design of absorption refrigeration (george vicatos)

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DESIGN OF ABSORPTION REFRIGERATIONMACHINES

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CHAPTER 1 - INTRODUCTION 1

CHAPTER 1


1.01.0 INTRODUCTIONINTRODUCTION

1.1 Historical Note

Gas absorption was known as early as 1770. Absorption refrigeration originated in 1824 byFaraday, who proved that certain gasses, which were believed to exist only in, vapour formcould be liquefied. One of these gasses was ammonia, which could be absorbed, in vastquantities by silver chloride crystals. His apparatus consisted of a closed inverted “V” tube,which contained in one end the ammonia silver chloride crystals, Figure 1.1. That end of thetube was heated and the opposite end cooled with water. Soon the ammonia gas was releasedfrom the compound and liquid ammonia appeared in the cool end of the tube. When heremoved the heat and the water container, he observed that the liquid began to boil violentlychanging again into vapour and at the same time the crystals reabsorbed the ammonia vapour.The region of the apparatus containing the liquefied ammonia was intensely cold as theammonia drew heat from its environment in order to evaporate [A5]. Faraday’s experimental

apparatus was the first absorption machine of the intermittent type.The first continuously working absorption refrigeration system using sulphuric acid and wateras absorbent and refrigerant respectively was invented by Carrè in 1859, who in the same year,operated the first ammonia-water absorption refrigerator.

His system consisted of components capable of assisting the refrigerant through a continuouscycle, as shown in Figure 1.2.

Figure 1.1 Faraday’s experimental apparatus


The refrigerant enters the evaporator where it evaporates at low pressure and temperature bydrawing heat from the environment. The vapour leaving the evaporator is absorbed in a liquid,which has high affinity for the refrigerant and transferred via a liquid pump into the boiler orgenerator. There, heat is applied which reduces the affinity of the liquid, and drives off therefrigerant vapour at high pressure, which then passes to the condenser to be liquefied.

The liquid refrigerant enters the evaporator again and the cycle is repeated. The remainingliquid in the generator, which is weak in refrigerant, passes through a throttling valve in theabsorber to receive new vapour refrigerant. After it has been enriched, it flows through itsown cycle. Since the generator, solution throttle valve, absorber and pump are involved incompressing the refrigerant vapour by thermal action, they are called the “thermalcompressor”.

Early in the 20th century the idea and the application of the absorption system was shelved,mainly due to its high power consumption, giving ground to the development of the fullyenclosed ammonia compression refrigeration. In other words, the thermal compressor wassubstituted by the mechanical compressor, which was placed there to withdraw the refrigerantvapour from the evaporator and then to compress it. In all other respects, the refrigerationcycle is identical in both systems.

Absorption refrigeration was revived again around the 1930’s with the invention of the so-called “candle fridge”, Figure 1.3, by the two Swedish researchers, B. Von Platen and C.Munsters. It is a domestic-size, three-fluid system (refrigerant, absorbent and a pressureequalising inert gas), the cycle of which is based on the theory of partial pressures. To boil therefrigerant off the solution, the system used initially the heat from a paraffin or a gas burner[B7]. It was further developed to utilise gas, as well as either a 12V, 120V or 240V supply,but still only for domestic purposes.

Figure 1. 2 Schematic arrangement of the simple two-fluid absorption cycle


The main reason for its limited size is due to the solution pumping arrangement, which reliesupon a percolator-type pump. This pump brings the generator’s solution into a higher leveland thereafter the fluid circulation depends upon potential levels. Since medium and large-scale industrial refrigerators require large and definite amounts of fluid flow, the percolator-type pump cannot meet the requirements. A further drawback to the potential level flow is itsinability to survive movement and inclination, as this would disturb the fluid levels.

Despite this ingenious development by the two Swedish researchers, the absorption unit hasacquired a bad reputation due to the irresponsible craftsmanship of various manufacturingfirms and due to lack of understanding of the absorption behaviour. The development wasmainly through a trial and error construction with a minimal backing of theoretical knowledge[S11].

Studies in the last two decades improved the absorption refrigerator and showed that the unitis capable of meeting the demands of the modern refrigeration industry.

Indeed, refrigeration units of cooling capacity in the order of 2 to 5MW exist in some parts ofthe world, which by far exceed the maximum capacity obtained by a single vapourcompression refrigerator [J4]. For example, there are two absorption refrigeration installations

Figure 1.3 Line diagram of the three-fluid absorption refrigerator unit


each capable of 22.1MW cooling capacity at -5oC evaporator temperatures. These were builtin 1981 for the former USSR, by BORSIG GmbH, Berlin [H5]. They are both powered bysuperheated steam and are used to cool by-products from the process of syntheticunvulcanized rubber (caoutchouc). Unfortunately, there are no performance reports published.

1.2 Powering methods of the absorption cycle

The absorption cycle could use a low-grade heat source, in the temperature range of 70 oC to120 oC.

Sources of low-grade heat are numerous, as for example, solar energy, low-pressure steam,flue and exhaust gases, geothermal, etc. These sources of energy are available; at least someof them at minimal cost and their utilisation has obvious advantages.

A number of countries have launched research programmes to convert solar energy into heat,to power absorption type refrigerators, air-conditioners and heat pumps directly.

Renato Lazzarin [L1] has published results of a two-year experiment in North Italy, describinghow solar energy was used, either directly or stored, in order to create a working temperatureenvironment for an ammonia-water absorption heat pump. The plant was provided with aseasonal storage, so that useful solar heat could be collected by solar collectors all year roundand used when the solar energy was poor or non-available. The earth storage was connectedwith an energy roof installation and alternated in providing the cold source between the winterand summer months. The performance of the plant was anything but satisfactory. The mainsource of inefficiency was the poor heat exchange between the ground and the earth storagecomponents and even greater, the low performance of the absorption heat pump within theexperimental working temperatures.

Exell et al. [E3] published their work on mathematical modelling of an intermittent ammonia-water absorption refrigerator powered through flat solar collectors. Their results show that forthe climate of Thailand, the average daily yield of ice should be 3.2 Kg per m2 of collector.

Agarwal et al. [A3] reported on results from a laboratory model of a solar poweredintermittent refrigeration system-using refrigerant R22 and DMF (Dimethyl Formamide),capable of cooling 60kg of water daily from 30oC to 15oC. In the month of July the averagerefrigeration temperature was 5oC for about 1.5 hours, while in January the averagetemperature was maintained at -3oC for a period of 3 hours.

Their proposed water-cooler system uses a water-cooled condenser during daytime vapourgeneration and a water-cooled absorber during night time. From the performancespecifications it could be deducted that their intermittent refrigeration unit requires enormousamounts of cooling water to produce the required effect. On the other hand, the authors claimthat the importance of an intermittent system lies in its simplicity of its operation on, accountof the combined use of the solar collector as generator and absorber. However, in their designthe two components are independent and separate as to overcome the problem of cooling. Thisresults in a sequence of opening and closing of control valves at sunset and in the early hoursof the morning. If this sequence is automated their unit could require the usage of high formsof energy.

Professor I. Borde of Israel, advisor of GALIL Advanced Technologies [G1] gives evidenceabout the development of an absorption refrigerator utilising waste heat and solar energy, toprovide refrigeration in the range of 0oC to -3oC. According to the report, a “novel”


combination of working fluids was used, with the intention of moving away from theconventional ammonia-water system. Without the constituents of the refrigerant-absorbentpair being revealed, it is stated that the refrigerant belongs to the “FREON” group and theabsorbent is an organic liquid solvent. Subsequent papers by the same author report onhydrogenated chlorofluorocarbons and Dimethyl Formamide (DMF) or Tetraethylene GlycolDimethyl Ether (TEG.DME) combinations.

The project was for a 250 ton capacity refrigeration plant, to be used in agricultural centres.The company produced an analysis, which compares the proposed absorption refrigerator tothe vapour compression refrigerator, showing the former to be about 60% more economical inthe machinery set-up and service, and about 50% more economical in power consumption.

Alvares and Trepp [A6] from the University of Brazil report on a mathematical model of asolar driven aqua-ammonia absorption refrigeration system. The modelling was done in such away that the coefficient of performance (COP) could be calculated with the components of thesystem being able to be “turned on” or “turned off” or varied in characteristics. In this waythirteen absorption cycles were studied in the search for the optimum coefficient ofperformance. The cycle, which gave the highest performance, was that which had the highestrefrigerant concentration, and included a solution heat exchanger and a vapour-liquid heatexchanger (pre-cooler). The COP achieved by this cycle was 0.602.

Kaushik and Bhardwaj [K3] from the Indian Institute of Technology investigated an ammoniawater absorption cycle for solar refrigeration, heat pump, and air conditioning operations.With the aid of a numerical analysis, it was found that at high generator temperatures the COPwas reduced. It was also shown that an increase of condenser’s temperature improves theperformance at higher generator temperatures. In a subsequent paper by Kaushik, Kumar andChandra [K4] a study is presented of a cascade system of two absorption refrigeratorspowered by separate solar collectors. Their system could achieve lower evaporatortemperatures than the single stage absorption refrigerator, but the overall COP is lower thanthat of the single stage.

El-Shaarawi and Ramadan [E2] from Alazhar University in Egypt, manufactured and testedan intermittent solar absorption refrigerator. Their paper describes the construction of therefrigeration unit as well as the solar collectors. The experimental data compare favourablywith the proposed theoretical model.

Al-Marafie, Suri and Maheshwari [A4] from the University of Kuwait, analysed in a techno-economic study three cycles: an absorption system powered by flat plate solar collector, anabsorption system powered by a solar pond and a vapour compression refrigerator poweredeither directly through the network or through solar photovoltaic collectors. Their results showthat while the flat plate solar collector was not economically viable, the solar pond showed apromising and attractive alternative. On the other hand solar photovoltaic cells could becomecompetitive in the future only if their unit cost drops drastically.

The above mentioned publications indicate that it is a world wide tendency to utilise the mostabundant source of energy for refrigeration and air-conditioning purposes and it is for thisreason that the research on absorption refrigeration, inclines towards utilising solar energy.

However, the efforts are focused on refining the solar panels and the solar generator. Studieson the steam-powered absorption cycle and on the refinement of the thermodynamic analysisof the absorption refrigeration cycle itself, have been neglected. The steam-poweredabsorption refrigerator is being regarded as a “standard absorption system” and is only re-examined if other machinery and cycles are incorporated. This approach of investigation was


adopted by Agarwal et al. [A2] from the Indian Institute of Technology, who analysed withthe aid of computers a combined refrigeration cycle. The cycle consisted of a vapourcompression refrigerator, the compressor of which was powered by a steam turbine, and anabsorption refrigerator powered by the exhaust steam of the turbine. Amongst otherperformance observations, they praise that the proposed system as a whole, was superior tothe absorption system alone. This conclusion however, is erroneous, as the performance of thevapour compression refrigerator and that of the absorption refrigerator cannot be compared,let alone when the absorption cycle is compared with a whole combined cycle.

