APPLIED

www.elsevier.com/locate/apenergy

Applied Energy 80 (2005) 383–399ENERGY

Theoretical performances of variousrefrigerant–absorbent pairs in a

vapor-absorption refrigeration cycle by the useof 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, partic-

ularly 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 perfor-

mances and some new insights on understanding the cycle process are shown.

� 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 � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.apenergy.2004.04.011

384 A. Yokozeki / Applied Energy 80 (2005) 383–399

applications, the well-known refrigerant–absorber systems (H2O/LiBr and NH3/

H2O) are still being used for certain applications, particularly in the field of indus-

trial applications or large-scale water chiller systems. Recently, more attention has

been directed towards the recovery of waste heat using the NH3/H2O 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–con-

centration (TPX) and enthalpy–temperature (HT) diagrams are required. These

charts correspond to the familiar PH (pressure–enthalpy) or TS (temperature–en-

tropy) 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 capacitydata for solution properties, while the vapor-phase properties are calculated with the

refrigerant EOS. Sometimes, the solubility data are correlated using theoretical so-

lution (often called ‘‘activity’’) models [4,7]. However, such models are limited in

their use to temperatures well below the refrigerant critical temperature, and mod-

eling 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 de-

sirable to model the vapor-absorption cycle process with thermodynamically validEOS 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 infor-mation 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/H2O [13].

A. Yokozeki / Applied Energy 80 (2005) 383–399 385

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 com-

monly cited as absorbents. Refrigerants are R-22 and several HFC compounds as

well as ammonia for NH3/H2O. Although many pairs have been examined here, thepurpose 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:

P ¼ RTV � b

� aðT ÞV ðV þ bÞ ð1Þ

aðT Þ ¼ 0:427480R2T 2

c

PcaðT Þ ð2Þ

b ¼ 0:08664RTcPc

ð3Þ

The temperature-dependent part of the a parameter in the EOS for pure compounds

is modeled by the following empirical equation [10]:

aðT Þ ¼X6 3

k¼0

bkTcT

�� TTc

�k

ð4Þ

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 sol-

ubility (PTX) data. On the other hand, the temperature-dependent part of the aparameter 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].

386 A. Yokozeki / Applied Energy 80 (2005) 383–399

kij ¼lijljiðxi þ xjÞljixi þ lijxj

; where kii ¼ 0; ð5Þ

aðT Þ ¼ 1þ b1

TcT

�� TTc

�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 interms of binary interaction parameters [11], which may be regarded as a modified

van der Waals–Berthelot mixing formula:

aðT Þ ¼XNi;j¼1

ffiffiffiffiffiffiffiffiaiaj

p ð1� f ðT ÞkijÞxixj; ai ¼ 0:427480R2T 2

ci

PciaiðT Þ; ð7Þ

f ðT Þ ¼ 1þ CijT ; where Cij ¼ Cji and Cii ¼ 0; ð8Þ

b ¼ 1

2

XNi;j¼1

ðbi þ bjÞð1� mijÞxixj; bi ¼ 0:08664RTciPci

;

where mij ¼ mji; mii ¼ 0; ð9Þ

where Tci is the critical temperature of the ith species; Pci is the critical pressure of theith 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

ln/i ¼ � lnPVRT

1

�� bV

�þ b0iV � b

� ab0ibRT ðV þ bÞ þ

abRT

a0ia

�� b0i

bþ 1

�ln

VV þ b

;

ð10Þ

where b0i and a0i are given by

b0i ¼XNj¼1

ðbi þ bjÞð1� mijÞxj � b; ð11Þ

a0i ¼ 2XNj¼1

ffiffiffiffiffiffiffiffiaiaj

pxj 1

(� kij �

xixjðlji � lijÞð1þ CijT Þðljixi þ lijxjÞ2

)ð12Þ

A. Yokozeki / Applied Energy 80 (2005) 383–399 387

A thermodynamically derived function relevant to the present study is the en-

thalpy (H ), which is given, in a general form

H ¼Z XN

i¼1

C0pixi dT þ a

b

�� T

bdadT

�ln

VV þ b

þ RTPVRT

�� 1

�

� RT 2

V � bdbdT

þ abdbdT

1

V þ b

�� 1

bln 1

�þ bV

��þ C ð13Þ

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

ideal-gas heat capacity for each compound C0pi in Eq. (13) is modeled by the poly-

