1

Measurements of (p, ρ, T) properties for propane in the temperature

range from 280 K to 440 K at pressures up to 200 MPa

H. Miyamoto1,3 and M. Uematsu2

1 JSPS-PD, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi,

Kohoku-ku, Yokohama 223-8522, Japan. 2 Center for Multiscale Mechanics and Mechanical Systems, Keio University, 3-14-1,

Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan. 3 To whom correspondence should be addressed.

2

ABSTRACT

Measurements of (P, ρ, T) properties for propane compressed liquid phase have

been obtained by means of a metal-bellows variable volumometer in the temperature

range from 340 K to 400 K at pressures up to 200 MPa. The volume-fraction purity of

propane used was 0.9999. The expanded uncertainties (k=2) of temperature, pressure,

and density measurements have been estimated to be less than 3 mK, 1.5 kPa (p≦7

MPa), 0.06 % (7 MPa＜p≦50 MPa), 0.1 % (50 MPa＜p≦150 MPa), and 0.2 % (p＞

150 MPa) , and 0.11 %, respectively. In region more than 100 MPa at 280 K and 440 K,

the uncertainty in density measurements rise up to 0.15 % and 0.23 %, respectively.

Four (p, ρ, T) measurements at the same temperatures and pressures as literature values

have been conducted for comparison. In addition, vapour pressures were measured at

temperatures from 280 K to 369 K. Moreover, the comparisons of the available

equations of state with the present measurements are reported.

KEY WORDS: measurement, propane; PρT property; vapour pressure.

3

1. INTRODUCTION

In previous publication [1,2] we reported measurements of the vapour pressure and

(p, ρ, T) for isobutane by a metal-bellows variable volumometer in uncivilized ranges of

temperatures from 280 K to 440 K at pressures up to 200 MPa. In this paper, the results

of (p, ρ, T) measurements for propane by the same apparatus are presented in the

compressed liquid phase for temperatures from 340 K to 400 K at pressures up to 200

MPa. Measurements of other ranges in temperatures from 280 K to 440 K are in

progress. In addition, vapour pressure measurements at T = (280 to 369) K are also

reported.

As for propane, several sets of (p, ρ, T) data were reported in the literature as

summarized in Table I. Thomas and Harrison [6] measured total 736 points of (p, ρ, T)

data in the temperature range from 258 K to 623 K at pressures up to 40 MPa by means

of mercury piezometer. Prior to 1984, most of measurements have been executed by

using volumometer, for directly density determination, except the precise measurement

by Haynes [7]. On the other hand, comparatively new informations for (P, ρ, T)

property measurements were reported from 2002 to 2005 as summarized in Table I.

These sets of accurate measurements from three literatures were obtained by means of

buoyancy methods (single-sinker densimeter below 30 MPa [10] and two-sinker

densimeter below 12 MPa [11]) and vibrating tube densimeter below 7 MPa [12], for

indirectly density determination.

2. EXPERIMENTAL

The measurements were carried out using the same apparatus employed in the

previous work [1,2]. The experimental procedures are described in detail elsewhere

[13].

The schematic diagram of the present experimental apparatus is shown in Fig. 1. A

sample of known mass was loaded into a bellows container in a pressure vessel.

4

Nitrogen gas from a pressure-measuring system was supplied to the outside of the

bellows container to compress, or expand the bellows. The pressure of the nitrogen gas

was measured with three different pressure gauges depending on the pressure ranges: an

air-piston pressure gauge (Ruska：model 2465) for p≦7 MPa, and two oil-operated

dead-weight pressure gauges (Futaba：model T and model TL2) for 7 MPa＜p＜30 MPa

and p≧30 MPa, respectively. The nitrogen gas was pressurized up to 200 MPa with a

pressure intensifier using the hand pump and controlled by a screw pump. The pressure

of the nitrogen gas was transmitted to the oil-operated dead-weight pressure gauges

with the help of a nitrogen-to-mercury-to-oil separator. The pressure of the sample was

obtained by subtracting the difference between the internal and external pressures of the

bellows from the pressure values of the nitrogen gas outside the bellows.

