Preliminary selection of R-114 replacement refrigerants using fundamental thermodynamic parameters (RP-1308).

INTRODUCTION

Over the last 25 or so years, the worldwide phase-out of chlorofluorocarbons (CFCs) and hydrofluorochlorocarbons (HCFCs) has led to active research and development programs by the HVAC&R industry, manufacturers, universities, and governments with the aim of identifying and developing new fluids and equipment. The most commonly pursued short-term solution is to retrofit CFC applications with appropriate HCFCs and hydrofluorocarbons (HFCs), and longer-term solutions include replacing CFC and HCFC applications with appropriate HFCs or "natural" (e.g., water, air, ammonia, carbon dioxide, hydrocarbon) refrigerants and/or to develop new equipment and cycles. The twin environmental concerns of ozone depletion and global warming are the principal driving forces behind these changes. While the Montreal Protocol and its amendments have addressed the ozone depletion problem, more recent initiatives (for example, the Kyoto Protocol) are attempting to address the global warming problem. As a response, the industry has developed measures that account not only for a refrigerant's direct contribution but also a refrigerant's indirect contribution to global warming. The total equivalent warming impact (TEWI) is one such measure that accounts for a refrigerant's direct contribution through leakage of the refrigerant into the atmosphere and its indirect effect related to the amount of carbon dioxide generated from burning fossil fuels to power the refrigeration system. Another similar measure is the life-cycle climate performance (LCCP), which, in addition to including the effects captured by TEWI, also attempts to account for other indirect effects related to the manufacturing, transporting, recycling, etc., of the refrigerant.

Even though CFCs are scheduled for phase-out, many will still be used for some time. For example, R-11, R-12, R-113, and R-114 are presently used in industrial processes operating under high ambient conditions and in high-temperature heat pumps, with R-114 being the most widely used refrigerant in these applications. However, as this equipment is being considered for replacement or for new applications, alternative heating technologies are being considered since no known and viable non-CFC retrofit refrigerants are available. Moreover, with the recent increase in primary energy costs and expected price pressures for primary energy persisting into the near future, it is anticipated that there will be a renewed interest in high-temperature heat pumps for many possible applications. Therefore, a strong need exists to identify and develop new refrigerants and technologies to allow for the continued application and expanded use of high-temperature heat pumps despite the scheduled phase-out of CFC refrigerants. The scope of this paper, however, is somewhat more limited than finding direct replacements for these CFC refrigerants. In particular, what is addressed is this question: What should be the thermodynamic parameters of a replacement refrigerant for R-114 in high-temperature heat pumping applications?

When considering replacement refrigerants, either for existing or new applications, a good starting point for the performance potential of the various alternative refrigerants in an idealized vapor-compression refrigeration cycle. This approach avoids unnecessary, costly, and time-consuming experimentation and detailed system modeling. In particular, simplified analytical approaches (see, for example, Brown [2007]) can indicate a few promising refrigerants from a much longer list of potential refrigerants. This shortened list can then be investigated in depth using conventional approaches such as experimentation or detailed system modeling. Regardless of which approach one chooses to pursue, typical measures of performance potential for heat pumping applications include the heating coefficient of performance ([COP.sub.H]) and the volumetric heating capacity (VHC), where [COP.sub.H] is a measure of energy efficiency (operating costs [Didion 1999]) and VHC indicates equipment size (capital costs [Didion 1999]).

It is known from previous studies (e.g., McLinden [1990], Morrison [1994], Didion [1999]) that properties and characteristics such as cost, stability, toxicity, flammability, environmental impact, liquid viscosity, liquid thermal conductivity, materials compatibility, solubility with lubricants, etc., are all extremely important. As a first-cut approximation, however, the thermodynamic properties critical point temperature and vapor molar heat capacity can provide an indication of how a particular refrigerant will perform in an idealized vapor-compression refrigeration cycle. In particular, increasing the critical point temperature implies a higher [COP.sup.H] and a lower VHC; conversely, decreasing the critical point temperature implies a lower [COP.sup.H] and a higher VHC. Furthermore, molecular complexity provides an indication of the value of the vapor molar heat capacity and thus the shape of the refrigerant's two-phase saturation lines, i.e., its vapor dome. As the vapor molar heat capacity increases, expansion-side losses increase and the likelihood of wet compression increases (to avoid this detrimental effect, larger superheats are required).

