Article pubs.acs.org/IECR
High-Temperature, High-Pressure Volumetric Properties of Propane, Squalane, and Their Mixtures: Measurement and PC-SAFT Modeling Babatunde A. Bamgbade,*,†,‡ Yue Wu,†,‡ Ward A. Burgess,† Deepak Tapriyal,†,§ Isaac K. Gamwo,† Hseen O. Baled,†,∥ Robert M. Enick,†,∥ and Mark A. McHugh†,‡ †
National Energy Technology Laboratory, Office of Research and Development, U.S. Department of Energy, Pittsburgh, Pennsylvania 15236-0940, United States ‡ Department of Chemical and Life Science Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, United States § URS, Pittsburgh, Pennsylvania 15236, United States ∥ Department of Chemical and Petroleum Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States S Supporting Information *
ABSTRACT: This study reports the high-temperature, high-pressure density data for propane, squalane, and their binary mixtures for five compositions at temperatures to 520 K and pressures to 260 MPa. The density measurements are obtained with a floating-piston, variable-volume, high-pressure view cell. From the density data, the isothermal and isobaric excess molar volumes upon mixing are computed. For the mixture compositions studied here, the excess volume is mostly negative, showing a minimum at 0.6550 mole fraction of propane and becomes less negative as the propane concentration increases. The perturbedchain statistical associating fluid theory (PC-SAFT) equation of state (EoS) provides good representation for the experimental data. A mean absolute percent deviation (δ) of 1.4% is obtained with the PC-SAFT EoS when using propane and squalane pure component parameters fit to density data at high-temperature, high-pressure conditions.
1. INTRODUCTION High-temperature, high-pressure (HTHP) densities of alkanes and their mixtures continue to garner interest for their importance in many industrial applications, such as in refrigeration cycles, lubricants, polymer processing, and energy sources. For instance, the world reliance on fossil fuels, which are primarily composed of alkane mixtures, is projected to continue to grow over the next several decades. This has led to the search for new oil reserves at depths of several miles below sea floor. The reservoir conditions at these depths approach 533 K and 240 MPa, and are typically encountered in the ultradeep formations in the Gulf of Mexico.1,2 In addition, information on the density of hydrocarbon mixtures is vital in the estimation of recoverable oil in a reservoir. In modeling studies, hydrocarbon HTHP density data are used to test and improve the performance of equations of state (EoS) models to reliably represent the thermodynamic properties of a wide variety of compounds. As such, there has been an increase in the HTHP studies on the thermodynamic properties for hydrocarbons and their mixtures including propane and squalane. Lemmon et al.3 reported the available literature data for pure propane from which they proposed a reference EoS for pure propane. Similarly, Mylona et al.4 reported detailed HTHP density and viscosity data for pure squalane. Beyond this, Ito et al.5 recently reported the pure propane density data at temperatures to 600 K while Schmidt et al.6 reported pure squalane density data to 473 K. However, both data sets were only reported to a maximum pressure of 200 MPa. Furthermore, the experimental studies on asym© XXXX American Chemical Society
metric binary mixtures of propane with long-chain alkanes at HTHP conditions are scarce in the literature. This gap in the literature has recently been addressed to an extent with publications on HTHP mixtures of propane with octane, decane, and eicosane.7−9 For the propane−squalane system, Nanu et al.10 reported the vapor−liquid equilibrium properties for the mixtures at temperatures to 473 K for 14 different mixture compositions. Aalto et al.11 reported the volumetric properties of the mixture but only in the vicinity of the critical point of propane and at a single mixture composition, which is in excess of 0.996 mole fraction of propane. We report new experimental density data for propane, squalane, and their mixtures at five compositions at three isotherms to 520 K and pressures to 260 MPa. The mixture of propane and squalane constitutes an asymmetric mixture due to the large size difference between propane and squalane molecules. The density data are obtained using a variable volume-view cell, which we have previously used to measure HTHP density for many aliphatic, 12,13 cyclic,12,14 and aromatic12,15 hydrocarbons. The mixture experimental data are correlated with the modified Tait equation16 from which the excess molar volumes are computed at constant temperatures and pressures. The reference EoS for propane3 is however used to represent the volumetric properties of Received: March 29, 2015 Revised: May 12, 2015 Accepted: June 9, 2015
A
DOI: 10.1021/acs.iecr.5b01173 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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density, Uc, is Uc(ρ) = (0.90%)(ρ) (at a coverage factor k = 2 for an interval having a confidence level of approximately 95%).
