Capillary Condensation of Binary and Ternary Mixtures of N-Pentane

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Cite This: Langmuir 2018, 34, 1967−1980 pubs.acs.org/Langmuir

Capillary Condensation of Binary and Ternary Mixtures of n‑ − − Pentane Isopentane CO2 in Nanopores: An Experimental Study on the Eﬀects of Composition and Equilibrium Elizabeth 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 the chemical and physical behavior of fluids. While some quantitative understanding is available for how pure fluids behave in nanopores, there is little such insight for mixtures. This study aims to shed light on how nanoporosity impacts the phase behavior and composition of confined mixtures through comparison of the effects of static and dynamic equilibrium on experimentally measured isotherms and chromatographic analysis of the experimental fluids. To this end, a novel gravimetric apparatus is introduced and validated. Unlike apparatuses that have been previously used to study the confinement-induced phase behavior of fluids, this apparatus employs a gravimetric technique capable of discerning phase transitions in a wide variety of nanoporous media under both static and dynamic conditions. The apparatus was successfully validated 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 were measured using the static method. While the equilibrium time was found important for determination of confined phase transitions, flow rate in the dynamic method was not found to affect the confined phase behavior. For all measurements, the results indicate qualitative transferability of the bulk phase behavior to the confined fluid.

1. INTRODUCTION lower pressures in an isothermal system or at higher fl temperatures in an isobaric systemin confinement than in Although the study of pure, single-component uids in fi nanopores has been broadly undertaken, there is very little the bulk. This con nement-induced phase change, called capillary condensation, has been reported in the literature, see knowledge as to how mixtures in nanopores behave. A 3 fi Barsotti et al. for a comprehensive review, yet most of the quantitative realization of nanocon nement-induced mixture fl behavior is prerequisite to breakthroughs in many fields from associated studies involve single-component uids in simple pore systems far removed from those encountered in the medicine and biology to materials science and electrochemistry. 3 An example of how significantly a comprehensive under- reservoir setting. Those studies that have been carried out on ff fl multicomponent fluids are scarce, providing little overall insight standing of the e ects of nanoporosity on uid mixtures can fi fl impact each of these scientific endeavors can be found in into the phase behavior of con ned uid mixtures. The majority petroleum engineering, where the ability to accurately predict of the experimental studies have been carried out under isobaric fi fi fl conditions to probe the confinement-induced bubble point. A con ned mixture behavior could signi cantly in uence the fi economic valuation of shale and tight gas reservoirs. limited number of studies have observed the con nement- induced dew point, while a few others have focused more on Within the next few decades, natural gas consumption is fi fl projected to increase more than that of any other energy the structure of the con ned uid during the phase transition 1 with emphasis on phase separation. To the best of our resource. Much of this growth in demand will be satiated by fi vastly increasing production from shale and tight gas knowledge, none have witnessed the con ned critical point of reservoirs.1 In spite of this, very little is known about the mixtures. fl fl Studies on the confined bubble point include the work of physics of uid ow, transport, and storage in these reservoirs. 4 5 6,7 8 In particular, there is virtually no understanding of fluid phase Cho et al., Luo et al., Jones and Fretwell, and Yun et al. fi While all the studies, except for that of Luo et al.,5 witnessed behavior in such systems. Shale gas reservoirs are typi ed by fi nanopores, which constitute a significant fraction of their total depression of the con ned bubble point with respect to that of porosity.2 The scale of these pores, alone, regardless of their chemistry or geometry, may alter the phase behavior of the Received: December 4, 2017 confined fluids from their bulk counterparts. Specifically, the Revised: January 9, 2018 vapor-to-liquid phase transition may occur earlierthat is, at Published: January 23, 2018

