder and the adsorbent pack. Thediagram in Figure 4 illustrates
the differences between theequilibration of our apparatus and other
gravimetric appara-tuses by emphasizing the constant and changing
properties,such as pressure and density, associated with each.
Interestedreaders are referred to Rouquerol et al.21 for a
comprehensivediscussion on the data analysis required for more
traditionalgravimetric setups (Figure 4a), while a
comprehensivediscussion of the data analysis employed with our
apparatusis presented in section 3.1.
2.2.2. Flow-Through Method. In the flow-through method,gas
mixtures were injected continuously into the core holderusing one
cylinder of the Quizix pump, while the secondcylinder received the
effluent and provided back pressureregulation. The Quizix pump had
the ability to apply flow ratesfrom 0.0001 to 200 cm3/min and could
also apply backpressures from below atmospheric pressure to 700
bar. Toprogress from one data point of an isotherm to another,
thepressure was increased using either the back pressure or
theinjection cylinder (no discrepancy between the two was
found),while the gas was flowed continuously before, during, and
afterthe change in pressure. At each data point, constant flow
andpressure were maintained for at least 2 h, where the
minimumequilibrium time was adopted from the static method.
2.2.3. Compositional Analysis. For both the static anddynamic
measurements, the compositions of the bulk fluidmixtures, both at
the beginning of the experiments (while allfluid was in the gas
phase) before it had come into contact withthe adsorbent and at the
end of the isotherms (once the bulkbubble point had been crossed)
while the bulk fluid was incontact with the adsorbent were measured
using the gaschromatograph. Note that the compositions of the
fluids wereall measured in situ, for the gas chromatograph was
directlyplumbed into the system, as shown in Figure 2. In this
way,chromatographic analysis of the fluid involved removing 111
μLof fluid directly from the plumbing of the system for
analysis.Because this volume accounts for 0.22% of the total volume
ofour core holder and an even smaller percentage of the volumeof
the entire system (Figure 2), the effect of its removal on
thepressure and composition of the adsorbate were
considerednegligible. In the dynamic measurements, additional
analysis ofthe adsorbate was undertaken at the end (i.e., once
equilibriumhad been achieved) of each dose using the same in situ
samplingprocedure.
Figure 4. A comparison of the equilibration of more
traditionalgravimetric apparatuses used in the literature (a) to
that of ourgravimetric apparatus (b). Note that the volume of the
confined fluidmay change because of the strain of the adsorbent,
but because thestrain generally does not observably affect the
measured isotherms,22
this change in volume is considered to be negligible in this
work.
Figure 5. Characteristic pressure equilibration curve for a
single dose of fluid taken from data for CO2 at 224.35 K. Note that
the factory-specifiedresponse times of the pressure transducers and
the observed response times of the balance were less than 1 s.
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2.2.4. Measurement Accuracy. To gauge the accuracy of
theapparatus, the uncertainties associated with it were
identifiedand analyzed. The accuracy of the overall apparatus
depends onthe accuracies of the mass readings, the pressure
measurements,and the compositional analyses of the experimental
fluids (inthe case of mixture experiments). First, the manufacturer
statedabsolute repeatability of the balance is 0.06 mg, whereas
itsrepeatability at nominal load (500 g) is 0.035 mg and at lowload
(20 g) is 0.01 mg. The mass of the core holder, adsorbent,and
adsorbate combined was within 300−400 g throughout allexperiments;
therefore, we consider the repeatability to bebetter than 0.035 mg.
This uncertainty is insignificant, as it isseveral orders of
magnitude smaller than the amounts adsorbedgiven in Figures 6−12.
Note that housing the balance on top of
the antivibration table above the environmental chamber
(seeFigure 2) mitigated the addition of any inaccuracies due to
theexperimental conditions, such as changes in temperature
orvibrations. Throughout all experiments, the balance wasmaintained
at local atmospheric pressure at approximately 21°C as recommended
by the manufacturer.The Rosemount pressure transducer and the
Leybold
vacuum gauge were characterized by
manufacturer-specifiedaccuracies equal to or better than ±0.24 and
±0.0036 bar,respectively. The uncertainties in pressure associated
with themeasurements for CO2 and n-pentane are given in Table
2,where they are shown to be insignificant.