propane, since the Tait equation gives poor representation of the volumetric properties of gases. The perturbed-chain statistical associating fluid theory (PC-SAFT) EoS17 is used to model the density of propane, squalane, and their mixtures. The PC-SAFT EoS requires three pure-component parameters for each nonassociating compound for calculations, which can be obtained either by fitting the EoS directly to experimental data17,18 or from group contribution methods.19,20 We have previously reported that the PC-SAFT EoS14,15,18,21,22 with pure-component parameters obtained from low-pressure experimental data does not give reliable predictions of HTHP density. In those earlier studies, the PC-SAFT EoS was fitted to the HTHP experimental data that gives rise to improved PCSAFT EoS density predictions but poorer predictions for vapor−liquid equilibria phase behavior. Furthermore, the purecomponent parameters can be estimated from group contribution methods available in the literature.19 The performance of the PC-SAFT EoS with these different sets of parameters is described subsequently in this manuscript.
3. RESULTS AND DISCUSSION 3.1. Experimental Density Results. Experimental density data are reported in the Supporting Information, Table S1 for pure propane, Table S2 for pure squalane, and Tables S3−S7 for propane-squalane mixtures, for five mixture compositions. The measurement temperatures range from 323 to 525 K, while the pressure ranges from 4 to 260 MPa. More than one-third of the experimental data points are repeated showing good reproducibility of the experimental data. As expected, the mixture density data decrease with increase in propane concentration and/or temperature and increase with increasing pressure. 3.1.1. Propane. The thermodynamic properties of propane have been studied over wide temperature and pressure conditions leading to development of several reference equations of state (EoS). Lemmon et al.3 developed the latest in the series of reference EoS that represent the thermodynamic properties of propane and cover temperatures to 650 K and pressures to 1000 MPa. In the development and validation of the reference EoS, Lemmon et al.3 utilized a very large pool of experimental data from almost 200 references. The uncertainty in the density data calculated from the reference EoS is less than 0.1%, and the calculated data also agree with the data reported in the NIST Chemistry Webbook24 within 0.1%. However, at temperatures in excess of 480 K, experimental density data are lacking beyond 60 MPa and especially lacking at the HTHP conditions related to oil recovery processes in ultradeep reservoirs. This study reports the experimental density data for propane at 324.1, 424.6, and 514.4 K at pressures to 210 MPa. Under these conditions the density ranges from 336 to 536 kg/m3. Recently, Ito et al.,5 using a metal-bellows variable volumometer technique, reported the density data for propane to 673 K and 200 MPa with average experimental uncertainty within 0.3% of the density data. Thus, Figure 1 shows the deviation plots of the data calculated from the Lemmon et al. reference EoS3 from the experimental data of Ito et al.5 and data obtained in this study. The mean absolute percent deviation (δ, eq 1) between the density reported in this study and the calculated density with the Lemmon et al. reference EoS is 0.4 at 324.1 K, 0.4 at 424.6 K, and 0.3 at 514.4
2. EXPERIMENTAL SECTION 2.1. Materials. Propane and squalane are purchased from Sigma-Aldrich with 0.9997 and 0.99 mass fraction purities, respectively. All chemicals are used as received. 2.2. Procedure. The detailed description of the highpressure view cell used in this study has been provided in previous publications along with the experimental technique used to obtain density data.7,12,13,21,23 The only modification made in the current cell is the use of a window-holder, made out of Inconel just like the view cell, that eliminates the elastomeric o-rings previously needed to seal the sapphire window in the front end of the view cell. The internal volume of the view cell is determined with a linear variable differential transformer (LVDT, Schaevitz Corp., model 2000 HR) that tracks the position of a floating piston as the system is pressurized. The LVDT reading is calibrated with NIST density data24 at 323, 423, and 523 K using n-decane and at 323 and 423 K using propane. The system pressure is measured with a Viatran pressure transducer, while the system temperature is measured with a type K thermocouple calibrated against an immersion thermometer (Fisher Scientific, calibrated using methods traceable to NIST