Analysis of using binary cryogenic mixtures containing nitrogen and alkanes or alkenes in cryocoolers

Cryogenics 36 (1996) 69-13 0 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved 001 l-2275/96/$15.00 ELSEVIER

Analysis of using binary cryogenic mixtures containing nitrogen and alkanes or alkenes in cryocoolers M. Xu, Y. He and Z. Chen School of Energy and Power Engineering, 710049, China Received

19 January

1995; revised

25 April

Xi’an Jiaotong

University,

Xi’an, Shaanxi

1995

This paper describes the working mechanism of binary cryogenic mixtures containing nitrogen and alkanes or alkenes. The Peng-Robinson equation of state is used to calculate the mixed free enthalpy of these mixtures and a method to calculate the mutual solubility is also suggested. Finally, the vapour-liquid, liquid-liquid and vapourliquid-liquid equilibria of these mixtures are analysed. Therefore, an effective method to predict the characteristics of new kinds of binary cryogenic substances is provided in this paper.

Keywords: binary cryogenic mixture; phase equilibria; cryogenics

Nomenclature l f AG AS K L P R T Tb AT, V X

Y

Fugacity Fugacity in mixture Mixed free enthalpy Isothermal integral (Joule-Thomson Binary interaction parameter Liquid phase Pressure Gas constant Temperature Normal boiling point Isenthalpic integral (Joule-Thomson Vapour phase Mole fraction in liquid phase Mole fraction in vapour phase

Greek letter Y effect)

Activity

coefficient

Superscript L

Liquid plastic property

Subscripts i

effect)

In the 195Os, with the development of military industry and advanced science and technology, it was necessary to develop a kind of cooling source with refrigerating temperature ~80 K and a capacity 0.5-1.0 W, to cool down sensors, such as infrared detectors, etc. Therefore, the miniature cryocooler has been produced and developed quickly. The Joule-Thomson (JT) cryocooler, shown in Figure 1, has been widely used in the field of advanced science and technology. For a long time, only pure gas had been used as the working fluid of a miniature J-T cryocooler. Early in the 1970s Alfeev’ found that if gas mixtures were used as the working fluids of miniature J-T crvocoolers, the efficiencv r of the cycle might be increased by lo-12 times. The essential prerequisite condition of using gas mix-

j 1 2

Component identity Component identity Alkane-rich or alkene-rich liquid phase Nitrogen-rich liquid phase

tures is that the evaporating temperature in the throttling cycle of a cryocooler must be kept almost constant and close to the liquid nitrogen range-about 80 K. One effective method is to use partially soluble mixtures. In order to analyse the working mechanism of using cryogenic mixtures, a further analysis of the phase equilibria of these mixtures is necessary. This paper describes an effective method to predict the characteristics of the working fluid of cryogenic mixtures.

Disadvantages

of using pure working

The basic requirements of a miniature be described as follows:

Cryogenics

1996 Volume

fluids

JT cryocooler

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can

69

Binary

cryogenic

inlet

mixtures

in cryocoolers:

h&h

pressure

M. Xu et al.

outlet 1

gas

5

i

I

the isenthalpic integral J-T effect, AT,. The greater the ATh, the less the cooling time.

low

pressure

gas

For pure fluids, the relationships AT, are

regenerator

throttling vavle

Figure 1

Schematic

diagram

of a Joule-Thomson

cryocooler

Refrigerating temperature. This is restricted by the operating requirements of the detector and is usually in the range 77-80 K. For an open-cycle cryocooler exhausting at atmospheric pressure, refrigerating temperature is directly related to the normal boiling point Tb of the working fluid. Evidently, nitrogen is the most suitable working fluid, evaporating around 77-80 K. Refrigerating capacity. The gas consumption in an open-cycle cryocooler is directly related to the maximum refrigerating capacity, while the refrigerating capacity of an ideal-cycle cI’yocooler, shown in Figure 2, is equal to the isothermal integral effect AHT. The greater the AHT, the larger the refrigerating capacity per mole, and the less the consumption of the high pressure gas. Cooling time. This is the time needed to reach the steady operating temperature and is directly related to

between

Tb, AHT and

AT,, = -AH,Ic,~

(1)

AHT = 11.72R,T$T

(2)

Equation ( 1) is given by Gustafsson’ and Equation (2) is derived from experimental data. The relationship between AHT and Tb shown in Figure 3 is calculated by the PerryRobinson (PR) equation of state and Equation (2). From Figure 3, we can see that the higher the Tb, the greater the AH,. We must use a low boiling point fluid, such as nitrogen, however, to attain a low operating temperature in an opencycle cryocooler, as described above, because the evaporator operates at the normal boiling point of the working fluid. This motivated us to search for mixtures which would be able to simultaneously attain a low refrigerating temperature, such that the refrigerating temperature remains almost constant in the range of liquid nitrogen, and in turn to attain a high refrigerating capacity.

