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Fluids for high temperature heat pumps
Fluids for high temperature heat pumps M. P. Bertinat The Electricity Council Research Centre, Capenhurst, Chester CH 1 6ES, U K Received 13 September 1985
The theoretical performances of some 250 potential work fluids in vapour compression heat pumps condensing at 150°C and evaporating at 100°C have been predicted, using expressions for coefficient of performance (COP) and minimum superheat that involve only easily accessible physical properties. Expected correlations were found between COP and critical temperature, between specific compressor displacement and normal boiling point, Tbp,and between condensing pressure and Tbp.Correlations were also found between minimum superheat and both molecular weight and critical pressure. From these correlations, the desirable basic properties of a high temperature heat pump fluid are deduced. The principle of corresponding states is invoked to explain the connection between minimum superheat and critical pressure, and hence the reason why perfluorinated compounds tend to make poor work fluids. (Keywords:heat pumps;heat pumpfluids;thermodynamics)
Fluides pour les pompes fi chaleur/t haute tempbrature Les performances th~oriques d'environ 250 fluides actifs possibles dans les pompes ~ chaleur ~ compression de vapeur condensant & 150°C et kvaporant ~ IO0°C ont ~t~ pr~vues ~ l'aide d'expressions du coefficient de performance (COP) et d'une surchauffe minimale ne comprenant que les propri~t~s physiques facilement accessibles. On a trouvd des corrdlations entre le COP et la temperature critique, entre le ddplacement sp~cifique du compresseur et le point tf ~bullition normal, Tbp, et entre la pression de condensation et Tbr On a trouv~ aussi des correlations entre la surchauffe minimale, d'une part, et la masse molkculaire et la pression critique, ~fautre part. A partir de ces correlations on d~duit les proprikt~s fondamentales souhaitables d'un fluide pour pompe ~ chaleur ~ haute temperature. Le principe des dtats correspondants est invoqu~ pour expliquer la relation entre la surchauffe minimale et la pression critique et ainsi la raison pour laquelle les compos~s perfluor~s ont tendance ~ faire de mauvais fluides actifs.
(Mots cl6s: pompes ~tchaleur; fluides pour pompe fi chaleur; thermodynamique)
The maximum condensing temperature currently available from commercial vapour compression heat pumps is ~ 120°C, this being the maximum temperature for which Rl14 is a suitable work fluid. To go to higher temperatures a different fluid is needed, and all of those previously proposed (e.g. Rl13, R216, Fluorinol, methanol, PP1, water) have at least one major problem, be it toxicity, flammability, poor thermodynamic performance o r insufficient thermal or chemical stability. Two possible reasons for this are that previous studies have been blinkered in their choice of fluids, or that the ideal high temperature work fluid is an unattainable goal. The fluids considered for heat pump use are generally restricted to those for which comprehensive thermodynamic data are available, so that the various heat pump performance parameters can be evaluated directly from tables or charts. In the present search for a fluid suitable for 150°C condensing, a wider range of compounds was considered, including some specially-synthesized fluorine compounds, few of whose properties were known. This forced the author to develop a method of estimating the thermodynamic performance parameters of any fluid from the sparsest of basic data. With this method, it was possible to analyse a number of novel compounds that were thought to have potential as high temperature work fluids, and it began to emerge that ideal fluids from the point of view of stability, toxicity and flammability tend to be poor thermodynamically. Thus, the study was expanded to include a large number of compounds that, 014(L7007/86/010043~)8503.00 © 1986 Butterworth & Co (Publishers) Ltd and IIR
despite having obvious disadvantages in other respects, at least looked as if they might be thermodynamically attractive.
Thermodynamic performance parameters To make a thermodynamic comparison of heat pump fluids, it is convenient to consider them in an ideal vapour compression (IVC) cycle. This is defined as one in which the fluid is evaporated isothermally, compressed isentropically, condensed isothermally, and expanded isenthalpically: there is no liquid subcooling, but there is a minimum amount of vapour superheat to prevent liquid compression. In general, the superheat of a vapour will either increase or decrease during isentropic compression according to the particular fluid involved. For those fluids where it increases (type A fluids), the minimum superheat, SH, refers to the discharge superheat resulting from compressing initially saturated vapour (Figure la), whilst for those fluids where superheat decreases (type B fluids), SH refers to the suction superheat required so that the compressed vapour is just saturated (Figure lb). The three most important thermodynamic performance parameters for a heat pump fluid are: 1. coefficient of performance (COP), defined as the ratio of condenser heat output to compressor work input; 2. specific compressor displacement (SCD), defined as the volume of vapour drawn into the compressor per unit condenser heat output; and
Rev. Int. Froid 1986 Vol 9 Janvier
43
Fluids for high temperature heat pumps: lid. P. Bertinat
T~,T~
Nomenclature
COP COP ° Co ACp L
Lc, Lsat MW n Pc Pcrit QDSH
SCD
SH SH 1
SH °
Lp Tcrit
Coefficient of Performance (the ratio of condenser heat output to compressor work input) Approximate COP obtained using W ° and Q~sH Specific heat at constant pressure Difference between ideal gas and real gas values for Cp Latent heat of vaporization Values of L at condensing temperature Tc and at mean saturation temperature T~a, Molecular weight Number of atoms per molecule Condensing pressure Critical pressure Heat associated with desuperheating a type A fluid after compression Approximate value of QnsH using SH ° and Cp(~t) Specific compressor displacement (the volume of vapour drawn into the compressor per unit condenser heat output) Minimum superheat in an IVC cycle (always positive) The quantity (1-~) ATsm, positive and equal to SH ° for a type B fluid, negative and equal to - S H ° for a type A fluid Approximate value of SH, equal to
11-
Normal boiling point Critical temperature
Vsat, K
AV AVsa, W Wo
Greek letters
O"
#D Z
C O P ~ C O P ° = (Lc + QDSH)/£sat • (A ['(sat/Vs). ('F--sat/A T-sat) (1)
zIAT~t
(2)
where: ATsa t is the difference between the condensing and evaporating temperatures Tc-TE; Tsat is the mean saturation temperature, (Tc+ TE)/2; Lc and L~at are the latent heats of vaporization at Tc and Tsar; AV~at is the difference between vapour and liquid specific volumes at T~t; and ~ is the specific volume of superheated vapour at the mean superheat temperature. X is the dimensionless ratio (ilL V/CpA V) evaluated at Ts~,,where fl is the isobaric thermal expansion coefficient and Cp is the isobaric specific heat. Q~sR is the (approximate) heat associated with desuperheating after compression, equal to Cp(Tsat)SH° for a type A fluid and zero for a type B fluid. The specific compression displacement (SCD) is given by: L ° S C D ~~ V1/(cWQDsH)
(3)
where V~ is the specific volume at the compressor inlet,
Int. J. Refrig. 1986 Vol 9 January
Isobaric thermal expansion coefficient, ( 1/V)(OV/¢3T)p Intermolecular interaction parameter Molecular size parameter Molecular dipole moment Superheat parameter (BL V/CpA V) Value of Z at Tssat
General terms Type A fluid Type B fluid IVC cycle
The first and third of these can be approximated by the following expressions (see Appendix):
44
v1
EIAT:~,
3. minimum superheat (SH), defined above.
sn~sn°~[1-
~at
Condensing and evaporating temperatures Mean saturation temperature, (Tc + TE)/2 Temperature difference, Tc - TE Specific volume of vapour entering compresso r Specific volumes of vapour at ~., and at mean compression temperature Difference between vapour and liquid specific volumes Value of A V at ~at Compression work Approximate W obtained by using ~at values
Fluid that superheats during isentropic compression Fluid that desuperheats during isentropic compression Ideal vapour compression cycle as defined in text
and the approximation involved is that of Q~sH (see above and Appendix). Two other important parameters are the saturation pressures at Tc and TE. Estimates of all the quantities in Equations (1)-(3), apart from Cp, can be made from a fluid's critical temperature, T~nt, critical pressure, Petit, and normal boiling point, Tbp, using the principle of corresponding states. In its simplest form, this principle asserts that the equation of state of a substance depends only upon its T~rit and Pcrit, but a more useful form is the three-parameter version of Pitzer 1 which introduces an 'acentric factor' to take account of the shape of the molecule as well. The Lee and Kesler method z'3 is a convenient way of using this acentric factor, and although the method was developed specifically for non-polar molecules, its results are surprisingly accurate for both polar and non-polar molecules. All the fluids in this study were analysed using the Lee and Kesler method. Not even T~.t and Petit values were available for many of the fluids to be assessed, so these values also had to be estimated. This was done using the group contribution method of Lydersen 4' 3, or a modified version of this in the case of some of the highly fluorinated compounds. The only input data required were Tbp and the structural chemical formula. To estimate Cp, the appropriate ideal gas value was first obtained, either from the literature or using the group
Fluids for high temperature heat pumps." M. P. Bertinat a /
---
\
(/
I
rc
/
SH
\
X\
I
/
TE
/
\
S b
..._
I-.
