Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Adsorption Isotherms of Liquid Isomeric Mixtures Thomas Goetsch,† Patrick Zimmermann,†,‡ Bettina Scharzec,§ Sabine Enders,‡ and Tim Zeiner*,† †
Institute of Chemical Engineering and Environmental Technology, TU Graz, Inffeldgasse 25, A-8010 Graz, Austria Institute of Technical Thermodynamics and Refrigeration Engineering, Karlsruhe Institute of Technology, Engler-Bunte-Ring 21, D-76131 Karlsruhe, Germany § Department of Biochemical and Chemical Engineering, Laboratory of Fluid Separations, TU Dortmund University, Emil-Figge-Straße 70, D-44227 Dortmund, Germany Downloaded via DURHAM UNIV on August 3, 2018 at 09:42:32 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
‡
ABSTRACT: To separate linear and branched molecules in a liquid state, adsorption on porous materials is a promising separation method. To calculate the adsorption isotherms, a combination of lattice cluster theory and density functional theory was introduced recently, allowing the prediction of branched molecules’ adsorption isotherms based on the knowledge of the adsorption isotherms of the pure linear substances. However, these models are not practicable for process simulation and optimization because of their high numerical effort. Therefore, a simpler adsorption model based on the lattice cluster theory was developed to provide the results of the density functional theory approach for process development. In addition to the adsorption isotherm calculations, the model also considers the overall mass balance of the adsorption process. The model was validated for the adsorption of two binary, liquid alkane systems on three different adsorbents. Therefore, adsorption isotherms of these mixtures on activated coal, zeolite, and silica gel were measured. A good agreement of experimental and calculated adsorption isotherms was observed for all systems.
1. INTRODUCTION The separation of isomers is very challenging in chemical industries because of close physical properties.1 One example for the separation of isomers can be found in the gasoline industry. Gasoline mainly contains linear and branched alkanes. Its quality is characterized by the research octane number (RON), which differs significantly for linear and branched alkanes, i.e., the higher the degree of branching, the higher the RON.2 While additives like olefins or aromatics have been added to gasoline in order to raise its RON,3 new regulations restrict the use of these additives in order to reduce the negative impact of gasoline on the environment.4 Hence, in order to raise the quality of gasoline, linear alkanes have to be removed from the mixture of isomers. Distillation as one the most often applied unit operations is not suitable for the separation of close-boiling mixtures, because a high number of theoretical stages would be required, leading to an uneconomical process. Adsorption on porous solids is a promising alternative, where linear and branched isomers can be separated by means of size exclusion because of different molecular architectures.2,3,5−7 Another effect leading to a separation between linear and branched molecules is a denser packing of the linear molecules on the surface.2 However, the size exclusion effect is supposed to dominate; therefore, the choice of an adsorbent having the right pore size distribution is essential for the performance of the adsorption process. Currently, the separation of alkane isomers is performed by applying zeolites having a pore size of 5 Å.2,7,8 For the design of an adsorption process, the underlying adsorption isotherms have to be known. Recently, a general overview about the © XXXX American Chemical Society
separation of isomers using adsorption including experimental and modeling work was given in the literature.9 Usually, for the thermodynamic treatment of molecules using equations of state, pure-component parameters have to be adjusted using pure-component experimental data, like vapor pressure or saturated liquid densities. For systems containing branched molecules, this procedure is often not possible because branched molecules are barely available in high purity, and consequently no high-precision experimental data can be measured. To overcome this limitation, a model able to predict thermodynamic properties of branched molecules based on the knowledge of experimental data of the linear analogue would be desirable. The lattice cluster theory (LCT) developed by Freed and co-workers10−12 directly considers the molecular architecture within the Helmholtz free energy, where the molecular architecture is defined by architectural coefficients from the chemical formula. The LCT was successfully applied for the prediction of solid− liquid−liquid equilibria of mixtures made of linear alkanes, branched alkanes, and methanol or ethanol13 and the corresponding binary subsystems.14 Additionally, the phase behavior of mixtures containing hyperbranched polymers could be modeled successfully.15−21 Upon introduction of empty lattice sites, also compressible mixtures can be described.11 This approach leads to an equation of state Received: Revised: Accepted: Published: A