In the sections that follow, these previous studies are expanded and it is shown that the critical temperature, the ideal gas specific heat at constant pressure, and the acentric factor largely determine the [COP.sub.H] and VHC in an idealized vapor-compression refrigeration cycle. Simulation results are presented and acceptable ranges for the above-listed thermodynamic parameters are provided for refrigerants operating in typical R-114 heat pumping applications.

OVERALL MODELING APPROACH

As a first step in evaluating the performance potential of a refrigerant in a particular application, one could calculate its [COP.sub.H] and VHC in an idealized vapor-compression refrigeration cycle (see Figure 1), which includes two irreversibilities--one due to superheating of the refrigerant prior to and during compression and one due to a fully irreversible expansion process leading to both lost work potential and lost refrigeration capacity. Careful observation of Figure 1 further shows that the shape of the temperature-entropy (T-s) state diagram and the locations of the application temperatures relative to the critical temperature determine the [COP.sub.H] and VHC (for more detailed discussions, see, for example, Morrison [1994] or Didion [1999]). This idealized vapor-compression refrigeration cycle does not capture all the irreversibilities of a real cycle, e.g., irreversible heat transfers and pressure losses in the heat exchangers. It does, however, provide a good indication of how a particular refrigerant will perform in an actual cycle, particularly if one accounts for compressor irreversibilities via isentropic efficiency. Therefore, one could calculate [COP.sub.H] and VHC in an idealized vapor-compression refrigeration cycle in order to select a few promising refrigerants from a much longer list of potential refrigerants. This shortened list could then be investigated in depth via experimentation and detailed system modeling.

[FIGURE 1 OMITTED]

In a recent paper, Brown (2007) successfully used the Peng-Robinson Equation of State (P-R EoS) to accurately simulate [COP.sub.H] and VHC for a wide range of refrigerants, including R-114, in an idealized vapor-compression refrigeration cycle. In this paper, the P-R EoS implemented in REFPROP 8.0 (Lemmon et al. 2007) is used. In order to use the process described in Brown (2007), one must know several fundamental thermodynamic parameters, namely, the refrigerant's critical temperature [(T.sub.c)], critical pressure [(P.sub.c)], critical density [([rho].sub.c)], acentric factor ([omega]), molecular weight (M), one saturated liquid density [([rho].sub.f)] data point, and the ideal gas specific heat at constant pressure (C.sub.p.sup.o]) as a function of temperature. Brown showed that with these known inputs, one could predict the [COP.sup.H] and the VHC for a group of 24 refrigerants (Table A1) with absolute errors of 1.5% and 2.7%, respectively, compared to the values calculated using the default, high-accuracy equations in REFPROP (Lemmon et al. 2007). It was further shown that for new and alternative refrigerants, where these input data may not be well known, one could (1) use the group contribution methods of Ambrose (see Reid et al. [1987a]) and Joback (see Reid et al. [1987b]) to predict [T.sub.c], [P.sub.c], [[rho].sub.c], and [c.sub.p.sup.0] and (2) use the method of Reid et al. (1987c) to predict [omega]. Following this approach, Brown showed that for the same group of 24 refrigerants, knowing only their normal boiling point (NBP) temperatures and their molecular structures, one could predict the [COP.sub.H] and VHC with absolute errors of 2% and 10%, respectively, compared to the values calculated using default equations in REFPROP (Lemmon et al. 2007).

Here, the approach of Brown (2007) is used to answer the question what should be the fundamental thermodynamic parameters of a replacement refrigerant for R-114 in high-temperature heat pumping applications? (Note: McLinden [1990] used a somewhat similar approach to the one reported in this paper to find "optimum" refrigerants for non-ideal cycles. In particular, McLinden used the principle of corresponding states to determine the optimum [T.sub.c] and optimum [c.sub.p.sub.0] for refrigerator applications.) In this paper, the approach is to parametrically study the effects of [T.sub.c], [c.sub.p.sup.0], and [omega] on [COP.sub.H] and VHC using the P-R EoS, which then allows one to determine the "ideal" R-114 replacement refrigerant. Note: in the following discussion, it should become clearer why [P.sub.c],[[rho].sub.c], M, and [[rho].sub.f] also do not need to be parametrically studied.