I SH m
"E
/
~-
•
/
/ /
S Figure 1 (a) Temperature--entropy diagram for a type A fluid IVC cycle. Compression begins on the saturation curve ( - - - ) . (b) Temperature-entropy diagram for a type B fluid IVC cycle. Compression ends on the saturation curve ( - - - ) Figure l(a) Diagramme temp&ature-entropie pour un cycle I V C (~ compression de vapeur id~ale) de fluide de type A. La compression d~bute sur la courbe de saturation ( - - - ) . (b ) Dia#ramme temp&ature-entropie pour un cycle IVC de fluide de type B. La compression finit sur la courbe de saturation ( - - -)
contribution method of Benson et al.5'3. (The latter again required the structural formula.) To this was added the real fluid correction, ACp, calculated by the Lee and Kesler method. Thus the only essential data required to estimate the performance parameters for any fluid were its normal boiling point and its structural chemical formula. However, known values of T~nt, Peat and Cp were used, when available, in preference to estimated ones.
pounds: less attractive than perfluoro compounds for reasons of stability, toxicity and flammability, but thermodynamically better; 4. all the appropriate members of those common aliphatic series that it was thought might be sufficiently stable and unreactive: most of these are highly flammable but many of them looked good thermodynamically; 5. all the fluorine derivatives of the series in 4, above, for which the boiling points could be found, and also in some cases chlorine derivatives, although the latter were not expected to be sufficiently stable for 150°C use: many of these also looked good thermodynamically; 6. the few inorganic compounds that had suitable T~,t and Tbp: apart from water, these are all far too toxic or unstable, or both, for serious consideration, but they were included for completeness. Altogether the list comprised 247 fluids, seven of them inorganic and the rest organic. Although many of these can be immediately ruled out for various reasons, it is instructive to look at how the values of the three thermodynamic parameters, COP, SCD and SH, correlate with the basic physical properties of the fluids. When the COP of each fluid, evaluated for a 100/150°C IVC cycle, is plotted against its molecular weight (MW), its normal boiling point (Tbp), its critical temperature (T~at) and its critical pressure (Pc.t), it is apparent that COP depends strongly on T~.t, very weakly on Tbp,and not at all on MW or Pent (although the maximum value of COP at a g i v e n Vcrit does seem to depend upon Pcrit)" Figure 2 shows the T~.t plot. The strong positive correlation (high T~.t high COP) can be explained by the decrease in (Lc/[sat) as the critical temperature is approached. The weak correlation with Tbp is probably an indirect reflection of this since Tcnt and Tbp are related. A good work fluid should have a COP of 1>6, and Figure 2 indicates that Tc.t~>200°C is probably a sufficient (though not necessary) condition for a fluid to satisfy this criterion. Similarly, SCD appears to depend strongly on Tbp but only weakly on T~ntand not at all on MW or P~nt. Figure 3 shows the Tbp plot, and the positive correlation (high Tbp ~ high SCD) is a result of the fact that the saturated vapour pressure at a fixed evaporating temperature (100°C) is closely related to Tbp. The weak correlation of 8.0 7.5
Analysis of 250 fluids The aim of the investigation was to find the best fluid for use in a heat pump condensing at 150°C and evaporating at 100°C, so the initial selection criteria were Tcrit ~ 170°C, to ensure that (Lc/E~t) was reasonably close to unity, and Tbp~<100°C, to ensure that pressures were never sub-atmospheric. A list of fluids was drawn up consisting of the following categories: 1. commercially available perfluoro compounds such as perfluoro-n-hexane (PP1): these are attractive because in general they are chemically stable, non-toxic and nonflammable, but unfortunately none looked very good thermodynamically; 2. specially synthesized perfluoro compounds: results the same as 1 above; 3. specially synthesized partially fluorinated com-
7.0 6.5
.0 ÷
4-
6.0 5.5 5.0 4.54.0 4150
I 200
I 250
I 300
I 350
400
Terlt (°C}
Figure 2 COP versus critical temperature for 240 organic (+) and seven inorganic (I-q) fluids assuming an IVC cycle evaporating at 100°C and condensing at 150°C Figure 2 COP en fonction de la temperature critique pour 240 fluides oroaniques (+) et 7 fluides inoroaniques (D) en supposant une temperature d'$vaporation du cycle I V C de IO0°C et une temperature de condensation de 150°C
Rev. Int. Froid 1 9 8 6 Vol 9 Janvier
45
Fluids for high temperature heat pumps." M. P. Bertinat 1.2
1.0
+
~+,p/'~'÷+
,~ 0.8
% r~ 0.6 0.4
~.÷
0.2-
0.0 0
+
. ~"°*
*t';g
+
I
I
20
40
Tbp
I
I
60
80
T~ri,oce
(4)
P c r i t o c / 3 / o -3
(5)
100
(°C)
Figure 3 Specific compressor displacement versus normal boiling point for 247 fluids. + , Organic fluids; [-], inorganic fluids Figure 3 D~placement sp~vifique du compresseur en fonction du point tl'~bullition normal pour 247 fluides. +, Fluides oryaniques; IS], Jluides inorganiques
SCD with T.it again reflects the connection between Tbp and T~,,. A good work fluid should have a small SCD, preferably <0.4 m s M J- ~, and to satisfy this criterion, a necessary condition would appear to be Tbp~<80°C and a sufficient condition Tbp~40°C. The behaviour of the third performance parameter, SH, can be seen by plotting the quantity SH ~= (1 - ~)A T~,, against the four basic physical parameters. Positive values of SH~ imply suction superheats of type B fluids, whilst negative values imply discharge superheats of type A fluids. As can be seen from Figures 4 and 5, there is an obvious positive correlation with molecular weight (high MW ~ high SH0, although the scatter is rather high, and an even stronger negative correlation with P~t (high P,,t ~ low SH~). Fluids with low Pcrit have large values of SH~, i.e. they are strongly type B. Fluids with very high P~r~thave negative values of SH~, i.e. they are type A. The cross-over point seems to be around P , , = 48 bar, and an ideal fluid will thus have Petit somewhere near this value. It is also likely to have MW in the range 50-150. A fourth parameter of importance for a high temperature work fluid is its saturation pressure at the condensing temperature. If this condensing pressure, Pc, is significantly higher than standard engineering values, say ~ 20 bar, then special components will be required in the construction of the heat pump and the cost will be greatly increased. Plots of Pc against MW, Tbp, T,, and P , , , indicate a strong correlation only with Tbp.This is not surprising since Tbp and Pc are both simply aspects of the variation of saturation pressure with temperature. A necessary condition for Pc ~<20 bar would appear to be Tbp~>25'C, and a sufficient condition Tbp> 50°C.
