Thermophysical capability of ozone-safe working fluids for an organic rankine cycle system

Thermophysical capability of ozone-safe working fluids for an organic rankine cycle system

Heat Recovery Systems & ClIP Vol. 13, No. 5, pp. 409418, 1993 Printed in Great Britain 0890-4332/93 $6.00 + .00 © 1993 Pergamon Press Ltd THERMOPHYS...

542KB Sizes 0 Downloads 25 Views

Heat Recovery Systems & ClIP Vol. 13, No. 5, pp. 409418, 1993 Printed in Great Britain

0890-4332/93 $6.00 + .00 © 1993 Pergamon Press Ltd

THERMOPHYSICAL CAPABILITY OF OZONE-SAFE WORKING FLUIDS FOR AN ORGANIC RANKINE CYCLE SYSTEM M. J. LEE,* D. L. TIEN and C. T. SHAO Department of Chemical Engineering, National Taiwan Institute of Technology, Taipei 106, Taiwan (Received 1 November 1992) Abstract--The thermodynamic performance of a variety of working fluids circulated in an ideal organic Rankine cycle (ORC) engine has been evaluated with the aid of the Iwai-Margerum-Lu equation of state. Two merit number indices were also calculated to represent the inherent beat-transfer capability of the working media at evaporation and condensation, respectively. The result indicated that the thermophysical capability of compounds correlates with the fluid's normal boiling point, critical pressure and molecular weight. It also showed that HCFC-123 could be one of the most favourable ozone-safe working fluids for the ORC energy-recovery system.

NOMENCLATURE a~ b, u

Co C~ 1 k M

MW

Na ni

P Q~ap Q~d R

S SG Snmin

T V

VPQ

w, wp Z

parameters in the IML equation of state constant pressure heat capacity (J K - t mol- ~) constant pressure heat capacity at ideal-gas state (J K - ~mol- ~) performance index thermal conductivity (W m - ~K - ~) merit number of fluids molecular weight (g mol- l ) Avogadro's number (kmol- i ) exponent weight factor pressure (bar); (Pa) in equation (A-2b) heat absorbed per mol of circulated working fluids in waste-heat boiler (J mol- ~) heat rejected per mol of circulated working fluids in condenser (J mol- ~) gas constant (J mol-i K - t ); (j kmol-1 K - i ) in equation (A-2b) entropy (J mol- t K - ~) specific gravity minimum superheat of vapor at condenser (K) temperature (K) molar volume (m 3 mol- i ) volume of turbine-inlet vapor per MJ heat absorbed (m 3 MJ - l ) energy output for turbine (J mol -~) energy required for circulation pump (J mol -I ) compressibility factor

Greek symbols fl ~ ~/ ~/~ 0 p a co

gyration of radius (nm 10 - j ) polarity parameter cycle efficiency viscosity (Pa s) characteristic viscosity (Pa s) energy shape-factor density ( g c m - 3) surface tension (dyn c m - i ) acentric factor

Superscripts id (ri)

ideal the ith reference fluid

Subscripts b c cond

at normal-boiling condition critical property at condensing temperature

*To whom correspondence should be addressed. 409

410 eft evap 1 r sh tpp v vpq l 6 113

M.J. Lli eta/. efficiency at evaporating temperature liquid phase reduced property superheatof vapor at condenser inlet thermophysicalperformance vapor phase VPQ pointsof the ideal ORC path in T-S diagrams performanceof CFC-113 1. I N T R O D U C T I O N

