Applied Energy 80 (2005) 383–399

APPLIED ENERGY www.elsevier.com/locate/apenergy Theoretical performances of various refrigerant–absorbent pairs in a vapor-absorption refrigeration cycle by the use of equations of state
A. Yokozeki
*
DuPont Fluoroproducts Laboratory, Chestnut Run Plaza 711, Wilmington, DE 19880, USA Accepted 27 April 2004 Available online 28 July 2004

Abstract The vapor-absorption refrigeration cycle is an old and well-established technique, particularly with ammonia/water and water/LiBr systems. New types of refrigerant–absorbent pairs are also being actively studied. Modeling the cycle performance requires thermodynamic properties, which have been largely based on empirical correlation equations fitted to a large amount of experimental data such as solubility at various temperatures, pressures, and compositions. In this report, we have demonstrated, for the first time, a thermodynamically consistent model based on the equations of state for refrigerant–absorbent mixtures. Various commonly known binary-pairs for the absorption cycle are used as examples. Cycle performances and some new insights on understanding the cycle process are shown. Ó 2004 Elsevier Ltd. All rights reserved.
Keywords: Vapor absorption cycle; Equations of state; Refrigerant; Absorbent; Modeling; Cycle performance; Solubility; Enthalpy

1. Introduction The vapor-absorption refrigeration cycle is more than 100 years old. Although the vapor-compression cycle took over most of air-conditioning and refrigerating
*

Tel.: +1-302-999-4575; fax: +1-302-999-2093. E-mail address: akimichi.yokozeki@usa.dupont.com (A. Yokozeki).

0306-2619/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2004.04.011

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applications, the well-known refrigerant–absorber systems (H2 O/LiBr and NH3 / H2 O) are still being used for certain applications, particularly in the field of industrial applications or large-scale water chiller systems. Recently, more attention has been directed towards the recovery of waste heat using the NH3 /H2 O system [1]. Besides these traditional binary-pairs, in the late 1950s, some pioneering studies were made to propose new refrigerant–absorbent pairs for the vapor-absorption cycle, using fluoroalkane refrigerants with organic absorbents [2,3]. Such studies continue actively even at the present time, especially in academic institutions [4–6]. In order to understand the vapor-absorption cycle and to evaluate the cycle performance, thermodynamic property charts such as temperature–pressure–concentration (TPX) and enthalpy–temperature (HT) diagrams are required. These charts correspond to the familiar PH (pressure–enthalpy) or TS (temperature–entropy) diagram in the vapor-compression cycle analysis. However, the use of these charts may not be as straightforward as with vapor compression in a compressor, where the compression process is theoretically a single isentropic path, while the vapor-absorption cycle employs the so-called generator–absorber solution circuit, and several thermodynamic processes are involved. The PH or TS diagram in the vapor-compression cycle is constructed using equations of state (EOS), and the cycle performance and all the thermodynamic properties can be calculated in a thermodynamically consistent way. On the other hand, thermodynamic charts for the vapor-absorption cycle are usually made by empirical correlations, which are fitted to experimental solubility and heat capacity data for solution properties, while the vapor-phase properties are calculated with the refrigerant EOS. Sometimes, the solubility data are correlated using theoretical solution (often called ‘‘activity’’) models [4,7]. However, such models are limited in their use to temperatures well below the refrigerant critical temperature, and modeling solutions at high generator-temperatures will become invalid. Then, it is clear that the combined use of empirical-fitting equations or partially correct equations with the gas phase EOS may not always be completely consistent. Thus, it is desirable to model the vapor-absorption cycle process with thermodynamically valid EOS only. Perhaps, one of the most significant benefits of using EOS is that, even above the critical temperature of refrigerants, thermodynamic properties can be correctly calculated [8]. Although modeling refrigerant mixtures with EOS is familiar, refrigerant and non-volatile compound mixtures are traditionally treated with empirical correlation models by air conditioning and refrigeration engineers, e.g., refrigerant–lubricant oil solubility. One of the difficult problems using EOS for such mixtures would be how to set up EOS parameters for non-volatile compounds without much information about the critical parameters and vapor-pressure data. However, we have overcome this problem and successfully demonstrated the usefulness of EOS models, which have been applied to refrigerant–lubricant oil-solubility data [9,10]. Therefore, similar EOS models can be used for the present study to calculate all thermodynamic properties consistently. To our best knowledge, no such work has been reported in the literature for the vapor-absorption cycle process, except for NH3 /H2 O [13].

