Capillary Condensation of Binary and Ternary Mixtures of n ... - coifpm

Article Cite This: Langmuir 2018, 34, 1967−1980

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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 npentane 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 Although the study of pure, single-component fluids in nanopores has been broadly undertaken, there is very little knowledge as to how mixtures in nanopores behave. A quantitative realization of nanoconfinement-induced mixture behavior is prerequisite to breakthroughs in many fields from medicine and biology to materials science and electrochemistry. An example of how significantly a comprehensive understanding of the effects of nanoporosity on fluid mixtures can impact each of these scientific endeavors can be found in petroleum engineering, where the ability to accurately predict confined mixture behavior could significantly influence the economic 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 energy resource.1 Much of this growth in demand will be satiated by vastly increasing production from shale and tight gas reservoirs.1 In spite of this, very little is known about the physics of fluid flow, transport, and storage in these reservoirs. In particular, there is virtually no understanding of fluid phase behavior in such systems. Shale gas reservoirs are typified by nanopores, which constitute a significant fraction of their total porosity.2 The scale of these pores, alone, regardless of their chemistry or geometry, may alter the phase behavior of the confined fluids from their bulk counterparts. Specifically, the vapor-to-liquid phase transition may occur earlierthat is, at © 2018 American Chemical Society

lower pressures in an isothermal system or at higher temperatures in an isobaric systemin confinement than in the bulk. This confinement-induced phase change, called capillary condensation, has been reported in the literature, see Barsotti et al.3 for a comprehensive review, yet most of the associated studies involve single-component fluids in simple pore systems far removed from those encountered in the reservoir setting.3 Those studies that have been carried out on multicomponent fluids are scarce, providing little overall insight into the phase behavior of confined fluid mixtures. The majority of the experimental studies have been carried out under isobaric conditions to probe the confinement-induced bubble point. A limited number of studies have observed the confinementinduced dew point, while a few others have focused more on the structure of the confined fluid during the phase transition with emphasis on phase separation. To the best of our knowledge, none have witnessed the confined critical point of mixtures. 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 witnessed depression of the confined bubble point with respect to that of Received: December 4, 2017 Revised: January 9, 2018 Published: January 23, 2018 1967

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

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same pressure and temperature, so that the confined fluid did not comprise a homogenous mixture.10 Thus, confinement could not only affect the phase transitions of fluids, such as natural gas, but also their compositions, including the pore fluid occupancy in the event of confinement-induced phase separation. This could prove important to the ultimate recovery of shale gas, because the pore fluid occupancy dictates the mechanisms 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 in nanopores, a novel gravimetric apparatus11 is introduced for the study of both pure fluids and mixtures in a variety of porous media using both static and dynamic processes. Unlike the apparatuses used in previous studies of confined fluid mixtures, such as the isobaric differential scanning calorimetry5 and positron annihilation spectroscopy measurements9 or the isothermal volumetric measurements of Yun et al.,8 our apparatus uses changes in mass to directly measure the amount of fluid adsorbed. This allows for isothermal measurements that are more relevant to shale gas recovery than isobaric measurements, that is, temperature can generally be considered constant in gas reservoirs, and more accurate12 than volumetric measurements, which cannot measure the adsorbed amount directly but rather depend on equations of state to calculate it. Similarly, this apparatus has the ability to facilitate large quantities of adsorbents, including core plugs housed in highpressure core holders. Such a high capacity gravimetric apparatus has not been previously reported in the literature. Although the evaluation of the confined phase behavior of reservoir fluids in core plugs was beyond the scope of this study, the ability of the apparatus to support a core holder and its associated plumbing was tested and validated throughout this study by utilizing a titanium core holder packed with MCM-41 for all experiments herein. In this work, the apparatus was first validated using isothermal capillary condensation data in the literature for pure carbon dioxide and pure n-pentane and with bulk condensation data for both compounds from the National Institute of Standards and Technology (NIST).13 Next, building upon the data for the pure component isotherms, binary isotherms of carbon dioxide and n-pentane were measured for the first time using a static method and then a dynamic, flow-through method. Finally, two ternary mixture isotherms for CO2, n-pentane, and isopentane were measured. To the best of our knowledge, these are the first isotherms displaying the confinement-induced vapor-to-condensed phase transitions of gas mixtures with more than two components. With respect to the findings of Alam et al.,9 only adsorption paths were used for all measurements to negate the effect of the enrichment of the confined fluid by the bulk liquid when they are in direct contact prior to the desorption. In this work, the observed abrupt increase of adsorption in the isotherms of mixtures is termed mixture capillary condensation.