The pressure vessel was immersed in a thermostatted oil bath filled with 110 ℓ of

silicone oil. The temperature was measured with a 25 Ω platinum resistance

thermometer (Tinsley：5187SASS), which was inserted into a well drilled in the

pressure vessel, by a thermometer bridge (Tinsley：type 5840DS). The density of the

sample could be changed by increasing or decreasing the pressure of the nitrogen gas

along each isotherm. The volume change of the bellows was detected by the bellows

displacement with a linear variable differential transformer with a resolution of 0.5 µm.

After the sample had been confirmed to be in thermodynamic equilibrium by

monitoring the variation of temperature and the piston of the bellows, we finally

obtained (P, ρ, T) values of the sample in the bellows.

3. RESULTS OF CALIBRATION AND ERROR ANALYSIS

In the present study, we choice the coverage factor k = 2 and therefore the

confidence level in the present measurements was estimated to be about 95 %. We are

considering that no more elements of uncertainty have to be added throughout the

following estimation of the expanded uncertainties at present.

5

The platinum resistance thermometer was calibrated with the precision of ±1 mK

on ITS-90 at the National Physical Laboratory, Teddington, UK in 2003. The

uncertainty of the temperature measurements due to the thermometer bridge used was

estimated to be ±1 mK. The resistance of the thermometer at the triple-point

temperature of water was measured periodically. The temperature of the silicone oil

filled in the thermostatted bath was controlled within a fluctuation of ±1 mK during the

measurements of a given isotherm. And total expanded uncertainty (k = 2) in

temperature measurements is 3 mK.

The pressure of the nitrogen gas was measured with three different pressure gauges

depending on the pressure ranges: an air-piston pressure gauge (Ruska：model 2465)

with the precision of 0.01 % for p≦7 MPa, and two oil-operated dead-weight pressure

gauges (Futaba：model T and model TL2) for 7 MPa＜p＜30 MPa and p≧30 MPa,

respectively. The precision of two oil-operated pressure gauges used were 0.03 % for

p≦50 MPa, 0.05 % for 50 MPa＜p≦150 MPa, and 0.10 % for p＞150 MPa. The

pressure difference between internal and external pressure of the bellows was calibrated

as a function of the bellows displacement, temperature, and pressure with the standard

deviation of 0.3 kPa. The effect of hysteresis of the bellows due to compression and

expansion was confirmed to be negligible. The expanded uncertainty (k=2) in pressure

measurements are finally estimated to be 1.5 kPa (p≦7 MPa), 0.06 % (7 MPa＜p≦50

MPa), 0.1 % (50 MPa＜p≦150 MPa), and 0.2 % (p＞150 MPa).

Inner volume of the bellows container can change from 25 cm3 to 11 cm3, whose

variation with the bellows displacement has been calibrated with known density of

water in the temperature range from 280 K to 440 K at pressures up to 200 MPa. The

water employed was de-ionized, twice distilled, and degassed more than four times by

freeze-thaw cycling with liquid nitrogen. The density values of water used were those

calculated by IAPWS-95 formulation [14]. The result of calibration was correlated as a

function of the bellows displacement, temperature, and pressure with the standard

6

deviation of 0.04 %. The mass of the sample was measured with a precision chemical

balance (Chyo Balance：Jupiter) with an uncertainty of ±2 mg. The sample density ρ can

be then calculated directly from the mass of the sample loaded and the inner volume of

the bellows. The sample of propane was supplied by Takachiho Chemical Industrial Co.,

Ltd., Ibaragi, Japan, and its volume-fraction purity analyzed by the supplier was 0.9999.

Before the sample loading to the bellows, the sample was degassed using the same

procedure as that for water before its use in the experiment. The total uncertainty in

density was calculated by applying the Gaussian error-propagation formula, which

included the superimposed systematic uncertainty from the function of the inner volume

of bellows, the random error of the correction of the inner volume of bellows, the

uncertainty of IAPWS-95 formulation, and the uncertainty of the mass of the sample.