The fully halogenated compounds (chlorofluorocarbons, CFC) should be replaced by ozone-safe substances in the near future to protect global environment. CFCs were used widely as refrigerants, cleaning agents, propellants, etc. Some of them, such as CFC-I 1, CFC-113 and CFC-114 were also employed as a working fluid for organic Rankine cycle (ORC) engines to recover low-temperature waste-heat or to convert solar energy into power [1]. The efforts in searching for new working media are progressing [2-6]. Currently several CFC alternatives including HCFC-22, HCFC-123, HCFC- 124, HFC(hydrofluorocarbons)- 134a, HCFC- 142b and HFC- 152a are becoming commercially available. It is of continuous interest to evaluate the thermophysical capability of the ozone-safe compounds for ORC systems. As given in the literature [1, 7, 8], a good working fluid for a power cycle system should have the following desirable characteristics: high cycle efficiency, small specific volume, low vapor superheat requirement, moderate vapor pressures in the heat-exchange units (generally above atmospheric pressure but not too much above 20 bar), low viscosity and surface tension, high thermal conductivity, suitable thermal stability limit, compatible with engine materials and lubricating oil, noncorrosive, nonflammable, nontoxic, low in cost, etc. Actually, no substance meets all these demands. Prediction of the thermophysical capability of substances, with the aid of proper thermodynamic models, could help us to select potential working media from numerous compounds. A set of empirical correlations for the thermodynamic properties of CFC-113 has been developed previously to implement the technoeconomic analysis on an ORC energy recovery system [9]. To evaluate the cycle performance for a diversity of working fluids, it would be convenient to replace those individual correlations by a reliable generalized thermodynamic model. Pradhan and Larson [10] conducted a power cycle analysis by using a corresponding-states model and Bertinat [11] simulated a high-temperature heat pump operation with the aid of the Lee-Kesler equation [12]. In the last decade, several promising cubic equations of state have been developed. Among these new equations of state, the Iwai-Margerum-Lu (IML) equation of state [13] has been reported to be generally useful for predicting the thermodynamic properties of various classes of fluids [14, 15]. This equation of state has been applied recently to study the CFC-alternatives for refrigeration systems [16, 17] and was also used in the present study. Transport properties of working media are needed to evaluate the fluid's heat-transfer capability. These properties include viscosity, thermal conductivity, surface tension and liquid heat capacity, which can be calculated, respectively, from our corresponding-state models [! 4, 18], the Latini et al. model [19], the Brock and Bird model [19], and the Rowlinson-Bondi model [19]. In this work, we attempt to evaluate the thermodynamic performance of various working fluids circulated in an ideal ORC system. The inherent heat-transfer capability of these fluids was also evaluated. The fluids being studied include halogenated substances, hydrocarbons, ethers, alcohols, esters, ketones, amines and inorganic compounds. According to the calculation results, some criteria for selecting thermodynamically proper working media were presented and several ozone-safe compounds for the ORC system were suggested. 2. O R G A N I C R A N K I N E CYCLE S I M U L A T I O N The thermodynamic performance of a given fluid for an ORC engine can be evaluated from cycle simulation. Since dry-type fluids (i.e. fluids with a positive slope of the saturated vapor curve in

Ozone-safe working fluids

411

the T-S diagram) have no condensation problems in the expansion process only when the turbine-inlet vapor is saturated, these type of fluids are preferable to the wet-type fluids. The path of an ideal ORC system in a T-S diagram is illustrated in Fig. 1 for a dry-type fluid. It is assumed that an isobaric process takes place through each of the heat-transfer units (6 ~ 2 and 3 ~ 5), an isentropic process through the expansion and pumping units (2 ~ 3 and 5 ~ 6), the outlet of the condenser to be a saturated liquid (point 5), and the outlet of the evaporator to be a saturated vapor (point 2). The ORC system without any regenerator is specified by two operation variables, for example, by evaporating temperature (Tevap)and condensing temperature (Teo,a). While these two temperature levels were given, state properties of the streams across each unit can be calculated by a standard procedure with an equation of state, for example, the IML equation of state [13] for this study. On the basis of one mol of circulating working fluid, the ideal cycle efficiency (Eid) is given by

(1)

Eid = ( W ~ - W~d)lQev~p,

where Qewp denotes the heat absorbed by one mole of working medium in the waste-heat boiler which was calculated from the molar enthalpy difference of the working fluid streams across the boiler, Witd is the turbine's ideal work output and W~ is the ideal energy requirement of the liquid circulation pump. Meanwhile, the volume of turbine-inlet vapor per unit energy recovery (VPQ) was calculated from the following equation: VPQ = V2/(Q~v~p x 10-6),

(2)

where V2 is the molar volume of the turbine-inlet vapor. Equation (2) is similar to the specific compressor displacement for refrigeration systems. A good working fluid should have a small VPQ. The minimum superheat of condenser-linet vapor (SHm~.) was calculated from SHmin ---- T¢o.d- T 3.

