A contribution to the evaluation of the economic perspectives of absorption chillers

International Journal of Refrigeration 220 (1999) 67±76

A contribution to the evaluation of the economic perspectives of absorption chillers T. Berlitz a,*, P. Satzger a, F. Summerer b,1, F. Ziegler a, G. Alefeld b,² a ZAE Bayern, Walther-Meiûner-Str. 6, D-85748 Garching, Germany Technische UniversitaÈt MuÈnchen, Physik Dept., Inst. E 19, James-Franck Str. 1, D-85748 Garching, Germany

b

Received 10 March 1997; received in revised form 20 April 1997; accepted 28 April 1998

Abstract The development of new working pairs and cycles extends the ®eld of application of absorption systems with corresponding environmental bene®ts. The performance of standard cycles can be enhanced, e.g. by multi-staging. For each application the suitable working pair and cycle can be chosen regarding thermodynamical and economical aspects. Still, the performance strongly depends on the given external conditions. In this paper, basic thermodynamic constraints stemming from those conditions and valid for all sorption cycles are derived using the concept of endo-reversibility. Fundamental economic conclusions can be drawn. Subsequently, real machines are analysed. A comparison with manufacturers data and experimental data is made. The working pairs lithium bromide/water and binary hydroxide solution/water are discussed. q 1998 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Absorption; One-stage system; Two-stage system; Absorbate; Thermodynamics

Contribution aÁ l'eÂvaluation des perspectives eÂconomiques des refroidisseurs aÁ absorption Resume Le deÂveloppement de nouveaux couples et cycles de travail eÂlargit le champ d'application des systeÁmes aÁ absorption ainsi que les bienfaits pour l'environnement. La performance des cycles traditionnels peut eÃtre ameÂlioreÂe, par exemple en utilisant des systeÁmes multi-eÂtageÂs. Pour chaque application, le couple et le cycle de travail qui conviennent seront seÂlectionneÂs en tenant compte des facteurs thermodynamiques et eÂconomiques. Dans cet article, les contraintes thermodynamiques impliqueÂes dans ces conditions (qui s'appliquent aÁ tous les cycles aÁ sorption) sont deÂriveÂes du concept d'endoreÂversibiliteÂ. On peut en tirer des conclusions eÂconomiques de base avant d'analyser de vrai systeÁmes. Les auteurs examinent des donneÂes des fabricants par rapport aux donneÂes expeÂrimentales. Les meÂrites des couples de travail bromure de lithium/eau ou solution d'hydroxyde binaire/eau sont examineÂes. q 1998 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs: Absorption; SysteÁme mono-eÂtageÂ; SysteÁme bi-eÂtageÂ; Absorbat; Thermodynamique

* Corresponding author. ² Deceased 1 Present address: Hans GuÈntner GmbH, PO Box 1345, D-82243 FuÈrstenfeldbruck, Germany

Nomenclature A C®rst Crunning

0140-7007/99/$ - see front matter q 1998 Elsevier Science Ltd. All rights reserved. PII: S 0140-700 7(98)00040-1

Heat exchanger area (m 2) First cost (Ecu/MW) Running cost (Ecu/MWh)