The expanded uncertainty (k=2) in density measurements are finally estimated to be

0.11 %. In region more than 100 MPa at 280 K and 440 K, the uncertainty in density

measurements rise up to 0.15 % and 0.23 %, respectively, due to the uncertainty in

density of IAPWS-95 formulation of water used for the calibration of the inner volume

of the bellows container.

4. RESULTS

We carried out total 63 points (p, ρ, T) measurements for temperatures between 340

K and 400 K at pressures up to 200 MPa. The experimental results are given in Table II.

In addition, vapour pressures ps were measured at T = (280 to 369) K, and the results are

given in Table III. Four density measurements were also carried out at the same

conditions of temperature and pressure as literature values by Reamer et al. [3], Dittmer

et al. [4], Thomas and Harrison [6], and Kratzke and Müller [8], for the purpose of

comparison. The results are given in Table IV.

5 DISCUSSION

7

Table IV shows a comparison of the (p, ρ, T) measurements with literature data

[3,4,6,8]. (p, ρ, T) data by Reamer et al. [3] and Kratzke and Müller [8] agree with the

present measurements within ±0.01 % and ±0.03 % in density, respectively. The

data by Dittmer et al. [4] and Thomas and Harrison [6] reasonably agreed with the

present ones by 0.14 % and 0.15 % in density, respectively.

Figure 2 shows relative density deviations of the present measurements from

Helmholtz-type equation of state proposed by Miyamoto and Watanabe [15]. The

behaviors of density values calculated from the pressure-explicit mBWR-type equation

of state developed by Younglove and Ely [16] and the Multi-parameter Helmholtz-type

equation of state developed by Span and Wagner [17] are also included for comparisons.

The functional form of the Miyamoto-Watanabe model is given below.

),(),(),( r0 δτφδτφδτφ +==RTf

(1)

[ ]∑=

−−++++=7

4ii

0i

03

02

01

0 )nexp(1lnalnaaaln),( τττδδτφ (2)

∑∑

∑∑

==

==

−+−+

−+=

19

17i

3dti

16

14i

2dti

13

9i

dti

8

1i

dti

r

)exp(a)exp(a

)exp(aa),(

iiii

iiii

δδτδδτ

δδτδτδτφ (3)

In this model, f denotes the Helmholtz free energy, and the ideal-gas state

contribution, ),(0 δτφ , is expressed by Eq. (2) and the residual real-fluid contribution,

),(r δτφ , by Eq. (3). Independent variables are the inverse reduced temperature, τ =

TC/T , and the reduced density, δ = ρ/ρC , while TC and ρC denote the critical

temperature and pressure, respectively. R is the gas constant for propane with R = Rm/M

where Rm is the universal gas constant and M is the molar mass. The values of the

8

coefficients, 0ia , ni, and ai , and the exponents, ti and di, were determined by means of

linear and nonlinear fitting procedures for adjusting to any thermodynamic property

data simultaneously.

The new literature data (Claus et al. [10], Glos et al. [11], and Kayukawa et al. [12])

reasonably agreed with the present measurements. Especially, the systematic

agreements between our data and the data by Claus et al. [10] clarify excellent

reliability of the procedure of their measurement and the single-sinker densimeter in

pressures up to 30 MPa. In higher pressure region above 103 MPa, the behaviors of

calculated density values from three models (by Younglove and Ely [16], Miyamoto

and Watanabe [15], and Span and Wagner [17]) and the present measurements

reasonably agreed as shown in Fig. 2, although it is an extrapolated region for three

models. It was partly caused by the existence of the precise measurements of Dittmer et

al. [4] in higher pressure region up to 103 MPa. The necessity of the improvements of

the models in higher temperature region at middle range of pressures are also confirmed

from Fig. 2.

