ELSEVIER 0140-7007(95)00065-8

Int J. Refrig. Vol. 19, No. 1, pp. 19-24, 1996 Copyright ~ 1996 Elsevier Science Ltd and IIR

Printed in Great Britain. All rights reserved 0140-7007/96/$15.00 + .00

Evaluation of absorption cycles with respect to COP and economics

F. S u m m e r e r Techn i sche Universit~it MiJnchen, Phys ik D e p a r t m e n t , Ins t i tu t E l 9 ,

J am es -F ranck -S t r a l3e 1, 85748 G a r c h i n g , G e r m a n y Received I February 1995; revised 14 August 1995

The calculation of the performance of absorption heat pump cycles or the comparison of different types of machine cannot be done in a reasonable way without considering the first cost of the machine and especially the cost of the heat exchangers, as their area and particularly the distribution of the area between the respective components of the heat pump determine the COP. Therefore it makes sense only to compare machines that are optimized in this respect. A good way to evaluate cycles is to calculate the maximum COP in terms of the total cost of the heat exchangers. For that purpose a computer program was developed for different absorption heat pump cycles with water as refrigerant. The calculation method is simple and thus the result reliable. The program is suitable for evaluating double-lift, single-, double- and some triple-effect cycles, each one with different absorption fluids and with different options, such as different solution flows (parallel, serial), different types of absorber (spray- or falling-film absorber), and different types of generator (pool- or falling-film generator). With this instrument different cycles or similar cycles with different features can be compared. An economically significant estimation of the performance of a cycle working under defined conditions is possible. (Keywords: absorption cycles; performance; economy; evaluation; computer program)

Evaluation des cycles a assorption, en fonction du COP et du cout des equipements

Sans tenir compte, d'emblOe, du co~t de la mach&e frigorifique, et notamment celui des Ochangeurs de chaleur, il n 'est possible ni defaire un calcul correct de la performance des cycles d'absorption des pompes h chaleur, ni de comparer diff~rents types de machines. En effet, le COP est d~terminO surtout en fonction de la surface de ces Ochangeurs, et particulibrement de la r~partition de ces surfaces entre les different composants de la pompe h chaleur. II convient done de comparer seulement les machines qui sont optimis~es gt cet ~gard. Un bon moyen d'~valuation des cycles consiste h calculer le COP maximum, en Jonction de sa d~pendance vis-h-vis du co~t total des ~changeurs de chaleur. Pour ce faire, on a mis au point un programme informatique pour les diff~rents cycles d'absorption des pompes h chaleur fonctionnant avec de l'eau comme frigorigbne. La m~thode de calcul est simple et le r~sultat est donc fiable. Le programme convient it I'~valuation des cycles h effet simple, double et triple, chacun ayant diff~rents fluides d'absorption et diff~rentes options en ce qui concerne, par exemple, I'~coulement de solution (en parallble ou en s~rie), le type d'absorbeur (pulv~risation ou h film tombant ) et les types de gOnkrateur (h Obullition libre ou gt film tombant). Ce programme permet de comparer diff~rents cycles ou bien des cycles semblables ayant diffOrents caract~ristiques. I1 est possible de faire une ~valuation ~conomique de la performance d'un cycle fonctionnant sous des conditions bien dOfinies. (Mots-cl6s: cycles d'absorption; performance; 6conomie: 6valuation; programme informatique)

Before planning and building a new absorption heat pump the designer wants to assess both the performance the cost of the machine. For that purpose he either has to write his own computer program for each new cycle and change in this cycle, or he has to be satisfied with rough estimations. In fact there are methods to estimate quickly but only approximately the COP of any kind of possible absorption cycle r . Bes ides their low accuracy these estimations also do not take into account any economic aspects.

More accurate evaluations can be done with a computer program 2, commercially available, which allows the calculation of all types of cycle without individual programming. However, the program does

not satisfy all needs for evaluating the performance of a cycle, because the design, i.e. the distribution of the area of the heat exchangers between the different components of the machine, is part of the input data and not the consequence of an optimization procedure of the calculation. In other words, the program delivers some information about one special design of a machine, but in order to get information about possible improvements the program has to be run several times.

