Simulated performance and cofluid dependence of a CO2-cofluid refrigeration cycle with wet compression

International Journal of Refrigeration 25 (2002) 1123–1136 www.elsevier.com/locate/ijrefrig

Simulated performance and cofluid dependence of a CO2-cofluid refrigeration cycle with wet compression George Mozurkewicha,*, Michael L. Greenfielda, William F. Schneidera, David C. Zietlowb, John J. Meyerc a Ford Motor Company Research Laboratory, Dearborn MI 48121-2053, USA Bradley University, Department of Mechanical Engineering, Peoria, IL 61625, USA c Visteon Automotive Systems, Plymouth, MI 48170, USA

b

Received 29 May 2001; received in revised form 17 October 2001; accepted 5 November 2001

Abstract Recent experiments demonstrate the viability of a low-pressure CO2-cofluid compression refrigeration cycle in which CO2 and a non-volatile cofluid are circulated in tandem and co-compressed in a compliant scroll compressor. This work explores the theoretical performance limitations of such a cycle operating under environmental conditions representative of automotive air conditioning and studies the dependence of this performance on the properties of the CO2-cofluid mixture. The vapor–liquid equilibrium and thermodynamic properties of the mixture are described using a previously reported activity-coefficient model. A coupled system of physically based equations that allows for consideration of both ideal and real hardware components is used to represent the system hardware and its interaction with the environment. The system efficiency is analyzed in terms of entropy generation rates in the various hardware components; entropy generation in the internal heat exchanger—a component required to achieve sufficiently low cooling temperatures—strongly influences overall system efficiency. The vapor pressure of the CO2-cofluid mixture and the heat of solution of CO2 in cofluid have large and somewhat independent contributions to the system performance: lower saturation pressure lowers the optimal operating pressures at fixed CO2 loading, while increasingly negative heat of solution contributes to higher specific refrigeration capacity and efficiency. # 2002 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Refrigerant; Mixture; Carbon dioxide; Liquid; Compression; Resorption; Desorption; Performance; Modelling

Simulation de la performance et impact sur la performance d’un cycle frigorifique a` compression utilisant du dioxyde de carbone en me´lange avec un liquide Mots cle´s : Syste`me frigorifique ; Frigorige`ne ; Me´lange ; Dioxyde de carbone ; Liquide ; Compression ; Re´sorption ; De´sorption ; Performance ; Mode´lisation

* Corresponding author. Tel.: +1-313-845-5038; fax: +1313-322-7044. E-mail address: [email protected] (G. Mozurkewich). 0140-7007/02/$20.00 # 2002 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(02)00004-X

1124

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

1. Introduction Carbon dioxide is receiving increased attention as an alternative vapor-compression refrigerant. CO2 is attractive as a refrigerant because it is a ‘‘natural’’ material, present in abundance in the environment [1]. The quantities used in air conditioning systems are far too small to have any direct contribution to atmospheric radiative forcing. Several implementations of the transcritical CO2 refrigeration cycle have been described in the literature [2–7]. A practical concern with the transcritical CO2 cycle is its extremely high operating pressures. When used for air conditioning, the pressure in the gas cooler (analogous to the condenser) increases with ambient temperature and may exceed 12 MPa when ambient temperature reaches 43
C [7]. Another practical consideration is efficiency, measured as the coefficient of performance (COP). The environmental benefit of an alternative air conditioning system is a function not only of the environmental friendliness of the refrigerant but also of its impact on the energy required and consequent CO2 produced to satisfy the cooling requirements. On a total environmental warming index (TEWI) basis, which incorporates both the direct (refrigerant release) and indirect (energy efficiency) contributions of a refrigeration system to global warming, analysis indicated a R134a system to be superior in all but the most mild climates to a presumed poorer efficiency transcritical CO2 system [8]. In a more recent experimental comparison, McEnaney et al. [7] found that a transcritical CO2 system with enhanced hardware could achieve COPs comparable to that of a standard R134a vapor-compression system under the same environmental conditions. The environmental friendliness of CO2 refrigerant can be retained with reduced operating pressure and improved efficiency by introducing a second fluid (‘‘cofluid’’) into which CO2 can absorb [9]. Absorption and desorption of CO2 from solution replace condensation/gas cooling and evaporation of pure CO2. These processes occur at significantly lower pressures while retaining adequate refrigeration capacity. We will use the term ‘‘cofluid cycle’’ to describe a refrigeration cycle in which the working fluid is a mixture of a volatile refrigerant and a nonvolatile liquid whose purpose is to reduce the operating pressures of the cycle. This cycle is an extreme case of a zeotropic working fluid. The concept of adding a cofluid to the refrigerant is not new: the first related patent was published in 1895 [10]. Subsequent calculations indicated that cofluid cycles offer the potential for significant improvements over traditional vapor compression [11]. Recently, interest in this technology has increased because of its potential environmental benefits, and several pilot facilities have been built [12–15]. The typical hardware configuration is the so-called vapor-compression cycle with

solution circuit. Groll and coworkers have presented a simplified cycle model for this configuration and applied it to ammonia–water [16] and CO2–acetone [17] working fluid mixtures. In 1999, Spauschus et al. [18] described a cofluid cycle that eliminates the separate solution circuit by ‘‘wet compression’’ of the CO2 and cofluid simultaneously in a compliant scroll compressor. Promising performance under conditions relevant to automotive air conditioning was demonstrated. The wet compression system has the advantage—critical in automotive applications— that the hardware and control requirements are comparable to the current R134a vapor compression system. In parallel work, a cycle model for deriving the maximum possible COP consistent with the CO2-cofluid mixture properties and external environmental conditions was developed [19]. The mixture properties were described in terms of an activity-coefficient-based model, which provides a very flexible treatment of solution behavior but requires extensive experimental data for parameterization. The approach was illustrated for a low-volatility cofluid, N-methyl-2-pyrrolidone (NMP). Subsequent work [20] compared the activity-coefficient model with an equation-of-state (EOS) approach that is less dependent on experimental data but is more limited in the cofluids it can treat. The two were shown to produce equivalent results for both CO2–NMP and CO2–acetone mixtures. The cycle model was also extended to treat non-ideal hardware components [20]. After a review of the activity-coefficient-based thermodynamic formulation, this paper describes a cycle model for the CO2-cofluid refrigeration system with wet compression in a form suitable for both ideal and nonideal hardware. The inherent limitations on the cycle efficiency are discussed in terms of entropy-generation rates, with an emphasis on the important role of the internal heat exchanger. Finally, the cycle model is used to assess the dependence of cycle performance (defined to include COP and refrigeration capacity) on the equilibrium properties of the CO2-cofluid mixture, as well as on the relative proportions of CO2 and cofluid, for both hypothetical and real cofluids.