the bulk, the results must be viewed in the context of the experimental path. The two paths available for studies of confined phase phenomena are adsorption and desorption. In adsorption, the initial phase of the bulk fluid is gaseous. Adsorption experiments are exemplified in the literature by the works of Jones and Fretwell7 and Yun et al.,8 who used positron annihilation spectroscopy and a volumetric flow-through approach, respectively. In desorption, the initial phase of the bulk fluid is liquid. Desorption experiments are represented in the literature by studies employing density scanning calorimetry measurements, such as that of Luo et al.5 Although the adsorption and desorption experiments both result in confinement-induced shifts of the fluid phase transitions, the results are quantitatively different. Alam et al. explained this difference in their positron annihilation spectroscopy study of the confined dew points of binary mixtures of nitrogen and argon.9 They found inequalities between the confined dew points measured using adsorption and desorption to result from enrichment of the confined fluid by the bulk fluid during desorption.9 Thus, although adsorption and desorption both qualitatively indicate confinement-induced shifts of the phase transition, the degree to which those shifts occur is highly dependent 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 static approach in which the fluid within the pores was stationary at equilibrium, the study of Yun et al. involved fluids that were always flowing and therefore experienced dynamic equilibrium.8 Putting this into the context of natural gas production, the static and dynamic experiments approximately represent different yet complimentary situations throughout the life of a reservoir. For example, the static experiments best approximate unproduced reservoirs in which fluids are stationary, the situation of which is relevant to the original gas in place calculations. Conversely, dynamic experiments best approximate reservoir processes in which fluids are flowing, such as production and injection, but with a constant flow rate. Experimentally, the two methods differ in that during static experiments, the overall (confined plus bulk) composition of the fluid is constant while during the flow-through experiments, only the bulk composition of the fluid is maintained constant by the flow. Except for this methodological difference, there is no evidence for any difference in the underlying concept as both can provide the desired capillary condensation. However, comparison between them would support decision making in choosing the experimental setup if one decides to apply gravimetric measurements. Nonetheless, in evaluating the data generated by these experiments, knowledge of the structure of the fluidthe number and location of the molecules of each component within the pores is also necessary. Although, often no preferential adsorption is observed, such as in the work of Alam et al.,9 there are cases in which it may significantly alter the structure of the confined mixture beyond what is expected, that is, confinement-induced phase transitions may be disproportionately skewed by the more selectively adsorbed component. In measuring the capillary condensation of binary mixtures of n-hexane and perfluoro-n-hexane, Kohonen and Christenson observed co-condensation between muscovite mica surfaces using a surface force apparatus.10 Essentially, both an n-hexane-rich phase and a perfluoro-n-hexane-rich phase condensed, but they occurred separately, albeit at the

2. MATERIALS AND METHODS 2.1. Materials. Three MCM-41 samples were obtained from Glantreo, Ltd. MCM-41 is a mesoporous silica wellknown throughout the literature for its easily tuned pore size and simple pore geometry, consisting of uniform, unconnected cylindrical pores.14 Using nitrogen adsorption isotherms at 77 K, Barrett−Joyner−Halenda (BJH)15 and Dollimore−Heal (D−H)16 analyses gave average pore sizes of 3.51 and 3.70 nm, respectively, for the first sample, 2.59 and 2.78 nm for the 1968


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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.

using a customized Agilent 7890B gas chromatograph from Separation Systems, Inc. 2.2. Experimental Setup and Procedure. Isotherms were measured using a novel gravimetric apparatus11 that allows for both static and flow-through measurements of adsorption, desorption, and capillary condensation in adsorbent packs at temperatures from 173.15 to 503.15 K. An environmental chamber (Thermotron) with precise temperature control of ±0.1 K was used as a thermostat. Throughout the experiments, a Rosemount pressure transducer (Emerson) and a Leybold TM 101 vacuum gauge were used to measure positive and negative (i.e., below atmospheric) pressures, respectively, at a frequency of once per second. As with all gravimetric apparatuses, the phase of the confined fluid was determined by the relationship between its mass and pressure. The mass of the MCM-41 pack was measured continuously at a frequency of once per second throughout the experiments with an accuracy ±0.00001 g using an XPE 505C mass comparator from Mettler Toledo. A custom-made data acquisition box and LabVIEW computer program were used to log all data. A schematic of the experimental setup is presented in 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 or air. This was to prevent irregularities in the data due to physisorbed water. It was determined that no heat was necessary to achieve appropriate outgassing between consecutive isotherms where neither air nor water was present as long as the same vacuum level could be achieved between the isotherm measurements. 2.2.1. Static Method. In the static method, for experiments involving both pure gases and mixtures, a variable dosing volume was used to incrementally increase the gas content (mass) to change the pressure of the system under isothermal conditions, while the system was closed between doses. In all cases, the dosing volume was simply a combination of valves and variable lengths of tubing plumbed directly into the system. For experiments with pure carbon dioxide, the dosing volume was fed directly by the gas cylinder. For the pure n-pentane and the mixture experiments, the dosing volume was fed by a dualcylinder 6000 series Quizix pump (Chandler Engineering). This