nomial form

C0p ¼ C0 þ C1T þ C2T 2 þ C3T 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 evapo-

rator 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 bal-

ance gives

Qg þ Qe þ Wp ¼ Qc þ Qa ð15Þ

From the material balance in the absorber or generator, we have

msxa ¼ ðms � mrÞxg; ð16Þ

and this provides a mass-flow-rate ratio, f , as defined by

f � ms

mr

¼ xgxg � xa

; 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), re-

spectively. 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, theenergy-balance equation becomes

Qh � H2ð � H3Þ msð � mrÞ ¼ H1ð � H4Þms � Wp; ð18Þ

whereH is the enthalpy; the subscriptnumbers (1, 2, 3, and4) correspond to the locations

shown in Fig. 1. From Eq. (18), the generator-inlet enthalpy, H1, can be obtained:

H1 ¼ H4 þ ðH2 � H3Þð1� 1=f Þ þ Wp=mr ð19Þ

Refrigerant Gas Flow Rate: mr Qc

Qg

HeatH

Qa

Qe

Liquid Pumping Power: Wp

mr : Refrigerant Gas Flow Rate

Heat Exchanger:with efficiency = 1. 0

ms – mr

Absorber: Ta

Generator: Tg Condenser: Tcon

Evaporator: Teva

1

7

6

5

4

3

2

ms : Solution Flow Rate

ms

mr

Fig. 1. A schematic diagram of a simple vapor-absorption refrigeration cycle.

388 A. Yokozeki / Applied Energy 80 (2005) 383–399

From the energy balance around the generator, the generator heat input, Qg, isgiven by

Qg ¼ H5mr þ H2 msð � mrÞ � H1ms ð20Þ

By eliminating H1 from this equation with Eq. (19), Eq. (20) can be written as

Qg=mr ¼ H5 � H4f þ H3ðf � 1Þ � Wp=mr ð21Þ

Similarly, the heat rejection in the absorber, Qa, is given by

Qa=mr ¼ H3ðf � 1Þ þ H7 � H4f ð22Þ

Condenser and evaporator heats per unit mass flow are

Qc=mr ¼ H5 � H6 ð23Þ

Qe=mr ¼ H7 � H6 ð24Þ

A. Yokozeki / Applied Energy 80 (2005) 383–399 389

Then, the system performance is defined by a heat ratio, g (output power divided by

input power), i.e.

g ¼ 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

ð25Þ

This can be expressed in terms of H and f :

COP ¼ H7 � H6

H5 þ H3ðf � 1Þ � H4fð26Þ

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 EOSmodel discussed above.

3. Analyses and results

3.1. EOS Parameters

First, we have to set up our EOS parameters. The pure component EOS constantsfor 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 ab-

sorbents 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

(AADs) in pressure, where AAD �Pn

i¼1 j1� PcalðiÞ=PobsðiÞj=n, is less than 2% for

good quality VLE data.

Table 1

EOS constants of pure refrigerants and absorbentsa

Compound Molar

mass

Tc (K) Pc (kPa) b0 b1 b2 b3

R-22 86.47 369.17 4978 1.0011 0.43295 )0.06214 0.0150

R-32 52.02 351.26 5782 1.0019 0.48333 )0.07538 0.00673

R-125 120.22 339.19 3637 1.0001 0.47736 )0.01977 )0.0177R-134 101.03 391.97 4641 1.0012 0.48291 )0.05070 0

R-134a 101.03 374.21 4059 1.0025 0.50532 )0.04983 0

R-143a 84.04 346.20 3759 1.0006 0.45874 )0.04846 )0.0143R-152a 66.05 386.44 4520 1.0012 0.48495 )0.08508 0.0146

NH3 17.03 405.40 11,333 1.0018 0.46017 )0.06158 0.00168

H2O 18.02 647.10 22,064 1.0024 0.54254 )0.08667 0.00525

PEC5 472 751 1059 1.0 * 0 0

PEC9 696 774 690 1.0 * 0 0

PEB6 528 800 969 1.0 * 0 0

PEB8 640 793 772 1.0 * 0 0

DMA 87.1 656 4018 1.0 * 0 0

DMF 73.1 650 4415 1.0 * 0 0

DEGDME 134.2 607 2852 1.0 * 0 0

TrEGDME 178.2 651 2307 1.0 * 0 0

TEGDME 222.3 704 1934 1.0 * 0 0

NMP 99.1 722 4520 1.0 * 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.