May 23, 2018 July 16, 2018 July 18, 2018 July 19, 2018 DOI: 10.1021/acs.iecr.8b02296 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research (LCT-EOS), which is able in principle to predict the thermodynamic properties of the isomers.22,23 In order to predict the adsorption isotherms of isomers, Zimmermann et al.9 developed a theoretical method based on density functional theory (DFT) in combination with the above-mentioned LCT-EOS. Within this combination of LCTEOS and DFT, model parameters are adjusted to pure component adsorption isotherms of the linear isomer. Afterward, pure component adsorption isotherms of the branched isomer as well as mixture adsorption isotherms containing linear and branched isomer can be predicted. Unfortunately, this theoretical approach implies a relatively large numerical effort such that it cannot be used in process simulation software. Identical arguments hold true for powerful methods based on molecular simulation, which are available in the literature.2,24−37 An overview of the molecular simulation methods is given in ref 9. Therefore, a new model, suitable for process simulation software, is required and will be developed in this contribution. The new model will be focused on the liquid-phase adsorption, because the theoretical investigations applying LCT-EOS and DFT show clearly that the separation effect in the liquid phase is larger than that in the gas phase.9 The fundamental approach for the new model is the real adsorbed solution theory (RAST)38 introducing an activity coefficient for the adsorbed phase. However, the new approach introduces also activity coefficients for the corresponding bulk phase, where the activity coefficients are calculated using LCT in its incompressible version. In contrast to other works, e.g. refs 39 and 40, using RAST, we also take the swelling of the adsorbent into account, because expansion and contraction of porous solids caused by solid−fluid intermolecular forces during fluid adsorption were observed.41 The developed model was validated for two binary systems, i.e. n-hexane−2,3-dimethylbutane and n-octane−2,2,4-trimethlypentane. Besides the well-suited zeolite, also activated carbon and silica gel having broader pore size distributions were applied as adsorbent. The purpose is to test whether the new model is able to describe all kinds of separation efficiencies, ranging from almost perfect separations to very poor separations. The development of excellent adsorbents for the separation of alkane isomers was reported in the literature.42,43
chemical potentials of the components must be equal in both phases: μiI + Δμ Network = μiII
i = A, C
(1)
where ΔμNetwork takes the swelling of the adsorbent into account. The calculation of ΔμNetwork will be explained later. For the calculation of the chemical potentials occurring in eq 1, we applied an incompressible version of the LCT in this work.15 This assumption is reasonable, as we consider incompressible liquids. The LCT, introduced by Freed and co-workers,11 is a thermodynamic model, which is able to consider the molecular architecture directly within the calculation of the Helmholtz free energy. Because their partition function for structured molecules on a lattice is not solvable analytically, the Helmholtz free energy is written in a double series of the lattice coordination number 1/z and the dimensionless interaction energy of nearest neighbor segments ε/kBT. This series expansion is truncated at the second order as suggested by Dudowicz and Freed.11 The lattice coordination number z was chosen to be 6 in accordance with earlier publications.13,14 ε/kBTis defined as ε = εii + εjj − 2εij
(2)
The three expressions εii, εjj, and εij represent the interaction energies between two segments of type ii, jj, and ij, respectively. The LCT is a lattice model, where the compositions are written in terms of segment fractions. The segment fraction can be calculated by eq 3, where ni is the number of molecules of component i, Ni represents the number of segments component i is divided into, and NL stands for the total number of lattice sites. ϕi =
niNi NL
(3)
The Gibbs free energy (segment-molar) of a multicomponent system is defined as11,15,21 ΔGLCT = NLRT
∑ i
ϕi Ni
lnϕi −
ΔE1 ΔE2 ΔS − − NLR NLRT NLRT
(4)