second sample, and 6.06 and 6.32 nm for the third sample. For the first sample, small angle X-ray scattering indicated the presence of hexagonal unit cells with a lattice parameter of 4.78 nm, while transmission electron microscopy (TEM) showed particle size to be approximately 1 μm in diameter. TEM micrographs of the 3.70 nm MCM-41 used in this study are shown in Figure 1. The properties of all of the adsorbents considered in this work are given in Table 1. Table 1. Comparison of the Adsorbent Characteristics Referenced in This Work to Those Used in This Study adsorbent this work: 2.78 nm this work: 3.70 nm this work: 6.32 nm Morishige & Nakamura17 Russo et al.18

BET surface area [m2/g]

D−H pore size [nm]

BJH pore size [nm]

1043

2.78

2.59

832

3.70

3.51

586

6.32

6.06

NLDFT pore size [nm]

865

4.4

934

4.57

For the purposes of this work, three packs of the MCM-41 were used, where each sample of MCM-41 was packed into its own titanium core holder using the packing procedure described by Saraji.19 Through geometric calculations, the 2.78, 3.70, and 6.32 nm MCM-41 packs were found to have interparticle void volumes of 46.7, 46.6, and 47.0 cm3, respectively. The total volume of each core holder was 56.4 cm3, that is, in all three cases, the MCM-41 took up approximately 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 experiments, the n-pentane was first dried with calcium hydride. Subsequently, the fluid was distilled and then stored under helium. Gas mixtures were prepared using a gravimetric gas mixing system developed in-house for this purpose. The compositions of the mixtures were confirmed through a combination of fixed gas and detailed hydrocarbon analysis 1969


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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 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 at standard conditions, and allowed for precise pressure control of the bulk mixtures to prevent liquid dropout. During the static measurements, each new dose of gas introduced into the system was allowed to equilibrate until the pressure of the system became constant. Equilibrium time for both the adsorption and capillary condensation regions of isotherms has been discussed in the literature by Naumov,20 who found that for cyclohexane at 297 K in Vycor glass with pores of approximately 6 nm diameter, adsorption equilibrium occurred within 1 h, while capillary condensation equilibrium could not be achieved even after 4 h.20 Therefore, according to the findings of Naumov, if time is divided equally among all data points, those for adsorption may be at equilibrium, while those for capillary condensation may not. To determine the effects of nonequilibrium on the shape and condensation pressures of the pure component isotherms, an isotherm for carbon dioxide at 234.35 K was measured in which doses of gas at different pressures for both adsorption and capillary condensation were left to equilibrate for 4 h.

During those time periods, pressure and mass data were recorded at 5, 10, 30, 60, 120, 180, and 240 min. The resulting isotherms 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 capillary condensation pressure at 120 min. Although beyond the scope of this study, this may also have implications for determination of the hysteresis critical temperature, as hysteresis may be artificially induced through variations in the equilibrium time. Similarly, it may affect the method used to locate the pore critical temperature. Using a method proposed by Morishige and Nakamura, locating the pore critical temperature is reliant upon the slope of the isotherm,17 which may also be affected by increasing or decreasing the time allowed for equilibrium, as shown in Figure 3. It is important to note that our apparatus is fundamentally different from the more traditional gravimetric apparatuses presented in the literature, as shown in Figure 4. Most traditional gravimetric apparatuses utilize a weighing pan suspended in a gaseous atmosphere of the adsorbate, where 1970


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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 pressure were maintained for at least 2 h, where the minimum equilibrium time was adopted from the static method. 2.2.3. Compositional Analysis. For both the static and dynamic measurements, the compositions of the bulk fluid mixtures, both at the beginning of the experiments (while all 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 contact with the adsorbent were measured using the gas chromatograph. Note that the compositions of the fluids were all measured in situ, for the gas chromatograph was directly plumbed into the system, as shown in Figure 2. In this way, chromatographic analysis of the fluid involved removing 111 μL of fluid directly from the plumbing of the system for analysis. Because this volume accounts for 0.22% of the total volume of our core holder and an even smaller percentage of the volume of the entire system (Figure 2), the effect of its removal on the pressure and composition of the adsorbate were considered negligible. In the dynamic measurements, additional analysis of the adsorbate was undertaken at the end (i.e., once equilibrium had been achieved) of each dose using the same in situ sampling procedure.