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Ctotal Total cost (Ecu/MWh) COPenrev Coef®cient of performance (endo-reversible cycle) COPrev Coef®cient of performance (reversible cycle) D Lifelong operation hours (h) d Film thickness (mm) i Counter; i ˆ 0,1,2¼ I Solution inventory on tubes (l/kW) Itot Total solution inventory (l/kW) Q Heat ¯ow rate (W) qw Speci®c capacity (W/kg) qf Speci®c capacity related to ¯uids (W/kg) r Density (kg/m 3) rf Density of ¯uids (kg/m 3) s Wall thickness (mm) t External temperature (K) T Internal temperature (K) DT Temperature difference (K) U Overall heat transfer coef®cient (W/m 2K) V Volume per cooling capacity (m 3/kW) W Weight per cooling capacity (kg/kW) 1. Introduction Absorption heat pumps and refrigeration machines have gained increased interest, especially in Europe, in the recent years. More and more, they are regarded not only as environmentally friendly alternatives to CFC-based systems, but also as energy-ef®cient heating and cooling technology, if only applied in an appropriate system. The development of new cycles will give rise to a large extension of their ®eld of application. For each application the suitable working pair and cycle have to be chosen regarding thermodynamic and economic aspects. The performance, however, strongly depends on the given external conditions and not just on the speci®c working pair and design. To be more speci®c, the external conditions set the limits and within these limits performance will be dependent from cycle design, working pairs, and detailed design. Consequently, in comparing different cycles, working ¯uids, or design details, conclusions which are not speci®c to a particular application can almost never be drawn. This statement is also true for the comparison of liquid sorption and solid sorption cycles, and it is the reason for us to start off with the discussion of application constraints ®rst. The most stringent application constraints, of course, are the temperatures of the heat sinks and sources which are relevant for the machine, i.e. the external temperatures. This discussion leads us to the concept of endo-reversible cycles as a ®rst approximation. In a project sponsored by the Commission of the European Communities [1] an attempt for a comparison of different liquid and solid sorption cycles was done, the results of which are published in another paper in this issue of the International Journal of Refrigeration [2]. In

the present paper we want to elaborate on the basis from which the ®gures for that comparison are derived as far as liquid sorption systems are concerned. To this end, we ®rst want to give a rough estimate about the economics of multistage sorption chillers using an endo-reversible approach. We then want to shortly discuss the kind of liquid sorption cycles which have been used for the comparison in the synthesis paper in this journal [2]. In addition, we will discuss some ®gures of merit for real cycles also. 2. Economics of heat driven endo-reversible cycles The economics of heat driven cooling machines to a large extent are determined by the heat exchangers required to operate the cycle. Consequently, fundamental economical relationships can be derived using the concept of endoreversible cycles [3±8]. A thermodynamic cycle is called endo-reversible when the only irreversibilities of this cycle are associated with the heat exchange between the cycle itself and its surroundings, i.e. the heat sinks and heat sources. At least in simple absorption cycles the internal irreversibilities are small [9]. The main difference from real sorption cycles to endo-reversible systems is hidden in the (reversible) characteristics of the working pairs which lead to the necessity of multi-staging [10]. Consequently, it is interesting to approximate sorption systems by endo-reversible cycles: to discuss the limitations and to set limits to the bene®ts of staged processes. Moreover, using the concept of endoreversible cycles basic economical statements can be derived independently from the speci®c kind of heat transformation system being used. This approach has been published elsewhere [10±12]. Consequently in this paper we will restrict ourselves to the discussion of some results. 2.1. Internal and external temperatures A sorption machine transfers heat between different temperature levels. As an example in Fig. 1 a system with three temperature levels is depicted. The only equipment necessary to bring heat into or out of the system are heat exchangers with a suf®cient area to be able to transfer the according amounts of heat Qi (i ˆ 1,2,3). We want to make sure that at this stage of the discussion we do not consider the solution ®eld properties to be restrictive. This may sound odd, but it is preferable to ®xing, e.g. the stage numbers, because the optimal stage number is not known beforehand. The heat exchange area which has to be installed is a function of the heat transfer coef®cients and of the driving temperature differences (DTi) between the external heat carrier (ti) and internal process temperatures (Ti). If the only irreversibilities are those attributed to this heat exchange the cycle is endo-reversible according to the de®nition given above. The coef®cient of performance for

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69

The internal temperatures are determined by the driving temperature differences DTi, i.e. by the amount of heat exchanger area installed. For in®nite heat exchanger area DTi ˆ 0 and Ti ˆ ti, yielding the maximum COPrev: COPrev ˆ

1=t1 2 1=t2 1=t0 2 1=t1

…2†

With decreasing heat exchanger area the driving temperature differences, DTi, increase, and consequently the COPenrev decreases: COPenrev ˆ