It is obvious that the LCT is based on the Flory−Huggins theory (FH)44 because the first term represents the entropic contribution of FH. The remaining terms represent corrections to the FH mean field: ΔS stand for entropic corrections, and ΔE1 and ΔE2 are first-order and second-order enthalpic corrections, respectively. All corrections can be determined from Tables I−III published by Dudowicz and Freed11 and corrections that were introduced by Dudowicz et al.45 The LCT is able to take the molecular architecture into account, which is done by defining architecture parameters. While originally six architecture parameters were used to define the molecular architecture,11 it was shown23 that three architecture parameters are sufficient for unambiguously defining the molecular architecture. These are the number of bonds N1,i, the number of two consecutive bonds N2,i, and the number of three consecutive bonds N3,i. All architecture parameters can be derived from the chemical formula. Regarding the two binary systems that were investigated, the architecture parameters listed in Table 1 were applied in this work. Regarding the adsorbent, it was assumed that it is a linear chain containing 500 segments. This assumption was taken because the influence of the chain length on the adsorption should be
2. THEORY The aim of this contribution is the development of a model for calculating liquid-phase adsorption isotherms of binary mixtures containing a linear and a branched alkane. Besides accurately describing the composition of bulk phase and adsorbed phase, the mass balance should also be solved by the model. The porous adsorbent is assumed to be present only in the adsorbed phase. Besides the adsorbent, all molecules adsorbed within the pores and on the surface of the adsorbent are related to the adsorbed phase (phase I). All remaining molecules, which are not adsorbed, are assumed to build the bulk phase (phase II). The linear molecules can more easily enter the pores than their branched isomers because of the smaller kinetic diameter. From the thermodynamic point of view, a ternary system containing linear alkane (A), adsorbent (B), and branched alkane (C) must be considered; hereby, the adsorbent (B) is immobilized as solid and regarded as a network of linear carbon chains. Regarding the calculation of the binary adsorption isotherms, it was assumed that bulk phase and adsorbed phase are in equilibrium. Thus, the B
DOI: 10.1021/acs.iecr.8b02296 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research Table 1. Architecture Parameters of the LCT for n-Hexane, 2,3-Dimethylbutane, n-Octane, and 2,2,4-Trimethylpentane n-hexane 2,3-dimethylbutane n-octane 2,2,4-trimethylpentane
Ni
N1,i
N2,i
N3,i
6 6 8 8
5 5 7 7
4 6 6 10
3 4 5 5
purity: 0.98) were measured. The composition of the bulk phase was measured by gas chromatography with toluene (VWR; molar purity: 0.995) as well as dibutyl-ether (Alfa Aesar; molar purity: 0.99) as internal standard. Additionally, three porous adsorbents were investigated in this work: activated carbon (in pellet form) was purchased from VWR International; silica gel (as powder) was purchased from Sigma-Aldrich; zeolite (spherical shape; surface area: 653 m2· g−1; pore volume: 0.2725 m3·g−1) was purchased from Merck. 3.2. Pore Size Distribution Measurements. The pore size distribution was measured using a Belsorp-mini II (Bel, Japan, Inc.) instrument by the volumetric nitrogen adsorption technique. The measurement accuracy of surface area has a resolution of 0.01m2 and a reproducibility of 1.5%. Nakai et al.47 provide more information about this experimental method. The evaluation of the pore size distribution function was performed by nonlocalized density functional theory.48 The software calculates the pore size distribution curve by fitting the integrated adsorption equation isotherms to the experimental ones and by minimizing the deviation. Integration over the pore size distribution results in the pore volume, Vpore. 3.3. Measuring Adsorption Isotherms. In this work, binary liquid-phase adsorption isotherms between a linear and a branched alkane were determined applying a static batch method. First of all, binary samples of known composition were prepared. Afterward, a well-defined amount of solid adsorbent was added to the sample, which was then sealed with parafilm in order to keep impurities outside the sample. For a combination of binary system and adsorbent, always the same mass ratio of binary alkane mixture and adsorbent was applied. This is important to ensure always the same amount of adsorption sites for the molecules within the binary mixture. The samples were closed from the surroundings and placed in a temperature-controlled water bath. Then, equilibration of bulk phase and adsorbed phase had to be awaited. In the literature, times between a few hours and several days were observed;49 therefore, a