An alternative approach towards absorption heat pump working pair screening

Renewable Energy xxx (2016) 1e12

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An alternative approach towards absorption heat pump working pair screening Paris Chatzitakis a, Belal Dawoud b, * a b

Viessmann Werke Allendorf GmbH, Viessmann Str. 1, 35108, Allendorf (Eder), Germany OTH-Regensburg Technical University of Applied Sciences, Faculty of Mechanical Engineering, Galgenberg Str. 30, 93053, Regensburg, Germany

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 April 2016 Received in revised form 3 August 2016 Accepted 5 August 2016 Available online xxx

The successful market penetration of modern absorption heat pumps (AHP) today is critically dependent on their thermodynamic performance as well as other key factors like cost, reliability and inherent safety. Conventional AHPs have a proven record in the first two aspects but crucial shortcomings in the last two. For this reason it has been imperative to search for alternative working pairs that could potentially provide comparable performance while also satisfying the rest of the conditions to the best extent possible. As part of a systematic approach towards this direction, a detailed cycle analysis was performed, utilizing an idealized AHP system containing a real working pair, which enabled the identification of five dimensionless parameters and key thermophysical properties that influence the system's thermodynamic efficiency and the circulation ratio. In order to validate those findings, these parameters were calculated and compared between conventional and alternative AHP refrigerants. It turned out that low molecular weight ratios between absorbent and refrigerant have a beneficial effect on both coefficient of performance and the circulation ratio. Furthermore, both the refrigerant acentric factor and the absorbent vaporization enthalpy shall be minimized to obtain better performance. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Absorption heat pump Working pair Coefficient of performance

1. Introduction Progress in the field of heat pumps has been steadily increasing over the last decade, driven primarily by a growing market demand, which in turn has being “fueled” by volatile oil and gas prices. Moreover, stricter international climate protection and safety regulations have been methodically pushing the industry towards new research areas, in pursuit of better performing and environmentally-friendlier substances. Thermally driven heat pumps on the other hand, belonged for many decades to a niche market, focused primarily on industrial or commercial applications, mainly due to the fact that such systems were bulky, capital intensive and often deemed unsafe for a domestic environment. Today however, this picture is slowly changing as breakthroughs in manufacturing processes are opening new possibilities for small scale efficient residential units. Commercially available absorption systems have traditionally been dominated by ammonia/water and water/lithium bromide (LiBr) working pairs. Although very efficient systems in terms of

* Corresponding author. E-mail address: [email protected] (B. Dawoud).

thermodynamic performance, significant disadvantages or flaws have slowed their adoption and commercialization. More specifically, ammonia/water heat pumps present considerable hazards due to ammonia's toxicity, corrosiveness and high system pressure whereas water/LiBr systems are considered safer but also plagued by severe temperature limitations and even higher corrosion problems [8]. Alternative absorption heat pump working pairs have already been extensively reviewed by Donnellan et al. (2015), Shrikirin et al. (2001), and Sun et al. (2012) [5,17,18] with main focus on replacements for water, as the absorbent, in the case of ammonia, and LiBr in the case of water. A smaller part of the studies concerns refrigerant replacement with organic substances like alcohols, amines and hydrocarbons. Additionally, over the last few years organic ionic liquids have been gaining momentum as potential absorbent candidates. Nevertheless, despite all efforts there is still no recognized alternative working pair with the potential to exceed the success of the two conventional pairs [8]. For this reason, a number of researchers have worked on pinpointing the fundamental working pair criteria that influence thermodynamic efficiency in order to facilitate the identification of alternative working pairs.

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Nomenclature

u

COP cp CR f H K1-K5 Mi m_ j

Subscripts 1 component 1, refrigerant 2 component 2, absorbent 1e10 state points in Fig. 1 abs absorber conditions c critical point ce condenser-evaporator average conditions cool cooling con condenser conditions des desorption eva evaporator conditions gen generator conditions genin generator inlet conditions genout generator outlet conditions HP heat pump shex solution heat exchanger conditions sol solution tot total v vaporization xs excess mixing property

p Q_ RV SSC T Хi,j Yi,j

coefficient of performance average mass specific heat capacity [J/kg K] circulation ratio function mass specific enthalpy [J/kg] dimensionless parameters molecular weight of component i (i ¼ 1e2) mass flow of stream j (j ¼ 1e10) [kg/s] vapor pressure [Pa] heat flow [W] relative volatility [-] specific solution circulation [l/s kW] temperature [K] liquid molar fraction of component i in stream j vapor molar fraction of component i in stream j

Greek letters activity coefficient of component i in stream j vapor mass fraction of component i in stream j liquid mass fraction of component i in stream j mass density

gi,j z i,j x i,j r

Iedema (1982) [10] performed a quasi-quantitative analysis of an idealized single and double stage absorption heat pump. Among some of the major assumptions for the working pair were that specific heat capacities, vaporization enthalpies and excess mixing enthalpies were all independent from temperature. The conclusions concerning the thermodynamic performance pointed towards a low ratio of excess mixing enthalpy to vaporization enthalpy, a high vaporization enthalpy, a strong negative deviation from Raoult's law and low solution specific heat capacities. Hodgett (1982) [9] presented a simplified approach for the coefficient of performance (COP) that depended on three dimensionless parameters, the ratio of excess mixing enthalpy to vaporization enthalpy, the ratio of pump work to vaporization enthalpy and the generator sensible heat duty to vaporization enthalpy. The final requirements for an efficient working pair included, a high solution density, a large concentration difference between rich and poor solution, high concentrations for both rich and poor solution and a low solution specific heat capacity. Perez-Blanco (1984) [15] investigated the influence of non-ideal solutions' negative deviation from Raoult's law on the COP and the circulation ratio (CR) of ammonia single stage absorption heat pumps. The conclusions were that there is an optimum temperature and concentration dependence of the activity coefficients and that too strong negative deviations are undesirable. Furthermore, it is stated that the absorbent specific heat capacity must be as low as possible. Eisa & Holland (1987) [6] reviewed previous literature works and collected a list of desirable properties for the working pair. Specifically, the refrigerant should exhibit a high vaporization enthalpy, a low heat capacity per unit mass and low boiling point. The absorbent should have as low a vapor pressure as possible, a low heat capacity per unit mass and create solutions with the refrigerant with high negative deviations from Raoult's law, low viscosity and density. Furthermore, they also investigated the influence of various ions in wateresalt solutions on the heat of solution, vapor pressure lowering and solubility. Narodoslawsky et al. (1988) [13] followed an analytical method based partly on semi-empirical relations and concluded that high