Figure 4. A comparison of the equilibration of more traditional gravimetric apparatuses used in the literature (a) to that of our gravimetric apparatus (b). Note that the volume of the confined fluid may change because of the strain of the adsorbent, but because the strain generally does not observably affect the measured isotherms,22 this change in volume is considered to be negligible in this work.

any phase change within the adsorbent on the weighing pan causes depletion (in the case of adsorption) of the adsorbate atmosphere as the gas molecules are drawn into the pore space. This allows for the measurement of mass uptake curves, but also necessitates corrections for buoyancy as the density and pressure of the adsorbate atmosphere change. In our apparatus, both the adsorbent and the bulk adsorbate are housed within the core holder, so that for each dose of adsorbate, the mass of the dose is constant, although the phase may change. The injected dose initially causes an abrupt increase in the detected pressure that then decreases as the system equilibrates as shown in Figure 5. The more gas that is adsorbed, the more the pressure of the bulk adsorbate will decrease after each dose. Because of this pressure behavior, the equilibrium during the

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-specified response times of the pressure transducers and the observed response times of the balance were less than 1 s. 1971


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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 simply to ensure that the results generated by one or the other were not outliers. Because both fell within the accuracy of the method, we did not analyze any additional mixtures.

Figure 6. Comparison of adsorption isotherms for CO2 measured in this study in 3.70 nm MCM-41 and those measured in the literature in 4.4 nm MCM-41.17 The correlation of the isotherms indicated the validity of the apparatus used in this study, while differences between 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 carbon dioxide isotherms were measured using the static method to ensure that the apparatus could reproduce both capillary condensation pressures and bulk condensation pressures. The comparison of the isotherms generated in this work to those available in the literature can be found in Figure 6 with an additional isotherm at a fourth temperature not yet reported in the literature. The fourth isotherm was useful for comparison with the mixture isotherms, as discussed later in this paper. As stated in the introduction, we emphasize that the overall purpose of this study was to determine the effects of confinement on the phase transition pressures and composi-

the antivibration table above the environmental chamber (see Figure 2) mitigated the addition of any inaccuracies due to the experimental conditions, such as changes in temperature or vibrations. Throughout all experiments, the balance was maintained 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-specified accuracies equal to or better than ±0.24 and ±0.0036 bar, respectively. The uncertainties in pressure associated with the measurements for CO2 and n-pentane are given in Table 2, where they are shown to be insignificant. 1972


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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: mc =

m − m0 − VB × ρ Ma × ma

(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 fluid), VB is the bulk volume of the core holder, ρ 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 mc is the 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 °C and 3.23 mbar, where m = 374.31 g, m0 = 374.24 g, VB = 46.6 mL, 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 chamber precipitated ice onto the core holder. Note that the ice precipitated onto the outside of the core holder; it did not come into contact with the adsorbate or adsorbent at any point. Ice precipitation was observed both visually and through the mass readings and necessitated the addition of an extra term, Δmice, to the equation to subtract the mass of the ice from the final value for amount adsorbed. Δmice was obtained from the balance data by calculating the change in mass of the core holder over time not due to the addition of more adsorbate. Recognizing the constancy of the combined mass of the adsorbed and confined fluid over the equilibrium time of a single dose of adsorbate, as discussed in section 2.2.1, Δmice was

Figure 8. n-Pentane isotherms compared to those reported in the literature.18 The correlation of the isotherms indicated the validity of the apparatus used in this study, while differences between them were attributed to differences in the properties of the adsorbents used. The pore size used in this work was 3.70 nm, while that used in the literature was 4.57 nm. P0 is the bulk saturation pressure of n-pentane at the relevant experimental temperature.

tions of fluid mixtures, not the amount of the adsorbed fluid. Thus, correcting the absolute amount adsorbed for the excess amount adsorbed is optional in view of our ultimate goal. Moreover, making this correction removes the bulk phase transition from our isotherms, thus inhibiting our efforts to examine the confined phase transitions as they relate to the bulk phase transitions. However, we make the correction for CO2 in Figure 7 to show the equality of the capillary condensation pressures of both the corrected and uncorrected isotherms. The correction was made by subtracting out the weight of the bulk fluid. In essence, the bulk volume (the interparticle volume available to the bulk fluid) of the core holder (46.6 cm3) was multiplied by the bulk CO2 density at 1973


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Figure 10. Isotherms for binary mixtures of CO2 and n-pentane measured using the static method. The confined and bulk condensation pressures of pure CO2 are included for ease of comparison. No confinement-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.