1=…t1 1 DT1 † 2 1=…t2 2 DT2 † 1=…t0 2 DT0 † 2 1=…t1 1 DT1 †

…3†

Please note that the numerical value of the COP in Eqs. (1) and (3) is of course identical. 2.2. Heat exchanger area

Fig. 1. Internal (Ti) and external (ti) temperature levels in a heat driven cooling system. Fig. 1. TempeÂratures interne (Ti) et externe (ti) d'un systeÁme de refroidissement utilisant une source de chaleur.

cooling (COPenrev) of such a cycle COPenrev ˆ

1=T1 2 1=T2 1=T0 2 1=T1

…1†

is determined by the internal temperatures only. On the other hand, not the internal temperatures, Ti, but the external temperatures, ti, are ®xed by the application.

We can now discuss the heat exchange area which is required in order to run such a cycle. It will be in®nitely large, of course, if we approach the reversible limit. If we allow the COP to be smaller we need less exchange area to produce a given cooling demand. On the other hand, when the COP is very small, an in®nite amount of exchange area is also required, because a large quantity of area now is required to accept the driving heat and to dump the reject heat. Consequently, if we normalize the sum of the area of all heat exchangers to the cooling capacity, at a certain point the demanded area becomes a minimum. The behaviour described above is depicted in Fig. 2. The external temperatures of driving heat, heat sink and heat source were assumed to be 1278C, 308C and 78C respectively. For simplicity, all heat transfer coef®cients, U,

Fig. 2. Required speci®c heat exchanger area for attaining the endo-reversible COP. The external temperatures of driving heat, heat sink and heat source were assumed to be 127, 30 and 78C. Fig. 2. Super®cie d'eÂchangeur de chaleur requise a®n d'obtenir un COP endoreÂversible. On a considere que les tempeÂratures externes de la chaleur d'entraõÃnement, du puits thermique et de la source de chaleur eÂtaient de 1278C, 308C et 78C respectivement.

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Fig. 3. Comparison of the costs for an endo-reversible chiller (bold solid curve) and a single-effect absorption chiller (thin solid curve) with temperatures as in Fig. 2. Straight dashed lines are lines of constant overall cooling cost (see text). Fig. 3. Comparaison des couÃts de fonctionnement d'un refroidisseur endoreÂversible (courbe continue grasse) et un refroidisseur aÁ absorption a simple effet (courbe solide maigre) avec des tempeÂratures donneÂes en Fig. 2. Les lignes droites hachureÂes montrent le couÃt global du refroidissement (voir le texte).

have been assumed to equal 2 kW/m 2K. Moreover, it has been assumed that all driving temperature differences, DTi, are equal. The last assumption is reasonable, as it can be shown [10,12] that with the prevailing conditions an economic optimum for the design of the cycle is approached with equal driving temperature differences DTi. Under these conditions, the speci®c total transfer area (normalized with the cooling capacity) is given by [10]   X A 2 1 1 COPenrev …4† ´ ˆ Q0 UDT COPenrev The COPenrev by itself is a function of DT via Eq. (3). The COPrev of the totally reversible cycle is as high as 2.95 according to Eq. (2). If we allow for a 10 K driving temperature difference the COP of the endo-reversible cycle is reduced to 1.24 according to Eq. (3). The area to install following Eq. (4) then amounts to 0.18 m 2/kW. This is very close to the minimal total area to be installed, which amounts to 0.13 m 2/kW as can be seen in Fig. 2. In this region, however, the COP is a very strong function of the heat exchange area. A COPenrev of 0.54 is attained at the point of minimum area with a large driving temperature difference of about 22 K. With a 10% increase in area to 0.14 m 2/kW we can attain a COP of 0.87, which is a 60% increase. 2.3. Economics From an economic point of view the installed heat exchanger area determines both the ®rst cost of a machine and, via the COP, the operating or running cost. In Fig. 3 speci®c running cost (energy cost) is plotted against speci®c