standards). The observed temperature variation for each reported isotherm−isopleth combination is within 0.2 K. In a typical experiment, the empty view cell is flushed with propane three times and then degassed before squalane is loaded to within ±0.0002 g into the cell. Propane, to within ±0.002 g, is then loaded into the cell using a high-pressure transfer vessel. After addition of propane and before disconnection of the transfer vessel from the view cell, the transfer vessel is chilled in liquid nitrogen to minimize the loss of propane from the transfer line when the line is disconnected from the view cell. The average estimated uncertainty is within 0.0003 for the reported propane mole fractions. Once the cell is heated to a desired temperature and pressurized to a select pressure, the piston position is recorded to obtain a data point. For each isotherm, the pressure for a given measurement is chosen in a nonmonotonic manner to minimize any potential experimental artifacts in the measurements. The standard uncertainties, u, are u(T) = 0.2 K, u(P) = 0.07 MPa below 56 MPa, and u(P) = 0.35 MPa for 56−270 MPa. The estimated accumulated (combined) uncertainty in the reported mixture
Figure 1. Percent density deviations for experimental propane densities (ρExpt) obtained in this study (open symbols) and data reported by Ito et al.5 (filled symbols) from predicted densities using Lemmon et al.’s reference EoS3 (ρEoS) at (○) 324.1 K, (●) 360.0 K, (△) 424.6 K, (▲) 440.0 K, (◇) 514.4 K, and (◆) 550.0 K. B
DOI: 10.1021/acs.iecr.5b01173 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research K, which are well within the experimental uncertainty for the reported density in this study. δ=
1 n
n
∑ 1
ρi ,experimental − ρi ,predicted ρi ,experimental
× 100 (1)
3.1.2. Squalane. In this study, experimental density data for pure squalane are measured at 323.4, 423.7, and 511.5 K and at pressures to 240 MPa. The high-pressure density of squalane has been reported in the literature at temperatures to 473 K and pressures to 200 MPa. The present study extends the literature data to 511.5 K and to 240 MPa. Figure 2 compares
Figure 2. Temperature and pressure distribution of literature density data for squalane as compared to the squalane density data obtained in the present study. The figure excludes literature data only collected at 0.1 MPa.4,25−34 Shown are the data of Schmidt et al.6 (○), Fandino et al.35 (□), Ciotta et al.36 (△), Tomida et al.37 (◇), Kumagai et al.38 (▽), Fandino et al.39 (×), Kuss et al.40 (+), and the data obtained in this study (●).
the range of experimental conditions for density data obtained in this study with the experimental conditions reported in the literature for squalane. The figure does not include references that only reported density data at atmospheric pressures.4,25−34 Mylona et al.4 correlated the modified Tait equation16 to the available literature density data at both atmospheric and high pressures but only to a maximum temperature of 473 K. The Tait equation, with the parameters reported by Mylona et al., is used to compare the experimental data obtained in this study to data available in the literature. The δ between the Tait equation and the reported data in the present study is 0.7 at temperatures to 423.7 K. When the parameters of the Tait equation are extrapolated to 511.5 K, which is beyond the limits of the experimental data used to obtain the parameters, the δ becomes 0.9, a value almost equal to the estimated uncertainty for the reported density data in the present study. 3.1.3. Propane−Squalane Mixtures. Figure 3 shows the mixture density obtained in this study along with the pure component densities for propane and squalane. Experimental density data are reported for five mixture compositions for the propane−squalane mixtures containing 0.6555, 0.7960, 0.9208, 0.9439, and 0.9752 mole fraction of propane, which correspond to 0.1653, 0.2892, 0.5480, 0.6368, and 0.8040 weight fraction of propane, respectively. The temperature (∼324, ∼424, and ∼518 K) and pressure ranges (4−265 MPa) are similar to the experimental ranges investigated for the pure components. As shown in Figure 2, mixture densities increase with increase in pressure and decreases with increase in temperature and/or propane concentration. To our knowledge, there are no high-
Figure 3. Experimental density data for the propane (1)−squalane (2) binary mixtures measured in this study at about 324 (a), 424 (b), and 518 K (c). The propane mole fractions, x1, are 0 (◆), 0.6550 (○), 0.7960 (□), 0.9208 (◇), 0.9439 (△), 0.9708 (×), and 1 (●). Lines drawn to guide the eyes through data points.