We also calculated numerically the derivatives of density with respect to pressure at

constant temperature and those of density with respect to temperature at constant

pressure using the present results given in Table II. Using these derivatives, we

calculated isothermal compressibility ratios Tα and volume expansion coefficients β

by the following equations;

( ) ( ) ( )⎭⎬⎫

⎩⎨⎧

−−−

+−−−

−=

⎟⎟⎠

⎞⎜⎜⎝

⎛∆∆

≅⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

=

++

+

+1ii

i1-i

i1-ii1-i

1ii

1ii

1i1-ii

1

11

PPPP

PPPPPP

pp TTT

ρρρρρ

ρρ

ρρ

α

(4)

9

( ) ( ) ( )⎭⎬⎫

⎩⎨⎧

−−−

+−−−

−−=

⎟⎠⎞

⎜⎝⎛

∆∆

−≅⎟⎠⎞

⎜⎝⎛

∂∂

−=

++

+

+i1i

1-ii

1-ii1-ii

i1i

i1i

1-i1ii

1

11

TTTT

TTTTTT

TT pp

ρρρρρ

ρρ

ρρ

β

(5)

In both equations, the subscript i denotes the order of the data in each isotherm or

isobar listed in Table II. The differences of heat capacities, CP–CV, were also calculated

by Eq. (6). Those values are illustrated in Fig. 3 as a function of temperature at various

pressures.

TTp

VPTp

TTCC

αβ

ρρρ

ρ

22

2 =⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

⎟⎠⎞

⎜⎝⎛

∂∂

=− (6)

The behaviors of isobars calculated from Miyamoto-Watanabe model are also

included for comparison. The error bar of each datum shows the expanded uncertainties

(k=2). The slopes of isobars decrease by increasing pressure as shown in Fig. 3. The

equation of state can represent the present result almost within the expanded

uncertainties except in the region below 20 MPa. Although only two sets of literature

caloric property data, the isochoric heat capacity data by Goodwin [18] and the isobaric

heat capacity data by Yesavage et al. [19,20], are available for liquid propane at

pressures below 30 MPa and 14 MPa respectively, almost enough reproducibility

regarding the caloric properties of the equation of state can be confirmed by the present

work. It could be also noted, however, that the representation of the model regarding the

changes of temperature and pressure dependencies of caloric properties in such middle

range of pressures should also be revised.

Moreover, based on the present vapour-pressure measurements given in Table III,

we revised the Wagner-type vapour-pressure correlation for propane which is given

below.

10

( ) ( ) ( )xxxxxPP . −+++= 1AAAAln 5.4

45.2

351

21CS (7)

In this correlation, x = 1 – T/TC, TC denotes the critical temperature, 369.818 K and

PC is the critical pressure, 4246.5 kPa measured by Higashi [21]. In Eq. (7), the

numerical constants were determined as A1 = −6.756136, A2 = 1.520012, A3=

−1.406769, and A4 = −2.057997. The relative pressure deviation of the present

experimental data from Eq. (7) are shown in Fig. 4. As the result, most of the present

measurements are well represented by Eq. (7) within ±1.1 kPa, which is less than the

experimental uncertainty, including data close to the critical temperature. The

vapour-pressure data by Reamer et al. [3], Helgeson and Sage [22], Teichmann [23],

Kratzke [24], and Thomas and Harrison [6] were also included in Fig. 4. Although the

reliable data by Thomas and Harrison [6] show systematic deflections with calculated

values from Eq. (7), the absolute pressure deviations are less than ±1.4 kPa.

REFERENCES

1. H. Miyamoto, J. Takemura, and M. Uematsu, J. Chem. Thermodyn. 36:919

(2004).

2. H. Miyamoto and M. Uematsu, to appear in J. Chem. Thermodyn.(2005).

3. H. H. Reamer, B. H. Sage, and W. N. Lacey, Ind. Eng. Chem. 41:482 (1949).

4. P. Dittmer, F. Schulz, and G. Strese, Chemie-Ing.-Techn. 34:437 (1962).

5. J. F. Ely and R. Kobayashi, J. Chem. Eng. Data 23:221 (1978).

6. R. H. P. Thomas and R. H. Harrison, J. Chem. Eng. Data 27:1 (1982).

7. W. M. Haynes, J. Chem. Thermodyn. 15:419 (1983).

8. H. Kratzke and S. Müller, J. Chem. Thermodyn. 16:1157 (1984).

9. G. C. Straty and A. M. F. Palavra, J. Res. Natl. Bur. Stand. 89:375 (1984).

10. P. Claus, G. Schilling, R. Kleinrahm, and W. Wagner, Internal Report,

11

Ruhr-Universität Bochum (2002, cited as Ref. 40 in [11]).

