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Ind. Eng. Chem. Res. 2009, 48, 11202–11210
Phase Equilibria of Mixtures Containing Glycol and n-Alkane: Experimental Study of Infinite Dilution Activity Coefficients and Modeling Using the Cubic-Plus-Association Equation of State Waheed Afzal,†,‡ Martin P. Breil,§ Pascal The´veneau,† Amir H. Mohammadi,† Georgios M. Kontogeorgis,*,§ and Dominique Richon*,† MINES ParisTech, CEP/TEP-Centre Energe´tique et Proce´de´s, 35 Rue Saint Honore´, 77305 Fontainebleau, France, and IVC-SEP, Department of Chemical and Biochemical Engineering, Technical UniVersity of Denmark, DK-2800 Kgs. Lyngby, Denmark
In this work, we report the infinite dilution activity coefficients for four n-alkanes (n-pentane, n-hexane, n-heptane, and n-octane) in monoethylene glycol in the temperature range from 298 to 334 K and at atmospheric pressure. Experimental data were measured using a previously described inert gas stripping technique. The new experimental data are compared with the literature data whenever possible. The experimental infinite dilution activity coefficients of several alkanes from n-pentane to n-hexadecane in monoethylene glycol, diethylene glycol, triethylene glycol, and tetraethylene glycol previously reported in the literature, along with the data measured in this work have been modeled using the cubic-plus-association (CPA) equation of state (EoS). Satisfactory results have been obtained using temperature-independent interaction parameters. Useful remarks are presented about the application of infinite dilution activity coefficient data for estimating binary interaction parameters of the CPA EoS for the description of whole vapor-liquid equilibria. Furthermore, the variation in the values of the interaction parameters is discussed for different glycol systems. 1. Introduction Oil and gas are often produced with several undesired impurities from reservoirs including water, acid gases, etc. During production, transportation, and processing operations large quantities of chemicals are often used. For example, glycols and methanol are often used for inhibiting gas hydrate and ice formation in production, transportation, and processing facilities. Glycols are also widely used in the dehydration of natural gases for dew point (or saturation temperature) depression on the order of 40 to 70 K to avoid free water condensation at low temperatures and high pressures.1 Mutual absorption of gas components and glycols during these processes creates complex engineering problems related to glycol recovery and regeneration from spent glycols, loss of glycols in the gas phase, distribution of glycols in product gas streams, process economics, environmental impact, etc.1 Knowledge of the phase behavior of systems involving hydrocarbon and glycol is therefore necessary to address these problems. Often, the predictions of the thermodynamic models are inadequate in the absence of consistent thermodynamic data. On the other hand, experimental measurements are expensive and time-consuming. One way of working out these problems is to develop and extend more realistic thermodynamic models requiring experimental data at the minimum level and work for a wide range of temperatures and pressures and at multiple situations (vaporliquid, liquid-liquid, solid-liquid equilibria). No universal model is currently available which can work under multiple situations without empirical parameters adjusted on the experimental data. To the contrary, the predictive capability of most * To whom correspondence should be addressed. E-mail: richon@ ensmp.fr. Phone: +33 164694965. Fax: +33 164694968 (D.R.). E-mail:
[email protected]. Phone: +45 45252859. Fax: +45 45882258 (G.M.K.). † MINES ParisTech. ‡ W.A. was on external stay at the Technical University of Denmark for the modeling part of this study. § Technical University of Denmark.