acentric factor

performance working pairs should show high refrigerant vaporization enthalpies at normal boiling point and an extremum of excess mixing Gibbs free energy between
1000 and
2000 J/mol preferably located at high refrigerant concentrations. Additionally, it is argued that the absorbent should also have a high boiling point vaporization enthalpy, a low acentric factor (definition can be found in the appendix Eq. (48)), a low reduced boiling point, a high critical temperature and low critical pressure. On the other hand, the refrigerant should have a high acentric factor, a high reduced boiling point, a low critical temperature and a high critical pressure. Nowaczyk (1991) [14] carried out a literature review summarizing that, the refrigerant should have a high specific vaporization enthalpy, a high critical temperature, a flat vapor pressure curve. In addition, the solution with the absorbent should have a high negative deviation from Raoult's law, a low excess mixing enthalpy, low specific heat capacity, a low viscosity, a high density and a high difference in boiling points. Alefeld, Radermacher and Hwang (1994) [1] pointed out that the refrigerant should exhibit a low heat capacity to vaporization enthalpy (per unit mass) ratio in order to obtain a high efficiency. Additionally, the resulting pressure ratios between the high pressure and low pressure sides should be low and the refrigerant volumetric heat capacity should be as high as possible. However, the lack of success of these partially qualitative screening processes signifies the need for an alternative quantitative approach. Accordingly, this study gives a hand towards improving the quantitative understanding of the multitude of parameters that influence the performance of absorption heat pumps/ chillers. An AHP model that made very few assumptions for the working pair properties, but did consider a perfect mechanical apparatus is introduced. This entailed no external heat losses, no friction or pressure losses. The system, a simple single-effect absorption heat pump, comprised an evaporator, an absorber, a solution pump, a solution heat exchanger, a generator with an optional rectifier column, a condenser, an expansion and a solution valve (Fig. 1). All components were assumed to contain infinite heat and mass transfer surfaces and therefore were always able to

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In most cases the absorbent's vapor pressure (p2,abs) is so low, relative to the refrigerant, so that Eq. (4) approximates to:

X1;1 z

p1;eva p1;abs g1;1

(5)

The same approach can be applied for the high-pressure side (Eq. (6) for the generatorecondenser subsystem) in order to calculate the poor solution concentration (X1,4), assuming again pure refrigerant in the condenser and equilibrium. Eq. (7) is again the approximation of Eq. (6) for the cases of negligible absorbent vapor pressure.

X1;4 Fig. 1. Schematic of the single-stage absorption heat pump process.

establish equilibrium conditions, in order to facilitate a better understanding of the multiple cycle loss mechanisms and simplify the assessment of the AHP potential. After detailed mass and energy balances, practical relations for the coefficient of performance, the circulation ratio and the specific solution circulation have been derived and the key influencing parameters on each have been identified. In turn followed an investigation into correlating these performance characteristics with basic working-pair thermophysical properties and finally the application of the derived relations on actual refrigerants and solutions, in order to validate those correlations. The concept of connecting performance characteristics to basic substance properties serves to establish a more targeted working pair candidate screening procedure, since the available basic property information, like the critical point properties, is much larger and more accurate than the more intricate parameters such as enthalpies and vapor pressures.


 p1;con
p2;gen g2;4 1
X1;4 ¼ X1;2 ¼ p1;gen g1;4 p1;con
p2;gen g2;4 ¼ p1;gen g1;4
p2;gen g2;4

X1;4 z

(6)

p1;con p1;gen g1;4

(7)

The first step of the cycle analysis is a simple vapor-liquid equilibrium for the low-pressure side (absorber-evaporator subsystem). The assumptions are that the evaporator contains pure refrigerant and is in equilibrium with the absorber. The terms poor/ rich solution will refer to the solution with a low/high refrigerant concentration, respectively.

Eqs. (5) and (7) show that refrigerants with high vapor pressures ratios (p1,eva/p1,abs or p1,con/p1,gen), or flat vapor pressure curves have the potential to reach higher equilibrium refrigerant concentrations, in agreement with Nowaczyk (1991) [14]. Moreover, low activity coefficients can boost the equilibrium concentrations even higher. However, in order to achieve the maximum refrigerant concentration difference, as the literature dictates, the vapor pressure curve needs to be flatter between the evaporator and absorber temperatures and steeper between the condenser and generator temperatures. The refrigerant activity coefficients also need to be as low as possible at the absorber temperature level and as high as possible at the generator temperature level. This special behavior confirms the need for a negative deviation from Raoult's law, stated by many researchers, but also the requirement for an activity coefficient specific temperature dependence, as advocated by Perez-Blanco (1984) [15] and more indirectly by Narodoslawsky et al. (1988) [13] through the excess mixing Gibbs energy. Another important VLE parameter is the absorbent's relative volatility (Eqs. (8) and (10)). This is defined as the measure that describes the ease of separation between two components through distillation. In order to calculate it, one needs the generator vapor phase molar fractions, which can be adequately estimated from Dalton's law of partial pressures (Eq. (9)). Assuming that the vapor pressure range is low enough, the vapor fugacity coefficients can be safely considered to be equal to 1 [4].

p ¼ peva ¼ pabs

RV2 ¼

2. Thermodynamic cycle analysis 2.1. Vapor liquid equilibria (VLE)

(1)

The pressure in both components is equalized (Eq. (1)) and amounts to the partial vapor pressures of the contained substances present, as stated in the activity coefficient theory.

peva ¼ p1;eva

(2)


 pabs ¼ p1;abs g1;1 X1;1 þ p2;abs g2;1 1
X1;1

(3)

where X1,1 is the molar fraction of the refrigerant (1) in stream 1 (see Fig. 1), or otherwise the rich solution concentration. Consequently from Eqs. (1) to (3):

X1;1 ¼


 p1;eva
p2;abs g2;1 1
X1;1 p1;eva
p2;abs g2;1 ¼ p1;abs g1;1
p2;abs g2;1 p1;abs g1;1

 Y2;5 X2;4 Y2;5 X1;4  ¼ Y1;5 X1;4 Y1;5 X2;4

(8)

Y1;5 pgen ¼ p1;gen g1;4 X1;4

(9)

Combining Eqs. (8) and (9) gives:

RV2 ¼

Y1;5 ¼

p2;gen g2;4 X2;4 =pgen X2;4 p1;gen g1;4 X1;4 =pgen X1;4

¼

p2;gen g2;4 p1;gen g1;4

(10)

p1;gen g1;4 X1;4 1 ¼ p1;gen g1;4 X1;4 þ p2;gen g2;4 X2;4 1 þ p2;gen g2;4 X2;4 p1;gen g X1;4 1;4

¼ (4)

1 1 þ RV2

X2;4 X1;4

(11)

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Eq. (11) demonstrates that in the generator, higher liquid refrigerant concentrations (X1,4) result in higher vapor concentrations and consequently can reduce rectification losses, in the case of absorbents with significant vapor pressures. Vapor concentrations also seem to be inversely proportional to the absorbent's relative volatility. Some researchers approximated the relative volatility to the boiling point difference between absorbent and refrigerant. This approximation however, may be somewhat misleading since substances with the same boiling point can display significant vapor pressure differences at another temperature. One more thing that needs to be noted at this point is that the relative volatility is a temperature and concentration dependent parameter. For carrying out the species balance, the mass (weight) fractions are necessary. The refrigerant mass fractions of the streams 1, 4 & 5 are defined by Eqs. (12)e(14).

x1;1 ¼

x1;4

X1;1 M1 1 ¼ X1;1 M1 þ X2;1 M2 1 þ X2;1 M2 X1;1 M1

X1;4 M1 1 ¼ ¼ X1;4 M1 þ X2;4 M2 1 þ X2;4 M2 X1;4 M1

z1;5 ¼

Y1;5 M1 1 1 ¼ ¼ Y1;5 M1 þ Y2;5 M2 1 þ Y2;5 M2 1 þ RV2 X2;4 M2 Y1;5 M1 X1;4 M1

m_ 10 ¼ m_ 5



z1;5
x1;4 x1;1
x1;4

 (23)

z1;5
x1;4 x2;4

(24)

2.3. Solution circulation calculations The combination of Eqs. (22) and (24) provides an important design and operational parameter known as the circulation ratio (CR), which is defined as the ratio of the mass of solution circulated per mass of refrigerant circulated through the evaporator [11]. It is essentially a system-sizing indicator. Using Eqs. (12) and (13):

CR ¼

1
x14 m_ 1 ¼ ¼ x1;1
x1;4 m_ 10

(13)

X

M

1 1
X1;4 M1;4 1 þX2;4 M2

X1;1 M1 X1;1 M1 þX2;1 M2

X

M

1
X1;4 M1;4 1 þX2;4 M2

X2;4 M2 X1;4 M1 þX2;4 M2 1;1 M1 X1;4 M1 þX1;1 M1 X2;4 M2
X1;1 M1 X1;4 M1
X2;1 M2 X1;4 M1 ðX1;1 M1 þX2;1 M2 ÞðX1;4 M1 þX2;4 M2 Þ

¼X (14)

2.2. Mass balance calculations The second analysis step is a mass balance for the complete system (Fig. 1). This includes the rectifying column with distillate reflux. Applying the same assumptions as before and considering ideal column operation after the generator, the top product is presumed to be pure refrigerant and the bottom product in equilibrium with the vapor coming from the generator, i.e. streams 4, 5 and 6 are in equilibrium. The following mass balance equations can then be written:

m_ 1 ¼ m_ 3 ¼ m_ 2 þ m_ 10

(15)

m_ 2 ¼ m_ 4

(16)

m_ 3 þ m_ 6 ¼ m_ 5 þ m_ 4 ¼ m_ 5 þ m_ 2

(17)

m_ 1 x2;1 ¼ m_ 2 x2;2

(18)

m_ 5 z2;5 ¼ m_ 6 x2;6

(19)

x1;1 ¼ x1;3

(20)

  2
 X2;4 X1;1 þ X2;1 M M1 X2;4 M2 X1;1 M1 þ X2;1 M2 ¼ ¼ X1;1 M1 X2;4 M2
X2;1 M2 X1;4 M1 X1;1 X2;4
X2;1 X1;4  
 2 1
X1;4 X1;1 þ X2;1 M M1

 ¼ X1;1 1
X1;4
X1;4 1
X1;1  
 2 1
X1;4 X1;1 þ X2;1 M M1 ¼ X1;1
X1;1 X1;4
X1;4 þ X1;4 X1;1   1
X1;4 M X1;1 þ X2;1 2 ¼ X1;1
X1;4 M1 (25) AHP designers always try to keep this parameter at a minimum, since it affects parasitic loads and system costs [6]. More specifically, higher solution flows from the absorber to the generator and back increase pumping and sensible heat exchange duties. Eq. (25) shows that in order to minimize the CR, the refrigerant rich and poor solution molar fraction difference (X1,1
X1,4) must be as high as possible and the poor solution molar fraction (X1,4) must be also high, confirming the requirements by Hodgett (1982) [9]. Addi  2 tionally, the molecular weight ratio M must be as low as M1 possible. However, the refrigerant mass flow does not offer a very comprehensive reference to the AHP's useful effect. A more practical variation is the specific solution circulation (SSC), defined as the solution volume flow per kW of cooling power in the evaporator, see Eq. (30):

SSC ¼

(21)

From these equations, the mass flow of the various streams can be expressed as a function of the vapor mass flow exiting the generator ðm_ 5 Þ.

z1;5
x1;4 m_ 1 ¼ m_ 5 x1;1
x1;4

x2;1 x2;4

(12)

From the equations above, it is clear that the refrigerant mass fraction in each stream is also dependent on the molecular weight ratio between the absorbent and refrigerant.

x2;6 ¼ x2;4 ¼ x2;2

m_ 4 ¼ m_ 5

(22)

¼




CR

rsol;abs Hv;1;eva
cp1;ce ðTcon
Teva Þ



CR   p1;ce rsol;abs $Hv;1;eva 1
Hcv;1;eva ðTcon
Teva Þ

(26)

Low SSCs require a low CR, a high refrigerant vaporization enthalpy and a high solution density, falling in line with observations by Hodgett (1982) and Nowaczyk (1991) [9,14]. Moreover, the ratio of the refrigerant specific heat capacity to vaporization enthalpy should be as low as possible, in accord with Alefeld &

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Radermacher (1994), Eisa & Holland (1987) and Gluesenkamp et al. (2011) [1,6,7]. 2.4. Energy balance calculations The next step would be an energy balance for the critical components such as the generator, the solution heat-exchanger and the evaporator, i.e. all parts necessary for the final calculation of the COP. The same initial assumptions should apply. In the generator, the high temperature heat input is utilized as sensible heat, latent heat and excess heat of desorption in the case of non-ideal mixtures. All enthalpies are calculated using average ideal solution heat capacities in order to facilitate the calculations.