2. Thermodynamic properties model The thermodynamic model [19] provides state functions of CO2 mixed with a cofluid. It requires as inputs the physicochemical properties of pure CO2 and cofluid and the fugacity and density of the mixture as a function of temperature and concentration. These mixture properties are readily extracted from vapor–liquid equilibrium measurements [21]. The circulating refrigerant is assumed to consist of CO2 and a non-volatile cofluid in a fixed molar ratio, Y. (The non-volatility assumption is consistent with the

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

practical implementation [18] and EOS model [20], and it considerably simplifies the model.) Because the total composition is fixed, the mixture has two independent thermodynamic degrees of freedom in either the singlephase (‘‘fully resorbed’’) or two-phase regions, which we choose to be temperature T and pressure P. T, P, and Y determine the equilibrium concentration of CO2 in the liquid phase, which we express as the mole ratio of dissolved CO2 to cofluid, n. Assuming the circulating composition equals the charged composition, Y is the maximum attainable value of n, corresponding to a completely liquefied mixture. The functional relationship between equilibrium values of T, P, and n is provided by phase equilibrium, i.e. the requirement of equal CO2 fugacities f kCO2 in the two phases k: f LCO2 ðn; T; PÞ ¼ f V CO2 ðT; PÞ

ð1Þ

sN ¼

1 MWcofl nðf       hsoln n; Tf ; Pf   R ln f LCO2 n; Tf dn Tf 0

þ Rnf MWcofl lnf V CO2 ðTf ; Pf Þ

ð5Þ

where MWcofl is the cofluid molecular weight. hsoln, the composition-dependent enthalpy associated with transferring a mole of CO2 from the vapor to the liquid phase at a particular liquid composition, is an important determinant of cofluid performance in the refrigeration cycle. hsoln can be calculated using the temperature derivatives of the CO2 fugacities [21]. Eqs. (2) and (3) yield       @ lnf
CO2 hsoln @ lnCO2 @ lnCO2 ¼  þ R @ 1=T P @ 1=T P @ 1=T P;n

The CO2 vapor fugacity is given by fV CO2 ðT; PÞ

¼ CO2 ðT; PÞ P

ð6Þ ð2Þ

where CO2 , the fugacity coefficient, can be obtained from a CO2 EOS [22]. The liquid-phase fugacity is the product of the CO2 mole fraction, x=n / (n + 1), a standard-state condensed-phase CO2 fugacity f 0CO2 ðT; PÞ [19,23], and an activity coefficient CO2 ðn; T; PÞ, which accounts for differences in CO2 solubility among cofluids: f LCO2 ðn; T; PÞ ¼ x CO2 ðn; T; PÞf oCO2 ðT; PÞ

ð3Þ

Eqs. (1)–(3) can be solved numerically for any one of T, P, or n. For given Y, the mixture enthalpy h and entropy s per kg of cofluid can be obtained from pure component properties plus the fugacity models. The reference state h=0 and s=0 consists of separated CO2 vapor and pure liquid cofluid at T ref=253.15 K and P ref=10 kPa. We construct a three-legged pathway from this reference state to a two-phase final state specified by Tf, Pf, and nf [19]. In the first leg the pure fluid heat capacities are integrated from T ref to Tf, and in the second the thermal expansion coefficients are integrated from Pref to Pf. In the final leg, nf moles of CO2 per mole of cofluid are transferred from the vapor to the liquid phase. The corresponding enthalpy and entropy changes are obtained by integrating the differential heat of solution, hsoln, leading to nðf 1 hN ¼  hsoln ðn; Tf ; Pf Þdn MWcofl 0

1125

ð4Þ

Thus, hsoln separates into a cofluid-independent ‘‘ideal’’ part (hideal soln ) given by the first two terms and a cofluid-dependent ‘‘excess’’ heat of solution (hexcess soln ). For the temperatures and pressures of interest here, hideal soln ranges from 10 to 14 kJ/mol of CO2 transferred, while hexcess soln is typically negative but smaller in magnitude. Solving the phase equilibrium relationship and evaluating the thermodynamic functions is thus reduced to determining the activity coefficient, CO2 , of the mixture. It is convenient to express CO2 in terms of an activity coefficient model fit to measurements of equilibrium CO2 vapor pressure over mixtures of known composition. The van Laar model [21] with four adjustable parameters, ln ðn; TÞ ¼ 

A0 þ A1 ðTc =TÞ 1 þ ½ C0 þ C1 ðTc =TÞ n

2

ð7Þ

has been found empirically to describe several CO2cofluid mixtures adequately (Tc=304.1 K is the critical temperature of CO2) [19]. hexcess soln is given by RTc 2 1 þ ½ C0 þ C1 ðTc =TÞ n

 2½ A0 þ A1 ðTc =TÞ C1 n

A1  1 þ ½ C0 þ C1 ðTc =TÞ n

hexcess soln ðn; TÞ ¼ 

ð8Þ and thus depends on CO2 concentration and on temperature. The forms of the van Laar model and the standard state fugacity ensure that the calculated pressure and heat of solution will vary smoothly with composition down to completely desorbed CO2 (n=0), a

1126

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

requirement for properly treating the lower integration limits of Eqs. (4) and (5). Examples of fitting the van Laar model to available CO2–NMP and CO2–acetone vapor pressure data have been presented [19,20]. Agreement is generally good over a range of temperatures and compositions. A schematic P–h diagram for a CO2-cofluid mixture with given Y is shown in Fig. 1. The phase diagram contains a two-phase mixture (lower right) and a single liquid phase (upper left) separated by the ‘‘full resorption’’ boundary. The familiar ‘‘dome’’ shape of the twophase region (as found for a pure, volatile refrigerant) is absent because the high temperatures and enthalpies required to vaporize the cofluid are above the range shown.

tions are fixed, including the desorber air :inlet temperature, TD,in, and air heat-capacity rate, Cair;D : , and the analogous resorber quantities, TR,in and Cair;R . These heat-capacity rates [24] (units W K1) are defined as the product of the air flow : rate and specific heat. The desorber cooling load Qc is also specified. The air outlet temperatures, TR,out and TD,out, and the cofluid flow : rate, m, are not specified but are determined as part of the solution. The cycle is governed by nine simultaneous equations [19], seven in the form fi=0. Let Ti and hi be the temperature and enthalpy per unit mass at state point i. For the isenthalpic expansion, f1 ¼ h4  h5

ð9Þ

For isentropic compression, 3. Refrigeration cycle model f2 ¼ ðs1  s2 ÞT0 A model of the refrigeration cycle can be constructed by describing each hardware component using physically based equations. A schematic of the hardware is inset in Fig. 1 [18], and a representative cycle is plotted on the P–h diagram. The cycle operates as follows: a combination of vapor (pure CO2) and liquid (a solution of CO2 in cofluid) is compressed from point 1 to point 2, raising the pressure and forcing some of the vapor into the liquid phase. Heat is rejected to the environment in the resorber (2–3), cooling the mixture and causing more of the vapor to be absorbed. The remaining vapor and ‘‘strong’’ liquid are further cooled in an internal heat exchanger (3–4). The cool, fully liquefied mixture is then passed through an expansion device (4–5), decreasing the pressure, dropping the temperature further, and releasing some of the CO2 into the vapor phase. Heat is extracted from the refrigerated space into the desorber (5–6) as the temperature of the mixture rises and further CO2 escapes from the liquid phase. Finally, the fluids are further warmed in the internal heat exchanger (6–1), completing the cycle. The goal in modeling this cycle is to quantify its theoretical performance and to find the best possible coefficient of performance (COP). Therefore, we make the following idealizing assumptions: (1) Thermodynamic equilibrium is attained at each point in the cycle. (2) The system operates in steady state. (3) The loading, Y, of the circulating refrigerant mixture is uniform throughout the system. To ensure that the heat-transfer processes obey the minimum requirements of thermodynamics, the heat exchangers are described using the concept of effectiveness [24]. Furthermore, to retain some of the limitations of realistic operation, the external environmental condi-