Molecular implications Several deductions can be made from the above analysis about the kind of molecule likely to make a good heat pump fluid. There are many aspects of a molecule that might be important, such as its size, shape, mass, polarity, bond strengths, etc. but most of these can be considered in terms of their effects on the two fundamental molecular forces, namely the forces between the atoms within a molecule (intramolecular forces or bond strengths) and the forces between different molecules (intermolecular forces). The
46
former determine the basic chemical and thermal stability of the molecule, whilst the latter determine the thermodynamic properties of a fluid composed of such molecules. According to the principle of corresponding states, the critical temperature and pressure of a fluid consisting of simple, non-polar, spherical molecules depend upon the strength of the intermolecular interactions, e, and the linear dimensions of the molecules, a, according to the simple relations6:
Int. J. Refrig. 1986 Vol 9 January
Although few of the fluids involved here have molecules that even approximately fit the description non-polar and spherical, these simple relations do seem to account, qualitatively at least, for some of the variations in their critical properties. Consider for instance, the fluids whose critical properties and dipole moments, #D, are given in Table 1. From the first two entries it can be seen that in simple alkanes, increasing the carbon chain length raises Tcrit but l o w e r s Pcrit" This can be explained by an increased 40
+ ~**+ * + *
20 0 -20 z~
t/3
+
Q 4. o
40
g
°
-60 D
-80 -100 -120
D 0
I
I
I
I
I
I
I
I.,
50
100
150
200
250
300
350
400
450
MW
Figure 4 Minimum suction superheat versus molecular weight for 247 fluids. +, Organic fluids; D, inorganic fluids. Negative values imply positive discharge superheat (type A fluids) Figure 4 Surchauffe minimale d /'aspiration en Jonction de lu masse moleculaire POUr 247 fluides. +, Fluides organiques; D, fluides inorganiques. Les valeurs nd~gatives impliquent une surchau~fe au refoulement positive (.[luides de type A) 40
*.,. *+.,. + ÷÷
01
*
*
-20 -40
÷
o
o
D
-80
-
-100
-
-120
I
101
I
l
I
l I Ill
i a
102
i
,
i
i i
ii 103
Pcrit (bar)
Figure 5 Minimum suction superheat versus critical pressure for 247 fluids. + , Organic fluids; [-], inorganic fluids Figure 5 Surchauffe minimale d I'aspiration en fonction de la pression critique pour 247 ,fluides. + , F/uides organiques; El, .fluides inorguniques
Fluids for high temperature heat pumps. M. P. Bertinat Table 1
Critical properties and dipole moments of a selection of organic fluids Tableau 1 Propridt~s critiques et moments dipolaires de quelques fluides
organiques Tcrit
Pcrit
//D
Fluid
(°C)
(bar)
(Debyes)
C5H12 C6H 14 C6Fla C7F16 CH3CH 3 CHaCH2F CH3CH2NH z CH3CH2OH
196 234 178 202 32 102 183 243
34 29 18 16 48 49 55 64
0 0 0 0 0 2.0 1.3 1.7
Although the actual specific heat will generally be less than the classical value because of quantization of the vibrational energy levels, Cp can still be expected to depend upon n. Moreover, since the molecular volume is also likely to depend upon n, Cp can be expected to be a function of tr 3, the molecular volume parameter. Thus: L ,-~s
(6)
and: C o ~ f(n) ,-~f(a 3)
(7)
whence: interaction strength accompanied by a proportionately greater increase in effective molecular size, both expected effects of increasing the length of the molecule. The same effect is seen in the next two fluids, which are perfluoroalkanes. However these perfluoroalkanes have lower T~nt and considerably lower Pent than the corresponding alkanes, and this can be explained by the weaker interactions and larger molecules of the perfluoroalkanes. Even fluids in which the molecular interactions are very different from those of simple fluids, seem to show trends in T~nt and Pent in qualitative agreement with the simple relations given above. Thus the next two fluids in Table I, ethane and ethyl fluoride, show the effect of a molecular dipole moment on T~nt and P~nt: both these quantities increase, consistent with the fact that interrnolecular forces are increased by the presence of a permanent dipole moment. Even higher values of T~ntand Pent are seen with the last two entries in the Table, ethylamine and ethanol, consistent with the fact that these fluids are subject to even stronger intermolecular forces as a result of hydrogen bonding. In the section 'Analysis of 250 fluids', it was shown that a good heat pump fluid should have a high T~nt,to give a high COP, and a moderately high P~nt, to give a low superheat. The former requirement was explained by the relatively rapid reduction of latent heat with temperature as T, it is approached, but the P¢~t requirement was unexplained. Now this requirement can also be understood, at least qualitatively. According to Equation (2), SH 1 is proportional to (1 -~), where the quantity f( = fl VL/CpA V is a measure of the slope of the vapour saturation curve on a T S diagram (see Appendix). The variation of SH 1 with P~,t is thus analogous to the variation of SH~ with Z, since SH~ decreases with increasing P~dt(or ~) and goes through zero for P~m= 48 bar (~ = 1). The problem then is to find the connection between Pent and ~. Z can be considered to be the product of three separate factors, namely L/Cp, fl and V/A V, and the last of these can be ignored since it is generally very close to unity unless T is very close to T~dt. Consider, however, the L/Cp term. The molar latent heat, L, can be expected to depend linearly upon the strength of the intermolecular interactions, e, since both quantities are directly related to the energy required to separate molecules. The molar specific heat, Cp, on the other hand, might be expected to increase with n, the number of atoms in each molecule, since classically, the total kinetic energy of an n-atom molecule is just 3/2 n k T (Reference 7), and this will give a contribution to molar specific heat proportional to n.
L/Cp
g/f(G 3)
~
(8)
which implies that L/Cp, and hence X, depends upon e and a in much the same way as Pent does [Equation (4)]. The validity of Equations (6)--(8) can be seen from Figures 6-8 where the data for the 14 organic fluids listed in Table 2 are plotted as L versus T~nt(since T~n,~ e); Cp versus n; and L / C p versus Petit. The agreement with the predictions is obvious. The relatively small range of T,i t covered by the 14 fluids (450-540 K) means that most of the correlation between L/Cp and P~ntcomes from the 1/Cp variation. (Note that these data relate to a constant reduced temperature, T/T~n t = 0.9, rather than a constant 30 25 A
2O
4.
"7.
"6 E
÷
15
v
10i
5 ~
0 160 Figure 6
I
I
I
I
I
180
200
220
240
260
280
Tcrlt (°C) Latent heat of vaporization versus critical temperature for the
fluids in Table 2 Figure 6 Chaleur latente de vaporisation en fonction de la temperature critique pour les fluides du Tableau 2 ~0,
400 4-
'7,
"6 300 E 200 -
J
1000 0
I
I
I
I
5
10
15
20
25
Number of atoms per molecule, n Figure 7 Specific heat at constant pressure versus number of atoms [aer molecule for fluids in Table 2 Figure 7 Chaleur massique d pression constante en fonction du nombre d'atomes par moldcule pour les fluides du Tableau 2
Rev. Int. Froid 1986 Vol 9 Janvier
47
Fluids for high temperature heat pumps." M. P. Bertinat atoms), which means large n, small P , i , and large SH 1. Polar molecules, and molecules that are subject to hydrogen bonding, are generally good because their relatively large intermolecular forces mean that one can get a high enough Tent with quite small molecules, corresponding to high Pcri~ and low SH t. However, the interactions can be too strong and the molecules too small. With the alcohols for instance, whose molecules undergo hydrogen bonding, the smallest members of the
actual temperature, to prevent the variation of L with T/T~t overshadowing its variation with e.) The third factor of X, namely fl, has relatively little effect at constant reduced temperature, as can be seen by comparing Figure 9, where flL/Cp is plotted against Petit, with Figure 8. The effect of fl is to sharpen slightly the correspondence with Pcrit. However, it should be noted that if fluids are compared at different reduced temperatures (for example at constant actual temperature) then/3 is much more important since both fl and L vary more rapidly with T/rcrit than does their product, ilL. Note that according to Figure 9,/3L/Cp = 1 corresponds to P~r~t~50 bar for these 14 fluids, which compares favourably with the findings in the section 'Analysis of 250 fluids', that for SH .~0, P~nt~48 bar. It would appear then that the observed correlation between SHx and Pc~ is a reflection of the dependence of both Cp and Petit o n the number of atoms per molecule, n. Moreover, by plotting flL/Cp against n as in Figure 10, it can be deduced that the optimum value of n, corresponding to SH ~0, is probably ~ 10. It is now possible to see why certain fluids came out badly in the thermodynamic analysis whilst others came out well. Perfluoro compounds are bad because of the relative weakness of their intermolecular interactions. To get a high enough T~ntto give a reasonable COP at 150°C, one has to go to quite large molecules (at least six carbon
2.0
1.5
0.5
0.0 0
I 20
I 10
I 30
I 40
I 50
I 60
I 70
80
Pcrit (bar) Figure 9 flL/Cp versus critical pressure for the fluids in Table 2 Figure 9 flL/Cp en fonction de la pression critique pour les fluides du Tableau 2
250
2.0
200
1.5150
1.0 100
0.5
50 Ot .... 0
I 10
I 20
I 30
I 40
I 50
I 60
I 70
0.0 80
Pcr|t (bar) Figure 8 Ratio of latent heat to specific heat versus critical pressure for the fluids in Table 2 Figure 8 Rapport de chaleur latente [z la chaleur massique en fonction de la pression critique pour les fluides du Tableau 2
0
I
I
I
I
5
10
15
20
25
Number of atoms per molecule, n flL/Cp versus number of atoms per molecule for fluids in
Figure 10 Table 2 Figure l0 flL/Cp en fonction du numbre d'atomes par molecule pour les fluides du Tableau 2
Table 2 Properties of a selection of organic compounds to show the connection between X and Pcrit. Values of L, Cp and fl are all estimated for a reduced temperature (T/Tcrit) of 0.9 Tableau 2 Propri~t~s de quelques compos~s organiques pour montrer la relation entre Z et P,.rir Les valeurs de L, Cp et fl sont routes estim~es pour une temperature r~duite (T/T.,,) de 0.9 Compounds
n (atoms/molecule)
Tcrit (°C)
Pcrit (bar)
L (Jmol-t)
Cp ( J m o l - t K 1)
103 x fl (K t)
Methanol Ethanol Propanol Diethyl ether Butyl ethyl ether Di-isopropyl ether Ethylamine P ropylamine Butylamine Ethyl chloride R 113 Heptane Perfluoroheptane Perfluorohexane
6 9 12 15 21 21 10 13 16 8 8 23 23 20
240 243 264 193 258 227 183 224 251 187 214 267 202 178
79.5 64 51 36 30 29 56 47 41 53 34 27 16 18
22 600 24 000 25 100 16 500 21400 18 700 15 700 17 600 19 900 15 700 16 500 19 700 21300 18 900
97 131 168 183 270 255 139 174 214 128 191 291 431 368
7.45 6.83 6.75 8.12 7.23 7.56 8.98 8.08 7.38 8.48 8.35 7.48 7.47 8.16
48
Int, J. Refrig. 1986 Vol 9 January
Fluids for high temperature heat pumps." M. P. Bertinat
series (methanol, ethanol) have too large a Pc,t and give a high discharge superheat (SHt large and negative). The effect is even worse with water, where strong hydrogen bonding and small molecules result in a very high Per~t (221 bar) and a correspondingly high discharge superheat. Moreover, even T¢,~t is too high with water (374°C), since although this implies high COP, it also implies a high Tbp and hence a high SCD. A compromise is obviously desirable.
