Absorption heat pump performance for different types of solutions

Absorption heat pump performance for different types of solutions

H. Perez- Blanco

Key words: heat pumps, absorption heat pumps, binary solutions

Performance de la pompe chaleur & absorption pour diff6rents types de solutions L "int~rOt croissantport~ aux pompes a chaleur a absorption a conduit a effectuer des recherches sur de nouveaux fluides actifs. Dans cette #tude, la thermodynamique des solutions binaires est appfiqu#e ~ un modble de pompe a chaleur simple

pour d~terminer que/ type de solution optimise /a performance thermique pour un frigorig#ne donn~ (ammoniac).

On trouve que, bien que des solutions qui pr~sentent une d#viation n#gative par rapport ~ la /oi de Raou/t devraient conduire ~ de meilleures performances, il existe une d6viation limite pour /a solution. On #tudie aussi /'influence de la temp#rature et de/a concentration sur /e coefficient d'activit~ du frigorigene et /'on indique les domaines optimisant la performance des pompes b cha/eur.

Increasing interest in absorption heat pumps has led to research on new working fluids. In this work, the thermodynamics of binary solutions is applied to a simple heat pump model to determine which type of solution optimizes thermal performance for a given refrigerant (ammonia).

It is found that although solutions with neg-

ative deviations from Raoult's law enhance the performance, there is a limit as to how strongly the solution should negatively deviate. The dependence of the refrigerant activity coefficient on temperature and concentration is also studied, and the ranges that optimize heat pump performance are indicated.

N o m e n c l a t u re

B dimensionless parameter characterizing the nonideali ty of the working solution at the absorber condit ions

cp molar specific heat h partial molal enthalpy, kJ kg -1 mol -~ H enthalpy, kJ kg -~ mol -~ k parameter characterizing the solution at the

absorber and generator, K -m m dimensionless parameter characterizing

temperature dependence of the activity coefficient

n number of moles of solution circulated for one mole of refrigerant absorbed; also, parameter indicating concentration dependence

p pressure, N m -2 Q heat exchanged per unit of refrigerant evap-

orated in the evaporator, kJ r heat of vaporization, kJ mo1-1 R universal gas constant, kJ mol -~ K -1 T absolute temperature, K

x &

7

refrigerant mole fraction indicates variation, error recuperator effectiveness activity coefficient of refrigerant in solution

Subscripts and superscripts

a absorber ab absorbent c condenser e evaporator g generator H hot generator temperature i state L cold evaporator temperature M intermediate absorber/condenser delivery

temperature 0 pure substance r refrigerant ref reference

The working fluids of an absorption heat pump determine to a large extent the materials of construction

The author is Staff Scientist, Oak Ridge National Laboratory, 9102- 2. PO Box Y, Oak Ridge, TN 37830, USA. Work sponsored by the Office of Buildings Energy Research and Development, US Depart- ment of Energy under contract W-7405-eng-26 with the Union Carbide Corporation. Paper received 13 May 1983.

as well as the heat pump performance. Since both of these factors greatly influence the cost of bui lding and operating a heat pump, the search for new working fluids generally focuses on those that wi l l either improve the performance or decrease the initial cost of the unit. The search for new pairs is a diff icult undertak- ing. For each candidate pair, pressure-temperature-

0140-7007/84/00211 5-0853.00 © 1984 Butterworth S ~ Co (Publishers) Ltd and IIR Volume 7 Num¢ro 2 Mars 1984 115

concentration (p-T-x) and enthalpy-temperature- concentration (H-T-x) charts must be determined before the cycle performance can be calculated. The values of transport properties such as thermal con- ductivity, diffusivity, and viscosity must be known before a heat pump prototype can be designed.

These undertakings tend to be costly, especially when they involve large-scale efforts to collect data. It is not surprising that criteria to narrow the search for new pairs were formulated early. 1 Here, we are solely concerned with finding out which types of solution could improve the coefficient of performance (COP) of single-effect absorption heat pumps.