Third, the accuracy associated with compositional analysiswas
determined by measuring the compositions of two binarymixtures of
carbon dioxide and n-pentane multiple times (sixand nine
measurements were taken for the first and secondmixtures which
comprised 68% CO2 and 32% n-pentane and77% CO2 and 23% n-pentane,
respectively) and thencalculating their standard deviations. The
standard deviationsfor the first and second mixtures were 1.8 mol %
(coefficient ofvariation = 2.3) and 4.1 mol % (coefficient of
variation = 5.5),respectively. These coefficients of variation are
within thosespecified by the measurement method, ASTM D6729,
forselected compounds in ASTM D6729.23 As is shown in section3.2,
these uncertainties are insignificant and do not adverselyimpact
the quality of the data. We used two different mixturessimply to
ensure that the results generated by one or the otherwere not
outliers. Because both fell within the accuracy of themethod, we
did not analyze any additional mixtures.
3. RESULTS AND DISCUSSION3.1. Validation with Pure Components.
First, pure
carbon dioxide isotherms were measured using the staticmethod to
ensure that the apparatus could reproduce bothcapillary
condensation pressures and bulk condensationpressures. The
comparison of the isotherms generated in thiswork to those
available in the literature can be found in Figure6 with an
additional isotherm at a fourth temperature not yetreported in the
literature. The fourth isotherm was useful forcomparison with the
mixture isotherms, as discussed later inthis paper.As stated in the
introduction, we emphasize that the overall
purpose of this study was to determine the effects ofconfinement
on the phase transition pressures and composi-
Figure 6. Comparison of adsorption isotherms for CO2 measured
inthis study in 3.70 nm MCM-41 and those measured in the literature
in4.4 nm MCM-41.17 The correlation of the isotherms indicated
thevalidity of the apparatus used in this study, while differences
betweenthem were attributed to differences in the equilibrium times
and theproperties of the adsorbents used.
Figure 7. Isotherm for carbon dioxide at 224 K in 3.70 nm
MCM-41.The isotherm is plotted both in terms of absolute amount
adsorbedand the amount adsorbed after the mass of the bulk fluid
has beendiscounted. Note that removing the mass of the bulk fluid
does notaffect the capillary condensation pressure (the inflection
point of thecondensation jump), as highlighted by the dashed red
line. Thedifferent regions of the isotherms are highlighted by
arrows.Adsorption and capillary condensation are confined phase
phenomena,while the bulk phase transition is not.
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tions of fluid mixtures, not the amount of the adsorbed
fluid.Thus, correcting the absolute amount adsorbed for the
excessamount adsorbed is optional in view of our ultimate
goal.Moreover, making this correction removes the bulk
phasetransition from our isotherms, thus inhibiting our efforts
toexamine the confined phase transitions as they relate to thebulk
phase transitions. However, we make the correction forCO2 in Figure
7 to show the equality of the capillarycondensation pressures of
both the corrected and uncorrectedisotherms. The correction was
made by subtracting out theweight of the bulk fluid. In essence,
the bulk volume (theinterparticle volume available to the bulk
fluid) of the coreholder (46.6 cm3) was multiplied by the bulk CO2
density at
the pressure and temperature of each data point in the
isothermas given by NIST13 and then subtracted from the
absolutemass, resulting in the mass of the confined fluid. The mass
ofthe confined fluid was then converted into millimoles using
themolar mass of CO2 (44.01 g/mol) and divided by the mass ofMCM-41
in the core holder (e.g., 8.35 g) to achieve the sameunits (mmol/g)
that were used by Morishige and Nakamura.17
This is expressed in the following equation:
ρ=
− − ××
mm m V
M mc0 B
a a (1)
where m is the measured mass at each data point, m0 is themass
of the core holder and adsorbent under high vacuum (i.e.,the mass
of the core holder and adsorbent in the absence offluid), VB is the
bulk volume of the core holder, ρ is the densityof the bulk
adsorbate, Ma is the molar mass of the adsorbate, mais the mass of
the adsorbent within the core holder, and mc isthe amount of the
confined phase.The same procedure was used for the n-pentane
isotherms.