m
,,, /
/
/ /
/ /
S Figure AI
shown)
///~ /
\X
g
a
e \ \
S Figure A2 Schematic IVC cycle plus general isentrope fg (type A fluid shown) Figure A2 CyclelVCsch~matique+isentropeg~n~ralfg(lefluideAest pr~sent~)
vapour and saturated liquid. Consideration of a type A fluid also leads to Equation (A2). Replacing the integrand in this equation by mid-point values gives an approximate value for W, which is denoted as W°: W ° = 9"s(L/T A V)r,,,A Tsat
Appendix: derivation of equations for COP and minimum superheat Compression work The work done in compressing a vapour isentropically from pressure P~ to P2 c a n be written as:
(A1)
1
where the subscript s denotes constant entropy, and the fact that d H = T d S + V d P has been used. Consider the T-S diagram for a type B IVC cycle shown in Figure AI: here ab corresponds to isobaric superheating, be to isentropic compression, and mn to a general isobar intermediate between P, and P~. Since (VdP)~ = (V, dPn) = (V, dP~) the Clausius-Clapeyron equation gives: gn(g/rAg)m dTm
Cycle I VC sch~matique+ isobare g~nkralmn (le fluide Best
/
/
1 Pitzer, K. S., Curl, R. F. The Thermodynamic Properties of fluids Institution of Mechanical Engineers, London (1957) 2 Lee, B. I, Kesler, M. G. A generalised thermodynamic correlation based on three-parameter corresponding states, Am lnst Chem Eng J (1975) 21(3) 510-527 3 Reid, R. C., Prausaitz, J. M., Sherwood, T. K. The Propertiesof Gases and Liquids 3rd Edn, McGraw Hill, New York, USA (1977) 4 Lydersen, A. L. Estimation of Critical Properties of Organic Compounds University of Wisconsin College of Engineering Experimental Station, Report 3, Madison, WI USA (April 1975) 5 Benson, S. W, Cruikshank, F. R. et al. Chem Rev (1969) 69 279-324 6 Hirschfelder, J., Curtis, C., Bird, R. Molecular Theory of Gases and Liquids John Wiley and Sons, New York, USA (1964) Ch. 4 7 Feynman, R. P., Leighton, R. B., Sands, M. The Feynman Lectures on Physics Vol. l, Addison-Wesley, London, UK (1965) 39-12
Schematic IVC cycle plus general isobar mn (type B fluid
Figure A l pr~sent~)
References
W=
/a
/
These criteria imply that molecules should be fairly small ( ~ 10 atoms per molecule) and that they should interact with each other fairly strongly. Unfortunately, this seems to rule out the perfluoro compounds, despite their being ideal from several points of view (stability, toxicity, flammability), becuase they generally exhibit relatively weak intermolecular interactions.
(Vd P)~
n
/ /
1. high T~nt,to give near unity (Lc/L~at) and hence large COP; 2. fairly low Tbp, to give small V1 and hence small SCD, but not so low as to give excessive discharge pressure; and 3. fairly high P~nt, to give flL/Cp .~ 1 and hence small SH.
dHs=
I m
From a theoretical study of 250 potential work fluids for high temperature compression heat pumps, it appears that to be thermodynamically suitable a fluid should have:
1
I
/
Summary and conclusions
W=
I
(A2)
where L denotes latent heat of vaporization and A V the difference between the specific volumes of saturated
(A3)
where ~at=(Tc+TE)/2, A T s a t = T c - T E , and ~ is the specific volume at T=(Tb+T~)/2 and P=P~t(~,t). The problem of estimating W has thus been reduced to that of estimating a latent heat, a liquid density and two vapour specific volumes, all of which can be done by standard methods. However, since the temperature to which corresponds depends on Tb, the amount of superheat implicit in the IVC cycle must first be determined before Equation (A3) can be used. Minimum superheat Consider the T S diagram for a type A IVC cycle shown in Figure A2. Here ba corresponds to isobaric desuperheating, eb to isentropic compression, and fg to a general isentrope intermediate between Sa and So. The superheat at b is given by:
SH =
dT~
(A4)
and since at constant pressure T d S = Cp dT (Cp is the specific heat at constant pressure), whilst dS~ = dSr, this
Rev. Int. Froid 1986 Vol 9 Janvier
49
Fluids for high temperature heat pumps: M. P. Bertinat can be written as: b
SH =
fa(T/Cp)g
dSf
(A5)
Now using one of Maxwell's relations, dSf can be written:
d S f = (C p/ T )rd Tf - (fl V )rdP r
(A6)
where fl is the isobaric coefficient of thermal expansion, (1/V)(OV/t~T)p, from which the Clausius-Clapeyron equation gives: dS r= (Cp/T)f[ 1 - (ilL V/CpA V)] 6t Tr
(T/Cp)g(Cp/T)f( 1 - Zr) dTf
(A8)
where the dimensionless number Z has been defined by:
Z =- (ilL V/CpA V)~,
(A9)
The same Equation (A8) results from considering the suction superheat necessary for a type B fluid except that the limits on the integral are reversed. Since SH as defined is positive, this implies that Z is > 1 for a type A fluid but < 1 for a type B fluid, and in general it can be written that:
(T/Cp)p(Cp/T)~,]I --)(1dTsat
SH =
(A10)
~TF?
where SH is discharge superheat for X> 1 and suction superheat for Z < 1. An approximate value can be obtained by replacing the integrand with mid-point values (as with W °) and noting that the first two factors tend to cancel each other out. Thus SH ° is defined as: S H ° ~ I 1 - ~[AT~,
(All)
where ~-X(T=0. The estimation of SH has now been reduced to the estimation of the same quantities as for W (specific volumes and latent heat at T~t) plus the vapour specific heat also at ~a~. Note that the ideal work fluid will have ~ ~ 1.
Coefficient of performance The COP in an IVC cycle is given by: COP = (Lc + QDSH)/W
(A12)
where QDSHis the heat associated with desuperheating the high pressure vapour prior to condensing it. For a type B fluid, QDSH=0, but for a type A fluid it is given approximately by Cp(~)SH °, where Tp is the mean
50
Int. J. Refrig. 1986 Vol 9 January
type, S H et COP ~tant obtenu en utilisant les valeurs publi~es de l'enthalpie et de I'entropie
Fluid
(-)
SH (K)
COP' (-)
R21 R 12B 1 R 113 R 114 PP1
1.28 1.04 0.71 0.72 0.41
14.0 1.9 14.6 14.2 29.3
6.15 5.76 6.09 5.39 5.23
Type
SH (K)
COP (-)
A
14.5
A B B B
2.2 14.0 14.1 30.0
6.16 5.76 6.06 5.39 5.27
(A7)
Thus from Equations (A5) and (A7): SH =
Table AI Values of ~, SH '~ and C O P ° for five fluids compared with their type, SH and COP obtained using published enthalpy and entropy data Tableau A 1 Valeursde ~, S H et C O W pour 5 fluides compares avec leur
desuperheating temperature, (Ta+Tb)/2. As QDSH is generally small compared with Lc, the difference between Cp(~) and Cp(T~t) is not important, so QDSH can be approximated by the quantity: o -= Cp(Tsat)S H° QDSH --
(type A)
(A13)
Denoting the value of C O P obtained by using W ° and Q~,SHin Equation (A 12) as COP °, the following expression is obtained:
COP ° - ( L c + Q ~,SH)/L,,t. (A V~,/~). (T~t/A T~,,)
(A 14)
where Lsa t and A~a t denote quantities evaluated at T~t, and Q~sH is zero for type B fluids and is given by Equation (A13) for type A fluids. The only other quantity to be estimated in addition to those already needed for SH ° and W ° is another latent heat value, L c. As A V,~t~ ~,t unless ~,t is very close to Tcrit, whilst V~~ V~atunless SH ° is very large, the volume factor A ~ssat/ rarely deviates much from unity. Thus C O P ° is given approximately by (Lc//5,,,t)(~at/A T~t) in all cases. It should be noted that: 1. COP depends on the fractional rate of change of latent heat with temperature and not, as is often suggested, on the actual value of latent heat; and 2. the limiting value of COP in an IVC cycle is ~a,/A ~a, rather than the Carnot value of Tc/A~a .
Accuracy of these approximations To demonstrate the validity of the above approximations, the values of SH ° and COP ° obtained using them can be compared with the corresponding values of SH and C O P obtained using published entropy and enthalpy data. Table AI shows the results for four more or less conventional refrigerants working between 40 and 90°C, and also a perfluoro compound that has been considered for use in high temperature heat pumps, P P I , working between 100 and 150°C. It can be seen that the approximations are remarkably good, with SH ° differing from SH by < 1 K, and COW differing from COP by < 1~o in all cases.