(3)

3. H E A T - T R A N S F E R C A P A B I L I T Y Lee and Chao [17] defines the evaporating and condensing merit numbers (Mevap and M¢o.d) as

Mevap=

pl("°'4"rll-0'31"0"6-tt "~ 10

-0.'25~,0.SS_r t)v-0"70"0"275ou,

(4) (5)

M¢o,d = ql°'SkiSG~/3,

where Cp is heat capacity, q is viscosity, k is thermal conductivity, a is surface tension, P is vapor pressure, p is density and S G is specific gravity. Because those merit numbers are, respectively, proportional to the heat-transfer coefficient of nucleate boiling and that of condensation at R e < 2100, they could represent the inherent heat-transfer capability of a working fluid. Furthermore, the degree of freedom of a pure saturated fluid is unity so that the merit numbers can be

/ / 5

'-/1 T~o~

/4

/

/

S

Fig. 1. Ideal ORC path in the T-S diagram (Tcond

=

308 K, Tevap= 430 K).

M . J . LEE et al.

412

calculated after a state variable of the fluid was specified. For example, the evaporating temperature (Tevap) was given to calculate Mev,p. As mentioned earlier, the thermal conductivity, surface tension, and liquid heat capacity of saturated liquids can be estimated from the Latini et al. model [19], the Brock and Bird model [19], and the Rowlinson-Bondi model [19], respectively. Liquid viscosity was calculated from the two-reference-fluid corresponding-states model of Lee and Chao [14] for the halogenated compounds and the three-reference-fluid corresponding states model of Lee and Wei [18] for the rest of the fluids. Moreover, the IML equation of state [13] was applied to predict the fluid's vapor pressure, density and specific gravity. The expressions of those models are summarized in the Appendix. 4. T H E R M O P H Y S I C A L P E R F O R M A N C E INDICES Similar to the work of Lee and Chao [17], we defined five individual performance indices to represent the fluid's thermophysical capability. These indices are defined to be relative to the corresponding values of CFC-113 at the same operating temperature levels. I,~ = Cia/Eila13 /~pq = (VPQ),,3/(VPQ) /~h = I SHmi. ,,3

I/Isnmi. I

Ievap = Mevap/Mevap. t,3 Ico.d = Mcond/Mcond. 1,3.

(6) (7) (8)

(9) (10)

The variable with a subscript "11Y' denotes the performance value for CFC- 113. According to the above definitions, a fluid with the larger index value has the better performance. However, the value of lsh could be exaggeratedly large for a few fluids with a very small ISHm~, [ • Thus, the upper limit for Ish was set to be "two" according to the normal range of other indices. Another index, Itpp, was defined empirically as the product of the individual performance indices with exponent weighting factors (ni) to represent the overall thermophysical capability of a working fluid, Itpp

nl x Ish n2 = I~lr

x

n3 )< Ievap n4 × Icond. n5 /vpq

(1 l )

Since a good working fluid is supposed to have a balanced capability, the n i was set to be unity if the corresponding performance index was greater than unity. Otherwise, n~ was set to two. In this manner, the fluid having one or more poor individual performance indices may result in a low Itpp and the indices for the reference fluid (CFC-113) are always set to be unity. The compound was considered empirically as a potential working fluid if the following conditions were fulfilled: (1) /tpp > 1.0; (2) /eft> 0.9; (3) other performance indices > 0.8; and (4) pressures at the heat-exchanger units < 25 bar. 5. S I M U L A T I O N RESULT As an illustration, we specified Tevap= 430 K and T~o,d= 308 K for the ideal ORC system. A diversity of pure fluids, whose critical temperatures were well above 430 K, were selected to be studied. Table 1 lists the number of substances for each class. Among the ozone-safe halogenated refrigerants, the critical temperature of HFC-32, HCFC-22, HCFC-124, HFC-125, HFC-134a, HCFC-142b, HFC-143a, and HFC-152a were lower than 430K so that those fluids were not suitable for this application. In general, the physical properties including critical property, acentric factor and the heat capacity at ideal-gas states should be given for performing the simulation. These properties were mostly taken from the data bank compiled by Reid et al. [19], and the properties of HCFC-123

413

Ozone-safe w o r k i n g fluids Table 1. Working fluids studied in this paper

Halogenated hydrocarbons derivatives of Methane Ethane Ethylene Propane lsopropane Propylene