Beasley and Hester [B4] from University of Clemson, USA proposed a study for a pressuredriven absorption cycle. The cycle utilises a semi-permeable membrane to separate therefrigerant from the absorbent. The flow of refrigerant across the membrane is achieved by apressure differential in excess of the osmotic pressure. Since the refrigerant is separated in aliquid form and also in the absence of heat, there is no need for a condenser. The proposedsystem is only a theoretical model, as the performance of the membrane is unpredictable. Buton the other hand, the predicted coefficients of performance reach values matching the vapourcompression cycle.

1.3 Pumping methods of the working fluids

The method for the circulation of the working fluids depends on whether the unit operates onthe two or three-fluid principle.

The three-fluid system utilises the partial pressure of an inert low molecular weight gas (forexample hydrogen), to equalise the total pressures between the evaporator, absorber, generatorand condenser. The circulation thereafter is achieved by gravity effects, as shown in Figure1.3. In this three-fluid system, there is an optimum circulation rate of solution through theboiler and absorber and the “lift-tube” of the percolator pump must be designed to providethis optimum rate. In the smaller size three-fluid-unit the lift-tube operates under the influenceof surface tension at the bottom end of the tube, which dips into and breaks free from thesolution surface, the level of which is essential for the lift-tube performance [S10]. In the tubeitself, vapour bubbles and liquid slugs are formed in a regular manner.


Figure 1.4 shows in sequence the formation of the liquid slug in the lift-tube [S10]. Thesurrounding vapour pushes at the liquid surface causing the solution from the annular space torise in the tube. At the same time the level drops away from the tip of the tube, but due tosurface tension the liquid is still attached. As the lift-tube is the only escape route for thevapour, separation occurs and the liquid slug is pushed up by the rising vapour. New liquidfrom the absorber flows into the annulus and as soon the level touches the bottom tip of thelift-tube the process repeats itself.

In larger three-fluid refrigerators, boiling occurs inside the lift-tube and the liquid is pushedupward by the rising vapour.

In the two-fluid system (for example in moderate to large size units), there is a definitepressure difference between the absorber and the generator. This pressure difference has to bebridged by a pump. Pumps of different operating principles have been used for this purpose,such as piston, centrifugal, diaphragm, all of which require external “high grade” energy. It isusually an electric motor, which provides the motive power.

The type of pump used depends upon the refrigeration requirements and the temperature rangeof evaporator temperatures. For example, at low evaporator temperature, equivalent to sub-atmospheric pressures, a positive displacement pump is recommended. At higher evaporatortemperatures and large circulation rates, a centrifugal pump could be used.

The invention of the three-fluid system, has motivated the search to find ways to pump thesolution of a two-fluid system, by a pump, which requires a low-grade heat. In this way, theneed for higher-grade energy input can be reduced. This is possible by using pumpingmethods, which need power of the same quality as the generator. One of these methods is the“thermal pump”, the principle of which is based on the invention of Szucs [S14]. Animmediate advantage in incorporating a thermal pump is that the plant would be poweredexclusively by low-grade heat and because there is no mechanical movement, this would leadto minimum maintenance.

Figure 1. 4 Surface tension effect in the lift-tube arrangement


Such a pump was built and tested in an absorption unit by the author [V2]. Besides its highcost of construction it is reported that its intermittent behaviour caused instability to theabsorption machine during performance testing. Although this “thermal pump” requires heatenergy as a prime mover, tests showed that it needs electricity to supply its controls andvalves.

1.4 Refrigerants for absorption machines

There are many refrigerants available, but when considered for absorption machines theirnumber is diminished.

The criteria, which assist in the choice of refrigerant-absorbent combinations, depend on thethermophysical properties of the working fluids. These are:

a. The heat of vaporisation of the refrigerant. This is considered as one of the mosthighly valued properties of the refrigerant. It is responsible for the refrigerationeffect and the mass flow rate of the refrigerant to produce the required capacity.

b. The heat of solution. This is the heat which is released when the refrigerant isabsorbed in the absorbent. The same quantity of heat must be applied to thesolution (under the same conditions) for the refrigerant to be released from theabsorbent. These processes are called absorption and resorption respectively. Theheat of solution depends upon the affinity that the two substances have for eachother.

c. The vapour pressure of the refrigerant and the absorbent. This property determinesthe high and low pressures of the system. It is preferable that the differencebetween the vapour pressures of the refrigerant and the absorbent be as large aspossible. If the contrary occurs it is necessary to introduce a rectification column.

d. The volubility of the refrigerant in the absorbent. It is important for the absorbentto absorb large amounts of refrigerant in order to keep the solution mass flow ratessmall. However, the greater the volubility of the refrigerant in the absorbent thelarger the heat of solution and therefore, large heat exchangers will be required toremove the heat of solution.

e. The heat capacity of the solution. This property has an impact on the heat transferbetween the working fluids. Its value is the combined value of the two constituentsaccording to their concentration. A large value means a small mass flow rate of theworking fluids.

f. The viscosity of the solution. It determines the size of the tubes for a fullyturbulent flow.

g. The thermal conductivity of the solution. This property is involved with theevaluation of the heat transfer coefficient, needed for the heat exchanger’scalculations.

h. The toxicity of the working fluids. The toxic behaviour of the refrigerant or theabsorbent concerns safety and comfort. There is more concern now on whether thechemical compounds are in the long run environmental benign, rather than on thedirect human safety [K7].


i. The chemical stability of the working fluids. Decomposition of either constituentwould require frequent evacuation of the system. It is therefore essential, that therefrigerant, the absorbent and their mixtures, are stable within the working range ofthe absorption machine. For example, ammonia in the ammonia-water pair isunstable at temperatures of 170oC and above, producing inert gases, which cannotbe absorbed or removed from the system [B9].

j. The corrosive properties of the working fluids. This determines the constructionmaterial of the unit.

Researchers have reported a variety of chemical substances with the ability to absorbrefrigerant compounds.

Renz and Steikle [R4] used the following working fluids for their proposed continuousabsorption system:

a. ammonia-thiocyanate (NaSCN) aqua solution

b. R 22-Dimethyl ether - Tetraethylene glycol (DTG)

c. ternary system methanol-lithium bromide-zinc bromide

Their report compared mass, heat flow rates and component efficiencies, for all three workingfluids. It was concluded that, although the ammonia-salt solution appeared to have betterthermodynamic properties over the other two combinations and required no rectification, theformation of salt crystals was a drawback. This conclusion was confirmed by Blytas andDaniels [B6] who also reported on the thermodynamic properties of ammonia-NaSCNmixtures.

Tyagi et al. [T6] has reported on the coefficient of performance of an absorption unit with aselection of 26 different refrigerant-absorbent combinations. Emphasis was given to ammoniaas refrigerant combined with both water and organic solvents and with various salts toimprove the overall performance. Sulphur dioxide and refrigerants R21 and R22 were alsoincluded in the list, combined with organic compounds, but with mass flow rates of mixturesalmost double to those reported with the ammonia combinations.

Eiseman [E1] compared six halogenated absorption refrigerants in terms of their volubility,chemical stability, construction material decomposition and thermodynamic properties. Heconcluded that refrigerant R22 is to be preferred above all others, although it features anundesirable relative high pressure. The absorbent was Dimethyl ether-Tetraethylene glycol (anorganic solvent first used by Zellhoefer in combination with refrigerant R21) [E1, Z1, Z2].

Ammonia has been used for many decades as refrigerant for both absorption and compressionsystems. Therefore it could be treated as the centre of comparison for other refrigerants. Thereare of course certain drawbacks in using the ammonia-water combination in absorptionsystems:

1. ammonia is a toxic gas

2. it explodes when combined with the right amount of air

3. the condensing pressure is high

4. it becomes unstable at temperatures in the region of 170oC, producing inert gaseswhich have to be purged from the system. This becomes more apparent in the presenceof water


5. ammonia becomes very corrosive in the presence of water, to non-ferrous metals, inparticular to copper and its alloys. Therefore the construction of the units must beentirely of steel.

6. ammonia-water absorption plants require rectification. With good rectification, vapourconcentrations approaching unity is feasible. This can happen at the expense of thedistillate, part of which returns to the rectifier as reflux.

In past years the ammonia-water combination was used almost exclusively in absorptionsystems. It is only in the last two decades that other combinations have been considered andalthough higher coefficients of performance where achieved, there are still merits in theammonia-water combination, which have not, been overshadowed. Some of them are:

1. Water can absorb vast quantities of ammonia, therefore solution circulation rates andthe components involved are small.

2. A detailed data-bank exists for the thermodynamic properties of ammonia, water andtheir vapour and liquid mixtures.

3. Both ammonia and water can be obtained at low cost

4. If salts are added to the NH3-H2O mixture, such as LiNO3, LiSCN and NaSCN, thereis no need for vapour rectification. However, one must ensure against the danger ofcrystallisation.

An absorption machine designed for the ammonia-water combination still offers a largeground for study into more specific behaviour of its performance and in particular into theperformance of the components with respect to the mass and heat flow characteristics of theworking fluid.


1.5 Component analysis for 2-fluid systems

The absorption refrigeration system is composed of two cycles: namely, the refrigerant cycleand the solution cycle.

In the refrigerant cycle, the refrigerant goes through the condenser, the expansion valve andthe evaporator. In the solution cycle the refrigerant-absorbent solution goes through the socalled “thermal compressor” which consists of the absorber, the solution pump, the expansionvalve and the generator. All these comprise the simple absorption refrigeration cycle and theyare the minimum number of components the absorption refrigerator can have, Figure 1.5.

It has become an established procedure and practice to incorporate heat exchangers, in boththe refrigerant and the solution lines, in order to improve the cycle performance, Figure 1.6.

In the refrigerant line the vapour-liquid heat exchanger is placed between the condenser andthe expansion valve. This reduces the temperature of the liquid refrigerant prior to itsexpansion, thus increasing the refrigeration effect.

The absorber receives hot-weak solution from the generator, which has to be cooled first,before absorption can take place [M1]. On the other hand the generator receives cold-strongsolution from the absorber, which has to be heated, before liberation of the refrigerant cantake place. Therefore a major portion of generator energy requirement can be saved by aliquid-liquid heat exchanger, placed between the absorber and generator.

Figure 1. 5 Solution and vapour flow in the two-fluid absorption cycle


In the case where the absorbent is volatile, as for example in the water-ammonia mixture, adistillation column must be introduced between the generator and the condenser. This willimprove the purity of the refrigerant vapour, of course at the expense of the condenseddistillate, which is returned to the distiller as reflux. The distillation column complicates thethermodynamic analysis of the cycle and introduces a large increase in the cost of theabsorption machine.

1.5.1 Generator

The generator is the device through which heat is supplied to the solution in order to releasethe refrigerant from its absorbing medium. Its action is more complicated than just heating aliquid from one temperature to another. The generator’s process can be divided into a series ofstep processes [W3, M1]:

1. breaks up the bond of association between the refrigerant and the absorbent.