© 2018 American Chemical Society 1967 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article the bulk, the results must be viewed in the context of the same pressure and temperature, so that the confined fluid did experimental path. The two paths available for studies of not comprise a homogenous mixture.10 Thus, confinement confined phase phenomena are adsorption and desorption. In could not only affect the phase transitions of fluids, such as adsorption, the initial phase of the bulk fluid is gaseous. natural gas, but also their compositions, including the pore fluid Adsorption experiments are exemplified in the literature by the occupancy in the event of confinement-induced phase works of Jones and Fretwell7 and Yun et al.,8 who used positron separation. This could prove important to the ultimate recovery annihilation spectroscopy and a volumetric flow-through of shale gas, because the pore fluid occupancy dictates the approach, respectively. In desorption, the initial phase of the mechanisms by which various phases will be produced. bulk fluid is liquid. Desorption experiments are represented in In an effort to better understand the effect of confinement on the literature by studies employing density scanning calorimetry both the phase transitions and compositions of fluids in measurements, such as that of Luo et al.5 nanopores, a novel gravimetric apparatus11 is introduced for the Although the adsorption and desorption experiments both study of both pure fluids and mixtures in a variety of porous result in confinement-induced shifts of the fluid phase media using both static and dynamic processes. Unlike the transitions, the results are quantitatively different. Alam et al. apparatuses used in previous studies of confined fluid mixtures, explained this difference in their positron annihilation spec- such as the isobaric differential scanning calorimetry5 and troscopy study of the confined dew points of binary mixtures of positron annihilation spectroscopy measurements9 or the nitrogen and argon.9 They found inequalities between the isothermal volumetric measurements of Yun et al.,8 our confined dew points measured using adsorption and desorption apparatus uses changes in mass to directly measure the amount to result from enrichment of the confined fluid by the bulk fluid of fluid adsorbed. This allows for isothermal measurements that during desorption.9 Thus, although adsorption and desorption are more relevant to shale gas recovery than isobaric both qualitatively indicate confinement-induced shifts of the measurements, that is, temperature can generally be considered phase transition, the degree to which those shifts occur is highly constant in gas reservoirs, and more accurate12 than volumetric dependent on whether desorption or adsorption is taking place. measurements, which cannot measure the adsorbed amount Furthermore, the studies can be made either statically or directly but rather depend on equations of state to calculate it. using a flow-through method, such as that used by Yun et al.8 Similarly, this apparatus has the ability to facilitate large Whereas the other studies involving gas mixtures used a static quantities of adsorbents, including core plugs housed in high- approach in which the fluid within the pores was stationary at pressure core holders. Such a high capacity gravimetric equilibrium, the study of Yun et al. involved fluids that were apparatus has not been previously reported in the literature. always flowing and therefore experienced dynamic equilibrium.8 Although the evaluation of the confined phase behavior of Putting this into the context of natural gas production, the reservoir fluids in core plugs was beyond the scope of this static and dynamic experiments approximately represent study, the ability of the apparatus to support a core holder and different yet complimentary situations throughout the life of a its associated plumbing was tested and validated throughout reservoir. For example, the static experiments best approximate this study by utilizing a titanium core holder packed with unproduced reservoirs in which fluids are stationary, the MCM-41 for all experiments herein. situation of which is relevant to the original gas in place In this work, the apparatus was first validated using calculations. Conversely, dynamic experiments best approx- isothermal capillary condensation data in the literature for imate reservoir processes in which fluids are flowing, such as pure carbon dioxide and pure n-pentane and with bulk production and injection, but with a constant flow rate. condensation data for both compounds from the National 13 Experimentally, the two methods differ in that during static Institute of Standards and Technology (NIST). Next, experiments, the overall (confined plus bulk) composition of building upon the data for the pure component isotherms, the fluid is constant while during the flow-through experiments, binary isotherms of carbon dioxide and n-pentane were only the bulk composition of the fluid is maintained constant measured for the first time using a static method and then a by the flow. Except for this methodological difference, there is dynamic, flow-through method. Finally, two ternary mixture no evidence for any difference in the underlying concept as isotherms for CO2, n-pentane, and isopentane were measured. both can provide the desired capillary condensation. However, To the best of our knowledge, these are the first isotherms comparison between them would support decision making in displaying the confinement-induced vapor-to-condensed phase choosing the experimental setup if one decides to apply transitions of gas mixtures with more than two components. 9 gravimetric measurements. With respect to the findings of Alam et al., only adsorption Nonetheless, in evaluating the data generated by these paths were used for all measurements to negate the effect of the fi fl experiments, knowledge of the structure of the fluidthe enrichment of the con ned uid by the bulk liquid when they number and location of the molecules of each component are in direct contact prior to the desorption. In this work, the within the pores is also necessary. Although, often no observed abrupt increase of adsorption in the isotherms of preferential adsorption is observed, such as in the work of mixtures is termed mixture capillary condensation. Alam et al.,9 there are cases in which it may significantly alter the structure of the confined mixture beyond what is expected, 2. MATERIALS AND METHODS that is, confinement-induced phase transitions may be 2.1. Materials. Three MCM-41 samples were obtained disproportionately skewed by the more selectively adsorbed from Glantreo, Ltd. MCM-41 is a mesoporous silica well- component. In measuring the capillary condensation of binary known throughout the literature for its easily tuned pore size mixtures of n-hexane and perfluoro-n-hexane, Kohonen and and simple pore geometry, consisting of uniform, unconnected Christenson observed co-condensation between muscovite cylindrical pores.14 Using nitrogen adsorption isotherms at 77 mica surfaces using a surface force apparatus.10 Essentially, K, Barrett−Joyner−Halenda (BJH)15 and Dollimore−Heal both an n-hexane-rich phase and a perfluoro-n-hexane-rich (D−H)16 analyses gave average pore sizes of 3.51 and 3.70 phase condensed, but they occurred separately, albeit at the nm, respectively, for the first sample, 2.59 and 2.78 nm for the

1968 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

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 1 μm, while the particles were found to have a thin, elliptical geometry. second sample, and 6.06 and 6.32 nm for the third sample. For using a customized Agilent 7890B gas chromatograph from the first sample, small angle X-ray scattering indicated the Separation Systems, Inc. presence of hexagonal unit cells with a lattice parameter of 4.78 2.2. Experimental Setup and Procedure. Isotherms were nm, while transmission electron microscopy (TEM) showed measured using a novel gravimetric apparatus11 that allows for particle size to be approximately 1 μm in diameter. TEM both static and flow-through measurements of adsorption, micrographs of the 3.70 nm MCM-41 used in this study are desorption, and capillary condensation in adsorbent packs at shown in Figure 1. The properties of all of the adsorbents temperatures from 173.15 to 503.15 K. An environmental considered in this work are given in Table 1. chamber (Thermotron) with precise temperature control of ±0.1 K was used as a thermostat. Table 1. Comparison of the Adsorbent Characteristics Throughout the experiments, a Rosemount pressure trans- Referenced in This Work to Those Used in This Study ducer (Emerson) and a Leybold TM 101 vacuum gauge were used to measure positive and negative (i.e., below atmospheric) BET surface D−H pore BJH pore NLDFT pore adsorbent area [m2/g] size [nm] size [nm] size [nm] pressures, respectively, at a frequency of once per second. As with all gravimetric apparatuses, the phase of the confined fluid this work: 1043 2.78 2.59 2.78 nm was determined by the relationship between its mass and this work: 832 3.70 3.51 pressure. The mass of the MCM-41 pack was measured 3.70 nm continuously at a frequency of once per second throughout the this work: 586 6.32 6.06 experiments with an accuracy ±0.00001 g using an XPE 505C 6.32 nm mass comparator from Mettler Toledo. A custom-made data Morishige & 865 4.4 Nakamura17 acquisition box and LabVIEW computer program were used to Russo et al.18 934 4.57 log all data. A schematic of the experimental setup is presented in Figure 2. The integrity of the system was maintained by outgassing it For the purposes of this work, three packs of the MCM-41 at 373.15 K for at least 12 h after any exposure to humidity or were used, where each sample of MCM-41 was packed into its air. This was to prevent irregularities in the data due to own titanium core holder using the packing procedure physisorbed water. It was determined that no heat was described by Saraji.19 Through geometric calculations, the necessary to achieve appropriate outgassing between consec- 2.78, 3.70, and 6.32 nm MCM-41 packs were found to have utive isotherms where neither air nor water was present as long interparticle void volumes of 46.7, 46.6, and 47.0 cm3, as the same vacuum level could be achieved between the respectively. The total volume of each core holder was 56.4 isotherm measurements. cm3, that is, in all three cases, the MCM-41 took up 2.2.1. Static Method. In the static method, for experiments approximately 17% of the available volume. involving both pure gases and mixtures, a variable dosing For the adsorption experiments, carbon dioxide (99.9995%, volume was used to incrementally increase the gas content Airgas, Inc.), n-pentane (99.8%, Alfa Aesar), and isopentane (mass) to change the pressure of the system under isothermal (99%, Alfa Aesar) were used. For single-component experi- conditions, while the system was closed between doses. In all ments, the n-pentane was first dried with calcium hydride. cases, the dosing volume was simply a combination of valves Subsequently, the fluid was distilled and then stored under and variable lengths of tubing plumbed directly into the system. helium. Gas mixtures were prepared using a gravimetric gas For experiments with pure carbon dioxide, the dosing volume mixing system developed in-house for this purpose. The was fed directly by the gas cylinder. For the pure n-pentane and compositions of the mixtures were confirmed through a the mixture experiments, the dosing volume was fed by a dual- combination of fixed gas and detailed hydrocarbon analysis cylinder 6000 series Quizix pump (Chandler Engineering). This