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 VII and VIII. The binary mixtures measured statically and the confined and bulk condensation pressures of pure CO2 are included for ease of comparison.

in Figure 7. The bulk condensation was observed for all of the n-pentane and CO2 isotherms, though not always shown in the figures where the bulk amount was excluded. The bulk condensation pressure is equal to the vapor pressure and was used to determine the accuracy of the measurements through comparison with data available on the NIST website.13 For mixtures, there is no corresponding experimental data in the literature, while a conversion equivalent to that for pure gases is more complicated and heavily dependent on calculations using EOS. Therefore, we did not make any corrections for the adsorbed mixtures. As mentioned before, this does not prevent us from measuring the condensation pressure, which is simply signaled by an abrupt jump in the mass measurement. As shown in Table 2, the errors associated with the isotherms are relatively insignificant and are in agreement with the accuracies of the pressure measurements discussed in section 2.2.3.

taken to be the increase in measured mass throughout the duration of the equilibrium time and was calculated by subtracting the total recorded mass of the adsorbate dosed into the system from the final recorded mass at the attainment of equilibrium. Adding this correction gives: mc =

m − m0 − VB × ρ − Δm ice Ma × ma

(2)

Discounting the bulk fluid from the final reported measurements eliminates all bulk phase phenomena from the plotted isotherms, except in cases where experimental error causes the observation of residual bulk phase behavior. To fully illustrate both the confined and bulk phase transitions, the isotherm for CO2 at 224 K is plotted in Figure 7 in terms of both absolute mass and that which has been corrected for the mass of the bulk fluid. Note that the bulk phase transition is indicated by the rightmost abrupt increase in the amount adsorbed as described 1974


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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.

Table 2. Bulk and Capillary Condensation Pressures of CO2 and n-Pentane fluid

pore size [nm]

temperature [K]

bulk condensation: this work [bar]

bulk condensation: NIST13 [bar]

% difference

calculated error [% ϵ]b

capillary condensation [bar]a

CO2 CO2 CO2 CO2 n-pentane n-pentane n-pentane n-pentane n-pentane

3.70 3.70 3.51 3.70 3.70 3.70 2.78 3.70 6.32

224.35 234.00 243.00 250.00 257.95 267.95 297.95 297.95 297.95

6.91 10.17 14.22 17.73 0.11 0.19 0.68 0.68 0.68

7.16 10.36 14.21 17.85 0.12 0.19 0.68 0.68 0.68

3.5 1.8 0.07 0.67 2.7 0.48 0.21 0.35 0.29

3.4 2.3 1.7 1.3 3.3 1.9 0.53 0.53 0.53

3.44 5.96 8.56 10.82 0.024 0.042 0.19 0.19 0.42

The 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.

a

The supercriticality of the confined fluid is evident from Table 2, where the supercritical confined fluid in the 2.78 nm MCM-41 was found to exhibit an inflection point in its isotherm at the same pressure as the capillary condensation occurred for the 3.70 nm MCM-41. (Because different pore sizes cannot exhibit capillary condensation at the same pressure, we infer the supercriticality of the confined fluid in the 2.78 nm MCM-41.) However, the measurements in all three pore sizes, as shown in Table 2, resulted in the same bulk condensation pressure further validating the precision and accuracy of the apparatus. The equality of the bulk condensation pressures for the 6.32 and 3.70 nm MCM-41 is also shown in Figure 9. We therefore consider the similarity of our isotherms to those in the literature in addition to the agreement of our bulk measurements with those available from NIST13 (see Table 2) as validation of our apparatus. 3.2. Binary Mixtures: Static Experiments. For the binary mixtures of carbon dioxide and n-pentane, six isotherms were measured at five different temperatures in 3.70 nm MCM-41, as shown in Figure 10. Three isotherms (218.15 and 224.35 K) exhibited both the confined phase change and the bulk bubble point. One isotherm at 233.75 K displayed only the confined phase change because that of the bulk was beyond the pressure range used in the experiments. Similarly, no confinementinduced or bulk phase transitions appeared in isotherms IV and