The theoretical performances of some 250 potential work fluids in vapour compression heat pumps condensing at 150°C and evaporating at 100°C have been predicted, using expressions for coefficient of performance (COP) and minimum superheat that involve only easily accessible physical properties. Expected correlations were found between COP and critical temperature, between specific compressor displacement and normal boiling point, Tbp,and between condensing pressure and Tbp.Correlations were also found between minimum superheat and both molecular weight and critical pressure. From these correlations, the desirable basic properties of a high temperature heat pump fluid are deduced. The principle of corresponding states is invoked to explain the connection between minimum superheat and critical pressure, and hence the reason why perfluorinated compounds tend to make poor work fluids. (Keywords:heat pumps;heat pumpfluids;thermodynamics)
Fluides pour les pompes fi chaleur/t haute tempbrature Les performances th~oriques d'environ 250 fluides actifs possibles dans les pompes ~ chaleur ~ compression de vapeur condensant & 150°C et kvaporant ~ IO0°C ont ~t~ pr~vues ~ l'aide d'expressions du coefficient de performance (COP) et d'une surchauffe minimale ne comprenant que les propri~t~s physiques facilement accessibles. On a trouvd des corrdlations entre le COP et la temperature critique, entre le ddplacement sp~cifique du compresseur et le point tf ~bullition normal, Tbp, et entre la pression de condensation et Tbr On a trouv~ aussi des correlations entre la surchauffe minimale, d'une part, et la masse molkculaire et la pression critique, ~fautre part. A partir de ces correlations on d~duit les proprikt~s fondamentales souhaitables d'un fluide pour pompe ~ chaleur ~ haute temperature. Le principe des dtats correspondants est invoqu~ pour expliquer la relation entre la surchauffe minimale et la pression critique et ainsi la raison pour laquelle les compos~s perfluor~s ont tendance ~ faire de mauvais fluides actifs.
(Mots cl6s: pompes ~tchaleur; fluides pour pompe fi chaleur; thermodynamique)
The maximum condensing temperature currently available from commercial vapour compression heat pumps is ~ 120°C, this being the maximum temperature for which Rl14 is a suitable work fluid. To go to higher temperatures a different fluid is needed, and all of those previously proposed (e.g. Rl13, R216, Fluorinol, methanol, PP1, water) have at least one major problem, be it toxicity, flammability, poor thermodynamic performance o r insufficient thermal or chemical stability. Two possible reasons for this are that previous studies have been blinkered in their choice of fluids, or that the ideal high temperature work fluid is an unattainable goal. The fluids considered for heat pump use are generally restricted to those for which comprehensive thermodynamic data are available, so that the various heat pump performance parameters can be evaluated directly from tables or charts. In the present search for a fluid suitable for 150°C condensing, a wider range of compounds was considered, including some specially-synthesized fluorine compounds, few of whose properties were known. This forced the author to develop a method of estimating the thermodynamic performance parameters of any fluid from the sparsest of basic data. With this method, it was possible to analyse a number of novel compounds that were thought to have potential as high temperature work fluids, and it began to emerge that ideal fluids from the point of view of stability, toxicity and flammability tend to be poor thermodynamically. Thus, the study was expanded to include a large number of compounds that, 014(L7007/86/010043~)8503.00 © 1986 Butterworth & Co (Publishers) Ltd and IIR
despite having obvious disadvantages in other respects, at least looked as if they might be thermodynamically attractive.
Thermodynamic performance parameters To make a thermodynamic comparison of heat pump fluids, it is convenient to consider them in an ideal vapour compression (IVC) cycle. This is defined as one in which the fluid is evaporated isothermally, compressed isentropically, condensed isothermally, and expanded isenthalpically: there is no liquid subcooling, but there is a minimum amount of vapour superheat to prevent liquid compression. In general, the superheat of a vapour will either increase or decrease during isentropic compression according to the particular fluid involved. For those fluids where it increases (type A fluids), the minimum superheat, SH, refers to the discharge superheat resulting from compressing initially saturated vapour (Figure la), whilst for those fluids where superheat decreases (type B fluids), SH refers to the suction superheat required so that the compressed vapour is just saturated (Figure lb). The three most important thermodynamic performance parameters for a heat pump fluid are: 1. coefficient of performance (COP), defined as the ratio of condenser heat output to compressor work input; 2. specific compressor displacement (SCD), defined as the volume of vapour drawn into the compressor per unit condenser heat output; and
Rev. Int. Froid 1986 Vol 9 Janvier
43
Fluids for high temperature heat pumps: lid. P. Bertinat
T~,T~
Nomenclature
COP COP ° Co ACp L
Lc, Lsat MW n Pc Pcrit QDSH
SCD
SH SH 1
SH °
Lp Tcrit
Coefficient of Performance (the ratio of condenser heat output to compressor work input) Approximate COP obtained using W ° and Q~sH Specific heat at constant pressure Difference between ideal gas and real gas values for Cp Latent heat of vaporization Values of L at condensing temperature Tc and at mean saturation temperature T~a, Molecular weight Number of atoms per molecule Condensing pressure Critical pressure Heat associated with desuperheating a type A fluid after compression Approximate value of QnsH using SH ° and Cp(~t) Specific compressor displacement (the volume of vapour drawn into the compressor per unit condenser heat output) Minimum superheat in an IVC cycle (always positive) The quantity (1-~) ATsm, positive and equal to SH ° for a type B fluid, negative and equal to - S H ° for a type A fluid Approximate value of SH, equal to
11-
Normal boiling point Critical temperature
Vsat, K
AV AVsa, W Wo
Greek letters
O"
#D Z
C O P ~ C O P ° = (Lc + QDSH)/£sat • (A ['(sat/Vs). ('F--sat/A T-sat) (1)
zIAT~t
(2)
where: ATsa t is the difference between the condensing and evaporating temperatures Tc-TE; Tsat is the mean saturation temperature, (Tc+ TE)/2; Lc and L~at are the latent heats of vaporization at Tc and Tsar; AV~at is the difference between vapour and liquid specific volumes at T~t; and ~ is the specific volume of superheated vapour at the mean superheat temperature. X is the dimensionless ratio (ilL V/CpA V) evaluated at Ts~,,where fl is the isobaric thermal expansion coefficient and Cp is the isobaric specific heat. Q~sR is the (approximate) heat associated with desuperheating after compression, equal to Cp(Tsat)SH° for a type A fluid and zero for a type B fluid. The specific compression displacement (SCD) is given by: L ° S C D ~~ V1/(cWQDsH)
(3)
where V~ is the specific volume at the compressor inlet,
Int. J. Refrig. 1986 Vol 9 January
Isobaric thermal expansion coefficient, ( 1/V)(OV/¢3T)p Intermolecular interaction parameter Molecular size parameter Molecular dipole moment Superheat parameter (BL V/CpA V) Value of Z at Tssat
General terms Type A fluid Type B fluid IVC cycle
The first and third of these can be approximated by the following expressions (see Appendix):
44
v1
EIAT:~,
3. minimum superheat (SH), defined above.
sn~sn°~[1-
~at
Condensing and evaporating temperatures Mean saturation temperature, (Tc + TE)/2 Temperature difference, Tc - TE Specific volume of vapour entering compresso r Specific volumes of vapour at ~., and at mean compression temperature Difference between vapour and liquid specific volumes Value of A V at ~at Compression work Approximate W obtained by using ~at values
Fluid that superheats during isentropic compression Fluid that desuperheats during isentropic compression Ideal vapour compression cycle as defined in text
and the approximation involved is that of Q~sH (see above and Appendix). Two other important parameters are the saturation pressures at Tc and TE. Estimates of all the quantities in Equations (1)-(3), apart from Cp, can be made from a fluid's critical temperature, T~nt, critical pressure, Petit, and normal boiling point, Tbp, using the principle of corresponding states. In its simplest form, this principle asserts that the equation of state of a substance depends only upon its T~rit and Pcrit, but a more useful form is the three-parameter version of Pitzer 1 which introduces an 'acentric factor' to take account of the shape of the molecule as well. The Lee and Kesler method z'3 is a convenient way of using this acentric factor, and although the method was developed specifically for non-polar molecules, its results are surprisingly accurate for both polar and non-polar molecules. All the fluids in this study were analysed using the Lee and Kesler method. Not even T~.t and Petit values were available for many of the fluids to be assessed, so these values also had to be estimated. This was done using the group contribution method of Lydersen 4' 3, or a modified version of this in the case of some of the highly fluorinated compounds. The only input data required were Tbp and the structural chemical formula. To estimate Cp, the appropriate ideal gas value was first obtained, either from the literature or using the group
Fluids for high temperature heat pumps." M. P. Bertinat a /
---
\
(/
I
rc
/
SH
\
X\
I
/
TE
/
\
S b
..._
I-.