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Various refrigerant–absorbent pairs selected in the present study are neither particularly unique nor original. Absorbents are commonly known compounds, such as poly-alkylene glycol di-methyl ether, DMA (N,N-di-methyl acetamide), DMF (N,N-di-methyl formamide), etc., except for some polyol esters which are not commonly cited as absorbents. Refrigerants are R-22 and several HFC compounds as well as ammonia for NH3 /H2 O. Although many pairs have been examined here, the purpose of the present report is not to discuss individual performances and to select the best binary pairs but to demonstrate a thermodynamically-consistent EOS model and to understand the vapor-absorption cycle process with it.

2. Theoretical modeling 2.1. Thermodynamic properties In this study, we have employed a generic Redlich–Kwong (RK) type of cubic EOS [10,11], which is written in the following form: P¼ RT aðT Þ À V À b V ðV þ bÞ R2 Tc2 aðT Þ Pc ð1Þ

aðT Þ ¼ 0:427480 b ¼ 0:08664 RTc Pc

ð2Þ ð3Þ

The temperature-dependent part of the a parameter in the EOS for pure compounds is modeled by the following empirical equation [10]: 63 X  Tc T k aðT Þ ¼ bk ð4Þ À T Tc k¼0 The coefficients, bk , are determined so as to reproduce the vapor pressure of each pure compound. For absorbents, however, usually no vapor pressure data are available, or vapor pressures are practically zero at application temperatures, and furthermore, no data for the critical parameters (Tc and Pc ) exist. The critical parameters of the absorbents can be estimated in various ways [12]. As discussed in [10], rough estimates of critical parameters for high boiling-point compounds are sufficient for correlating the solubility (PTX) data. On the other hand, the temperature-dependent part of the a parameter for absorbents is significantly important when we try to correlate the PTX data of refrigerant–absorbent mixtures, although the vapor pressures of absorbents are essentially zero at the temperature of interest. Here, aðT Þ for an absorbent is modeled by only two terms in Eq. (4), as applied for the case of refrigerant/ lubricating-oil mixtures [10].

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kij ¼

lij lji ðxi þ xj Þ ; where kii ¼ 0; lji xi þ lij xj   Tc T aðT Þ ¼ 1 þ b1 À T Tc

ð5Þ

ð6Þ

The coefficient b1 in Eq. (6) will be treated as an adjustable-fitting parameter: see Section 3.1. Then, the a and b parameters for general N -component mixtures are modeled in terms of binary interaction parameters [11], which may be regarded as a modified van der Waals–Berthelot mixing formula: aðT Þ ¼
N X pffiffiffiffiffiffiffiffi ai aj ð1 À f ðT Þkij Þxi xj ; i;j¼1

ai ¼ 0:427480

2 R2 Tci ai ðT Þ; Pci

ð7Þ

f ðT Þ ¼ 1 þ Cij T ;

where Cij ¼ Cji

and

Cii ¼ 0; RTci ; Pci

ð8Þ

b¼

N 1X ðbi þ bj Þð1 À mij Þxi xj ; 2 i;j¼1

bi ¼ 0:08664

where mij ¼ mji ; mii ¼ 0;

ð9Þ

where Tci is the critical temperature of the ith species; Pci is the critical pressure of the ith species; xi is the mole fraction of the ith species. In the present model, there are four binary interaction parameters: lij , lji , mij , and Cij for each binary pair. It should be noted that, when lij ¼ lji in Eq. (8) and Cij ¼ 0 in Eq. (7), Eq. (6) becomes the ordinary quadratic-mixing rule for the a parameter. The present EOS model has been successfully applied for highly non-symmetric (with respect to polarity and size) mixtures, such as various refrigerant/oil mixtures [10] and ammonia/butane mixtures [11]. For phase-equilibrium (solubility) calculations, the fugacity coefficient /i for each compound is needed and derived for the present mixing rule     0 PV b b0i ab0i a ai b0i V 1À ; À þ ln /i ¼ À ln þ À þ 1 ln RT V V þb V À b bRT ðV þ bÞ bRT a b ð10Þ where b0i and a0i are given by b0i ¼
N X ðbi þ bj Þð1 À mij Þxj À b; j¼1

ð11Þ

a0i

( ) N X pffiffiffiffiffiffiffiffi xi xj ðlji À lij Þð1 þ Cij T Þ ¼2 ai aj xj 1 À kij À 2 ðlji xi þ lij xj Þ j¼1

ð12Þ

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A thermodynamically derived function relevant to the present study is the enthalpy (H ), which is given, in a general form     Z X N a T da V PV 0 þ RT H¼ Cpi xi dT þ À ln À1 b b dT V þb RT i¼1    2 RT db a db 1 1 b À þ À ln 1 þ þC ð13Þ V V À b dT b dT V þ b b where C is an arbitrary constant, which can be any value of our choice, but must be the same constant for any component mixtures within the system in question. The 0 ideal-gas heat capacity for each compound Cpi in Eq. (13) is modeled by the polynomial form
0 Cp ¼ C0 þ C1 T þ C2 T 2 þ C3 T 3