investment cost for the endo-reversible cooling system with the parameters given above (bold solid line). The COP which can be attained with a given amount of exchange area determines the necessary amount of driving heat for a speci®ed cooling capacity, which is converted to running cost by a value of 25 Ecu/MWh for the heat input. Thus, the running cost is arrived at by dividing 25 Ecu/MWh by the COP. The heat exchanger area is converted to ®rst cost by multiplying with a value of 250 Ecu/m 2. Let us ®rst discuss the bold solid line which represents our endo-reversible cooling system for the given operational conditions. It is immediately seen that the point of lowest ®rst cost is quite far from the point of lowest running cost. This means that the cheapest machine from a ®rst cost argument will never be the cheapest machine from a total cost point of view. The common task for any application now is to minimize the total cost of the system (straight dashed lines) made up from investment and running cost. Imagine there would be no ®rst cost for the cooling machine. Then the total cooling cost would be made up from operating cost only (intersection of the straight lines with the abscissa). If some ®rst cost has to be depreciated, in order not to increase total cost the operating cost has to be lower. Consequently, lines of constant total cost in a plot like that of Fig. 3 are linear, with the slope given only by lifelong running time D and ®nancial terms like interest rates, which have been neglected here: Ctotal ˆ Crunning 1

Cfirst D

…5†

The higher the lifelong on-time is, the smaller is the slope

T. Berlitz et al. / International Journal of Refrigeration 22 (1999) 67±76

of the straight lines; the higher the total cost is the larger are the intersections of the straight lines with the axes. The dashed lines in Fig. 3 are those lines of constant total costs which are arrived at with assuming for the cooling system a life of 10 years and a running time of 1000 h/a (steep lines) and 6000 h/a (¯at lines) respectively, with no interest taken into account. They touch the design curve of the cycle in the respective optimal design point with lowest possible total cost. At this point the ®rst cost and the running cost can be read from the graph. If one divides the energy cost of 25 Ecu/MWh by the running cost the COP in this optimal point results. Of course, for different running times, i.e. different applications, the design of the most economic machine is different. With lower running time, a relatively cheap (75 Ecu/kW) endo-reversible machine is the most economical with a total cost of 21 Ecu/MWh, which would still exhibit an incredibly high COP of about 1.8. For long running time a more expensive machine (150 Ecu/kW) is optimal, albeit with a total cost of cooling of only 13 Ecu/MWh and a COP of about 2.3. The cheapest machine from an investment consideration (costing about 32 Ecu/kW) is far from being the most cost effective machine from a total cost point of view in both cases. It is absolutely obvious that the COPs which result from this calculation are far higher than what is available on the market and what will be available in the near future. This situation gives us a ®rst hint that the development of sorption systems with enhanced ef®ciency is really an important issue. 2.4. Figures of merit From Fig. 3 the range of ®rst and running costs of costeffective endo-reversible cycles can be deduced. This range can be translated back to performance (COP) and heat transfer area. The ®rst cost of 75 to 150 Ecu/kW in the relevant range can be divided by the surface cost of 250 Ecu/m 2, and it can be concluded that for the prevailing conditions areas, A, between 0.3 and 0.6 m 2/(kW cooling) have to be installed for cost effective design at least. From these numbers very rough ®gures of merit can be derived, which can serve as upper limits for real cycles because they are derived for the endo-reversible limit. Still, it has to be kept in mind that the this limit can be shifted by changing the external temperatures and the heat transfer coef®cient. We can assume the heat transfer surface to be an area of tube with a wall thickness, s, of about 1 mm. The materials volume, V V ˆ As

…6† 3

is then between 0.3 and 0.6 dm /(kW cooling). For steel with a speci®c weight of r ˆ 8 kg/dm 3 we arrive at a total weight, W, of the tubes W ˆ Asr

…7†

71

which is between 2 and 5 kg/(kW cooling). The inverse of this number qw ˆ 1=…Asr†