I SH m
"E
/
~-
•
/
/ /
S Figure 1 (a) Temperature--entropy diagram for a type A fluid IVC cycle. Compression begins on the saturation curve ( - - - ) . (b) Temperature-entropy diagram for a type B fluid IVC cycle. Compression ends on the saturation curve ( - - - ) Figure l(a) Diagramme temp&ature-entropie pour un cycle I V C (~ compression de vapeur id~ale) de fluide de type A. La compression d~bute sur la courbe de saturation ( - - - ) . (b ) Dia#ramme temp&ature-entropie pour un cycle IVC de fluide de type B. La compression finit sur la courbe de saturation ( - - -)
contribution method of Benson et al.5'3. (The latter again required the structural formula.) To this was added the real fluid correction, ACp, calculated by the Lee and Kesler method. Thus the only essential data required to estimate the performance parameters for any fluid were its normal boiling point and its structural chemical formula. However, known values of T~nt, Peat and Cp were used, when available, in preference to estimated ones.
pounds: less attractive than perfluoro compounds for reasons of stability, toxicity and flammability, but thermodynamically better; 4. all the appropriate members of those common aliphatic series that it was thought might be sufficiently stable and unreactive: most of these are highly flammable but many of them looked good thermodynamically; 5. all the fluorine derivatives of the series in 4, above, for which the boiling points could be found, and also in some cases chlorine derivatives, although the latter were not expected to be sufficiently stable for 150°C use: many of these also looked good thermodynamically; 6. the few inorganic compounds that had suitable T~,t and Tbp: apart from water, these are all far too toxic or unstable, or both, for serious consideration, but they were included for completeness. Altogether the list comprised 247 fluids, seven of them inorganic and the rest organic. Although many of these can be immediately ruled out for various reasons, it is instructive to look at how the values of the three thermodynamic parameters, COP, SCD and SH, correlate with the basic physical properties of the fluids. When the COP of each fluid, evaluated for a 100/150°C IVC cycle, is plotted against its molecular weight (MW), its normal boiling point (Tbp), its critical temperature (T~at) and its critical pressure (Pc.t), it is apparent that COP depends strongly on T~.t, very weakly on Tbp,and not at all on MW or Pent (although the maximum value of COP at a g i v e n Vcrit does seem to depend upon Pcrit)" Figure 2 shows the T~.t plot. The strong positive correlation (high T~.t high COP) can be explained by the decrease in (Lc/[sat) as the critical temperature is approached. The weak correlation with Tbp is probably an indirect reflection of this since Tcnt and Tbp are related. A good work fluid should have a COP of 1>6, and Figure 2 indicates that Tc.t~>200°C is probably a sufficient (though not necessary) condition for a fluid to satisfy this criterion. Similarly, SCD appears to depend strongly on Tbp but only weakly on T~ntand not at all on MW or P~nt. Figure 3 shows the Tbp plot, and the positive correlation (high Tbp ~ high SCD) is a result of the fact that the saturated vapour pressure at a fixed evaporating temperature (100°C) is closely related to Tbp. The weak correlation of 8.0 7.5
Analysis of 250 fluids The aim of the investigation was to find the best fluid for use in a heat pump condensing at 150°C and evaporating at 100°C, so the initial selection criteria were Tcrit ~ 170°C, to ensure that (Lc/E~t) was reasonably close to unity, and Tbp~<100°C, to ensure that pressures were never sub-atmospheric. A list of fluids was drawn up consisting of the following categories: 1. commercially available perfluoro compounds such as perfluoro-n-hexane (PP1): these are attractive because in general they are chemically stable, non-toxic and nonflammable, but unfortunately none looked very good thermodynamically; 2. specially synthesized perfluoro compounds: results the same as 1 above; 3. specially synthesized partially fluorinated com-
7.0 6.5
.0 ÷
4-
6.0 5.5 5.0 4.54.0 4150
I 200
I 250
I 300
I 350
400
Terlt (°C}
Figure 2 COP versus critical temperature for 240 organic (+) and seven inorganic (I-q) fluids assuming an IVC cycle evaporating at 100°C and condensing at 150°C Figure 2 COP en fonction de la temperature critique pour 240 fluides oroaniques (+) et 7 fluides inoroaniques (D) en supposant une temperature d'$vaporation du cycle I V C de IO0°C et une temperature de condensation de 150°C
Rev. Int. Froid 1 9 8 6 Vol 9 Janvier
45
Fluids for high temperature heat pumps." M. P. Bertinat 1.2
1.0
+
~+,p/'~'÷+
,~ 0.8
% r~ 0.6 0.4
~.÷
0.2-
0.0 0
+
. ~"°*
*t';g
+
I
I
20
40
Tbp
I
I
60
80
T~ri,oce
(4)
P c r i t o c / 3 / o -3
(5)
100
(°C)
Figure 3 Specific compressor displacement versus normal boiling point for 247 fluids. + , Organic fluids; [-], inorganic fluids Figure 3 D~placement sp~vifique du compresseur en fonction du point tl'~bullition normal pour 247 fluides. +, Fluides oryaniques; IS], Jluides inorganiques
SCD with T.it again reflects the connection between Tbp and T~,,. A good work fluid should have a small SCD, preferably <0.4 m s M J- ~, and to satisfy this criterion, a necessary condition would appear to be Tbp~<80°C and a sufficient condition Tbp~40°C. The behaviour of the third performance parameter, SH, can be seen by plotting the quantity SH ~= (1 - ~)A T~,, against the four basic physical parameters. Positive values of SH~ imply suction superheats of type B fluids, whilst negative values imply discharge superheats of type A fluids. As can be seen from Figures 4 and 5, there is an obvious positive correlation with molecular weight (high MW ~ high SH0, although the scatter is rather high, and an even stronger negative correlation with P~t (high P,,t ~ low SH~). Fluids with low Pcrit have large values of SH~, i.e. they are strongly type B. Fluids with very high P~r~thave negative values of SH~, i.e. they are type A. The cross-over point seems to be around P , , = 48 bar, and an ideal fluid will thus have Petit somewhere near this value. It is also likely to have MW in the range 50-150. A fourth parameter of importance for a high temperature work fluid is its saturation pressure at the condensing temperature. If this condensing pressure, Pc, is significantly higher than standard engineering values, say ~ 20 bar, then special components will be required in the construction of the heat pump and the cost will be greatly increased. Plots of Pc against MW, Tbp, T,, and P , , , indicate a strong correlation only with Tbp.This is not surprising since Tbp and Pc are both simply aspects of the variation of saturation pressure with temperature. A necessary condition for Pc ~<20 bar would appear to be Tbp~>25'C, and a sufficient condition Tbp> 50°C.