1969 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

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

ff Figure 3. E ect of equilibrium time on the capillary condensation pressure and the structure of the isotherm for CO2 at 234.35 K. Data points were taken 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 be negligible. minimized air contamination of the n-pentane, which was liquid During those time periods, pressure and mass data were at standard conditions, and allowed for precise pressure control recorded at 5, 10, 30, 60, 120, 180, and 240 min. The resulting of the bulk mixtures to prevent liquid dropout. During the isotherms are shown in Figure 3. static measurements, each new dose of gas introduced into the In the case of Figure 3, the capillary condensation pressure at system was allowed to equilibrate until the pressure of the 30 min was estimated to be 2.8% higher than the capillary system became constant. condensation pressure at 120 min. Although beyond the scope Equilibrium time for both the adsorption and capillary of this study, this may also have implications for determination condensation regions of isotherms has been discussed in the of the hysteresis critical temperature, as hysteresis may be literature by Naumov,20 who found that for cyclohexane at 297 artificially induced through variations in the equilibrium time. K in Vycor glass with pores of approximately 6 nm diameter, Similarly, it may affect the method used to locate the pore adsorption equilibrium occurred within 1 h, while capillary critical temperature. Using a method proposed by Morishige condensation equilibrium could not be achieved even after 4 and Nakamura, locating the pore critical temperature is reliant h.20 Therefore, according to the findings of Naumov, if time is upon the slope of the isotherm,17 which may also be affected by divided equally among all data points, those for adsorption may increasing or decreasing the time allowed for equilibrium, as be at equilibrium, while those for capillary condensation may shown in Figure 3. not. To determine the effects of nonequilibrium on the shape It is important to note that our apparatus is fundamentally and condensation pressures of the pure component isotherms, different from the more traditional gravimetric apparatuses an isotherm for carbon dioxide at 234.35 K was measured in presented in the literature, as shown in Figure 4. Most which doses of gas at different pressures for both adsorption traditional gravimetric apparatuses utilize a weighing pan and capillary condensation were left to equilibrate for 4 h. suspended in a gaseous atmosphere of the adsorbate, where

1970 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

static method was defined as the point at which the data points for 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 by subtracting out the mass of the bulk fluid based on the geometries of the core holder and the adsorbent pack. The diagram in Figure 4 illustrates the differences between the equilibration of our apparatus and other gravimetric apparatuses by emphasizing the constant and changing properties, such as pressure and density, associated with each. Interested readers are referred to Rouquerol et al.21 for a comprehensive discussion on the data analysis required for more traditional gravimetric setups (Figure 4a), while a comprehensive discussion of the data analysis employed with our apparatus is presented in section 3.1. 2.2.2. Flow-Through Method. In the flow-through method, gas mixtures were injected continuously into the core holder using one cylinder of the Quizix pump, while the second cylinder received the effluent and provided back pressure regulation. The Quizix pump had the ability to apply flow rates from 0.0001 to 200 cm3/min and could also apply back pressures from below atmospheric pressure to 700 bar. To progress from one data point of an isotherm to another, the pressure was increased using either the back pressure or the injection cylinder (no discrepancy between the two was found), while the gas was flowed continuously before, during, and after the change in pressure. At each data point, constant flow and Figure 4. A comparison of the equilibration of more traditional pressure were maintained for at least 2 h, where the minimum gravimetric apparatuses used in the literature (a) to that of our equilibrium time was adopted from the static method. gravimetric apparatus (b). Note that the volume of the confined fluid 2.2.3. Compositional Analysis. For both the static and may change because of the strain of the adsorbent, but because the dynamic measurements, the compositions of the bulk fluid 22 strain generally does not observably affect the measured isotherms, mixtures, both at the beginning of the experiments (while all this change in volume is considered to be negligible in this work. fluid was in the gas phase) before it had come into contact with the adsorbent and at the end of the isotherms (once the bulk bubble point had been crossed) while the bulk fluid was in any phase change within the adsorbent on the weighing pan contact with the adsorbent were measured using the gas causes depletion (in the case of adsorption) of the adsorbate chromatograph. Note that the compositions of the fluids were atmosphere as the gas molecules are drawn into the pore space. all measured in situ, for the gas chromatograph was directly This allows for the measurement of mass uptake curves, but plumbed into the system, as shown in Figure 2. In this way, also necessitates corrections for buoyancy as the density and chromatographic analysis of the fluid involved removing 111 μL pressure of the adsorbate atmosphere change. In our apparatus, of fluid directly from the plumbing of the system for analysis. both the adsorbent and the bulk adsorbate are housed within Because this volume accounts for 0.22% of the total volume of the core holder, so that for each dose of adsorbate, the mass of our core holder and an even smaller percentage of the volume the dose is constant, although the phase may change. The of the entire system (Figure 2), the effect of its removal on the injected dose initially causes an abrupt increase in the detected pressure and composition of the adsorbate were considered pressure that then decreases as the system equilibrates as shown negligible. In the dynamic measurements, additional analysis of in Figure 5. The more gas that is adsorbed, the more the the adsorbate was undertaken at the end (i.e., once equilibrium pressure of the bulk adsorbate will decrease after each dose. had been achieved) of each dose using the same in situ sampling Because of this pressure behavior, the equilibrium during the procedure.