Previous work applied to absorption chillers established that solutions exhibiting large negative deviations from Raoult's law should lead to performance improvements, especially for non-volatile absorbentsJ Jacob, Albright, and Tucker determined that the de- sirability of strong negative deviations is limited because large refrigerant concentrations at the absorber outlet lead to reduced COP values. 2 A study of solution thermodynamics for negative deviations was carried out by Andrews and Rousseau, and it was determined that little could be done to improve the thermodynamic efficiency of the system via novel pairs, so future work should focus on pairs yielding small circulation losses. 3 A .substantial departure from the preceding con- cl~sions was tested by Macriss et al. when solutions exhibiting positive deviations from Raoult's law were investigated. 4 Circulation rates for these solutions may be unacceptably high, but some pairs exhibiting small negative deviations from Raoult's law and positive heats of mixing were identified. These pairs were deemed worthy of further research, since they may greatly enhance thermodynamic performance due to their low heats of mixing. Mansoori and Patel calculated upper and lower limits of the COP of solar cooling machines, based on the laws of thermodynamics. ~ A number of working pairs exhibiting negative deviations from Raoult's law were studied and their preferred ranges of applicability stated. Hodgett quantified the thermodynamic behaviour of the working fluids in terms of three dimensionless parameters which charac- terize the heat of mixing, the pump work, and the circulation thermodynamic losses. 6 To enhance performance, all three must be minimized.

ledema carried out a thermodynamic analysis of several working fluids for single- and double-effect absorption heat pumps] It was found that to optimize performance, the heats of mixing must be low, the negative deviations from Raoult's law large to minimize solution circulation, the refrigerant solubility high, and the solution specific heats small. The refrigerant heat of vaporization must be high and its vapour pressure low, especially for two-stage designs.

In summary, there is a consensus that solutions that deviate negatively from Raoult's law enhance performance. At the same time, it has been established that low heats of mixing and low thermodynamic circulation losses must also be sought. 4.6.7 Since the large negative deviations generally entail high heats of mixing and low circulation losses, 2,4 it is clear that it would be beneficial to understand how these properties are interrelated.

In this work, an effort is made to quantify the

Heat input

T Reeu~r~ r

H~t 3~ "°;2'"' )

~ J t

6

8

Heat input

J Fig. 1 Schematic of a single-stage absorption heat pump

Fig. 1 Schema d'une pompe ~ chaleur ~ absorption ~ un ~tage

desirable properties and their interrelations in order to maximize the COP. A simple, single-effect heating absorption cycle is defined as a basis for comparing its performance with different types of solutions, using ammonia as a refrigerant. The solutions are defined by the activity coefficient of the refrigerant in solution. Solutions ranging from ideal to strongly negative deviations from the ideal are considered, together with different parametric dependences of the activity coefficient on solution temperature and concentration. The parameters defining NH3-H20 solutions are calculated for comparison. Circulation rates and heat pump COPs are displayed for the various solution types.

The heat pump cycle

The simple absorption cycle considered here is shown in Fig. 1. Heat (Qg) is supplied in the generator at a high temperature, TH, whereas heat from the atmosphere at a low temperature, T L, is supplied in the evaporator (Qe). Heat is released to the heated space in the absorber (Qa) and condenser (Qc) at an intermediate temperature, TM, where TH> TM> TL. Fig. 2 shows the enthalpy concentration diagram for this cycle; this diagram is typical of mixtures in which both components are volatile. The symbols H, p, 7-, and x denote enthalpy, pressure, temperature, and refrigerant mole fraction, respectively. The subindexes g, a, and e stand for generator, absorber, and evaporator, respectively.

All the following expressions are formulated for one mole of evaporated refrigerant. In the generator (points 1 to 2), the solution is concentrated in absorbent by vaporizing the refrigerant. It is assumed that pure

118 International Journal of Refrigeration

refrigerant, saturated at the generator pressure, is obtained. A heat balance gives

Qg = nlH1 - n2H2 - h~, (1)

where QQ is the heat input to generator, n is the number of moles in solution, H is the solution molar enthalpy, and h ° is the pure refrigerant molar enthalpy.

When the absortent is volatile, some of it is vaporized with the refrigerant, and, subsequently, condensed in a purification column. In that case, (1) gives the net heat supplied, that is, the difference between the heat supplied to the generator and the heat removed from the purification column. The refrigerant is then condensed (points 5 to 6). The heat, Qc, delivered in the condenser is - ° o Qc-hs -h 6.

The liquid refrigerant is expanded to the evaporator (point 7) and evaporated (points 7 to 8) using heat from the environment. The heat supplied in the evaporator is Qe=h~-h~.

The vaporized refrigerant is absorbed in the absorber (points 3 to 4). A heat balance gives the heat, Q,, delivered in the absorber: Q.=n4H4+h~-n3H3.