Similar to the CO2 measurements, pure n-pentane isotherms at three temperatures already reported in the literature were also measured to further validate the accuracy of our experimental system for use with a variety of different fluids. The n-pentane isotherms can be found in Figures 8 and 9 and their corresponding bulk condensation is shown in Table 2. Figure 8 indicates the reliability of our apparatus in predicting capillary condensation through comparison to isotherms available in the literature. However, as previously discussed, the primary pore size used in this work was 3.70 nm, while Morishige and Nakamura reported their pore size to be 4.4 nm,17 and Russo et al. used 4.57 nm MCM-41.18 A full comparison of all adsorbents considered in this study can be found in Table 1. Because we used pores (i.e., the 3.70 nm MCM-41) with smaller size, our isotherms 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 the capillary condensation pressure. This is in agreement with data in the literature.24 Isotherm measurements in the 2.78 nm MCM-41 showed it to be below the pore critical size for npentane, thus it cannot be used for comparison of the confined vapor-to-liquid phase change. 1975


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

the vapor pressure of pure CO2 because of the high concentrations of CO2 in the mixtures. The bubble point values of the experiments and the calculations of the EOS were found to be consistent; they are within 5% of each other, except for test VIII. The differences are attributed both to the experimental uncertainty, as discussed in section 2.2.3, and errors inherent in the parameterization of the EOS which depends on the quality of the experimental phase-equilibrium data used to derive the binary interaction parameters. The consistency of the bulk bubble points found experimentally and computationally may be taken as an indication of the ability of the EOS to provide qualitative descriptions and quantitative estimates of the bulk phase behavior for use in helping elucidate the confined-fluid phenomena observed experimentally. Figure 13 also gives insight into the measured differences between the initial and final compositions shown in Table 3 for the binary mixtures measured statically. The material balance seems to alter the composition to a higher CO2 content as seen in test II as well as the ternary tests IX and X. However, if the initial composition has a low enough CO2 content to fall within the range of the LLE, such as in test III, and the new CO2 overall fraction is higher but still falls within the LLE range,

VI measured at 229.45 and 239.15 K because of the shorter range of pressures used for each. The accuracies of the isotherms were estimated as discussed in section 2.2.3, where the measurements on mixtures were found to be highly reliant on the dependability of the bulk fluid compositions. The measured bulk bubble points of the mixtures were then compared to data generated using the perturbed chain statistical associating fluid theory (PC-SAFT)25 equation of state (EOS) for a consistency check. The EOS parameters are given in the Appendix. The pressure-composition phase diagrams for the bulk mixtures are presented in Figure 13 using PC-SAFT at 218.15, 224.35, and 233.75 K, which correspond to temperatures used for the experimental isotherms in Figure 13 and Table 3. Within the EOS accuracy, there is a three-phase vapor−liquid−liquid equilibrium (VLLE) at lower temperatures, which occurs at 5.34 and 6.82 bar for 218.15 and 224.35 K, respectively. At 233.75 K, the VLLE disappears. In the presence of the VLLE, for example at 218.15 K, the bubble point is at the three-phase pressure (5.34 bar) as long as the overall mole fraction of CO2 is between 0.632 and 0.933 (the liquid−liquid equilibrium [LLE] range). Furthermore, as shown in Figure 13, the bubble points of the mixtures are all similar to 1976


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7.0 2.9

Bubble points are calculated using PC-SAFT at final compositions (impurities are included to nC5H12 for binaries and iC5H12 for ternaries). bMixture capillary condensation pressures were calculated as the inflection points of the condensation steps in the isotherms.

6.9 3.3 13.5 2.9 92.0 95.0 80.6 95.8

5.6 0.9 82.7 5.3 31.6 16.6 94.6 67.7

1.0 0.1 0.6 0.7 0.1 5.2 0.2 0.3 0.1 0.1 14.9 6.1 16.0 15.7 6.3 16.0 6.0 4.1 16.6 3.0 84.1 93.8 83.4 83.6 93.6 78.8 93.8 95.6 76.3 94.0 218.15 224.35 224.35 229.45 233.75 239.15 224.35 233.75 224.35 233.75 static static static static static static dynamic dynamic static static I II III IV V VI VII VIII IX X