Hydrocarbons

: 4 : 17 1 3 I 1

Alkanes Alkenes Dienes Alkynes Cyclics Aromatics

Others

: 33 : 17 : 6 : 3 : 12 : 7

Alcohols 13 Ethers 12 Amines 2 Ketones 5 Esters 15 Inorganic compounds

78

50

Butane Aromatics No. of compounds

35

were taken from McLinden [20]. The gyration of radius of fluids was taken from Reid et al. [21] or from Daubert and Danner [22] for viscosity calculation. If the properties of halogenated compounds were unavailable from the literature such as HCFC-122, their normal boiling point, critical temperature and pressure, and acentric factor were estimated from the method proposed by Chao [16]. Meanwhile, the group-contribution correlations of Joback [19] were applied to predict the critical volume and the heat capacity at ideal-gas states. Under the specified operating conditions, a wide range of individual performance values resulted from those 163 working fluids. Similar to the previous studies [11, 16, 17, 23], those performance values could be correlated with the fluid's physical properties. Figure 2 shows that fluids with a normal boiling point (Tb) ranging from 290 to 430 K could provide high ideal cycle efficiency (£id). The values of VPQ increased consistently with the fluids' Tb and the fluids with T~ less than about 330 K could give a smaller VPQ than that of CFC-113 as presented in Fig. 3. Figures 4 and 5 illustrate, respectively, that the evaporating and condensing pressures decrease with Tb and the favorable Tb range may be located between 290 and 320 K. As shown in Fig. 6, it appears that the values of rSHmin I decrease with critical pressure (Pc) and the fluids with Pc greater than 35 bar may give smaller [SHminl than that of CFC-113. Furthermore, the values of /evap decrease with molecular weight and Ico,d increase roughly with critical pressure as shown in Figs 7 and 8, respectively. The favorable molecular weight of the fluids would be smaller than 90 g mol- i. As shown above, it is concluded that fluids' molecular weights, normal boiling points and critical pressures could be the key properties for preliminarily selecting working fluids. According to this case study, fluids with a molecular weight smaller than 90 g mol-i, a normal boiling point between 290 K and 320 K, and a critical pressure higher than 35 bar are potentially able to provide a good thermophysical capability for the ORC energy-recovery system.

03.002I5

[]

Te,p ~=430K



hi

0,,%

A& O[]

.u



0.15 o

o.lo

a

A :ALcohoLs o : Hakog. :HCs o : E'Uners • :Esters

2. R e l a t i o n

between

I 550

O

• v

o.c~ 250

Fig.

[] []

A

: Ketones

Tb(K)

ideal cycle efficiency (~id) a n d T,w p = 430 K).

I 450

normal

I 550

boiling p o i n t

(Tcond=308K,

M . J . LEE et al.

414 I0 -

Tevop=430 K A :Alcohols [] : Holog,

I



[]

: HCs o : Ethers : Esters g : Ketones



& B i0~•

A

~tO-I

, ~ ~ p

-3

#

CFC-I13

I

ioe 250

550

Fig. 3. Relation between

L

I

450

Tb(K)

VPQ and normal boiling point

550

(Tco,d = 308 K, Tev,p = 430 K).

1o7 --

Tevop =4 3 0 K

" ~

~bl~m,A

CFC-II3

tO6

I:L~lo 5 --

~ :Alcohols

[] • o • V

o~

: Hotog. :HCs :Ethers : Esters : K~tones

'°4250

o

[]

am

o

I

I

3,50

450



1 55O

mb(K)

Fig. 4. Relation between saturated pressure at evaporating temperature and normal boiling point (Towp = 430 K).

I

I0 s

Tco~d•308K

@ ~°

:Ethers : Esters : Ketones

I03 250

m

t

I

350

450

0



I 550

T b (K)

Fig. 5. Relation between saturated pressure at condensing temperature and normal boiling point (Tcond = 308 K ) .

Ozone-safe working fluids I0

415

o

• []

-

-30





o

o:

A •

~0 && & 0 •



CFC-113

Te~ p = 4 3 0 K

"r (13 o

:ALcohoLs o : Hotog. • : HCs o : Ethers • : Esters v : Ketones a

-70

o

-IlO I0

I

I

I

I

I

I

2O

30

40

50

60

70

Pc

(bar)

Fig. 6. Relation between minimum superheat of condenser-inlet vapor and critical pressure (Tco.d = 308 K , Tev~p = 4 3 0 K).