In this paper a calculation routine will be presented that overcomes this limitation, leading to the opt imum design of the machine under consideration with the maximum achievable COP in terms of the heat exchanger cost. Technical restrictions such as minimum or maximum

19

20 F. Summerer

Nomenclature

C Total cost Cfix Cost of a machine (independent of heat

exchanger area) Chx Cost dependent on heat exchanger area COP Coefficient of performance

f

TK Xweak r/SHX

Specific solution flowrate Evaporation temperature Condensing temperature Concentration of the weak solution Efficiency of the solution heat exchanger

flowrates can be taken into account. For simplification, the examples presented in this paper are calculated only with heat exchanger area instead of heat exchanger cost: so, more general conclusions can be drawn.

Evaluation principles

When a new machine, i.e. a new cycle or a known cycle under different conditions (temperatures, working fluids etc.), is designed, both the COP and the first cost of the machine have to be estimated. The first cost of an absorption machine results from tubing, pumps, control units, heat exchangers and so on. The COP is determined in particular by the size of the heat exchangers. Therefore their costs Chx, depend strongly on the desired COP, whereas the cost, Cfix, of the rest of the machine is more or less independent of the COP. Thus the total cost C of an absorption machine can be expressed as follows:

C -- Chx(COP) + C~x (1)

Though the cost Cfix can also influence the COP (for example, a more expensive control unit could improve the COP), subsequently only the dependence on the heat exchangers will be considered.

The dependence of the cost of heat exchangers on the COP or vice versa is not a unique function. For a given total cost or area of the heat exchangers, different COPs can be obtained according to the distribution of the total area or cost between the different components of the heat pump. For example, it is most likely that doubling the heat exchanger area of the generator will not improve the cycle significantly, whereas doubling the solution heat exchanger will. Of course, the designer is interested only in the machine with the maximum COP for given cost. Therefore, a useful method for a cycle calculation should result in the curve shown schematically in Figure 1: it represents the maximum COP of the considered cycle for a given heat exchanger area. The curve starts from a minimum cost; it is not possible to build a machine with

n o 0 X X

X X

X X

total cost of heat exchangers per kW cooling capacity [$/kW]

Figure 1 Schematic result of a cycle evaluation

Figure 1 R6sulat sch6matique d'une ~valuation de cycle

less cost than this, depending on the design and the required capacity, of course. As this capacity probably will not be zero, the respective COP at this point can also not be zero: a COP of zero could only be achieved with an infinite driving power and thus with an infinite area of the generator (as will be discussed later). The COP rises with increasing money spent and finally reaches the highest possible value for infinite cost or area respectively. Below this curve there is numerous machines with the same cost and lower COP (as indicated by the crosses), which result from the above-mentioned indefinitions of the relation between cost and COP. These machines are not optimized and therefore useless, and should be discarded in the calculation.

In order to obtain comparable results, all the machines represented by the curve have to be calculated under the same external conditions: this means heat vector temperatures and cooling capacity. These values are therefore input data of the program presented in this paper. Other input data are heat transfer coefficients and specific cost of heat exchangers, yet these must not necessarily stay constant during the calculation (but they do in this program)•

Calculation method

One way to obtain a curve like that shown in Figure 1 is to calculate a certain cycle for a given cost of heat exchangers and to optimize the distribution of the area of the heat exchangers. Then it is necessary to repeat this procedure until sufficient pairs of COP and cost are available to draw the curve• The calculation of a machine for a given area or cost of heat exchangers requires iterations and is time consuming. It needs even more time to optimize such a machine because the calculation is rather complicated. There is a method 3 to estimate this

1 0

0 9

.-~ 0.8 o o 13- o 07 (.3

0 .6

0 .5

Figure 2 Figure 2 simple

[,

i .

'i

J : i ! : ~ i~ " • ~ ] , , •

;

0 005 010 015 020 025 030 035 040

total cost of heat exchangers per kW cooling capacity [$/kW]

Result of many calculations of a single-effect cycle

R6sulats d'un certain nombre de calculs d'un cycle h effet

Evaluation of absorption cycles with respect to COP and economics 21

+i

T E TK

Figure 3 The five constraints of a single-effect cycle Figure 3 Les cinqs contraintes d'un o,cle 5 effet simple

-1/'1"

opt imum distribution reasonably quickly, but it only works when the machine is far away from any technical or physical limits. It fails as soon as the process is near to crystallization limits, or operates with small driving temperatures. Moreover, this method is inexact, as it does not take into account all relevant parameters. In particular, the specific solution flowrate, which influ- ences both COP and heat exchanger area strongly, is not taken into consideration.