For example, using data from the n-pentane isotherm at 24.8
°Cand 3.23 mbar, where m = 374.31 g, m0 = 374.24 g, VB = 46.6mL, ρ
= 0.0000094 g/mL, Ma = 72.12 g/mol, and ma = 8.23 g,gives mc = 0.07
mmol/g.For low temperature experiments, approximately −40 °C
and
lower, humidity in the air of the thermostatic
chamberprecipitated ice onto the core holder. Note that the
iceprecipitated onto the outside of the core holder; it did notcome
into contact with the adsorbate or adsorbent at any point.Ice
precipitation was observed both visually and through themass
readings and necessitated the addition of an extra term,Δmice, to
the equation to subtract the mass of the ice from thefinal value
for amount adsorbed. Δmice was obtained from thebalance data by
calculating the change in mass of the coreholder over time not due
to the addition of more adsorbate.Recognizing the constancy of the
combined mass of theadsorbed and confined fluid over the
equilibrium time of asingle dose of adsorbate, as discussed in
section 2.2.1, Δmice was
Figure 8. n-Pentane isotherms compared to those reported in
theliterature.18 The correlation of the isotherms indicated the
validity ofthe apparatus used in this study, while differences
between them wereattributed to differences in the properties of the
adsorbents used. Thepore size used in this work was 3.70 nm, while
that used in theliterature was 4.57 nm. P0 is the bulk saturation
pressure of n-pentaneat the relevant experimental temperature.
Figure 9. n-Pentane isotherms in 3.70 and 6.32 nm MCM-41
at297.95 K. Variation in the pore size dramatically changes the
capillarycondensation pressure; however, both bulk condensation
pressureswere equal. The bulk condensation pressures are indicated
by the redline.
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taken to be the increase in measured mass throughout theduration
of the equilibrium time and was calculated bysubtracting the total
recorded mass of the adsorbate dosedinto the system from the final
recorded mass at the attainmentof equilibrium. Adding this
correction gives:
ρ=
− − × − Δ×
mm m V m
M mc0 B ice
a a (2)
Discounting the bulk fluid from the final reported measure-ments
eliminates all bulk phase phenomena from the plottedisotherms,
except in cases where experimental error causes theobservation of
residual bulk phase behavior. To fully illustrateboth the confined
and bulk phase transitions, the isotherm forCO2 at 224 K is plotted
in Figure 7 in terms of both absolutemass and that which has been
corrected for the mass of the bulkfluid. Note that the bulk phase
transition is indicated by therightmost abrupt increase in the
amount adsorbed as described
in Figure 7. The bulk condensation was observed for all of
then-pentane and CO2 isotherms, though not always shown in
thefigures where the bulk amount was excluded. The bulkcondensation
pressure is equal to the vapor pressure and wasused to determine
the accuracy of the measurements throughcomparison with data
available on the NIST website.13
For mixtures, there is no corresponding experimental data inthe
literature, while a conversion equivalent to that for puregases is
more complicated and heavily dependent oncalculations using EOS.
Therefore, we did not make anycorrections for the adsorbed
mixtures. As mentioned before,this does not prevent us from
measuring the condensationpressure, which is simply signaled by an
abrupt jump in themass measurement. As shown in Table 2, the errors
associatedwith the isotherms are relatively insignificant and are
inagreement with the accuracies of the pressure
measurementsdiscussed in section 2.2.3.
Figure 10. Isotherms for binary mixtures of CO2 and n-pentane
measured using the static method. The confined and bulk
condensation pressures ofpure CO2 are included for ease of
comparison. No confinement-induced or bulk phase transitions
appeared in isotherms IV and VI measured at229.45 and 239.15 K due
to the shorter range of pressures used for each.
Figure 11. Isotherms for binary mixtures of CO2 and n-pentane
measured in 3.70 nm MCM-41 using the flow-through method are
denoted as VIIand VIII. The binary mixtures measured statically and
the confined and bulk condensation pressures of pure CO2 are
included for ease ofcomparison.
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Similar to the CO2 measurements, pure n-pentane isothermsat
three temperatures already reported in the literature werealso
measured to further validate the accuracy of ourexperimental system
for use with a variety of different fluids.The n-pentane isotherms
can be found in Figures 8 and 9 andtheir corresponding bulk
condensation is shown in Table 2.Figure 8 indicates the reliability
of our apparatus in predictingcapillary condensation through
comparison to isothermsavailable in the literature.However, as
previously discussed, the primary pore size used
in this work was 3.70 nm, while Morishige and Nakamurareported
their pore size to be 4.4 nm,17 and Russo et al. used4.57 nm
MCM-41.18 A full comparison of all adsorbentsconsidered in this
study can be found in Table 1. Because weused pores (i.e., the 3.70
nm MCM-41) with smaller size, ourisotherms also show lower
capillary condensation pressures.We show this in Figure 9 by
including an additional isotherm
for the 6.32 nm MCM-41 at 297.95 K. As it can be seen,increasing
the pore size from 3.70 to 6.32 nm also increased thecapillary
condensation pressure. This is in agreement with datain the
literature.24 Isotherm measurements in the 2.78 nmMCM-41 showed it
to be below the pore critical size for n-pentane, thus it cannot be
used for comparison of the confinedvapor-to-liquid phase
change.