Table 2 compiles the predicted performance for some potential working fluids. We see that ethers with four carbon atoms (vinyl ethyl ether, diethyl ether, methyl propyl ether and methyl isopropyl ether), dienes and alkanes with five carbon atoms (2-methyl-1,3-butadiene, 3-methyl-1,2-butadiene, 1,2-pentadiene, trans-l,3-pentadine, 1,4-pentadiene, 2-methylbutane and pentane), HCFC-123 and HCFC-132b have good performances for the ORC system. Even though some chlorinated hydrocarbons also present comparable thermophysical capability, they have a high ozone depletion potential. Therefore, these substances were excluded from the list of favorable working media. The fluids with high Tbs and low Pc s such as ethers with five or more carbon atoms, hydrocarbons with six or more carbon atoms, aromatics, alcohols, ketones, and esters are unfavourable due to their low cycle efficiencies, high VPQ, high [SHmin[ or low saturated pressure at the condenser. Among the potential compounds, the ethers, dienes and alkanes are generally flammable and some of them are unsaturated compounds. Only HCFC-123 and HCFC-132b are saturated and nonflammable substances. However, the sub-atmospheric vapor pressure attained for HCFC-132b at the condenser and the Iovapfor HCFC-123 is slightly lower than unity. Under economical, safety and environmental considerations, HCFC-123 could be one of the most favorable working fluids for this application due to its nonflammability, low toxicity, low ISHmi, [ and VPQ, moderate vapor pressure, comparable cycle efficiency and inherent heat-transfer capability. The slightly low Ievapfor HCFC-123 could be improved by blending it with a proper amount of high Ie~apfluid such as diethyl ether, 2-methyl-l,3-butadiene and vinyl ethyl ether. 4

3 -

-Tevop = 4 3 0

Tcond = 3 0 ~ K

K

0 0 -

2 0

0

oOo

0 o

0

oo

t

oOd~8 ° nn

~o~,

I

o

0

0

50

°o

0

o

0

0 0

o 0

0

OOn o o9 o

o 0

CFC-113

o

0

o oo ~ ° ° ° °0 0 0

0

o

o CFC-113

0

o

o

I

I

t

I00

150

200

M.W. (g mot -~)

Fig. 7. Relation between evaporating index (Icvap) and molecular weight (Tev~p = 430 K).

0

30

I

I

I

I

I

55

40

45 Pe (bar)

50

55

Fig. 8. Relation between condensing index (I¢o.0) and critical pressure (Tco.d = 308 K).

M . J . LEr et al.

416

Table 2. Predicted performance of some potential working fluids circulated in the ideal ORC system*+

e,o°d

e,~

3.46 3.21 1.94 2.47 2.37

1.07 0.93 0.76 0.82 1.48

17.5 15.7 13.9 15.0 19.3

I. 10 1.04

1.57 1.70

0.98 1.30

17.9 21. I

1.08 1.05

2.98 1.34

1.31 0.59

23.7 14.4

Substance Vinyl ethyl ether Diethyl ether Methyl propyl ether Methyl isopropyl ether

letr 1.03 0.99 1.00 0.99

l~h 1.51 1.17 1.11 1.16

lv~ 1.39 1.53 1.31 1.65

letup 0.89 1.60 1.67 1.73

/cond 1.92 1.44 1.71 1.67

/tpp 3.29 4.04 4.15 5.42

2-methyl- 1,3-butadiene 3-methyl- 1,2-butadiene 1,2-pentadiene 1,3-pentadiene, trans 1,4-pentadiene

1.01 1.03 1.04 1.04 0.98

1.02 1.04 1.04 1.07 0.94

1.17 1.02 0.89 0.98 1.26

1.71 1.68 1.52 1.55 1.58

1.68 1.75 1.49 1.49 1.40

Pentane 2-methyl butane

0.97 0.95

0.90 0.90

1.38 1.66

1.36 1.35

HCFC- 123 HCFC- 132b

1.00 t .08

2.00 2.00

1.78 0.95

0.88 0.81

*T~vap ~ 430 K and

Tco.d =

bar 1.00 1.04 0.90 118

bar 19.8 20. I 18.0 21.7

308 K.

fCFC-113: ( = 0.21, SHmin = -39.45 K, VPQ = 0.045 m3MJ ], Pco,d= 0.66 bar, P~v~p= 13.8 bar.