ﬂ ﬁ Figure 5. Characteristic pressure equilibration curve for a single dose of uid taken from data for CO2 at 224.35 K. Note that the factory-speci ed response times of the pressure transducers and the observed response times of the balance were less than 1 s.

1971 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

2.2.4. Measurement Accuracy. To gauge the accuracy of the apparatus, the uncertainties associated with it were identified and analyzed. The accuracy of the overall apparatus depends on the accuracies of the mass readings, the pressure measurements, and the compositional analyses of the experimental fluids (in the case of mixture experiments). First, the manufacturer stated absolute repeatability of the balance is 0.06 mg, whereas its repeatability at nominal load (500 g) is 0.035 mg and at low load (20 g) is 0.01 mg. The mass of the core holder, adsorbent, and adsorbate combined was within 300−400 g throughout all experiments; therefore, we consider the repeatability to be better than 0.035 mg. This uncertainty is insignificant, as it is several orders of magnitude smaller than the amounts adsorbed given in Figures 6−12. Note that housing the balance on top of

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 adsorbed and the amount adsorbed after the mass of the bulk fluid has been discounted. Note that removing the mass of the bulk fluid does not affect the capillary condensation pressure (the inflection point of the condensation jump), as highlighted by the dashed red line. The different regions of the isotherms are highlighted by arrows. Adsorption and capillary condensation are confined phase phenomena, while the bulk phase transition is not.

Third, the accuracy associated with compositional analysis was determined by measuring the compositions of two binary mixtures of carbon dioxide and n-pentane multiple times (six and nine measurements were taken for the first and second mixtures which comprised 68% CO2 and 32% n-pentane and 77% CO2 and 23% n-pentane, respectively) and then calculating their standard deviations. The standard deviations for the first and second mixtures were 1.8 mol % (coefficient of variation = 2.3) and 4.1 mol % (coefficient of variation = 5.5), respectively. These coefficients of variation are within those specified by the measurement method, ASTM D6729, for selected compounds in ASTM D6729.23 As is shown in section 3.2, these uncertainties are insignificant and do not adversely impact the quality of the data. We used two different mixtures Figure 6. Comparison of adsorption isotherms for CO2 measured in simply to ensure that the results generated by one or the other this study in 3.70 nm MCM-41 and those measured in the literature in 17 were not outliers. Because both fell within the accuracy of the 4.4 nm MCM-41. The correlation of the isotherms indicated the validity of the apparatus used in this study, while differences between method, we did not analyze any additional mixtures. them were attributed to differences in the equilibrium times and the properties of the adsorbents used. 3. RESULTS AND DISCUSSION 3.1. Validation with Pure Components. First, pure the antivibration table above the environmental chamber (see carbon dioxide isotherms were measured using the static Figure 2) mitigated the addition of any inaccuracies due to the method to ensure that the apparatus could reproduce both experimental conditions, such as changes in temperature or capillary condensation pressures and bulk condensation vibrations. Throughout all experiments, the balance was pressures. The comparison of the isotherms generated in this maintained at local atmospheric pressure at approximately 21 work to those available in the literature can be found in Figure °C as recommended by the manufacturer. 6 with an additional isotherm at a fourth temperature not yet The Rosemount pressure transducer and the Leybold reported in the literature. The fourth isotherm was useful for vacuum gauge were characterized by manufacturer-specified comparison with the mixture isotherms, as discussed later in accuracies equal to or better than ±0.24 and ±0.0036 bar, this paper. respectively. The uncertainties in pressure associated with the As stated in the introduction, we emphasize that the overall ff measurements for CO2 and n-pentane are given in Table 2, purpose of this study was to determine the e ects of where they are shown to be insignificant. confinement on the phase transition pressures and composi-

1972 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

Figure 9. n-Pentane isotherms in 3.70 and 6.32 nm MCM-41 at 297.95 K. Variation in the pore size dramatically changes the capillary condensation pressure; however, both bulk condensation pressures were equal. The bulk condensation pressures are indicated by the red line.

the pressure and temperature of each data point in the isotherm as given by NIST13 and then subtracted from the absolute mass, resulting in the mass of the confined fluid. The mass of the confined fluid was then converted into millimoles using the molar mass of CO2 (44.01 g/mol) and divided by the mass of MCM-41 in the core holder (e.g., 8.35 g) to achieve the same units (mmol/g) that were used by Morishige and Nakamura.17 This is expressed in the following equation:

mm−−×0B V ρ mc = Mmaa× (1)