2. changes the temperature of the resulting liquid refrigerant to its saturation temperature.

3. vaporises the liquid refrigerant.

4 changes the temperature of the incoming strong solution to the generator’stemperature.

5. if the absorbent is volatile, it evaporates a certain amount of absorbent and raises itstemperature to the temperature of the generator.

1.5.2 Distillation column

Distillation is the process of separation, based on the difference in composition between aliquid and the vapour formed from it [R6]. In the case of the absorption refrigerator, thedistiller’s function is to enrich the refrigerant vapour by removing the vaporised absorbent. It

Figure 1. 6 Component arrangement of the improved absorption cycle


is placed between the generator and condenser and it can be either an integral part of thegenerator, or a separate component.

The generator-distiller integral component is used mainly for small capacity two-fluidabsorption machines and consists of a number of half-plates cascaded on top of the generator.The rising vapour comes into contact with the falling strong solution and thus it is “stripped”of the majority of the absorbent vapour. Ammonia concentrations in the region of 0.990 arefeasible.

The three-fluid absorption machines have only a tube connecting the generator to thecondenser, and the vapour is purified by condensation of the less volatile absorbent. Some ofthe refrigerant is also condensed and flows down the tube as reflux and therefore this tube isoften called “the reflux condenser”.

Reflux is of great importance in distillation practice, regardless whether the distiller is smallor large, a simple tube or an integral part of the generator. If reflux is absent, the distillerbecomes just a transfer line without the ability of distillation.

Distillation columns are classified into two general categories, in the way the separationprocess occurs:

1. the packed tower

2. the plate tower.

In the packed tower the separation occurs in a counter-flow action, between the rising vapourand the falling liquid.

In the plate tower, separation takes place from plate to plate in finite steps.

1.5.2.1 Packed towers

These are cylindrical columns, filled with uniform size particulate solids, Figure 1.7. On thesurface of these solids, contact occurs between the liquid and the vapour. The most common

Figure 1. 7


shape is the Raschig ring, Figure 1.7(a), a short hollow cylinder, having roughly the samelength as diameter [Y1].

These towers are the most popular, because of the low cost of construction, low pressure dropand high efficiency. But if mass flow rates require tower diameters in excess of 800mm,“channelling” occurs between the liquid and the vapour and there is no uniform reflux. Due tothe above, the plate-type tower is preferred for large scale operations.

1.5.2.2 Plate towersThese rectifying columns consist of an upright cylindrical shell, which has a number ofequally spaced horizontal plates. The rising vapour passes through the plates, while the liquidflows across the plate by gravity. The depth of the liquid is controlled by a weir positioned atthe end of the plate. The liquid flows over the weir and through down-pipes to the platebelow. The efficiency of contact between the gas and the liquid on a bubble plate, dependsupon complex hydraulic and diffuse phenomena, which in turn are functions of the fluids’properties and construction parameters of the plates [N3]. There are two types of plates whichare shown in the diagram of Figure 1.8:

1. the bubble-cup plate which consists of a number of slotted circular cups, positionedover vapour risers.

The bubble-cup distillation towers are efficient over a large range of flow rates, butthey are very costly due to the many components involved.

2. the sieve plate is no more than a flat plate punched with holes through which thevapour rises. The liquid flows across the plate and over the holes. The sieve plate has alow cost of construction, but it cannot operate through the same wide rate of flow rates

Figure 1. 8


as the bubble-cup. If the vapour flow rate is reduced by, between 50% to 70% of themaximum flow rate, the flow through the sieve plate becomes unstable. A furtherdecrease can result in a leakage of reflux liquid through the holes with a simultaneousdrop in efficiency.

1.5.3 Solution heat exchanger

The solution heat exchanger is part of the “thermal compressor”. Although it is not afundamental component for the absorption cycle, it is crucial to its performance.

It is of a simple design, that of the double tube, or a shell and tubes arrangement, with theweak hot solution flowing through the inner tube or tubes, while the cold strong solutionflows through the annulus in a counter-current direction.

Its function is to transfer heat from the hot weak solution to the cold strong solution and thusto reduce the amount of heat required at the generator and the amount of heat rejected fromthe absorber.

The design calculations in the past were simplified by assuming, either that there is a constanttemperature difference between the hot-end streams [R2], or that the strong solution maintainsits concentration right through the heat exchanger [K3, S13]. Practice has shown that it ispossible, for the strong solution to boil in the heat exchanger [V2].

1.5.4 Absorber

The absorber is involved in simultaneously occurring processes of mass and heat transfer. It isimportant, that the vapour pressure of the weak solution in the absorber is less than that of theevaporator. This will occur when the temperature of the weak solution is low. The absorberhas the function of ensuring a thorough mixing of the fluids, as well as removing the heat ofsolution released upon absorption. These functions lead to high efficiency demands on theabsorber whose performance is influenced by two main requirements.

Mass transfer requirement:

The absorption process must provide a contact area between the gas and the liquid solution aslarge as possible, with the ability to:

• increase the interface between the gaseous and liquid phases.• create a relative motion between the phases, thus increasing the mass transfer.

There are various existing designs of absorbers, which provide large contact areas. Theclassification according to the geometry of the absorber includes:

a. the packed column

b. the plate column

c. the bubble column

d. the spray column

e. the surface absorber or film absorbers


With respect to the creation of the interface between the liquid and the vapour, these absorberscan be grouped into three categories, Figure 1.9.

a. the liquid flows downwards over surfaces in the form of a thin film

b. the liquid is sprayed into the gas

c. the gas is injected into the liquid.

Heat transfer requirement:

The absorber must also provide a large area for heat transfer, because, in-order to satisfy themass transfer the temperature of the solution must be sufficiently low. Cooling the absorber isessential, but some absorbers, such as the packed and spray columns, might offer difficultiesin designing external cooling facilities.

To date, the predominant design of absorbers for refrigeration purposes is the water-cooledtype. With the development of the Von Platen Munsters unit for household refrigeration, theair-cooled absorber was introduced, but this is limited only to small refrigeration and air-condition units.

Figure 1. 9

CHAPTER 2 - ANALYSIS AND DESIGN OF AN ABSORPTION REFRIGERATOR 18

CH A P T E R 2

Part 1


2.02.0 GENERALGENERAL

The method of analysis presented in this chapter makes use of the ammonia-water enthalpy-concentration diagram. The enthalpy-concentration diagrams stem from the originaldevelopment of the treatment of binary mixtures by Mollier and Merkel, and are unique forevery binary absorbent-refrigerant mixture.

The following discussion on the graphical presentation of the absorption refrigeration processis based on the method developed by Bosnjakovic [B10]. He was an associate of Mollier, whoresearched the thermodynamic diagrams of binary mixtures and their application to a varietyof technological applications. This method can be found in a number of publications [C2, T2,W2], but up until now it has not been utilised to its full potential, as for example in designingand optimising an absorption refrigeration machine.

In the following sections, the cycle is analysed graphically and it will be shown that thecumbersome and complex mathematical analysis presented in textbooks and journals [R2,W3] can be substituted by a much easier to follow diagrammatic approach.

Literature search established that there were not available computerised equations estimatingthe enthalpies of the aqua-ammonia mixture that could compare accurately with the well-established enthalpy-concentration diagram.

Under the assumption that Bosnjakovic’s chart of aqua-ammonia [K10] represents the truevalues of the mixture, his chart was traced and the resulting curves were fitted with Fourierequations (Figure C1, APPENDIX C) [V2]. These equations are bounded between pure waterand pure ammonia concentrations and form an integral part of the computerised model.

2.12.1 PERFORMANCE OF AN ABSORPTION MACHINEPERFORMANCE OF AN ABSORPTION MACHINE

The absorption refrigeration machine could be treated theoretically as a combination of anengine producing work and as a refrigerator absorbing the same amount of work. Thetheoretical cycle analysis for an absorption machine shows that the coefficient of performance(COP) values obtained are much higher than the COP values obtained in practice.

With reference to the absorption refrigeration machine shown in Figure 2.1 (neglecting thework done by the solution pump WP) the overall heat balance can be written as:

QG QE QC QA QD+ ≥ + +

A corollary of the second law states that the COP of an ideal Carnot cycle operating betweentwo heat reservoirs depends only upon the temperatures of the heat reservoirs.

Assuming that the cooling temperatures for the distiller, condenser and absorber are equal to asink temperature TS, that is TD=TC=TA=TS, and also that the heat quantity QD can beincorporated in the heat rejected by the condenser, then for a generator’s temperature TG:

GT T

TQ

T TTG

G S

GE

S E

E

−

≤

−


For any absorption refrigeration system, the COP is defined as the ratio of the refrigerationcapacity to the amount of heat supplied to the generator.

Therefore the COP of the reversible cycle is given by:

COPQQ

TT

T TT T

E

G

E

G

G S

S E

= ≤−−

.

If values are assigned to the generator, evaporator and sink temperatures TG, TE and TS

respectively, then the coefficient of performance (COP) of the reversible cycle can berepresented in a graph similar to Figure 2.2. For example, if the generator is at 110oC and theevaporator and sink temperatures are at -20oC and 15oC respectively, then the theoretical COPis 1.79.

Figure 2. 1 Component arrangement of the single stage two-fluidabsorption system

Figure 2. 2 The effect of the temperature conditions on the COP of thereversible absorption refrigeration cycle.


The simulation, whichpredicts the performance ofa real machine (discussedlater in this chapter) forvarious temperatureconditions, produces curvesas shown in Figures 2.3 and2.4. The COP of a realcycle drops off after it hasreached a maximum value.

Figure 2.3 shows anincreasing gap between thereversible and real cycleCOPs.

As the temperature of theheat source increases, moreof the volatile absorbent isreleased together with therefrigerant. For this mixture

to be purified to the required concentration, more heat is rejected from the deflegmator.Concurrently the heat of reaction involved in both the generation and the absorption processesare highly irreversible. Therefore adopting the reversible cycle procedure to estimate the COPof the real absorption cycle is a totally impractical way.

For each sink temperatureTS it is possible to constructdiagrams similar to Figure2.4. Each curve is producedfor a specific evaporatortemperature, by simulatingdifferent temperatureconditions in the generator.As the generatortemperature increases, eachof these curves indicates asteep increase in thecoefficient of performanceuntil a maximum value isreached. This maximumpoint is identified by aparticular set of sink,evaporator and generatortemperature conditions.

Thus, at a given sink temperature TS, a family of the evaporator temperature curves depictsCOP maxima, as shown by the dots in Figure 2.4. Through these maxima, a curve is fittedwhich represents the maximum performance of the plant.

Figure 2. 3 Comparison of the COPs between a real and a reversiblecycle. Real cycle's data were obtained from author’s computerisedsimulation model.

Figure 2.4 Typical COP curves for a variety of evaporator andgenerator conditions


If this procedure is further extended to a range of sink temperatures, a surface of optimalconditions is produced. This surface has the characteristic that for every sink and evaporatortemperatures set, TS and TE respectively, an optimum generator’s temperature is identifiedwhich leads to a maximum coefficient of performance, Figure 2.5. These optimal generatortemperatures and COP maxima were obtained from simulated data, which were produced byvarying the generator temperature within a range of evaporator temperatures within a range ofsink temperatures.