…8†

is the weight-speci®c cooling capacity. It will be between 200 and 500 W/kg. Please be aware that this number can be 10 times as high if the wall thickness is reduced from 1 mm to 0.1 mm. This might be possible to achieve with compact plate heat exchangers. Of course, the heat exchanger tubes are just a part of the total weight. Without having more detailed ®gures we may assume the total weight to double or treble as compared to the weight of the exchangers. Consequently, the speci®c cooling capacity will not be larger than 50±250 W/kg. This global value, of course, will not bene®t from a reduction in wall thickness as much as the heat exchanger weight does. Another speci®c cooling capacity is the one which is related to the weight of working ¯uids only. The smallest amount of liquid is arrived at if falling ®lm heat exchangers are being used. The ®lm thickness, d , will not exceed 1 mm because it is not advisable to recirculate too much solution, and it will not be smaller than 0.1 mm because the ®lm tends to be unstable (bad wetting). Consequently the inventory of ¯uids, I, which is actually on the tubes I ˆ Ad

…9†

will be about 0.03 to 0.6 l/(kW cooling). In the case of very thin ®lms (0.03 l/kW) the total inventory will be determined from the amount of liquids in the pipes, pools, and receivers, rather than from the liquids on the exchange surfaces. As an estimate, we can argue that a total amount It of 1±3 l ¯uids per kW cooling capacity is a reasonable number for a lower limit. The speci®c weight r f of the working ¯uids used is not too far from 2 kg/l. We arrive at a ¯uid-speci®c cooling capacity qf ˆ 1=…It rf †

…10†

of 170±500 W/kg. If we want to relate to the sorption ¯uid, which might be expensive but only the minor part of the inventory, the speci®c cooling capacity of course will be larger. In order to arrive at the weight of the operating total system we have to add to the construction material and the working ¯uids the heat carrier (water) in the tubes. If we assume the use of tubes with an outer diameter of 16 mm we provide about 0.05 m 2 area per m tube length. In order to attain the said 0.3 to 0.6 m 2/kW cooling capacity we need between 6 and 12 m length of tubes per kW cooling capacity. Inside these tubes with an inner cross section of about 150 mm 2 there is a volume of 0.15 l of water as heat carrier per m tube length. This results in about 1±2 kg/kW for the contents of the tubes inside the exchangers. In total, we can expect a weight of roughly 7±25 kg/kW or a speci®c cooling capacity of 40±150 W/kg. From the tubes' outside volume of 0.02 l per m tube

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Table 1 Weight and volume of an endo-reversible chilling system Tableau 1. Poids et volume d'un refroidisseur endoreÂversible Heat exchange area Weight of exchanger tubes Weight of additional tubing Weight of ¯uid inventory Weight of heat carrier inside tubes Total weight Cooling capacity per system weight Volume of heat exchanger tubes Total Volume Cooling capacity per system volume

0.3±0.6 m 2/kW (cooling) 2±5 kg/kW (cooling) 2±10 kg/kW (cooling) 2±6 kg/kW (cooling) 1±2 kg/kW (cooling) 7±25 kg/kW (cooling) 40±150 W (cooling)/kg 1.2±2.4 l/kW (cooling) 2±10 l/kW (cooling) 100±500 W (cooling)/l

length or 1.2±2.4 l/kW, we can deduce a rough number for  s volume of 2±10 l/kW or 100±500 W/l, taking the system into account the void volume between the tubes with a factor of 2±4. The ®gures are repeated in Table 1 in order to elucidate their respective weight. It is obvious that complicated tubing must be avoided. Then, the weight of exchange area, tubing, and inventory will be in the same order of magnitude. This is of course mainly for small or medium capacities. For large chillers the weight of inventory and, especially, additional tubing is only marginal. Although the derivation of these ®gures looks somewhat crude, it is based on sound thermodynamics and consequently provides a good guess for the limits to the speci®c capacity of heat driven cooling systems. In the next paragraph we will be more speci®c by looking at real absorption systems.