ð10Þ

Here the temperature of ambient air, T0, is included solely for a numerical reason: it gives f2 and f1 the same units and similar magnitudes. Heat transfer in the resorber requires energy conservation between the refrigerant and air streams,   : : f3 ¼ ðh2  h3 Þ  Cair;R TR;out  TR;in =m

ð11Þ

The heat-transfer rate in the resorber can be parameterized in terms of an effectiveness, "R, by [24] :

  : : ð12Þ mðh2  h3 Þ ¼ "R T2  TR;in min Cair;R ; Crefr;R

in which the average heat-capacity rate in the resorber is defined by [19] : : Crefr;R  mðh2  h3 Þ=ðT2  T3 Þ

ð13Þ

Eq. (13) incorporates the energetic effect (analogous to latent heat) of CO2 molecules passing between the vapor and liquid phases as the temperature changes at constant pressure. : :Eq. (12) can be combined with f3=0 when Cair;R < Crefr;R or with Eq. (13) in the opposite case:

: : f4 ¼ "R T2 þ ð1  "R ÞTR;in  TR;out ; if Cair;R < Crefr;R "R TR;in þ ð1  "R ÞT2  T3 ; otherwise ð14Þ Similar equations hold for the internal heat exchanger f5 ¼ ðh3  h4 Þ  ðh1  h6 Þ

ð15Þ

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

1127

Fig. 1. Schematic P–h diagram for a CO2-cofluid mixture with state points for a refrigeration cycle. Inset: schematic of hardware for the CO2-cofluid refrigeration cycle with wet compression.

: : W ¼ mðh2  h1 Þ

: : Crefr;strong  mðh3  h4 Þ=ðT3  T4 Þ

ð16Þ

: : Crefr;weak  mðh1  h6 Þ=ðT1  T6 Þ

ð17Þ

:

: : mðh3  h4 Þ ¼ "int ðT3  T6 Þmin Crefr;strong ; Crefr;weak ð18Þ

: : f6 ¼ "int T6 þ ð1"int ÞT3 T4 ; if Crefr;strong < Crefr;weak "int T3 þ ð1"int ÞT6  T1 ; otherwise ð19Þ In terms of the cooling load, defined by : : Qc ¼ mðh6  h5 Þ

ð20Þ

the analogous desorber equations become   : : Cair;D TD;in  TD;out ¼ Qc

ð21Þ

: : Crefr;D  Qc =ðT6  T5 Þ

ð22Þ

:

  : : mðh6  h5 Þ ¼ "D TD;in  T5 min Cair;D ; Crefr;D

ð23Þ

: : f7 ¼ "D T5 þ ð1  "D ÞTD;in TD;out ; if Cair;D < Crefr;D "D TD;in þ ð1  "D ÞT5  T6 ; otherwise ð24Þ Once the equations are solved, the compressor power is calculated from

ð25Þ

The nine independent equations are the seven equations of the form fi=0 plus Eqs. (20) and (21). If the cooling load and the pressures at all 6 state points are given, these nine equations suffice to compute nine unknowns: six refrigerant temperatures, T1 through T6; : two air-outlet temperatures, TR,out and TD,out; and m. Thus, if the pressure drops in the heat exchangers are negligible, any desired performance parameter (COP, : m; etc.) can be calculated for a given pair (P1, P2) of suction and discharge pressures, and those two pressures can be varied systematically to optimize according to some criterion, such as maximizing the COP. (If the pressure drops are not negligible, these nine equations can readily be supplemented with four pressure-drop equations, one for each heat-exchanger refrigerant stream, to generate a solvable system of equations.) When all three effectivenesses are unity, these equations can be solved by an explicit procedure [19]. Although that important special case gives the highest COP consistent with thermodynamics and the imposed environmental conditions, a more general, iterative procedure based on the Newton–Raphson method [25] is used to solve the system of equations fi=0. The elements of the Jacobian matrix include derivatives of the form @hi =@Ti and @si =@Ti which are easily obtained from the equations above and are listed in the Appendix. The result of this procedure is the set of state-point temperatures corresponding to a particular choice of P1 and P2, from which the COP or any other desired property

1128

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

of the cycle can be calculated. The cycle that optimizes COP can be found by repeating the entire procedure while systematically varying P1 and P2 using a simplex routine [25]. In a real system, one can adjust pressures only indirectly, for example by varying the setting of the expansion device or the displacement volume of the compressor. The relationship between the pressures and the corresponding hardware values can be determined from appropriate physically based relations. For example, the mass flow is related to the compressor displacement volume, Vd, volumetric efficiency, V, and number of compressions per second, fc, by : V fc Vd $ 1 ¼ ð1 þ %Þm

ð26Þ

where $ 1 is the overall density (pure liquid or liquid plus vapor, depending on T and P) at point 1. The overall mass ratio % is related to the overall  mole ratio, Y,by the ratio of molecular weights, % ¼ MWCO2 =MWcofl Y, and the factor ð1 þ %Þ converts mass flow of cofluid into mass flow of mixture. Likewise, the mass flow through the expansion device is related to the pressure drop by : Cd A0 ½ 2ðP4  P5 Þ $ 4 1=2 ¼ ð1 þ %Þm

ð27Þ

where A0 is the expansion device orifice area, Cd is an appropriate discharge coefficient, and $ 4 is the overall density at point 4 (which turns out to be pure liquid). For any pair of suction and discharge pressures, these two equations suffice to calculate the appropriate hardware parameters. The computed optimal cycles are joint properties of the working-fluid mixture and of the imposed environmental conditions. The specific environmental conditions used here were chosen to represent an automotive air-conditioning system. In particular, the cooling load, : which sizes the system, is set to Qc =3.5 kW. Further, we adopt environmental conditions [18] that correspond roughly to driving at moderate speed on a very hot day. Specifically, the ambient air temperature into the resorber is set to 43
C, and, to account for recirculation from a partially cooled passenger compartment, the air-inlet temperature into the desorber is taken as 32
C. Air flow rates into the desorber and resorber are 0.12 and 1.13 m3 s1, respectively. The associated air heat-capacity rates are 145 and 1363 W K1 respectively, assuming dry air. Other environmental conditions have been considered [18,19]. In this paper we emphasize inherent limitations on cycle performance and their dependence on mixture properties, and thus choose to employ a single set of environmental conditions. The compressor work was minimized for each cofluid under the stated environmental conditions and for given Y, yielding : values for optimal COP and m. The specific refrigera-

: : tion capacity is defined as Qc =m ¼ h6  h5 , which has units of kJ kg1 of cofluid circulated.

