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Chapter 10

Thermophysical Properties of Natural Gas Mixtures Derived from Acoustic Cavity Measurements

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S. O. Colgate and A. Sivaraman Department of Chemistry, University of Florida, Gainesville, FL 32611-2046

Acoustic resonance measurements on a simulated natural gas mixture (13 components) confined to a cavity have been used to obtain sonic speeds, ideal gas heat capacities and second acoustic and density virial coefficients for the mixture between 298 Κ and 450 K. The results are also compared with two model predictions ( A G A 8 and NIST D D M I X ) . Comparison of experimental sonic speeds in normal-butane with earlier measurements (4) show good agreement. Sonic speed measure­ ments on n-butane have been extended to elevated temperatures.

Accurate determination of the thermodynamic properties of a multicomponent gas mixture is generally not possible using only information about the properties of the pure components. Data on some mixtures are inevitably required. The number and variety of mixtures of interest precludes detailed measurements on each of them and speaks to the need for predictive models. The art of property prediction for gas mixtures has advanced as the speed and power of numerical techniques and the availability of property measurements on select mixtures has grown. Although most models consider only pair-wise interactions, data on multicomponent mixtures are useful for testing the reliability of model predictions. Because of the importance of knowledge of gas mixture behavior to the natural gas and petroleum industries, experimental measurements on specific natural gases or simulated natural gases are particularly useful. In this work, an automated spherical acoustic resonator assembly developed for acquiring data on the thermodynamic sonic speed in gases was used to study η-butane and a thirteen component simulated natural gas.

Experimental The sample gaseous mixture was prepared by Scott Specialty Gases Co., Plumsteadville, P A (U.S.A.) from thirteen 99.99 mol per cent pure components 0097-6156/93/0514-0121$06.00/0 © 1993 American Chemical Society

In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

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blended together in specific proportions. The mixture was composed of nonhydrocarbons, light hydrocarbons and heavy hydrocarbons. Its composition is given in Table I. During the operations of transferring the gas mixture to the apparatus, the gas storage tank, connecting lines, valves and other accessories were heated, and temperature was controlled to maintain the pressure above 14 M P a which assures the homogeneity of the mixture as a single phase.

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Table I. Composition of the Simulated Natural Gas Mixture Component

Mole % (±0.001)

Nitrogen Carbon Dioxide Methane Ethane Propane N-Butane Iso-Butane N-Pentane Iso-Pentane N-Hexane N-Heptane N-Octane N-Nonane

1.810 1.410 83.479 6.990 3.780 1.140 0.479 0.304 0.306 0.229 0.051 0.017 0.005

The heart of the experimental apparatus is a spherical acoustic resonator of diameter 0.305 m (12") equipped with high temperature PZT-bimorph transducers. The design and construction of the system and the basic experimental procedures have been described elsewhere (i). The temperature and pressure were measured using a four wire platinum resistance thermometer and a digital absolute pressure gauge, respectively. These were calibrated against NIST Standards and are accurate to ±0.001 m K and ± 1 0 Pa, respectively. The system under study was continuously stirred and blended by action of the in-line circulation pump operating at 3 L min' . At this rate the pertubations in resonance frequency generated by the pumping action were well below 0.01 Hz. After reaching a level of stability for which the resonance being tracked by the data acquisition system remained centered within a 0.01 H z wide window, a minimum of forty measurements were made. The median of these was independent of pumping action for the rates used in this work. 1

A programmable signal synthesizer (HP3325A) and a lock-in amplifier (SR510) were programmed to scan, detect, isolate and track the first radial mode resonance under control of a Compaq A T computer. The temperature of the resonator was controlled to ±0.005 Κ at selected temperatures in the range 298 Κ to 450 K . The resonator was first maintained at a temperature of 300 Κ and evacuated thoroughly. The apparatus was then charged with nbutane to a pressure 59.71 kPa, and the first radial mode resonance frequency was located and locked onto by the computer. The first radial mode was In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

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10. COLGATE & SIVARAMAN

Thermophysical Properties ofNatural Gas

123

selected because of its sharpness and relatively low frequency. When using the spherical cavity resonator as an absolute sonic meter it is common to measure several radial modes, compute a value of the sonic speed for each one and determine an average. When using the apparatus as a relative sonic meter the sonic speed is inferred from the resonance response of system gas to that of a reference gas (argon). Experience has shown that the results are insensitive to which radial mode is used for comparison so long as the resonance frequency is well below the level where relaxation effects are important. Resonance frequency was measured at 14 kPa intervals up to 104.39 kPa. The system was then evacuated and the experiment repeated at a higher temperature. In this manner isothermal runs were performed on η-butane at 300.00 K , 348.15 K , 373.15 K, 423.15 Κ and 448.15 K. The experimental results are listed in Table II. Following collection of the η-butane data, similar experiments were performed on the gas mixture of Table I. First radial mode resonance frequencies were measured against system pressure over the range 101.36 kPa - 620.56 kPa for isotherms at 298.15 K, 323.15 K , 373.15 Κ and 423.15 K . The results are listed in Table III. Sonic Speed Calculation The sonic speed through a lossless fluid confined to a rigid spherical cavity can be deduced from the sphere radius r and the frequency f of an acoustic resonance associated with the normal mode of eigenvalue v n>4