3. Economics of real absorption chillers The design of a real machine, in addition to depending on the external restrictions which have been discussed up to now, depends strongly on the thermo-physical properties of the working ¯uids used. Consequently, even in the ideal (internally reversible) case not all points along the solid line shown in Fig. 3 can be realized with one single sorption cycle using a given working ¯uid. In other words: the solution ®eld forces us to realize a sub-optimal design as compared to the judgement from the endo-reversible point of view. In reality, all cycles have to be situated on the right hand side of the endo-reversible design curve: their COP is lower and the investment cost is larger. In order to verify this statement, a weak solid line has been plotted into Fig. 3, additionally. It represents the design curve attained numerically [13] for a single-effect cycle using LiBr/H2O as work-

ing pair and the same economical data as in the endoreversible calculation. The real cycles, of course, are more expensive due to the solution heat exchangers for the same COP as the endoreversible approximation, and perform worse due to restrictions of the working pairs and internal irreversibilities. From Fig. 3 we can deduce that their investment of about 0.2 m 2/ kW is similar to that of an endo-reversible cycle with heat transfer values of 2 kW/m 2K if it exhibits the same order of COP. However, it is interesting to note that from Fig. 3 it also can be deduced that the optimal investment for heat exchangers is even much less than that for the endo-reversible limit. Whereas in the latter case additional heat transfer surface still reduces running cost considerably, in the real case the thermodynamic limit is approached due to the restriction of the solution ®eld. The least cooling costs are being attained by the singleeffect cycle in the case of low running time (steep straight line) with 36 Ecu/MWh, and COP < 0.78, which is no bad design at all. In the case of long running time a still more expensive design is to be preferred with cooling cost of only 32 Ecu/MWh at a COP of more than 0.8. This is a quite high value, but it can be realized. From the comparison of the endo-reversible design curve (bold solid line) in Fig. 3 with the realistic design curve (weak solid line), it can be deduced that there is much room for improving the economics by multi-effect cycles. This will be veri®ed in Section 3.1. 3.1. Cycle basics Single-effect and double-effect absorption chillers are commercially available today and increase their market share every year, especially in the far eastern countries. Due to the necessity to save energy for environmental protection, the development of absorption machines which perform more ef®ciently is mandatory. Multi-effect absorption heat pump cycles have the well-proven potential to attain a performance which is superior to the performance of conventional cycles [14,15]. This implies a decrease in energy consumption as well as in cooling water demand or in installation requirements for cooling towers. The positive impact on the environment is obvious. However, to date only a few triple-effect machines have been tested in experimental plants or are under test. Fig. 4 is a schematic representation of a single-, one speci®c double- and one speci®c triple-effect absorption cycle. The simple rhombus is a representation of a singleeffect cycle in a implicitly underlying pressure vs temperature plot (Van T'Hoff or DuÈhring). The corners of the rhombus are the exchanger's evaporator (low pressure, lowest temperature), absorber (low pressure, middle temperature), condenser (high pressure, middle temperature), and generator (high pressure, highest temperature). Arrows to a corner represent heat input, arrows from a corner represent heat output. The number of arrows qualitatively represents the

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therefore the cost of heat exchangers can be determined only if heat transfer coef®cients are known. But this approach gives a quick survey over the potential in performance, which is very important if new cycles or new working ¯uids should be assessed. A computer code has been developed for that purpose [13,24]. In this paper it is used for optimizing the absorption machines using water as refrigerant. 3.2. Aqueous lithium bromide as working ¯uid pair

Fig. 4. Schematic pressure±temperature representation of three liquid sorption cycles with single-, double- and triple-effect performance. Fig. 4. RepreÂsentation scheÂmatique pression-tempeÂrature des trois cycles a sorption (a simple, aÁ double et aÁ triple effet).