In order to calculate the heat exchanged in each component, it is necessary to find the state points 1 through 8 (Fig. 2). For given generator (TH), absorber (TM), condenser (TM), and evaporator (TL) temperatures, the state points indicated in Fig. 2 can be determined as follows.

The solution coming out from the absorber is at the absorber temperature, T M, and at the evaporator pressure, Pe. This determines state 4, the solution enthalpy, and the equilibrium absorber concentration, xa. Note that thermodynamic equilibrium is assumed. Subcool- ing, if present, will reduce the equilibrium concen-

O Refrigerant mole froction x

Fig. 2 The heat pump cycle in the enthalpy concentration diagram

Fig. 2 L e cycle de la pompe ~ chaleur dans le diagramme enthalpie- concentration

tration. Similarly, state 2 is located at the generator temperature, TH, and at the condenser vapour pressure. For determining states 1 and 3, the amount of solution circulated must be known. The solution at the generator outlet is composed of n, moles of refrigerant and n, moles of absorbent. The total number of moles, n, is n=nr+na.

The number of moles to be circulated between the generator and the absorber in order to absorb one mole of refrigerant is the circulation ratio n given by

n= (1 - xa ) / ( x , - x~ ) (2)

The number of moles of refrigerant and absorbent are

nr=nx~ (3)

na=n-nr (4)

The effectiveness of the intermediate recuperator determines the state points 1 and 3 as follows. The maximum amount of heat that can be transferred in this recuperator is by cooling the solution coming out from the generator to the absorber temperature (state 2' in Fig. 2). This heat is given by

qma,=n (H2- H2,) (5)

The heat, q, actually transferred is

q=Sqmax (6)

where E is the effectiveness of the recuperator. In that case,

H3=H2 - q (7) n

and

H, =H4+ [q / (n+ 1 )] (8)

Since the concentrations of states 1 and 3 are those of states 4 and 1, respectively, the enthalpies as given by (7) and (8) completely define states 3 and 1.

The state points 5 and 6 have the refrigerant enthalpies of saturated vapour and liquid, respectively, at the condenser pressure. State 7 has the same enthalpy as state 6, since there is no change in enthalpy across the expansion valve. State 8 has the enthalpy of the saturated vapour at the evaporator pressure.

Once the heat exchanged in each component is calculated, the COP of the heat pump is given by

COP= (Qa+ Qc)/Qg (9)

The parasitic power spent by the pump has not been included in the definition of COP. This power is a function of the pressure difference between the absorber and the generator and of the solution's volumetric circulation rate. As shown later, the pressures are constant in our analysis, so that insight into the parasitic power requirements may be easily obtained from the circulation ratios.

Volume 7 Number 2 March 1984 117

The heat balance error is given by

• '~= ('~Oin- ~.Oout)/[~.,Oin4- 7Qou,)/2]

Thermodynamics of working pairs

To determine the COP of a heat pump cycle, the solution and refrigerant enthalpies at each state point must be determined. The enthalpy of a solution at state i is given by

H~= (n,hr+ naha)#n (1 O)

where h is the partial molal enthalpy, and r, a are refrigerant, absorbent, respectively. The partial motal enthalpies are a function of solution composition, temperature, and pressure. In the following, it is shown how the partial molal enthalpies are related to the refrigerant vapour pressure in solution.

The working solutions in heat pumps can be characterized by the deviations from Raoult's law experienced by the refrigerant vapour pressure. 1,2.8 These deviations can be quantified by the activity coefficient of the refrigerant in the solution. For a solution in equilibrium with a vapour phase that behaves as a perfect gas, the activity coefficient of the refrigerant, ?, is given by 9

7=p/p°x (11 )

where p is the vapour pressure of the refrigerant in solution, pO is the vapour pressure of the pure refrigerant at the temperature of the solution, and x is the refrigerant mole fraction. Since the vapour pressure p, of the refrigerant, in an ideal solution, is given by Raoult's law, p~=p°x, then ? measures (for perfect gas behaviour) the ratio of the actual to the ideal solution vapour pressure. For solutions with negative deviations, ~ is less than one. If the refrigerant deviates appreciably from perfect gas behaviour, then fugac- ities, as opposed to vapour pressures, must be used. However, these possibilities will not be covered here.