Another way to achieve results is a simple one. The COP of a cycle can be calculated with internal parameters exclusively. This means that the calculation does not consider external temperatures or areas of heat exchangers but only the parameters of the working fluid (temperatures, concentrations, and mass flows of water and absorbent). This thermodynamic calculation is very fast, because no long iterations are necessary. Then from the fixed external temperatures and heat transfer coefficients the area and the cost of each heat exchanger follow as a result (instead of a constraint). Of course, such a machine is not optimized, but if many such machines with different internal parameters are calculated it becomes more and more likely that the one with the highest possible COP for a certain cost has been hit; at least the best machine calculated is surely infinitely close to the optimum. Figure 2 shows schematically how the result of such calculations would look for a single-effect H 2 0 - L i B r chiller.

I f the points of best results are connected a curve results, as shown in Figure 1. The smoothness of this curve depends on the total amount of calculated machines and thus on the calculation time. Though there is not visible advantage in respect of calculation time as compared with the first method this simple method is very reliable because all free parameters are taken into account in the calculation.

085

O8

075

© (.3 07

0 65

0 6

i '_iiii!

015 020 025 0.30 035 040 045 050

total area of heat exchangers per kW cooling capacity [m~/kW}

Figure 4 Four different evaluations of the same single-effect cycle

Figure 4 Quatre ~valuations d!ff~rentes du mdme cycle h effet simph"

The concept

A computer program following the second method has been developed, at first for a single-effect H 2 0 - L i B r machine. Input data are all external temperatures, heat transfer coefficients for all components (fixed values), step sizes of the parameters and an exact cycle specifica- tion (absorber, generator type etc.). Moreover, specific cost (price/area) for each component can be entered in order to take into account that heat exchanger prices may be different for different components.

As independent parameters or constraints the follow- ing internal variable were chosen (Figure 3 ):

1. evaporation temperature, irE; 2. concentration of the weak solution, Xwe~G 3. condensing temperature, TK; 4. specific solution flowrate, f ; 5. efficiency of the solution heat exchanger, rlsHx.

If additionally one power, for example the cooling capacity, is given, the machine is completely defined by these five parameters. This means that all the other internal parameters, such as temperatures, concentrations and flowrates, result from the properties of the working fluid. An enthalpy balance with these quantities leads to the COP of the machine, and with the help of the given external temperatures and heat transfer coefficients the areas and the cost of the heat exchangers can be determined.

Numerous machines can be calculated by varying these five parameters independently of each other in definite steps within given limits of temperature, concentration, flowrate and efficiency of heat exchangers. The result of each single calculation is inter alia a COP and the total cost of the heat exchangers.

Table 1 Step sizes, number of calculated machines and calculation time of the four cycle evaluations Tableau 1 Ecarts, nombre de machines faisant objet du calcul et temps de calcul des quatre dvaluations de o, cles

A ire AT K AXweak A.f AT] SNX Numbers Time (K) (K) (%) (%)

Curve 1 3 3 2 3 5 3 t68 1.2s Curve 2 2 2 2 2 3 9 478 3.6 s Curve 3 1 l 1 1 2 200 319 77 s Curve 4 0.5 0.5 0.5 1 1 10 556 106 67 rain

22 F. Summerer

Table 2 Values of serial and parallel double-effect machine at one defined heat exchanger area per kW cooling capacity

Tableau 2 Valeurs obtenues avec une machine h double effet avec Ocoulement de la solution en s&ie et en parallble, pour une surface donnOe d'&'t angeur de chaleur, par k W de capacitO frigorifique

Constraints for both machines External temperatures (°C): Heat transfer coefficients (kW m -2 K-J )

Chilled water in 12.2 Evaporator 4 (overall) Chilled water out 6.67 Absorber 2.1 (overall) Cooling water in 29.4 Condenser I 3.7 (overall) Cooling water out 35 Condenser 2 10 (one side) Driving 300 Generator 1 3 (one side) (direct fired) Generator 2 2,3 (overall)