In particular, the parametric space is defined by the nondimensional value [[tau].sub.c] of the critical temperature ranging from 0.89 to 1.42, the nondimensional value CP of the ideal gas specific heat at constant pressure ranging from 0.18 to 1.45, and the nondimensional value AF of the acentric factor ranging from 0.59 to 2.14. Note: [[tau].sub.c] = [([T.sub.refrig]/[T.sub.R-114]).sub.c], CP = [([c.sub.p.sup.0]).sub.refrig]/[(['c.sub.p.sup.0]).sub.R-114] calculated at [T.sub.c], and AF = [[omega].sub.refrig]/[[omega].sub.R-114], and Table 1 provides some relevant thermodynamic parameters for R-114.

As previously suggested, it is not necessary to parametrically study M and [[rho].sub.f] since [COP.sub.H] and VHC calculations are independent of them. Therefore, in addition to [T.sub.c], [c.sub.p.sup.0], and [omega], one only needs to consider the possible effects [P.sub.c] and[[rho].sub.c] might have on [COP.sup.H] and VHC. First, [T.sub.c], [P.sub.c], and[[rho].sub.c] are not unrelated but can be related by the compressibility factor:

[Z.sub.c] = [[P.sub.c]/[[[rho].sub.c]R[T.sub.c]]] (1)

where the compressibility factor [z.sub.c] is a function of [T.sub.c], [P.sub.c], and M, and R is the universal gas constant. [z.sub.c] typically ranges in value from 0.22 to 0.30 for a wide range of fluids (Wark 1995). To verify this for refrigerants, 42 typical refrigerants (Table A2) and their known values of [T.sub.c], [P.sub.c], and[[rho].sub.c] were used to calculate [z.sub.c], resulting in a mean value of 0.27, a minimum value of 0.24, a maximum value of 0.28, and a standard deviation of 0.012. Second, since[[rho].sub.c] can be correlated with [c.sub.p.sup.0], the same group of 42 refrigerants was used to develop a power law correlation in [c.sub.p.sup.0]. In terms of nondimensional quantities, the resulting fit having an R-squared value of 0.92 is

[[delta].sub.c] = 1.083[CP.sup.[ - 0.723]], (2)

where [[delta].sub.c] = [([[rho].sub.refrig]/[rho]R-114).sub.c].

Figures 2 and 3 show, for the 42 refrigerants, the actual versus the predicted critical densities and critical pressures, respectively, calculated from Equation 1 with [z.sub.c] = 0.27 and Equation 2 in conjunction with their known critical temperatures. The figures include labels for refrigerants not falling within the [+ or -]10% band and for some typical refrigerants, namely, R-22, R-32, R-114, R-125, R-134a, and R-290. While the predictions show some scatter, they are generally within [+ or -]10%. Therefore, since [P.sub.c] and[[rho].sub.c] can be calculated using Equation 1 with [z.sub.c] = 0.27 and Equation 2, it should now be clearer why only [T.sub.c], [omega], and [c.sub.p.sup.0] need to be parametrically studied.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

RESULTS AND DISCUSSION

As previously discussed, the three variables that affect the shape of the T-s state diagram, and thus ultimately affect [COP.sub.H] and VHC, are [T.sub.c], [c.sub.p.sup.0], and [omega]. First, as [T.sub.c] increases for fixed [c.sub.p.sup.0] and [omega], the shape of the T-s state diagram does not change, but the critical point moves further from the application temperatures (Figure 4a). Second, [c.sub.p.sup.0] is the variable that has the most dramatic effect on the shape of the T-s state diagram. In particular, as [c.sub.p.sup.0] increases for fixed [T.sub.c] and [omega], the magnitude of the slope of the saturated liquid line decreases, whereas the magnitude of the slope of the saturated vapor line increases, eventually becoming infinite and finally decreasing as [c.sub.p.sup.0] increases further. In other words, as [c.sub.p.sup.0] increases, the vapor dome "leans over" to the right (Figure 5a). Third, as [omega] increases for fixed [T.sub.c] and [c.sub.p.sup.0] , the T-s state diagram broadens and the slope of the saturated liquid line decreases slightly (Figure 6a). Figures 4-6 show T-s and P-h state diagrams where each of the nondimensional quantities [[tau].sub.c], CP, and AF, which correspond to the variables [T.sub.c], [c.sub.p.sup.0], and [omega], respectively, are changed parametrically, while the other two are held constant.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