Advantages

of using cryogenic

Phase equilibrium

mixtures

calculation

Usually, there are two methods to calculate the phase equilibria of mixtures: the activity coefficient method and the EOS (equation of state) method. Both can be used to calculate vapour-liquid equilibria (VLE) and liquid-liquid equilibria (LLE). The activity method has a higher accuracy but needs more experimental constants; it is often used in the chemical industry, but for mixtures as throttling working fluids the available data are very limited. In addition, the EOS method is convenient for cycle calculations. In this paper, the EOS method is used to calculate both VLE and LLE. 25 /

1

/I 20 -

10 3 5-

0

I Figure 2

70

50

I I

Temperature

00

Schematic diagram of the ideal Joule-Thomson

Cryogenics

150 Temperature

I

T*

100

1996 Volume

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cycle

200

250

3 0

09

Figure 3 Relationship between AH, and Tb. High inlet pressure = 30.0 MPa; low outlet pressure = 0.1 MPa; temperature = 300 K. 1, Equation (2); 2, PR equation of state

Binary Equation

300 1

of state

In the EOS method, an equation of state fitting both the vapour phase and liquid phase is needed. Although the Benedict-Webb-Rubin-Starling (BWRS) equation is highly accurate for cryogenic systems and is often the first choice in industry, the PR equation of state3 is much simpler, and the parameters needed for applying it to mixtures are readily available. In addition, it gives reasonably accurate descriptions of cryogenic systems, so it will be used here for convenience. Judgement

cryogenic

of mutual

mixtures

in cryocoolers:

M. Xu et al.

a

1

250 g

solubility

Based on thermodynamic theory, we can judge whether the liquid phase of a mixture can be separated into two liquid phases by using the following relationship: AG = RT&, In xi + RTxxi In -yj = RTX xi In (5-y,) = RTZ% In @-$)

0. 0

0. 2 0.4 0.6 Nitrogen mole fraction

0. 0

o. 4 o. 6 o. 2 Nitrogen mole fraction

(3)

Therefore, the mixed free enthalpy can be calculated when the fugacities of pure fluids and mixtures are given, and then the partial solubility can be predicted according to the theory of thermodynamic equilibrium. Calculated

results

and discussion

Figure

4 shows the vapour-liquid equilibria of various mixtures at different values of the binary interaction parameter, K,. In Figure 4a, Kg= 0, and in Figure 4b, the values of K, are given by Walas4. From Figure 4, it can be seen that the bubble point curves often have a horizontal section over a large composition range near liquid nitrogen temperature, except for the N2-CH4 system. This behaviour, which is due to liquid-liquid equilibrium, is the reason why the cooling temperature can be kept constant and close to liquid nitrogen temperature. In addition, the effect of KU on the bubble point is much larger than that on the dew point, because the influence of KG on vapour phase fugacity is negligible. In the following calculations, the values of KU are all adopted from Walas4. The relationship between mixed free enthalpy and the mole fraction of nitrogen in the binary systems of N2-CH4, N2-C2H4, N,-C,H6 and N,-C3Hs at 70 K and 0.1 MPa is shown in Figure 5. AG’ denotes the total mixed free enthalpy when one liquid phase is separated into two liquid phases. From Figure 5a, we can find that AG’ is always greater than AG over the whole composition range for the binary mixture of nitrogen and methane. This implies that nitrogen is completely mutually soluble with methane and the liquid phase in this mixture cannot be separated into two liquid phases. For the mixtures of N,-C,H,, N,-C,H, and NZ-C3H8. shown in Figures 5b-d, respectively, AG’ is always less than AG over the range between points A and B. Thus, the liquid phases in these mixtures are unstable, and will be separated into two coexisting phases, a nitrogen-poor phase and a nitrogen-rich one; in other words, the three kinds of binary mixture are partially soluble between A and B. Figure 6 shows the phase equilibrium diagrams for the mixtures of nitrogen and alkanes or alkenes including N,C2H4, N2-C2H6 and N2-C3H8 at 0.1 MPa by using the PR equation to calculate the liquid and vapour phase fugacities.

0. 8

I. o

Figure 4 Vapour-liquid phase equilibria at 0.1 MPa. (a) Kc= 0; (b) Kii adopted from Walas4. 1, N,-CH,; 2, N2-CZH4; 3, N,-C,H,; 4, N,-C,H,; 5, N,-n-C,H10

From Figure 6, liquid-liquid phase equilibria exist for all of the three binary mixtures, and when the region of liquidliquid equilibria intersects the region of vapour-liquid equilibria, the liquid-liquid-vapour triple point appears. But for the nitrogen-rich liquid, the triple point is not visible on the scale of Figure 6c. Triple points of binary mixtures containing nitrogen and alkanes or alkenes calculated by phase equilibrium theory are shown in Table 1. If the mixtures are heated in the region of triple phase, the nitrogen-rich phase evaporates first and the~temperature remains constant until the nitrogen-rich liqutd phase has boiled off. In other words, heat will be absorbed at constant temperature just as in the boiling of pure liquid nitrogen. With further heating, the temperature will gradually rise to the dew point as the nitrogenpoor liquid gradually evaporates. Thus, if nitrogen mixtures are employed in a cryocooler, cooled sufficiently in the heat exchanger, then expanded through the throttling valve, becoming liquid-liquid-vapour mixtures, the initial heat added into the evaporator will not raise the evaporating temperature.