preliminary experiment was used to determine the time needed to reach equilibrium. In this preliminary experiment, equimolar mixtures were prepared for all three adsorbents. After 6, 24, 48, and 72 h, the adsorption was investigated. For every time step an individual sample was used. Preliminary experiments show that after 24 h the thermodynamic equilibrium was always established. After equilibrium was reached, a sample of the bulk phase was taken. In order to get pure samples of the bulk phase, an acetate membrane syringe filter holder was used for activated carbon and silica gel. The composition of the bulk phase was then analyzed by gas chromatography as described in the next section. In addition to the composition of the bulk phase, the composition of the adsorbed phase had to be determined. This composition is not accessible directly but can be determined indirectly by knowing the feed composition, the bulk-phase composition in equilibrium, and the total amount adsorbed. To determine the total amount adsorbed, which is defined to be all molecules adsorbed and all molecules within the pores, two different procedures were performed. Regarding zeolite as well as activated carbon, the total amount adsorbed was measured by weighing the adsorbent before and after the adsorption, respectively. Prior to that, the adsorbent was separated by suction filtration. The suction filtration was performed for 1.5 min. After that time zeolite achieved a
neglected and with this or higher chain lengths there is no impact on the modeled adsorption observed. After the adsorption of the alkanes, the adsorbent will have gained weight. To cover this effect in the model, the adsorbent is regarded as a network of cross-linked chains that can swell, where the gravimetric degree of swelling, q, can be calculated by eq 5: q=
mBfinal mBbegin
(5)
There are several approaches in the literature for describing swelling networks. Two of the most widely used theories are the phantom network46 theory and the affine network theory.44 The adsorbents investigated in this contribution are supposed to not swell that much; therefore, we applied the affine network theory introduced by Flory:44
i ϕ y Δμ Network = RT ·c Network ·jjjjϕB1/3 − B zzzz 2 { (6) k where ϕB is the segment fraction of the adsorbent and equals the mass fraction of adsorbent in phase I. This quantity corresponds to the reciprocal of q in eq 7. Within eq 6, cNetwork represents an adjustable parameter. Additionally, a mass balance was included in the new model. For this purpose α, the phase ratio between adsorbed phase and the feed mass mI (7) mFeed is introduced. Two component balances are sufficient to describe the overall mass balance of a three-component system: α=
wAFeed = wAI ·α + wAII·(1 − α)
(8)
wBFeed = wBI·α
(9)
here wi is the mass fraction. Combining the condition of equal chemical potentials of each isomer (eq 1) and the component balances (eqs 8 and 9) leads to a system of four equations, which must be solved simultaneously. In addition to cNetwork (eq 6), the interaction energy εAB/kB between adsorbent and linear alkane as well as the interaction energy εBC/kB between adsorbent and branched alkane are two more adjustable parameters. The interaction energy εAC/kB between linear and branched alkane was set to zero.
3. MATERIALS AND METHODS 3.1. Materials. In this contribution, liquid adsorption isotherms of the binary mixtures n-octane (Acros Organics; molar purity: 0.99) and 2,2,4-trimethylpentane (SigmaAldrich; molar purity: 0.99) as well as n-hexane (Merck; molar purity: 0.99) and 2,3-dimethylbutane (Alfar Aesar; C
DOI: 10.1021/acs.iecr.8b02296 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research constant mass and was weighed. Activated carbon could not be weighed directly after filtration because it did not achieve a constant mass after 1.5 min, which could be observed by a remaining film on the surface. Because a longer filtration at ambient temperature can disturb the equilibrium, a constant mass of the activated carbon was achieved by storing for 24 h at the adsorption temperature. The total amount adsorbed of the third adsorbent, i.e. silica gel, had to be determined differently because a small part of the silica gel always stuck to the wall of the vial. In addition to the pore volume, the density of the binary alkane mixture was measured for different compositions and temperatures between 283.15 and 303.15 K using a Densito 30PX oscillating tube densitometer from Mettler Toledo. The density measurements were repeated three times, and the average value was used. Afterward, the total amount adsorbed was calculated by eq 10: madsorbed = Vporeρadsorbed
Figure 1. Pore size distributions of zeolite (diamonds), activated carbon (triangles), and silica gel (circles).