pressure density data in the literature to compare to the propane−squalane mixture density data obtained in this study. 3.2. Modified Tait Equation. The modified Tait equation,16 eq 2, is fitted to the experimental data for squalane and propane−squalane mixtures to provide a facile method for density calculations at different temperatures and pressures. Although the modified Tait equation has been widely used to correlate experimental liquid density data, the equation does not provide very good representation for the volumetric properties of gases. Therefore, the Tait equation is not correlated to pure propane density data. The reference equation proposed by Lemmon et al.3 is used to represent the pure propane data for the purpose of interpolating the experimental data. ρ − ρ0 P+B = C log10 ρ P0 + B (2) C
DOI: 10.1021/acs.iecr.5b01173 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research P0 equals 0.1 MPa. ρ0 is the density at P0, and B and C are adjustable parameters determined from fitting the equation to experimental density data. Parameter C is independent of temperature, while ρ0 and B are temperature-dependent, and for hydrocarbons, both parameters decrease as the temperature increases. Table 1 lists the modified Tait equation parameters Table 1. Tait Equation Parameters, Mean Absolute Percent Deviation, δ, and Standard Deviation Values, λ, for each δ, Obtained for each Density Isotherm and Isopleth for the Propane (1)−Squalane (2) Binary Mixtures (C = 0.2232) x1
data points
T, K
ρ0, kg·m−3
B, MPa
δ
λ
0.0000 0.0000 0.0000 0.6550 0.6550 0.6550 0.7960 0.7960 0.7960 0.9208 0.9208 0.9208 0.9439 0.9439 0.9439 0.9752 0.9752 0.9752
19 18 21 24 23 23 14 16 14 25 23 19 25 14 21 23 23 15
323.4 423.7 511.5 323.6 423.6 516.0 324.2 420.5 523.5 324.5 424.0 515.3 322.6 424.2 521.5 324.4 426.5 522.5
780 711 638 731 648 569 675 569 422 550 388 295 555 339 223 507 286 211
85.364 46.565 23.676 67.144 30.713 13.393 48.697 15.051 2.603 13.929 1.934 0.576 20.000 0.951 0.124 14.120 0.537 0.137
0.12 0.26 0.19 0.16 0.15 0.04 0.09 0.15 0.54 0.15 0.37 0.39 0.32 0.90 1.42 0.26 1.47 1.08
0.11 0.22 0.20 0.27 0.18 0.03 0.11 0.11 0.30 0.22 0.33 0.49 0.20 0.65 1.07 0.35 1.04 0.84
for each isotherm−isopleth combination along with the mean absolute percent deviation, δ, and the standard deviation, λ, values. Table 1 shows that the Tait equation provides a poor representation of the experimental mixture density data for mixtures at the higher propane concentrations and at the highest temperatures. Likewise the density deviation plots for the propane mole fraction of 0.9439 (□) and 0.9752 (◆) isopleths in Figure 4 also show the largest deviations especially at ∼424 and ∼518 K, which is not unexpected since the Tait equation provides a poor representation of the volumetric properties of expanded, low density mixtures. 3.3. Molar Volumes and Excess Volumes. Molar volumes are calculated at constant temperature and pressure using the modified Tait equation as a means of interpolating experimental mixture density data. The Tait equation is also used to calculate pure squalane density data, while the reference equation by Lemmon et al.3 is used to calculate pure propane density data. Although not shown, a smooth linear relationship is observed for constant temperature and pressure plots of the molar volumes as a function of mixture mole fractions. The smooth linear trends were similarly observed for the molar volume for previously published propane−decane and propane−eicosane mixtures.7 Excess volumes of mixing for the propane−squalane mixture are calculated using eq 3 where VEx is the excess molar volume, ρm is the mass density of the mixture, and xi, Mi, and ρi are the mole fraction, molecular weight, and mass density of component i, respectively. The excess volumes are mostly negative for the propane−squalane binary system similar to the behavior exhibited for systems of compounds in the same chemical family. It has been theorized that the negative excess
Figure 4. Deviation plots of the propane (1)−squalane (2) mixture density data (symbols) obtained in this study from the fit of the modified Tait equation at (a) 324 K, (b) 424 K, and (c) 518 K, where x1 = 0.0000 (●), 0.6550 (○), 0.7960 (◇), 0.9208 (△), 0.9439 (□), and 0.9752 (◆).