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 lean in CO2 (16.6 mol %) because of gravity segregation of the experimental fluid, that is, some n-pentane dropped to the bottom of the gas storage vessel and injection of the liquid at the end of the isotherm resulted in enrichment of the bulk liquid with n-pentane. Gravity segregation was found to be a shortcoming of the in-house gas mixing system used for preparation of the adsorbates; however, improvements to the setup and methodology immediately following isotherm I precluded gravity segregation in all subsequent tests. In observing the mixture capillary condensation, it was found that for the binary isotherms, the confinement-induced phase 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 significantly higher concentration of carbon dioxide than npentane in the overall mixture compositions (i.e., inheritance of the bulk fluid behavior). This is supported by both the experimental data and the EOS calculations. As shown in Figure 13, the bulk mixtures, themselves, condense at pressures similar to pure CO2. If the phase behavior of the bulk mixtures is carried over to the confined mixtures, proximity of the mixture capillary condensation pressures to the pure CO2 capillary condensation is expected. In a similar manner, the tendency of behavior transferability between the bulk and confined mixtures is also supported in this work by isotherms II and III in Figure 13, where the mixture capillary condensation pressures did not significantly change despite a 10.4 mol % difference in the amount of CO2, echoing the similarity of their bulk bubble points shown in Figure 13. Other possible phenomena that, although not directly observed in this work, could impact the mixture capillary condensation pressures are confined phase separation and selective adsorptivity. For example, phase separation in the bulk liquid (i.e., the presence of the LLE shown in Figure 13) may predispose the condensed fluid to phase separation in confinement. In this way, the scale of the confinement and 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 isobutyric acid and deuterated water in controlled pore glass with an average pore size of 10 nm.26 In their observations, phases were seen to separate in such a way that the more wetting phase coated the pore walls and filled parts of the pore body, while the less wetting phase consisted only of small liquid bubbles within the pore space.26 Similarly, selective adsorptivity could also affect the mixture capillary condensation, causing it to occur similarly to the most wetting component. As has been previously reported, CO2 generally has greater affinity for MCM-41 silica because of its quadrupole moment27 and its ability to bond with the hydrogen atoms of the silanol groups attached to the surface of the silica.28,29 However, the increase in CO2 in the final 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 may be attributed to differences in the hydroxylation states of the MCM-41 used in this work and that used in the literature. As has been shown in a comprehensive study by Zhuravlev, the

a

3.53 5.44 3.68 5.49 1.78 9.67 0.90 3.23 6.85 9.87 6.76 9.91 6.73 9.0 6.7 9.6 1.1 1.7 0.3 0.4

5.52

2.84 3.59 3.60 3.24 4.24 3.84 5.34 6.88 6.76 5.17 6.60 6.51 0.7 0.1 0.7

mixture capillary condensation pressure [bar]b % difference calculated bulk bubble point [bar]a measured bulk bubble point [bar] impurities iC5H12 method test

temperature [K]

CO2

nC5H12

iC5H12

impurities

CO2

nC5H12

comparison with PC-SAFT final composition [mol %] initial composition [mol %]

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 Measurements

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through the bulk phase envelope or an indication of selective adsorptivity. In the case of the latter, the abrupt decrease in the concentration of CO2 at low pressures would indicate high selectivity during the adsorption phase of the isotherm. This is in 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 measurements, isopentanea naturally-occurring isomer of n-pentanewas found to be the most common impurity. To quantify the effect of this impurity on the binary measurements, two ternary mixtures of CO2, n-pentane, and isopentane were measured statically at 224.35 and 233.75 K. These temperatures were chosen for ease of comparison to both the pure CO2 isotherms and the binary mixture isotherms. The isotherms are shown in Figure 12, while the initial and final compositions of the mixtures used in each experiment as well as the bulk bubble points are given in Table 3. Unlike the static measurements made on the binary mixtures, the final compositions measured during the static ternary mixture experiments always gained CO2 in comparison to the initial compositions. Similar to the binary isotherms, the confined phase transitions of the ternary mixtures also occurred similarly to that of pure CO2 (Figure 12). Though differences in the adsorptivity of branched and normal alkanes31 may influence the chemistry, and therefore the phase behavior, of the confined fluid, they were not observed in this work, which may be due to small amounts of isopentane used in the experiments.