Molecular implications Several deductions can be made from the above analysis about the kind of molecule likely to make a good heat pump fluid. There are many aspects of a molecule that might be important, such as its size, shape, mass, polarity, bond strengths, etc. but most of these can be considered in terms of their effects on the two fundamental molecular forces, namely the forces between the atoms within a molecule (intramolecular forces or bond strengths) and the forces between different molecules (intermolecular forces). The
46
former determine the basic chemical and thermal stability of the molecule, whilst the latter determine the thermodynamic properties of a fluid composed of such molecules. According to the principle of corresponding states, the critical temperature and pressure of a fluid consisting of simple, non-polar, spherical molecules depend upon the strength of the intermolecular interactions, e, and the linear dimensions of the molecules, a, according to the simple relations6:
Int. J. Refrig. 1986 Vol 9 January
Although few of the fluids involved here have molecules that even approximately fit the description non-polar and spherical, these simple relations do seem to account, qualitatively at least, for some of the variations in their critical properties. Consider for instance, the fluids whose critical properties and dipole moments, #D, are given in Table 1. From the first two entries it can be seen that in simple alkanes, increasing the carbon chain length raises Tcrit but l o w e r s Pcrit" This can be explained by an increased 40
+ ~**+ * + *
20 0 -20 z~
t/3
+
Q 4. o
40
g
°
-60 D
-80 -100 -120
D 0
I
I
I
I
I
I
I
I.,
50
100
150
200
250
300
350
400
450
MW
Figure 4 Minimum suction superheat versus molecular weight for 247 fluids. +, Organic fluids; D, inorganic fluids. Negative values imply positive discharge superheat (type A fluids) Figure 4 Surchauffe minimale d /'aspiration en Jonction de lu masse moleculaire POUr 247 fluides. +, Fluides organiques; D, fluides inorganiques. Les valeurs nd~gatives impliquent une surchau~fe au refoulement positive (.[luides de type A) 40
*.,. *+.,. + ÷÷
01
*
*
-20 -40
÷
o
o
D
-80
-
-100
-
-120
I
101
I
l
I
l I Ill
i a
102
i
,
i
i i
ii 103
Pcrit (bar)
Figure 5 Minimum suction superheat versus critical pressure for 247 fluids. + , Organic fluids; [-], inorganic fluids Figure 5 Surchauffe minimale d I'aspiration en fonction de la pression critique pour 247 ,fluides. + , F/uides organiques; El, .fluides inorguniques
Fluids for high temperature heat pumps. M. P. Bertinat Table 1
Critical properties and dipole moments of a selection of organic fluids Tableau 1 Propridt~s critiques et moments dipolaires de quelques fluides
organiques Tcrit
Pcrit
//D
Fluid
(°C)
(bar)
(Debyes)
C5H12 C6H 14 C6Fla C7F16 CH3CH 3 CHaCH2F CH3CH2NH z CH3CH2OH
196 234 178 202 32 102 183 243
34 29 18 16 48 49 55 64
0 0 0 0 0 2.0 1.3 1.7
Although the actual specific heat will generally be less than the classical value because of quantization of the vibrational energy levels, Cp can still be expected to depend upon n. Moreover, since the molecular volume is also likely to depend upon n, Cp can be expected to be a function of tr 3, the molecular volume parameter. Thus: L ,-~s
(6)
and: C o ~ f(n) ,-~f(a 3)
(7)
whence: interaction strength accompanied by a proportionately greater increase in effective molecular size, both expected effects of increasing the length of the molecule. The same effect is seen in the next two fluids, which are perfluoroalkanes. However these perfluoroalkanes have lower T~nt and considerably lower Pent than the corresponding alkanes, and this can be explained by the weaker interactions and larger molecules of the perfluoroalkanes. Even fluids in which the molecular interactions are very different from those of simple fluids, seem to show trends in T~nt and Pent in qualitative agreement with the simple relations given above. Thus the next two fluids in Table I, ethane and ethyl fluoride, show the effect of a molecular dipole moment on T~nt and P~nt: both these quantities increase, consistent with the fact that interrnolecular forces are increased by the presence of a permanent dipole moment. Even higher values of T~ntand Pent are seen with the last two entries in the Table, ethylamine and ethanol, consistent with the fact that these fluids are subject to even stronger intermolecular forces as a result of hydrogen bonding. In the section 'Analysis of 250 fluids', it was shown that a good heat pump fluid should have a high T~nt,to give a high COP, and a moderately high P~nt, to give a low superheat. The former requirement was explained by the relatively rapid reduction of latent heat with temperature as T, it is approached, but the P¢~t requirement was unexplained. Now this requirement can also be understood, at least qualitatively. According to Equation (2), SH 1 is proportional to (1 -~), where the quantity f( = fl VL/CpA V is a measure of the slope of the vapour saturation curve on a T S diagram (see Appendix). The variation of SH 1 with P~,t is thus analogous to the variation of SH~ with Z, since SH~ decreases with increasing P~dt(or ~) and goes through zero for P~m= 48 bar (~ = 1). The problem then is to find the connection between Pent and ~. Z can be considered to be the product of three separate factors, namely L/Cp, fl and V/A V, and the last of these can be ignored since it is generally very close to unity unless T is very close to T~dt. Consider, however, the L/Cp term. The molar latent heat, L, can be expected to depend linearly upon the strength of the intermolecular interactions, e, since both quantities are directly related to the energy required to separate molecules. The molar specific heat, Cp, on the other hand, might be expected to increase with n, the number of atoms in each molecule, since classically, the total kinetic energy of an n-atom molecule is just 3/2 n k T (Reference 7), and this will give a contribution to molar specific heat proportional to n.
L/Cp
g/f(G 3)
~
(8)
which implies that L/Cp, and hence X, depends upon e and a in much the same way as Pent does [Equation (4)]. The validity of Equations (6)--(8) can be seen from Figures 6-8 where the data for the 14 organic fluids listed in Table 2 are plotted as L versus T~nt(since T~n,~ e); Cp versus n; and L / C p versus Petit. The agreement with the predictions is obvious. The relatively small range of T,i t covered by the 14 fluids (450-540 K) means that most of the correlation between L/Cp and P~ntcomes from the 1/Cp variation. (Note that these data relate to a constant reduced temperature, T/T~n t = 0.9, rather than a constant 30 25 A
2O
4.
"7.
"6 E
÷
15
v
10i
5 ~
0 160 Figure 6
I
I
I
I
I
180
200
220
240
260
280
Tcrlt (°C) Latent heat of vaporization versus critical temperature for the
fluids in Table 2 Figure 6 Chaleur latente de vaporisation en fonction de la temperature critique pour les fluides du Tableau 2 ~0,
400 4-
'7,
"6 300 E 200 -
J
1000 0
I
I
I
I
5
10
15
20
25
Number of atoms per molecule, n Figure 7 Specific heat at constant pressure versus number of atoms [aer molecule for fluids in Table 2 Figure 7 Chaleur massique d pression constante en fonction du nombre d'atomes par moldcule pour les fluides du Tableau 2
Rev. Int. Froid 1986 Vol 9 Janvier
47
Fluids for high temperature heat pumps." M. P. Bertinat atoms), which means large n, small P , i , and large SH 1. Polar molecules, and molecules that are subject to hydrogen bonding, are generally good because their relatively large intermolecular forces mean that one can get a high enough Tent with quite small molecules, corresponding to high Pcri~ and low SH t. However, the interactions can be too strong and the molecules too small. With the alcohols for instance, whose molecules undergo hydrogen bonding, the smallest members of the
actual temperature, to prevent the variation of L with T/T~t overshadowing its variation with e.) The third factor of X, namely fl, has relatively little effect at constant reduced temperature, as can be seen by comparing Figure 9, where flL/Cp is plotted against Petit, with Figure 8. The effect of fl is to sharpen slightly the correspondence with Pcrit. However, it should be noted that if fluids are compared at different reduced temperatures (for example at constant actual temperature) then/3 is much more important since both fl and L vary more rapidly with T/rcrit than does their product, ilL. Note that according to Figure 9,/3L/Cp = 1 corresponds to P~r~t~50 bar for these 14 fluids, which compares favourably with the findings in the section 'Analysis of 250 fluids', that for SH .~0, P~nt~48 bar. It would appear then that the observed correlation between SHx and Pc~ is a reflection of the dependence of both Cp and Petit o n the number of atoms per molecule, n. Moreover, by plotting flL/Cp against n as in Figure 10, it can be deduced that the optimum value of n, corresponding to SH ~0, is probably ~ 10. It is now possible to see why certain fluids came out badly in the thermodynamic analysis whilst others came out well. Perfluoro compounds are bad because of the relative weakness of their intermolecular interactions. To get a high enough T~ntto give a reasonable COP at 150°C, one has to go to quite large molecules (at least six carbon
2.0
1.5
0.5
0.0 0
I 20
I 10
I 30
I 40
I 50
I 60
I 70
80
Pcrit (bar) Figure 9 flL/Cp versus critical pressure for the fluids in Table 2 Figure 9 flL/Cp en fonction de la pression critique pour les fluides du Tableau 2
250
2.0
200
1.5150
1.0 100
0.5
50 Ot .... 0
I 10
I 20
I 30
I 40
I 50
I 60
I 70
0.0 80
Pcr|t (bar) Figure 8 Ratio of latent heat to specific heat versus critical pressure for the fluids in Table 2 Figure 8 Rapport de chaleur latente [z la chaleur massique en fonction de la pression critique pour les fluides du Tableau 2
0
I
I
I
I
5
10
15
20
25
Number of atoms per molecule, n flL/Cp versus number of atoms per molecule for fluids in
Figure 10 Table 2 Figure l0 flL/Cp en fonction du numbre d'atomes par molecule pour les fluides du Tableau 2
Table 2 Properties of a selection of organic compounds to show the connection between X and Pcrit. Values of L, Cp and fl are all estimated for a reduced temperature (T/Tcrit) of 0.9 Tableau 2 Propri~t~s de quelques compos~s organiques pour montrer la relation entre Z et P,.rir Les valeurs de L, Cp et fl sont routes estim~es pour une temperature r~duite (T/T.,,) de 0.9 Compounds
n (atoms/molecule)
Tcrit (°C)
Pcrit (bar)
L (Jmol-t)
Cp ( J m o l - t K 1)
103 x fl (K t)
Methanol Ethanol Propanol Diethyl ether Butyl ethyl ether Di-isopropyl ether Ethylamine P ropylamine Butylamine Ethyl chloride R 113 Heptane Perfluoroheptane Perfluorohexane
6 9 12 15 21 21 10 13 16 8 8 23 23 20
240 243 264 193 258 227 183 224 251 187 214 267 202 178
79.5 64 51 36 30 29 56 47 41 53 34 27 16 18
22 600 24 000 25 100 16 500 21400 18 700 15 700 17 600 19 900 15 700 16 500 19 700 21300 18 900
97 131 168 183 270 255 139 174 214 128 191 291 431 368
7.45 6.83 6.75 8.12 7.23 7.56 8.98 8.08 7.38 8.48 8.35 7.48 7.47 8.16
48
Int, J. Refrig. 1986 Vol 9 January
Fluids for high temperature heat pumps." M. P. Bertinat
series (methanol, ethanol) have too large a Pc,t and give a high discharge superheat (SHt large and negative). The effect is even worse with water, where strong hydrogen bonding and small molecules result in a very high Per~t (221 bar) and a correspondingly high discharge superheat. Moreover, even T¢,~t is too high with water (374°C), since although this implies high COP, it also implies a high Tbp and hence a high SCD. A compromise is obviously desirable.