390 A. Yokozeki / Applied Energy 80 (2005) 383–399

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 mixturesin 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 powerWp, since it is usually insignificant with respect to

other thermal powers. In addition, several assumptions are made, which are not ex-

plicitly 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 iso-enthalpic, 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.

Table 2

Coefficients for ideal-gas heat capacity (Jmol�1 K�1] in Eq. (14)

Compound C0 C1 C2 C3 Ref.a

R-22 17.30 0.16180 )1.170� 10�4 3.058� 10�7 [12]

R-32 20.34 0.07534 1.872� 10�5 )3.116� 10�8 [19]

R-125 16.58 0.33983 )2.873� 10�4 8.870� 10�8 [19]

R-134 15.58 0.28694 )2.028� 10�4 5.396� 10�8 [19]

R-134a 12.89 0.30500 )2.342� 10�4 6.852� 10�8 [19]

R-143a 5.740 0.31388 )2.595� 10�4 8.410� 10�8 [19]

R-152a 8.670 0.2394 )1.456� 10�4 3.392� 10�8 [19]

NH3 27.31 0.02383 1.707� 10�5 )1.185� 10�8 [12]

H2O 32.24 1.924� 10�3 1.055� 10�5 )3.596� 10�9 [12]

PEC5 57.97 2.1551 )1.01� 10�3 2.62� 10�7 E

PEC9 84.38 3.5852 )1.81� 10�3 4.36� 10�7 E

PEB6 2.594 2.7280 )1.42� 10�3 5.43� 10�7 E

PEB8 15.80 3.4430 )1.82� 10�3 6.30� 10�7 E

DMA )2.678 0.47905 )2.87� 10�4 1.94� 10�7 E

DMF 0.87 0.38484 2.45� 10�5 5.98� 10�8 E

DEGDME 77.21 0.38424 3.04� 10�5 )1.04� 10�7 E

TrEGDME 62.63 0.71397 )2.93� 10�4 1.15� 10�7 E

TEGDME 77.84 0.89232 )3.77� 10�4 1.25� 10�7 E

NMP )2.677 0.47905 )2.87� 10�4 1.94� 10�7 E

aRef.: used references and E: estimated from group contribution methods in [12]. See Table 1 for the

notation of absorbents.

A. Yokozeki / Applied Energy 80 (2005) 383–399 391

• Pressures in the condenser and the generator (Pcon and Pg) are the same, and sim-

ilarly, 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 evapora-

tor (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, andthe 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 com-

positions, 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 ob-

tained 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 user-

friendly 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.

Table 3

Binary interaction parameters of refrigerant–absorbent pairs determined from experimental PTX dataa

Binary systems

(1)/(2)

l12 l21 m12;21 C12;21

(� 10�3)

b1

(absorbent)

AAD

(%)

Ref.

R-32/PEB6 )0.006 )0.006 0.0265 0 0.59299 1.28 [16]

R-32/PEB8 0.0891 0.0293 0.0434 0 0.70415 1.82 [15]

R-125/PEC5 )0.045 )0.047 0.0022 0 1.5266 1.13 [16]

R-125/PEB6 )0.041 )0.041 0.0050 0 1.3008 0.99 [16]

R-125/PEB )0.006 )0.006 0.0092 0 1.4136 1.82 [15]

R-125/PEC9 0.1175 0.0552 0.0255 0 1.3785 1.29 [15]

R-134a/PEC5 0.0515 0.0272 0.0227 0 1.1142 1.18 [16]

R-134a/PEB6 0.0172 0.0172 0.0171 0 0.94843 1.06 [15]

R-134a/PEB8 0.0076 0.0076 0.0088 0 1.1861 0.81 [15]

R-143a/PEB6 0.1252 0.0588 0.0261 0 1.4349 0.90 [15]