where m is the measured mass at each data point, m0 is the mass of the core holder and adsorbent under high vacuum (i.e., the mass of the core holder and adsorbent in the absence of fl ρ uid), VB is the bulk volume of the core holder, is the density of the bulk adsorbate, Ma is the molar mass of the adsorbate, ma is the mass of the adsorbent within the core holder, and m is Figure 8. n-Pentane isotherms compared to those reported in the c 18 the amount of the confined phase. literature. The correlation of the isotherms indicated the validity of ff The same procedure was used for the n-pentane isotherms. the apparatus used in this study, while di erences between them were ° attributed to differences in the properties of the adsorbents used. The For example, using data from the n-pentane isotherm at 24.8 C pore size used in this work was 3.70 nm, while that used in the and 3.23 mbar, where m = 374.31 g, m0 = 374.24 g, VB = 46.6 ρ literature was 4.57 nm. P0 is the bulk saturation pressure of n-pentane mL, = 0.0000094 g/mL, Ma = 72.12 g/mol, and ma = 8.23 g, at the relevant experimental temperature. gives mc = 0.07 mmol/g. For low temperature experiments, approximately −40 °C and tions of fluid mixtures, not the amount of the adsorbed fluid. lower, humidity in the air of the thermostatic chamber Thus, correcting the absolute amount adsorbed for the excess precipitated ice onto the core holder. Note that the ice amount adsorbed is optional in view of our ultimate goal. precipitated onto the outside of the core holder; it did not Moreover, making this correction removes the bulk phase come into contact with the adsorbate or adsorbent at any point. transition from our isotherms, thus inhibiting our efforts to Ice precipitation was observed both visually and through the examine the confined phase transitions as they relate to the mass readings and necessitated the addition of an extra term, Δ bulk phase transitions. However, we make the correction for mice, to the equation to subtract the mass of the ice from the fi Δ CO2 in Figure 7 to show the equality of the capillary nal value for amount adsorbed. mice was obtained from the condensation pressures of both the corrected and uncorrected balance data by calculating the change in mass of the core isotherms. The correction was made by subtracting out the holder over time not due to the addition of more adsorbate. weight of the bulk fluid. In essence, the bulk volume (the Recognizing the constancy of the combined mass of the interparticle volume available to the bulk fluid) of the core adsorbed and confined fluid over the equilibrium time of a 3 Δ holder (46.6 cm ) was multiplied by the bulk CO2 density at single dose of adsorbate, as discussed in section 2.2.1, mice was

1973 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

ﬁ Figure 10. Isotherms for binary mixtures of CO2 and n-pentane measured using the static method. The con ned and bulk condensation pressures of ﬁ pure CO2 are included for ease of comparison. No con nement-induced or bulk phase transitions appeared in isotherms IV and VI measured at 229.45 and 239.15 K due to the shorter range of pressures used for each.

fl Figure 11. Isotherms for binary mixtures of CO2 and n-pentane measured in 3.70 nm MCM-41 using the ow-through method are denoted as VII fi and VIII. The binary mixtures measured statically and the con ned and bulk condensation pressures of pure CO2 are included for ease of comparison. taken to be the increase in measured mass throughout the in Figure 7. The bulk condensation was observed for all of the duration of the equilibrium time and was calculated by n-pentane and CO2 isotherms, though not always shown in the subtracting the total recorded mass of the adsorbate dosed figures where the bulk amount was excluded. The bulk into the system from the final recorded mass at the attainment condensation pressure is equal to the vapor pressure and was of equilibrium. Adding this correction gives: used to determine the accuracy of the measurements through comparison with data available on the NIST website.13 mm−−×−Δ0B Vρ m ice mc = For mixtures, there is no corresponding experimental data in Mmaa× (2) the literature, while a conversion equivalent to that for pure gases is more complicated and heavily dependent on Discounting the bulk fluid from the final reported measurements eliminates all bulk phase phenomena from the plotted calculations using EOS. Therefore, we did not make any isotherms, except in cases where experimental error causes the corrections for the adsorbed mixtures. As mentioned before, observation of residual bulk phase behavior. To fully illustrate this does not prevent us from measuring the condensation both the confined and bulk phase transitions, the isotherm for pressure, which is simply signaled by an abrupt jump in the CO2 at 224 K is plotted in Figure 7 in terms of both absolute mass measurement. As shown in Table 2, the errors associated mass and that which has been corrected for the mass of the bulk with the isotherms are relatively insignificant and are in fluid. Note that the bulk phase transition is indicated by the agreement with the accuracies of the pressure measurements rightmost abrupt increase in the amount adsorbed as described discussed in section 2.2.3.

1974 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

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 statically measured binary isotherms are included for ease comparison, as are the capillary condensation and bulk condensation pressures for pure CO2. n Table 2. Bulk and Capillary Condensation Pressures of CO2 and -Pentane pore size temperature bulk condensation: this bulk condensation: calculated error capillary condensation ﬂuid [nm] [K] work [bar] NIST13 [bar] % diﬀerence [% ϵ]b [bar]a

CO2 3.70 224.35 6.91 7.16 3.5 3.4 3.44

CO2 3.70 234.00 10.17 10.36 1.8 2.3 5.96

CO2 3.51 243.00 14.22 14.21 0.07 1.7 8.56

CO2 3.70 250.00 17.73 17.85 0.67 1.3 10.82 n-pentane 3.70 257.95 0.11 0.12 2.7 3.3 0.024 n-pentane 3.70 267.95 0.19 0.19 0.48 1.9 0.042 n-pentane 2.78 297.95 0.68 0.68 0.21 0.53 0.19 n-pentane 3.70 297.95 0.68 0.68 0.35 0.53 0.19 n-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 by dividing the error associated with either the pressure transducer (for pressures above 1 bar) or the vacuum gauge (for pressures below 1 bar) by the NIST13 bulk condensation pressure and multiplying the result by 100. fi fl Similar to the CO2 measurements, pure n-pentane isotherms The supercriticality of the con ned uid is evident from at three temperatures already reported in the literature were Table 2, where the supercritical confined fluid in the 2.78 nm also measured to further validate the accuracy of our MCM-41 was found to exhibit an inflection point in its experimental system for use with a variety of different fluids. isotherm at the same pressure as the capillary condensation The n-pentane isotherms can be found in Figures 8 and 9 and occurred for the 3.70 nm MCM-41. (Because different pore their corresponding bulk condensation is shown in Table 2. sizes cannot exhibit capillary condensation at the same pressure, fi fl Figure 8 indicates the reliability of our apparatus in predicting we infer the supercriticality of the con ned uid in the 2.78 nm capillary condensation through comparison to isotherms MCM-41.) However, the measurements in all three pore sizes, available in the literature. as shown in Table 2, resulted in the same bulk condensation However, as previously discussed, the primary pore size used pressure further validating the precision and accuracy of the in this work was 3.70 nm, while Morishige and Nakamura apparatus. The equality of the bulk condensation pressures for 17 the 6.32 and 3.70 nm MCM-41 is also shown in Figure 9.We reported their pore size to be 4.4 nm, and Russo et al. used therefore consider the similarity of our isotherms to those in 4.57 nm MCM-41.18 A full comparison of all adsorbents the literature in addition to the agreement of our bulk considered in this study can be found in Table 1. Because we measurements with those available from NIST13 (see Table 2) used pores (i.e., the 3.70 nm MCM-41) with smaller size, our as validation of our apparatus. isotherms also show lower capillary condensation pressures. 3.2. Binary Mixtures: Static Experiments. For the binary We show this in Figure 9 by including an additional isotherm mixtures of carbon dioxide and n-pentane, six isotherms were for the 6.32 nm MCM-41 at 297.95 K. As it can be seen, measured at five different temperatures in 3.70 nm MCM-41, as increasing the pore size from 3.70 to 6.32 nm also increased the shown in Figure 10. Three isotherms (218.15 and 224.35 K) capillary condensation pressure. This is in agreement with data exhibited both the confined phase change and the bulk bubble 24 in the literature. Isotherm measurements in the 2.78 nm point. One isotherm at 233.75 K displayed only the confined MCM-41 showed it to be below the pore critical size for n- phase change because that of the bulk was beyond the pressure pentane, thus it cannot be used for comparison of the confined range used in the experiments. Similarly, no confinement- vapor-to-liquid phase change. induced or bulk phase transitions appeared in isotherms IV and