conventional models ranges from poor to average; they often need temperature dependent parameters for representing the experimental data. Cubic equations of state have been widely used in the oil and gas industry. However, these models are often inadequate in dealing with the systems involving associating fluids like water, alcohols, and glycols. One of the promising alternatives, offering several advantages, over the classical thermodynamic models is the cubic-plusassociation equation of state (CPA EoS).2,3 Although the CPA EoS possesses quite reasonable predictive character, often a binary and system specific interaction parameter is required to correlate experimental data without temperature dependency.2,3 The need of a binary interaction parameter requires experimental binary data. Instead of using vapor-liquid equilibrium (VLE) data, infinite dilution activity coefficient (γ∞ij ) data can also be used. γ∞ij data is easy and rapid to measure as compared to whole VLE data.4-6 Moreover, only one γ∞ij data point is required at each temperature, offering a great advantage. By definition, γ∞ij characterizes the behavior of a liquid mixture, in general, and of a single solute molecule fully surrounded by solvent molecules, in particular, indicating the maximum nonideality of the system.4,5 It can provide insights about the solute-solvent interactions in the absence of solute-solute interactions.6,7 The γ∞ij data offer various advantages, including fitting excess free energy (GE) models, as a strict test for thermodynamic models (e.g., CPA EoS) in highly nonideal situations. Moreover, γij∞ data can be used to adjust the parameters of a thermodynamic model to predict the existence of azeotropes or solubility, Table 1. Chemical Information (Supplier, Purity, and CAS Registry Number) compound
supplier
monoethylene glycol Sigma-Aldrich n-propane Sigma-Aldrich n-hexane Sigma-Aldrich n-heptane Sigma-Aldrich n-octane Sigma-Aldrich
10.1021/ie900856q CCC: $40.75 2009 American Chemical Society Published on Web 10/09/2009
purity (GC %) CAS registry no. >99 99 99 99 99
107-21-1 74-98-6 74-98-6 142-82-5 111-65-9
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Figure 1. Schematic diagram of setup based on the inert gas stripping technique for experimental measurements.11 Description: BF, bubble flow meter; C, chromatograph; D, dilutor; d.a.s., data acquisition system; He, helium cylinder; E1, E2, heat exchangers; FE, flow meter electronic; FR, flow regulator; L, sampling loop; LB, liquid bath; O, O-ring; PP, platinum resistance thermometer; S, saturator; SI, solute injector; Sp, septum; SV, sampling valve; TR, temperature regulator; VSS, variable speed stirrer.
calculate limiting separation factors necessary for the design of distillation processes, calculate Henry’s law coefficients or partition coefficients, etc.4-7 For γ∞ij experimental measurements, several useful experimental techniques have been developed over the years.7,8 γ∞ij can also be calculated from experimental thermophysical and phase equilibrium data by extrapolation to infinite dilutions.7,8 It is pertinent to mention that the experimental techniques for “direct” measurements are developed for γ∞ij of light components in heavy ones only. The measurements of γ∞ij of heavy components in light components still remain a challenge for experimentalists. γ∞ij of hydrocarbons in some glycols has been reported by several authors, the data have been compiled by Gmehling and co-workers in the DECHEMA data series.4,5 This compilation reveals a frequent scatter of γ∞ij data reported by several authors. In the absence of rigorous thermodynamic consistency tests for experimental γ∞ij data, it is not easy to comment on the accuracy of the data. Limited γ∞ij data are also available for n-alkanes in diethylene glycol (DEG), triethylene glycol (TEG), and tetraethylene glycol (TeEG). In this work, we report experimental γ∞ij data of n-pentane (C5), n-hexane (C6), n-heptane (C7), and n-octane (C8) in monoethylene glycol (MEG), in the temperature range 298-334 K and at atmospheric pressure. These data were measured using a previously described inert gas stripping technique.9-11 Experimental γ∞ij data were also collected from the literature for several alkanes, generally from n-pentane to n-hexadecane in MEG, DEG, and TEG. For the modeling of these data, the CPA EoS2 has been used. It is demonstrated that γ∞ij data can successfully be used for the estimation of binary interaction parameters in the CPA EoS for each binary mixture. The variation in the values of interaction parameters for several binary mixtures containing glycols is highlighted. In the absence of any data, useful remarks are presented for “guessing” the
values of the binary interaction parameters for various mixtures containing n-alkanes and glycols. 