This pore size is larger than the kinetic diameter of n-hexane and n-octane but smaller than the kinetic diameter of 2,3dimethylbutane and 2,2,4-trimethylbutane.6 Hence, only the linear alkanes should be able to enter the pores; therefore, zeolite should achieve an almost perfect separation of linear and branched alkanes. Activated carbon and silica gel also offer pores with a size of approximately 5 Å. However, there are fewer pores with this size in comparison to zeolite. Additionally, Figure 1 shows that activated carbon as well as silica gel possess a bimodal pore size distribution with pores having sizes much larger than 5 Å. This allows the branched alkanes to enter also the porous adsorbent, leading to a poorer separation of linear and branched alkanes. Regarding activated carbon and silica gel, it is obvious that silica gel has fewer pores with 5 Å and more pores with larger sizes. Thus, silica gel should achieve the worst separation efficiency of the three investigated adsorbents. 4.2. Parameter Estimation Procedure. For the adjustment of the three adjustable parameters (cNetwork, εAB/kB, and εBC/kB), the following procedure was applied: All three model parameters were simultaneously fitted to experimental adsorption isotherm data as well as swelling data for the binary system n-octane−2,2,4-trimethylpentane at one particular temperature by minimizing the mean squared error of the model’s deviation from the experimental data. Afterward, the network parameter cNetwork remained constant at this value for all other temperatures because it is assumed to not depend on temperature. In contrast to the network parameter cNetwork, the interaction energies εij/kB are dependent on temperature and were adjusted subsequently to adsorption isotherm data for different temperatures. When the system was switched to nhexane−2,3-dimethylbutane, the network parameter cNetwork was still fixed to the adjusted value because it was assumed that the adsorbent behaves in a manner similar to that observed for the system n-octane−2,2,4-trimethylpentane. Thus, only the two interaction energies εij/kB were adjusted for every temperature. The obtained model parameters are collected in Tables 2 and 3. The used network parameter cNetwork for the different adsorbent are 2.2 (activated carbon), 0.9 (silica gel), and 3.4 (zeolite). 4.3. n-Octane−2,2,4-Trimethylpentane. The separation efficiency for the three different adsorbents is shown in Figure 2 for the binary system n-octane−2,2,4-trimethylpentane at a temperature of 293.15 K. Here, the mass fraction of n-octane in the bulk phase is shown on the x-axis and the mass fraction of n-octane in the adsorbed phase is shown on the y-axis. This means that data
(10)
All adsorption experiments were repeated three times to evaluate the experimental error as deviation from the average value. 3.4. Analytics. The composition of the binary mixtures containing n-octane and 2,2,4-trimethylpentane was determined using a GC from Shimadzu (type GC-14B). It was equipped with a FS-Supreme-5mn HT column (30 m length, 32 mm inner diameter, and 0.25 μm film thickness). The content of linear and branched alkane was analyzed by a flame ionization detector with a temperature of 543.15 K. Calibration curves with relative deviations of 0.39% for n-octane and 0.46% for 2,2,4-trimethylpentane were prepared for binary mixtures with differing compositions. As internal standard, dibutyl-ether was used. Every adsorption isotherm was measured in triplet, whereby every sample was analyzed three times. The average composition out of these runs was used for further evaluation. The separation of n-octane and 2,2,4-trimethylpentane was achieved with the following GC method: First, a temperature of 313.15 K is set up within the column. After the temperature is maintained at this value for 140 s, the temperature is raised to 368.15 K with a heating rate of 30 K min−1. After reaching the final temperature, the column is cooled to the initial temperature and the GC run is finished. A complete GC run took 250 s, where typical retention times were 130 s for 2,2,4trimethylpentane, 170 s for n-octane, and 215 s for dibutyl ether. Regarding the binary system containing n-hexane and 2,3dimethylbutane, the same GC but a slightly different method was used. Toluene was used as internal standard. Calibration curves with an accuracy of 0.21% for n-hexane and 1.37% for 2,3-dimethylbutane were achieved. First, the temperature of the column is raised to 343.15 K and held constant for 6 s. Afterward, a heating rate of 4 K min−1 is applied to further raise the temperature to 355.15 K. Then, the column is heated to 373.15 K with a heating rate of 18 K min−1. As typical retention times, 120 s for 2,3-dimethylbutane, 125 s for nhexane, and 215 s for toluene were observed.