wettability (and therefore the selective adsorptivity) of silica is highly dependent on its state of hydroxylation.30 Note that within the scope of this work, the only isotherms where selectivity can be inferred from the enrichment or depletion of components in the final composition are those for which no liquid−liquid equilibrium was observed in the bulk. 3.3. Binary Mixtures: Flow-Through Experiments. Two isotherms for binary mixtures were measured using the flowthrough method at 224.35 and 233.75 K. The first isotherm was measured at 224.35 K using a flow rate of 0.1 cm3/min. The flow rate was varied from 1 to 0.01 cm3/min throughout the duration of the second isotherm measured at 233.75 K. Qualitatively, no differences were observed among the data generated for isotherm VIII using different flow rates. Little difference was observed between the binary isotherms measured statically and those measured dynamically, that is, both exhibited confinement-induced phase transitions similar to those of pure CO2. Therefore, the flow, itself, was not observed to significantly affect the mixture capillary condensation pressure. Unlike the majority of the static measurements where the final composition of the bulk fluid (in contact with the confined fluid) exhibited a change in the concentration of CO2, those measured dynamically exhibited a final composition close to their initial composition. This is mainly attributed to the constant composition of the bulk fluids used in the flowthrough experiments. Moreover, both mixtures were composed of more than 90% CO2, which meant that after the bulk bubble point 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 characteristic of each isotherm. This is shown in Figure 14, where the

4. CONCLUSIONS AND REMARKS A novel gravimetric apparatus for measuring the capillary 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 npentane 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 using the two methods, the one that is most convenient may yet be applied to both cases. We suggest that this may hold true even in studies using highly selective adsorbents, as the static method may still be employed by using a larger reservoir of bulk fluid as the adsorbate, so that changes in the composition of the bulk fluid brought on by the selectivity remain negligible. In this work, the static measurements were preferred simply because they required less experimental fluid than the dynamic measurements and were less time-consuming and complicated to conduct.

Figure 14. Progression of the compositions of the effluents during the dynamic measurements is plotted with regard to the experimental pressures at which the effluent was bypassed to the gas chromatograph.

composition at zero pressure is the composition of the bulk fluid before it had come into contact with the adsorbent and the compositions corresponding to all other data points were taken only after equilibrium (i.e., 2 h) had occurred. The variance of the composition of the effluent between the initial and final pressures may either be a byproduct of progression 1978


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displaying the mixture capillary condensation of fluids with 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.

As displayed in Figure 15, comparison of the confined fluid behavior to the bulk showed transferability of the bulk mixture

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APPENDIX PC-SAFT parameters used in this work are shown in Table A1. ASSOCIATED CONTENT

* Supporting Information S

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)

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AUTHOR INFORMATION

Corresponding Author

Figure 15. Confinement-induced phase transition of isotherm II (static method) plotted with respect to the bulk phase envelope of the fluid (solid black line), the bulk vapor pressure of pure CO2 (solid red line), and the measured capillary condensation pressures for pure CO2 (filled red circles and dashed red line). Isotherm VIII (dynamic method) is added for rough comparison. Empty black circles are the measured mixture capillary condensation pressures while the empty black squares are the corresponding measured bulk bubble points.

*E-mail: [email protected]. ORCID

Elizabeth Barsotti: 0000-0002-4106-5543 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support of Saudi Aramco, Hess Corporation, and the School of Energy Resources and the College of Engineering and Applied Science at the University of Wyoming. From the Piri Research Group at the University of Wyoming, we also thank Henry Plancher for his help in preparing the adsorbates and Alimohammad Anbari and Evan Lowry for their technical support.

behavior to the confined mixtures regardless of the experimental method. Because all of the mixtures were characterized by large overall mole fractions of CO2, the pressures of the mixture phase transitions occurred in the proximity of the respective condensation pressures of pure CO2. In Figure 15, the mixture capillary condensation of isotherms II and VIII are plotted with respect to their bulk phase envelope, along with the bulk and confined phase transitions for pure CO2. Figure 15 also exemplifies the magnitudes of the confinement-induced shifts of the phase transitions observed throughout this study. For example, the mixture capillary condensation pressures of both isotherms II and VIII were found to occur approximately halfway between the bulk dew point and bubble point. This finding is representative of all the confinement-induced phase transitions measured for mixtures in this work, including the ternary mixtures, which to the best of our knowledge are the first experimental isotherms

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REFERENCES

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Table A1. PC-SAFT Parameters Used in This Worka i/j 32

CO2 nC5H1232 iC5H1225

m

σ [Å]

ϵ/kB [K]

CO2

2.5834 2.6747 2.5620

2.5564 3.7656 3.8296

151.7666 232.1710 230.7500

b = −1.502 × 10−4 b=0

nC5H12

iC5H12

a = 0.1767

a = 0.14 a = 0.01

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 correlations over experimental data;33,34 kij between the isomers is estimated due to the absence of experimental data. 1979


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Capillary Condensation of Binary and Ternary Mixtures of n ... - coifpm

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