5

iii The ratio of the rich and poor solution absorbent mass fractions. In the evaporator the low temperature heat input is utilized exclusively as latent heat. However, due to the isenthalpic expansion through the expansion valve, the condensate enters the evaporator as a saturated two-phase mixture and therefore absorbs less heat for the evaporation process [7]. This internal loss is represented in the following equation:

Q_ eva ¼ m_ 10 Hv;1;eva
m_ 10 cp;1;ce ðTcon
Teva Þ   cp;1;ce ¼ m_ 10 Hv;1;eva 1
ðTcon
Teva Þ Hv;1;eva

(30)



 Q_ gen ¼ m_ 3 x1;3 cp;1;gen þ x2;3 cp;2;gen $ Tgenout
Tgenin þ m_ 5 z1;5 Hv;1;gen þ m_ 5 z2;5 Hv;2;gen þ m_ 5 Hxs;des  ¼ m_ 5


 z1;5
x1;4
x c þ x2;3 cp;2;gen $ Tgenout
Tgenin þ z1;5 Hv;1;gen þ z2;5 Hv;2;gen þ Hxs;des x1;1
x1;4 1;3 p;1;gen

In the solution heat exchanger it is accepted that only sensible heat is exchanged, therefore:

   _ 
m_ 1 x1;1 cp;1;shex þ x2;1 cp;2;shex Tgenin
Tabs ¼ m4 x1;4 cp;1;shex 
 þ x2;4 cp;2;shex Tgenout
Tabs (28)



(27)

  cp;1;ce z1;5
x1;4 Hv;1;eva 1
ðTcon
Teva Þ Q_ eva ¼ m_ 5 x2;4 Hv;1;eva

(31)

2.5. COP calculation By combining Eqs. (27) and (31), the cooling coefficient of performance, COPcool, can be calculated as follows:

By combining Eq. (28) with Eqs. (22) and (23):



COPcool ¼

Q_ eva ¼ z
x
1;5 1;4 Q_ x gen

x1;1
x1;4



z1;5
x1;4 cp;1;ce Hv;1;eva 1
Hv;1;eva ðTcon
Teva Þ x2;4 1;3 cp;1;gen

þ x2;3 cp;2;gen

(32)


 Tgenout
Tgenin þ z1;5 Hv;1;gen þ z2;5 Hv;2;gen þ Hxsdes


 Tgenout
Tgenin ¼ Tgenout
Tabs 1  0 x2;1 $ x1;4 $cp;1;shex þ x2;4 $cp;2;shex A   @1
x2;4 $ x1;1 $cp;1;shex þ x2;1 $cp;2;shex (29)

If the average heat capacities of the poor and rich solution streams in the solution heat exchanger have values very close to each other, Eq. (29) becomes:

 
 x2;1 Tgenout
Tgenin ¼ Τ genout
Tabs 1


x2;4


! 
1
x1;1  ¼ Τ genout
Tabs 1

1
x1;4    x1;1
x1;4
¼ Τ genout
Tabs 1
x1;4

Eq. (29) shows that the generator temperature output-input difference depends on: i The absorber - generator temperature difference. ii The heat capacity ratio of the poor and rich solutions at their respective average temperatures.

(33)

and combined with Eq. (32) gives:



COPcool ¼ z
x
1;5 1;4 x2;4



z1;5
x1;4 c Hv;1;eva 1
Hp;1;ce ðTcon
Teva Þ x2;4 v;1;eva

x1;3 cp;1;gen þ x2;3 cp;2;gen


 Tgenout
Tabs þ z1;5 Hv;1;gen þ z2;5 Hv;2;gen þ Hxsdes

(34)

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which can be also rewritten as:

c

COPcool ¼

ðTcon
Teva Þ 1
Hp;1;ce v;1;eva ðx1;3 cp;1;gen þx2;3 cp;2;gen Þ ðTgenout
Tabs Þ Hv;1;eva

z x

þ z 1;5
x2;4 1;5

1;4

Hv;1;gen Hv;1;eva

z x

þ z 2;5
x2;4 1;5

1;4

Hv;2;gen Hv;1;eva

þz

x2;4 x

1;5
1;4

(35)

Hxsdes Hv;1;eva

cp;1 ¼ f ðTc $pc Þ Hv;1 COPcool ¼

1
K1 K2 þ K3 þ K4 þ K5

(36)

where K1 to K5 represent dimensionless parameters that need to be minimized in order to maximize the COPcool as well as the heat pump coefficient of performance (COPHP), since:

COPHP ¼ 1 þ COPcool

(37)

Parameters K2 and K5 have already been considered, partly at least, by Hodgett (1982) and Iedema (1982) [9,10]. These studies considered absorbents with no vapor pressure, thus reducing K4 to zero, and vaporization enthalpies independent from temperature, resulting in K3 equal to 1.

2.6. COP parameter analysis Parameter K1 represents the internal loss of an isenthalpic expansion (flashing) in the evaporator, which can be further broken down to the heat pump's temperature lift ðTcon
Teva Þ and the   cp;1;ce refrigerant heat capacity to vaporization enthalpy ratio Hv;1;eva . Since the temperature lift is defined by the system boundary conditions, parameter K1 can only be otherwise minimized through the reduction of the previous ratio, as mentioned by Alefeld et al. [1]. A thorough investigation on this ratio and its possible correlation to basic thermophysical properties has been conducted. It turned out, that a basic correlation could be established between the refrigerant heat capacity to vaporization enthalpy ratio and the product of critical pressure and temperature:

(38)

