Capillary Condensation of Binary and Ternary Mixtures of n ... · pentane using static and...

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

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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

Langmuir Article

DOI: 10.1021/acs.langmuir.7b04134Langmuir 2018, 34, 1967−1980

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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.

Langmuir Article


1975


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.

Langmuir Article


1976


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.

Langmuir Article


1977


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.

Langmuir Article


1978


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.

Langmuir Article


1979

http://pubs.acs.orghttp://pubs.acs.org/doi/abs/10.1021/acs.langmuir.7b04134http://pubs.acs.org/doi/abs/10.1021/acs.langmuir.7b04134http://pubs.acs.org/doi/suppl/10.1021/acs.langmuir.7b04134/suppl_file/la7b04134_si_001.pdfmailto:[email protected]://orcid.org/0000-0002-4106-5543http://dx.doi.org/10.1021/acs.langmuir.7b04134

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(25) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation ofState Based on a Perturbation Theory for Chain Molecules. Ind. Eng.Chem. Res. 2001, 40, 1244−1260.(26) Schemmel, S.; Rother, G.; Eckerlebe, H.; Findenegg, G. H. Localstructure of a phase-separating binary mixture in a mesoporous glassmatrix studied by small-angle neutron scattering. J. Chem. Phys. 2005,122, 244718.(27) Chang, S.-C.; Chien, S.-Y.; Chen, C.-L.; Chen, C.-K. Analyzingadsorption characteristics of CO2, N2 and H2O in MCM-41 silica bymolecular simulation. Appl. Surf. Sci. 2015, 331, 225−233.(28) dos Santos, T. C.; Bourrelly, S.; Llewellyn, P. L.; Carneiro, J. W.d. M.; Ronconi, C. M. Adsorption of CO2 on amine-functionalisedMCM-41: experimental and theoretical studies. Phys. Chem. Chem.Phys. 2015, 17, 11095−11102.(29) Roque-Malherbe, R.; Polanco-Estrella, R.; Marquez-Linares, F.Study of the Interaction between Silica Surfaces and the CarbonDioxide Molecule. J. Phys. Chem. C 2010, 114, 17773−17787.(30) Zhuravlev, L. T. The surface chemistry of amorphous silica.Zhuravlev model. Colloids Surf., A 2000, 173, 1−38.(31) Harrison, A.; Cracknell, R.; Krueger-Venus, J.; Sarkisov, L.Branched versus linear alkane adsorption in carbonaceous slit pores.Adsorption 2014, 20, 427−437.(32) Tan, S. P.; Piri, M. Equation-of-State Modeling of Confined-Fluid Phase Equilibria in Nanopores. Fluid Phase Equilib. 2015, 393,48−63.(33) Besserer, G. J.; Robinson, D. B. Equilibrium phase properties ofisopentane-carbon dioxide system. J. Chem. Eng. Data 1975, 20, 93−96.(34) Besserer, G. J.; Robinson, D. B. Equilibrium-Phase Properties ofn-Pentane-Carbon Dioxide System. J. Chem. Eng. Data 1973, 18, 416−419.

Langmuir Article


1980

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