Bubble Point Measurements of n-Propane + n

Bubble Point Measurements of n-Propane + n-Decane Binary Mixtures with Comparisons of Binary Mixture Interaction Parameters for Linear Alkanes Elisabeth Manseld,∗ Ian H. Bell, and Stephanie L. Outcalt

Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO 80305 E-mail: elisabeth.mans[email protected] Phone: +1(303)497-6405. Fax: +1(303)497-5030

Abstract To develop comprehensive models for multi-component natural gas mixtures (and other applications), it is necessary to have binary interaction parameters for each of the pairs of constituent uids that form the mixture. The determination of accurate mixture interaction parameters rely on reliably collected experimental data. In this work, we have carried out an experimental campaign to measure the bubble point pressures of mixtures of n -propane and n -decane, a mixture that has been thus far poorly studied. The experimental measurements of bubble point states span a composition range (in n propane mole fraction) from 0.269 to 0.852, and the bubble point pressures are measured in the temperature range from 270 K to 370 K. These data, in conjunction with data from a previous publication on mixtures of n -butane + n -octane and n -butane + n nonane, are used to determine binary interaction parameters. The newly-obtained 1

binary interaction parameters for the mixture of n -propane and n -decane represent the experimental bubble-point pressures given here to within 8%, as opposed to previous deviations up to 19%.

Introduction Many of the separation processes related to the energy industry require some knowledge of the vapor-liquid equilibria of hydrocarbon mixtures. A testament to this is the work done by the GERG (a consortium of European gas companies) to develop an equation of state for the thermodynamic properties of natural gases covering the gas and liquid regions including the vapor-liquid phase equilibrium. 1,2 The GERG equation enables the prediction of thermal and caloric properties of 21 natural gas components and their mixtures. In the absence of experimental data, empirical equations of state, such as the GERG, may fail to produce accurate property predictions. This is especially true for the predictions of mixture properties. In this work, data for n -propane + n -decane binary systems, along with previously published data on n -butane + n -octane and n -butane + n -nonane binary systems 3 , are utilized to t mixture parameters. Very few data sets of these mixtures exist in the literature 47 and comparisons to the GERG-2008 equation showed considerable deviations, prompting the need for additional measurements and improved mixture modeling. The thermodynamic properties of the mixture are modeled by the use of a multi-parameter mixture model. This family of models has seen wide application because it is a Helmholtzenergy based model, and therefore all other thermodynamic properties can be obtained from derivatives of the Helmholtz energy 1,2,8,9 . For instance, the pressure of the mixture can be obtained from

( ) ∂αr p = ρRT 1 + δ (τ, δ) . ∂δ

(1)

The non-dimensionalized residual Helmholtz energy αr is expressed in terms of the reduced 2

density δ = ρ/ρr (¯ x) and the reciprocal reduced temperature τ = Tr (¯ x)/T . The reducing functions ρr (¯ x) and Tr (¯ x) contain the binary interaction parameters as is described below.

Materials and Methods Materials n -Propane and n -decane were obtained from commercial sources and used without further purication. The stated manufacturer purities were as follows: n -propane 99.999 % and n -decane > 99 %. These purities were conrmed in our laboratory by analysis with gas chromatography-mass spectrometry (GC-MS) (Table 1). Spectral peaks were interpreted with guidance from the NIST/EPA/NIH Mass Spectral Database. 10 Water content was veried using coulometric Karl Fischer titrations according to ASTM Standard Test Method E1064-00 11 (Table 1) and 1 H NMR and

13

C NMR measurements.

Table 1: Measured and manufacturer determined purity of mixture components Chemical n -propane n -decane

Manufacturer Specication 99.999 % >99 %

GC-MS 99.99999 % 99.57 %

Karl Fisher 20 ± 20 ppm

1

H NMR

99.99 ± 0.02 %

13

99.8 ± 0.1 %

Mixture preparation Mixtures were prepared gravimetrically in sealed 300 mL stainless steel cylinders. Mixture preparation has been explained in detail previously. 3 Briey,

n -decane was added to the

stainless steel cylinder, then degassed by freezing in liquid nitrogen and evacuating the headspace. This was repeated three times. After degassing, the mass of the n -decane in the cylinder was determined by use of the double-substitution weighing design. 12 The density of ambient air was calculated based on measurements of temperature, pressure, and relative humidity, and the sample masses were corrected for the eects of air buoyancy. 13 n -Propane was transferred to the sample cylinder directly from the manufacturer's cylinder, and the 3

C NMR

sample mixture was degassed three times. The mass of

n -propane was then determined.