For example, if the sink temperature (temperature of the condensate) is 30oC and refrigerationis required at -15oC, then the optimum temperature of the weak solution in the generator is92oC. These conditions predict a maximum COP of 0.586, (see Figure 2.5).

The equations which predict the optimum values of the coefficient of performance andgenerator temperature have the form of polynomials in eq. (2.1) and (2.2) respectively.

These relations apply for the temperature ranges: TS=5oC to 45oC and TE=-55oC to -5oC

(2.1) ( ) ( ) ( ) ( ) ( ) ( ) ( )COP f f T f

Tf

TTs Ts E Ts

ETs

E

max .= + + +0 1 2 32

1 1

(2.2) ( ) ( ) ( ) ( ) ( ) ( ) ( )T g g T g T g ToptTs Ts E Ts E Ts E8

0 1 2 2 3 3= + + +. . . T8 is taken to be the generator’s

representative temperaturewhere

(2.3) ( ) ( ) ( ) ( )f a a T a T a TTsj j j

Sj

Sj

S= + + +0 1 2

2

3

3. . . for j=0 .... 3

(2.4) ( ) ( ) ( ) ( )g b b T b T b TTsj j j

Sj

Sj

S= + + +0 1 2

2

3

3. . . for j=0 .... 3

Further the coefficients for eq. (2.3) and (2.4) above are tabulated below in Table 2.1.

Table 2.1COPmax T8

opt

a00 6.55132 x 10-1 b0

0 -7.26209

a10 -1.56484 x 10-2 b1

0 2.91205

a20 9.30096 x 10-4 b2

0 -1.86364 x 10-2

a30 -1.36564 x 10-5 b3

0 1.85319 x 10-4

a01 4.41648 x 10-3 b0

1 -2.58944

a11 -2.77987 x 10-4 b1

1 1.24279 x 10-1

a21 1.98907 x 10-5 b2

1 -4.42468 x 10-3

a31 -2.66527 x 10-7 b3

1 4.29658 x 10-5

a02 -6.19823 b0

2 -6.52162 x 10-2

a12 5.77539 x 10-2 b1

2 6.98244 x 10-3

a22 7.47419 x 10-3 b2

2 -2.38075 x 10-4

a32 -1.36508 x 10-4 b3

2 2.26658 x 10-6

a03 -32.7816 b0

3 -8.99504 x 10-4

a13 4.40948 x 10-1 b1

3 9.7008 x 10-5

a23 1.80843 x 10-2 b2

3 -3.27227 x 10-6

a33 -3.80018 x 10-4 b3

3 3.05454 x 10-8


Figure 2. 5 Optimisation curves for the ammonia-water absorption refrigeration machines


2.2.2.2. GRAPHICAL EVALUATION OF THE HEAT EFFECTS OFGRAPHICAL EVALUATION OF THE HEAT EFFECTS OFTHE ABSORPTION CYCLE.THE ABSORPTION CYCLE.

2.2.1. General

The analysis presented in this chapter, is based on the design of an aqua-ammonia absorptionrefrigeration plant given a desired evaporator temperature and refrigeration capacity. Thedesign will be explained with the aid of the enthalpy-concentration (h-x) diagram for the aqua-ammonia mixture as proposed by Bosnjakovic [B10].

In an attempt to support the proposed procedure in designing and optimising an ammonia-water absorption machine, certain methods from literature will be reviewed and discussed.

2.2.2 Individual component design of the plant

2.2.2.1 The evaporation process and estimation of the operatingpressures

In designing the evaporator of an absorption refrigeration machine, the following statementshould be considered:

“Once the refrigerant enters the evaporator, it receives heat and evaporates. The condition inthe evaporator depends upon the pressure-temperature-concentration equilibrium of theammonia-water mixture.”

Figure 2. 6


The diagram in Figure 2.6 shows liquid-vapour equilibria during the evaporation of a 0.900concentration mixture at 2bar vapour pressure.

The saturation temperature of the liquid with concentration 0.900 is approximately -18oC. Theconstruction diagram shows the concentration of its vapour at position a’. The remainingliquid (lower in concentration) receives heat at a higher temperature and its vapour is at alower concentration too. This remaining liquid could only evaporate completely at point b’where its saturation temperature is approximately 62oC. This is shown by the isotherm b-b’.

The construction lines in Figure 2.7 show complete vaporisation of different concentrationaqua-ammonia mixtures. The vapour at point b’ has concentration 0.950 and its saturationtemperature is approximately 50oC. A vapour with concentration 0.995 at point a’ is saturatedat a temperature approximately 20oC.

This illustrates that even at high concentrations approaching pure ammonia, completeevaporation of the refrigerant liquor, will require high saturation temperatures, which areundesirable in the evaporator.

Figure 2. 7


Despite the above, literature searchshows that it is customary, as anexercise, to assume saturated vapourconditions at the exit of the pre-cooler, such as points a’, b’ and c’, asshown in Figure 2.7. According toFigure 2.8 which shows a schematicevaporator and pre-cooler assembly,it is claimed by Threlkeld [T2], thatthe refrigeration effect is the enthalpydifference either (h5-h4) or (h6-h3),and assumes that point 6 is on thesaturated vapour curve. Thus therefrigeration effect is maximised.

This is exactly one of the stumblingpoints, where theoretical analyses presented in publications [R2, T2, W2] design theevaporator from data collected from existing plants and not from the refrigerationrequirements.

However, it is correctly assumed that at points 3 and 15 the liquid is saturated. As shown inFigure 2.9(a), the high and low pressure curves are drawn through the intersection pointsbetween an ammonia concentration x3 (a design parameter) and given sink TS and evaporatorT15 temperatures respectively. But what Figure 2.9(a) also shows is, that point 6 and itssaturation temperature T6 are established independently to the location of point 3, and henceto the sink temperature TS. Because points 3 and 6 belong to the “hot-side” streams of the pre-cooler, Figure 2.8, the exit temperature T6 must be always less or equal to the sinktemperature TS. Because this condition is violated in Figure 2.9(b), the assumption that point 6is saturated, is invalidated.

Of course there is aconcentration x3=x15,which together with thetemperature T15 willproduce a low pressurePLOW, such that thevapour at point 6 willhave a saturationtemperature T6 less or atleast equal to the sinktemperature TS. Butbecause PLOW-T15-x15

are linked with anequilibrium constraint,assuming a value foreither PLOW or x3

renders the procedureredundant.

Figure 2. 8

(a) (b)

Figure 2.9


Proposed procedureBefore any other process is analysed, a decision must be made on the purity of therefrigerant/absorbent mixture leaving the distillation column. The literature search on thesubject established that a concentration within the range of 0.990 to 0.995 is quite common.This mixture in the condenser and evaporator establishes the working pressures of the system.

The analysis of the evaporator (without a pre-cooler) using the enthalpy-concentrationdiagram, begins by assuming that the concentration of the ammonia is 0.990 and the averageevaporator temperature TE is given. The average evaporator temperature TE, is boundedbetween two limits, TEmin =T15 and TEmax=T5. The low temperature limit, T15 is thetemperature which the ammonia/water mixture attains at the entrance to the evaporator atpoint 15. The upper temperature limit T5 occurs at the exit of the evaporator, point 5. It is thedesigner’s task to define these two temperature limits.

From point 15, which is the inlet to the evaporator, and onward, the mixture receives heat atconstant pressure.

As the mixture passes through the throttling valve, it “flushes” and the first vapour producedwill have a concentration equivalent to the saturation point 15V along the isotherm T15 inequilibrium with the liquid at point 15L , Figure 2.10(a).

At ammonia concentrations such as 0.990 and higher, the isotherms are almost vertical lines.Also because the mass of the vapour produced at the throttling valve is negligible compared tothe liquid it can be assumed, within the accuracy of the enthalpy-concentration diagram, thatthe concentrations x15L and x3 are identical.

(a) (b)

Figure 2.10 Schematic h-x diagram of the evaporation process


The construction of Figure 2.10(b) starts with the location of point 15L at the intersection ofthe temperature curve T15 and the concentration line x3= 0.990. At this intersection, the lowpressure PLOW of the cycle is indicated.

The vapour point 15V is at the intersection of the isotherm T15 and the vapour low pressurecurve. With a similar construction, the isotherm T5 locates the points 5L and 5V at the lowpressure liquid and vapour curves respectively.

The environmental sink temperature TS intersects the 0.990 concentration line at point 3. Theliquid pressure curve which passes through point 3 is the high pressure of the cycle.

The concentration line x3 intersects the isotherm 5L-5V at point 5 which represents thecondition of the mixture at the exit of the evaporator. The refrigeration effect is the enthalpydifference (h5-h15).

2.2.2.2 Vapour-liquid heat exchanger (pre-cooler)

Since it is desirable that the enthalpy of the refrigerant be lower than it is when it leaves thecondenser, the use of a pre-cooler is indicated.

An energy balance around the pre-cooler yields:

h h h h QPR6 5 3 4− = − =

The maximum heat transfer QPRmax is:

( )C T T QPRmin max. 3 5− =

and the effectiveness is:

( )( )

E = =−−

QQ

T T C

T T CPR

PR

C

max min

.

.6 5

3 5

Since CC=Cmin the effectiveness becomes:

( )( )

E =−−

T T

T T6 5

3 5

For an effectiveness E=1, the above equationgives: T6=T3=TS.

Notwithstanding the comments in paragraph 2.2.2.1, the pre-cooler is designed to receivevapour at temperature T5 (evaporator’s design specification) and deliver vapour at atemperature approaching TS (condenser’s conditions).

According to Bosnjakovic [B10], the construction of Figure 2.11 shows the quantity QPRmax asthe enthalpy difference between point 3 and point G at the intersection of the temperature

Figure 2. 11


curve T5 with the 0.990 line. By assuming an effectiveness, E=0.7 the pre-cooler’s load is setas the enthalpy difference:

(h3-h4) = E .QPRrmax.

Figure 2.11 shows a condition in which point 5 is in the wet vapour region.

At concentrations near pure ammonia where the isotherms are almost vertical, the temperaturedifference (T5-T15) will approach zero and the vapour at point 5 will approach saturationconditions.

2.2.2.3 Determining the conditions at the condenser and the strengthof the strong solution required for the plant

With reference to Figure 2.1, the condenser receives vapour at point 1. This point represents ahigh pressure saturated vapour which has the same ammonia concentration as the saturatedliquid at point 3. In Figure 2.12, the vapour high pressure curve together with theconcentration 0.990 locates point 1. The enthalpy difference (h1-h3) is the condenser’s load QC

per kg of refrigerant.

The low pressure curve and the sink temperature TS intersect at point 7 which fixes theconcentration of the strong solution xST.