Fig. 2 portrays this correlation using data from a sample of 765 organic compounds with critical temperatures spanning between 400 and 650 K [2]. The trend is quite clear; namely, that higher critical temperatures combined with higher critical pressures tend to yield lower heat capacity to vaporization enthalpy ratios and therefore lower isenthalpic expansion losses and, consequently, K1 values. The absolute values of the ratio itself appear to be relatively insignificant (0.002e0.01), but combined with the relevant temperature difference can amount to a considerable COP influence (see Tables 2 and 3). Parameter K2 can be considered as the generator sensible heat duty relative to the evaporator ideal latent heat duty (pure refrigerant evaporation without the expansion losses). It contains the same property ratio found in K1, only this time as the solution heat capacity at generator temperature to refrigerant vaporization enthalpy at evaporator temperature ratio. Furthermore, parameter K2 is proportional to the generator e absorber temperature difference (Tgenout
Tabs). The absorber temperature is defined again by the system boundary conditions, whereas the generator temperature is a design parameter as will be shown in chapter 2.6. In summary, the minimization of parameter K2 requires a low generator temperature, a low absorbent heat capacity and a high refrigerant critical temperature and pressure. Parameter K3 represents the ratio between refrigerant generator and ideal evaporator latent heat duties. It can be broken down to two terms, a relation between the refrigerant's generator liquid and   z x vapor mass fractions z 1;5
x2;4 and the refrigerant vaporization 1;5 1;4   H enthalpy ratio between the generator and evaporator Hv;1;gen . By v;1;eva combining Eqs. (8), (13) and (14) the following relation can be derived:






z1;5 x2;4 z1;5 1
x1;4 X2;4 Y1;5 1 ¼ ¼ ¼ z1;5
x1;4 z1;5
x1;4 X2;4 Y1;5
X1;4 Y2;5 1
X1;4 Y2;5 X2;4 Y1;5 ¼

1 1
RV2 (39)

Fig. 2. Correlation between refrigerant heat capacity to vaporization enthalpy ratio at 273.15 K.

Eq. (39) shows that the first term of parameter K3 is entirely dependent on the absorbent's relative volatility. More specifically, lower relative volatilities reduce the term towards unity. The second term, as also pointed out in a previous paper, represents the inverted cooling COP of a purely theoretical heat pump where all internal thermodynamic losses have been eliminated and the heat inputs are utilized solely for the evaporation of refrigerant [3]. A correlation for this parameter can be derived from a typical vaporization enthalpy equation as given by Watson (1943) [19]:

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7

Table 1 Dimensionless parameter and COP optimization.

Refrigerant critical pressure Refrigerant critical temperature Refrigerant acentric factor Refrigerant vaporization enthalpy Absorbent vaporization enthalpy Absorb./refrig. mol. weight ratio Absorbent rel. volatility Refrigerant rich sol. activity coeff. Refrigerant poor sol. activity coeff Refr. rich/poor sol. activity coeff. ratio Refrigerant density Absorbent density Refrigerant spec. heat capacity Absorbent spec. heat capacity Excess mixing enthalpy Generator temperature

K1

K2

High High

High High

K3 Low

Low

K4

K5

Low Low High Low Low Low

Low Low High Low Low Low Low

Low

Low Low

SSC

Literature

High High/Low Low High

High Low High High High

Low High

Low Low Low

Low Low High High

Low Low Low

Low Low

Low

COP High High/Low Low High Low Low Low Low Low

High/Low High/Low Low Low Low

High

Table 2 Performance parameters and COP results for various refrigerant candidates combined with DMEU.

Vaporiz. Enth. @273.15 K [kJ/kg] Mass [email protected] K [kg/m3] Critical temperature [K] Critical pressure [bar] Acentric factor u Absorbent molar mass ratio M2/M1 Absorbent relative volatility RV2 Generator temperature [K] K1 K2 K3 K4 K5 COPcool

Ammonia

Water

Methanol

Ethanol

Isopropanol

Trifluoroethanol

1261.3 580.1 405.7 112.80 0.253 6.70 0.07% 380.07 0.149 0.314 0.527 0.002 0.094 0.909

2481.8 992.3 647.1 220.64 0.344 6.34 10.55% 367.53 0.067 0.090 1.022 0.252 0.109 0.633

1209.5 772.6 512.5 80.84 0.556 3.56 2.90% 376.94 0.083 0.149 0.864 0.068 0.062 0.803

955.8 772.2 514.0 61.37 0.631 2.48 5.16% 374.33 0.100 0.182 0.889 0.131 0.060 0.713

803.5 766.8 508.3 47.65 0.665 1.90 7.14% 376.84 0.125 0.258 0.849 0.220 0.060 0.631

456.4 1356.6 501.9 48.09 0.641 1.14 4.83% 378.10 0.152 0.321 0.787 0.144 0.052 0.650

Table 3 Performance parameters and COP results for various refrigerant candidates combined with DMEU neglecting absorbent vapor pressure. Refrigerant theoretical potential.

Absorb. relative volatility RV2 Generator temperature [K] K*1 K*2 K*3 K*4 K*5 * COPcool Potential utilization COPcool/COP*cool

Ammonia

Water

Methanol

Ethanol

Isopropanol

Trifluoroethanol

0.00% 380.09 0.149 0.314 0.526 0.000 0.093 0.912 99.67%

0.00% 369.88 0.067 0.094 0.918 0.000 0.045 0.883 71.69%

0.00% 378.06 0.083 0.152 0.839 0.000 0.052 0.880 91.25%

0.00% 376.16 0.100 0.188 0.843 0.000 0.045 0.836 85.29%

0.00% 379.66 0.125 0.271 0.783 0.000 0.041 0.799 78.97%

0.00% 380.17 0.152 0.333 0.743 0.000 0.044 0.758 85.75%

* Neglecting the absorbent vapor pressure (RV2 ¼ 0).

Hv;1;gen ¼ Hv;1;eva



Tc
Tgen Tc
Teva

n (40)

generator vaporization enthalpy also refers to the absorbent   Hv;2;gen Hv;1;eva . Using the same approach as for parameter K3, the following relation can be derived:

where n is a constant. For a given temperature difference between generator and evaporator the vaporization enthalpy ratio decreases exponentially with decreasing critical temperature. Fig. 3 shows the correlation between vaporization enthalpy ratio and critical temperature from a sample of 3500 organic substances with critical temperatures between 395 and 650 K [20]. Parameter K4 represents the ratio between absorbent generator and refrigerant ideal evaporator latent heat duties, in other words a parameter linked to rectification losses. In this case the mass frac  z x tion relation includes the absorbent vapor phase z 2;5
x2;4 and the 1;5

1;4









M2 X2;4

M2 z2;5 x2;4 1
z1;5 1
x1;4 M X ¼ ¼ Y M1 X ¼ 1 1 1;4 1;5 z1;5
x1;4 z1;5
x1;4
1;4 RV
1



¼

M2 M1



1 X1;4 1 RV2

Y2;5

X2;4

2


1


1

(41)

Indeed this term depends on the molar mass ratio, the absorbent's relative volatility and the refrigerant poor solution molar

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P. Chatzitakis, B. Dawoud / Renewable Energy xxx (2016) 1e12

coefficient, a low refrigerant critical temperature, a low refrigerant acentric factor and finally a low absorbent generator vaporization enthalpy relative to the refrigerant evaporator vaporization enthalpy. It should also be noted that, K4 decreases with decreasing generator temperatures since it is directly dependent on the refrigerant generator vapor pressure. Parameter K5 represents the ratio between generator excess desorption enthalpy and ideal evaporator latent heat duty. As with the other parameters, the first term is a mass fraction ratio, Eq. (44), and the second is the ratio between desorption enthalpy and   xsdes evaporator refrigerant vaporization enthalpy HHv;1;eva . Again, with the combination of Eqs. (8), (13) and (14): M2 Y2;5

Fig. 3. Correlation between vaporization enthalpies ratio (at 273.15 K and 393.15 K) and critical temperature Tc.