4. Theoretical limitations on cycle performance Even for the case of ideal hardware, the efficiency of the CO2-cofluid cycle with wet compression is much less than that of a Carnot cycle. In analyzing the limitations of the cycle performance, it is useful to refer to the Guoy-Stodola or lost-work theorem, which is derived in standard textbooks [26]. In the context of refrigeration systems, it can be written : : : W ¼ Wrev þ T0 I

ð28Þ

: and could be called the ‘‘extra-work theorem.’’ Here W is the rate at which work must be done on the actual system. Its two contributions are the reversible work, : Wrev , which is the rate at which work would be done on a corresponding reversible (Carnot) system, and the : : irreversible work, T0 I. I is the irreversibility rate, or rate of entropy generation of the universe, caused by operation of the refrigeration system. T0 is the ambient temperature; that is, the temperature of the reservoir to which all heat must eventually be ejected. The expansion device operates irreversibly, and the : rate of entropy generation in it is simply mðs5  s4 Þ. Similarly, the rate of entropy generation in the internal heat exchanger is the sum of the increase on the weak : side and the decrease on the strong side: m½ ðs1  s6 Þþ ðs4  s3 Þ . The hot air out of the resorber eventually attains the temperature of the ambient air, T0=TR,in; likewise, the cold air out of the desorber comes to the temperature of the air in the refrigerated space. Therefore, the air sides are treated as infinite heat reservoirs whose temperatures are fixed at their respective inlet temperatures: : : : ID ¼ mðs6  s5 Þ  Qc =TD;in

ð29Þ

: : : IR ¼ mðs3  s2 Þ þ mðh2  h3 Þ=TR;in Each of these quantities is non-negative because the corresponding processes occur spontaneously. In an ideal, isentropic compressor, the entropy generation is zero. We now consider the inherent thermodynamic limitations on cycle performance for a representative cofluid. Because heat exchange ineffectiveness and compressor inefficiency have been shown to simply magnify the trends in cooling capacity and system efficiency found with ideal hardware [20], we assign each heat exchanger unit effectiveness ("R="D="int=1) and take compression to be adiabatic and reversible. The cofluid is chosen

1129

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

to be NMP, with van Laar parameters and temperaturedependent density and heat capacity as listed in Table 1. The results for a loading Y=0.36 are shown in Table 2. The optimal COP is found to be 3.98, which differs slightly from the value in Ref. [19] because of a revised NMP heat capacity [27] and an improved calculation of CO2 vapor entropy [28]. Although  the reversible (Carnot) COP is TD;in = TR;in  TD;in ¼ 27:7, the optimal COP is much lower, due to the considerable irreversibilities that arise even in ideal components. The isenthalpic expansion is inherently irreversible and, in this thermodynamically limiting case, is a large contributor to irreversibility. The other sources of irreversibility arise in the various heat exchangers as a result of heat transfer through non-zero temperature differences. These temperature differences are a consequence of the unequal heat-capacity rates of the interacting streams and are present even in ideal (infinite area, counterflow) heat exchangers. In the resorber and desorber, the air-side heat-capacity rates are constant and fixed by the external conditions, and the refrigerant streams them. Specifically, in the : do not match : deso1 rber, Cair;D (145 compared to Cref;D ; in : W K ) is small 1 the : resorber, Cair;R (1363 W K ) is large compared to Cref;R . Entropy generation in these components is an unavoidable consequence of interaction with the specified environment. In a counterflow internal heat exchanger, entropy generation : when the average heat: is minimized capacity rates, Cref;weak and Cref;strong , are exactly matched, a situation we describe as ‘‘balanced.’’ Balance implies that the temperature change of the strong fluid equals that of the weak fluid, or equivalently that the temperature difference across the two ends of the exchanger are equal (T3 – T1=T4 – T6). In the ideal case of unit effectiveness in the internal heat exchanger, the inlet temperature of each stream equals the outlet temperature of the other (T1=T3 and T4=T6). Even in this latter case, however, entropy generation in the internal heat exchanger does not vanish. Because the heat-capacity rate of the refrigerant includes the effect of CO2

absorption or desorption, it is a function of temperature, pressure, and composition. Thus, while the average heat-capacity rates are equal in the balanced heat exchanger, the differential heat-capacity rates vary, producing temperature differences and generating entropy. The effect can be understood with reference to Fig. 2, which shows the variation in temperature of the strong and weak streams across the counterflow internal heat exchanger as a function of increase in enthalpy. The differential heat-capacity rates of the two streams are the reciprocals of the slopes of the two lines. The equality of the average heat-capacity rates is readily apparent. Also evident are the inequalities in internal temperatures and differential heat capacities. On the weak side, the differential heat capacity gradually decreases as a greater fraction of CO2 is driven from the liquid phase. On the strong side, a ‘‘kink’’ in the differential heat capacity (near 32
C) reflects a transition from a two phase mixture on the right to the fully liquefied state on the left, where the contribution of CO2 absorption to heat capacity vanishes. The position of the kink corresponds to the intersection of the 3–4 segment on the P–h diagram (Fig. 1) with the full resorption boundary and can be adjusted by moving the cycle up or down along the pressure axis. It is through such shifting that the average heat-capacity rates of the two streams attain balance, and this balancing is a major factor determining the locations of the state points on the P–h diagram for the optimal cycle. The suction and discharge pressures that optimize COP imply particular hardware values through Eqs. (26) and (27). Conversely, different hardware values produce pressures other than the optimum. The behavior of such a non-optimized situation was examined by arbitrarily changing the pressures P1 and P2 with respect to their values in the optimal cycle. Results for a 10% increase and for a 10% decrease in both pressures appear in the last two columns in Table 2. COP is decreased in both cases. The irreversibility increases in the desorber and decreases in the resorber result from

Table 1 van Laar activity coefficient parameters for cofluids studied in this work. The last three columns give references for heat capacity, density, and phase-equilibrium data Cofluid a

NMP Acetone NPGDAb GBLc a b c

MW (g mol1)

A0

A1

C0

C1

Heat capacity

Density

Phase equilibrium

99.13 58.08 188.16 86.09

1.386 1.993 0.372 1.573

0.833 1.797 0.510 0.774

0.832 3.247 4.047 1.100

0.564 3.091 2.614 0.831

[27,30] [32] [27,30] [37]

[21] [33–36] [27,30] [27]

[30,31] [33–36] [27,30] [27]

N-methyl-2-pyrrolidone. Neopentylglycol diacetate. g-Butyrolactone.

1130

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

Table 2 Application of lost-work theorem [Eq. (28)], to the optimal, ideal-hardware cycle and to cycles with non-optimal suction and discharge pressures. The cofluid is NMP with CO2 loading Y=0.36 Optimal cycle

10% Pressure increase

10% Pressure decrease

: I(W K1) In expansion device In desorber In resorber In internal heat exchanger

0.928 0.886 0.188 0.383

1.331 0.929 0.130 1.316

1.302 0.894 0.184 0.522

Work (W) Reversible Irreversible Total

126 754 880

126 1172 1298

126 918 1044

COP

3.98

2.70

3.35

Discharge pressure (kPa) Suction pressure (kPa) : : Q: c =m(kJ / kg cofluid) C: ref;weak (W K1) C: ref;strong (W K1) C: ref;D (W K1) Cref;R (W K1)

1864 1016

2050 1118

1678 914

15.8 571 571 749 492

9.5 1021 902 1326 872

13.9 630 682 814 540

increased refrigerant-side heat-capacity rates. In the desorber, the mismatch with the small air-side heatcapacity rate is larger, causing larger irreversibility, while, in the resorber, the refrigerant heat-capacity rate : more closely approaches that on the air side, reducing I. The most important effect, however, occurs in the internal heat exchanger. The two heat-capacity rates, which were closely balanced in the optimal cycle, now differ, generating irreversibility in the pressure-increase case almost as large as that in the expansion device. Thus the balance of heat-capacity rates in the internal heat exchanger largely controls the optimization of COP. In the more common compression cycle with solution circuit, liquid and vapor streams are compressed separately before mixing at the resorber inlet [29]. This mixing process is highly irreversible and limits the theoretical efficiency of the cycle. In contrast, wet compression allows phase equilibration to occur within the compressor and in principle incurs no additional mixing irreversibility, although in practice equilibration is unlikely to be complete in a real compressor. An approximate calculation1 for the otherwise optimal cycle in 1

In this calculation, the CO2 vapor and CO2-cofluid solution were compressed separately between the : suction and discharge pressures that optimized the cycle. I was calculated by mixing the resulting streams adiabatically.

