SECTION 2

First Law and Second Law Analysis of an Absorption Refrigeration System

Although the analysis of the reversible cycle by means of the reversed Carnot relation is useful for determining the limit- ing conditions, we shall now consider a more detailed analysis of a real cycle with irreversibilities. In this section the analysis consists of mass and energy balances around the various components as well as around the whole system.

A schematic diagram of an absorption refrigeration system is shown in Fig. 5(6) A binary mixture with appropriate properties (for example, NE - H,0, H,So, - #30) is vaporized in the gener- ator by the addition of a quantity of heat a, at the generator pressure Pue As a result vapor refrigerant, for example, ammonia, is produced. Let x = 0 denote pure absorbent and x = 1 denote pure refrigerant concentration. The pressure Py is chosen so that the entire refrigerant vapor can be liquefied in the con- denser. For the fluid flow through the expansion valve, the condensate is throttled to the lower pressure Pe and the satu- ration temperature falls. In this way the liquid can evaporate at a lower vaporization temperature, Ty with the addition of the

heat quantity Q (the so-called refrigeration capacity).

The cool refrigerant vapor (3)* coming from the evaporator

• Specified nunabers in parentheses, ( ), refer to the corre-

sponding sections which is labeled in Fig. 5.

Rectifier |

7is) G0);

Generator

solulons "

Weal

Condenser Qu, 2)

15

solution

exchanger

Absorber

t,

Fig.5. Typical

aosorpiio

Te Latiineeation exit remigerdion § sysicim

, 16

is sent into the absorber where it is absorbed by the cool solu-

tion with the removal of an amount of heat Q,- The refrigeration process of the absorption system is based on the fact that a cold vapor can be absorbed by a warm liquid solution.

The weak solution of composition, Xy Comes from the gener- ator, passes through the heat exchanger, is throttled in the solution’ valve to the absorber pressure, Poe and passes into the absorber. The cold vapor of state (3) is induced, and this is absorbed by the weak soliton thereby becoming a strong solu- tion. The absorption of vapor produces heat. In order to main- tain the absorber at a sufficiently low temperature, cooling water is circulated through coils in the absorber. The enriched cold solution is pumped to the higher generating pressure, Puy warmed through the heat exchanger, and is again vaproized in the generator. The rectifier provides the final drying effect by cooling and delivering pure refrigerant vapor to the condenser. The drip from the rectifier is returned to the generator. In

this way the total cycle continuously works without interruption.

(6) (7)

2.1. Mass Balance In steady-state operating conditions, the quantities of mass eipplied to and removed from each apparatus mcee be equal. This refers both to the total quantity of the mixture as well as to a simple constituent. For the purpose of finding the rate of flow of pure refrig- erant to the condenser, let M,, where n= 1, 2, 2a, 3, 4, 4a, 5,

eee, 10, denote the mass of fluid that crosses the various

17

sections indicated on Fig. 5. Hence, at the absorber, the refrigerant mass balance is 2 Me, =) M. 1 Mexs = MNS SIE + Mae a) in which X= Xs = X= Xo denotes the weight concentrations of

the strong liquid solution, and

% = %y = *ya = *B = *1or denotes weight concentration of the weak solution. For each pound of refrigerant absorbed from the evaporator, the amount of refrigerant circulated in terms of the weight con-

centrations of strong solution (x,) and of weak solution (x,,) is

(1b, /1b,, of 4) (2)

This means that for each pound of the refrigerant vapor produced, the specific solution quantity G must be pumped from the absorber through the heat exchanger to the generator.

The quantity of weak solution that flows back to the absorb-=

er is

xX. = gc (1b,/1b, of Ms) (3)

From equations (2) and (3) we can see that the anavierte degassing breadth, X, 7 Xye the larger must be the specific solu- tion circulated; nevertheless, this is still restricted by the chemical composition of the refrigerant absorbent solution.

Further

My = My = My, = My (4)

18

No = Mg = Mp = Mg +l (4)

In assuming the fluid flows steadily, the amounts of material stored in the generator and the rectifier do not change with time. For the refrigerant flow in the generator,

Xpily = Xgllg + 1 (5) Substituting the assumed values for Xo and Xge or X and xy into (5) we can get the values of My and Mg.

To find the amount of vapor leaving the generator and the amount of condensate returning to it, we equate the quantities flowing into and out of the rectifier; we have

M +1 (6)

ge Mao For the refrigerant alone, we have Xgllg = Xoo + 2 (7)

where X19: 28 has been shown above, is identical with Xge The concentration Xge on the other hand, is that for the refrigerant and absorbent in the vapor phase which is in equilibrium with the weak solution (liquid phase) at the pressure and temperature existing in the generator. To find the maximum values of Xo and Xo: We can refer to tables and charts which give the maximum concentrations of the refrigerant and absorbent, for both the vapor and liquid phases, as functions of the pressure and tem-

perature.