volumes observed in asymmetric systems such as this one result from the small molecules filling the void spaces between the much larger molecules.8 For example, parts a−c of Figure 5 show representative results for the excess volume of the propane−squalane mixture as a function of propane mole fraction for the 324, 424, and 518 K isotherms at 30, 100, and 160 MPa. Figure 5d shows a similar plot for the 30 MPa isobar at 324, 424, and 518 K. The magnitude of the excess volume decreases as the pressure increases, while it increases with increase in temperature. The trends of the excess volume with pressure and temperature are also similar to those observed for previously reported propane binary mixture with octane8 and with decane and eicosane.7 In the present study, the most negative value of the excess volume for the propane−squalane mixture is obtained at a propane mole fraction of 0.6550, where the highest degree of packing for the mixture exists. However, the trends depicted in Figure 5 exhibit some hysteresis D
DOI: 10.1021/acs.iecr.5b01173 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 5. Excess volumes for propane−squalane mixtures as a function of propane mole fraction for isotherms: (a) 324 K, (b) 424 K, (c) 518 K for 30 (○), 100 (◇), and 160 MPa (△); (d) for 30 MPa isobar at 324 K (○), 424 K (◇), and 518 K (△). Lines serve to guide the eyes.
pressure curve and experimental phase behavior data.18 For this study, PC-SAFT EoS calculations are carried out using the pure component parameters fit to low pressure (Low-P) data and fit to HTHP density data. Both Low-P17 and HTHP18 parameters have been reported in the literature for propane, while only the Low-P parameters have been reported for squalane.42 New HTHP parameters are thus obtained for squalane by fitting the PC-SAFT EoS to the HTHP density data for pure squalane obtained in this study. These fitted pure-component parameters are listed in Table 2.
especially at high propane concentrations due to the relatively small magnitude of the excess volumes. As an explanation for this observation, Pecar and Dolecek41 noted how a small difference in density can lead to a large difference in the calculated excess volumes. Note also that the Tait equation used to interpolate data at constant temperatures and pressures performed poorly at high propane concentrations where most of the hysteresis exists. Therefore, more precise experimental data and a more accurate correlation are needed to obtain more accurate values for the excess volume of the mixtures. V Ex (m 3·kmol−1) =
1 ρm (kg·m−3) 2
−
∑ i=1
2
Table 2. Fitted PC-SAFT Pure-Component Parameters, m, σ, and ε/kB for Propane, Mw = 44.1, and for Squalane, Mw = 422.8
∑ xiMi (kg·kmol−1) i=1
xiMi (kg·kmol−1) ρi (kg·m−3)
type
(3)
Low-P
4. MODELING EXPERIMENTAL DATA 4.1. Perturbed-Chain Statistical Associating Fluid Theory EoS (PC-SAFT EoS). Although the Tait equation is useful for interpolating mixture density data at specific mixture compositions, it is not an appropriate tool for representing the thermodynamic properties of mixtures over wide ranges of temperature, pressure, and composition. Therefore, the PCSAFT EoS17 is used to model HTHP densities for propane, squalane, and their mixtures obtained in this study. The three pure-component parameters, which are the number of segments, m, temperature-independent segment diameter, σ, and the interaction energy, ε/kB, are required for the PC-SAFT EoS calculations for the nonassociating fluids studied here. It has been previously reported that the PC-SAFT EoS with parameters from a fit of the vapor pressure curve tends to overpredict the density in the HTHP region.14,15,18,21,22 Conversely, the PC-SAFT EoS with parameters from a fit of HTHP density data provide a poor representation of the vapor
HTHP
compd 17
propane squalane42 propane18 squalanea
m
σ (Å)
ε/kB (K)
2.0020 10.5257 2.1994 16.6709
3.6184 4.1189 3.5381 3.5360
208.11 254.95 204.81 227.53
HTHP parameters for squalane obtained from fit of experimental density data for pure squalane reported in this study. a
The combining rules for the three parameters are given in eqs 4−6, where xi is the mole fraction of component i. The binary interaction parameter, kij, is set to zero for the mixture calculations given that propane and squalane both belong to the same chemical family. Table 4 lists pure component parameters obtained from group contribution (GC) methods19 using LowP and HTHP parameter sets and using the functional groups provided in Table 3. These GC parameters are then used for the PC-SAFT EoS density predictions of the mixture compounds investigated in this study. As such, a purely predictive PC-SAFT EoS model comparison to experimental data is obtained here by setting kij to zero and using the two different GC parameter sets. E
DOI: 10.1021/acs.iecr.5b01173 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research Table 3. Values for the PC-SAFT Group Contribution of each Functional Group for Both Low-P and HTHP Parameters from Burgess et al.19
type
group
no. of groups in propane
Low-P
−CH3 −CH2− −CH< −CH3 −CH2− −CH