11. S. Glos, R. Kleinrahm, and W. Wagner, J. Chem. Thermodyn. 36:1037 (2004).

12. Y. Kayukawa, M. Hasumoto, Y. Kano, and K. Watanabe, J. Chem. Eng. Data

50:556 (2004).

13. Y. Kabata, S. Yamaguchi, M. Takada, and M. Uematsu, J. Chem.Thermodyn.

24:785 (1992).

14. W. Wagner and A. Pruβ, J. Phys. Chem. Ref. Data 31:387 (2002).

15. H. Miyamoto and K. Watanabe, Int. J. Thermophys. 21:1045 (2000).

16. B. A. Younglove and J. F. Ely, J. Phys. Chem. Ref. Data 16:577 (1987).

17. R. Span and W. Wagner, Int. J. Thermophys. 24:41 (2003).

18. R. D. Goodwin, J. Res. Natl. Bur. Stand. 83:440 (1978).

19. V. F. Yesavage, Ph. D. Dissertation (Univ. of Michigan, Ann Arbor, 1968).

20. V. F. Yesavage, D. L. Katz, and J. E. Powers, J. Chem. Eng. Data 14:197 (1969).

21. Y. Higashi, Proc. 15th Symp. Thermophys. Prop., NIST/ASME, Boulder, CO,

USA, 2003.

22. N. L. Helgeson and B. H. Sage, J. Chem. Eng. Data 12:47 (1967).

23. J. Teichmann, Ph. D. Dissertation (Ruhr University, Bochum, 1978).

24. H. Kratzke, J. Chem. Thermodyn. 12:305 (1980).

12

Table I. Experimental PρT Property Data for Propane

First author Data Method P / MPa ρ / (kg·m-3) T / K Reamer [3] 306 mercury

piezometer 0.1− 69 1−576 311−511

Dittmer [4] 336 isochoric method 1.0−103 320−590 273−413 Ely [5] 222 isochoric method 0.3− 43 508−652 166−324 Thomas [6] 736 mercury

piezometer 0.6− 40 35−549 258−623

Haynes [7] 196 magnetic suspension densimeter

0.6− 37 493−741 90−300

Kratzke [8] 60 isochoric method 2.2− 61 441−565 247−491 Straty [9] 144 Burnett expansion

(isochoric) 0.2− 35 2−347 363−598

Claus [10] 130 single-sinker densimeter

2.0− 30 24−506 340−520

Glos [11] 72 two-sinker densimeter

0.2− 12 3−727 95−340

Kayukawa [12] 192 vibrating tube densimeter

0.2− 7 12−579 240−380

This work 63 bellows variable volumometer

3.0−200 335−631 340−400

13

Table II. Experimental results for the density ρ for propane at temperature T (ITS-90)

and pressure p

T / K 340.000 360.000 380.000 400.000

p / MPa ρ / (kg･m-3)

200.00 631.34 622.28 612.75 604.47

180.00 622.47 613.60 603.76 594.86

160.00 613.42 603.94 593.57 584.27

140.00 603.23 593.24 582.40 572.43

120.00 592.00 581.13 569.69 559.13

100.00 579.21 567.52 555.08 543.68

90.00 571.96 559.54 546.83 534.99

80.00 564.13 551.28 537.77 525.29

70.00 555.40 541.74 527.68 514.40

60.00 545.76 531.24 516.27 501.88

50.000 534.58 519.13 502.92 487.17

40.000 521.92 504.75 486.90 469.52

30.000 506.41 486.97 466.65 446.42

20.000 486.49 463.18 438.11 412.17

10.000 457.22 423.91 383.94 334.82

5.000 433.15 380.52

3.000 418.08

14

Table III. Experimental results for the vapour pressure ps for propane at temperature T

(ITS-90)

T / K ps / MPa

280.000 0.5831

300.000 0.9990

320.000 1.5998

340.000 2.4322

360.000 3.5563

365.000 3.8941

367.000 4.0368

369.000 4.1844

15

Table IV. Comparison of the density ρ for propane with the literature values

T / K p / MPa ρ / (kg･m-3) U / %a ε / %b Ref.