ð14Þ

2.2. Vapor-absorption refrigeration cycle A schematic diagram for a simple vapor-absorption refrigeration cycle used in the present study is shown in Fig. 1. The system is composed of condenser and evaporator units with an expansion valve similar to an ordinary vapor compression cycle, but the compressor unit is here replaced by an absorber–generator solution circuit, which has a vapor absorber, a gas generator, a heat exchanger, a pressure control (reducing) valve, and a solution liquid-pump. Theoretical cycle performances are modeled as follows. The overall energy balance gives Qg þ Qe þ Wp ¼ Qc þ Qa From the material balance in the absorber or generator, we have ms xa ¼ ðms À mr Þxg ; and this provides a mass-flow-rate ratio, f , as defined by ms xg f  ¼ ; mr xg À xa ð15Þ ð16Þ ð17Þ

where x is a mass fraction of an absorbent in solution, the subscripts a and g stand for the generator and absorber solutions, and mr and ms are mass flow rates of gaseous refrigerant and the absorber-exit solution (or solution pumping rate), respectively. This flow-rate ratio f is an important parameter for characterizing the system performance. When we assume a heat-transfer efficiency of unity in the heat exchanger, the energy-balance equation becomes Qh  ðH2 À H3 Þðms À mr Þ ¼ ðH1 À H4 Þms À Wp ; ð18Þ

where H is the enthalpy; the subscript numbers (1, 2, 3, and 4) correspond to the locations shown in Fig. 1. From Eq. (18), the generator-inlet enthalpy, H1 , can be obtained: H1 ¼ H4 þ ðH2 À H3 Þð1 À 1=f Þ þ Wp =mr ð19Þ

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Refrigerant Gas Flow Rate: mr

Qc

1
Generator: Tg

5
Condenser: Tcon

Qg

2 mr Heat Exchanger: HeatH with efficiency = 1. 0

6

m s – mr mr : Refrigerant Gas Flow Rate

3 ms 7
Evaporator: Teva

Qa
4

Absorber: Ta

ms : Solution Flow Rate

Qe

Liquid Pumping Power: W p
Fig. 1. A schematic diagram of a simple vapor-absorption refrigeration cycle.

From the energy balance around the generator, the generator heat input, Qg , is given by Qg ¼ H5 mr þ H2 ðms À mr Þ À H1 ms By eliminating H1 from this equation with Eq. (19), Eq. (20) can be written as Qg =mr ¼ H5 À H4 f þ H3 ðf À 1Þ À Wp =mr Similarly, the heat rejection in the absorber, Qa , is given by Qa =mr ¼ H3 ðf À 1Þ þ H7 À H4 f Condenser and evaporator heats per unit mass flow are Qc =mr ¼ H5 À H6 Qe =mr ¼ H7 À H6 ð23Þ ð24Þ ð22Þ ð21Þ ð20Þ

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Then, the system performance is defined by a heat ratio, g (output power divided by input power), i.e. g¼ Qe Qg þ WP

However, the solution pumping-power, Wp , is usually much smaller than Qg , and it is customary to use a COP (coefficient of performance) defined as COP ¼ Qe Qg H7 À H6 H5 þ H3 ðf À 1Þ À H4 f ð25Þ

This can be expressed in terms of H and f : COP ¼ ð26Þ

Enthalpies at all locations and solubilities in the absorber and generator units will be calculated in a thermodynamically consistent way by the use of the present EOS model discussed above.

3. Analyses and results 3.1. EOS Parameters First, we have to set up our EOS parameters. The pure component EOS constants for refrigerants in the present study have been taken from our previous works [10,11], and are listed in Table 1 for the sake of completeness. As for selected absorbents in this study, the critical parameters have been estimated from group contribution methods [12] together with known boiling-points [14–16], and are shown in Table 1. The accuracy in critical parameters for these high boiling-point materials is not so important for correlating solubility data [10]. However, the b1 parameter in Eq. (6), as mentioned earlier, can be significantly important, and will be treated as an adjustable parameter in the analysis of binary-solubility data. In order to calculate thermal properties with the EOS, the ideal-gas heat capacity for each pure compound is needed as a function of temperature: see Eq. (14). The coefficients for Eq. (14) are listed in Table 2, where those for absorbents have been all estimated by group contribution methods [12]. It is stated that errors in the estimated ideal-gas heat capacity are generally less than 2% [12]. Next, we analyze solubility (VLE: vapor–liquid equilibrium) data of refrigerant/ absorbent binary mixtures in order to determine the EOS parameters for mixtures. The four binary-interaction parameters, lij , lji , mij , and Cij , and the absorbent b1 parameter for each binary pair have been determined by non-linear least-squares analyses with an object function of relative pressure-differences. The results for 27 selected binary-mixtures are shown in Table 3. Average absolute relative deviations Pn (AADs) in pressure, where AAD  i¼1 j1 À Pcal ðiÞ=Pobs ðiÞj=n, is less than 2% for good quality VLE data.