Sample cylinders were prepared with the goal of lling the sample cylinder to between 280 mL and the maximum volume of 300 mL at the target composition, at ambient temperature. The standard deviation of the repeat weighings was at most 1.5 mg. The uncertainty of the measured mixture composition will be discussed in detail in a later section and is given in each data table.

Measurements A schematic of the instrument used to make the measurements is shown in Figure 1 and has been previously described in detail. 14 Briey, a cylindrical stainless steel cell with an internal volume of 30 mL housed the sample. The cell and all of the system valves were housed inside a temperature-controlled, insulated aluminum block. Sample pressure measurements were recorded in 5 K increments from 270 K to 370 K. As the cell temperature was increased, the liquid inside the cell expanded, and it was necessary to periodically release a small amount of liquid from the bottom of the cell to maintain a vapor space. Repeat measurements were conducted at a minimum of two temperatures for each mixture composition to establish the repeatability of the measurements and to determine if the loss of small amounts of the liquid phase aected the sample composition to the extent that duplicate measurements at a given temperature yielded dierent bubble point pressures. Under this measurement conguration, eorts were made to ensure that the most accurate bubble points of the sample were measured, but assumptions were made. These assumptions include: (1) the liquid composition in the cell is equal to the bulk composition of the mixture in the sample bottle, and (2) by loading the cell almost full of liquid with only a very small vapor space remaining, the pressure of the vapor phase is the bubble point pressure of the liquid composition at a given temperature.

4

Figure 1: Schematic of the apparatus used to make bubble-point measurements

Uncertainty Analysis All mixture uncertainty analysis was performed using REFPROP Version 9.1.1.10 15 and using the GERG-2008 equation of state 1 for comparison. The interaction parameters used for the mixtures are given in Table 2. The expanded uncertainty for our bubble point measurements was previously reported. Briey, the uncertainty is calculated by the root-sum-of-squares method, taking into account ve principle sources of uncertainty: temperature, pressure, sample composition, measurement repeatability, and head pressure correction. 16 The standard platinum resistance thermometer (SPRT) and the pressure transducer used for our measurements were calibrated immediately prior to starting the measurements. A dierence of pressure at 0.03 K from the measured temperature was factored into the calculation to account for uncertainty in the SPRT. The manufacturers stated uncertainty of the pressure transducer is 0.01 % of full range, or 0.7 kPa. As a conservative estimate of the pressure uncertainty, the greater of 0.7 5

kPa or 0.1 % has been used in the calculation of the overall combined uncertainty of the bubble point pressures reported here. The uncertainty in the composition of the mixture is by far the most dicult to estimate accurately. Sample purity, uncertainty in the determined masses during sample preparation, and the transfer of the mixture sample into the measuring system aect the composition of the uid mixture. To account for the possibility that the degassing of the samples was not complete, a calculation was done assuming that air represented a 0.001 mol fraction impurity in each of the mixtures. Nitrogen was used to represent air in the calculations. Table 2: Current state-of-the-art binary interaction parameters from NIST REFPROP Mixture n -propane + n -decane n -butane + n -octane n -butane + n -nonane

βT γT 0.985331233 1.1409053 1 1.0331801 1 1.0140964

βv γv 0.984104227 1.053040574 1 1.046905515 1 1.049219137

The repeatability of our bubble point measurements was determined by repeating measurements at a minimum of two temperatures for each sample studied. The standard deviation was then taken as the repeatability. To be conservative in our uncertainty estimates, the largest of the standard deviation values for each mixture was used as the repeatability value in the calculation of overall combined uncertainty for each point in that mixture. The pressure transducer was maintained at 313 K during measurements. For temperatures of 315 K and above, the head pressure was calculated for each point and treated as an uncertainty in the calculation of the overall uncertainty in the reported bubble point pressures. The reported overall combined uncertainty for each point was calculated by taking the root sum of squares of the pressure equivalents of the temperature and composition uncertainties, the uncertainty in pressure, the measurement repeatability, and head pressure corrections. This number was multiplied by two (coverage factor, k=2) and is reported as an uncertainty in pressure as well as a percent uncertainty for each bubble point.