In this work, a parametric dependence of the refrigerant activity coefficient on concentration and temperature is postulated. This postulated function is of the form

y = e x p [ - B ( 1 - x ) °] (12)

where 0~<x~< 1. For any given concentration and for a value of B

greater than zero, this parameter characterizes how strongly the solution deviates from Raoult's law. The larger B is, the stronger the negative deviation of the solution. The parameter n characterizes the dependence of the activity coefficient on concentration. For a value of n greater than zero and for given values of B and x, increasing values of n indicate solutions with progressively smaller negative deviations from Raoult's law.

In this work, it is assumed that the refrigerant concentration can be varied from zero to one. Thus, phase separation (as it occurs in LiBr-H20 solutions) is excluded from this analysis. When the refrigerant

concentration is zero, the refrigerant vapour pressure, given by

P=TP°X (13)

must be zero. When the concentration approaches one, the refrigerant vapour pressure approaches that of the pure refrigerant, as in ideal solutions. Thus, it may be verified that for

n> 1 and B>O, (14)

the following conditions hold: when x-,O, then p--,O, and when x - , l , then p_,pO; and #p/#x.-.,p °.

It is possible to show that (12), subject to the conditions in (13) and (14), does not have inflexion points in the range O < x < 1, so that phase separation is excluded from the analysis. 1°

In general, the activity coefficient depends on the solution temperature. To take this dependence into account, the constant B is replaced by

B=kT m (15)

where k is a constant, T is the solution temperature, and m is a parameter indicating the temperature dependence of the activity coefficient. For values of m less than zero, the activity coefficient increases with temperature. The larger the absolute value of m, the more strongly the activity coefficient depends on temperature. In general, the value ofm depends on the solution concentration. For the sake of simplicity, it wilt be taken as constant for our analysis, but it should be regarded as an average value of 1hose corresponding to the high and low cycle concentrations.

Once the activity coefficient has been specified, the partial molal enthalpies may be easily calculated as follows. The refrigerant partial molal enthalpy is

hr=h~__RT2Cq In y aT I~x

(16)

where h ° is the refrigerant molar enthatpy at the solution temperature and pressure, and R is the universal gas constant.

The absorbent partial molal enthalpy is calculated from the Gibbs-Duhem equation. At constant pressure and temperature, dha= [x/(1 - x ) ] (#hJ#x)dx, which integrated from x=O to x gives

x

ha=ha - Z/(1 -z)](#h,/#z)dz

0

(17)

Substitution of (12) and (15) into (16) and (17) yields

hr=h°+ RT~+ 'km(1 - x ) ° (18)

and x

ha=h°+ RT~+~kmn!z(1 - z)n- 2dz

0

(19)

118 Revue Internationale du Froid

For our calculations, the value of the integral in (1 9) was determined numerically using Simpson's rule. The enthalpy of the pure absorbent at T was calculated as

h°=Cp,ab(T - Tref)

where T,e f is a reference temperature. In order to investigate cycle performance for different

solution types, a refrigerant is chosen, together wi th generator, absorber, condenser, and evaporator temperatures. The choice of refrigerant and of condenser and evaporator temperatures defines the pressures in the generator and absorber. The equil ibr ium concentration in the absorber is then determined by solving the fo l lowing equation, which establishes the equality of the evaporator pressure to the refrigerant vapour pressure in solution. From (11) and (1 2),

p~'a exp I - B ( 1 --xa)n]=pe °

where B= kT~. The equil ibr ium concentration in the generator is

determined similarly. Once x a and x 0 are known, the circulation ratio and the number of moles of refrigerant and absorbent are determined by using (6), (7) and (8). The solution enthalpy at states 2 and 4 is next calculated using (1 8), (1 9), and (10). Equations ( 9 ) - (12) are then employed to calculate the enthalpy of state points 3 and 1. The refrigerant enthalpies (points 5 to 8) are obtained from property tables. With this information, the COP (9) is determined.

Calculat ion for NH3-HzO

To understand the usefulness of (1 2) in characterizing the thermodynamic behaviour of a working pair for an absorption heat pump, the performance of the simple cycle (Fig. 1) is calculated for NH3-H20 in two different ways, In the first, the state points and the COP are calculated conventionally from the tabulated properties of NH3-H20 solutions. 7 In the second, the parameters characterizing this pair are calculated, and the performance is determined using the formulas for binary solutions presented in the previous section.

The fo l lowing temperatures are adopted: generator, TH=400 K; absorber, condenser, TM=320 K; evaporator, TE= 280 K.