R-152a/PEC5 0.1343 0.0421 0.0465 0 0.76002 0.94 [16]

R-152a/PEC9 0.0264 0.0264 0.0301 0 0.87442 0.87 [15]

R-152a/PEB6 0.0014 0.0014 0.0184 0 0.65012 0.95 [15]

R-152a/PEB8 0.0873 0.0336 0.0416 0 0.73357 1.94 [15]

NH3/H2O )0.316 )0.316 )0.0130 0 0.54254* 4.30 [13]

R-22/DEGDME )0.286 )0.286 0.0 )1.09 1.1256 3.10 [20]

R-22/TEGDME )0.180 )0.601 0.1197 )2.04 0.22827 3.42 [3]

R-22/DMA )0.156 )0.156 0.0253 0 0.23760 3.80 [5]

R-22/DMF )0.076 )0.076 )0.1248 7.70 0.40733 8.40 [3,21]

R-22/NMP )0.204 )0.204 )0.0294 0 0.39816 3.89 [5]

R-134a/DEG-DME )0.036 )0.102 0.0275 0 1.12564 1.75 [4]

R-134a/DMA )0.103 )0.091 )0.0389 0 0.37076 0.92 [4]

R-134a/DMF )0.171 )0.122 )0.0951 0 0.40733 0.94 [4]

R-134a/TEG-DME )0.040 )0.096 0.0185 0 1.46898 1.68 [4]

R-134a/TrEG-DME )0.027 )0.074 0.0243 0 1.13364 1.15 [4]

R-134a/DEG-DME )0.041 )0.099 0.0231 0 1.12564 1.77 [4]

R-134/TEGDME )0.246 )0.246 0 )1.17 1.25000 2.94 [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.

392 A. Yokozeki / Applied Energy 80 (2005) 383–399

The well-known refrigerant–absorbent pairs, NH3/H2O and H2O/LiBr, have also

been calculated and are shown in Table 4. Here, a few comments are needed. In the

case of NH3/H2O, the absorbent H2O 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 H2O/LiBr, we

have not developed the EOS model. Instead, we have employed empirical-correlationdiagrams for the thermodynamic properties [18]: i.e. a temperature–pressure–con-

centration diagram and an enthalpy–temperature diagram.

In the vapor-absorption refrigeration cycle, the absorber–generator solution cir-

cuit 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

Table 4

Comparisons of theoretical cycle performancesa

Binary systems

(1)/(2)

Pcon; Pg(kPa)

Peva; Pa(kPa)

f xg(mass %)

xa(mass %)

Qe (kW) COP

R-22/DEGDME 1531 680 2.22 57.7 31.7 161 0.425

R-22/TEGDME 1531 680 2.14 64.3 34.2 161 0.464

R-22/DMA 1531 680 2.23 48.6 26.8 161 0.472

R-22/DMF 1531 680 2.11 40.2 21.1 161 0.539

R-22/NMP 1531 680 2.16 51.9 27.9 161 0.484

R-32/PEB6 2486 1106 12.9 89.8 82.8 250 0.361

R-32/PEB8 2486 1106 22.7 91.6 87.5 250 0.277

R-125/PEC5 2011 909 4.95 85.5 68.2 82 0.194

R-125/PEB6 2011 909 4.71 85.2 67.1 82 0.204

R-125/PEB8 2011 909 7.01 87.7 75.1 82 0.167

R-125/PEC9 2011 909 13.4 89.6 82.9 82 0.117

R-134/TEGDME 810 322 2.42 62.0 36.3 165 0.403

R-134a/PEC5 1015 414 8.51 89.7 79.1 151 0.248

R-134a/PEB6 1015 414 8.52 89.8 79.2 151 0.256

R-134a/PEB8 1015 414 12.5 91.7 84.3 151 0.200

R-134a/DMA 1015 414 2.32 65.4 37.3 151 0.444

R-134a/DMF 1015 414 2.14 61.3 32.7 151 0.473

R-134a/TEG-DME 1015 414 3.21 81.2 55.9 151 0.332

R-134a/TrEG-DME 1015 414 3.07 77.0 51.9 151 0.364

R-134a/DEG-DME 1015 414 2.65 71.7 44.6 151 0.392

R-143a/PEB6 1835 836 16.8 91.1 85.6 130 0.165

R-152a/PEC5 907 372 12.3 92.0 84.5 248 0.300

R-152a/PEC9 907 372 21.6 93.9 89.6 248 0.228

R-152a/PEB6 907 372 12.1 92.2 84.6 248 0.319

R-152a/PEB8 907 372 19.1 93.4 88.5 248 0.249

NH3/H2O 1548 615 2.54 59.5 36.1 1112 0.646

H2O/LiBr 7.38 1.23 4.08 66.3 50.0 2502 0.833

aCycle 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.