6. CONCLUSIONS This work has evaluated the thermophysical capability of a variety of fluids used in an ideal ORC energy-recovery system with the aid of the Iwai-Margerum-Lu equation of state and the transport property correlations. The results showed that a fluid's normal boiling point, critical pressure and molecular weight could be the key variables used to select thermodynamically proper working fluids for an ORC system. It was also indicated that HCFC-123 could be one of the most favorable ozone-safe fluids for the application. REFERENCES 1. H. M. Curran, Use of organic working fluids in Rankine engines. J. Energy 5, 218-223 (1981). 2. M. O. McLinden and D. A. Didion, Thermophysical-property needs for the environmentally accepable halocarbon refrigerants. Int. J. Thermophys. 10, 563-576 (1989). 3. H. O. Spauschus, Compatibility requirements for CFC alternatives. Int. J. Refrg. 13, 73-78 (1990). 4. L. Kuijpers and S. M. Miner, The CFC issue and the CFC forum at the 1988 Purdue IIR. Int. J. Refrg. 12, 118-124 (1989). 5. H. Kurse, CFC research programmes in Western Europe. Int. J. Refrg. 13, 122-130 (1990). 6. K. Watanabe, Current thermophysical properties research on refrigerant mixtures in Japan. Int. J. Thermophys. 11, 433-453 (1990). 7. E. N. Ganic and J. Wu, On the selection of working fluids for OTEC power plants. Int. J. Energy 3, 9-22 (1980). 8. E. Wali, Working fluids for solar, Rankine-cycle cooling systems. Int. J. Energy 3, 631-639 (1980). 9. K. M. Lee, S. F. Kuo, M. L. Chien, and Y. S. Shih, Parameters analysis on organic Rankine cycle energy-recovery system. Energy Convers. Mgmt 28, 129-136 (1988). 10. A.V. Pradhan and V. H. Larson, Power cycles analyses by generalized thermodynamic properties. In Proc. 15th IECEC, Seattle, Washington, pp. 680-685 (1980). 11. M. P. Bertinat, Fluids for high temperature heat pumps. Int. J. Refrg. 9, 43-50 (1986). 12. B. I. Lee and M. G. Kesler, A generalized thermodynamic correlation based on three-parameter corresponding states. A1ChE J. 21, 510-527 (1975). 13. Y. Iwai, M. R. Margerum, and B. C.-Y. Lu, A new three-parameter cubic equation of state for polar fluids and fluid mixtures. Fluid Phase Equilibria 42, 21-41 (1988). 14. M. J. Lee and Y. L. Chao, Correlation of thermophysical properties of halogenated refrigerants. Fluid Phase Equilibria 67, 111-125 (1991), 15. D. S. Jan and F. N. Tsai, A new four-parameter cubic equation of state for fluids. Canad. J. Chem. Eng. 69, 992-996 (1991). 16. Y. L. Chao, Thermophysical analysis for CFC alternatives. MS. thesis in Chemical Engineering; National Taiwan Institute o f Technology, Taipei, Taiwan, July 1990. 17. M. J. Lee and Y. L. Chao, Thermophysical performance of CFC-alternatives in refrigeration systems. J. Chinese Inst. Chem. Eng. 23, 143-151 (1992). 18. M. J. Lee and M. C. Wei, Corresponding-states model for viscosity of liquids and liquid mixtures. J. Chem. Eng. Jpn. 26, 158-164 (1993). 19. R. C. Reid, J. M. Prausnitz and B. E. Poling, The Properties of Gases and Liquids, 4th Edn. McGraw-Hill, New York (1987). 20. M. O. McLinden, Thermodynamic properties of CFC alternatives: a survey of the available data. Int. J. Refrg. 13, 149-162 (1990). 21. R. C. Reid, J. M. Prausnitz and T. K. Sherwood, The Properties of Gases and Liquids, 3rd Edn. McGraw-Hill, New York (1977). 22. T. E. Daubert and R. P. Danner, Data compilation tables of properties of pure compounds. Design Institute for Physical Property Data, AIChE, New York (1984). 23. H. Kruse and U. Hesse, Possible substitutes for fully halogenated chlorofluorocarbons using fluids already marked. Int. J. Refrg. 11, 276-283 (1988).