2.2, Energy Balance! 5) + (6)

For any piece of apparatus, the energy equation for steady

flow, neglecting the change in kinetic energy and potential

energy terms, is

E = 2£(Mh) - £(Mh) 5, (8)

out where E denotes the work input for the pump or heat transfer for all other pieces of equipments, Z(Mh) gas denotes the enthalpy of all the fluids that flow out while 2(Mh) 4 denotes the enthalpy for all the fluids that flow in, based on unit mass of the re-

frigerant flowing through the evaporator.

(1) Heat Exchanger Neglecting heat transfer with the surroundings, the equation is Moho + Mh) - Nghe - Nghg = 0 (9) (2) Generator In the generator, the energy input of the strong solu- tion is Moho. the energy supplied by the drips from the rectifier is My QMyo° the energy leaving with the weak solu- tion, as it flows into the heat exchanger, is Mghg, and the energy leaving with the vapor as it flows to the rectifier is Mghtge Hence the energy balance is E = Qe = Mghg + Moho - Mohy - Mi ohy (10) where Qe denotes the amount of heat supplied to the gener-

ator per unit mass of refrigerant passing through the

evaporator.

(3)

(4)

20

Similarly, for the rectifier, the condenser, the evaporator and the absorber, we can get the simplified energy equations

according to equation (8) as follows:

Q, = hy + Myghyg - Nghg (11) Q, = hy - hy (12) Qe = hy - fgg (13) Q, = Mghs - Myahy, - hy (14)

where Qn Q and 25 represent the amount of net heat

cc? Qe transfer in the rectifier, the condenser, the evaporator and

the absorber, respectively.

Pump Work This can be calculated approximately by the usual equation for ideal pump work

fs 144 G Vo(Py - Py) Pp” 778 in which Q denotes the ideal pump work input in BTU per

(15)

pound of refrigerant vapor which circulates through the evaporator; Py and Py denote the generator and the evapo- rator pressure in pounds per square inch absolute, respect- ively; Ve denotes the specific volume in cubic feet per pound of strong solution as it enters the pump from the absorber,

Or, by equation (8)

%® ‘= Mghg - Mehe = Mg(hg - he) (16)

(5)

(6)

2.3.

(1)

218

Overall Heat Balance

For a heat balance, all energies supplied to and re- aor from the whole system are identical. Suwnmarizing the above energy equations, we have

Qt 0,4 O40, 49,42, = 0 (17)

Steam Consumption

A commercial ton of refrigeration is equal to the ab- sorption of heat in the evaporator at the rate of 288,000 BTU per day or 12,000 BTU per hour. The value of 12,000 BIU per hour is based on the heat required to melt one ton of ice in one day or 144 x -— = 12,000 BLU/nour, where 144 BTU is the latent heat of fusion of ice at atmospheric pres- sure. Thus the steam consumption in the generator per ton

per hour is

Q = z ~~ 000 (18) e fg

where he, is the latent heat of the heating medium (such as

steam) at the temperature of the heating coil. Second Law Analysis of An Absorption Refrigeration System

Introduction

The Second Law of thermodynamics states that no process can be devised whose sole result is the absorption of heat from a reservoir (source) of one temperature and transfer of

this heat to a reservoir of higher temperature; or by itself

(2)

22

heat can not flow, by any means, uphill. In accordance with this stateaent, for the purpose of the transfer of a certain amount of heat from a cold storage temperature to the sur- rounding temperature, there must exist a process which can cause this heat transfer; however, the Second Law of thermo- dynamics has not restricted the kinds of necessary compen- sating process, Therefore, the process may be selected as mechanical work of compression, or by thermal energy input combined with fluids that have suitable properties. The absorption refrigeration system is considered to be a successful system in utilizing the combination of the re- corded methods,

Furthermore, there are a number of additional ways by which it might be possible to effect varying degrees of im- provement in the performance of an absorption refrigeration system. To discuss all such methods in detail is beyond the scope of this report. Before we consider the problem to im- prove the performance of an absorption refrigeration system we have to have a concept of determining the minimum heat expenditure required to attain a desired cooling capacity.

In this section, entropy change for each process, performance ratio, concepts of availability and irreversi-

bility are involved.

Entropy Changes No cycle is more efficient than a completely revers-

ible cycle. If each process of a cycle undergoes a revers-

23

ible process, and all other systems associated with the eycle undergo reversible process, the total change of en- tropy of the universe is zero. Nevertheless, if any process of a cycle undergoes an irreversible process, the entropy of the universe must be increased due to the entropy creation during this process. This also means that the amount of entropy change due to the irreversibility is the direct measurement of the resulting loss on efficiency due to the irreversible process.

Since entropy is a state property, the entropy change of any process, regardless of the reversibility or irre- versibility of the process, can be evaluated by the integral

of = along any reversible path, or by the equational form

II Sr = Sp = f (Prey (19)

in which subscripts I and II denote initial and final state of a process, respectively.

For a cyclic analysis, the end state being the same as the initial state, fas = 0.

Furthermore, by the Clausius inequality a <0 (20)

where the equal sign indicates the limiting or reversible cycle, while §2 <0 holds for any cycle which is composed of irreversible processes.