After the action of the pump, the strongsolution at point 13 (see Figure 2.1) maintainsits concentration and it is at high pressure, butwith hardly any change in temperature. Theposition of point 13 can be established, oncethe increase of the solution’s enthalpy due tothe work WP of the pump is calculated.Because WP is small compared to the other heateffects in the cycle, point 13 is expected to bevery close and above point 7. The process tolocate point 13 is described in paragraphs2.2.2.6 and 2.2.2.7.

The strong solution concentration lineintersects the high pressure curve at point 10eq.Through this point the temperature curve T10eq

passes which represents the state at whichvapour liberation is initiated.

Figure 2. 12 h-x diagram


2.2.2.4 Determining the conditions at the generator

The next step aims at establishing the concentration of the weak solution leaving the generatoron its way to the absorber at point 8. This is achieved in the following way:

With reference to Figure 2.13, Point 7 represents the conditions of the strong solution as itleaves the absorber. The strong liquor is pumped through the heat exchanger, (see Figure 2.1)from a non-equilibrium state at point 13 and arrives at the generator at a condition describedby point 10. Heat supplied to the generator raises the temperature of this liquor to itssaturation condition at point 10eq. At this point extra heat supplied to the generator willliberate ammonia and will increase the saturation temperature of the solution to values higherthan T10eq. Any of these temperatures could be the representative generator temperature T8,which immediately establishes the concentration of the weak solution xWE.

Figure 2. 13


It is precisely at this point that the procedure demands improvement. Surely this is the pointwhere the designer requires the optimum generator conditions. If the conditions in thegenerator are not optimised, then the heat demand in the generator is not minimal. This isexplained by the following step-by-step procedure:

The isotherms through points 8 and 10eq intersect the vapour high pressure curve at points 1A

and 1B. These are the vapour points in equilibrium with the weak solution and strong solutionsrespectively. The T8 and T10eq isotherms, when extended intersect the refrigerant ammoniaconcentration line at points 1C and 1D.

When the generator operates at a temperature T8, according to distillation theory [F1], point 1C

represents the point of minimum reflux. The enthalpy difference (h1c-h1) is the heat QD

rejected from the deflegmator.

Assume that the strong solution is heated inthe heat exchanger from its condition atpoint 13 to a temperature T10 that passesthrough point 10 on the xST concentrationline, Figure 2.13.

The generator receives strong solution withconcentration xST at a mass flow rate of (f)kg so that 1kg of vapour with concentrationy is released, Figure 2.14.

At the same time (f-1) kg of weak solutionwith concentration xWE is returned to theabsorber.

A heat balance on the ammonia flowthrough the generator/distiller yields:

(2.5) ( ) ( )Q Q f h h h hG D− = − + −. 8 10 1 8

and the mass balance gives:

( )y x f f xWE ST. . .1 1+ − =

or

(2.6) fy x

x x

WE

ST WE=

−−

On the h-x diagram of Figure 2.13, a point “A” can be located on the y concentration suchthat:

( )h h f h hA = − −8 8 10.

Figure 2.14 Mass and heat fluxes around thegenerator and deflegmator. Refer to Figure 2.1 foractual position within the plant.


This is the equation of a straight line of negative slope (f), joining point 8 to point A andpassing through point 10.

Substituting into eq. (2.5) the heat required by the generator becomes:

(2.7) Q Q h hG D A= + −1

Eq. (2.6) is represented in Figure 2.13 by the ratio of the linear segments that constitute theline 8-A. If a unit length is assigned to the length (xST-xWE), then (y-xWE) = f and (y-xST)=f-1.From the similar triangles 8-K-A and 10-L-A it can be observed that the ratio (8-10):(10-A)represents the ratio of the mass flow rates of the vapour to the weak solution. That is, 1:(f-1)

Eq. (2.6) also indicates that the rate of relative circulation (f), is inversely proportional to theconcentration difference (xST-xWE). Since the concentration xST is fixed, it can be depictedfrom Figure 2.13 that (xST-xWE) depends on the temperature difference (T8-T10eq).

If the generator’s temperature T8 is reduced towards the limit temperature T10eq, point 1C willalso reduce towards the low limit point 1D, and the difference (xST-xWE) will diminish. Theformer reflects to the deflegmator’s heat QD approaching a minimum value (h1D-h1), and thelatter reflects to a rapid increase in the heat rate through the generator, due to an excessivelyhigh rate of relative circulation (f).

This is shown by the big solid arrows on the enthalpy-concentration diagram of Figure 2.13,which together with eq. (2.7) indicates that larger amounts of heat have to be supplied to thegenerator in order to maintain a constant mass rate of vapour.

On the other hand an increase of the generator temperature leads to a steeper isotherm T8 thatin turn corresponds to a larger amount of heat QD rejected from the deflegmator. This alsoincreases rapidly the heat demand in the generator, which is shown by the big hollow arrowson the enthalpy-concentration diagram.

In addition to the above, for a particular temperature T8, a reduction of the heat demand QG isindicated as T10 approaches T10eq.

In order to minimise the heat QG required by the generator1 the temperature T8 must beoptimised to T8

opt and the heat exchanger must be designed to supply the solution at itssaturation temperature T10eq.

1 The term “heat required by the generator” represents the net heat received by the fluids in the generator/distiller

assembly, for the production of a constant vapour mass rate at concentration y at the exit of the distillation column.


2.2.2.5 Purification of the refrigerant mixture

Rectification is a well-known process and literature is available for a vast number of mixtures.

Due to mixing of the solutions in the generator, it is assumed that the bulk solution has aconcentration which is the average between the weak and strong solutions. This solution hasconcentration xM and is in equilibrium with its vapour of concentration y11 leaving thegenerator, Figure 2.15. Since the vapour concentration y11 is less than the ammoniaconcentration 0.990 at point 1, vapour purification is required.

The purity of the refrigerant ammonia/water vapour mixture leaving the distillation column atpoint 1, can be achieved by a number of plates in the column determined by either of the twowell known methods:

• the MCCabe-Thiele method, which uses a graphical approach plotting values on a vapourconcentration versus liquid concentration diagram. This method requires a priorknowledge of the required reflux ratio.

Figure 2.15 The Ponchon-Savarit diagram depicting the generator’s and the concentratingcolumn’s working conditions for an aqua-ammonia mixture at 10bars pressure


• the Ponchon-Savarit method, in which specific enthalpy values of the binary mixture areplotted against liquid-vapour concentrations. This is a most popular approach as inderiving the number of theoretical plates, the reflux ratio can also be established. Thismethod is illustrated in Figure 2.15 and supported by the explanation to follow:

For any part of the column between two cross-sections, such as “a” and “b” in Figure 2.16,the mass flux entering the control sectionequals that leaving:

M M M Mya xa yb xb− = −

The same relationship holds for any othercontrol section along the column and thereforeit must equal to a constant. If the controlsection includes the deflegmator, that isbetween sections “1” and “i” the constant willbe the mass flux of the distillate.

Thus the mass balance equation becomes:

M M Myi xi− = 1

The conservation of ammonia mass betweensections “i” and “1” yields:

M y M x M xyi i xi i. . .− = 1 1

The heat balance around the deflegmatoryields:

M h M h M h Qyi yi xi xi D. . .− = +1 1

A combination of the above equations gives the governing equation for the deflegmator’s heatper kg of distillate.

M

M

y x

y xyi i

i i1

1=−−

( ) ( )M

Mh h h h

QM

yiyi xi xi

D

11

1

. − = − +

If the control section includes the whole distillation column, then xi and yi are substituted byx12 and y11 respectively.

The distillation column receives vapour of concentration y11 at point 11 and returns to thegenerator solution of concentration x12 at point 12, Figure 2.16.

Figure 2. 16


The concentration x12 is identified by constructing the Ponchon-Savarit diagram of Figure2.15 in the following way:

The vapour at point 11 is saturated and in equilibrium with the mixture with concentration xM.

The position of the pole π min is located at the extension of the line joining points 8 and 11 tothe ammonia concentration 0.990 line [B10, F1]. An operation under this pole position would

require an infinite number of plates in the column. The position of the operating pole π is atthe extension of the line joining points 10eq and 11 to the ammonia concentration 0.990, [F1]

Starting from point 1 (y1=0.990), a horizontal line meets the construction curve at point “b”from which a vertical line locates point “a1” on the liquid high pressure line. The reflux liquidat point “a1” is in equilibrium with the vapour at point 1 and these two points are joint with

the isotherm (a1-1). The section line from the pole π to point “a1” intersects the vapour highpressure line at a point “a”. Since the liquid at point “a1” has concentration higher than that ofthe strong solution (which is considered the “feed” to the column), a second plate is required.A similar construction for the second plate locates point 12 on the liquid high pressure line.Since the reflux liquid at point 12 has concentration less than that of the feed (point 10eq) athird plate is not required.

It can be seen from Figure 2.15 that the location of the reflux liquid at point 12 is very close tothat of the bulk solution at point M.

Construction of diagrams similar to that of Figure 2.15 for different pressures andcombination of weak and strong solutions, also indicate the same result.

It was felt appropriate to assume that the concentrations of the reflux liquid x12 and of the bulksolution xM are equal.

Thus the reflux heat QD is measured in relation to known quantities:

(2.8) ( ) ( )Q My xy x

h h h hD =−−

− − −

1

1 12

11 1211 12 1 12. .

The quantityQ

MD

1

is the heat rejected from the deflegmator for the production of 1kg of

distillate of concentration y1.

The amount of the reflux liquid MR to the top plate of the column is calculated by:

(2.9) M M RR = 1 .

where R is called Reflux Ratio, which is defined as:

(2.10) R

Q

M

h h

D

=−

1

1 3

The above quantities can be evaluated graphically on the enthalpy-concentration diagram asshown in Figure 2.15.


2.2.2.6 The solution pump

A heat balance around the pump gives:

( )W f h hP = −. 13 7

This value is reflected by the enthalpy difference (hB-hA) in Figure 2.15. The enthalpy difference (h13-h7) isequal to the heat supplied to the strong solution. Thepump load WP is proportional to the specific volume ofthe solution vf:

(2.11) ( )W f P PPP

High Low f= −1

ην. . .

where ηP is the mechanical efficiency of the pump.

and vf is calculated by the polynomials described in section 2.4.4

2.2.2.7 Optimising the solutionheat exchanger

The strong solution in the stream betweenpoints 13 and 10 receives heat from the hotsolution in the streams between points 8 and 9,Figure 2.17.

Thus, the temperature of the strong solutionwill rise along the same concentration xST,from point 13 to point 10, while thetemperature of the weak solution will fallalong the same concentration xWE, from point8 to point 9, Figure 2.18.

An energy balance around the heat exchangerin Figure 2.17 would give:

h h

h h

f

f8 9

10 13 1

−−

=−

The strong solution at point 13 is notsaturated, hence the location of point 13 isfound indirectly after the pump’s load isevaluated by eq. (2.11).

On the y concentration line of Figure 2.18, apoint B is located such that the enthalpydifference (hB-hA) = WP. A line joining point

B to point A, intersects the strong solution concentration line at point 13.