2. Experimental Section The chemicals used in this work along with their purities and suppliers are presented in Table 1. MEG was treated with thermal molecular sieve (UOP type 3A) prior to its use in the experimental measurements. Special precautions were taken to minimize any possibility of contamination of glycol with water from air, because of its hygroscopic nature. All other chemicals were used without any further treatment. The experimental technique used for the determination of γ∞ij data is based on inert gas stripping via exponential dilutor principle described by Leroi et al.9 The experimental setup and protocols have been previously described.10-12 The schematic diagram of the experimental setup is presented in Figure 1. Briefly, the setup consists of two transparent glass cells: the saturator (marked as S) and dilutor (marked as D). The first cell saturates the preheated helium with solvent in order to minimize losses in the next cell in series, the dilutor, where helium strips the solvent out of the solute. Helium is also used in the gas chromatograph (GC) carrier gas. Each cell houses microcapillaries to reduce the bubble sizes of the striping gas at the bottom of the cell for ensuring equilibrium between the bubble and bulk of the liquid reached before the bubble leaves the solution. Both cells are immersed inside a water temperature bath which can regulate temperature within 0.1 K. The composition of vapor phase over the dilutor cell can be monitored by a GC equipped with a flame ionization detector (FID) by means of an automatic sampling valve. The flow of helium at the inlet and outlet of the cells are measured by suitable flow meters. The measuring sensors and meters are calibrated. The experimental protocol consists of the following
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steps: the known quantities of solvent were introduced into the saturator and dilutor cells. A constant flow of helium as the stripping gas was set to a given value by means of a mass flow regulator. The flow rate was adjusted to a “suitable” value until there was no influence of the flow rate on measured data. The stripping gas was bubbled through the stirred liquid phase in order to strip out the volatile solute introduced in small quantities from solvent in the dilutor. The composition of the vapor phase where stripping gas is leaving the solution inside the dilutor was periodically sampled and analyzed by gas chromatography using a sampling valve. The peak area from gas chromatographs for solute decreased exponentially with time. At low pressures, the infinite dilution activity coefficient of the solute can be calculated from the following expression provided by Leroi et al.:9 γ∞ij
1 ) sat Pi
1 - ln(si /sit)0)nRT t Psat j 1 D 1+ + VG ln(si /sit)0) P t
(
)
(1)
where n is the total number of moles of solvent (j) inside the dilutor, VG (m3) is vapor phase volume in the dilutor cell, T (K) is the temperature in the dilutor, P (Pa) is the pressure in sat the dilutor, Psat i (Pa) and Pj (Pa) are saturation pressures, R (J -1 -1 mol K ) is the universal gas constant, t (s) is time, and si is area of the peak of solute (i), obtained from chromatographs of vapor phase periodically (si is in arbitrary units). The term (1/t) ln(si/si t)0) is the slope of the linear plot between reciprocal of time (s) and the natural logarithm of the surface area of the solute’s peak obtained from chromatographs of vapor phase analysis with time. D (m3 s-1) is the flow rate of the stripping gas (helium) at the exit of the dilutor at same temperature and pressure as of measurements and can be corrected using following equation:11 D ) Dfm
T Pfm Tfm P
γ∞ij ≡ limnif0 γi(T, P, ni, nj)
(4)
where the mole numbers of the other components are kept fixed. This limit will have a finite value. The activity coefficient at infinite dilution for a binary system can be calculated using a suitable thermodynamic model, for instance, an equation of state:4,5 ln γ∞ij (T, P, nj) ) limnif0[ln φˆ i(T, P, ni, nj)] - ln φi(T, P) (5) where i and j indicate the solute and solvent, respectively. For the calculation of infinite dilution activity coefficients, it is necessary to calculate fugacity coefficients. This is possible by partial differentiation of the Helmholtz energy with respect to number of moles at constant temperature and volume. The CPA EoS has been used for this purpose,2,13-17 and the model is briefly described here. The CPA EoS has previously been applied for phase equilibrium modeling of associating fluids.16,17 The CPA EoS is an association model based on Wertheim’s perturbation theory18-21 for accounting for strong interactions due to hydrogen bonding. This theory uses a potential function that closely imitates hydrogen bonding in order to develop a model for systems with a repulsive core and multiple hydrogen bonding sites.18-22 The CPA EoS proposed by Kontogeorgis et al.2 combines the Soave-Redlich-Kwong equation of state (SRK EoS)23 and the association term derived from Wertheim’s Table 2. Association Schemes Based on the Terminology of Huang and Radosz26
(2)
where the subscript fm represents measured quantities at flow meters. The common experimental techniques used for the measurement of infinite dilution activity coefficients including gas stripping techniques have a standard deviation on measured data (σln γ∞) in the range 0.02-0.05.4-7 However, as the immiscibility among the fluids increases (e.g., hydrocarbon-MEG mixture), the precise measurement becomes more difficult. Under such conditions, the uncertainty is often reported in percentage.11 In this work, the uncertainty in temperature is estimated to be lower than (0.1 K whereas the uncertainty on γ∞ij is within 5%. 3. Thermodynamic Modeling Using Cubic-PlusAssociation Equation of State At phase equilibrium, the activity coefficient, γi, can be defined as γi(T, P, n) ≡
ˆfi(T, P, n) φˆ i(T, P, n) ai(T, P, n) ) ) xi xifi(T.P) φi(T, P)
(3)
where T is temperature, P is pressure, n is the array of mole numbers, ai is the activity, xi is the mole fraction, φi is the fugacity coefficient, and fi is the fugacity of solute i at equilibrium. The activity coefficient of solute-component i in solvent-component j at infinite dilution is defined as4,5
a
The 5D scheme for DEG is not used in the modeling because of limited experimental data.
Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009 18-21
theory, as in statistical associating fluid theory (SAFT). The SRK EoS is a cubic equation in volume while the CPA EoS is not a cubic equation. The cubic part of the CPA EoS accounts for the physical interactions between the molecules while the association part takes into account the specific site-site interaction due to hydrogen bonding between like molecules (self-association) and unlike molecules (crossassociation and solvation). The association term, based on Wertheim’s first-order thermodynamic perturbation theory (TPT1), was introduced by Chapman et al.24,25 in the context of SAFT. The association term in the CPA EoS is based on the same assumptions as the corresponding term of SAFT. These assumptions are the following:14,15 the activities of different bonding sites on the same molecule are assumed independent of each other, and therefore, there is no steric hindrance effect; one site on the same molecule can bond only to one other site on another molecule; there is no double bonding between molecules. Ringlike bonding structures and interamolecular associations are not taken into account. The CPA EoS can be expressed in terms of pressure as a sum of the SRK term and the association term; the second term is in the form proposed by Michelsen and Hendriks.27 This is identical to the previous expressions,2,24-26 but mathematically much simpler for computations:27 P)
R(T) RT Vm - b Vm(Vm + b) 1 RT 1 ∂ln g 1+ 2 Vm Vm ∂(1/Vm)
(
)∑ i
xi
∑ (1 - X Ai
Ai)
(6)
where Vm is the molar volume, XAi is the fraction of A sites on molecule i that do not form bonds with other active sites, and xi is the mole fraction of component i. R(T) and b are the energy and the co-volume parameters, respectively. The letters i and j are used to index the molecules while A and B indicate the bonding sites on a given molecule. XAi, which is the key property in the association term, can be described as2,14,15 XAi-1 ) 1 +
1 Vm
∑x ∑x
AiBj
(7)
Bj∆
j
j
Bj
where Bj indicates summation over all sites. ∆AiBj, the association or bonding strength between site A on molecule i and site B on molecule j, is given by2,14,15
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[ ( ) ]
24-26
∆AiBj ) g(Vm)ref exp
AiBj
ε RT
- 1 bijβAiBj
(8)
where εAiBj and βAiBj are the association energy and volume of interaction between site A of molecule i and site B of molecule j, respectively, and g(Vm)ref is the radial distribution function for the reference fluid (i.e., fluid of hard spheres). The radial distribution function, derived from the CarnahanStarling equation of state,28 in SAFT and the CPA EoS is given by2,14,15 g(Vm)ref )
2-η 2(1 - η)3
1 b 4Vm
with η )
(9)
where η is the reduced fluid density. Kontogeorgis et al.,2,13 however, showed that the use of the Carnahan-Starling radial distribution function28 in the CPA EoS remains an approximation because it employs the van der Waals repulsive term of SRK which is not the case in the SAFT based models. They have therefore used a simpler expression for the radial distribution function:2,13 g(Vm)ref )
1 1 - 1.9η
1 b 4Vm
with η )
(10)
The CPA EoS with the simplified radial distribution function presented in eq 10 is called simplified CPA or the sCPA EoS. All thermodynamic modeling performed in this work is based on the sCPA EoS. 3.1. Parameters for Pure Compounds and Association Schemes. The energy parameter R(T) in the physical part of the CPA EoS is given by a Soave-type temperature dependency: R(T) ) ao[1 + c1(1 - √Tr)]2
(11)
where Tr is the reduced temperature (T/TC) of the component i. The CPA EoS has five pure component parameters: three for nonassociating components (a0, b, c1) and two additional parameters for associating components (εAiBi, βAiBi). The five pure-component parameters are usually obtained by fitting experimental vapor pressure and saturated liquid density data. For nonassociating components, the three parameters can either be obtained by fitting vapor pressure and liquid density data or in the conventional way from critical temperatures (TC), pressures (PC), and the acentric factor (ω). The conventional way for estimating the energy and the covolume parameters of the SRK EoS can also be used:
Table 3. CPA EoS Pure Component Parameters Used in This Work fluid MEG DEG TEG TeEG n-C5 n-C6 n-C7 n-C8 n-C9 n-C10 n-C11 n-C12 n-C13 n-C14 n-C15 n-C16 a
assoc scheme Molar mass (g mol-1) TC (K) ω (-) b (L mol-1) a0 (L2 bar mol-2) a0/Rb (K) c1 (-) εR-1 (K) β × 103 (-) 4C 4C 6D 7D naa na na na na na na na na na na na
na: non-associating.