The supercriticality of the confined fluid is evident fromTable
2, where the supercritical confined fluid in the 2.78 nmMCM-41 was
found to exhibit an inflection point in itsisotherm at the same
pressure as the capillary condensationoccurred for the 3.70 nm
MCM-41. (Because different poresizes cannot exhibit capillary
condensation at the same pressure,we infer the supercriticality of
the confined fluid in the 2.78 nmMCM-41.) However, the measurements
in all three pore sizes,as shown in Table 2, resulted in the same
bulk condensationpressure further validating the precision and
accuracy of theapparatus. The equality of the bulk condensation
pressures forthe 6.32 and 3.70 nm MCM-41 is also shown in Figure 9.
Wetherefore consider the similarity of our isotherms to those inthe
literature in addition to the agreement of our bulkmeasurements
with those available from NIST13 (see Table 2)as validation of our
apparatus.
3.2. Binary Mixtures: Static Experiments. For the binarymixtures
of carbon dioxide and n-pentane, six isotherms weremeasured at five
different temperatures in 3.70 nm MCM-41, asshown in Figure 10.
Three isotherms (218.15 and 224.35 K)exhibited both the confined
phase change and the bulk bubblepoint. One isotherm at 233.75 K
displayed only the confinedphase change because that of the bulk
was beyond the pressurerange used in the experiments. Similarly, no
confinement-induced or bulk phase transitions appeared in isotherms
IV and
Figure 12. Isotherms for ternary mixtures at 224.35 and 233.75 K
in 3.70 nm MCM-41 are denoted as isotherm IX and X, respectively.
The staticallymeasured binary isotherms are included for ease
comparison, as are the capillary condensation and bulk condensation
pressures for pure CO2.
Table 2. Bulk and Capillary Condensation Pressures of CO2 and
n-Pentane
fluidpore size[nm]
temperature[K]
bulk condensation: thiswork [bar]
bulk condensation:NIST13 [bar] % difference
calculated error[% ϵ]b
capillary condensation[bar]a
CO2 3.70 224.35 6.91 7.16 3.5 3.4 3.44CO2 3.70 234.00 10.17
10.36 1.8 2.3 5.96CO2 3.51 243.00 14.22 14.21 0.07 1.7 8.56CO2 3.70
250.00 17.73 17.85 0.67 1.3 10.82n-pentane 3.70 257.95 0.11 0.12
2.7 3.3 0.024n-pentane 3.70 267.95 0.19 0.19 0.48 1.9
0.042n-pentane 2.78 297.95 0.68 0.68 0.21 0.53 0.19n-pentane 3.70
297.95 0.68 0.68 0.35 0.53 0.19n-pentane 6.32 297.95 0.68 0.68 0.29
0.53 0.42
aThe capillary condensation pressures were calculated as the
inflection points of the condensation steps in the isotherms. b% ϵ
was calculated bydividing the error associated with either the
pressure transducer (for pressures above 1 bar) or the vacuum gauge
(for pressures below 1 bar) by theNIST13 bulk condensation pressure
and multiplying the result by 100.