Fig. 2. Temperature profiles in the internal heat exchanger, corresponding to the optimal cycle in Table 2. The horizontal coordinate stands in one-to-one correspondence with location inside the exchanger.

Table 2 finds the potential mixing irreversibility to be : I 1.2 W K1 if CO2 and cofluid streams were compressed separately before mixing, which would reduce the COP from 3.98 to 2.81.

5. Dependence of performance on CO2-cofluid mixture properties The results above demonstrate the performance limitations imposed on the wet-compression CO2-cofluid cycle by the hardware configuration and external environmental conditions. The CO2-cofluid mixture properties and ratio of CO2 to cofluid also strongly influence cycle performance, and we explore these dependences here. Although the heat capacity, density, and thermal expansion coefficient of the pure cofluid do enter into the thermodynamic description of the mixture, the cycle performance depends on these parameters relatively weakly. A much stronger dependence is found on the equilibrium vapor pressure Pvap(n,T) and the differential heat of solution hsoln(n,T) of CO2 vapor over cofluid at a given temperature and liquid composition. The variations in these properties among cofluids are captured in the CO2 activity coefficient (n, T). We consider the effects of equilibrium vapor pressure and heat of solution on the cycle performance using two approaches. First, we simplify the thermodynamic property model and derive simpler equations for the enthalpy and entropy changes between any two points. This leads to analytic expressions for the cooling capacity, work, and COP within this simplified model. A set of hypothetical cofluids are then studied systematically to determine how changes in CO2 solubility, heat of solution, and loading affect cycle performance. Second, the complete thermodynamic property model is applied

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

to CO2 mixtures with four real cofluids (acetone, NMP, NPGDA, GBL), and the differences in cycle performance are interpreted using the expressions and results obtained from the simplified approach. The hypothetical cofluids are not intended to represent experimentally realizable systems; their main use is in helping to interpret the model results obtained with the real fluids. The simplified thermodynamic property model retains the major features of the complete thermodynamic approach [19], neglecting less important ‘‘correction’’ terms. In particular, the CO2 vapor phase is assumed to behave ideally [i.e. CO2  1 in Eq. (2)], the heat capacities of CO2 and cofluid are taken to be constants (37.0 and 183.4 J mol1 K1, respectively), compression of pure cofluid is taken to contribute negligibly to the mixture enthalpy and entropy, and hsoln is assumed to be constant for all compositions and temperatures. To satisfy this last requirement, we adopt a condensedphase CO2 standard state fugacity f oCO2 ðT; PÞ [i.e. in Eq. (3)] that obeys the Clausius–Clapeyron equation:   D1 1 1 o  lnf CO2 ðTÞ ¼ lnD0 þ ð30Þ R T To with T
=300 K and constants D0=6631 kPa and D1=– 16.21 kJ mol1 chosen to be representative of an ideal CO2-cofluid mixture. With  [Eq. (3)] taken to be unity this model describes a mixture that obeys Raoult’s law [P vap ðn; TÞ ¼ xf oCO2 ðTÞ] and has a constant hsoln=D1. To explore the effects of deviations from Raoult’s law, we consider a simplified van Laar model [Eq. (7)] for  in which C0=C1=0.2 Choosing positive or negative A0 has the effect of scaling Pvap upward or downward at constant hsoln, while choosing positive or negative A1 and setting A0=A1(Tc / T
) has the effect of decreasing or increasing j hsoln j at fixed Pvap(n, 300 K). Under these simplifying assumptions, the enthalpy and entropy differences between any two arbitrary (T, P, n) points take on particularly simple forms:    hj  hi ¼ YCp;CO2 þ Cp;cofl Tj  Ti ð31Þ   þhsoln nj  ni MW1 cofl

     Tj pj YCp;CO2 þ Cp;cofl ln  YRln Ti pi     nj ni 1 þ nj  þ R ln MW1 þhsoln cofl Tj Ti 1 þ ni

sj  si ¼



ð32Þ 2 Defining the activity coefficient based on Raoult’s law requires that  !1 as x !1 and thus that at least one of the Ci be non-zero. To satisfy this restriction, we can consider C0 to be non-zero but small enough to have a negligible effect on the mixture properties over the composition range of interest.

1131

Approximate expressions can: now be derived for the : specific refrigeration capacity Qc =m ¼ h6  h5 and spe: : cific work W=m ¼ h2  h1 in the ideal refrigeration cycle, where the subscripts refer to the labeling in Fig. 1. For the former, we first note that because the expansion process is isenthalpic, h6 h5=h6 h4. As shown above, in an ideal cycle with unit effectiveness heat exchangers, maximum COP is attained when T6=T4, and thus h6 h4 has contributions only from the transfer of CO2 from the liquid to the vapor phase. Noting that the composition at point 4 is Y, Eq. (31) gives : : Y  n6 Qc =m ¼ h6  h4 ¼ j hsoln j MWcofl Y ¼ j hsoln j MWcofl

ð33Þ

where =1 – n6/Y is the fraction of CO2 in the vapor phase at the desorber exit. Applying the same simplified phase equilibrium model,  can be related to the suction pressure P1 and desorber exit temperature T6 by ! 1 P1  ¼1 ð34Þ Y  ðT6 Þf oCO2 ðT6 Þ  P1 These equations suggest the specific refrigeration capacity should increase with increasing |hsoln| and Y. It should also increase with decreasing suction pressure, because more CO2 desorbs from the liquid phase. An exact expression : : for the specific work of isentropic compression, W=m, within this simplified thermodynamic model can be obtained by setting Eq. (32) to zero and substituting into Eq. (31). It is more informative, however, to introduce further simplifications into Eq. (32) first. From cycle-model calculations using the environmental conditions described above, 1 < T2 / T1 < 1.1, so that for the compression process the entropy expression can be expanded to

    T2  T1 p2  YRln s2  s1 ¼ YCp;CO2 þ Cp;cofl T1 p1      n2 n2 n1 T2 T1 1 þ n2 þhsoln  þ R ln MW1 cofl T1 n2 T1 1 þ n1 ð35Þ The last term in the braces is roughly invariant in the optimized cycles and in exploring trends among cofluids can be approximately ignored. Further, the relative composition change (n2 – n1)/n2 during compression is much greater than the relative temperature change (T2 – T1)/T1, so that the latter can be approximately ignored in the hsoln term. Setting the remainder of Eq. (35) to zero and combining with Eq. (31) yields