The effectiveness of the intermediate recuperator is assumed to be 0.7. The assumption that the refrigerant behaves as a perfect gas (11 ) is not ful ly satisfied at the generator condit ions, but no correction was intro- duced to account for this.

Employing (1 2) at a given concentration and at two different temperatures, the value of the parameter m is given by

In(In 71/In 72) m= (20)

In(TIlT2)

Similarly, applying (12) to two different concentrations at constant temperature, the concentration parameter n is given by

Table 1. State points for simple cycle

Tableau 1. Etats caract~ristiques d'un cycle simple

Property diagram Activity coefficient a

State Refrigerant Enthalpy, Refrigerant Enthalpy, point mass kJ kg -1 mol kJ kg -1

fraction fraction mol -~

1 0.475 227.3 0.498 -27284.0 2 0.317 418.7 0.312 - 6542.0 3 0.317 153.3 0.312 -21478.7 4 0.475 23.3 0.498 -42220.8 5 1 1477.0 1 528.2 6 1 411.7 1 - 537.5 7 1 411.7 1 - 537.5 8 1 1442.1 1 506.0

aB=-2.1, m =-2.7, n=2

Table 2. Values defining cycle performance

Tableau 2. Valeurs d~finissant la performance du cycle

Property Activity Differ- diagram coefficient ence, %

Equilibrium mol fractions

Generator 0.330 0.31 2 5.4 Absorber 0.489 0.498 1.8 Circulation ratio 3.212 2.71 2 1 5.5

Net heat exchanged, kJ kg -~ mol -~

Absorber 31 463.6 29 343.0 6.7 Condenser 18110.2 18110.2 Generator 32 056.7 29 722.0 7.2 Evaporator 17 517.1 1 7 517.1

COP 1.55 1.60 3.2

Heat blance error 0 - 0.018 (A), %

In(In 7111n 72) n= (21)

In[(1 - X l ) / ( 1 - x 2 ) ]

The values of m obtained from (20) at the low and high concentrations (mass fractions 0.31 7 and 0.41 7, Table 1) are - 1 . 2 2 (between 345 and 395 K) and - 4 . 2 7 (between 319 and 369 K), respectively. An average value of - 2 . 7 was adopted. The value of n obtained from (21) at 322 K is 2.1 between the mole fractions 0.31 2 and 0.514, so a value of 2 was adopted. The parameter B was found to be - 2 . 1 from the absorber equil ibr ium condit ions. The molar specific heat of water was adopted as constant and is equal to 75.4 kJ kg- lmol -~, and the reference temperature for enthalpy calculations is 400.7 K.

Table 1 shows the state points corresponding to the cycle as determined from the property diagram and from the activity coefficient. A direct comparison of the values in this table is diff icult because the enthalpies are expressed on different bases and wi th different temperature references. Table 2 shows the values defining the cycle COP for one mole of refrigerant evaporated in the evaporator. These values are inde-

Volume 7 Num6ro 2 Mars 1984 119

pendent of the reference temperature. The value of the COP, calculated via the activity coefficient, is 3% larger than that calculated from the H-x diagram. In spite of the approximations made in characterizing the activity coefficient, the values of COP and of heat exchanged are reasonably close to each other.

Cycle performance for different solutions

To understand how to optimize heat pump performance via different absorbent-refrigerant pairs, the parameters defining the activity coefficient were varied, and the corresponding values of COP and circulation ratio were determined. Calculations were carried out using a desktop programmable HP.41C computer. A program was developed that has as inputs the various parameters, the heats of condensation and evaporation, and the generator and absorber temperatures. The outputs are the heats exchanged in the absorber and in the generator, the cycle COP, the circulation ratio, and the heat balance error. In all cases, this error was less than 0.05%, The recuperator effectiveness was taken to be 0.7.

The influence of the temperature parameter on the

.9

~5 2

Concentrotion parameter n = 2 Temperature parameter m

2

- 4

I I I 2 4 6

Parameter B

Fig. 3 Circulation ratio versus parameter B for activity coeff icients increasing w i th temperature

fig. 3 Taux de circulation en fonction du param#tre B pour des coefficients d'activit~ augrnentant avec la temp#rature

8 E

1.6

1.5

Concentration parometer n = 2 T~-=mture porameter m

_ " ~ .