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Table 1 EOS constants of pure refrigerants and absorbentsa Compound R-22 R-32 R-125 R-134 R-134a R-143a R-152a NH3 H2 O PEC5 PEC9 PEB6 PEB8 DMA DMF DEGDME TrEGDME TEGDME NMP Molar mass 86.47 52.02 120.22 101.03 101.03 84.04 66.05 17.03 18.02 472 696 528 640 87.1 73.1 134.2 178.2 222.3 99.1 Tc (K) 369.17 351.26 339.19 391.97 374.21 346.20 386.44 405.40 647.10 751 774 800 793 656 650 607 651 704 722 Pc (kPa) 4978 5782 3637 4641 4059 3759 4520 11,333 22,064 1059 690 969 772 4018 4415 2852 2307 1934 4520 b0 1.0011 1.0019 1.0001 1.0012 1.0025 1.0006 1.0012 1.0018 1.0024 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 b1 0.43295 0.48333 0.47736 0.48291 0.50532 0.45874 0.48495 0.46017 0.54254 * * * * * * * * * * b2 )0.06214 )0.07538 )0.01977 )0.05070 )0.04983 )0.04846 )0.08508 )0.06158 )0.08667 0 0 0 0 0 0 0 0 0 0 b3 0.0150 0.00673 )0.0177 0 0 )0.0143 0.0146 0.00168 0.00525 0 0 0 0 0 0 0 0 0 0

a PEC5: pentaerythritol tetra-pentanoate, PEC9: pentaerythritol tetra-nonanoate, PEB6: pentaerythritol tetra-2-ethylbutanoate, PEB8: pentaerythritol tetra-2-ethylhexanoate, DMA: N,N-di-methyl acetamide, DMF: N,N-di-methyl formamide, DEGDME: di-ethylene glycol di-methyl ether, TrEGDME: tri-ethylene glycol di-methyl ether, TEGDME: tetra-ethylene glycol di-methyl ether, NMP: N-methyl-2-pyrrolidone. bi : coefficients for Eq. (4), and *: to be determined from solubility data analyses: see text and Table 3.

3.2. Absorption-cycle performance Now that we have all the necessary EOS parameters for the present refrigerant/ absorbent pairs, we can calculate any thermodynamic properties for these mixtures in a thermodynamically consistent way. The performance of the vapor-absorption refrigeration cycle is based on a simple ideal cycle shown in Fig. 1, and the theoretical model has been described in Section 2.2. Here, we neglect the pumping power Wp , since it is usually insignificant with respect to other thermal powers. In addition, several assumptions are made, which are not explicitly stated in Section 2.2: • There are no pressure drops in the connecting lines. • The refrigerant expansion process from the condenser to the evaporator is isoenthalpic, as usual in vapor-compression cycle calculations. The condition at Point 7 in Fig. 1 (exit of evaporator) is a pure refrigerant dew point with T ¼ Teva . • The condition at Point 6 is a refrigerant bubble point and there is no subcooled liquid. The condition at Point 5 (inlet to condenser) is a superheated state of a pure refrigerant with P ¼ Pcon and T ¼ Tg .

A. Yokozeki / Applied Energy 80 (2005) 383–399 Table 2 Coefficients for ideal-gas heat capacity (J molÀ1 KÀ1 ] in Eq. (14) Compound R-22 R-32 R-125 R-134 R-134a R-143a R-152a NH3 H2 O PEC5 PEC9 PEB6 PEB8 DMA DMF DEGDME TrEGDME TEGDME NMP C0 17.30 20.34 16.58 15.58 12.89 5.740 8.670 27.31 32.24 57.97 84.38 2.594 15.80 )2.678 0.87 77.21 62.63 77.84 )2.677 C1 0.16180 0.07534 0.33983 0.28694 0.30500 0.31388 0.2394 0.02383 1.924 Â 10À3 2.1551 3.5852 2.7280 3.4430 0.47905 0.38484 0.38424 0.71397 0.89232 0.47905 C2 )1.170 Â 10 1.872 Â 10À5 )2.873 Â 10À4 )2.028 Â 10À4 )2.342 Â 10À4 )2.595 Â 10À4 )1.456 Â 10À4 1.707 Â 10À5 1.055 Â 10À5 )1.01 Â 10À3 )1.81 Â 10À3 )1.42 Â 10À3 )1.82 Â 10À3 )2.87 Â 10À4 2.45 Â 10À5 3.04 Â 10À5 )2.93 Â 10À4 )3.77 Â 10À4 )2.87 Â 10À4
À4