Ozone-safe working fluids

417

APPENDIX 1. Iwai-Margerum-Lu equation of state [13]: P

RT V-b

a(T) V2+ub(V-b)

(A-l)

with u = 0.333/Z~ - 1.95

a( r)

=

(A-la) (A-lb)

QacOt(T)R2T~ / Pc

(A-lc)

b = D,~ RT~/P~ fl.c = (1 + ufl¢ - u]/~)2~/[(l

(A-ld)

- flc)2(2 + ufl¢)]

(A-le)

(A.10

~'~= (l -- 2fl~)/[(! - flc)2(2 + ufl¢)]. The value of fie is given by the smallest root of the following equation:

(A-lg)

.#~ + 3#o- 1 =0. The temperature dependence of a was generalized by ~t(T) = [1 + m(l -- T~r'5)]2/T°'4

(A-lh)

a(T) = [1 + m(1 - T°'5)]2/(0.57667T~rs + 0.43352)

(A-ii)

m = - 0 . 2 5 w 2 + 1.31to - (0.209/Zc) + 0.5275.

(A-I j)

for T~ > 0.7, and for Tr < 0.7. Moreover,

2. Two-reference-fluid corresponding state model for estimating the viscosity of saturated liquids of halogenated compounds [14]: to -- to{r0

In rb = In ~1~'~) + to(r2) -- (.o(ri)[In g] ~r21 -- In r/~6~]

(A-2)

with (A-2a)

rb = r//r/=

n=

: MW3P~'~ '/6 = \ RT, N~ J

(A-2b)

r/~n) = 1.7458 + (1.5075/Tr) - 3.4630T r + 1.5865T~

(A-2c)

r/~r2) = --2.5451 + (2.7625/Tr) + 2.6749Tr -- 1.4141T 2

(A-2d)

co(rl) = 0.171 (Halon-1301)

(A-2e)

to(r2) = 0.246 (CFC-114)

(A-2f)

Tr = T/(TcO )

(A-2g)

0 = 1.43046 - (0.154255/Z~) + 2.87111 x 10-4To,

(A-2h)

and

where to denotes the acentric factor of the fluids. 3. Three-reference-fluid corresponding-state model for estimating the viscosity of liquids other than the halogenated compounds [18]:

17r=t/~r')'~ Ot--o~(rl)r"'r2>-"cm'*a'~"'~3)-I-"<'"+ .......... (,, L"

r/--ol(r') Qt(rl) (t/~r2)-

=,,2,_

F/(rl))

]I

(A-3)

with ~r = In[0//r/=) + 1].

(A-3a)

The definitions o f ~/= and Tr are the same as equations (A-2b) and (A-2g), respectively, and n represents the gyration of radius o f fluids. The substance-specific energy shape-factor 0 and polar parameter, fl =, together with the correlations o f r/~m, ~/~2) and r/~ ~3) are given elsewhere [18]. 4. Latini model for thermal conductivity [19]. k = A(! - Tr)°3ST~-0/6)

(A-4)

.4 = .4 =T;/(MWJTD,

(A-4a)

with

where A = and exponents i, j, k are characteristic parameters for each family of substances. The parameter values can be found in ref. [19].

M . J . LEE et al.

418 5. Brock and Bird model for surface tension [19]:

es = P ~ T ~ , 3 Q ( 1

~,.'.,-5)

. - 7"~) L'~

with Q=0.1196

1+

Tb, ln(P,/I.O1325)\ -

~

I --- ]rhr

1--0.279

/

c A - 5a '

where r~, = r u ! ' L .

(A-5b)

6. R o w l i n s o n - B o n d i model for liquid heat capacity [19]:

(Cpt- C~)/R = 1.45 + 0.45(I -- T r ) ~+ 0.25~o[17.11 + 25.2(1 - Tr)~3T~-~ + 1.742(1 - T~) t], where C~- is the heat capacity at ideal-gas states and ~ is the acentric factor.

~A-6)