Literature

373.124 36.207 485.82 485.07 n.a. -0.15 [6]

373.124 32.852 479.35 480.00 0.1 0.14 [4]

373.399 30.225 473.52 473.37 n.a. -0.03 [8]

377.567 68.95 527.84 527.81 0.2 -0.01 [3]

a Experimental uncertainties reported in the literature.

b Relative density difference ε = 100 δρ / ρ of the literature values from the present

ones.

16

FIGURE CAPTIONS

Fig. 1. Schematic diagram of the present apparatus. A: Pressure vessel and Bellows,

B: Platinum Resistance Thermometer, C: Thermometer Bridge, D: Digital

Indicator, E: Galvanometer, F: Linear Variable Differential Transformer, G:

Digital Multimeter, H: P.I.D. Controller, I: Thyristor Regulator, J: Stirrer, K:

Sub-Heater, L: Main-Heater, M: Cooler, O: Bourdon Gauge, P: N2-to-Hg-to-oil

Separator, Q: Hand Pump, R: Air-Piston Pressure Gauge, S: Pressure

Controller, T: Oil-Operated Dead-Weight Pressure Gauge (30 MPa to 200

MPa), U: Oil-Operated Dead-Weight Pressure Gauge (7 MPa to 30 MPa), V:

Valves, W: Vacuum Pump, X: Personal Computer.

Fig. 2. Relative density deviation of the present measurements for propane from

Miyamoto-Watanabe model [15]. , This work; ･････, Younglove-Ely

model [16]; ――, Span-Wagner model [17]; , Claus et al. [10]; , Glos et

al. [11]; ＊, Kayukawa et al. [12].

Fig. 3. Distribution of the CP-CV values for propane along isobars., 10 MPa; , 20

MPa; , 30 MPa; , 50 MPa; , 100 MPa; , 180 MPa; ――,

Miyamoto-Watanabe model [15].

Fig. 4. Relative deviations of the experimental vapour pressure values from the

present correlation (7) for propane plotted against T. , This Work; ＊,

Reamer et al. [3]; , Helgeson and Sage [22]; ＋, Teichmann [23]; ,

Kratzke [24]; , Thomas and Harrison [6].

17

V3V2

V4

A

B

E

F

C

V1D

G

W

J LI

K

H

MX

V22

V23

V24

V25 V26

V27

W

O

V18

X

V13P

V12

T

U

V10V11

N2V9

V8

V16

O

V7

V6

R

S

OV17

V5

V20 P

QV21

SV14

V15V28

Fig. 1 Miyamoto and Uematsu

18

-0.5

0.0

0.5

0 50 100 150 200

T = 380.000 K

-0.5

0.0

0.5

0 50 100 150 200

T = 400.000 K

100

( ρex

p –

ρca

l ) / ρ

cal

-0.5

0.0

0.5

0 50 100 150 200

T = 340.000 K

p / MPa

-0.5

0.0

0.5

0 50 100 150 200

T = 360.000 K

Fig. 2 Miyamoto and Uematsu

19

400

500

600

700

800

900

1000

1100

1200

350 360 370 380 390

T / K

CP

- CV

/ (J･

kg-1･ K

-1)

180 MPa

100 MPa

50 MPa

30 MPa

20 MPa

10 MPa

Fig. 3 Miyamoto and Uematsu

20

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

250 270 290 310 330 350 370

T / K

100

( PS -

PS,

cal )

/ P

S,ca

l

+1.0 kPa

-1.0 kPa

T c = 369.818 K

Fig. 4 Miyamoto and Uematsu