Figure 2. 17

Figure 2. 18


If the heat exchanger supplies the strongsolution at a condition described by point 10,then point C is located at the extension of theline 8-10 to the y concentration line. Theenthalpy difference (h10-h13) is the heatreceived by the strong solution per kg ofstrong solution. This quantity is equivalent tothe enthalpy difference (hB-hC) per kg ofvapour of concentration y and it is shown bythe triangles 8-10-13 and 8-C-B.

It is also the same heat supplied by the weaksolution. A line drawn from point C throughpoint 13 intersects the weak solutionconcentration line at point 9. The enthalpydifference (h8-h9) is the heat supplied by theweak solution per kg of weak solution.

From Figure 2.18, the triangles C-8-9 and C-10-13 show that the heat (f-1).(h8-h9) is theequal to the heat (f).(h10-h13).

The limit position of point 9 is shown inFigure 2.19 where T9=T13 and the weaksolution imparts the maximum heat to thestrong solution.

If the amount of heat exchanged is sufficient to raise the temperature of the strong solutionbeyond the equilibrium point 10eq, that is (h10-h13)>(h10eq-h13), then boiling will occur andthere will be a change in the concentration of the strong solution. The total concentration ofpoint 10 in Figure 2.19 is xST, but the liquid and the vapour have concentrations correspondingto the equilibrium points 10L and 10V respectively.

Because in the presence of a two-phase flow in tubes there is a notable reduction of the heattransfer coefficient, this is an undesirable condition in the heat exchanger. Therefore the heatexchanger should be designed to deliver the strong solution at its equilibrium temperaturemarked by point 10eq.

2.2.2.8 The absorption process

The absorber receives a weak solution at point 14, the properties of which depend upon thethrottling of the solution at point 9. A heat and mass balance around the throttle, Figure 2.20would give:

h h x x xWE9 14 9 14= = =

The throttling of the weak solution is shown in the h-x diagram of Figure 2.21 where, points 9and 14 coincide, but the respective streams have different state properties.

Figure 2. 19


A heat balance around the absorber in Figure2.20 gives:

(2.12) ( )Q h h f h hA = − + −6 9 9 7.

Which is represented by the line

Q h hA K= −6

Point K is located on the y concentration line such that: ( )h h f h hK = − −9 9 7.

The line 14-6 represents the mixing linebetween the weak solution and thevapour. If the mixing is doneadiabatically, the resulting solution willhave concentration xST and enthalpyh7

*. The process between points 7 and7* is entirely in the wet vapour regionand because the absorber delivers liquidand not vapour, the wet vapour mixtureat point 7* must be liquefied. The totalheat QA rejected from the absorberduring this process is the sum of theheat (hL-hK) involved to cool the weaksolution and the heat of mixing (h6-hL).This is equivalent to the heat QA/frejected from the absorber per unit massof strong solution.

Figure 2. 20

Figure 2. 21 The throttling of the weak solution and theabsorption processes


2.32.3 A CASE STUDYA CASE STUDY

The examples discussed in references [R2] and [T2] are typical cases of analyses for existingunits. The present example will demonstrate the usage of the h-x diagram for a possiblesolution to a refrigeration demand. The h-x diagram of Figures 5.22 to 5.25 is that of [K10].

2.3.1 Problem statement

It stems from the discussion of section 2.2.2.1, that the evaporator temperature will not beconstant. Therefore a range of working temperatures must be specified rather than a singleevaporator temperature.

Assume that, due to refrigeration requirement the cooling coils must be designed to operatebetween -15oC and -12oC. Also due to cooling in the condenser and absorber the temperatureof the condensate and of the solution is 30oC.

2.3.2. A step-by-step analysis

Step-1 Determining the operating pressures of the system

The analysis begins with an assumed value of the concentration of the condensate (which isusually quite high) 0.990

On the h-x diagram, Figure 2.22, a vertical line is drawn at the 0.990 concentration valuewhich intersects the 30oC and the -15oC temperatures, which constitute the design conditions.The intersection points 3 and 15L determine the high pressure (11.34bar) and low pressure(2.2bar) respectively.

Step-2 Determining the inlet and outlet conditions of the cooling coils

The evaporator exit temperature -12oC, also a design condition, marks point C on the liquidlow pressure line and point E on the vapour low pressure line, Figure 2.22. The isotherm C-Ecrosses the 0.990 concentration line at point 5 which marks the state of the wet vapour at theevaporator’s exit.


The -12oC temperature curve intersects the 0.990 concentration line at point G. The enthalpydifference (h3-hG) indicates the theoretical maximum heat transfer through the pre-cooler. Inthis procedure, 70% of this maximum heat is transferred from the condensed liquid to the coldvapour.

Thus point 4 is established and the heat (h5-h4) specifies the refrigeration effect (1180.91kJ/kg). The exit of the pre-cooler, point 6 can be located on the y=0.990 concentration verticalline such that (h6-h5)=(h3-h4).

Step-3 Determining the condenser’s condition

Vapour from point 1 condenses to liquid at point 3. Point 1 is located at the intersection of thevapour high pressure line and the concentration 0.990. The enthalpy difference (h1-h3) is theheat rejected from the condenser (1265 kJ/kg)

Step-4 Determining the strong solution concentration

The strong solution concentration is obtained by drawing a vertical line from the intersectionof the low pressure and the design sink temperature TS=30oC, to the base, Figure 2.23. Thestrong solution concentration line intersects the liquid high pressure line at point 10eq. Thispoint marks the minimum temperature for vapour liberation from the generator.

Figure 2. 22


The temperature contours above T10eq mark the range of possible generator workingtemperatures which will produce the same refrigeration effect and heat rejection from thecondenser.

Step-5 Optimisation of the generator’s temperature

From Figure 2.5, the design sink and evaporator temperatures TS=30oC and T15=-15oCrespectively, give the optimum weak solution temperature in the generator T8

opt=92oC. Thistemperature curve is highlighted in Figure 2.23.

Step-6 Determining the weak solution concentration

The weak solution concentration is obtained by drawing a vertical line from the intersection ofthe high pressure line and the weak solution temperature T8

opt, to the base.

Step-7 Determining the deflegmator’s heat effects and the Pole position π

Figure 2. 23


Point M on the high pressure line is the average concentration of the bulk solution in thegenerator and is at equilibrium with its vapour at point 11, Figure 2.23. The extension of theoperating section-line 10eq-11 of the distillation column intersects the 0.990 concentration line

at the pole position π. The heat (hπ-h1)=145.66kJ/kg is rejected from the deflegmatornecessary to produce vapour at concentration 0.990, at point 1.

The ratio of the enthalpy differences (hπ -h1)/(h1-h3) is the reflux ratio.

Step-8 Determining the circulation rates of the solutions and the heat effects of thepump, heat-exchanger, absorber and generator

The extensions of the lines 8-10eq and 8-7 meet the 0.990 concentration line at points F and Drespectively, Figure 2.24. The work required by the pump WP is calculated according to eq.(2.11) and the polynomials (2.15) and (2.16) in section 2.4.4. This value is estimated asWP=1.38 kJ per kg of strong solution. Thus point 13 could be located above point 7, such that(h13-h7)=1.37 kJ/kg. Because this is such a small quantity, it is difficult to locate point 13directly.

Since the line 8-D represents the ratio of the mass rates, the lever rule is applied to locatepoint L on the 0.990 concentration line, such that the ratio (8-7):(8-D) = (7-13):(D-L) = 1:f.

This ratio establishes the mass flow rate of the strong solution f = 13.76 kg/kg of refrigerant.The work required by the pump is then (f).WP = 19 kJ/kg of refrigerant and this locates pointL above point D. The line 8-L intersects the strong solution concentration line at point 13.

Point 9 is located at the intersection of the extension of the F-13 line and the weak solutionconcentration line. The weak solution gives up heat which is measured along its concentrationline as the difference (h8-h9) per kg of weak solution. This heat is gained by the strongsolution and is measured along its concentration line as the difference (h10eq-h13) per kg ofstrong solution.

The heat difference (h10eq-h13) per kg of strong solution is equivalent to the enthalpy difference(hF-hL)=3367.74kJ/kg of refrigerant. The heat required by the generator is the enthalpy

difference (hπ-hF)=2029.47kJ/kg and the heat rejected from the absorber is the enthalpydifference (h6-hK)=1818.76kJ/kg.

It can be observed from Figure 2.24 and the above analysis, that the absorber and the heatexchanger are the only two components to be affected if the work of the pump is not included.The error involved in the heat exchanger in this case will be 0.56% and for the absorber1.04%

Step-9 Determining the COP

The coefficient of performance of the above optimised cycle is calculated as the ratio of therefrigeration effect (measured in step-2) and the heat required by the generator (measured instep-8). This ratio is 0.582 and it verifies the predicted maximum coefficient of performance(COPmax = 0.586) obtained by the optimisation curves of Figure 2.5


2.3.3 Comments on the optimisation procedure

Figures 2.24 and 2.25 show the final steps towards the optimisation of the plant. However, itcan be observed that a large amount of heat is exchanged in the heat exchanger.

In an attempt to justify the above, let it be assumed that points 8 and 10eq coincide, in whichcase points 9 and 13 will coincide too. In the diagram of Figure 2.24, this will reflect to theline 8-D being parallel to the concentration line 0.990. This will translate to an “infinite” massflow rate through the heat exchanger and of course an “infinite” heat exchanged between thesolutions. Apart from the heat exchanger becoming 100% efficient, the heat supplied to thegenerator (QG+QEX) will only maintain a hot solution circulation through the heat exchangerwithout any vapour being produced. This condition refers to the “cut-off” point or the“minimum” temperature T8 depicted in the performance curves of Figures 2.3 (real cycle) and2.4.

Because of the almost vertical rise in the coefficient of performance at temperatures close toT8=T10eq, the mass and heat rates in the heat exchanger are still excessively high, whichrenders its size much larger than any other component in the plant. For this purpose a limit hasto be imposed to the relative size of the heat exchanger.

In the production of data for the optimisation curves of Figure 2.5, the heat exchanger’s heat islimited to twice the heat required by the generator. Hence, all the generator's temperaturesbelow the one corresponding to this limit are omitted. Of course this limitation does not applywhen the full trend of performances is required. In the above example, the heat exchanger’sheat is about 1.66 times the heat required by the generator (see Figure 2.24).