4. RESULTS 4.1. Pore Size Distribution. The pore size distributions of the three adsorbents investigated in this work are shown in Figure 1. It can be seen that the pore size distributions differ for all three adsorbents. Zeolite shows a very sharp pore size distribution, with pores having a size of approximately 5 Å. D
DOI: 10.1021/acs.iecr.8b02296 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
First, the adsorption of n-octane−2,2,4-trimethylpentane on activated carbon was investigated. In Figure 3, the calculated adsorption isotherms of this system as well as the calculated swelling behavior of activated carbon are compared with experimental data. Regarding the experimental data, it is obvious that the temperature has an effect on the separation efficiency. The higher the temperature, the better is the separation efficiency indicated by a larger distance to the diagonal (left side of Figure 3). Within the model, the separation efficiency is characterized by the difference between the two interaction energies. While the difference is 13 K for a temperature of 283.15 K, a difference of 31 K can be found for a temperature of 303.15 K (Table 2). The fact that the separation efficiency increases with increasing temperature was also predicted by the DFT in combination with the LCT-EOS.9 The comparison of the experimental adsorption isotherms and the calculated isotherms shows that the model is able to describe the different adsorption efficiencies in good agreement with experimental data. The degree of swelling of activated carbon is also dependent on temperature. It can be seen on the right side of Figure 3 that for higher temperatures the degree of swelling is smaller. This means that in total fewer molecules are adsorbed at higher temperatures. This finding is covered within the calculations by lowering the individual interaction energies of linear and branched alkane with rising temperatures (Table 2). When the experimental swelling data are compared with the calculated ones, it can be seen that the model calculates lower degrees of swelling for higher temperatures, where the difference between the three temperatures agrees well with the difference between the experimental data. However, as can be seen in Figure 3, the slopes of experimental and calculated data are slightly different. The same binary system was then investigated on silica gel. In Figure 2, it was observed that no separation between noctane and 2,2,4-trimethylpentane was achieved for a temperature of 293.15 K. As can be seen in Figure 4, also no separation is possible for temperatures of 283.15 and 303.15 K, meaning that linear and branched alkanes can enter pores equally well for all temperatures. This finding is covered by nearly equal interaction energies between silica gel and the octane isomers (Table 2). A slightly higher adsorption was measured for 2,2,4-trimethylpentane; therefore, its interaction energy with silica gel is a bit higher than for n-octane. Because the ability of the molecules for entering the pores is not dependent on temperature, it is clear that the degree of swelling is also not dependent on temperature, which can be seen on the right side of Figure 4. When experimental data are compared with the calculations, a very good agreement of both can be observed. Finally, the adsorption of the binary system n-octane−2,2,4trimethylpentane was investigated on zeolite. Because of the very sharp pore size distribution (Figure 1), an almost perfect separation of linear and branched alkane was observed for a temperature of 293.15 K (Figure 2). The same separation efficiency was achieved for temperatures of 283.15 and 303.15 K (Figure 5). Almost over the whole composition range, a mass fraction of 1 within the adsorbed phase was measured for the linear alkane for all investigated temperatures. This means that the linear alkane shows a very strong preferential adsorption on zeolite, which is covered by a large interaction energy (Table 2). The branched alkane, on the other hand, is not able to enter the
Table 2. Adjusted Interaction Energies between Adsorbent and n-Octane (εAB/kB) as Well as between Adsorbent and 2,2,4-Trimethylpentane (εBC/kB) for Three Different Adsorbents at Three Different Temperatures T (K)
283.15
293.15
303.15
activated carbon εAB/kB (K) εBC/kB (K)
−61 −48
−58 −41
−51 −20
silica gel εAB/kB (K) εBC/kB (K)
−11 −13
−11 −13
−11 −14
zeolite εAB/kB (K) εBC/kB (K)
−135 0
−135 0
−135 0
Table 3. Adjusted Interaction Energies between Adsorbent and n-Hexane (εAB/kB) as Well as between Adsorbent and 2,3-Dimethylbutane (εBC/kB) for Three Different Adsorbents at Three Different Temperatures T (K)
283.15
293.15
303.15
activated carbon εAB/kB (K) εBC/kB (K)
−64 −52
−51 −30
−41 −10
silica gel εAB/kB (K) εBC/kB (K)
−13 −15
−13 −15
−13 −16
zeolite εAB/kB (K) εBC/kB (K)
−135 0
−135 0
−135 0
Figure 2. Adsorption isotherms of the binary system n-octane−2,2,4trimethylpentane on zeolite (diamonds), activated carbon (triangles) and silica gel (circles) at a temperature of 293.15 K.