391

C3 3.058 Â 10 )3.116 Â 10À8 8.870 Â 10À8 5.396 Â 10À8 6.852 Â 10À8 8.410 Â 10À8 3.392 Â 10À8 )1.185 Â 10À8 )3.596 Â 10À9 2.62 Â 10À7 4.36 Â 10À7 5.43 Â 10À7 6.30 Â 10À7 1.94 Â 10À7 5.98 Â 10À8 )1.04 Â 10À7 1.15 Â 10À7 1.25 Â 10À7 1.94 Â 10À7
À7

Ref.a [12] [19] [19] [19] [19] [19] [19] [12] [12] E E E E E E E E E E

a Ref.: used references and E: estimated from group contribution methods in [12]. See Table 1 for the notation of absorbents.

• Pressures in the condenser and the generator (Pcon and Pg ) are the same, and similarly, the evaporator and absorber pressures (Peva and Pa ) are equal. • The condition at Point 3 (solution inlet to the absorber) is a solution’s bubble point specified with the absorber pressure (Pa ) and a solution concentration of the generator (xg ). • Temperatures in the generator (Tg ), absorber (Ta ), condenser (Tcon ), and evaporator (Teva ) are specified as a given cycle condition. • The refrigerant-gas flow rate (mr ) is set to be 1 kg/s, without loss of generality, and the insignificant absorbent vapor is neglected. The first step in cycle calculations is to obtain Peva and Pcon as saturated-vapor pressures of a pure refrigerant at given temperatures: Bubble-Point P routine [7]. Then, using the usual TP (temperature–pressure) Flash routine [7], absorbent compositions, xg and xa , in the generator and absorber units are calculated. This provides f (flow rate ratio) in Eq. (17). The thermodynamic properties at Point 3 are determined from the assumption (5): Bubble-Point T routine [7]. The enthalpy at Point 1 is obtained from Eq. (19). Enthalpies at all other points are easily calculated with known T , P , and compositions. Thus, the necessary quantities for the performance evaluation can be obtained using the equations listed in Section 2.2. Cycle performances for the present binary systems are summarized in Table 4 with selected thermodynamic quantities, where the specified temperatures for the cycle condition are: Tg =Tcon =Ta =Teva ¼ 100=40=30=10° C, and mr ¼ 1 kg/s. For the present study, a userfriendly computer program has been employed [17], and any desired cycle conditions can be easily evaluated. The results in Table 4 are examples of many such case studies.

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Table 3 Binary interaction parameters of refrigerant–absorbent pairs determined from experimental PTX dataa Binary systems (1)/(2) R-32/PEB6 R-32/PEB8 R-125/PEC5 R-125/PEB6 R-125/PEB R-125/PEC9 R-134a/PEC5 R-134a/PEB6 R-134a/PEB8 R-143a/PEB6 R-152a/PEC5 R-152a/PEC9 R-152a/PEB6 R-152a/PEB8 NH3 /H2 O R-22/DEGDME R-22/TEGDME R-22/DMA R-22/DMF R-22/NMP R-134a/DEG-DME R-134a/DMA R-134a/DMF R-134a/TEG-DME R-134a/TrEG-DME R-134a/DEG-DME R-134/TEGDME l12 )0.006 0.0891 )0.045 )0.041 )0.006 0.1175 0.0515 0.0172 0.0076 0.1252 0.1343 0.0264 0.0014 0.0873 )0.316 )0.286 )0.180 )0.156 )0.076 )0.204 )0.036 )0.103 )0.171 )0.040 )0.027 )0.041 )0.246 l21 )0.006 0.0293 )0.047 )0.041 )0.006 0.0552 0.0272 0.0172 0.0076 0.0588 0.0421 0.0264 0.0014 0.0336 )0.316 )0.286 )0.601 )0.156 )0.076 )0.204 )0.102 )0.091 )0.122 )0.096 )0.074 )0.099 )0.246 m12;21 0.0265 0.0434 0.0022 0.0050 0.0092 0.0255 0.0227 0.0171 0.0088 0.0261 0.0465 0.0301 0.0184 0.0416 )0.0130 0.0 0.1197 0.0253 )0.1248 )0.0294 0.0275 )0.0389 )0.0951 0.0185 0.0243 0.0231 0 C12;21 (Â 10À3 ) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 )1.09 )2.04 0 7.70 0 0 0 0 0 0 0 )1.17 b1 (absorbent) 0.59299 0.70415 1.5266 1.3008 1.4136 1.3785 1.1142 0.94843 1.1861 1.4349 0.76002 0.87442 0.65012 0.73357 0.54254* 1.1256 0.22827 0.23760 0.40733 0.39816 1.12564 0.37076 0.40733 1.46898 1.13364 1.12564 1.25000 AAD (%) 1.28 1.82 1.13 0.99 1.82 1.29 1.18 1.06 0.81 0.90 0.94 0.87 0.95 1.94 4.30 3.10 3.42 3.80 8.40 3.89 1.75 0.92 0.94 1.68 1.15 1.77 2.94 Ref. [16] [15] [16] [16] [15] [15] [16] [15] [15] [15] [16] [15] [15] [15] [13] [20] [3] [5] [3,21] [5] [4] [4] [4] [4] [4] [4] [3]