n e

Ferris (i) has listed values of v for the first 84 resonance modes, and values for higher modes are easily calculated if needed. Although we have found for this apparatus the thermal and viscous boundary effects and losses due to precondensation (2-5) or adsorption and compliance of the resonator walls are small (4-5), they can be reasonably accounted for by operating the system in a relative rather than absolute mode. This was done by comparing the respective resonance frequency as measured above with that observed when the apparatus was filled with a reference gas of well known behavior. Argon is such a gas and was used as a standard in these measurements. The sonic speed in argon has been carefully measured in this laboratory and the results have been shown to be in close agreement with other reported values (2,5). Using this method, the sonic speed in the gas mixture was taken to be nt

V

f

2

= ' A , (W Ar)

where f and f^ are the measured resonance frequencies for the same vibration mode of the system gas and of pure argon; c is the sonic speed of argon under the conditions of pressure and temperature for which the frequency measurements are made. gas

A r

In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

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Table I I . Sonic speeds in normal butane T/K

p/kPa ( ± 0.01 kPa)

f/Hz ( ± 0.005 Hz)

c/(m/sec) ( ± 0.01 m/sec)

300.00

59.71 70.95 82.46 91.84 104.39

1001.35 998.67 995.84 993.74 990.61

213.51 212.94 212.33 211.89 211.22

348.15

51.92 61.99 71.50 82.67 92.39 101.77

1078.91 1077.23 1075.85 1073.82 1072.23 1070.85

230.02 229.67 229.37 228.94 228.60 228.31

373.15

51.51 61.64 71.85 82.12 91.70 101.77

1115.51 1114.11 1112.87 1111.23 1110.02 1108.70

238.15 237.85 237.58 237.23 236.98 236.69

423.15

51.71 61.99 70.81 82.74 91.91 102.05

1185.00 1184.06 1183.17 1182.09 1181.20 1180.27

252.61 252.41 252.22 251.99 251.80 251.60

448.15

51.02 61.99 71.50 82.74 92.26 102.12

1217.29 1216.29 1215.43 1214.46 1213.61 1212.98

259.49 259.28 259.10 258.89 258.71 258.57

In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

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Table I I I . Sonic speeds in a simulated natural gas mixture T/K

p/kPa (± 0.01 kPa)

f/Hz ( ± 0.005 Hz)

c/(m/sec) (±0.01 m/sec)

298.15

101.36 207.88 315.79 414.39 517.26 620.96

1853.08 1850.54 1847.70 1845.14 1842.33 1839.91

395.10 394.56 393.95 393.40 392.81 392.29

323.15

101.36 217.12 311.45 415.29 521.40 620.96

1919.95 1917.59 1915.70 1913.55 1911.42 1909.55

409.60 409.10 408.70 408.24 407.79 407.39

373.15

101.01 207.40 312.07 416.73 522.78 620.96

2043.68 2042.54 2041.39 2040.24 2039.19 2037.95

436.30 436.06 435.81 435.57 435.34 435.08

423.15

101.31 211.88 310.34 413.91 518.16 620.62

2156.06 2155.59 2155.16 2154.67 2154.13 2153.60

459.61 459.51 459.42 459.31 459.20 459.09

Results and Discussion n-Butane. The principal purpose of this work was to generate experimental data on a well defined gas mixture with the characteristics of natural gas to help support the evaluation and development of predictive models. Although the reliability of the present spherical acoustic resonator apparatus for sonic speed measurements had been demonstrated in earlier publications (2-4), the recent report of sonic speed measurements on n-butane in another spherical resonator by Ewing and co-workers (5) provided the opportunity for a comparison of the performance of two similar units. The present measurements on n-butane were made with this in mind, and care was taken to ensure that the low temperature states of this study overlapped the

In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

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SUPERCRITICAL FLUID ENGINEERING SCIENCE

higher temperature states of Ewing, et al. The present work also extended the temperature range of sonic speed measurements in η-butane to 450 K . Figure 1 shows the variation in sonic speed with pressure for the five isotherms of η-butane. The results of Ewing, et al. at 300 Κ are shown in the figure as solid squares. The general agreement is clearly indicated. The average deviation of the Ewing values from the present ones is 0.01%. The actual deviations are shown in Figure 2.