points lying on the diagonal (black line) achieve no separation between linear and branched alkanes. Regarding Figure 2, it can be seen that silica gel leads to a poor separation. The experimental data of all investigated compositions are located on the diagonal. Zeolite on the other hand achieves an almost perfect separation with n-octane mass fractions of approximately 1 in the adsorbed phase. The separation efficiency of activated carbon lies between that of zeolite and silica gel. Therefore, the experimental data confirm the theoretical considerations made from the pore size distributions. E
DOI: 10.1021/acs.iecr.8b02296 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
Figure 3. Left side: Adsorption isotherms of the binary system n-octane−2,2,4-trimethylpentane on activated carbon at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The lines were calculated by the adsorption model. Right side: Degree of swelling of activated carbon for the binary system n-octane−2,2,4-trimethylpentane at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The mass fraction of activated carbon was always 0.4.
Figure 4. Left side: Adsorption isotherms of the binary system n-octane−2,2,4-trimethylpentane on silica gel at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The lines were calculated by the adsorption model. Right side: Degree of swelling of silica gel for the binary system n-octane−2,2,4-trimethylpentane at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The mass fraction of silica gel was always 0.55.
Figure 5. Left side: Adsorption isotherms of the binary system n-octane−2,2,4-trimethylpentane on zeolite at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The solid lines were calculated by the adsorption model. Right side: Degree of swelling of zeolite for the binary system n-octane−2,2,4-trimethylpentane at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The mass fraction of zeolite was always 0.60.
greater than 1, leading to a not perfect match with these experimental data. Regarding the degree of swelling of zeolite, it is obvious that the model is not able to describe the constant value but calculates increasing degrees of swelling for increasing mass fractions of n-octane in the feed. This finding shows the limitation of our model, especially the assumption underlying eqs 1 and 6. In comparison to the swelling of crosslinked polymers, hydrogels for instance, the degree of swelling is very small, and therefore, the applied swelling model (eq 6) must be very precise, especially for small degrees of swelling values. On the other hand, the introduced chemical potential
pores and adsorb onto the zeolite because of its larger kinetic diameter; therefore, its interaction energy with zeolite was set to zero. Regarding the experimental swelling data, it can be seen that the degree of swelling rapidly increases for low noctane mass fractions and remains at a constant value for mass fractions of n-octane in the feed larger than 0.08. When experimental data and calculations are compared, a very good agreement can be seen for the adsorption isotherms. Some experimental data with mass fractions greater than 1 were measured because of uncertainties within the analytics. Of course, our calculations are restricted to mass fractions not F
DOI: 10.1021/acs.iecr.8b02296 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
Figure 6. Left side: Adsorption isotherms of the binary system n-hexane−2,3-dimethylbutane on activated carbon at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The lines were calculated by the adsorption model. Right side: Degree of swelling of activated carbon for the binary system n-hexane−2,3-dimethylbutane at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The mass fraction of activated carbon was always 0.42.
Figure 7. Left side: Adsorption isotherms of the binary system n-hexane−2,3-dimethylbutane on silica gel at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The lines were calculated by the adsorption model. Right side: Degree of swelling of silica gel for the binary system n-hexane−2,3-dimethylbutane at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The mass fraction of silica gel was always 0.53.