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VI measured at 229.45 and 239.15 K because of the shorterrange
of pressures used for each.The accuracies of the isotherms were
estimated as discussed
in section 2.2.3, where the measurements on mixtures werefound
to be highly reliant on the dependability of the bulk
fluidcompositions. The measured bulk bubble points of the
mixtureswere then compared to data generated using the
perturbedchain statistical associating fluid theory (PC-SAFT)25
equationof state (EOS) for a consistency check. The EOS
parametersare given in the Appendix. The pressure-composition
phasediagrams for the bulk mixtures are presented in Figure 13
usingPC-SAFT at 218.15, 224.35, and 233.75 K, which correspondto
temperatures used for the experimental isotherms in Figure13 and
Table 3. Within the EOS accuracy, there is a
three-phasevapor−liquid−liquid equilibrium (VLLE) at lower
temper-atures, which occurs at 5.34 and 6.82 bar for 218.15 and
224.35K, respectively. At 233.75 K, the VLLE disappears. In
thepresence of the VLLE, for example at 218.15 K, the bubblepoint
is at the three-phase pressure (5.34 bar) as long as theoverall
mole fraction of CO2 is between 0.632 and 0.933 (theliquid−liquid
equilibrium [LLE] range). Furthermore, as shownin Figure 13, the
bubble points of the mixtures are all similar to
the vapor pressure of pure CO2 because of the highconcentrations
of CO2 in the mixtures.The bubble point values of the experiments
and the
calculations of the EOS were found to be consistent; they
arewithin 5% of each other, except for test VIII. The
differencesare attributed both to the experimental uncertainty, as
discussedin section 2.2.3, and errors inherent in the
parameterization ofthe EOS which depends on the quality of the
experimentalphase-equilibrium data used to derive the binary
interactionparameters. The consistency of the bulk bubble points
foundexperimentally and computationally may be taken as
anindication of the ability of the EOS to provide
qualitativedescriptions and quantitative estimates of the bulk
phasebehavior for use in helping elucidate the
confined-fluidphenomena observed experimentally.Figure 13 also
gives insight into the measured differences
between the initial and final compositions shown in Table 3
forthe binary mixtures measured statically. The material
balanceseems to alter the composition to a higher CO2 content as
seenin test II as well as the ternary tests IX and X. However, if
theinitial composition has a low enough CO2 content to fall
withinthe range of the LLE, such as in test III, and the new
CO2overall fraction is higher but still falls within the LLE
range,
Figure 13. Bulk phase diagrams for binary mixtures of CO2 and
n-pentane at (a) 218.15, (b) 224.35, and (c) 233.75 K calculated
using the PC-SAFTequation of state. V, L1, and L2, represent vapor,
CO2-rich liquid, and CO2-lean liquid phases, respectively. Vertical
lines are the measured finalcompositions of the tests indicated in
the legend.
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then the measured final composition is dominated by theheavier
CO2-lean liquid (L2 in Figure 13). Note that althoughtest I fell
within the LLE, its final composition is excessivelylean in CO2
(16.6 mol %) because of gravity segregation of theexperimental
fluid, that is, some n-pentane dropped to thebottom of the gas
storage vessel and injection of the liquid atthe end of the
isotherm resulted in enrichment of the bulkliquid with n-pentane.
Gravity segregation was found to be ashortcoming of the in-house
gas mixing system used forpreparation of the adsorbates; however,
improvements to thesetup and methodology immediately following
isotherm Iprecluded gravity segregation in all subsequent tests.In
observing the mixture capillary condensation, it was found
that for the binary isotherms, the confinement-induced
phasechanges occurred at pressures similar to those for pure
carbondioxide. The similarity appeared to be greater at
lowertemperatures, as shown in Figure 13, and is attributed to