In order to obtain a sense of the performance potentials of generic replacement fluids, [[tau].sub.c], CP, and AF were parametrically varied, where [[tau].sub.c] ranged from approximately 0.89 to 1.42, CP ranged from approximately 0.18 to 1.45, and AF ranged from approximately 0.59 to 2.14. Note: the simulated cycle had a constant evaporation temperature of 26.7[degrees]C (80[degrees]F), a constant condensation temperature of 85[degrees]C (185[degrees]F), a condenser subcooling of 5.56[degrees]C (10[degrees]F), a compressor isentropic efficiency of 85%, and an evaporator superheat that ensured saturated or superheated vapor at the condenser inlet (however, the minimum evaporator superheat was 11.11[degrees]C [20[degrees]F]). Some of the simulation points are shown in Figures 7 and 8 for [COP.sub.H] and VHC, respectively. Note: each of the curves represents parametric changes in only one of the three variables [[tau].sub.c], CP, or AF, while the other two parameters remain constant with values of 1. Figure 7 shows that (1) [COP.sub.H] increases as a strong function of increasing [[tau].sub.c], (2) [COP.sub.H] reaches a maximum at a CP value of approximately 0.5, and (3) [COP.sub.H] increases somewhat as a relatively weak function of increasing AF. Figure 8 shows that (1) VHC decreases as a strong function of increasing [[tau].sub.c], (2) VHC decreases with increasing CP, and (3) VHC decreases somewhat as a relatively weak function of increasing AF. These results suggest that one could choose an optimum arrangement of the parameters [[tau].sub.c], CP, and AF in order, for example, to maximize [COP.sub.H] or to maximize VHC or to maximize [COP.sub.H] for a given value of VHC or to maximize VHC for a given value of [COP.sub.H]. For example, to maximize [COP.sub.H] independent of VHC, [[tau].sub.c] should have a value of 1.42, CP should have a value of approximately 0.5, and AF should have a value of 2.14. Given these parameters, the relative [COP.sub.H] ratio ([COP.sub.H,refrig]/[COP.sub.H,R-114]) is 1.09 and the relative VHC ratio ([VHC.sub.refrig]/[VHC.sub.R-114]) is 0.02. As a second example, to maximize VHC independent of [COP.sub.H], [[tau].sub.c] should have a value of 0.89, CP should have a value of 0.18, and AF should have a value of 0.59. Given these parameters, the relative [COP.sub.H] ratio is 0.86 and the relative VHC ratio is 9.47. Note: these "optimum" values are based on the parameter space defined earlier. Figures 7 and 8, however, are less helpful when attempting to answer questions such as "What parameters would maximize [COP.sub.H] for a given value of VHC?" or "What parameters would maximize VHC for a given value of [COP.sub.H]?" To help answer these types of questions, the results are plotted in Figure 9a, with CP as a function of [[tau].sub.c] in a set of three curves, which set the bounds on the values of VHC being within [+ or -]10%, [+ or -]25%, or [+ or -]50% of the value of R-114. Figure 9a, therefore, could be used to help one locate a combination of CP and [[tau].sub.c] that would yield a desired value of VHC. One limitation of Figure 9a is that it does not include the functional dependence of AF; however, as can be seen from Figures 7 and 8, the functional dependence of AF on both [COP.sub.H] and VHC is relatively weak. Therefore, Figure 9a is a useful representation of the approximate overall functional dependence of [[tau].sub.c], CP, and AF on [COP.sub.H] and VHC.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