a l12 ; l12 ; m12 ; C12 : binary interaction parameters, b1 : absorbent adjustable parameter in Eq. (4) or (6), *: not varied in the analysis for water. AAD %: average absolute relative deviation of fit in pressure. Ref.: references for solubility data used in the present analysis. See Table 1 for the notation of absorbents.

The well-known refrigerant–absorbent pairs, NH3 /H2 O and H2 O/LiBr, have also been calculated and are shown in Table 4. Here, a few comments are needed. In the case of NH3 /H2 O, the absorbent H2 O has a non-negligible vapor pressure at the generator exit, and in practical applications a rectifier (distillation) unit is required in order to separate the refrigerant from the absorbent water. In the present study, we have neglected such an effect and the extra power requirement. Thus, the calculated COP is overestimated for the present performance comparison. For H2 O/LiBr, we have not developed the EOS model. Instead, we have employed empirical-correlation diagrams for the thermodynamic properties [18]: i.e. a temperature–pressure–concentration diagram and an enthalpy–temperature diagram. In the vapor-absorption refrigeration cycle, the absorber–generator solution circuit corresponds to a compressor in the ordinary vapor-compression refrigeration cycle, and the evaporator and condenser parts are in principle the same for both cycles. Thus, it is important to know how the generator and absorber behave at

A. Yokozeki / Applied Energy 80 (2005) 383–399 Table 4 Comparisons of theoretical cycle performancesa Binary systems (1)/(2) R-22/DEGDME R-22/TEGDME R-22/DMA R-22/DMF R-22/NMP R-32/PEB6 R-32/PEB8 R-125/PEC5 R-125/PEB6 R-125/PEB8 R-125/PEC9 R-134/TEGDME R-134a/PEC5 R-134a/PEB6 R-134a/PEB8 R-134a/DMA R-134a/DMF R-134a/TEG-DME R-134a/TrEG-DME R-134a/DEG-DME R-143a/PEB6 R-152a/PEC5 R-152a/PEC9 R-152a/PEB6 R-152a/PEB8 NH3 /H2 O H2 O/LiBr Pcon ; Pg (kPa) 1531 1531 1531 1531 1531 2486 2486 2011 2011 2011 2011 810 1015 1015 1015 1015 1015 1015 1015 1015 1835 907 907 907 907 1548 7.38 Peva ; Pa (kPa) 680 680 680 680 680 1106 1106 909 909 909 909 322 414 414 414 414 414 414 414 414 836 372 372 372 372 615 1.23 f 2.22 2.14 2.23 2.11 2.16 12.9 22.7 4.95 4.71 7.01 13.4 2.42 8.51 8.52 12.5 2.32 2.14 3.21 3.07 2.65 16.8 12.3 21.6 12.1 19.1 2.54 4.08 xg (mass %) 57.7 64.3 48.6 40.2 51.9 89.8 91.6 85.5 85.2 87.7 89.6 62.0 89.7 89.8 91.7 65.4 61.3 81.2 77.0 71.7 91.1 92.0 93.9 92.2 93.4 59.5 66.3 xa (mass %) 31.7 34.2 26.8 21.1 27.9 82.8 87.5 68.2 67.1 75.1 82.9 36.3 79.1 79.2 84.3 37.3 32.7 55.9 51.9 44.6 85.6 84.5 89.6 84.6 88.5 36.1 50.0 Qe (kW) 161 161 161 161 161 250 250 82 82 82 82 165 151 151 151 151 151 151 151 151 130 248 248 248 248 1112 2502 COP 0.425 0.464 0.472 0.539 0.484 0.361 0.277 0.194 0.204 0.167 0.117 0.403 0.248 0.256 0.200 0.444 0.473 0.332 0.364 0.392 0.165 0.300 0.228 0.319 0.249 0.646 0.833

393

a Cycle conditions: Tg /Tcon /Ta /Teva ¼ 100/40/30/10 °C and mr ¼ 1 kg/s. See Table 1 for the notation of absorbents.