M2 X2;4

1 þ M1 Y1;5 1 þ M1 X1;4 RV2 x2;4 1
x1;4 ¼ ¼ ¼ z1;5
x1;4 z1;5
x1;4 1
X1;4 Y2;5 1
RV2 X2;4 Y1;5 

¼

2 1þM M1

1 X1;4


1 RV2

1
RV2

(44)

Just like parameter K4, the minimization of parameter K5 requires a low molecular weight ratio between absorbent and refrigerant, a low absorbent relative volatility, a low generator excess desorption enthalpy relative to the refrigerant evaporator vaporization enthalpy and a high molar poor solution concentration (meaning a low refrigerant critical temperature, a low refrigerant acentric factor and a low activity coefficient). For most mixtures, the excess enthalpies are usually one order of magnitude lower than the vaporization enthalpy. In addition, K5 also has the same generator temperature dependency as K4. 2.7. SSC parameter analysis

Fig. 4. Correlation between generator/condenser vap. pressure ratio and the acentric factor and critical temperature.

concentration. The latter, as can be seen from Eq. (42), which is derived from Eqs. (6) and (10), also depends on the absorbent's relative volatility, the refrigerant vapor pressure ratio between the condenser and generator temperatures and the refrigerant poor solution activity coefficient. p

X1;4

p

g

As already mentioned in chapter 2.3, the requirements for minimizing the specific solution circulation (SSC), Eqs. (45) and (46), are a high refrigerant evaporator vaporization enthalpy, a high solution density, a low absorbent/refrigerant molecular weights ratio a high refrigerant poor solution molar concentration and a high refrigerant rich-poor solution molar concentration difference. A more detailed analysis with the use of Eqs. (5) and (7), shows that low refrigerant activity coefficients for the rich and poor solutions are also beneficial. More specifically the rich solution refrigerant activity coefficient should be as low as possible compared to that of the poor solution. Also, just like in the case of

p

2;gen 2;4 1;con 1;con p1;con
p2;gen g2;4 p1;gen g1;4
p1;gen g1;4 p1;gen g1;4
RV2 ¼ ¼ ¼ p2;gen g2;4 p1;gen g1;4
p2;gen g2;4 1
RV2 1


p1;gen g1;4

(42) Lee & Kesler (1975) [12] developed an expression of vapor pressure as a function of temperature, acentric factor and critical temperature.

ln p ¼ f0 ðTc ; TÞ þ u f1 ðTc ; TÞ

(43)

Following this approach, the refrigerant vapor pressure ratio ! p1;con p1;gen

was correlated with the product ðu þ 1ÞTc for the same

sample of 765 organic compounds, for a generator temperature of 393.15 K and a condenser temperature of 313.15 K (Fig. 4) [2]. In summary, the minimization of parameter K4 requires a low molecular weight ratio between absorbent and refrigerant, a low absorbent relative volatility, a low refrigerant poor solution activity

Fig. 5. Correlation between ideal molar CR and the acentric factor u and critical temperature Tc.

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P. Chatzitakis, B. Dawoud / Renewable Energy xxx (2016) 1e12

parameter K1, the refrigerant critical pressure and temperature should be high.

SSC ¼

CR




rsol;abs Hv;1;eva
cp1;ce ðTcon
Teva Þ





 ¼

1
X1;4 X1;1
X1;4

 

2 X1;1 þ X2;1 M M1




 

rsol;abs Hv;1;eva
cp1;ce ðTcon
Teva Þ

(45)

poor solution refrigerant concentrations (X14) and therefore lower CRs and SSCs. Table 1 summarizes the requirements on each related working pair property that minimizes K1-K5 and, consequently, maximizes COP and those needed to minimize the SSC. It is worth noticing that not all parameters benefit from the same working pair property trend. More specifically, parameters K1 and K2 require high refrigerant critical temperatures, whereas K3, K4 and K5 require a low critical temperature. Accordingly, the relative order of magnitude of K1-K5 shall decide on the final COP trend of each working pair. The SSC shows a similar contradiction between the ideal molar CR and the refrigerant heat capacity to vaporization enthalpy ratio. Addition-

  0 1 2 X1;1 þ X2;1 M M1 p1;abs p1;gen g1;4
p1;abs p1;con A    z@ g1;4 p1;eva p1;gen g
p1;abs p1;con p1;ce rsol;abs Hv;1;eva 1
Hcv;1;eva ðTcon
Teva Þ 1;1

ideal molar CR ¼

p1;abs p1;gen
p1;abs p1;con p1;eva p1;gen
p1;abs p1;con

9

(46)

ally, the SSC benefits from high generator temperatures and absorbent relative volatilities, whereas the COP shows the opposite

(47)

Additionally, the ideal molar CR, Eq. (47), which is basically the molar circulation ratio for an ideal mixture with an absorbent with negligible vapor pressure, must be also low. Using the same approach as in K4, the ideal molar CR was correlated with the product ðu þ 1ÞTc for the same sample of 765 organic compounds with critical temperatures spanning between 400 and 650 K (Fig. 5) [2], while using the evaporator, absorber and condenser temperatures as defined in chapter 4 and a generator temperature Tgen ¼ 393.15 K. Just like in the previous instances, low acentric factors and low critical temperatures produce favorable ideal molar CRs. However, this relation doesn't take into account the effect of the absorbent's vapor pressure, or in other words the absorbent's relative volatility. As can be seen from Eq. (42), an increase in RV2 results in a decrease to the poor solution refrigerant concentration and consequently, from Eq. (45), a decrease to the SSC. Finally, Eq. (42) also shows that the generator temperature has an indirect effect on the SSC. Higher generator temperatures result in higher generator vapor pressures, which in turn produce lower

Fig. 7. Comparison of COP parameter K3 for the six refrigerant candidates relative to the generator temperature.