m
,,, /
/
/ /
/ /
S Figure AI
shown)
///~ /
\X
g
a
e \ \
S Figure A2 Schematic IVC cycle plus general isentrope fg (type A fluid shown) Figure A2 CyclelVCsch~matique+isentropeg~n~ralfg(lefluideAest pr~sent~)
vapour and saturated liquid. Consideration of a type A fluid also leads to Equation (A2). Replacing the integrand in this equation by mid-point values gives an approximate value for W, which is denoted as W°: W ° = 9"s(L/T A V)r,,,A Tsat
Appendix: derivation of equations for COP and minimum superheat Compression work The work done in compressing a vapour isentropically from pressure P~ to P2 c a n be written as:
(A1)
1
where the subscript s denotes constant entropy, and the fact that d H = T d S + V d P has been used. Consider the T-S diagram for a type B IVC cycle shown in Figure AI: here ab corresponds to isobaric superheating, be to isentropic compression, and mn to a general isobar intermediate between P, and P~. Since (VdP)~ = (V, dPn) = (V, dP~) the Clausius-Clapeyron equation gives: gn(g/rAg)m dTm
Cycle I VC sch~matique+ isobare g~nkralmn (le fluide Best
/
/
1 Pitzer, K. S., Curl, R. F. The Thermodynamic Properties of fluids Institution of Mechanical Engineers, London (1957) 2 Lee, B. I, Kesler, M. G. A generalised thermodynamic correlation based on three-parameter corresponding states, Am lnst Chem Eng J (1975) 21(3) 510-527 3 Reid, R. C., Prausaitz, J. M., Sherwood, T. K. The Propertiesof Gases and Liquids 3rd Edn, McGraw Hill, New York, USA (1977) 4 Lydersen, A. L. Estimation of Critical Properties of Organic Compounds University of Wisconsin College of Engineering Experimental Station, Report 3, Madison, WI USA (April 1975) 5 Benson, S. W, Cruikshank, F. R. et al. Chem Rev (1969) 69 279-324 6 Hirschfelder, J., Curtis, C., Bird, R. Molecular Theory of Gases and Liquids John Wiley and Sons, New York, USA (1964) Ch. 4 7 Feynman, R. P., Leighton, R. B., Sands, M. The Feynman Lectures on Physics Vol. l, Addison-Wesley, London, UK (1965) 39-12
Schematic IVC cycle plus general isobar mn (type B fluid
Figure A l pr~sent~)
References
W=
/a
/
These criteria imply that molecules should be fairly small ( ~ 10 atoms per molecule) and that they should interact with each other fairly strongly. Unfortunately, this seems to rule out the perfluoro compounds, despite their being ideal from several points of view (stability, toxicity, flammability), becuase they generally exhibit relatively weak intermolecular interactions.
(Vd P)~
n
/ /
1. high T~nt,to give near unity (Lc/L~at) and hence large COP; 2. fairly low Tbp, to give small V1 and hence small SCD, but not so low as to give excessive discharge pressure; and 3. fairly high P~nt, to give flL/Cp .~ 1 and hence small SH.
dHs=
I m
From a theoretical study of 250 potential work fluids for high temperature compression heat pumps, it appears that to be thermodynamically suitable a fluid should have:
1
I
/
Summary and conclusions
W=
I
(A2)
where L denotes latent heat of vaporization and A V the difference between the specific volumes of saturated
(A3)
where ~at=(Tc+TE)/2, A T s a t = T c - T E , and ~ is the specific volume at T=(Tb+T~)/2 and P=P~t(~,t). The problem of estimating W has thus been reduced to that of estimating a latent heat, a liquid density and two vapour specific volumes, all of which can be done by standard methods. However, since the temperature to which corresponds depends on Tb, the amount of superheat implicit in the IVC cycle must first be determined before Equation (A3) can be used. Minimum superheat Consider the T S diagram for a type A IVC cycle shown in Figure A2. Here ba corresponds to isobaric desuperheating, eb to isentropic compression, and fg to a general isentrope intermediate between Sa and So. The superheat at b is given by:
SH =
dT~
(A4)
and since at constant pressure T d S = Cp dT (Cp is the specific heat at constant pressure), whilst dS~ = dSr, this
Rev. Int. Froid 1986 Vol 9 Janvier
49
Fluids for high temperature heat pumps: M. P. Bertinat can be written as: b
SH =
fa(T/Cp)g
dSf
(A5)
Now using one of Maxwell's relations, dSf can be written:
d S f = (C p/ T )rd Tf - (fl V )rdP r
(A6)
where fl is the isobaric coefficient of thermal expansion, (1/V)(OV/t~T)p, from which the Clausius-Clapeyron equation gives: dS r= (Cp/T)f[ 1 - (ilL V/CpA V)] 6t Tr
(T/Cp)g(Cp/T)f( 1 - Zr) dTf
(A8)
where the dimensionless number Z has been defined by:
Z =- (ilL V/CpA V)~,
(A9)
The same Equation (A8) results from considering the suction superheat necessary for a type B fluid except that the limits on the integral are reversed. Since SH as defined is positive, this implies that Z is > 1 for a type A fluid but < 1 for a type B fluid, and in general it can be written that:
(T/Cp)p(Cp/T)~,]I --)(1dTsat
SH =
(A10)
~TF?
where SH is discharge superheat for X> 1 and suction superheat for Z < 1. An approximate value can be obtained by replacing the integrand with mid-point values (as with W °) and noting that the first two factors tend to cancel each other out. Thus SH ° is defined as: S H ° ~ I 1 - ~[AT~,
(All)
where ~-X(T=0. The estimation of SH has now been reduced to the estimation of the same quantities as for W (specific volumes and latent heat at T~t) plus the vapour specific heat also at ~a~. Note that the ideal work fluid will have ~ ~ 1.
Coefficient of performance The COP in an IVC cycle is given by: COP = (Lc + QDSH)/W
(A12)
where QDSHis the heat associated with desuperheating the high pressure vapour prior to condensing it. For a type B fluid, QDSH=0, but for a type A fluid it is given approximately by Cp(~)SH °, where Tp is the mean
50
Int. J. Refrig. 1986 Vol 9 January
type, S H et COP ~tant obtenu en utilisant les valeurs publi~es de l'enthalpie et de I'entropie
Fluid
(-)
SH (K)
COP' (-)
R21 R 12B 1 R 113 R 114 PP1
1.28 1.04 0.71 0.72 0.41
14.0 1.9 14.6 14.2 29.3
6.15 5.76 6.09 5.39 5.23
Type
SH (K)
COP (-)
A
14.5
A B B B
2.2 14.0 14.1 30.0
6.16 5.76 6.06 5.39 5.27
(A7)
Thus from Equations (A5) and (A7): SH =
Table AI Values of ~, SH '~ and C O P ° for five fluids compared with their type, SH and COP obtained using published enthalpy and entropy data Tableau A 1 Valeursde ~, S H et C O W pour 5 fluides compares avec leur
desuperheating temperature, (Ta+Tb)/2. As QDSH is generally small compared with Lc, the difference between Cp(~) and Cp(T~t) is not important, so QDSH can be approximated by the quantity: o -= Cp(Tsat)S H° QDSH --
(type A)
(A13)
Denoting the value of C O P obtained by using W ° and Q~,SHin Equation (A 12) as COP °, the following expression is obtained:
COP ° - ( L c + Q ~,SH)/L,,t. (A V~,/~). (T~t/A T~,,)
(A 14)
where Lsa t and A~a t denote quantities evaluated at T~t, and Q~sH is zero for type B fluids and is given by Equation (A13) for type A fluids. The only other quantity to be estimated in addition to those already needed for SH ° and W ° is another latent heat value, L c. As A V,~t~ ~,t unless ~,t is very close to Tcrit, whilst V~~ V~atunless SH ° is very large, the volume factor A ~ssat/ rarely deviates much from unity. Thus C O P ° is given approximately by (Lc//5,,,t)(~at/A T~t) in all cases. It should be noted that: 1. COP depends on the fractional rate of change of latent heat with temperature and not, as is often suggested, on the actual value of latent heat; and 2. the limiting value of COP in an IVC cycle is ~a,/A ~a, rather than the Carnot value of Tc/A~a .
Accuracy of these approximations To demonstrate the validity of the above approximations, the values of SH ° and COP ° obtained using them can be compared with the corresponding values of SH and C O P obtained using published entropy and enthalpy data. Table AI shows the results for four more or less conventional refrigerants working between 40 and 90°C, and also a perfluoro compound that has been considered for use in high temperature heat pumps, P P I , working between 100 and 150°C. It can be seen that the approximations are remarkably good, with SH ° differing from SH by < 1 K, and COW differing from COP by < 1~o in all cases.