SHX 1 1.3 (overall) SHX 2 1.4 (overall)

Result for total specific area o f 0.215 m e per k W cooling capacity (calculated with McNeely data)

Internal temperatures (°C): Evaporator Absorber inlet (from solution heat exch.) Absorber max. (equilibrium strong solution) Absorber outlet (equilibrium weak solution) Condenser 1 a (condensing temperature) Generator 1 a inlet (from solution heat exch.) Generator I a min (equilibrium weak solution) Generator 1" outlet Condenser 2 b (condensing temperature) Generator 2 b inlet (from solution heat exch.) Generator 2 b min (equilibrium) Generator 2 b out (equilibrium)

Power (kW): Evaporator (= cooling capacity) Absorber Condenser I a Generator I a Condenser 2 b Generator 2 b

Concentrations (wt%): Strong solution After generator 2 b (serial flow) Weak solution Specific solution flowrate (fix)

Heat exchanger areas (m2): Evaporator Absorber Condenser I a Condenser 2b/generator la Generator 2 b Solution heat exchanger 1 (low temp.) Solution heat exchanger 2 (high temp.)

total:

COP (cooling)

Serial flow Parallel flow

3.00 4.00 41.28 40.38 44.57 44.36 35.95 35.88 41.00 39.00 86.44 71.19 84.59 75.95 89.29 85.35 97.29 92.35

136.79 132.63 144.19 137.03 149.97 147.85

1.000 1.000 1.215 1.196 0.537 0.515 0.553 0.568 O.553 0.568 0.752 0.711

61.31 60.63 59,25 56.93 56.29 14.00 14.00

0.042 0.05 l 0.066 0.067 0.021 0.029 0.024 0.022 0.002 0.002 0.048 0.049 0.O47 O.O3O 0.250 0.250

1.330 1.406

a Intermediate pressure; b high pressure

0 8 5

0.8 .

0 7 5

~ o~

0 .65 IX_ o tO 0 . 6

055 J

( ~-~ 01.20 I - - - - ~ -- ~ . . . . . ~ - - - 4 ~ -

0 .15 0 2 5 0 .30 0 3 5 0 .40 0 4 5 0 5 0

total area of heat exchangers per kW cooling capacity [m2/kW]

Figure 5 Complete results of a single-effect cycle

Figure 5 R~sultat compl~t de l'dvaluation d'une machine ~ effet simple

1 6

1.5

_~ 1.4

o 13 cl o o 12

1 1

1.0

values of table 2

Figure 6 Figure 6

015 0.20 0.25 0.3o 035 0 40

total area of heat exchangers per kW cooling capacity [m2/kW]

Comparison of two double-effect cycles

Comparaison de deux cycles h double effet

Evaluation of absorption cycles with respect to COP and economics 23

1.0

O 0

0.9

0.8

07 02 03 0.4 0.5 06

total a r e a of heat exchangers per kW cooling capacity [m2/kW]

Figure 7 Compar ison of two single-effect machines with different chilled water temperatures

Figure 7 Comparaison de deux machines Z1 effet simple ~ diff~rentes tempOratures d'eau refroidie

As will be shown later, thousands of machines have to be calculated. Therefore it is not reasonable or even possible to store all the data for COP and cost of heat exchangers. Instead, the decision as to which data are stored and which are abandoned is made after each single calculation. To do this, the program subdivides an estimated range of COP, for example from COP = 0.3 to COP = 0.8, into 50 cells at the beginning, the first cell running from 0.3 to 0.301, the second from 0.301 to 0.302 and so on. After each calculation the resulting COP is assigned to the corresponding COP cell. For every cell one value of cost is stored. The result of each subsequent calculation is compared with the stored one. If the cost is higher the result is skipped; if it is lower the new value replaces the old one. Thus at the end of a calculation run, out of a great number of calculated machines, the 50 best ones with their COP, cost and the five constraints that lead to the result, are retained.

Of course it would also be possible to divide the cost into cells and then to calculate the highest COP for each cell. However, it is much easier to estimate the range of COP than that of cost at the beginning of the calculation.