I I 1 2 4 6

Parameter B

Fig. 4 COP values versus parameter B for activi ty coeff icients increasing w i th temperature

Fig. 4 COP en fonction du param~tre B pour des coefficients d'activit# augmentant avec la temperature

I.E

Concentrat~n parometer n =2

E Temperature parometer m =2

• 1~ 14 - 80

8 • ~ , .3 60 f ,

f o 12 4 0

I.t 20

/

1.0 I I I 0 0 2 4 6

Parameter B

Fig. 5 COP values versus parameter B for activi ty coeff icients decreasing w i th temperature

Fig. 5 COP en fonction du param#tre B pour des coefficients d'activit# diminuant avecla temperature

17

f

c

16

"6

u

'~ Concentration parameter n = 2

o 1.5-- Temperature par(]rneter m =-2

Specific heat ratio

" " ~ 075

i25

1.4 I I I 2 4 6

Parameter B

Fig. 6 Inf luence of the absorbent specific heat on the COP

Fig. 6 Influence de la chaleur massique de I'absorbant sur le CO P

COP was studied first for solutions ranging from ideal (B=0) to strongly negative deviations from the ideal (B=6). A molal specific heat ratio of absorbent to refrigerant of 1.25 was adopted. The concentration parameter was held constant and equal to 2. The circulation ratio versus the parameter B is shown in Fig. 3. As B increases, that is, as the solution becomes increasingly negative deviating, the circulation ratio decreases• As the activity coefficient becomes progressively more temperature dependent, that is, as m decreases, the spread in concentration between the absorber and the generator increases, and the circulation ratio decreases. The values of the circulation ratio are roughly proportional to the pump power requirements. Thus, solutions close to ideal (B=0) have large parasitic power requirements, which decrease for increasing values of B and decreasing values of m. The values of the COP versus the parameter B are shown in Fig. 4. For all values of m, the COP increases as the

1 2 0 International Journal of Refrigeration

solution deviates negatively from Raoult's law until it reaches a maximum; it then decreases for large negative deviations. This decrease is particularly large for a value of m equal to - 4 . This occurs because as the activity coefficient's dependence on temperature increases, the heats of mixing increase, and so does the heat exchanged in the absorber and generator, thus reducing the COP. The problem is compounded by the large spread in concentration between the absorber and generator, which limits the amount of heat that can be recovered in the intermediate recuperator. From this figure, it appears that moderate dependence of the activity coefficient on temperature will optimize the COP. However, it should be noted that the difference between a maximum form of - 4 and one of - 2 is only 6%.

As shown in Fig. 5, the large circulation ratios associated with positive values of m tend to con- siderably decrease the COP.

The influence of the specific heat of the pure absorbent was studied next. The parameters m and n were held at - 2 and 2, respectively. The specific heat of the absorbent determines its pure state enthalpy, employed in (19). Fig. 6 shows that decreasing the ratio of molal specific heats from 1.25 to 0.75 increases the COP by 4.4% for a value of B equal to one. For.a value of B equal to six, this increase is about 1.5%

The sensitivity of the COP and of the circulation ratio to the concentration parameter n is shown in Fig. 7. As the parameter n varies from 2 to 1.1, the COP increases by 1 to 2% for increasing B values, To conform with (19), values ofn smaller than one were not studied. It is thus clear that reducing the value of this parameter has relatively little influence on the COP.

S u m m a r y a n d c o n c l u s i o n s

In this study, the performance of a single-effect absorption heat pump was studied using NH 3 as a refrigerant. The binary working solution was characterized by the refrigerant activity coefficient. The activity coefficient was made dependent on three parameters: B describing how strongly the solution deviates from Raoult's law; m indicating how strongly the activity coefficient depends on the solution temperature; and n indicating how strongly the activity coefficient depends on the concentration.