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1996 Volume

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Binary

cryogenic

mixtures

in cryocoolers:

M. Xu et al.

0

-50 2 4 3 B

-100 -150

50

-200

0

-250 AG

B

-50

-300 -350 0.0

I

I

0.2

-100

h

0.4

0.6

0.8

1. 0

A p 1 0. 0

50

300

d

250 0

200

r\ 2 -50

B A

3 -? 3

150 100

%

50

-100

0 -50

-150

I

0

0. 2

0. 4

I

,

0. 6

0. 8

-100

L

0.0

: )

Nitrogen mole fraction Figure 5 Mixed free enthalpy N&.ZHG (d) Nz-CaHa

Comparison

with experimental

results

2

An effective method for finding new combinations cryogenic substances is suggested.

Cryogenics

A@

r

0.2

0.4

0.6

0.6

and mole fraction of nitrogen in nitrogen mixtures at 70 K and 0.1 MPa. (a) N,-CH,;

Conclusions

72

AC

1996 Volume

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1.0

Nitrogen mole fraction

Figure 7 shows the vapour-liquid phase equilibrium of a mixture of nitrogen and methane at a temperature of 100 K. The results are compared with the data given by Parrish and Hiza5. From Figure 7, it can be seen that the predicted results are consistent with the experimental data. Figure 8 shows the vapour-liquid phase equilibria of a mixture of nitrogen and propane at temperatures of 114.1, 118.3 and 122.2 K. Also, the results are compared with the data given by Poon and Lu6. It can be seen that there is little difference between the calculated results and the experimental data, and that this is satisfactory for cryogenic engineering.

1

I 0. 4

Nitrogen mole fraction

Nitrogen mole fraction

3

I 0. 2

2

of

3

(b) N,-C,H,;

(c)

The phase equilibria are calculated using the PR equation of state, and the working mechanism of the partially mutual binary mixtures, containing nitrogen and alkanes or alkenes, is revealed. The calculated results are compared with the experimental data, and the accuracy of the suggested method is satisfactory for cryogenic engineering.

Table 1 Liquid-liquid-vapour nitrogen mixtures at 0.1 MPa

equilibria triple points of binary

Component

2 mole fraction

Component 2

Temperature (K)

L, (%)

L, (%) v

>;d

77.40 77.57

87.77 80.73

5.14 1.86

3.158 3.378 x lo-’ 10”

CZ,H: r&h,

77.22 77.21

95.01 94.04

0.08 0.01

1.223 x lo-“’ 5.465 x IO-l4

Binary

cryogenic

mixtures

in cryocoolers:

M. Xu et al.

0. 8

a

&P.

A-

18( /-\ g

0.6

8

140 5 E K F

1oc

60 _ 0. 5

0. 0

1. 0

0. 0

0. 2 0. 4 0. 6 Nitrogen mole fraction

Nitrogen mole fraction

Figure7 Vapour-liquid nitrogen and methane imental results

b 180

0. 8

1.

phase equilibria of the mixture of at 100K and comparison with exper-

3. 0 A

2.5 - * 0

2

100

1.5 !z B G 1.0

60

0. 5

Exp.

0. 5 0. 0

Nitrogen mole fraction

0. 0

0. 04

0. 12

0. 06

0. 16

Nitrogen mole fraction Figure6 Vapour-liquid phase equilibrium of the mixture of nitrogen and propane at 114.1, 118.3 and 122.2 K, and comparison with experimental results. 1 (A), T= 114.1 K; 2 (x), T= 118.3 K; 3 (01, T= 122.2 K

Acknowledgement The financial support provided dation of the Education appreciated.

2

by the Doctorate’s FounCommission of China is greatly

References

0. 5 Nitrogen mole fraction

1. 0

Figure6 Phase equilibria in the mixtures of nitrogen and alkanes or alkenes at 0.1 MPa. (a) N,-C,H,; (b) N,-C2HB; (c) N2C,H,. 1, Vapour phase; 2, two-phase of vapour phase and liquid phase; 3, alkane-rich and alkene-rich liquid phase; 4, nitrogenrich liquid phase; 5, two-phase of alkane-rich and alkene-rich liquid phase

Alfeev, V.N. et al. UK Patent No. 1 336 892 (1973) Gustafsson, 0. On the Joule-Thomson effect for gas mixtures Physica Scripfa (1970) 2 7-15 Peng, D.Y. and Robinson, D.B. A new two-component equation of state Ind Eng Chem Fundament (1976) 15 59 Walas, S.M. Phase equilibrium in chemical engineering Butterworth, Boston (1985) Parrish, W.R. and Hiza, MJ. Liquid-vapor equilibria in the nitrogen-methane system between 95 and 120 K Adv Clyog Eng (1973) 19 300-307 Poon, D.P.L. and Lu, B.C.Y. Phase equilibrium for systems containing nitrogen, methane, and propane Adv Cryog Eng (1973) 19 292299

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