At first sight this method seems to need too long a processing time. However, the use of internal parameters only, which avoids complicated iteration processes, leads to a fairly fast calculation. The program, written in Turbo Pascal calculates, for example, about 1000 single- effect machines per second on a 66 MHz 486 processor and about 2600 on a 90 MHz pentium processor.

The number of machines that have to be calculated to obtain good results for one cycle evaluation is found empirically. This is shown in Figure 4 for a single-effect H 2 0 - L i B r chiller. Each of the four evaluations was performed under exactly the same input conditions except the step sizes. Specific prices were set equal to 1, so that the total cost of each heat exchangers is identical to the area. The four curves were obtained with different step sizes and thus with different numbers of calculated machines and consequently different calculation times. Table 1 shows the steps in which the five parameters were varied, the number of calculated machines and the calculation time on a 90 MHz pentium processor. TE, TK and Xweak were varied within the given limits of external temperatures , f from 7 to 15 and ~/SHX from 50% to 90%.

It can be seen from curve 2 that already with large steps

2.0

8 1.5

P, 0 0

ranges ,

~'~.., coP,.,

0.5

~ ffect

. . . . single effect

0 15 0.20 0.25 030 0.35

total a r e a of heat exchangers per kW cooling capacity [m2/kW]

Figure 8 Region of realistic COP

Figure 8. Fourchette r(aliste du COP

good results can be achieved within a short calculation time. There is only a small improvement from curve 2 to curve 3. The difference between curve 3 and 4 is hardly visible and surely smaller than the uncertainty in any economical assumptions.

Note that all the calculations are performed at present without considering any losses of energy or any pressure drops. Real machines would probably have a somewhat lower COP.

Another interesting fact is that none of the curves really starts vertically at a minimum COP: rather, the complete results of an evaluation leads to a curve as shown in Figure 5 (in Figure 4 the lower branch was suppressed).

At first sight the lower branch in Figure 5 seems to be unreasonable: The COP becomes lower and lower with increasing area of heat exchangers and approximates a non-zero value. This can be explained as follows. The minimum area of heat exchangers at the left-hand side of Figure 5 is achieved with the smallest solution heat exchanger and the highest specific solution flowrate. (Normally, to reach this minimum the solution heat exchanger is omitted completely; in this case it has an efficiency of 50% because this was fixed as a constraint. The specific solution flowrate is at its maximum value of 15.) From this starting point with a definite non-zero COP the latter can decrease only if the losses due to a poor or even missing exchange of the heat in the solution circuit increase. This is the case if the temperatures of the condenser and the generator increase until the maximum generator temperature is reached, which is the external temperature. As the driving temperature difference approaches zero at this point, the area of the generator becomes infinitely large and the COP minimal but not zero because the solution flowrate stays finite.

Of course, this lower branch of the curve is only of academic interest, and it will be omitted in the following.

First tests with this simple calculation method were so promising that it was obvious to apply it to multistage cycles. However, multistage cycles are more complicated, and defined by a higher number of independent para- meters, which have to be varied. Hence the required calculation time for getting a really straight curve, e.g. for double-effect cycles, is some hours and for triple-effect cycles even some days. However, satisfactory results can be obtained within some minutes or within an hour.

24 F. Summerer

Examples

Though the program, called ABSOCALC, was created to calculate with heat exchanger cost the following examples have been performed only with heat exchanger area (specific prices were set to 1). At present ABSOCALC can evaluate single-effect, double-effect, double-lift and three different triple-effect cycles with water as refrigerant. Data for the absorption fluids LiBr, binary hydroxides and ternary hydroxides from different sources are included, but an extension to other absorbents such as acids is easily possible. For all cycles, several options, such as spray or circulation absorber, pool or falling film, steam-driven, water-driven or direct-fired generator, can be used. So it is even possible to compare different options of the same cycle. Figure 6, for example, shows a comparison of two double-effect H20-LiBr machines.

Again, as previously and in all further calculations, specific prices were set equal to 1 and the cooling capacity to 1 kW: that is, the x-axis represents the total area of heat exchangers per kW of cooling capacity. The specific solution flowrate was kept constant at f = 14, which is a typical value for machines with a falling-film absorber. (Lower solution flowrates would lead to higher COP but probably also to wetting problems in the absorber.)