1132

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

: : W=m ¼ h2  h1  RT1

Y lnðP2 =P1 Þ MWcofl

ð36Þ

In the ideal cycle, T1 is set by the external resorber environmental conditions, so that the specific compression work should scale with the logarithm of the discharge to suction pressure ratio and with the CO2 loading. Finally, an approximate expression for COP can be obtained by combining Eqs. (33) and (36): : : COP ¼ Qc =W 

j hsoln j RT1 lnðP2 =P1 Þ

ð37Þ

Because of the similar dependences of the specific capacity and work on Y, to first order COP has no explicit dependence on Y and scales linearly with hsoln and . The cycle state points that maximize COP within the simplified thermodynamic properties model can be obtained using the procedures described above. Table 3 shows the calculated state points for a baseline CO2-cofluid mixture with =1 and Y=0.4 (O), as well as for mixtures with van Laar parameter A0 adjusted to vary Pvap (A and B), A0 and A1 adjusted to vary hsoln (C and D), and Y adjusted to vary the CO2 loadings (E, F, and G). Across the series of CO2-cofluid mixtures A!O!B, the CO2 loading and differential heat of solution are held constant while , and as a result Pvap(n, T), are varied such that for a given temperature and CO2 composition, A has a 40% lower and B a 40% higher vapor pressure than the baseline mixture O. This uniform, temperature-independent scaling causes both the optimal suction (P1) and discharge (P2) pressures to scale by the same factors. The ratio of these two remains essentially constant, and as a consequence the specific work is also constant, in accord with Eq. (36). Similarly, this uniform pressure scaling causes the CO2 desorbing fraction  to remain constant and therefore the specific refrigeration capacity and COP to also remain constant.

Thus, the only effect of a uniform increase or decrease of Pvap is to shift the optimal operating pressure upward or downward. Across the series of CO2-cofluid mixtures C!O!D, the differential heat of solution is varied over a range typical of real CO2-cofluid mixtures, as shown below. The heat of solution is intimately connected with the temperature dependence of , so these mixtures not only differ in heat of solution but also in Pvap at all temperatures other than T
=300 K. As shown in Table 3, this coupling is manifested in the optimal cycles as a decrease in the suction pressure and an increase in the discharge pressure with increasing j hsoln j, leading to increases in ln(P2/P1) of roughly 50% from C to O to D. The specific work increases in parallel, as suggested by Eq. (36), although the increase is partially offset by higher order terms neglected in this expression. The specific refrigeration capacity also increases with j hsoln j. This increase arises from a combination of two effects [Eq. (33)]: first, a direct effect from the increase in energy transported per molecule of CO2, and second, an indirect effect from the increase in the CO2 desorption fraction . This desorption fraction is related to the desorber exit temperatures T6 by Eq. (34); larger j hsoln j increases T6 and thereby f oCO2 ðT6 Þ and . The specific capacity is a slightly stronger function of j hsoln j than is the specific work, so that the COP increases slowly with increasing j hsoln j. Finally, the series of mixtures (E, O, F, G) probe the effect of increasing CO2 loading Y from 0.2 to 0.8 for otherwise fixed mixture properties. As shown in Table 3, as Y is increased, the optimal suction and discharge pressures increase monotonically. This relationship between CO2 loading and discharge pressure is easily understood with reference to the model P–h diagram (Fig. 1): increasing Y pushes the full resorption boundary upward on the diagram, which, to maintain balance in the internal heat exchanger, drives the optimal dis-

Table 3 Calculated optimal cycle parameters of a series of CO2-cofluid mixtures represented by the simplified thermodynamic properties model : : : : f oCO2 ð300 KÞ P1 P2 ln (P2/P1) T4 (=T6) T2  Qc =m W=m COP Y hsoln

1 1 ( C) (kJ kg ) (kJ kg1) (kJ mol ) (kPa) (kPa) (kPa) ( C) O

0.4

16.215

6631

955

2115

0.79

17.0

54.6

0.45

29.67

5.04

5.89

A B

0.4 0.4

16.215 16.215

4022 9284

578 1340

1285 2955

0.80 0.79

17.1 17.0

54.6 54.5

0.46 0.45

29.83 29.51

5.07 5.01

5.89 5.89

C D

0.4 0.4

14.215 18.215

6631 6631

1030 900

1953 2230

0.66 0.91

14.6 18.4

52.4 56.1

0.36 0.50

23.30 36.42

4.02 6.07

5.79 6.00

E F G

0.2 0.6 0.8

16.215 16.215 16.215

6631 6631 6631

550 1300 1550

1083 2973 3754

0.68 0.83 0.88

12.3 20.7 25.4

54.7 58.9 63.1

0.35 0.52 0.60

11.35 50.77 78.92

2.03 8.25 12.37

5.59 6.15 6.38

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

charge pressure to higher values. The specific work is expected to increase proportionally to Y [Eq. (36)] and this effect is magnified by the gradual increase in pressure ratio. The specific capacity also increases proportionally to Y [Eq. (33)], and this effect too is magnified by an increase in the CO2 desorption fraction  [Eq. (34)] with Y. Again, the specific capacity increases more rapidly than the specific work, and over the range of compositions studied here the COP increases slowly with Y.

6. Performance of real CO2-cofluid mixtures In contrast to the simplified CO2-cofluid mixtures just considered, real mixtures have more complicated temperature- and composition-dependent properties that complicate the analysis of their performance in the wetcompression CO2-cofluid cycle. The strongest determinants of the performance in an ideal cycle are hsoln and Pvap. These quantities are obtained by fitting the activity-coefficient model [Eq. (8)] to experimental data. A useful way to visualize them is to plot hsoln against Pvap over representative ranges of temperature and liquid phase composition. Fig. 3 shows such a plot for the four real cofluids listed in Table 1 over 0 < T < 40
C and 0.05< ! < 0.20. (In comparing cofluids of differing molecular weights, it is more convenient to represent compositions in terms of mass ratios ! rather than mole ratios n; the two are related by !=n (MWCO2 =MWcofl ).) In general, the lowest pressures and most negative differential heats of solution are found at the lowest temperatures and compositions. For a given cofluid, raising the temperature or increasing the liquid-phase CO2 concentration raises Pvap considerably and diminishes the magnitude of hsoln by 10–20%. The range of heats of solution is fairly narrow, varying by approximately 20% among cofluids. CO2-acetone has an advantage of

Fig. 3. Differential heat of solution hsoln and equilibrium vapor pressure Pvap of four CO2-cofluid mixtures, evaluated over 0
1133

approximately 2 kJ mol1 over the other mixtures. The pressure ranges are significantly larger, with the CO2acetone mixture having an appreciably smaller CO2 vapor pressure than the CO2 mixtures with NMP, NPGDA, or GBL. Among the latter, CO2-NPGDA has the lowest minimum and maximum pressures. Because of its lower pressure range and greater differential heat of solution, acetone is expected to perform best in the cycle, with the other three cofluids performing comparably to each other. As we show below, simulations largely bare these trends out. For each of these CO2-cofluid mixtures of Table 1, we determined ideal cycles that maximize COP over a range of CO2 loadings using the full thermodynamic models. To account for the differing molecular weights of the cofluids, the loading is expressed in terms of the total mass ratio %=Y (MWCO2 =MWcofl ) rather than the mole ratio Y. Fig. 4 shows the optimal discharge pressures as

Fig. 4. Dependence of optimal discharge pressure on mass ratio % for CO2 with several cofluids.