specified temperatures. The effect of the generator temperature, Tg , while keeping other temperatures constant is shown in Fig. 2, using an R-134a/DMF pair as an example, and similarly the effect of the absorber temperature, Ta , is shown in Fig. 3. The COP increases nearly linearly as temperatures decrease in both cases. The increase in COP means that the generator’s heat-input increases as can be seen in Eq. (25), since here the evaporator heat (for a fixed temperature) is constant in the present example. The behavior of the absorber’s heat-rejection corresponds to the generator’s heat-input amount. On the other hand, the mass-flow-rate ratio f behaves in opposite directions between the generator and absorber in a highly non-linear fashion, as the temperature (Tg or Ta ) varies. The steep increase in f at low Tg or high Ta can be easily understood. When Tg becomes low, or Ta becomes high, the temperature difference between Tg and Ta gets smaller, which results in a smaller solubility difference between xg and xa . Then, the behavior in f can be explained from Eq. (17). A large value of f requires a large solution pumping-power. Thus, possible temperature

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9 8

0.60 0.58

Mass Flow Rate Ratio, f

R-134a/DMF System
7

0.56 0.54

6 5 4 3

0.52

COP

0.50 0.48 0.46 0.44

2 1 70 75 80 85 90 95 100 105 110 115

0.42 0.40 120

Generator Temperature,Tg [oC]
Fig. 2. Generator-temperature Tg effect on performance for the R-134a/DMF system. Other temperatures are fixed: Ta =Tcon =Teva ¼ 30=40=10 °C.

16 14

0.50 0.49

Mass Flow Rate Ratio, f

R-134a/DMF System

0.48 0.47

12 10 8 6 4 0.42 2 0 25 30 35 40 45 50 0.41 0.40 0.46

COP

0.45 0.44 0.43

Absorber Temperature, Ta [oC]
Fig. 3. Absorber-temperature Ta effect on performance for the R-134a/DMF system. Other temperatures are fixed: Tg =Tcon =Teva ¼ 100/40/10 °C.

ranges in operating Tg and Ta must be limited in practical applications. Although the behaviors described above are based on a particular system (R-134a/DMF), they are qualitatively the same for all other cases including H2 O/LiBr, but the operating Tg

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and Ta limits are significantly different among the absorber–refrigerant pairs due to the solubility differences.

4. Discussion Cycle calculations for a vapor-absorption refrigeration cycle are rather simple and straightforward, particularly by the use of EOS, as demonstrated in the present study. However, understanding results is not so obvious, compared with the case of an ordinary vapor-compression cycle. In the latter, a high pressure/temperature refrigerant gas is produced by a vapor compressor, where the thermodynamic process is theoretically a single isentropic step: inlet and exit enthalpies of the compressor are sufficient for describing the compressor work. In the vapor-absorption cycle, however, the process generating the corresponding high pressure/temperature gas is more complicated, since we have to know enthalpies at several different locations as well as refrigerant–absorbent solubility differences at the absorber and generator units (related to the f value), as seen in Eqs. (17), (21) and (22). The condenser and evaporator performance is the same for both cycles at given temperatures, and is easily understood based on the latent heat of vaporization (or condensation). Roughly speaking, the refrigerating effect is the latent heat at the evaporator, which increases with an increase in the temperature difference between Tc and Teva . Thus, at a given Teva , the latent heat is larger for a refrigerant with a higher Tc . In addition, the molar latent heat (J/mol) is generally not so much different among refrigerants at their boiling-points (or far away from Tc ), while the specific latent heat (J/kg) can be significantly different due to a large difference in molar masses. These factors can explain large differences in the calculated refrigerating power Qe among refrigerants in Table 4. It is common wisdom that searching for a proper absorbent is to look for a compound which has high solubility for a refrigerant and also a very high boilingpoint relative to the refrigerant. Thus, it is instructive to show how the solubility (VLE) curve is related to the cycle performance. As an example, we use systems of R-134a/DMF, R-134a/TEGDME, R-134a/PEB6, and R-134a/PEB8, which have COP/f values of 0.473/2.14, 0.332/3.21, 0.256/8.52, and 0.200/12.5, respectively: see Table 4. The solubility curves are shown in Figs. 4 and 5 at a constant T of 323.15 K. Indeed, the good solubility at the absorbent-rich side, which is indicative of concaveupward or near-linear vapor pressures variations, corresponds to good performance. It should be remembered here that the good solubility (or absorption) is related to the negative pressure deviation from Raoult’s law. A couple of comments may be worth to mention here. Since the normal boilingpoint of the DMF is relatively low (426 K) [14], there are discernible vapor-phase compositions of DMF (dotted curve in Fig. 4(a) at as low as 323.15 K. This means that the R-134a/DMF system may require a rectifier after the generator, similar to the case of NH3 /H2 O as mentioned earlier. In this respect, it is instructive to compare this system with the case of NH3 /H2 O, and the VLE curve at the same temperature is shown in Fig. 6. Another comment is about the R-134a/PEB8 pair, which shows