6

Results and Discussion Experimental Data Bubble point pressures for ve compositions of n -propane + n -decane binary mixtures were measured from 270 to 370 K (Tables 3, 4, 5, 6, 7). The uncertainty in the pressure was calculated and reported for each point and is given as an absolute value, as well as a percentage. The deviation from the GERG-2008 equation of state as implemented in REFPROP is given in the nal column. As seen previously for mixtures of low molecular weight linear alkanes with high molecular weight linear alkanes, 3 the deviation from the GERG-2008 predicted value increases with higher n -decane composition. Figure 2 illustrates the temperature and pressure range of our data, as compared to existing literature data. It can be seen that the data presented here are mostly at lower temperatures and pressures than that of the literature. The experimental data of Tin and coworkers is solid-liquid-vapor phase data. 4 It is provided here for comparison, but not used further in the text.

7

Table 3: Measured bubble point pressures for the system n -propane(1) + n -decane(2) at temperature T, pressure P, and liquid mole fraction x1 =0.731. Standard uncertainties u are u(T ) = 0.03 K and u(x1 ) = 1.78 x 10−5 . The values for u(P ) are given in the table. T/K 270.00 275.00 280.00 285.00 285.00 290.00 290.00 295.00 300.00 300.00 305.00 310.00 315.00 315.00 320.00 320.00 325.00 325.00 330.00 330.00 335.00 340.00 345.00 350.00 355.00 360.00 365.00 370.00

P/kPa 313.52 365.03 421.76 483.56 483.62 551.33 552.15 626.26 707.93 707.79 796.24 891.91 991.98 993.51 1100.52 1100.05 1203.46 1192.51 1309.73 1309.68 1439.13 1576.56 1721.22 1872.35 2030.24 2197.17 2370.02 2550.34

x1 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731 0.731

u(P )/kPa 4.13 4.21 4.29 4.37 4.37 4.45 4.45 4.53 4.62 4.62 4.76 4.91 6.18 6.18 6.35 6.35 6.52 6.51 6.65 6.65 6.80 7.02 7.21 7.40 7.66 7.95 8.19 8.45

(u(P )/P)×100 1.32 1.15 1.02 0.90 0.90 0.81 0.81 0.72 0.65 0.65 0.60 0.55 0.62 0.62 0.58 0.58 0.54 0.55 0.51 0.51 0.47 0.45 0.42 0.40 0.38 0.36 0.35 0.33

8

(1-PEOS /Pexp )×100 -1.81 -1.45 -1.26 -1.28 -1.27 -1.33 -1.18 -1.23 -1.15 -1.17 -1.11 -1.06 -1.30 -1.15 -1.40 -1.44 -2.59 -3.53 -3.91 -3.92 -3.90 -3.84 -3.81 -3.83 -3.87 -3.82 -3.81 -3.76

Table 4: Measured bubble point pressures for the system n -propane(1) + n -decane(2) at temperature T, pressure P, and liquid mole fraction x1 =0.726. Standard uncertainties u are u(T ) = 0.03 K and u(x1 ) = 8.36 x 10−4 . The values for u(P ) are given in the table. T/K 270.00 275.00 280.00 285.00 290.00 295.00 295.00 300.00 300.00 305.00 305.00 305.00 310.00 315.00 315.00 315.00 320.00 320.00 325.00 325.00 325.00 330.00 335.00 340.00 345.00 350.00 355.00 360.00 365.00 370.00

P/kPa 311.98 361.33 417.09 478.50 546.77 621.12 622.86 703.77 703.80 789.97 791.16 792.09 883.80 986.17 985.25 986.82 1092.67 1092.77 1182.63 1182.62 1186.52 1307.04 1431.75 1571.75 1721.82 1865.24 2027.28 2192.82 2354.31 2533.71

x1 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726 0.726

(u(P )/P)×100 1.93 1.68 1.47 1.29 1.14 1.02 1.02 0.91 0.91 0.82 0.82 0.82 0.75 0.78 0.78 0.78 0.71 0.71 0.67 0.67 0.67 0.62 0.58 0.55 0.51 0.48 0.46 0.44 0.43 0.41

u(P )/kPa 6.02 6.08 6.13 6.19 6.25 6.32 6.32 6.39 6.39 6.51 6.51 6.51 6.64 7.67 7.67 7.67 7.80 7.80 7.93 7.93 7.93 8.17 8.34 8.57 8.82 9.03 9.41 9.66 10.04 10.41