Fig. 5. Dependence of fraction of vapor phase CO2 at desorber exit, , in the optimized cycle on mass ratio % for CO2 with several cofluids.

1134

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

Fig. 6. Dependence of specific work (lower curves) and specific refrigeration capacity (upper curves) in the optimized cycle on mass ratio % for CO2 with several cofluids.

a function of % for these four mixtures. At a given %, the discharge pressures follow the trends in Pvap shown in Fig. 3, with CO2-acetone operating at a much lower pressure than the other three mixtures. Similar trends are seen in the suction pressure as well. As % is increased, the optimal discharge pressures increase monotonically: most rapidly for CO2-GBL, which has the highest Pvap range, and least rapidly for acetone, which has the lowest Pvap range. This relationship between CO2 loading and discharge pressure is exactly analogous to that observed in the simple cofluid model above, and again arises from the requirement of balance in the internal heat exchanger. The ratio of suction to discharge pressures increases slowly from 1.6 to 1.8 at small % and tends towards 2.2 at the largest values of %. The computed desorbed CO2 fraction  for the four CO2-cofluid mixtures as a function of % is shown in Fig. 5. All four mixtures behave similarly, with the fraction increasing slowly with % from approximately 0.2 to almost 0.5, similar in range to that found with the simple thermodynamic properties: model. The computed : specific refrigeration capacities Qc =m ¼ h6  h5 for the four cofluids as a function of % are shown in Fig. 6. As expected from Eq. (33) and the simple mixture model, the capacities scale monotonically with the loading. CO2-acetone has a slightly larger specific capacity than the other mixtures, largely reflecting its advantage in hsoln. The variations in  introduce a slight upward curvature of specific capacity with %. The rate of increase of  is smaller for CO2-acetone than for CO2 with NMP, NPGDA, or GBL, offsetting its advantage in hsoln at larger %. These latter effects are all relatively small: because the heats of solution and CO2 desorbed fractions are similar, the main determinant of specific

Fig. 7. Dependence of optimal COP on mass ratio for CO2 with several cofluids.

refrigeration capacity for the four cofluids is simply the amount of CO2 circulated with a given mass of cofluid. As noted above, the optimized pressure ratio P2/P1 is similar across cofluids and grows only slowly with %. Thus, from Eq. (36), the optimal specific compression work is expected to grow approximately linearly with loading and to be approximately independent of cofluid. As shown in Fig. 6, the calculated specific work follows this general form closely. Finally, the similar scaling of the specific capacity and specific work with % produces COPs that increase only gradually with loading, as shown in Fig. 7. At a given %, CO2–acetone has a 15– 20% advantage in COP over the other three mixtures, consistent with its slightly higher j hsoln j.

7. Conclusions We have theoretically analyzed a refrigeration cycle involving co-circulation and wet-compression of CO2 and a non-volatile absorbing liquid (‘‘cofluid’’) for a representative set of externally imposed environmental conditions and cooling load. The treatment assumes steady state and the maintenance of thermodynamic equilibrium between the liquid and vapor phases at all points throughout the cycle. The hardware characteristics are not specified but rather are allowed to vary to satisfy the requirements of the given environmental conditions and working fluid properties. In accord with Eq. (28), maximum theoretical efficiency (COP) is obtained when the overall entropy generation rate of the cycle is minimized. The component that has the largest effect on entropy generation is the internal heat exchanger. Minimum entropy generation and maximum efficiency are attained when the heat-

1135

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

capacity rates on the strong and weak sides of the internal heat exchanger are equal (‘‘balanced’’), and deviations from balance rapidly degrade the theoretical performance. Calculations using a simplified thermodynamic properties model show that the two most important determinants of the cycle performance are Pvap, the vapor pressure of CO2 over the particular cofluid, and hsoln, the enthalpy associated with the transfer of CO2 from vapor to cofluid. Pvap largely determines the operating pressures. For a fixed range of permissible operating pressures, lower vapor pressure allows higher CO2 loading, which in turn leads to higher specific capacity and higher COP. For given Pvap, higher j hsoln j increases the specific refrigeration and COP. Comparisons among real cofluids are more complicated but follow the same general trends. Among the four CO2cofluid mixtures considered here, CO2-acetone, with its larger j hsoln j and lower Pvap range, is expected to have higher performance than CO2 with NMP, NPGDA, or GBL. These results illustrate the theoretical performance potential of the CO2-cofluid compression refrigeration cycle and the dependence of this performance on refrigerant properties. Comparisons have been made under a single set of imposed environmental conditions while allowing the hardware parameters to adjust to maximize COP. More realistic estimates of performance require consideration of mass and heat transfer and of the behavior of real hardware components, as well as consideration of a broader range of environmental conditions. Such analyses are the subject of on-going work.

Acknowledgements We thank Chris Seeton and Derryl Wright of Spauschus Associates Inc. and Professor Leonard Stiel of Polytechnic University for discussions and for access to experimental data prior to publication. We particularly wish to acknowledge the contributions and encouragement of the late Hans Spauschus and the late David Henderson.

Appendix The matrix elements ij  @fi =@xj , xj ¼ f T1 ; T2 ; T3 ; T4 ; T5 ; T6 ; TR; out g, are obtained from the cycle-model equations in the main text through partial differentiation. From Eq. (9), the nonzero elements of the first row are

14 ¼

@ h4 ; @ T4

15 ¼ 

@ h5 @ T5

ð38Þ

Similarly the nonzero elements of the remaining rows are

21 ¼ T0

32 ¼

@ s1 ; @ T1

@ h2 ; @ T2

22 ¼ T0

33 ¼ 

@ s2 @ T2

@ h3 ; @ T3

ð39Þ

37 ¼ 

: Cair;R : m

ð40Þ

: :

42 ¼ "R ; 43 ¼ 0; 47 ¼ 1; if Cair;R < Crefr;R

42 ¼ 1  "R ; 43 ¼ 1; 47 ¼ 0; otherwise ð41Þ @ h1 ; @ T1 @ h6 ¼ @ T6

51 ¼ 

56

53 ¼

@ h3 ; @ T3

54 ¼ 

@ h4 ; @ T4

ð42Þ

8

61 ¼ :0; 63 ¼ 1 : "int ; 64 ¼ 1; 66 ¼ "int ; > > < if Crefr;strong < Crefr;weak > 61 ¼ 1; 63 ¼ "int ; 64 ¼ 0; 66 ¼ 1  "int ; > : otherwise ð43Þ



75 ¼ "D ;

75 ¼ 1  "D ;

76 ¼ 0;

76 ¼ 1;