The following ranges were considered:

0~<B~<6, -4~<m~<2, and2~<n~<l.1

The absorbent specific heat was taken at 1.25 and 0.75 of the refrigerant specific heat at the absorber temperature. For all cases considered where m is less than zero, the COP is small for ideal solutions (B=O), increases with increasing values of B, reaches a maximum somewhere in the range of 1<~B<~3, and decreases for increasing values of B. The maximum of all COP values takes place for a specific heat ratio of 0.75 and for B=1.2, m = - 2 , and n=1.1, whereas the smallest of all maxima takes place for a specific heat ratio of 1.25 and for B=1.2, m = - 4 , and n=2. The difference between the two maxima is 11%. It thus appears that, within the ranges considered, the heat

1.7

~ . " ~ . . . . . . -- ~ "-........... " - - I . I

' ~ " " ~ _ ~ ~ 2 . 0

- " " " ' ~ . ' T - ~ - - - 15 z ' ~ ' ~ . . . . I.I

~.4 I I I -O 2 4 6

Parameter B

Fig. 7 COP values versus parameter B for different dependences of the activity coefficient on concentration

Fig. 7 CO Pen fonction du param~tre B pour diff~ren tes relations de la concentration.-coefficient d'acdvit#

pump performance is not strongly dependent on the actual values of the parameters. For values ofm greater than zero, the COP is limited by the large circulation ratios.

A number of simplifying assumptions, embodied in the calculation, call for caution in interpreting the results. Perhaps the farthest reaching one is the assumption that the solution behaviour may be characterized by an average value of the temperature parameter m. However, as shown in the example developed for NH3- H20, the error associated with this assumption may not be too large. Thus, if the error embodied is neglected, it is clear that solutions that deviate negatively from Raoult's law enhance the heat pump COP. However, the negative deviations (given by the value of B) do not completely define the performance. The grade of dependence of the activity coefficient on solution temperature and concentration is also of importance.

In general, it appears that ideal or very strongly negative deviating solutions, coupled with strong temperature and concentration dependences, are un- desirable. For NH 3 as refrigerant, the following ranges are of interest for COP optimization:

1 < B < 3 , O < m < - 2 , and n~ l

Furthermore, the absorbent specific heat must be as small as possible.

It is significant that the parameters calculated for NH3-H20 solutions fall within or very close to the ranges indicated above. This shows that, from the standpoint of performance, it may be hard to improve on this combination for the simple cycle considered here. Although the following variables have not been considered in this analysis, it is clear that refrigerant vapour pressure and heat of vaporization can signif- icantly influence performance, as shown, for instance, in Ref. 7.

R e f e r e n c e s

Buffington, R. M . Qualitative requirements for absorbent- refrigerant combinations Refrig Eng 57 4 (1949) 343-45 and 384-88

Volume 7 Number 2 March 1984 121

2 Jacob, X., Albright, C. F., Tucker, W. H. Factors affecting the coefficient of performance for absorption air conditioning systems, ASHRAE Trans 75 1 (1969) 103-10

3 Andrews, D. H., Rousseau, R. A. Solution thermodynamics for absorption refrigeration, American Gas Asso- ciation Report, No M 10050

4 Macriss, R. A., Cole, J. T.. Kouo, M. T., Zawacki , T. S. Analysis of advanced conceptual designs for single-family- size, Institute of Gas Technology report to DOE, Contract No. EG-T1 -C-03 (1979)

5 Mansoori, G. A., Patal, V. Thermodynamic basis for the choice of working fluids for solar absorption cooling systems So/Energy 22 (1979) 483-91

6 Hodgett, D. L. Absorption heat pumps and working pair developments in Europe since 1979, presented at the In- ternational workshop on absorption fluids R and D needs. Berlin (1982)

7 ledema, P. D. Mixtures for the absorption heat pump Int J Refrig 5 5 (1982) 262-73

8 Denbigh, K. The principles of chemical equilibrium, Cam.- bridge University Press, Cambridge (1971)

9 ASHRAE handbook and product director, 1981 fundamen- tals, American Society of Heating, Refrigerating, and Air- Conditioning Engineers, Atlanta (1981)

10 Hildebrand, J. H., Scott, R. L. The solubility of nonelec- trolytes, Reinhold Publishing Corp, New York (1950)

Corrigenda

D i t c h e v , S., Popov , V. Heat and mass exchange during freezing of meat prepacks in a dynamic disperse medium. Vol 6 no 4 (July 1983) 209-210.

Equation (1) should read

In N u = 1 8 .80+ In Re °.°77- In A r 135

B o g r o w , A. Les groupes fr igori f iques pour le transport routier ~ Iongue distance. Historique et evolut ion. Vol 6 no 4 (July 1983) 225-230.

Some figures in this paper were printed wi th the wrong caption.

Figure number given in original paper

1 3 3 6 4 1 6 9 7 11 8 4 9 8

11 7

Correct number

122 Revue Internationale du Froid

Documents

Absorption heat pump performance for different types of solutions