thesignificantly higher concentration of carbon dioxide than
n-pentane in the overall mixture compositions (i.e., inheritance
ofthe bulk fluid behavior). This is supported by both
theexperimental data and the EOS calculations. As shown inFigure
13, the bulk mixtures, themselves, condense at pressuressimilar to
pure CO2. If the phase behavior of the bulk mixturesis carried over
to the confined mixtures, proximity of themixture capillary
condensation pressures to the pure CO2capillary condensation is
expected. In a similar manner, thetendency of behavior
transferability between the bulk andconfined mixtures is also
supported in this work by isotherms IIand III in Figure 13, where
the mixture capillary condensationpressures did not significantly
change despite a 10.4 mol %difference in the amount of CO2, echoing
the similarity of theirbulk bubble points shown in Figure 13.Other
possible phenomena that, although not directly
observed in this work, could impact the mixture
capillarycondensation pressures are confined phase separation
andselective adsorptivity. For example, phase separation in the
bulkliquid (i.e., the presence of the LLE shown in Figure 13)
maypredispose the condensed fluid to phase separation
inconfinement. In this way, the scale of the confinement andthe
wetting preference of the adsorbent may be manifested inseparation
of the phases so that the more wetting phase fills thepore
space.10,26 This phenomenon was observed experimentallyby Schemmel
et al. who used small-angle neutron scattering torecord the phase
separation of binary liquid mixtures ofisobutyric acid and
deuterated water in controlled pore glasswith an average pore size
of 10 nm.26 In their observations,phases were seen to separate in
such a way that the morewetting phase coated the pore walls and
filled parts of the porebody, while the less wetting phase
consisted only of small liquidbubbles within the pore space.26
Similarly, selective adsorptivitycould also affect the mixture
capillary condensation, causing itto occur similarly to the most
wetting component. As has beenpreviously reported, CO2 generally
has greater affinity forMCM-41 silica because of its quadrupole
moment27 and itsability to bond with the hydrogen atoms of the
silanol groupsattached to the surface of the silica.28,29 However,
the increasein CO2 in the final overall compositions for tests II,
IX, and Xinferred in Table 3 seem to contradict this, indicating
that morepentane is adsorbed throughout all of the isotherms
measuredin this work. This observation is under further
investigation butmay be attributed to differences in the
hydroxylation states ofthe MCM-41 used in this work and that used
in the literature.As has been shown in a comprehensive study by
Zhuravlev, theT
able
3.InitialandFinalCom
position
sof
theBulkFluids
forAllof
theMixturesMeasuredin
ThisWorkAlong
withAccuraciesfortheBulkBub
blePoint
Measurements
initialcompositio
n[m
ol%]
finalcompositio
n[m
ol%]
comparison
with
PC-SAFT
test
method
temperature
[K]
CO
2nC
5H12
iC5H
12impurities
CO
2nC
5H12
iC5H
12impurities
measuredbulk
bubble
point[bar]
calculated
bulk
bubble
point[bar]a
%difference
mixture
capillary
condensatio
npressure
[bar]b
Istatic
218.15
84.1
14.9
1.0
16.6
82.7
0.7
5.17
5.34
3.24
2.84
IIstatic
224.35
93.8
6.1
0.1
94.6
5.3
0.1
6.60
6.88
4.24
3.59
III
static
224.35
83.4
16.0
0.6
67.7
31.6
0.7
6.51
6.76
3.84
3.60
IVstatic
229.45
83.6
15.7
0.7
Vstatic
233.75
93.6
6.3
0.1
5.52
VI
static
239.15
78.8
16.0
5.2
VII
dynamic
224.35
93.8
6.0
0.2
92.0
6.9
1.1
6.73
6.85
1.78
3.53
VIII
dynamic
233.75
95.6
4.1
0.3
95.0
3.3
1.7
9.0
9.87
9.67
5.44
IXstatic
224.35
76.3
16.6
7.0
0.1
80.6
13.5
5.6
0.3
6.7
6.76
0.90
3.68
Xstatic
233.75
94.0
3.0
2.9
0.1
95.8
2.9
0.9
0.4
9.6
9.91
3.23
5.49
aBubblepointsarecalculated
usingPC
-SAFT
atfinalcom
positio
ns(impuritiesareincluded
tonC
5H12forbinariesandiC
5H12forternaries).bMixture
capillary
condensatio
npressureswerecalculated
astheinflectio
npointsof
thecondensatio
nstepsin
theisotherm
s.