Figure 8. Left side: Adsorption isotherms of the binary system n-hexane−2,3-dimethylbutane on zeolite at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The lines were calculated by the adsorption model. Right side: Degree of swelling of zeolite for the binary system n-hexane−2,3-dimethylbutane at temperatures of 283.15 K (diamonds; solid line), 293.15 K (triangles; dashed line), and 303.15 K (circles; dotted line). The mass fraction of zeolite was always 0.62.
model. In contrast, regarding activated carbon and silica gel, all mentioned factors are relevant. Here, the procedure of representing these effects by the adjustable parameters is justified. 4.4. n-Hexane−2,3-Dimethylbutane. Besides the binary system n-octane−2,2,4-trimethylpentane, also the binary system n-hexane−2,3-dimethylbutane was investigated. Both mixtures behave similarly. Again, the separation of linear and branched alkane is almost perfect on zeolite, whereas no separation was observed for the adsorption on silica gel. Activated carbon shows medium separation efficiency, which is dependent on temperature. The experimental adsorption
for the swelling equilibria in eq 1 covers different effects related to the adsorbent. Such effects are pore-size distribution, pore geometry, accessibility of the pores for the molecules, and energetic heterogeneity of the pores. These effects are not directly included in our model but indirectly covered within the adjustable parameters. In the case of zeolite, the accessibility of the pores is the most important quantity because the pore-size distribution is quite narrow (Figure 1). Here, the inclusion of this effect into the interaction energy does obviously not work for the description of the degree of swelling. Nevertheless, the extreme sharp separation represented by the adsorption isotherm can be covered by the G
DOI: 10.1021/acs.iecr.8b02296 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
kB = Boltzmann constant mi = Mass of component i ni = Number of molecules of component i Ni = Segment number of component i N1,i = Number of bonds within component i N2,i = Number of two consecutive bonds within component i N3,i = Number of three consecutive bonds within component i NL = Total number of lattice sites q = Degree of swelling R = Universal gas constant ΔS = Entropic corrections within LCT T = Temperature Vpore = Pore volume wi = Mass fraction of component i z = Coordination number
isotherms as well as degrees of swelling are compared with the calculations in Figure 6 for activated carbon, in Figure 7 for silica gel, and in Figure 8 for zeolite. Table 3 contains the adjusted interaction energies. The calculated adsorption isotherms describe the experimental data mostly within the experimental error, in all three cases. Regarding the degree of swelling, the modeling results fit the experimental values for activated carbon and for silica gel, but not for the zeolite.
5. CONCLUSIONS In this contribution, a model for describing liquid-phase adsorption on porous adsorbents of mixtures containing linear and branched isomers was developed. Besides calculating the adsorption isotherms, the model also considers the swelling of the adsorbent. The model was applied for the two binary mixtures n-octane−2,2,4-trimethylpentane and n-hexane−2,3dimethylbutane and for the three porous adsorbents activated carbon, silica gel, and zeolite. The molecular architecture of the alkane isomers was considered by the LCT, which directly incorporates the molecular architecture in the Helmholtz free energy. The porous adsorbent was treated as a linear chain that is able to swell. All three adsorbents possessed a different pore size distribution, leading to different adsorption efficiencies. Zeolite showed an almost perfect separation of linear and branched alkane, whereas silica gel achieved no separation. Activated carbon showed a separation efficiency that is between those two values, and the adsorption depends on temperature. Within the model, the adsorption efficiency can be described by interaction energies between the adsorbent and the individual alkane isomers. A good agreement between experimental adsorption isotherms and calculated ones could be observed for all systems. Thus, the model is able to describe all kinds of separation efficiencies between no separation and ideal separation. Regarding the degree of swelling of the three adsorbents, temperature dependence was observed where the lowest degrees of swelling were achieved for the highest temperatures. The model is able to describe this temperature dependence; however, an agreement with experimental data could be observed only for activated carbon and silica gel, but not for zeolite.
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GREEK LETTERS α = Phase ratio ε = Interaction energy defined by eq 2 ϕi = Segment fraction of component i ρadsorbed = Density of adsorbed mixture μ = Chemical potential
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Tim Zeiner: 0000-0001-7298-4828 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is part of the Collaborative Research Centre “Integrated Chemical Processes in Liquid Multiphase Systems” coordinated by the Technische Universität Berlin. Financial support by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged (TRR63).
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NOTATION cNetwork = Network parameter defined in eq 6, di = Pore diameter ΔE1 = First-order enthalpic corrections within LCT ΔE2 = Second-order enthalpic corrections within LCT ΔGLCT = Segment-molar Gibbs energy within LCT H
DOI: 10.1021/acs.iecr.8b02296 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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