62.07 106.12 150.18 194.23 72.15 86.18 100.21 114.23 128.26 142.29 156.31 170.33 184.36 198.39 212.41 226.44
720.0 744.6 769.5 795.0 469.7 507.6 540.2 568.7 594.6 617.7 639.0 658.0 675.0 693.0 708.0 723.0
0.5068 0.6221 0.7560 0.9174 0.2515 0.3013 0.3495 0.3996 0.4435 0.4923 0.5303 0.5764 0.6174 0.6430 0.6863 0.7174
0.0514 0.0921 0.1289 0.1666 0.0910 0.1079 0.1254 0.1424 0.1604 0.1787 0.1979 0.2162 0.2308 0.2505 0.2745 0.2961
10.82 26.41 38.83 52.49 18.20 23.68 29.18 34.88 41.25 47.39 55.25 62.41 68.07 76.62 85.64 94.92
2531.7 3448.8 3622.5 3789.5 2405.1 2640.0 2799.8 2944.9 3094.2 3190.5 3357.7 3471.0 3546.4 3678.4 3752.0 3855.5
0.6744 0.7991 0.9100 1.6261 0.7986 0.8313 0.9137 0.9942 1.0463 1.1324 1.1437 1.1953 1.2795 1.2906 1.3404 1.3728
2375.8 2367.6 1420.0 856.7 na na na na na na na na na na na na
14.1 6.40 20.0 23.4 na na na na na na na na na na na na
ref 14 14 30 30 14, 15 14, 15 14, 15 14, 15 14, 15 14, 15 14, 15 14, 15 this work 14, 15 14, 15 14, 15
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R(T) ) 0.42748
R2TC2 [1 + c1(1 - √Tr)]2 PC
c1 ) 0.48 + 1.574ω - 0.176ω2 RTC b ) 0.08664 PC
(12)
In this work, however, the pure-component parameters were obtained by fitting experimental vapor pressure and saturated liquid density data and using the mean absolute error (MAE) as an objective function: MAE )
1 N
N
∑ |y
CPA i
- yexp i |
(13)
i)1
where y is the property in question and N is number of data points. The use of the CPA EoS requires knowledge of the critical properties for parameter estimation. Considering the difficulties associated with the determination of experimental critical properties, an alternative approach, eliminating their need, has been presented.15 The association term of CPA in general depends upon the nature of the association. Huang and Radosz26 have provided a framework of association schemes in order to address the problem. They have presented a criterion for assigning different association schemes to various associating fluids. According to their approach, the associating fluids are analyzed in terms of Table 4. Experimental Infinite Dilution Activity Coefficient Data of Various Solutes (n-Alkanes) in Solvents (n-C12 or MEG) at Different Temperatures and Atmospheric Pressurea
Figure 2. Infinite dilution activity coefficients of n-pentane in n-dodecane at different temperatures. Symbols: (O) experimental data from this work; (∆) data from the DECHEMA data compilation;4,5 (×) data from the work of Letcher and Moolan.32 The line represents the tendency curve.
Figure 3. Infinite dilution activity coefficients of n-pentane in MEG, experimental data, and modeling. Symbols: (•) experimental data from this work; (]) data from the DECHEMA data compilation.5 The line is the CPA EoS with kij ) 0.035.
γij∞
T (K) solute C5; solvent C12 298.1 298.2 298.2 318.1 318.1 333.6
0.94 0.93 0.93 0.84 0.84 0.81 solute C5; solvent MEG
298.7 298.7 298.7 308.4 308.4 318.8 318.8 333.7 333.7
252 254 244 215 218 174 171 139 141 solute C6; solvent MEG
298.8 298.8 318.7 333.7 333.7
469 431 361 240 244 solute C7; solvent MEG
298.7 298.7 318.7 333.7
1082 1024 779 526 solute C8; solvent MEG
298.7 298.7 318.8 333.7 a
2168 2081 1584 1186
Uncertainty on temperature is estimated to be lower than 0.1 K, whereas on γij∞ it is lower than 5%.