respective heat load. By adding two further exchange units (a generator and a condenser) to a single-effect cycle, double-effect performance can be attained. Two more exchange units lead to triple-effect performance. Many other cycle con®gurations are known which exhibit double-, triple-, or even higher effect performance [15± 23]. In this paper, we restrict ourselves to the con®gurations of Fig. 4. There is also a large variety of potential working pairs. We are discussing water±lithium bromide and water± hydroxide only. As in the case of endo-reversible cycles, a real cycle should be optimized in the sense that all individual heat exchangers are designed with an area in relation to the other exchangers which gives the maximum COP for a given total cost or, as an approximation, for a given total exchange area. Again, the total area of heat exchangers and

State of the art for commercially available chillers is the working pair LiBr/Water with a COP of 0.7 for the singleeffect and 1.2 for the double-effect cycle. Triple-effect chillers are not yet on the market, but in development in several laboratories [25]. Cost curves which are based on the design curves published previously [24] for the three cycles of Fig. 4 are shown in Fig. 5, which is made up in the same way as Fig. 3. However, in this plot realistic heat transfer data have been used. Moreover, the temperature t2 had been adjusted to 200 and 3008C respectively, in order to account for the high temperature input which is required for multi-staging. The large bene®t from this multi-staging can easily be seen. For comparison, the endo-reversible cost curve of Fig. 3 has also been incorporated (thin dashed line). With the arguments given above, there seems to be almost no range for cost-effective application of single-effect cycles. However, it has to be taken into account that the increased complexity in control and piping as well as the potential need for more expensive materials is not considered in this ®gure. These features would shift the cost curves to higher investment cost thus rendering the simple cycles more economical. In order to verify this last statement, in addition, several data for commercial chillers [26] have been incorporated in Fig. 5. The symbols denote single-effect (O) and doubleeffect (B), using the same energy cost of 25 Ecu/MWh as before. The running costs are somewhat higher than in the

Fig. 5. Comparison of the total costs for the cycles of Fig. 4. Fig. 5. Comparaison des couÃts globaux des cycles de la Fig. 4.

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Fig. 6. Maximum COP for single-effect and double-effect cycles using hydroxides as working ¯uid in dependence of the installed speci®c heat exchanger area; temperatures as before. Fig. 6. COP maximale de cycles aÁ simple effet ou aÁ double effet utilisant des solutions d'hydroxyde comme ¯uide actif avec une deÂpendence visaÁ-vis de la super®cie speÂci®que de l'eÂchangeur; les tempeÂratures sont les meÃmes qu'au-dessus.

cost curves, due to some additional irreversibilities. The investment is quite a bit larger, which is due to the part of investment not accounted for in our calculation and, of course, the pro®t of the manufacturer, sales agent etc. It is interesting to note that, as jugded from the exchanger cost, the difference between single-effect and double-effect is not so large. The main difference in sales price, consequently, should stem from control and other features which are due to the larger complexity. 3.3. Aqueous hydroxide as working ¯uid pair Today almost all commercially available absorption water chillers operate on LiBr/water. Their main components, the heat exchangers, are usually shell and tube heat exchangers. However, the working pair LiBr/water, although being the best available today, is not an ideal one. Its main problem is the small temperature lift attainable due to crystallization of the high concentrated LiBr solution. Hence the ®eld of application is limited to installations with rather low heat sink temperatures, which means that no cheap air-cooled chiller can be installed. One possibility to reach a higher temperature lift is to use hydroxide solutions as absorbent for water [27±37]. In this paper a mixture of 50% NaOH and 50% KOH is assumed for application, which has already been proposed by Altenkirch in 1930 [27]. An internal temperature lift of about 90 K, which is about twice that of LiBr, could be possible [34]. A drawback of hydroxides is the severe corrosion problem. This, however, also exists with LiBr and seems to be manageable there. Moreover, highly corrosion resistant materials become more and more available and cheaper. Another drawback of the hydroxides is the bad heat transfer in a falling ®lm absorber. This can be solved by using rotating absorbers [33] or an adiabatic spray absorber [35±38].