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1.4 1.2

T = 323.15 K

Pressure, MPa

1.0 0.8 0.6 0.4

VLE Region
0.2 0.0 0 10 20 30 40 50 60 70 80 90 100

(a)

R-134a mass % in DMF
1.4 1.2

T = 323.15 K
Pressure, MPa
1.0 0.8 0.6 0.4 0.2 0.0 0
(b)

VLE Region

10

20

30

40

50

60

70

80

90

100

R-134a mass % in TEGDME

Fig. 4. Pressure composition (solubility) diagrams at 323.2 5 K. Lines: calculated with the present EOS. Dotted line: dew point curve. Solid circles: experimental data [4]. (a) R-134a/DMF system and (b) R-134a/ TEGDME system.

miscibility limits. In contrast to conventional wisdom, it is quite surprising to see that even such a partially-immiscible system may be used for the vapor-absorption cycle, although only the miscible region can be used and the performance is not so great. Finally, the present purpose was to demonstrate the use of the EOS to understand the vapor-absorption cycle in a thermodynamically consistent way. However, a few words with respect to the choice of refrigerant–absorbent pairs as well as the cycle performance should be given. When we speak of the utilization of waste energy (heat), COP is not an issue, although a higher efficiency for energy recovery is

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1.4 1.2

T = 323.15 K

Pressure, MPa

1.0 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 50 60 70 80 90 100

VLE Region

(a)
2.0 1.8 1.6

R-134a mass % in PEB6

T = 323.15 K

LLE Region (immiscible)
VLLE

Pressure, MPa

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 50 60

VLE Region
70 80 90 100

(b)

R-134a mass % in PEB8

Fig. 5. Pressure composition (solubility) diagrams at 323.2 5 K. Lines: calculated with the present EOS. Solid circles: experimental data [15]. (a) R-134a/PEB6 system and (b) R-134a/PEB8 system.

desirable. Even only a 10% recovery of the waste heat will be better than 100% wasted. Of course, in actual cases we have to consider the capital and operating costs of the additional equipment. Traditional pairs (NH3 /H2 O and H2 O/LiBr) have excellent cycle performances, which are better than other systems studied here. However, both systems may not be always the best choices for all applications, since they require a huge physical size of the unit (H2 O/LiBr), or a toxicity problem with ammonia, etc. COP comparisons between the vapor-compression cycle and the vapor-absorption cycle cannot be simply made without qualification. When low cost electricity is available, the former having its intrinsic high COP is no doubt the best choice. However, in the case of the utilization of waste heat, or solar energy, the latter will find uniquely suited applications [1,22].

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2.4 2.0

T = 323.15 K

Pressure, MPa

1.6 1.2 0.8 0.4 0.0 0 10 20 30 40 50 60 70 80 90 100

VLE Region

Ammonia mass % in Water
Fig. 6. Pressure composition (solubility) diagrams at 323.2 5 K for NH3 /H2 O. Lines: calculated with the present EOS. Dotted line: dew point curve. Symbols: literature data [13].

5. Concluding remarks Analyzing solubility (PTX) data of various refrigerant–absorbent pairs in the literature with the proposed EOS, we have successfully demonstrated the usefulness of the EOS model for the vapor-absorption cycle process. All thermodynamic properties have been consistently calculated, and some new insights on the cycle have been obtained.

Acknowledgements The author thanks Emeritus Professor Koichi Watanabe at Keio University, Japan for providing him with the experimental solubility data in Ref. [4].

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[1] Erickson DC, Anand G, Kyung I. Heat-activated dual-function absorption cycle. ASHRAE Trans 2004;110(1). [2] Eiseman BJ. A comparison fluoroalkane absorption refrigerants. ASHRAE J 1959;1(12):45. [3] Mastrangelo SVR. Solubility of some chlorofluorohydrocarbons in tetraethylene glycol ether. ASHRAE J 1959;1(10):64. [4] Nezu Y, Hisada N, Ishiyama T, Watanabe K. Thermodynamic properties of working-fluid pairs with R-134a for absorption refrigeration system. In: Natural Working-Fluids 2002, IIR Gustav Lorentzen Conf. 5th., China, Sept. 17–20, 2002, p. 446–53. [5] Fatouh M, Murthy SS. Comparison of R-22 absorpion pairs for cooling absorption based on P–T–X data. Renewable Energy 1993;3(1):31–7.

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