Figure 4. Infinite dilution activity coefficients of n-hexane in MEG, experimental data, and modeling. Symbols: (•) experimental data from this work; (0) data from the DECHEMA data compilation.4,5 The line is the CPA EoS with kij ) 0.031.
the number of all possible “proton donor” or negative and “proton acceptor” or positive sites, in a rigorous fashion. After labeling all the possible interaction sites on the molecule, an association scheme is assigned either based on the rigorous molecular evaluation (called a rigorous association scheme) or by introducing some assumptions to assign a simpler association scheme (called, an assigned association scheme). MEG, DEG, TEG, and TeEG are generally assigned the 4C association scheme neglecting the presence of the additional ether sites (-O-) in DEG, TEG, and TeEG when compared to MEG. Recently, Breil and Kontogeorgis30 have shown that additional association sites can be taken into account in TEG and TeEG due to the oxygen atoms in the molecule. These schemes (denoted as 6D and 7D) improve the performance of the model. They have not tested DEG with the new type of schemes (5D) although it contains one additional negative (oxygen) site than MEG. These association schemes for various glycols are presented in Table 2. In this work, we have used the rigorous association schemes, 6D and 7D for TEG and TeEG, respectively. For DEG, we have used the 4C association scheme
Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009
Figure 5. Infinite dilution activity coefficients of n-heptane in MEG, experimental data, and modeling. Symbols: (•) experimental data from this work; (∆) data from the DECHEMA data compilation.4,5 The line is the CPA EoS with kij ) 0.029.
Figure 6. Infinite dilution activity coefficients of n-octane in MEG, experimental data, and modeling. Symbols: (•) experimental data from this work; (O) data from the DECHEMA data compilation.4,5 The line is the CPA EoS with kij ) 0.025.
because of scarcity of experimental data. The pure component parameters for the associating (glycols) and nonassociating (nalkanes) compounds used in this work are presented in Table 3. The parameters for n-tridecane are estimated using experimental data retrieved from DIPPR-DIADEM.29 The parameters for the remaining components have been taken from the literature.14,15,30 3.2. Mixing and Combining Rules. In order to extend CPA EoS to mixtures, mixing rules are required for the physical (SRK) part. The mixing and combining rules for R(T) and b are the classical van der Waals one fluid theory R(T) )
∑ ∑xxR
i j ij
i
j
and b )
∑ ∑xxb
i j ij
i
(14)
j
where the classical combining rules are used: Rij ) √RiRj(1 - kij) and bij )
bi + bj 2
(15)
Combining rules for the association energy and volume parameters are needed between different cross-associating molecules, e.g. water-alcohol or water-glycol systems, in order to calculate the value of the association strength, ∆AiBj. The hydrocarbon-glycol mixtures do not exhibit the phenomenon of cross association; therefore, the combining rules are not needed. Detailed presentation of combining rules for crossassociating mixtures is given elsewhere.14,31 The binary interaction parameters (kij) were obtained manually by a trial-and-error approach to minimize the MAE (eq 13) over the entire range of temperature for which data were available.