Figure 2. 24


Figure 2. 25 The complete graphical presentation of the heat effects of the optimised absorption cycle

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TThhee hhiigghh pprreessssuurree iinn tthhee ccoonnddeennsseerr iissddeetteerrmmiinneedd iitteerraattiivveellyy.. IItt iiss nnoott aassssttrraaiigghhttffoorrwwaarrdd aann aapppprrooaacchh aass tthhee lloowwpprreessssuurree,, bbeeccaauussee ooff tthhee pprreesseennccee ooff tthheepprree--ccoooolleerr aanndd ooff tthhee vvaappoouurr fflluusshhiinngg aatttthhee eexxppaannssiioonn vvaallvvee.. TThhee iitteerraattiivveepprroocceedduurree iiss ssuuppppoorrtteedd bbyy FFiigguurreess 22..2266aanndd 22..2277 aanndd iiss eexxppllaaiinneedd aass ffoolllloowwss::

TThhee PP--TT--xx rreellaattiioonn hhaass ttwwoo uunnkknnoowwnnffaaccttoorrss,, vviiss.. PPhhiigghh aanndd xx33

SSuuppppoossee aa mmiixxttuurree ooff ccoonncceennttrraattiioonn xx33’’ lleeaavveess tthheeccoonnddeennsseerr..

FFiigguurree 22..2277 ddeeppiiccttss tthhee wwaayy iinn wwhhiicchh tthhee hhiigghh pprreessssuurreeiiss ddeetteerrmmiinneedd wwiitthh tthhee aaiidd ooff tthhee eenntthhaallppyy--ccoonncceennttrraattiioonn ddiiaaggrraamm..

TThhee ssiimmiillaarriittyy ooff tthhee ttrriiaanngglleess 44--1155LL--BB aanndd 1155VV--1155LL--DDggiivveess tthhee ffoolllloowwiinngg rreellaattiioonn::

((22..1133))x xy x

h h

h hy x

x

3 15

15 15

15 15

4 15

' −−

=−

−

TThhee qquuaannttiittiieess yy1155,, hh1155yy aanndd hh1155xx ccaann bbee ddeetteerrmmiinneedd bbyytthhee pprrooppoosseedd rreellaattiioonnsshhiippss ddeessccrriibbeedd iinnAAPPPPEENNDDIICCEESS AA aanndd BB..

FFrroomm tthhee aabboovvee rreellaattiioonn,, tthhee ccoonncceennttrraattiioonn xx33’’ iiss aannuunnkknnoowwnn ffaaccttoorr tthhaatt ccaann bbee eevvaalluuaatteedd oonnccee hh44 iissddeetteerrmmiinneedd uussiinngg hheeaatt ttrraannssffeerr rreellaattiioonnss..

WWiitthh rreeffeerreennccee ttoo FFiigguurree 22..2266 tthhee mmaaxxiimmuumm hheeaattttrraannssffeerr iiss bbeettwweeeenn TT33 aanndd TT55.. PPooiinntt ““AA”” ccaann bbeellooccaatteedd iinn FFiigguurree 22..2277 aass tthhee iinntteerrsseeccttiioonn ooff tthhee TT55

iissootthheerrmm wwiitthh tthhee xx33’’ ccoonncceennttrraattiioonn lliinnee,, ssuucchh tthhaatt hh33’’--hhAA==QQPPRRmmaaxx.. PPooiinntt ““AA”” iiss tthhee lloowweesstt lleevveell tthhaatt ppooiinntt 44

ccaann rreeaacchh aalloonngg tthhee ccoonncceennttrraattiioonn lliinnee xx33’’.. TThhee eenntthhaallppyy hhAA iiss eevvaalluuaatteedd aatt aa ffiiccttiittiioouussssaattuurraatteedd pprreessssuurree PPAA,, uussiinngg aa PPAA--TT55--xx33’’ rreellaattiioonnsshhiipp..

IItt iiss uuppoonn tthhee ddeessiiggnneerr’’ss ddeecciissiioonn ttoo pprreeddeetteerrmmiinnee tthhee eeffffeeccttiivveenneessss ooff tthhee pprree--ccoooolleerr.. AAnnaacccceeppttaabbllee vvaalluuee ffoorr aa vvaappoouurr--lliiqquuiidd hheeaatt eexxcchhaannggeerr iiss EE==00..77.. TThheerreeffoorree ppooiinntt ““44”” ccaann bbeellooccaatteedd oonn tthhee xx33’’ ccoonncceennttrraattiioonn lliinnee,, ssuucchh tthhaatt hh44==hh33’’--((hh33’’--hhAA)).. EE

TThhee ccoonncceennttrraattiioonn xx33’’ aanndd tthhee eenntthhaallppyy hh44 aarree ccaallccuullaatteedd wwiitthhiinn aann iitteerraattiivvee lloooopp uunnttiill tthheeccoonncceennttrraattiioonn xx33’’ ccoonnvveerrggeess..

AAss aa bbyy--pprroodduucctt ooff tthhiiss iitteerraattiivvee ccaallccuullaattiioonn,, tthhee ssaattuurraatteedd hhiigghh pprreessssuurree PPHHIIGGHH ooff tthhee ssoolluuttiioonnwwiitthh ccoonncceennttrraattiioonn xx33 iiss aallssoo eessttiimmaatteedd aanndd uuppddaatteedd..

FFiigguurree 22.. 2266



CCAALLCCUULLAATTIIOONNSSAAppppllyyiinngg eeqq.. ((22..1133)),, tthhee ffoolllloowwiinngg vvaalluueess aarree ccaallccuullaatteedd::WWiitthh PPLLOOWW==22..119988 bbaarrss aanndd xx1155==00..999900

eeqq..((bb11)) ggiivveess:: hh1155xx==--7777..8899 kkJJ//kkggeeqq.. ((bb33)) ggiivveess:: hh1155yy==11224433..4422 kkJJ//kkgg

WWiitthh TT1155==225588..1155 KK aanndd xx1155==00..999900eeqq.. ((cc11)) ggiivveess:: yy1155==00..99999999999922

TT55==--1122ooCC==226611..1155 KK ((aassssuummee 33ooCC iinnccrreeaassee iinn rreeffrriiggeerraanntt tteemmppeerraattuurree iinnssiiddee tthhee eevvaappoorraattoorr))aanndd wwiitthh tthhee aassssuummppttiioonn tthhaatt xx33’’==00..999900,,

eeqq.. ((aa11)) ggiivveess:: PPAA==22..55001166 bbaarrss

WWiitthh PPAA==22..55001166 aanndd xx33’’==00..999900eeqq.. ((bb11)) ggiivveess:: hhAA==--6633..996644 kkJJ//kkgg

WWiitthh TT33==2255ooCC==229988..1155 KK aanndd xx33’’==00..999900,,eeqq.. ((aa11)) ggiivveess:: PPHHIIGGHH==99..771188 bbaarrss

WWiitthh PPHHIIGGHH==99..771188 aanndd xx33’’==00..999900eeqq.. ((bb11)) ggiivveess:: hh33’’==110099..776677 kkJJ//kkgg

QQPPRRmmaaxx== hh33’’-- hhAA==117733..7733 kkJJ//kkgg

WWiitthh tthhee aassssuummppttiioonn tthhaatt tthhee pprree--ccoooolleerr’’ss eeffffeeccttiivveenneessss iiss EE==00..77,,QQPPRR==00..77xx117733..7733==112211..661122 kkJJ//kkgghh44==hh33’’-- QQPPRR==--1111..884444 kkJJ//kkgg

TThheenneeqq.. ((22..1133)) ggiivveess:: xx33’’==00..9999004499

AAfftteerr aa mmuullttiippllee iitteerraattiioonn tthhee eenndd vvaalluueess aarree::PPHHIIGGHH==99..773311 {{22}}hh33==111100..1111 kkJJ//kkgg {{33}}hh44==--1111..4444 kkJJ//kkgg {{44}}xx33==00..9999005500 {{55}}QQPPRR==112211..554499 kkJJ//kkgg


22..44..22 DDeetteerrmmiinnaattiioonn ooff tthhee eevvaappoorraattoorr ccooiill aanndd pprree--ccoooolleerr ccoonnddiittiioonnss

TThhee mmiixxttuurree aatt ppooiinntt 55 iiss aa wweett vvaappoouurr.. TThheettoottaall eenntthhaallppyy hh55 wwiillll bbee ccoonnssttiittuutteedd bbyy tthheepprrooppoorrttiioonnss ooff ssaattuurraatteedd vvaappoouurr aanndd ssaattuurraatteeddlliiqquuiidd,, FFiigguurree 22..2288..

TThhee eenntthhaallppyy ooff tthhee vvaappoouurr aatt tthhee eexxiitt ooff tthheepprree--ccoooolleerr iiss eevvaalluuaatteedd uussiinngg tthhee hheeaatt bbaallaanncceeeeqquuaattiioonn hh66==hh33++hh55--hh44.. TThhee tteemmppeerraattuurree TT66 oofftthhee vvaappoouurr hhoowweevveerr,, iiss ccaallccuullaatteedd iitteerraattiivveellyy.. IIttiiss aaddjjuusstteedd uunnttiill aa ccoonncceennttrraattiioonn--pprreessssuurreeccoommbbiinnaattiioonn xxSS66--PPLLOOWW wwiillll ggiivvee tthhee ttoottaalleenntthhaallppyy ooff tthhee mmiixxttuurree hh66..


WWiitthh TT55==226611..1155 KK aanndd PPLLOOWW==22..119988 bbaarrss aanndd uussiinngg SSiimmppssoonn’’ss rruullee oonn eeqq ((aa11)) ttoo eevvaalluuaattee xx55,,eeqq.. ((aa11)) ggiivveess:: xx55==00..8811888866

WWiitthh xx55==00..8811888866 aanndd TT55==226611..1155 KK,,eeqq..((cc11)) ggiivveess:: yy55==00..999999996688

AA cchheecckk wwhheetthheerr tthhee mmiixxttuurree iiss aa ssuuppeerrhheeaatteedd oorr aa wweett vvaappoouurr iiss bbaasseedd oonn FFiigguurree 22..2288 aanndd iissaass ffoolllloowwss::

my xy x

mS55 3

5 33=

−−

. ==00..005522223355 kkgg//ss

wwhheerree mmSS55 iiss mmaassss ooff tthhee eennttrraaiinneedd lliiqquuiidd iinn tthhee mmiixxttuurree aanndd iitt mmuusstt bbee ppoossiittiivvee ffoorr aa wweettvvaappoouurr ccoonnddiittiioonn..