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wettability (and therefore the selective adsorptivity) of silica
ishighly dependent on its state of hydroxylation.30 Note thatwithin
the scope of this work, the only isotherms whereselectivity can be
inferred from the enrichment or depletion ofcomponents in the final
composition are those for which noliquid−liquid equilibrium was
observed in the bulk.3.3. Binary Mixtures: Flow-Through
Experiments. Two
isotherms for binary mixtures were measured using the
flow-through method at 224.35 and 233.75 K. The first isotherm
wasmeasured at 224.35 K using a flow rate of 0.1 cm3/min. Theflow
rate was varied from 1 to 0.01 cm3/min throughout theduration of
the second isotherm measured at 233.75 K.Qualitatively, no
differences were observed among the datagenerated for isotherm VIII
using different flow rates. Littledifference was observed between
the binary isothermsmeasured statically and those measured
dynamically, that is,both exhibited confinement-induced phase
transitions similar tothose of pure CO2. Therefore, the flow,
itself, was not observedto significantly affect the mixture
capillary condensationpressure.Unlike the majority of the static
measurements where the
final composition of the bulk fluid (in contact with the
confinedfluid) exhibited a change in the concentration of CO2,
thosemeasured dynamically exhibited a final composition close
totheir initial composition. This is mainly attributed to
theconstant composition of the bulk fluids used in the flow-through
experiments. Moreover, both mixtures were composedof more than 90%
CO2, which meant that after the bulk bubblepoint was crossed, only
one phase was present rather than two,as seen in Figure 13.However,
the composition of the effluent from the core
holder was seen to vary throughout the pressures
characteristicof each isotherm. This is shown in Figure 14, where
the
composition at zero pressure is the composition of the bulkfluid
before it had come into contact with the adsorbent andthe
compositions corresponding to all other data points weretaken only
after equilibrium (i.e., 2 h) had occurred. Thevariance of the
composition of the effluent between the initialand final pressures
may either be a byproduct of progression
through the bulk phase envelope or an indication of
selectiveadsorptivity. In the case of the latter, the abrupt
decrease in theconcentration of CO2 at low pressures would indicate
highselectivity during the adsorption phase of the isotherm. This
isin agreement with other studies, such as that of Yun et al.,8
which show high selectivity at low pressures.3.4. Ternary
Mixtures. In the binary mixture measure-
ments, isopentanea naturally-occurring isomer of n-pen-tanewas
found to be the most common impurity. Toquantify the effect of this
impurity on the binary measurements,two ternary mixtures of CO2,
n-pentane, and isopentane weremeasured statically at 224.35 and
233.75 K. These temperatureswere chosen for ease of comparison to
both the pure CO2isotherms and the binary mixture isotherms. The
isotherms areshown in Figure 12, while the initial and final
compositions ofthe mixtures used in each experiment as well as the
bulk bubblepoints are given in Table 3.Unlike the static
measurements made on the binary mixtures,
the final compositions measured during the static ternarymixture
experiments always gained CO2 in comparison to theinitial
compositions.Similar to the binary isotherms, the confined
phase
transitions of the ternary mixtures also occurred similarly
tothat of pure CO2 (Figure 12). Though differences in
theadsorptivity of branched and normal alkanes31 may influencethe
chemistry, and therefore the phase behavior, of the confinedfluid,
they were not observed in this work, which may be due tosmall
amounts of isopentane used in the experiments.
4. CONCLUSIONS AND REMARKS
A novel gravimetric apparatus for measuring the
capillarycondensation of both pure fluids and mixtures in a wide
varietyof adsorbents was introduced. It was successfully
validatedagainst data available in the literature for both pure CO2
and n-pentane in MCM-41. The study was then expanded to
generateisotherms for binary and ternary mixtures using both static
anddynamic methods.Throughout the experiments, the equilibrium time
was found
to have large impacts on the determination of confined
phasetransitions, while the confined phase behavior was observed
tobe independent from the flow rate of the fluid mixtures over
therange of flow rates employed in the dynamic method.
However,qualitatively, one may be preferred over the other
forinvestigation into specific phenomena. For example, the
staticmethod may be used to simulate reservoir- or
aquifer-basedsystems in which fluid is predominately immobile, such
asvirgin shale gas reservoirs or CO2 plumes in ultratight rock.
Onthe other hand, the dynamic method may be used toapproximate
flow-through porous media situations. Using thesame example, such
situations could include CO2 injection orhydrocarbon production
from tight rock. But because nodifference has yet been observed
between the data generatedusing the two methods, the one that is
most convenient mayyet be applied to both cases. We suggest that
this may hold trueeven in studies using highly selective
adsorbents, as the staticmethod may still be employed by using a
larger reservoir ofbulk fluid as the adsorbate, so that changes in
the compositionof the bulk fluid brought on by the selectivity
remain negligible.In this work, the static measurements were
preferred simplybecause they required less experimental fluid than
the dynamicmeasurements and were less time-consuming and
complicatedto conduct.
Figure 14. Progression of the compositions of the effluents
during thedynamic measurements is plotted with regard to the
experimentalpressures at which the effluent was bypassed to the gas
chromatograph.
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As displayed in Figure 15, comparison of the confined
fluidbehavior to the bulk showed transferability of the bulk
mixture
behavior to the confined mixtures regardless of theexperimental
method. Because all of the mixtures werecharacterized by large
overall mole fractions of CO2, thepressures of the mixture phase
transitions occurred in theproximity of the respective condensation
pressures of pureCO2. In Figure 15, the mixture capillary
condensation ofisotherms II and VIII are plotted with respect to
their bulkphase envelope, along with the bulk and confined
phasetransitions for pure CO2.Figure 15 also exemplifies the
magnitudes of the confine-
ment-induced shifts of the phase transitions observedthroughout
this study. For example, the mixture capillarycondensation
pressures of both isotherms II and VIII werefound to occur
approximately halfway between the bulk dewpoint and bubble point.