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Figure 7. Infinite dilution activity coefficients of n-hexane in DEG. Description: (solid line) CPA EoS with kij ) 0.073; (symbols) data reported in the DECHEMA data compilation from different authors.4,5
Figure 8. Infinite dilution activity coefficients of n-decane in DEG. Description: (solid line) CPA EoS with kij ) 0.04, (symbols) data from the DECHEMA data compilation.4,5
were carried out in order to validate the experimental protocols and techniques. The new experimental γ∞ij data are reported in Table 4. A comparison of the experimental data with the literature data4,5 is presented in Figure 2 to demonstrate the reliability and repeatability of the experimental work. The relative average absolute deviation (RAAD) between our results and the literature data4,5 is less than 2% which is within the labeled experimental uncertainty of the data from Letcher and Moolan.32 The RAAD can be defined as RAAD(%) )
100% N
N
∑ i
|
yCPA - yexp i i yexp i
|
(16)
4.2. Infinite Dilution Activity Coefficients of n-Alkanes in Glycols. The experimental infinite dilution activity coefficient data of n-alkanes (i) in glycols (j), reported in the literature, show a rather high level of dispersion, especially in low to moderate temperature ranges. For example, γ∞ij , of n-alkanes in MEG, exhibit more than 1 order of magnitude deviation among various data sets collected in the DECHEMA data series.4,5 This is illustrated for mixtures containing n-alkane-MEG in Figures 3-6. For higher glycols (TEG, TeEG), the dispersion in the
4. Results and Discussion 4.1. Infinite Dilution Activity Coefficient: Reliability of Experimental Work. Experimental measurements of the infinite dilution activity coefficients of n-pentane (i) in n-dodecane (j)
Figure 9. Infinite dilution activity coefficients of n-hexadecane in DEG. Description: (solid line) CPA EoS with kij ) 0.005, (symbols) data from the DECHEMA data compilation.5
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modeling section. Two binary systems involving n-alkanes (C6, C10, and C16) and DEG have previously been reported,4,5,33 these data were used in our modeling with the CPA EoS, and the results are presented in Figures 7-9. The binary systems involving n-alkanes and TEG and TeEG are also studied with the CPA EoS, and comparisons are made where experimental data are available in the open literature. The γ∞ij data of n-alkanes in TEG reported by Sun et al.34 and Pierotti et al.33 cover a wide range of temperature and were used here for modeling purposes. The results are presented in Figure 10. It is interesting to note that the limited data sets compiled in the DECHEMA data series,4,5 other than those of Sun et al.,34 generally show lower values of γ∞ij for systems containing TEG. The binary systems containing n-alkanes and TeEG were modeled using experimental γ∞ij data reported by Sun et al.,34 and the results are presented in Figure 11. Few systems involving TEG and TeEG and n-alkanes have also been studied recently.30 The CPA model results are generally found quantitatively successful using a single temperature-independent interaction parameter. The new and previously reported kij values are presented in Table 5 for all the binary systems involving n-alkane and glycols, studied in this work. Moreover, relative deviation between calculated and experimental properties and the number of experimental data points used for the determination of binary interaction parameters are also presented in the Table 5. Modeling of n-alkane-MEG and n-alkane-DEG mixtures shows an average 6% and 7% relative average absolute deviation between calculated and experimental γ∞ij . However, the deviation for n-alkane-TEG and n-alkane-TeEG mixtures is less than 5%. The CPA kij values are also presented graphically in Figure 12 versus the carbon number of n-alkanes for various n-alkane-glycol mixtures, either determined in this work or from previous studies. Generally, the comparison between previously reported14-17,30 binary interaction parameters and the parameters from this work shows good agreement except for two mixtures containing n-alkane-MEG where our kij values are smaller (about 40%). This discrepancy may be attributed to the use of liquid-liquid equilibrium (LLE) data in the previous studies instead of VLE (or γ∞ij data). It further shows that the CPA EoS has, in some cases, limitations in dealing with multiple situations (VLE, LLE, and solid-liquid equilibrium (SLE))
Figure 10. Infinite dilution activity coefficients of n-alkanes in TEG. Description: (symbols) data from the DECHEMA data compilation4,5 (*) n-hexadecane in TEG, ()) n-tridecane in TEG, (×) n-decane in TEG, (+) n-nonane in TEG, (O) n-octane in TEG, (∆) n-heptane in TEG, (0) n-hexane in TEG. The lines are based on the CPA EoS with kij presented in Table 5.
Figure 11. Infinite dilution activity coefficients of n-alkanes in TeEG. Description: (symbols) data from the work of Sun et al.34 (×) n-decane in TeEG, (+) n-nonane in TeEG, (O) n-octane in TeEG, (∆) n-heptane in TeEG. The solid lines are based on CPA EoS modeling with kij presented in Table 5.