The general form of the entropy balance equations, for

any process, can be expressed by

24

2g

createa * / T (21)

ry +5 [Sout +48

stored in which qsin and Sout are entropy fluxes due to the fluid flow, and T is the temperature of the fluid which emits the heat which is transferred.

In the following discussions, in which the system is in steady state condition, the last term of the above equation is zero. Further, in an analysis of an absorption refrige- ration system, as has been shown diagramatically on Fig. 5, we shall consider the surroundings, or atmosphere, as the cooling water that flows to the condenser. The temperature of this cooling water (or atmosphere) is designated as To. The temperature of the steam supplying heat to the generator and the refrigerated space are each assumed to be constant and are designated as T, and Ty respectively.

Further, in an analysis of a practical problem, a finite temperature difference must exist in each heating or cooling process, so that the heat can be transferred. Nevertheless, if we assume that in the absorber there is a great amount of cooling water which circulates through the absorber, the temperature of the absorber can be taken as the cooling water inlet temperature instead of taking the average temperature of the cooling water in the absorber. This will be done also for the condenser and for the recti- fier. The total heat flow to the surrounding, or cooling

water at temperature Tt) is composed of the heat transferred

from the absorber (Q,)5 that transferred from the condenser

25

(Q.), and the rest from the rectifier (Q,)+ Consequently, the total amount of entropy increase of the cooling water is

Bo ¥ 9. 468 2 c x Sasoer = 7 T) (22)

Equations of entropy balances for these three process- es, according to the equation US reaved = BS out = 28 an = di a under steady state conditions, are, for each pound of

refrigerant condensed,

dQ, Screated,a = (1,8. = My yee 83) ef T) (23) 2%, fh Soreated,c = (sp ~ S)) wd TS (24) 42, Sereatea,r = ($1 + “yoSi9 ~ MoS) - J ae (25)

Soreated,a represents the amount of entropy creation due to the mixing of fluids of different temperatures in the absorber. In the condenser, if the pressure drops due to fluid friction, and a finite temperature difference is con- sidered to exist between the condensing refrigerant and the

cooling water, the total amount of entropy creation due to

these two irreversibilities is

5 = created,c ~ f.c

(26)

u

> a + Fe 1 is ee

where subscripts f and aT, denote the friction and the

finite temperature difference, (Te - Ty), in the condenser,

26

respectively. This method of analysis is still available for other apparatus, such as the evaporator, the generator, or the absorber, if the finite temperature differences are not neglected. In the evaporator, in the present analysis, we still assume that the amount of heat received by the refrigerant in the evaporating coil is transferred from a large reservoir at the saturation temperature of the refrig- erant in the evaporator so that the finite temperature dif- ference is neglected. The amount of entropy flow from the refrigerated space to the evaporating refrigerant is f “ e

Hence the equation of entropy balance for the evaporating

process becomes

dQ, Soreated,e (Sp, 1d 82) of a ew (27) Similarly, for the generating process, m Soreated,g = (MgSg + MgSg - MoS - My 95y9) -f T (28)

The pumping process is considered here to be an isentropic process, i.e.

s 0 (29)

created,p For the heat exchanger, the solution valve, and the expansion valve, we assume that there are no heat transfers to or from surroundings, i.e. Qax = Qos = Qre = 0. Hence, the equations of entropy balances for these three apparatus

are

27

Screated, ex. = Ng(So ~ 86) + My (Sy Sg) (30)

Screated, vs. = My(Sy, - Sy) (31)

s

Screated,ve. = 52a ~ 52 (32)

The Clausius inequality for the non-ideal cycle is

3 e a a [cj

and for each process

S17 - Sy 2 a co) (34) Further,

*S universe ES. reated

= 4S.tmosphere ~ (3, + 8,) (35) in which 45. smosphere = 5.15, fh Soreated,s a Soreated,a 0 Soreated,o +S Ss +S

created,r - created,e created,ex

+S +S (36)

created,vs created,ve

(3) Performance Ratio”

The amount of work and/or heat required to move a certain quantity of heat from the cold storage room is an important factor in the analysis of an refrigeration system. In a compression refrigeration system, this factor is ex-

pressed by "coefficient of performance"; however, in an

• Some authors use "heat ratio" as an exchangeable term.

28

absorption refrigeration system the total energy input is the sum of the mechanical work which is done by the solution pump and the thermal energy which is supplied from the heat source temperature, Ty Therefore, before considering the performance ratio, we have to consider, with the aid of the Second Law, how much equivalent quantity of heat is con- sidered to be supplied from the heat source temperature, Tye corresponding to the actual pump work input. This equiva-

lent amount of heat may be expressed by the relation

ey oe. Sop = a=, a (37) From equations (17) and (33), we have Q Q 2,4 + 2 +2 < 42 = (38) ae Ty To

Substituting equation (17) into (38), and after rearranging, we get oy Tet tr

: ie) e £ a+ po te . (39) & qT, - To ‘p Ie qT - Th

The performance ratio, $ , of an absorption refrige- ration system is definea‘?0) as

Be Se

€ (40)

a Qe + Qo ey, 6 T, -T, “P

In. this section the subscripts q and k denote absorption

refrigeration systems and compression refrigeration systems,

respectively.