9

(1-PEOS /Pexp )×100 -1.70 -1.86 -1.75 -1.70 -1.50 -1.40 -1.11 -1.06 -1.06 -1.22 -1.06 -0.95 -1.27 -1.17 -1.27 -1.10 -1.38 -1.38 -3.63 -3.63 -3.29 -3.35 -3.64 -3.35 -2.95 -3.39 -3.18 -3.16 -3.62 -3.55

Table 5: Measured bubble point pressures for the system n -propane(1) + n -decane(2) at temperature T, pressure P, and liquid mole fraction x1 =0.512. Standard uncertainties u are u(T ) = 0.03 K and u(x1 ) = 7.77 x 10−5 . The values for u(P ) are given in the table. T/K 270.00 275.00 280.00 285.00 290.00 295.00 300.00 300.00 305.00 305.00 310.00 310.00 315.00 315.00 320.00 325.00 330.00 335.00 340.00 340.00 345.00

P/kPa 219.56 253.73 290.84 332.58 378.20 427.64 481.47 481.91 538.64 539.51 601.44 601.28 668.53 665.85 735.93 810.90 890.63 974.55 1057.58 1056.73 1143.83

x1 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512 0.512

u(P )/kPa 3.77 3.89 4.02 4.17 4.35 4.57 4.80 4.69 5.00 5.00 5.33 5.33 6.92 6.92 7.26 7.65 8.08 8.49 9.14 9.14 9.65

(u(P )/P)×100 1.72 1.53 1.38 1.25 1.15 1.07 1.00 0.97 0.93 0.93 0.89 0.89 1.04 1.04 0.99 0.94 0.91 0.87 0.86 0.86 0.84

10

(1-PEOS /Pexp )×100 -5.69 -5.49 -5.53 -5.22 -4.94 -4.72 -4.45 -4.36 -4.37 -4.20 -4.04 -4.07 -3.75 -4.17 -4.06 -3.88 -3.66 -3.46 -3.79 -3.88 -4.14

Table 6: Measured bubble point pressures for the system n -propane(1) + n -decane(2) at temperature T, pressure P, and liquid mole fraction x1 =0.305. Standard uncertainties u are u(T ) = 0.03 K and u(x1 ) = 8.69 x 10−5 . The values of u(P ) are given in the table. T/K 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 310.00 315.00 315.00 320.00 325.00 330.00 335.00 335.00 340.00 345.00 350.00 355.00 360.00 365.00 370.00

P/kPa 128.26 146.46 167.81 191.20 216.65 244.25 274.06 306.04 340.33 375.39 376.87 414.09 454.83 497.85 538.68 543.26 585.45 634.21 684.98 737.84 792.61 849.17 907.62

x1 u(P )/kPa 0.305 7.12 0.305 7.13 0.305 7.15 0.305 7.17 0.305 7.19 0.305 7.21 0.305 7.23 0.305 7.25 0.305 7.27 0.305 8.36 0.305 8.36 0.305 8.38 0.305 7.33 0.305 7.36 0.305 7.38 0.305 7.38 0.305 7.40 0.305 8.48 0.305 8.50 0.305 8.53 0.305 8.57 0.305 8.62 0.305 8.73

(u(P )/P)×100 5.55 4.87 4.26 3.75 3.32 2.95 2.64 2.37 2.14 2.23 2.22 2.02 1.61 1.48 1.37 1.36 1.26 1.34 1.24 1.16 1.08 1.01 0.96

11

(1-PEOS /Pexp )×100 -12.41 -12.76 -12.08 -11.41 -10.79 -10.19 -9.60 -9.05 -8.50 -8.41 -7.98 -7.90 -7.46 -7.03 -7.48 -6.58 -7.13 -6.80 -6.49 -6.17 -5.88 -5.60 -5.29

Table 7: Measured bubble point pressures for the system n -propane(1) + n -decane(2) at temperature T, pressure P, and liquid mole fraction x1 =0.148. Standard uncertainties u are u(T ) = 0.03 K and u(x1 ) = 3.22 x 10−5 . The values of u(P ) are given in the table. T/K 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 305.00 310.00 310.00 315.00 320.00 325.00 325.00 330.00 330.00 335.00 335.00 340.00 340.00 345.00 350.00 355.00 360.00 365.00 370.00