1975 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

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-SAFT ﬁ equation of state. V, L1, and L2, represent vapor, CO2-rich liquid, and CO2-lean liquid phases, respectively. Vertical lines are the measured nal compositions of the tests indicated in the legend.

VI measured at 229.45 and 239.15 K because of the shorter the vapor pressure of pure CO2 because of the high range of pressures used for each. concentrations of CO2 in the mixtures. The accuracies of the isotherms were estimated as discussed The bubble point values of the experiments and the in section 2.2.3, where the measurements on mixtures were calculations of the EOS were found to be consistent; they are found to be highly reliant on the dependability of the bulk fluid within 5% of each other, except for test VIII. The differences compositions. The measured bulk bubble points of the mixtures are attributed both to the experimental uncertainty, as discussed were then compared to data generated using the perturbed in section 2.2.3, and errors inherent in the parameterization of chain statistical associating fluid theory (PC-SAFT)25 equation the EOS which depends on the quality of the experimental of state (EOS) for a consistency check. The EOS parameters phase-equilibrium data used to derive the binary interaction are given in the Appendix. The pressure-composition phase parameters. The consistency of the bulk bubble points found experimentally and computationally may be taken as an diagrams for the bulk mixtures are presented in Figure 13 using indication of the ability of the EOS to provide qualitative PC-SAFT at 218.15, 224.35, and 233.75 K, which correspond descriptions and quantitative estimates of the bulk phase to temperatures used for the experimental isotherms in Figure behavior for use in helping elucidate the confined-fluid 13 and Table 3. Within the EOS accuracy, there is a three-phase − − phenomena observed experimentally. vapor liquid liquid equilibrium (VLLE) at lower temper- Figure 13 also gives insight into the measured differences atures, which occurs at 5.34 and 6.82 bar for 218.15 and 224.35 between the initial and final compositions shown in Table 3 for K, respectively. At 233.75 K, the VLLE disappears. In the the binary mixtures measured statically. The material balance presence of the VLLE, for example at 218.15 K, the bubble seems to alter the composition to a higher CO2 content as seen point is at the three-phase pressure (5.34 bar) as long as the in test II as well as the ternary tests IX and X. However, if the overall mole fraction of CO2 is between 0.632 and 0.933 (the initial composition has a low enough CO2 content to fall within − liquid liquid equilibrium [LLE] range). Furthermore, as shown the range of the LLE, such as in test III, and the new CO2 in Figure 13, the bubble points of the mixtures are all similar to overall fraction is higher but still falls within the LLE range,

1976 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

then the measured ﬁnal composition is dominated by the heavier CO2-lean liquid (L2 in Figure 13). Note that although test I fell within the LLE, its ﬁnal composition is excessively b lean in CO2 (16.6 mol %) because of gravity segregation of the

easurements experimental ﬂuid, that is, some n-pentane dropped to the

5.52 bottom of the gas storage vessel and injection of the liquid at the end of the isotherm resulted in enrichment of the bulk pressure [bar] liquid with n-pentane. Gravity segregation was found to be a shortcoming of the in-house gas mixing system used for mixture capillary condensation preparation of the adsorbates; however, improvements to the setup and methodology immediately following isotherm I precluded gravity segregation in all subsequent tests. erence

ff In observing the mixture capillary condensation, it was found that for the binary isotherms, the confinement-induced phase %di changes occurred at pressures similar to those for pure carbon dioxide. The similarity appeared to be greater at lower temperatures, as shown in Figure 13, and is attributed to the a significantly higher concentration of carbon dioxide than n- Mixture capillary condensation pressures were calculated as

b pentane in the overall mixture compositions (i.e., inheritance of the bulk ﬂuid behavior). This is supported by both the point [bar] experimental data and the EOS calculations. As shown in

calculated bulk bubble Figure 13, the bulk mixtures, themselves, condense at pressures similar to pure CO2. If the phase behavior of the bulk mixtures for ternaries). is carried over to the conﬁned mixtures, proximity of the 12 H

5 mixture capillary condensation pressures to the pure CO2 C i capillary condensation is expected. In a similar manner, the tendency of behavior transferability between the bulk and ﬁ

point [bar] con ned mixtures is also supported in this work by isotherms II and III in Figure 13, where the mixture capillary condensation measured bulk bubble pressures did not signiﬁcantly change despite a 10.4 mol %

for binaries and ﬀ di erence in the amount of CO2, echoing the similarity of their 12 bulk bubble points shown in Figure 13. H 5