Fig. 6. Comparison of COP parameter K2 for the six refrigerant candidates relative to the generator temperature.

Fig. 8. Comparison of COP parameter K4 for the six refrigerant candidates relative to the generator temperature.

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P. Chatzitakis, B. Dawoud / Renewable Energy xxx (2016) 1e12

Fig. 9. COP comparison for the six refrigerant candidates relative to the generator temperature.

Fig. 10. SSC comparison for the six refrigerant candidates relative to the generator temperature.

behavior. Hence, an optimum generator temperature can be targeted to obtain the maximum COP at a reasonable “minimum” SSC. 3. Simulation and results Based on the combination of Eqs. (29) and (32), it was attempted to investigate the cooling COP potential of six conventional as well as unconventional absorption heat pump refrigerant candidates. In order to achieve that, 1,3-dimethyl ethylene urea (DMEU) was selected as the absorbent for all cases, in order to establish an equal basis for a realistic comparison. Along this approach, it was also assumed that all refrigerant candidates show the same non-ideal molecular interactions with the solvent. All pure substance properties were taken from the NIST Thermodata Engine [2]. The activity coefficients were derived with the help of an NRTL model, whose parameters are listed in the Appendix (Eq. (49)e(52), Table 4). The calculations were performed using Microsoft Excel VBA. The system boundary conditions were defined as follows: ➢ Teva ¼ 273.15 [K] ➢ Tabs ¼ Tcond ¼ 313.15 [K] ➢ SSC ¼ 35 [l/(h kW)] Table 2 holds the calculated performance parameters, the

fundamental substance properties as well as the COP results for the listed refrigerants combined with DMEU. Additionally, Table 3 presents the refrigerant's theoretical potential by eliminating the absorbent's vapor pressure effect. The reasons for the distinction between the results of Tables 2 and 3 are to show the influence of the absorbent's vapor pressure, but also to allow for a certain degree of comparison between the refrigerant candidates. The rationale behind it becomes clearer at the end of chapter 4 where the overall candidate evaluation takes place. In addition, a sensitivity analysis was performed for parameters K2, K3, K4 and the COP with varying the generator temperature. Parameter K1 is generator temperature independent and parameter K5 involves the molecular interaction between refrigerant and absorbent (desorption excess heat), something that falls out of the scope of the current work. Parameter K2 (Fig. 6) seems to be universally increasing with the generator temperature (Tgenout). This is rather straightforward since it is influenced by the temperature difference between generator and absorber as well as the solution liquid heat capacity, a property that increases with temperature. Ammonia specifically, presents a steeper curve since the selected generator temperature range is approaching very closely to its critical point, where liquid heat capacity increases sharply. Parameter K3 (Fig. 7) looks to be minimally influenced by the generator temperature for the main group, with the exception of water and ammonia. In the first case the solvent's strongly increasing relative volatility and in the second case ammonia's rapidly declining generator vaporization enthalpy (again due to the critical point approach) seem to have the dominating effect. In terms of absolute values, it seems to be the parameter with the highest gravity on the final COP value. Parameter K4 (Fig. 8), given the curve arrangement, seems to be mostly affected by the absorbent's relative volatility, negligible for ammonia but rather detrimental for water. Overall, the COP results, as depicted in Fig. 9, indicate that ammonia holds the highest thermodynamic potential. In terms of performance parameters, ammonia scores very well with parameters K3 and K4 due to an extremely low critical temperature, a very low acentric factor, a low relative volatility and a low relative generator vaporization enthalpy to DMEU. However, the very low critical temperature and the high molecular weight ratio between absorbent and refrigerant affect parameters K1 and K2 rather negatively. Interestingly, it is the only refrigerant that increases its COP with the generator temperature, due to approaching its critical point. Water, on the other hand, presents quite a different image. Its exceptionally high vaporization enthalpy, critical temperature and pressure lead to significantly lower K1 and K2 parameters. The very high critical temperature though, as well as the high absorbent relative volatility result in significantly increased K3 and K4 parameters. This results in a modest COP value, rather far from its theoretical potential (COP*cool Table 3). Nevertheless, water displays remarkably lower SSCs (Fig. 10) compared to the rest of the candidates. This is attributed, again, to its extremely high critical pressure and vaporization enthalpy, as well as its high density and low acentric factor. Surprisingly though, ethanol shows significantly lower SSCs compared to methanol, despite its slightly lower critical pressure, vaporization enthalpy and its higher acentric factor. In this case, the beneficial effect derives from the decidedly lower absorbent molar mass ratio M2/M1. Methanol has a very similar theoretical potential as water, but contrary to Water-DMEU's much higher absorbent relative volatility (10.55%), methanol is able to utilize most of its theoretical potential COP (91.25%) as can be read in Tables 2 and 3, respectively. In general, the alcohols show a diminishing COP trend with

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P. Chatzitakis, B. Dawoud / Renewable Energy xxx (2016) 1e12