P/kPa 62.80 70.65 80.52 91.70 103.63 116.52 130.49 144.31 145.39 159.14 161.30 175.99 193.56 212.55 212.41 232.25 231.47 252.61 253.43 275.22 274.77 298.16 320.88 346.09 371.70 398.97 426.05

x1 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148 0.148

u(P )/kPa, k =2 (u(P )/P)×100 3.02 4.80 3.05 4.32 3.09 3.84 3.13 3.41 3.16 3.05 3.20 2.75 3.24 2.48 3.28 2.27 3.28 2.25 3.31 2.08 3.31 2.05 5.38 3.06 5.40 2.79 5.42 2.55 5.42 2.55 5.45 2.35 5.45 2.35 5.47 2.17 5.47 2.16 5.50 2.00 5.50 2.00 5.52 1.85 5.55 1.73 5.57 1.61 5.60 1.51 5.63 1.41 5.65 1.33

12

(1-PEOS /Pexp )×100 -17.62 -18.95 -18.09 -16.73 -15.69 -14.72 -13.71 -13.65 -12.81 -13.47 -11.96 -12.55 -11.85 -10.96 -11.03 -10.26 -10.63 -9.75 -9.39 -8.73 -8.91 -8.05 -7.80 -7.06 -6.53 -5.83 -5.47

Figure 2: Experimental data (open circles) plotted with literature data

13

Mixture Parameters According to the most recent formulation used in all the state-of-the-art libraries, the reducing parameters for the mixture (Tr and vr = 1/ρr ) can be given in a common form by

Yr (¯ x) =

N ∑

x2i Yc,i

N −1 ∑

+

i=1

N ∑

i=1 j=i+1

2xi xj

xi + xj Yij 2 βY,ij xi + xj

(2)

with the parameters dened by

Yr Tr

Yc,i Tc,i

βY,ij βT,ij

vr

1 ρc,i

βv,ij

Yij βT,ij γT,ij (Tc,i Tc,j )0.5 ( )3 1 1 1 βv,ij γv,ij + 1/3 8 ρ1/3 ρc,j c,i

These mixture reducing models are simply weighting functions of the critical properties of the pure uids that form the mixture. There is an additional adjustable parameter in the excess function Fij that is applied to the binary-specic excess function, though here the excess terms are not employed because there is insucient experimental data to t the excess terms. One important point to note is that the γ parameters are symmetric (γY,ij = γY,ji ), while the β parameters are not symmetric (βY,ij = 1/βY,ji ), and thus the order of uids in the binary pair is important and must be handled carefully when implementing the binary interaction parameters in the user's code. For the ij pair, there are a total of four adjustable parameters - βT,ij , γT,ij , βv,ij , and

γv,ij . The parameters t here (βT,ij , γT,ij ) have the strongest impact on the prediction of bubble points and can generally be t with a relatively small dataset size. New interaction

n -propane + n -decane binary system studied here, as well as for the previously published n -butane binary systems (n -butane + n -octane, n -butane + n -nonane). 3 The tting of these new interaction parameters proceeds using an evolutionary parameters are given for the

optimization approach as described in Bell 17 . The database REFPROP 9.1 15 developed by the National Institute of Standards and 14

Technology is the current state-of-the-art in mixture binary parameters, as it includes interaction parameters for 697 mixtures, with approximately 200 of these obtained from the literature 1,2,8,1822 as well as mixture interaction parameters that were t using in-house code. Other libraries that implement a signicant number of binary interaction parameters for high-accuracy mixture models are the open-source library CoolProp 5.1 23 comprising 220 binary pairs and the TREND 2.0 package from the University of Bochum, Germany 24 comprising approximately 215 binary pairs. After the tting procedure was carried out, the binary interaction parameters from Table 8 were obtained. Table 8: New interaction parameters Mixture

n -propane + n -decane n -butane + n -octane n -butane + n -nonane

βT 0.977575 0.992865 0.989867

γT 1.15138 1.04538 1.06894

βv 1 1 1

γv 1 1 1

In this work, we have t the binary interaction parameters βY,ij and γT,ij while setting the other binary interaction parameters βv,ij and γv,ij to 1. The tting algorithm described in Bell 17 is used to carry out the optimization of the binary interaction parameters. The totality of the available bubble-point data is used to t the binary interaction parameters using an evolutionary optimization approach. For more information on the algorithm, the user is directed to the work of Bell 17 .