C Other possible phenomena that, although not directly n impurities observed in this work, could impact the mixture capillary

12 condensation pressures are conﬁned phase separation and H 5

C selective adsorptivity. For example, phase separation in the bulk i liquid (i.e., the presence of the LLE shown in Figure 13) may 12

H ﬂ

5 predispose the condensed uid to phase separation in

C fi fi n con nement. In this way, the scale of the con nement and nal composition [mol %] comparison with PC-SAFT fi

2 the wetting preference of the adsorbent may be manifested in separation of the phases so that the more wetting phase ﬁlls the pore space.10,26 This phenomenon was observed experimentally by Schemmel et al. who used small-angle neutron scattering to record the phase separation of binary liquid mixtures of

impurities CO isobutyric acid and deuterated water in controlled pore glass 26

12 with an average pore size of 10 nm. In their observations, H 5 phases were seen to separate in such a way that the more C nal compositions (impurities are included to i ﬁ wetting phase coated the pore walls and ﬁlled parts of the pore 12

H body, while the less wetting phase consisted only of small liquid 5 26 C

n bubbles within the pore space. Similarly, selective adsorptivity could also aﬀect the mixture capillary condensation, causing it initial composition [mol %] 2 to occur similarly to the most wetting component. As has been ﬃ previously reported, CO2 generally has greater a nity for MCM-41 silica because of its quadrupole moment27 and its ability to bond with the hydrogen atoms of the silanol groups [K] CO attached to the surface of the silica.28,29 However, the increase

temperature ﬁ in CO2 in the nal overall compositions for tests II, IX, and X inferred in Table 3 seem to contradict this, indicating that more pentane is adsorbed throughout all of the isotherms measured in this work. This observation is under further investigation but

ection points of the condensation steps in the isotherms. ﬀ

ﬂ may be attributed to di erences in the hydroxylation states of the MCM-41 used in this work and that used in the literature. test method IIIIII static staticIV staticV static 218.15 224.35 static 224.35 84.1 229.45 93.8 14.9 83.4 233.75 6.1 83.6 16.0 93.6 15.7 6.3 1.0 0.1 0.6 16.6 0.7 94.6 82.7 67.7 0.1 5.3 31.6 0.7 0.1 0.7 5.17 6.60 6.51 5.34 6.88 6.76 3.24 4.24 3.84 2.84 3.59 3.60 VIVII staticVIII dynamicIX dynamicX 224.35 239.15 static 233.75 static 93.8 78.8 95.6 224.35 16.0 6.0 233.75 4.1 76.3 94.0 16.6 3.0 7.0 5.2 0.2 0.3 2.9 92.0 0.1 95.0 0.1 6.9 80.6 3.3 13.5 95.8 5.6 2.9 1.1 0.9 1.7 0.3 0.4 6.73 9.0 6.7 9.6 6.85 9.87 6.76 9.91 1.78 9.67 0.90 3.23 3.53 5.44 3.68 5.49 Bubble points are calculated using PC-SAFT at the in Table 3. Initial and Final Compositions of the Bulk Fluids for All of the Mixtures Measured in This Work Along with Accuracies for the Bulk Bubble Point M a As has been shown in a comprehensive study by Zhuravlev, the

1977 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article wettability (and therefore the selective adsorptivity) of silica is through the bulk phase envelope or an indication of selective highly dependent on its state of hydroxylation.30 Note that adsorptivity. In the case of the latter, the abrupt decrease in the within the scope of this work, the only isotherms where concentration of CO2 at low pressures would indicate high selectivity can be inferred from the enrichment or depletion of selectivity during the adsorption phase of the isotherm. This is components in the final composition are those for which no in agreement with other studies, such as that of Yun et al.,8 liquid−liquid equilibrium was observed in the bulk. which show high selectivity at low pressures. 3.3. Binary Mixtures: Flow-Through Experiments. Two 3.4. Ternary Mixtures. In the binary mixture measure- isotherms for binary mixtures were measured using the flow- ments, isopentanea naturally-occurring isomer of n-pen- through method at 224.35 and 233.75 K. The first isotherm was tanewas found to be the most common impurity. To measured at 224.35 K using a flow rate of 0.1 cm3/min. The quantify the effect of this impurity on the binary measurements, fl 3 ow rate was varied from 1 to 0.01 cm /min throughout the two ternary mixtures of CO2, n-pentane, and isopentane were duration of the second isotherm measured at 233.75 K. measured statically at 224.35 and 233.75 K. These temperatures ff Qualitatively, no di erences were observed among the data were chosen for ease of comparison to both the pure CO2 generated for isotherm VIII using different flow rates. Little isotherms and the binary mixture isotherms. The isotherms are difference was observed between the binary isotherms shown in Figure 12, while the initial and final compositions of measured statically and those measured dynamically, that is, the mixtures used in each experiment as well as the bulk bubble both exhibited confinement-induced phase transitions similar to points are given in Table 3. fl those of pure CO2. Therefore, the ow, itself, was not observed Unlike the static measurements made on the binary mixtures, to significantly affect the mixture capillary condensation the final compositions measured during the static ternary pressure. mixture experiments always gained CO2 in comparison to the Unlike the majority of the static measurements where the initial compositions. final composition of the bulk fluid (in contact with the confined Similar to the binary isotherms, the confined phase fl uid) exhibited a change in the concentration of CO2, those transitions of the ternary mixtures also occurred similarly to measured dynamically exhibited a final composition close to ff that of pure CO2 (Figure 12). Though di erences in the their initial composition. This is mainly attributed to the adsorptivity of branched and normal alkanes31 may influence fl fl constant composition of the bulk uids used in the ow- the chemistry, and therefore the phase behavior, of the confined through experiments. Moreover, both mixtures were composed fluid, they were not observed in this work, which may be due to of more than 90% CO2, which meant that after the bulk bubble small amounts of isopentane used in the experiments. point was crossed, only one phase was present rather than two, as seen in Figure 13. 4. CONCLUSIONS AND REMARKS However, the composition of the effluent from the core holder was seen to vary throughout the pressures characteristic A novel gravimetric apparatus for measuring the capillary of each isotherm. This is shown in Figure 14, where the condensation of both pure fluids and mixtures in a wide variety of adsorbents was introduced. It was successfully validated against data available in the literature for both pure CO2 and n- pentane in MCM-41. The study was then expanded to generate isotherms for binary and ternary mixtures using both static and dynamic methods. Throughout the experiments, the equilibrium time was found to have large impacts on the determination of confined phase transitions, while the confined phase behavior was observed to be independent from the flow rate of the fluid mixtures over the range of flow rates employed in the dynamic method. However, qualitatively, one may be preferred over the other for investigation into specific phenomena. For example, the static method may be used to simulate reservoir- or aquifer-based systems in which fluid is predominately immobile, such as virgin shale gas reservoirs or CO2 plumes in ultratight rock. On the other hand, the dynamic method may be used to approximate flow-through porous media situations. Using the same example, such situations could include CO2 injection or hydrocarbon production from tight rock. But because no difference has yet been observed between the data generated Figure 14. Progression of the compositions of the effluents during the using the two methods, the one that is most convenient may dynamic measurements is plotted with regard to the experimental ffl yet be applied to both cases. We suggest that this may hold true pressures at which the e uent was bypassed to the gas chromatograph. even in studies using highly selective adsorbents, as the static method may still be employed by using a larger reservoir of composition at zero pressure is the composition of the bulk bulk fluid as the adsorbate, so that changes in the composition fluid before it had come into contact with the adsorbent and of the bulk fluid brought on by the selectivity remain negligible. the compositions corresponding to all other data points were In this work, the static measurements were preferred simply taken only after equilibrium (i.e., 2 h) had occurred. The because they required less experimental fluid than the dynamic variance of the composition of the effluent between the initial measurements and were less time-consuming and complicated and final pressures may either be a byproduct of progression to conduct.