: : if Cair;D < Crefr;D otherwise ð44Þ

References [1] Lorentzen G. The use of natural refrigerants: a complete solution to the CFC/HCFC predicament. Int J Refrig 1995;18:190–7. [2] Robinson D, Groll E. Using carbon dioxide in a transcritical vapor compression refrigeration cycle. Sixth International Refrigeration Conference, Purdue University, 25 July 1996. [3] Wertenbach J, Kauf F. High pressure refrigeration system with CO2 in automobile air conditioning. CO2 Technology in Refrigeration, Heat Pump and Air Conditioning Systems, NTNU-Trondheim, 13–14 May 1997. [4] Gentner H. Passenger car air conditioning using carbon dioxide as refrigerant. Conference on Natural Working Fluids, Oslo, Norway, 2–5 June 1998. [5] Wertenbach J, Caesar R. An environmental evaluation of an automobile air conditioning system with CO2 versus HFC-134a as refrigerant. Conference on Natural Working Fluids, Oslo, Norway, 2–5 June 1998. [6] Pettersen J, Hafner A, Skaugen G, Rekstad H. Development of compact heat exchangers for CO2 air-conditioning systems. Int J Refrig 1998;21:180–93. [7] McEnaney R, Park YC, Yin JM, Hrnjak P. Performance of the prototype of a transcritical R744 mobile A/C system. Soc. Automotive Eng. 1999 [paper 1999– 01–0872].

1136

G. Mozurkewich et al. / International Journal of Refrigeration 25 (2002) 1123–1136

[8] Fischer SK, Sand JR, Total environmental warming impact (TEWI) calculations for alternative automotive air-conditioning systems. Soc Automotive Eng 1997 [paper 970526]. [9] Cheron J. Development of a resorption-absorption heat pump: study of solvent-solute couples. Comm Eur Communities 1984 [EUR 9467 FR]. [10] Osenbru¨ck, Verfahren zur Ka¨lteerzeugung bei Absorptionsmaschinen. Deutsches Reichspatent 1895 [DRP 84084]. [11] Altenkirch E., Kompressionska¨ltemaschine mit Lo¨sungskreislauf (vapor compression cycle with solution circuit). Ka¨ltetechnik 1950;2:251–9; Ka¨ltetechnik 1950;2:279–84; and Ka¨ltetechnik 1950;2:310–5. [12] Mucic V, Scheuermann B. Zwei-Stoff-KompressionsWarmepumpe mit Losungskreislauf (Two component compression heat pump with solution circuit), Pilot Plant Mannheim/Waldhof BMFT-Forschungsbericht T 1984: 84–197. [13] Stokar M, Trepp C. Compression heat pump with solution circuit, part 1: design and experimental results. Int J Refrig 1987;10:987–96. [14] Malewski WF. Integrated absorption and compression heat pump cycle using mixed working fluid ammonia and water. Proceedings of the 2nd International Workshop on Research Activities on Advanced Heat Pumps Graz September 1988. [15] Groll EA, Kruse H. Kompressionska¨ltemaschine mit Lo¨sungskreislauf fu¨r umweltvertra¨gliche Ka¨ltemittel. KK Die Ka¨lte und Klimatechnik 1992;45:206–18. [16] Groll E, Radermacher R. Vapor compression cycle with solution circuit and desorber/absorber heat exchange, ASHRAE Transactions 1994;100:73–83. [17] Groll E. Modeling of absorption/compression cycles using working pair carbon dioxide/acetone. ASHRAE Transactions 1997;103:863–71. [18] Spauschus HO, Henderson DR, Seeton CJ, Wright DC, Zietlow DC, Bramos GD, Abate W. Reduced pressure carbon dioxide cycle for vehicle climate control. Soc Automotive Eng 1999 [paper 1999–01–0868]. [19] Greenfield ML, Mozurkewich G, Schneider WF, Bramos GD, Zietlow DC. Thermodynamic and cycle models for a low-pressure CO2 refrigeration cycle. Soc Automotive Eng 1999 [paper 1999–01–0869]. [20] Mozurkewich G, Roberts RD, Greenfield ML, Schneider WF, Zietlow DC, Meyer JJ, Stiel LI. Cycle-model assessment of working fluids for a low-pressure CO2 climate-control system. Soc Automotive Eng 2000 [paper 2000–01–0578]. [21] Prausnitz JM, Lichtenthaler R, Azevedo EG. Molecular thermodynamics of fluid-phase equilibria. Prentice-Hall, Englewood Cliffs (NJ): 1986. [22] Pitzer KS, Sterner SM. Equations of state valid continuously from zero to extreme pressures for H2O and CO2. J Chem Phys 1994;101:3111–6 and 1995;16:511–8.

[23]

[24] [25]

[26] [27] [28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

Pitzer KS, Sterner SM. Equations of state valid continuously from zero to extreme pressures with H2O and CO2 as examples. Int J Thermophys 1995;16:511. Lyckman EW, Eckert CA, Prausnitz JM. Generalized reference fugacities for phase equilibrium thermodynamics. Chem Eng Sci 1965;20:685–91. Holman JP. Heat transfer, 4th ed. McGraw-Hill, New York: 1976 [pp. 403–404]. Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes. Cambridge University Press, Cambridge, 1986. Bejan A. Advanced engineering thermodynamics. Wiley, New York: 1997 [chapter 3]. Henderson DR, Seeton CJ. private communication. NIST Standard Reference Database 23: thermodynamic and transport properties of refrigerants and refrigerant mixtures—REFPROP, Ver. 6.01 (National Inst. of Standards and Technology, Gaithersburg, Maryland) 1998. Radermacher R. Thermodynamic and heat transfer implications of working fluid mixtures in Rankine cycles. Int J Heat Fluid Flow 1989;10:90–102. Henderson DR. Properties of working fluids for reduced pressure carbon dioxide systems. Soc Automotive Eng 1999 [paper 1999–01–1189]. Murrieta-Guevara F, Romero-Martinez A, Trejo A. Solubilities of carbon dioxide and hydrogen sulfide in propylene carbonate, N-methylpyrrolidone and sulfolane. Fluid Phase Equil 1988;44:105–15. Zubchenko YP, Shakhova SF, Ladygina OP. Solubility of carbon dioxide in N-methylpyrrolidone under pressure. Khim Prom-st 1985;9:535. Low DIR, Moelwyn-Hughes EA. The heat capacities of acetone, methyliodide, and mixtures thereof in the liquid state, Proc Royal Soc London 1962;A267:384– 94. Deshpande DD, Bhatagadde LG. Heat capacities at constant volume, free volumes, and rotational freedom in some liquids. Aust J Chem 1971;24:1817–22. Katayama T, Ohgaki K, Maekawa G, Goto M, Nagano T. Isothermal vapor-liquid equilibria of acetone-carbon dioxide and methanol-carbon-dioxide systems at high pressures. J Chem Eng Japan 1975;8: 89–92. Adrian T, Maurer G. Solubility of carbon dioxide in acetone and propionic acid at temperatures between 298 K and 333 K. J Chem Eng Data 1997;42:668–72. Chang CJ, Day C-Y, Ko C-M, Chiu K-L. Densities and P-x-y diagrams for carbon dioxide dissolution in methanol, ethanol, and acetone mixtures. Fluid Phase Equil 1997;131:243–58. Ismailov TS, Gabzalilova NR, Makhkamoov Kh. M. Complex study of physicochemical properties of gammabutyrolactone. Uzb Khim Zh 1988:48–50