Before concluding, it is useful to demonstrate another aspect of the power of the methodology, namely, not only its capability to evaluate generic replacement refrigerants but, in addition, its capability to evaluate particular refrigerants. For example, consider the potential R-114 replacements given in Devotta and Pendyala (1994) and in Bivens and Minor (1998) together with 39 fluids contained in REFPROP (Lemmon et al. 2007). Then, if the principal sorting criterion were chosen to be that [T.sub.c] must fall in the range from 110[degrees]C (230[degrees]F) to 200[degrees]C (392[degrees]F), the three cited sources would yield 21 potential replacement fluids. Note: this critical temperature range is determined from Figures 7 and 8 such that 0.5 < VHC ratio < 1.5; the critical temperature range would change if one were to impose a different VHC ratio range. (Note: this paper considers only replacement fluids cited in the three references listed above since it is not meant to be an exhaustive search for and presentation of all possible R-114 replacements but rather is an illustration of an overall selection methodology.) In addition to this primary sorting criterion there are, of course, dozens of possible secondary sorting criteria; however, in this paper, only three are applied: (1) flammability, (2) ozone depletion potential (ODP), and (3) global warming potential (GWP). Namely, fluids are considered to fail the secondary sorting criteria if (1) they are ANSI/ASHRAE Standard 34 Class 3 flammable refrigerants, (2) they have ODP > 0, and (3) they have GWP > 2000. These three secondary criteria are applied because of the strong reluctance by the industry to use highly flammable refrigerants in systems requiring large refrigerant charge and because of the ever-growing worldwide awareness and concern regarding environmental impacts. Table 2 lists the 21 refrigerants, together with values for [[tau].sub.c], CP, AF, [COP.sub.H] ratio, and VHC ratio, based on the reference cycle defined above. (Note: the sources for the property data for Table 2 are ASHRAE [2005], Bivens and Minor [1998], Brown [2007], IPCC [2001], REFPROP [Lemmon et al. 2007], and Reid et al. [1987a, 1987b, 1987c]). These 21 possible R-114 replacements also are shown on a CP vs. [[tau].sub.c] plot in Figure 9b. As previously stated, the functional dependence of AF is missing from the figure so that the VHC value predicted from locating CP and [[tau].sub.c] on the figure is only approximate. One could obtain a better estimate of VHC by "correcting" the prediction using the AF functional dependence shown in Figure 8. The power of Figures 9a and 9b is that one can obtain a reasonable estimate for VHC without having to resort to EoS modeling. For example, one could use the methods of Ambrose (see Reid et al. [1987a]) and Joback (see Reid et al. [1987b]) to easily predict [[tau].sub.c] and CP, respectively, for potential replacement fluids that are not well described, even before predicting other thermodynamic parameters with an EoS model. Finally, Figure 10 shows the [COP.sub.H] ratios and VHC ratios, listed from highest to lowest VHC ratios, for the 21 possible R-114 replacements described above.

Table 2. Twenty-One Potential R-114 Replacement Refrigerants

Refrigerant                   [[tau].sub.c]    CP       AF

                               Refrigerants Passing Secondary Criteria

R-143                                 1.029  0.695  1.044
R-152a                                0.923  0.587  1.091
R-236ca                               0.984  1.103  1.369
R-236cb                               0.963  1.109  1.274
R-236ea                               0.989  1.117  1.504
R-245ca                               1.069  1.128  1.405
R-245fa                               1.020  1.052  1.476
R-254cb                               1.001  0.989  0.980
R-717                                 0.968  0.281  1.016
RE245cb1                              0.971  1.158  1.417
[SF.sub.5][CF.sub.2]H                 0.997  1.035  1.075
[SF.sub.5][C.sub.2][F.sub.5]          0.980  1.475  1.313

                                Refrigerants Failing Secondary Criteria

R-12                                  0.920  0.592  0.714
R-123                                 1.091  0.923  1.119
R-124                                 0.944  0.847  1.143
R-142b                                0.979  0.733  0.921
R-236fa                               0.950  1.087  1.496
R-C318                                0.927  1.323  1.409
R-600                                 1.015  0.951  0.798
R-600a                                0.974  0.917  0.730
RE134                                 1.036  0.874  1.496