Both machines operate under exactly the same conditions and restrictions. In the case of the usual serial solution flow the total amount of weak solution is pumped first to the high-temperature and then to the low-temperature generator. In the case of parallel solution flow only a part of the weak solution is pumped to the high-temperature generator; another part is separated and pumped to the low-temperature generator. The result shows that the parallel version has the higher potential COP. This is easy to understand, because the serial machine has to exchange much more heat in the high-temperature solution heat exchanger. This can be seen in Table 2, where for both machines all data are listed for the marked point in Figure 6 (total area of heat exchangers per kW cooling capacity = 0.25m 2 kW l). The high-temperature solution heat exchanger of the machine with serial flow requires 0.047 m 2 kW -1 whereas the same component of the machine with parallel flow needs only 0.03 m 2 kW-1. The remaining

2 1 0.017m k W - a r e mainly distributed between the 2 1 evaporator (+0.009 m kW- ) and condenser 1

2 1 (+0.008 m kW- ), which increases the COP. However, this result alone cannot be the base of an

economical decision between the two machines, because the control facilities and their cost are different (Cflx in Equation (1)). Moreover, the difference between both types of machine will be much smaller if the specific solution flowrate (which was kept constant at 14) is lowered. However, this problem will not be discussed in this paper.

In the same way it is of course possible to evaluate one cycle with different working fluids or for different temperature conditions. Figure 7, for example, shows the result of two single-effect HzO-LiBr chillers driven by the heat of district heating plants: that is, the driving temperature is 90°C to 70°C (generator inlet and outlet). Machine 1 operates at standard temperature conditions, i.e. 12°C/6°C chilled water and 27°C/35°C cooling water. The only difference in machine 2 compared with machine

1 is a warmer chilled water of 18°C/16C, still sufficient for ceiling cooling. It is clear that, owing to the lower temperature lift, the COP of machine 2 is somewhat higher and the required area of heat exchangers smaller. This difference can be predicted precisely. If one takes into consideration that in this case the machines are very similar in control, pumps etc., the superiority of machine 2 is significant.

Conclusion

The total area of heat exchangers and therefore their cost can be determined only if heat transfer coefficients are known. One also should keep in mind that the price of a machine is not given by the area of heat exchangers alone. Nevertheless, the method described is a fast and simple way to estimate relative total cost, and it is a very good instrument for comparing similar machines under different conditions (see Figure 6). Moreover, this computer program gives a quick survey over the potential in performance, which is very important if new cycles or new working fluids need to be assessed.

Not only the potential but even realistic values of COP can be predicted, because almost every calculation results in a similar curve: after a steep rise from a minimum area of heat exchangers the COP approximates relatively quickly a maximum value. The measured COP of commercial systems ranges in a relatively small region close to the left end of the curves, as indicated by the hatched areas in Figure 8 for a single-effect and a double- effect H20-LiBr chiller. Therefore one can expect that COP values taken from that region of new calculated curves will also be close to the COP that is obtainable by new cycles under realistic economical conditions. Of course it is also possible to determine one point of the curve to be the optimum in respect of economics. It will be shown in a following paper that in most cases this point can be found at surprisingly high values of COP.

ABSOCALC is a very simple and reliable program to evaluate many different absorption cycles with water as refrigerant. If data for other refrigerants, such as, ammonia, were available in a suitable form, it would be easy to extend it to these fluids (at present for ammonia this method would need too long a processing time). In spite of the uncertainties in calculating the cost of machines the program is a good instrument for guessing what a machine can or cannot do. Its user- friendly structure makes it a valuable tool for designing a machine.

Acknowledgements

Stimulating discussions with Dr Felix Ziegler, Dr Jo V61kl and Professor Georg Alefeld are gratefully acknowledged.

References

1 Ziegler, F., Kahn, R., Summerer, F., Alefeid, G. Multi effect absorption chillers Int J Refrig (1993) 16 (5) 301-311

2 Grossman, G., Wiik, M. Advanced modular simulation of absorption systems Int J Refrig (1994) 17 (4) 231-244

3 Riesch, P. Absorptionswi~rmetransformator mit hohem Tempera- turhub Deutscher K/iRe- und Klimatechnischer Verein e.V. (DKV) (1991)