This finding is representative of all theconfinement-induced phase
transitions measured for mixturesin this work, including the
ternary mixtures, which to the bestof our knowledge are the first
experimental isotherms
displaying the mixture capillary condensation of fluids withmore
than two components.In spite of the significance of these findings,
they are
preliminary and necessitate future studies using morecomplicated
adsorbents, adsorbates, and flow processes tofully elucidate the
physics of fluid mixture phase behavior innanopores. Such studies
are included in our future work usingthe apparatus presented herein
which, given its successfulvalidation in both the static and
dynamic measurements ofpure-component, binary-component, and
multicomponentisotherms, provides a promising vehicle for this
research.
■ APPENDIXPC-SAFT parameters used in this work are shown in
Table A1.
■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting
Information is available free of charge on theACS Publications
website at DOI: 10.1021/acs.lang-muir.7b04134.
Measured isotherm data corresponding to carbondioxide,
n-pentane, and binary and ternary mixturesand compositional change
of mixtures (PDF)
■ AUTHOR INFORMATIONCorresponding Author*E-mail:
[email protected] Barsotti:
0000-0002-4106-5543NotesThe authors declare no competing financial
interest.
■ ACKNOWLEDGMENTSWe gratefully acknowledge the financial support
of SaudiAramco, Hess Corporation, and the School of EnergyResources
and the College of Engineering and Applied Scienceat the University
of Wyoming. From the Piri Research Group atthe University of
Wyoming, we also thank Henry Plancher forhis help in preparing the
adsorbates and Alimohammad Anbariand Evan Lowry for their technical
support.
■ REFERENCES(1) Singer, L. E.; Peterson, D. International Energy
Outlook 2016;2016; Vol. DOE/EIA-04.(2) Loucks, R. G.; Reed, R. M.;
Ruppel, S. C.; Jarvie, D. M.Morphology, Genesis, and Distribution
of Nanometer-Scale Pores inSiliceous Mudstones of the Mississippian
Barnett Shale. J. Sediment.Res. 2009, 79, 848−861.(3) Barsotti, E.;
Tan, S. P.; Saraji, S.; Piri, M.; Chen, J.-H. A review oncapillary
condensation in nanoporous media: Implications forhydrocarbon
recovery from tight reservoirs. Fuel 2016, 184, 344−361.
Figure 15. Confinement-induced phase transition of isotherm
II(static method) plotted with respect to the bulk phase envelope
of thefluid (solid black line), the bulk vapor pressure of pure CO2
(solid redline), and the measured capillary condensation pressures
for pure CO2(filled red circles and dashed red line). Isotherm VIII
(dynamicmethod) is added for rough comparison. Empty black circles
are themeasured mixture capillary condensation pressures while the
emptyblack squares are the corresponding measured bulk bubble
points.
Table A1. PC-SAFT Parameters Used in This Worka
i/j m σ [Å] ϵ/kB [K] CO2 nC5H12 iC5H12
CO232 2.5834 2.5564 151.7666 a = 0.1767 a = 0.14
nC5H1232 2.6747 3.7656 232.1710 b = −1.502 × 10−4 a = 0.01
iC5H1225 2.5620 3.8296 230.7500 b = 0 b = 0
aThe right part of the table contains the binary interaction
parameters: kij = a + bT; T is the absolute temperature. The kij
values are obtained fromcorrelations over experimental data;33,34
kij between the isomers is estimated due to the absence of
experimental data.
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(4) Cho, H.; Bartl, M. H.; Deo, M. Bubble Point Measurements
ofHydrocarbon Mixtures in Mesoporous Media. Energy Fuels 2017,
31,3436−3444.(5) Luo, S.; Lutkenhaus, J. L.; Nasrabadi, H.
Experimental Study ofConfinement Effect on Hydrocarbon Phase
Behavior in Nano-ScalePorous Media Using Differential Scanning
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Langmuir Article
DOI: 10.1021/acs.langmuir.7b04134Langmuir 2018, 34,
1967−1980
1980
http://dx.doi.org/10.1021/acs.langmuir.7b04134