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Simulated Natural Gas Mixture. The acoustic resonance measurements for the simulated natural gas mixture have been analyzed using a pressure series expansion: c

2

= Ao [1

+

( β / R T ) ρ + - ],

(3)

where c is the sonic speed, A

= Y°RT/M,

0

(4)

in which γ ° = C ° / C ° , R = gas constant and M = mole fraction mean of the molar mass. 0 is the second acoustic virial coefficient. The variations in c with system pressure for the four isotherms of the gas mixture are shown graphically in Figure 3. The prediction of two popular correlations, A G A 8 and D D M I X , are shown for comparison. Both models predict sonic speeds somewhat higher than the present measurements, and the disparity increases with increasing temperature. Over the range of pressures studied here and at 298.15 Κ the A G A 8 and D D M I X models give values about 0.09% and 0.18% higher than the measured sonic speeds, respectively. Deviations of the measured sonic speeds from the model values for this case are shown in Figure 4. The deviations increase to about 0.5% at the highest temperature of this study. The plots of c versus ρ in Figure 2 are quite linear suggesting that for these data Equation (3) may reasonably be truncated after the second term. Linear fits were typically good (r > 0.999). Higher order approximations did not improve the fits, and for this limited pressure range there was no need to keep terms in the expansion beyond the first two. Linear regressions of the results thus yield experimental values of the expansion coefficients in Equation (3). Values of AQ and 0 are listed in Table IV. The ratio of reference state heat capacities γ ° can be calculated using Equation 4, and the ideal gas heat capacity C ° may be calculated from γ ° as p m

v m

a

2

2

2

a

p

< V

m

=R[Y°/(Y°-1)]

The resulting values of γ ° and C ° p

m

(5)

are also listed in Table IV.

Results for C ° of the gas mixture are shown graphically in Figure 5. The reference state heat capacities ( C ° ) were fitted to a polynomial function and the resultant parameters along with the standard deviation (s) of the experimental points from the analytical function are: p m

p m

In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

10.

COLGATE & SIVARAMAN

Thermophysical Properties of Natural Gas

260 448.15 Κ

255

423.15 Κ

250 —Present π Ewing et al(1988)

245

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f

240

373.15 Κ

Ê

2 3 5

ϋ

230

348.15 Κ

225 220 215 210

3 0 0

50

60

70

80

90

Κ

100

110

p/kPa Figure 1. Sonic speeds in n-butane at elevated temperatures and compared with Ewing, et al. at 300 Κ.

0.05 h

υ ι

-0.05

-0.1

Figure 2. Deviation plot of present sonic data with that of Ewing, et al. at 300 Κ for butane.

In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

127

128

SUPERCRITICAL FLUID ENGINEERING SCIENCE

220000 423.15 Κ 0

210000 200000 ο φ

Ε eg

— P R E S E N T Ο A G A 8 ο D D M I X

-

190000 i\

ί

«I

til

373.15 Κ

180000

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Ο

170000 iï 160000

-φ

323.15 Κ

φ

'

150000 I 100

i 1 1

298.15 Κ

> — -

I

200

© — ©

φ

ιI ι

I

300

—$ , , , ι , ,

400

500

φ .

.

ι

.

600

.

.

.

700

ρ / kPa Figure 3. Square of the experimental sonic speed vs pressure for the simulated natural gas mixture at elevated temperatures and compared with the predictions of the A G A 8 and D D M I X models at 298.15 K .

B

(Cexp-CAGA8)

φ

(C exp - C DDMIX)

Figure 4. Deviation plot of present sonic data with that of the models A G A 8 and D D M I X at 298.15 Κ for the natural gas mixture.

In Supercritical Fluid Engineering Science; Kiran, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

10.

COLGATE & SIVARAMAN

Thermophysical Properties ofNatural Gas

Table IV. Values of A,,, ^, Y » a n d

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T/K

^/(m/sec)

2

129

C ' for the simulated natural gas mixture DM

j8 (cc/mol)

Y°

a

C

p m

° ( k J / k g m mol Κ )

298.15

156552.9

-68.2

1.2596

40.35

323.15

168125.0

-55.9

1.2480

41.84

373.15

190566.7

-33.1

1.2251

45.26

423.15

211346.8

-15.5

1.1981

50.28

1

4

Cp^ = 50.06589 - 1.10750 χ ΙΟ" (Τ/Κ) + 2.62806 χ ΙΟ" (Τ/Κ) (298