Refrigerant                   [COP.sub.H] Ratio  VHC Ratio

R-143                                     1.064      1.139
R-152a                                    0.993      2.669
R-236ca                                   1.012      1.017
R-236cb                                   0.952      1.134
R-236ea                                   0.986      1.022
R-245ca                                   1.055      0.609
R-245fa                                   1.033      0.841
R-254cb                                   1.012      1.167
R-717                                     1.029      5.527
RE245cb1                                  0.969      0.957
[SF.sub.5][CF.sub.2]H                     0.993      0.940
[SF.sub.5][C.sub.2][F.sub.5]              0.964      0.705
R-12                                      0.966      2.550
R-123                                     1.085      0.557
R-124                                     0.976      1.672
R-142b                                    1.032      1.603
R-236fa                                   0.948      1.224
R-C318                                    0.849      1.149
R-600                                     1.032      1.155
R-600a                                    0.991      1.475
RE134                                     1.048      1.155

Refrigerant                   Failure of Secondary Criteria

R-143                                                     -
R-152a                                                    -
R-236ca                                                   -
R-236cb                                                   -
R-236ea                                                   -
R-245ca                                                   -
R-245fa                                                   -
R-254cb                                                   -
R-717                                                     -
RE245cb1                                                  -
[SF.sub.5][CF.sub.2]H                                     -
[SF.sub.5][C.sub.2][F.sub.5]                              -
R-12                                                    CFC
R-123                                                  HCFC
R-124                                                  HCFC
R-142b                                                 HCFC
R-236fa                                         GWP = 9,400
R-C318                                         GWP = 10,000
R-600                                                    A3
R-600a                                                   A3
RE134                                           GWP = 6,100

[FIGURE 10 OMITTED]

CONCLUSIONS

The P-R EoS was used to investigate fundamental thermodynamic parameters that affect the selection of R-114 replacements in high-temperature heat pumping applications. It was shown that the critical temperature, the ideal gas specific heat at constant pressure, and the acentric factor are the three fundamental thermodynamic parameters that largely determine the performance ([COP.sub.H] and VHC) of refrigerants operating in idealized vapor-compression refrigeration cycles. It was shown that (1) the optimum range of [[tau].sub.c] depends on the desired VHC; (2) to maximize [COP.sub.H], CP should have values from approximately 0.35 to approximately 0.75, and to increase VHC, CP should be less than 1; and (3) to increase [COP.sub.H], AF should have larger values, and to increase VHC, AF should have smaller values. For the studied parametric space, the maximum achievable [COP.sub.H] ratio is 1.09 (with a corresponding VHC ratio of 0.02) and the maximum achievable VHC ratio is 9.47 (with a corresponding [COP.sub.H] ratio of 0.86). For the [COP.sub.H] ratio of 1.09, [[tau].sub.c] = 1.42, CP = 0.5, and AF = 2.14, and for the VHC ratio of 9.47, [[tau].sub.c] = 0.89, CP = 0.18, and AF = 0.59. Therefore, trade-offs become necessary due to the conflict between [COP.sub.H] and VHC. The process presented in this paper provides a framework for quickly and easily screening a large number of potential R-114 replacement refrigerants. One could easily create, from a much longer list, a focused list of potential replacements that could then be investigated in depth using the more conventional approaches of experimentation and detailed system modeling.

ACKNOWLEDGMENTS

The author would like to thank Drs. Eric Lemmon and Mark McLinden for making available a beta version of REFPROP 8.0 and for several helpful discussions. The author would also like to thank Dr. David Didion for many fruitful discussions over the past ten years, including recent ones regarding the subject of this paper.

NOMENCLATURE 

AF = relative acentric factor, [[omega].sub.refrig]/[[omega].sub.[R - 114]]

[COP.sub.H] = heating coefficient of performance

[COP.sub.H] ratio = [COP.sub.H,refrig]/[COP.sub.[H,R - 114]]

[c.sub.p.sup.0] = ideal gas specific heat at constant pressure evaluated at [T.sub.c], kJ [kmo1.sup.-1] [K.sup.-1] (Btu [lbmo1.sup.-1] [degrees][R.sup.-1])

CP = relative ideal gas specific heat at constant pressure, [([c.sub.p.sup.o]).sub.refrig]/[([c.sub.p.sup.o]).sub.[R - 114]]

h = enthalpy, kJ [kg.sup.-1] (Btu [lbm.sup-1])

H* = nondimensional enthalpy, [[h.sub.refrig] - [h.sub.[f,R - 114,T = 0[degrees]C]]]/[h.sub.[fg,R - 114, T = 0[degrees]C]]