1978 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

As displayed in Figure 15, comparison of the confined fluid displaying the mixture capillary condensation of fluids with behavior to the bulk showed transferability of the bulk mixture more than two components. In spite of the significance of these findings, they are preliminary and necessitate future studies using more complicated adsorbents, adsorbates, and flow processes to fully elucidate the physics of fluid mixture phase behavior in nanopores. Such studies are included in our future work using the apparatus presented herein which, given its successful validation in both the static and dynamic measurements of pure-component, binary-component, and multicomponent isotherms, provides a promising vehicle for this research. ■ APPENDIX PC-SAFT parameters used in this work are shown in Table A1. ■ ASSOCIATED CONTENT *S Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b04134. Measured isotherm data corresponding to carbon dioxide, n-pentane, and binary and ternary mixtures and compositional change of mixtures (PDF)

■ AUTHOR INFORMATION Figure 15. Confinement-induced phase transition of isotherm II Corresponding Author (static method) plotted with respect to the bulk phase envelope of the *E-mail: [email protected]. fl uid (solid black line), the bulk vapor pressure of pure CO2 (solid red ORCID line), and the measured capillary condensation pressures for pure CO2 (filled red circles and dashed red line). Isotherm VIII (dynamic Elizabeth Barsotti: 0000-0002-4106-5543 method) is added for rough comparison. Empty black circles are the Notes measured mixture capillary condensation pressures while the empty The authors declare no competing financial interest. black squares are the corresponding measured bulk bubble points. ■ ACKNOWLEDGMENTS fi behavior to the con ned mixtures regardless of the We gratefully acknowledge the financial support of Saudi experimental method. Because all of the mixtures were Aramco, Hess Corporation, and the School of Energy characterized by large overall mole fractions of CO2, the Resources and the College of Engineering and Applied Science pressures of the mixture phase transitions occurred in the at the University of Wyoming. From the Piri Research Group at proximity of the respective condensation pressures of pure the University of Wyoming, we also thank Henry Plancher for CO2.InFigure 15, the mixture capillary condensation of his help in preparing the adsorbates and Alimohammad Anbari isotherms II and VIII are plotted with respect to their bulk and Evan Lowry for their technical support. phase envelope, along with the bulk and confined phase transitions for pure CO2. ■ REFERENCES Figure 15 also exemplifies the magnitudes of the confinement-induced shifts of the phase transitions observed (1) Singer, L. E.; Peterson, D. International Energy Outlook 2016; throughout this study. For example, the mixture capillary 2016; Vol. DOE/EIA-04. condensation pressures of both isotherms II and VIII were (2) Loucks, R. G.; Reed, R. M.; Ruppel, S. C.; Jarvie, D. M. Morphology, Genesis, and Distribution of Nanometer-Scale Pores in found to occur approximately halfway between the bulk dew fi Siliceous Mudstones of the Mississippian Barnett Shale. J. Sediment. point and bubble point. This nding is representative of all the Res. 2009, 79, 848−861. confinement-induced phase transitions measured for mixtures (3) Barsotti, E.; Tan, S. P.; Saraji, S.; Piri, M.; Chen, J.-H. A review on in this work, including the ternary mixtures, which to the best capillary condensation in nanoporous media: Implications for of our knowledge are the first experimental isotherms hydrocarbon recovery from tight reservoirs. Fuel 2016, 184, 344−361.

a Table A1. PC-SAFT Parameters Used in This Work σ ϵ i/jm[Å] /kB [K] CO2 nC5H12 iC5H12 32 CO2 2.5834 2.5564 151.7666 a = 0.1767 a = 0.14 32 − × −4 nC5H12 2.6747 3.7656 232.1710 b = 1.502 10 a = 0.01 25 iC5H12 2.5620 3.8296 230.7500 b =0 b =0 a The right part of the table contains the binary interaction parameters: kij = a + bT; T is the absolute temperature. The kij values are obtained from 33,34 correlations over experimental data; kij between the isomers is estimated due to the absence of experimental data.

1979 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980 Langmuir Article

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1980 DOI: 10.1021/acs.langmuir.7b04134 Langmuir 2018, 34, 1967−1980