literature data is relatively smaller because of the relatively higher solubility of alkanes. Also, γ∞ij data of n-alkanes in other glycols (DEG, TEG, and TeEG) is generally limited. In this work, new γ∞ij data of n-alkanes (from C5 to C8) in MEG were measured, which are reported in Table 4. Our data follow approximately the average value of the literature data4,5 except for n-hexane for which our values agree to the lower average values reported in literature.4,5 The new data are presented in Figures 3-6 along with the literature data,4,5 when available, and the modeling results using the CPA EoS, described in the
Table 5. Temperature Independent Binary Interaction Parameters, kij, for Different Glycol Systems Studied in This Worka previous studies14-17,30
this work kij
MEG + n-pentane MEG + n-hexane MEG + n-heptane MEG + n-octane DEG + n-hexane DEG + n-heptane DEG + n-decane DEG + n-hexadecane TEG + n-hexane TEG + n-heptane TEG + n-octane TEG + n-nonane TEG + n-decane TEG + n-tridecane TEG + n-hexadecane TeEG + n-heptane TeEG + n-octane TeEG + n-heptane TeEG + n-decane
0.035 0.031 0.029 0.025 0.073
8.4 9.0 4.9 2.8 6.6
9 6 5 4 8
298-340 298-385 298-385 298-345 300-375
0.040 0.005 0.115 0.110 0.103 0.093 0.085 0.055 0.040 0.085 0.078 0.073 0.068
5.2 8.2 6.2 1.1 3.0 4.0 3.3 4.0 9.0 1.7 2.7 4.1 4.8
5 5 8 8 8 8 8 2 2 7 7 7 7
298-400 300-400 315-400 315-400 315-400 315-400 315-400 330-360 335-410 330-410 330-410 330-410 330-410
The literature14,30 kij values were obtained using LLE data.
no. of
γij∞
system
a
RAAD (% on
γij∞)
data used
T (K) app. range
kij
T (K app. range)
0.059 0.047
305-330 315-355
0.065
315-420
0.094 0.110 0.109 0.100 0.091
310-360 320-400 320-400 320-400
0.075, 0.101
300-360
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Note Added after ASAP Publication: After this paper was published ASAP October 9, 2009, corrections were made to the captions of Figures 5 and 7; the corrected version was reposted October 26, 2009. Literature Cited
Figure 12. Temperature-independent, binary interaction parameters (BIP) for n-alkanes and glycols in the CPA EoS reported in Table 5. Symbols: (O) n-alkanes and MEG; (∆) n-alkanes and DEG; (0) n-alkanes and TEG; (*) n-alkanes and TeEG. The solid symbols are based on this work, while the open ones are previously reported.14-17,30 The dotted lines are linear plots of kij against the carbon number of alkane for all the systems studied.
using the same system specific binary interaction parameter, especially at very dilute conditions (close to infinite dilution). Furthermore, Figure 12 shows a useful trend and a comparison among various alkane-glycol mixtures, which may be useful for obtaining interaction parameters for n-alkanes and glycols in the absence of phase equilibrium data. All the kij values for the binary systems containing n-alkanes and glycols are positive. The kij for TEG containing systems generally have higher numerical values than those for the systems involving TeEG, DEG, and MEG with the same n-alkane. The kij values of each alkane-glycol mixture decreases with increasing carbon number of alkanes. This behavior seems to be consistent up to n-hexadecane. It is also interesting to note that the kij values for TeEG-containing binary systems are somewhat lower than those of TEG but higher than those for DEG and MEG systems with the same alkane. 5. Conclusions We have reported infinite dilution activity coefficients data for n-alkanes (n-pentane, n-hexane, n-heptane, and n-octane) in MEG using an inert gas stripping experimental technique9 (Table 4). The experimental infinite dilution activity coefficients of several n-alkanes in MEG, DEG, TEG, and TeEG are satisfactorily modeled using the CPA EoS (Figures 3-11). The brief description of the model, the pure component parameters (Table 3), and the binary interaction parameters (Table 5) are presented. The deviation between new interaction parameters (based on VLE data) and the previously reported parameters is described. Considerable deviations for alkane-MEG mixtures are observed because of the fact that new interaction parameters are based on VLE data and the previously reported parameters are based on LLE data. The variation in the values of the interaction parameters was discussed for different glycol systems. The interaction parameters are positive and follow a linear trend with the carbon number of n-alkanes with the same glycol (Figure 12). The interaction parameters for alkanes-glycol mixtures are in the following order: TEG > TeEG > DEG > MEG. Acknowledgment W.A. wishes to thank the Higher Education Commission of Pakistan for providing a doctoral scholarship. The Gas Processors Association is gratefully acknowledged for the financial support under project GPA 992-3. Dr. Christophe Coquelet is thanked for fruitful discussions regarding the experimental work.
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ReceiVed for reView May 25, 2009 ReVised manuscript receiVed August 31, 2009 Accepted September 9, 2009 IE900856Q