M = molecular weight, kg [kmol.sup.-1] (lbm [lbmol.sup.-1])

NBP = normal boiling point temperature, [degrees]C ([degrees]F)

P = pressure, kPa (psia)

P* = nondimensional pressure, [P.sub.refrig]/[P.sub.[c,R - 114]]

s = entropy, kJ [kg.sup.-1] [K.sup.-1] (Btu lbm-1 [degrees][R.sup.-1])

S* = nondimensional entropy, [[s.sub.refrig] - [s.sub.[f,R - 114,T = 0[degrees]C]]]/[s.sub.[fg,R - 114,T = 0[degrees]C]]

T = temperature, [degrees]C ([degrees]F)

T* = nondimensional temperature, [T.sub.refrig]/[T.sub.[c,R - 114]]

VHC = volumetric heating capacity, kJ [m.sup.-3] (Btu [ft.sup.-3])

VHC ratio = [VHC.sub.refrig]/[VHC.sub.[R - 114]]

[delta] = relative density, [[rho].sub.refrig]/ [rho]R-114

[pi] = relative pressure, [[rho].sub.refrig]/[rho]R-114

[rho] = density, kg [m.sup.-3] (lbm [ft.sup.-3])

[tau] = relative temperature, [T.sub.refrig]/[T.sub.[R - 114]]

[omega] = acentric factor

Subscripts

c = critical

cond = condenser

evap = evaporator

f = saturated liquid

fg = difference between saturated vapor and saturated liquid property values

g = saturated vapor

refrig = refrigerant

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Reid, R.C., J.M. Prausnitz, and B.E. Poling. 1987c. The Properties of Gases and Liquids, 4th ed. New York: McGraw-Hill, p. 23.

Wark, K. 1995. Advanced Thermodynamics for Engineers. New York: McGraw-Hill, p. 165.

APPENDIX

Table A1. List of Refrigerants from Brown (2007)

R-11  R-41   R-134a   R-152a  R-236fa   R-600
R-12  R-123  R-141b    R-170  R-245ca  R-600a
R-22  R-124  R-142b    R-218  R-245fa  R-1270
R-32  R-125  R-143a  R-227ea    R-290  R-C318
Table A2. List of Refrigerants Used to Develop Equation 2 and
Figures 2 and 3

R-11    R-23   R-115   R-141b  R-227ea  R-338mccq    R-C270
R-12     R-32   R-116  R-142b  R-236ea      R-600    R-C318
R-13     R-41   R-123  R-143a  R-236fa     R-600a    R-E125
R-13I1   R-50   R-124  R-152a  R-245ca      R-717    R-E134
R-14    R-113   R-125   R-170  R-245fa      R-744    R-E245
R-22    R-114  R-134a   R-218    R-290     R-1270  R-E245mc

J. Steven Brown is an associate professor and the Chair of the Department of Mechanical Engineering, The Catholic University of America, Washington, DC.

J. Steven Brown, PhD, PE

Member ASHRAE

Received October 25, 2006; accepted April 16, 2007

This paper is based on findings resulting from ASHRAE Research Project RP-1308.

Table 1. Some Relevant Thermodynamic Parameters of R-114 (Lemmon et
al. 2007)

                                       SI

NBP                                           276.74 K

[T.sub.c]                                     418.83 K

[P.sub.c]                                     3257 kPa

[[rho].sub.c]                     3.39 kmol [m.sup.-3]

[omega]                                         0.2523

M                              170.92 kg [kmol.sup.-1]

[c.sub.p.sup.0](evaluated                        137.9
at [T.sub.c])              kJ [kmol.sup.-1] [K.sup.-1]

                                             I-P

NBP                                             498.13 [degrees]R

[T.sub.c]                                       753.89 [degrees]R

[P.sub.c]                                              472.4 psia

[[rho].sub.c]                             0.212 lbmol [ft.sub.-3]

[omega]                                                    0.2523

M                                       170.92 lbm [lbmol.sup.-1]

[c.sub.p.sup.0](evaluated                                    33.0
at [T.sub.c])              Btu [lbmol.sup.-1] [degrees][R.sup.-1]