A. Yokozeki / Applied Energy 80 (2005) 383–399 393

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 in-crease 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 temper-

ature (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 differencebetween Tg and Ta gets smaller, which results in a smaller solubility difference be-

tween 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

70 75 80 85 90 95 100 105 110 115 120Generator Temperature,Tg [oC]

0.40

0.42

0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.58

0.60

CO

P

1

2

3

4

5

6

7

8

9

Mas

sF

low

Rat

eR

atio

,f R-134a/DMF System

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.

25 30 35 40 45 50Absorber Temperature,Ta [oC]

0

2

4

6

8

10

12

14

16

Mas

sF

low

Rat

eR

atio

,f

0.40

0.41

0.42

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.50

CO

P

R-134a/DMF System

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.

394 A. Yokozeki / Applied Energy 80 (2005) 383–399

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 H2O/LiBr, but the operating Tg

A. Yokozeki / Applied Energy 80 (2005) 383–399 395

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 re-

frigerant 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, how-

ever, the process generating the corresponding high pressure/temperature gas is morecomplicated, since we have to know enthalpies at several different locations as well as

refrigerant–absorbent solubility differences at the absorber and generator units (re-

lated 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 Tcand Teva. Thus, at a given Teva, the latent heat is larger for a refrigerant with a higherTc. 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 boiling-

point 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 concave-

upward 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 boiling-

point 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/H2O as mentioned earlier. In this respect, it is instructive to compare

this system with the case of NH3/H2O, and the VLE curve at the same temperature is

shown in Fig. 6. Another comment is about the R-134a/PEB8 pair, which shows

0 10 20 30 40 50 60 70 80 90 100R-134a mass % in DMF

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Pre

ssu

re,M

Pa

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

T = 323.15 K

VLE Region

0 10 20 30 40 50 60 70 80 90 100R-134a mass % in TEGDME

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Pre

ssu

re,M

Pa

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

T = 323.15 K

VLE Region

(a)

(b)

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.

396 A. Yokozeki / Applied Energy 80 (2005) 383–399

miscibility limits. In contrast to conventional wisdom, it is quite surprising to seethat 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

0 10 20 30 40 50 60 70 80 90 100R-134a mass % in PEB6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Pre

ssu

re,M

Pa

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

T = 323.15 K

VLE Region

0 10 20 30 40 50 60 70 80 90 100R-134a mass % in PEB8

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Pre

ssu

re,M

Pa

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

T = 323.15 K

VLE Region

LLE Region(immiscible)

VLLE

(a)

(b)

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.

A. Yokozeki / Applied Energy 80 (2005) 383–399 397

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/H2O and H2O/LiBr) have ex-

cellent cycle performances, which are better than other systems studied here. How-ever, both systems may not be always the best choices for all applications, since they

require a huge physical size of the unit (H2O/LiBr), or a toxicity problem with

ammonia, etc. COP comparisons between the vapor-compression cycle and the va-

por-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].

0 10 20 30 40 50 60 70 80 90 100Ammonia mass % in Water

0.0

0.4

0.8

1.2

1.6

2.0

2.4

Pre

ssu

re,M

Pa

0.0

0.4

0.8

1.2

1.6

2.0

2.4

0.0

0.4

0.8

1.2

1.6

2.0

2.4

0.0

0.4

0.8

1.2

1.6

2.0

VLE Region

T = 323.15 K

Fig. 6. Pressure composition (solubility) diagrams at 323.2 5 K for NH3/H2O. Lines: calculated with the

present EOS. Dotted line: dew point curve. Symbols: literature data [13].

398 A. Yokozeki / Applied Energy 80 (2005) 383–399

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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