To assess the economics of hydroxide machines the simulated cycles have been equipped with ¯ash evaporation, spray absorption, and plate heat exchangers. The resulting design curves, analogous to Fig. 2, are shown in Fig. 6. As no commercial product is available, this basic plot has been preferred to the economic plot (Figs. 3 and 5). In addition, the results of two test plants [36,37] have been incorporated. From comparison of the design curves with the experimental data it can be seen that the design is not yet optimum, but is well inside the expected ballpark. 3.4. Figures of merit In order to conclude this paper we want to present ®gures of merit of some cycles which are derived from commercial or experimental plants. From Figs. 5 and 6, with using again the speci®c cost of 250 Ecu/m 2, we arrive at speci®c areas of between 0.15 and 0.3 m 2/kW cooling capacity depending on cycle type and design. These ®gures are valid both for aqueous lithium bromide and hydroxide solutions. The ®gures are at or even above the upper limit of the data given in the discussion of the endo-reversible approach. The reason is that we cannot overcome the limitations of the solution ®eld with investing greater transfer area. Thus, we are bound to the installation of a less performing and cheaper system. From the comparison with the data which has been derived above we can conclude that speci®c cooling capacities will never be larger than around 150 W/kg by weight and around 500 W/l by volume. With those ®gures in mind, it is interesting to look at real systems, both commercial and laboratory type. In Table 2 some ®gures have been collected. The double-effect and single-effect machines all are or have been commercially available except the last example, which is the prototype by ZAE Bayern [37]. The two single-effect/

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Table 2 Speci®c capacities of several real absorption chillers Tableau 2. Rendements de plusieurs refroidisseur aÁ absorption reÂels Working pair

Type of cycle

Chilling capacity (kW)

Capacity per unit weight (W/kg)

Capacity per unit volume (W/l)

H2O/LiBr H2O/LiBr H2O/LiBr H2O/LiBr H2O/LiBr H2O/LiBr H2O/LiBr

Double-effect Single-effect/double-lift Single-effect/double-lift Single-effect Single-effect Single-effect Single-effect

2500 2500 300 70 10 6 5

80 20 30 15 40 30 50

30 40 30 5 25 50 a 50 a

a

Not counting void volume.

double-lift machines are pilot plants which are being used for low temperature input [39]. The presented ®gures are still well below the theoretical ones, but it has to be noted that especially for the large machines there is some void space not accounted for. The conclusions may be two-fold. First, the theory does not account for many items which play an important role in reality. Second, there must be some room for improvement of the speci®c capacities of real cycles. Still, it will be hard to reduce weight and size by more than a factor of 2. Consequently, 100 W/l and 100 W/kg will be the limit for the speci®c capacity of absorption chillers. This is very reasonable if it is compared to the theoretical approximation of 500 W/l and 150 W/kg.

4. Conclusion In this paper we wanted to provide two pieces of information in order to discuss economical aspects of absorption heat pumping equipment. At ®rst, we wanted to establish practical limitations for the heat exchangers to install which are more stringent than those from reversible calculations, but which are yet easy to assess. We have done that with the concept of endo-reversible cycles and arrived at ®gures of merit of maximum 500 W/l and 150 W/kg for chilling application with heat input at 1278C. This is about the same capacity that we can expect from absorption systems from theoretical optimization, albeit with driving heat input at an appropriate higher temperature as required for the respective staging. Finally the schemes of some relevant cycles have been presented. First, water chillers operating on H2O/LiBr in various cycle con®gurations have been dicussed. Second, similar cycles using hydroxide solutions have been discussed. The wide solution ®eld of hydroxides can enlarge the ®eld of applications for the working ¯uid water. The speci®c capacities of these systems, as well as those of commercial apparatuses are not above 50 W/l and 50 W/

kg. We conclude that some (but only limited) room for improvement in compactness is still available.

Acknowledgements This work was sponsored by the Commission of the European Communities, contract JOU2-CT93-0440 and ERBCHRX-CT93-0391.

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