11

Table 4 NRTL model parameters. b12

b21

c12

c21

d12

e12

f12

f21

g12

g21

1.9E þ 02

6.28E þ 01


2.71E þ 04


1.71E þ 03

3.97E
02

3.16E
04


4.97E þ 00


1.48E þ 01


2.15E
01

6.05E
02

increasing molecular weight, primarily due to the decreasing vaporization enthalpy per mass, critical pressure, vapor pressure and an increasing acentric factor that affect K1, K2 and K4 negatively. Trifluoroethanol presents a small exception to this, despite its significantly lower vaporization enthalpy, less than half compared to ethanol. The reduced critical temperature and the increase in molecular weight and vapor pressure seem to influence parameters K3 and K4 favorably, thus bringing the COP value higher, between those of ethanol and isopropanol. Overall, it appears that COPs are increasing with decreasing generator temperatures, something that does not manifest in real systems, but as mentioned previously, the mechanical apparatus in this work achieves 100% heat exchanger efficiency. In real systems, as the generator temperature decreases, the circulation ratio increases significantly and with it the solution heat exchanger and absorber efficiencies decline proportionally, not to mention the increased solution pump duty. All parameters considered, real COP curves should display an optimum generator temperature. Indeed, AHP performance calculation is rather more complicated, especially in the absence of equilibrium. Unfavorable molecular interactions, external heat losses and finite heat exchanger surfaces, for instance, bring additional influences into play. These influences along with a comparison with experimental results fall into the scope of our future investigations. 4. Conclusions This work focused on developing a practical and quantitative mathematical model for the calculation of a single effect absorption heat pump potential and subsequently the identification of the thermophysical properties with the highest influence on it. This was achieved by isolating the system from “mechanical” efficiency factors, i.e. considering a real absorption working pair in a perfect heat pump apparatus. The cycle analysis, a combination of vaporliquid equilibria, mass and heat balances, revealed five dimensionless COP influencing parameters (K1-K5) in the form of specific enthalpies and mass fraction ratios, which shall all be minimized to maximize COP. All of the influencing parameters were then further investigated and correlated to working pairs' thermophysical properties. It turned out that, higher refrigerant critical temperatures combined with higher critical pressures are associated with lower heat capacity to vaporization enthalpy ratios and, therefore, lower isenthalpic expansion losses and, consequently, K1 values. In addition, a detailed analysis for the specific solution circulation (SSC) has been carried out. For the COP, the mass fraction ratios were all found to be dependent on the absorbent relative volatility and almost all of them (with the exception of K3) dependent on the ratio between absorbent and refrigerant molar masses. In practical terms, they tend to act as amplifiers to the inherent cycle thermodynamic losses. This study reveals that the molecular weight ratio between the absorbent and refrigerant does affect both the SSC and the COP, at least for absorbents with non-negligible vapor pressure. It can be concluded that, low molecular weight ratios have a beneficial effect on the system's performance. The SSC also shares the same dependencies. With the aim of validating the influence of these key working pair properties as well as the mathematical models, ammonia, water and several alcohols were simulated together with a

conventional solvent, DMEU. The analysis also evaluated the influence of the absorbent relative volatility and the generator temperature on the SSC, the COP and its dimensionless parameters K1eK5. As expected, ammonia and water hold the highest potentials among the candidates, but DMEU appears to be an unsuitable absorbent to water due to its high relative volatility. This could be the main reason behind water being a successful refrigerant solely with absorbents that have negligible vapor pressures. The results of this study agree to a large extent with the collective literature, with the exception of the refrigerant acentric factor and absorbent vaporization enthalpy. According to the results of this study, both refrigerant acentric factor and the absorbent vaporization enthalpy shall be minimized to obtain better performance. Appendix The definition of the acentric factor was originally stated by Pitzer (1955) [16] as a value that describes molecular spherical symmetry and is calculated by the following equation:

u ¼
log10

lim

ðp=pc Þ
1

ðT=Tc Þ¼0:7

(48)

Eqs. (49) to (52) show the NRTL general equations for species i in a mixture of n components. n   Pn X t G X Xkj Gik k¼1 kj ki ki ln gij ¼ P þ Pn n l¼1 Xlj Gli l¼1 Xlj Glk k¼1 0 1 P n B Xmj tmk Gmk C B C  Btik
m¼1 Pn C @ A l¼1 Xlj Glk

Gik ¼ expð
aik tik Þ

tik ¼ bik þ

cik þ fik ln T þ gik T T

aik ¼ dik þ eik ðT
273:15KÞ

(49)

(50) (51) (52)

The NRTL activity coefficient parameters for the refrigerant/ absorbent are listed in Table 4. References [1] G. Alefeld, R. Radermacher, Y. Hwang, Heat Conversion Systems, CRC Press, Boca Raton, 1994. [2] ASPEN Plus V7.3, Aspen Tecnology Inc, Burlington, 2011. [3] P. Chatzitakis, B. Dawoud, Identification of thermophysical properties and metrics for the preliminary investigation of favorable vapor absorption heat pump refrigeration candidates, in: Proceedings of the 3rd Innovative Materials for Processes in Energy Systems Symposium, Fukuoka, 2013, pp. 615e620. [4] K. Dahm, D. Visco, Fundamentals of Chemical Engineering Thermodynamics, Cengage Leraning, Stamford, 2015. [5] P. Donellan, K. Cronin, E. Byrne, Recycling waste heat energy using vapour absorption heat transformers: a review, Renew. Sustain. Energy Rev. 42 (2015) 1290e1304. [6] M.A. Eisa, F.A. Holland, A study of the optimum interaction between the working fluid and the absorbent in absorption heat pump systems, Heat. Recovery Syst. 7 (1987) 107e117.

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[7] K. Gluesenkamp, R. Radermacher, Y. Hwang, Trends in absorption machines, in: Proceedings of the 12th International Sorption Heat Pump Conference, Padua, 2011, pp. 13e22. [8] K.E. Herold, R. Radermacher, S.A. Klein, Absorption Chillers and Heat Pumps, second ed., CRC Press, Boca Raton, 2016. [9] D.L. Hodgett, Absorption heat pumps and working pair developments in Europe since 1974, in: Proceedings of New Working Pairs for Absorption Processes Workshop, Berlin, 1982, pp. 57e70. [10] P.D. Iedema, Mixtures for the absorption heat pump, Int. J. Refrig. 8 (1982) 262e268. [11] A. Kühn, Thermally Driven Heat Pumps for Heating and Cooling, Uni€tsverlag der TU Berlin, Berlin, 2013. versita [12] B.I. Lee, M.G. Kesler, A generalized thermodynamic correlation based on three-parameter corresponding states, AIChE J. 21 (3) (1975) 510e527. [13] M. Narodoslawsky, G. Otter, F. Moser, Thermodynamic criteria for optimal

absorption heat pump media, Heat Recovery Syst. CHP 8 (1988) 221e233. [14] U. Nowaczyk, Kriterien zur Auswahl von Arbeitsstoffgemischen für Absorptionsprozesse und Erste Auswahlmessungen, DKV, Essen, 1991. [15] H. Perez-Blanco, Absorption heat pump performance for different types of solutions, Int. J. Refrig. 7 (2) (1984) 115e122. [16] K. Pitzer, The volumetric and thermodynamic properties of fluids I. Theoretical basics and virial coefficients, J. Am. Chem. Soc. 77 (13) (1955) 3427e3433. [17] P. Shrikirin, S. Aphornratana, S. Chungpaibulpatana, A review of absorption refrigeration technologies, Renew. Sustain. Energy Rev. 5 (2001) 343e372. [18] J. Sun, L. Fu, S. Zhang, A review of working fluids of absorption cycles, Renew. Sustain. Energy Rev. 16 (2012) 1899e1906. [19] K.M. Watson, Thermodynamics of the liquid states, generalized prediction of properties, Ind. Eng. Chem. 35 (1943) 171e177. [20] C.L. Yaws, Thermophysical Properties of Chemicals and Hydrocarbons, William Andrew, New York, 2008.

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