Impact of New Interaction Parameters The new interaction parameters were implemented to determine deviations from the equation of state (EOS). Deviations from predicted values using the mixture interaction parameters in Table 2 were as high as 20% for mixtures with a low n -propane composition (Figure 3, top). When the new mixture interaction parameters (Table 8) were implemented, this deviation drops to less than 10 % for the low

n -propane compositions, without a signicant shift in

deviation for most of the reported literature data (Figure 3, bottom). To better visualize 15

the n -propane + n -decane data and the projected phase envelope with the new interaction parameters, a 3-dimensional projection of the phase envelope is given (Figure 2). This 3D projection can be manipulated in the website given in Supporting Information. The interaction parameters applied to the literature measurements for octane systems (Figure 4). 3,25,26 For the

n -butane + n -

n -butane + n -octane systems, measurements by

Manseld and Outcalt had not been included previously and deviations were up to -20 % from the predicted values and only in the negative direction. With the new interaction parameters, these deviations are more uniformly centered around zero and are well distributed with other measurements reported in the literature. The previous literature measurements 25,26 show little change with the new parameters. Finally, for the binary system of n -butane + n -octane, there is only one data set in the literature. 3 The deviations from the predicted values were reported to deviate as much as 131 %. With the new interaction parameters, deviations less than 2 % and are centered around zero (Figure 5).

Conclusions In this work, bubble point pressures of mixtures of n -propane and n -decane were measured over the temperature range of 270 K to 370 K for a composition range (in n -propane mole fraction) from 0.269 to 0.852. These data, in conjunction with data from a previous publication on mixtures of n -butane + n -octane and n -butane + n -nonane, were used to determine binary interaction parameters. A new and entirely automatic evolutionary optimization tting procedure was employed for obtaining the binary interaction parameters. The newlyobtained binary interaction parameters for

n -propane

+

n -decane

systems represent the

experimental bubble-point pressures to within 8 % where previous deviations were on the order of 19 %. It is expected that the new binary interaction parameters obtained with the tting algorithm published in Bell 17 will better represent bubble-point data in linear alkane

16

systems, such as those studied here.

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(19) Lemmon, E. W.; Jacobsen, R. T. Equations of State for Mixtures of R-32, R-125, R-134a, R-143a, and R-152a.

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(21) Akasaka, R. A Thermodynamic Property Model for the R-134a/245fa Mixtures. 15th International Refrigeration and Air Conditioning Conference at Purdue, July 14-17, 2014. 2014. (22) Akasaka, R. Thermodynamic property models for the diuoromethane (R-32) + trans-1,3,3,3-tetrauoropropene (R-1234ze(E)) and diuoromethane + 2,3,3,3tetrauoropropene (R-1234yf) mixtures.

Fluid Phase Equilib. 2013, 358, 98104.

(23) Bell, I. H.; Wronski, J.; Quoilin, S.; Lemort, V. Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp.

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(24) Span, R.; Eckermann, T.; Herrig, S.; Hielscher, S.; Jäger, A.; Thol, M. TREND. Thermodynamic Reference and Engineering Data 2.0. 2015. (25) Fichtner, D. A. Phase Relations of Binary Hydrocarbon Series n-Butane-n-Octane. M.Sc. thesis, The Ohio State University, 1962. (26) W.B. Kay, D. F., J.Genco Vapor-Liquid Equilibrium Relationships of Binary Systems Propane-n-Octane and n-Butane-n-Octane.

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Acknowledgement The purity analysis of the pure uids was provided by Dr. Tara Lovestead and Dr. Jason Widegren of NIST. Contribution of the U.S. Government. Not subject to copyright. 19

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n -propane + n -decane phase envelope usable in all

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3D rendering of n-propane + n-decane phase envelope

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Figure 3: Experimental deviation from GERG vs. n -propane composition with the mixture interaction parameters from REFPROP (top) and this work (bottom) for the n -propane and n -decane mixture. 57

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Figure 4: Experimental deviation from GERG vs.n -butane composition with the mixture interaction parameters from REFPROP (top) and this work (bottom) for n -butane + n octane mixtures. 3,25,26

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Figure 5: Experimental deviation from GERG vs. n -butane composition with the mixture interaction parameters from REFPROP (top) and this work (bottom) for n -butane + n nonane mixture. 3

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