KKnnoowwnn ppaarraammeetteerrss UUnnkknnoowwnn ppaarraammeetteerrssttoottaall mmaassss ooff rreeffrriiggeerraanntt -- MM55 ttoottaall mmaassss ooff ssaattuurraatteedd ssoolluuttiioonn -- MMSS55

ttoottaall ccoonncceennttrraattiioonn ooff rreeffrriiggeerraanntt xx33 ttoottaall mmaassss ooff ssaattuurraatteedd vvaappoouurr -- MMVV55

ccooiill eexxiitt tteemmppeerraattuurree -- TT55 eenntthhaallppyy ooff ssaattuurraatteedd ssoolluuttiioonn -- hhSS55

llooww pprreessssuurree -- PPLLOOWW eenntthhaallppyy ooff ssaattuurraatteedd vvaappoouurr -- hhVV55



TThheenn tthhee mmaassss ooff tthhee vvaappoouurr iiss:: mmVV55==mm55--mmSS55==11-- mmSS55==00..9944777766 kkgg//ss

WWiitthh PPLLOOWW==22..119988 bbaarrss aanndd yy55==00..999999996688eeqq.. ((bb33)) ggiivveess:: hhVV55==11224433..8866 kkJJ//kkgg

WWiitthh PPLLOOWW==22..119988 bbaarrss aanndd xx55==00..8811888866eeqq.. ((bb11)) ggiivveess:: hhSS55==--118800..447700 kkJJ//kkgg

TThhee ttoottaall eenntthhaallppyy aatt ppooiinntt 55 iiss::hh55== mmSS55.. hhSS55++ mmVV55.. hhVV55

hh55==11116699..446611 kkJJ//kkgg {{66}}TThhee ttoottaall eenntthhaallppyy aatt ppooiinntt 66 iiss::

hh66==hh33++hh55--hh44==11229911..0011 kkJJ//kkgg {{77}}AAnndd tthhee rreeffrriiggeerraattiioonn eeffffeecctt iiss ggiivveenn bbyy::

RR..EE..==hh55--hh44==11118800..99 kkJJ//kkgg {{88}}

TThhee tteemmppeerraattuurree aatt tthhee eexxiitt ooff tthhee pprree--ccoooolleerr iiss ffoouunndd iitteerraattiivveellyy aass ffoolllloowwss::AAssssuummee TT66==TT55==226611..1155 KK aanndd xx66==xx55==00.. 8811888866

WWiitthh xx66== 00.. 8811888866 aanndd PPLLOOWW==22..119988 bbaarrss,,eeqq.. ((bb11)) ggiivveess:: hhXX66==--118800..447700 kkJJ//kkgg

WWiitthh xx66==00.. 8811888866 aanndd PPLLOOWW==22..119988 bbaarrss aanndd uussiinngg SSiimmppssoonn’’ss rruullee oonn eeqq.. ((aa11)) ttoo eevvaalluuaattee TT66,,eeqq.. ((aa11)) ggiivveess:: TT66==226611..1155 KK

WWiitthh xx66== 00.. 8811888866 aanndd TT66==226611..1155 KKeeqq..((cc11)) ggiivveess:: yy66==00..99999999668822

WWiitthh yy66== 00.. 99999999668822 aanndd PPLLOOWW==22..119988 bbaarrss,,eeqq..((bb33)) ggiivveess:: hhVV66==11224433..886611 kkJJ//kkgg

SSiimmiillaarrllyy aa cchheecckk wwhheetthheerr tthhee mmiixxttuurree iiss aa ssuuppeerrhheeaatteedd oorr aa wweett vvaappoouurr,, iiss aass ffoolllloowwss::

my xy x

mS66 3

6 63=

−−

. ==00..005522226633 kkgg//ss

TThheenn tthhee mmaassss ooff tthhee vvaappoouurr iiss:: mmVV66==mm66-- mmSS66==11-- mmSS66==00..9944777744 kkgg//ss

AA tteesstt ttoottaall eenntthhaallppyy aatt ppooiinntt 66 iiss:: hh66tteesstt== mmSS66.. hhSS66++ mmVV66.. hhVV66==11116699..4422 kkJJ//kkgg

TThhee ccoonncceennttrraattiioonn xx66 iiss aaddjjuusstteedd uunnttiill hh66tteesstt== hh66 ffrroomm eeqq.. {{77}}

AAfftteerr aa mmuullttiippllee iitteerraattiioonn tthhee eenndd vvaalluueess aarree::TT66==229966..1144 KKhh66tteesstt== 11229911..000066 kkJJ//kkgg


22..44..33 AAbbssoorrbbeerr

TThhee ooppeerraattiinngg ccoonnddiittiioonnss iinn tthhee aabbssoorrbbeerr aarree ssuucchh tthhaatt aa ssttrroonngg ssoolluuttiioonn iiss pprroodduucceedd aatttteemmppeerraattuurree TT77 aanndd pprreessssuurree PPLLOOWW..

WWiitthh rreeffeerreennccee ttoo tthhee PPhhDD tthheessiiss bbyy KKeeiizzeerr [[KK55]],, aann aabbssoorrbbeerr ccoouulldd bbee ccoonnssttrruucctteedd ttoo ddeelliivveerr aassaattuurraatteedd ssoolluuttiioonn aatt aa pprreessssuurree lloowweerr tthhaann tthhee eevvaappoorraattoorr’’ss pprreessssuurree..

TThheerreeffoorree,, iinn tthhee pprrooppoosseedd ssiimmuullaattiioonn mmooddeell tthhee ccoonncceennttrraattiioonn xxSSTT ooff tthhee ssttrroonngg ssoolluuttiioonn ccaannbbee ccaallccuullaatteedd uunnddeerr tthhee ssaattuurraatteedd ccoonnddiittiioonnss ooff tteemmppeerraattuurree TT77 aanndd pprreessssuurree PPLLOOWW..


WWiitthh PPLLOOWW ==22..119988 bbaarrss aanndd TT77==229988..1155 KK,, aa SSiimmppssoonn’’ss rruullee iitteerraattiioonn oonn eeqq.. ((aa11)) eevvaalluuaatteess tthheeccoonncceennttrraattiioonn ooff tthhee ssttrroonngg ssoolluuttiioonn xxSSTT

eeqq.. ((aa11)) ggiivveess:: xxSSTT==00..443333 {{99}}

WWiitthh xxSSTT==00..443333 aanndd PPLLOOWW ==22..119988 bbaarrss,,eeqq.. ((bb11)) ggiivveess:: hh77==--112244..9900 kkJJ//kkgg {{1100}}


22..44..44 PPuummpp

OOnnccee tthhee ssttrroonngg ssoolluuttiioonn ppaasssseess tthhrroouugghh tthhee ppuummpp ttoo tthhee hhiigghh pprreessssuurree ssiiddee,, iitt bbeehhaavveess aass aassuubb--ccoooolleedd ssoolluuttiioonn.. TThheerreeffoorree tthhee pprrooppeerrttiieess ooff tthhee fflluuiidd aatt ppooiinntt 1133,, ccaannnnoott bbee ffoouunndd bbyyeeqquuiilliibbrriiuumm rreellaattiioonnsshhiippss..

TThhee wwoorrkk ooff tthhee ppuummpp WWPP iiss pprrooppoorrttiioonnaall ttoo tthhee ssppeecciiffiicc vvoolluummee ooff tthhee ssoolluuttiioonn vv77 aanndd iissccaallccuullaatteedd aass::

((22..1144)) W MP P

vPhigh low

P

=−

7 7η.

TThhee ssppeecciiffiicc vvoolluummee ooff tthhee ssoolluuttiioonn iiss ggiivveenn bbyy::

( )v x v x va w7 7 7 7 71= + −. .

wwhheerree

vv77aa iiss tthhee ssppeecciiffiicc vvoolluummee ooff tthhee ssaattuurraatteedd lliiqquuiidd aammmmoonniiaa

vv77ww iiss tthhee ssppeecciiffiicc vvoolluummee ooff tthhee ssaattuurraatteedd wwaatteerr

TThhee ssppeecciiffiicc vvoolluummeess ooff aammmmoonniiaa aanndd wwaatteerr aarree ggiivveenn bbyy tthhee ffoolllloowwiinngg ppoollyynnoommiiaallss aassssuuggggeesstteedd bbyy [[HH55]] aanndd [[KK11]] rreessppeeccttiivveellyy..

((22..1155)) ( ) ( ) ( ) ( ) ( )v v v T v T v T v Ta7 0 1 2

23

34

4= + + + +. . . .

((22..1166)) ( ) ( )[ ] ( )v a b c t e P P f g tw d

low E

h

7 = + − − − − − −. . .∆

wwhheerree

[[vv77aa]]==mm33//kkgg,, [[vv77

aa]]==ccmm33//gg,, [[PP]]==iinntt AAttmm

TThhee ccooeeffffiicciieennttss ooff tthhee aabboovvee eeqquuaattiioonnss aarreeggiivveenn iinn TTaabbllee 22..22

TThhee eenntthhaallppyy ooff tthhee ssoolluuttiioonn aatt ppooiinntt 1133 iiss tthheessuumm ooff tthhee ssoolluuttiioonn aatt ppooiinntt 77 aanndd tthhee wwoorrkkddoonnee bbyy tthhee ppuummpp::

h h WP13 7= +

IItt iiss aassssuummeedd tthhaatt tthhee tteemmppeerraattuurree iinnccrreeaassee iiss iinnssiiggnniiffiiccaanntt.. TThheerreeffoorree TT1133==TT77..

TTaabbllee 22..22SSaattuurraatteedd lliiqquuiidd

CCooeeffff.. AAmmmmoonniiaa CCooeeffff WWaatteerrvv((00)) 22..994411xx1100--33 aa 33..008866vv((11)) --22..884400xx1100--55 bb 00..889999vv((22)) 11..777744xx1100--77 cc 337744..110000vv((33)) --55..000000xx1100--1100 dd 00..114477vv((44)) 44..995555xx1100--1133 ee 00..440000

ff 221188..550000gg 338855..000000hh 11..660000



TThhee mmaassss rraattee ooff tthhee ssttrroonngg ssoolluuttiioonn iiss ccaallccuullaatteedd aaccccoorrddiinngg ttoo eeqq.. ((22..66))..TThhuuss

mm77==55..333322 kkgg//ss {{1111}}

WWiitthh TT77==229988..1155 KK aanndd PPLLOOWW==22..119988//11..001133==22..11669977 AAttmmeeqq.. ((22..1155)) ggiivveess:: vv77

aa==99..005599xx1100--44 mm33//kkggeeqq.. ((22..1166)) ggiivveess:: vv77

ww==99..66448877xx1100--44 mm33//kkgg

TThhee ttoottaall ssppeecciiffiicc vvoolluummee ooff tthhee mmiixxttuurree iiss::vv77==xxSSTT.. vv77

aa ++ ((11-- xxSSTT)).. vv77ww==88..880055 xx1100--44 mm33//kkgg

TThhee wwoorrkk bbyy tthhee ppuummpp iiss ggiivveenn bbyy eeqq.. ((22..1144))..TThhuuss

WWPP==00..996611 kkJJ//kkgg {{1122}}

TThhee hheeaatt rraattee ooff sstteeaamm 1133 iiss::QQ1133==((hh77++WWPP))..mm77==--666600..8800 kkJJ//kkgg {{1133}}


22..44..55 SSoolluuttiioonn hheeaatt eexxcchhaannggeerr

WWiitthh rreeffeerreennccee ttoo sseeccttiioonn 22..22..66,, tthhee ssttrroonngg ssoolluuttiioonn iinn ssttrreeaamm 1100 iiss ssaattuurraatteedd aatt PPhhiigghh.. TThheerreeffoorreetthhee tteemmppeerraattuurree TT1100 iiss ccaallccuullaatteedd bbyy aa PPHHIIGGHH--TT1100eeqq--xx1100eeqq rreellaattiioonn..

TThhee hheeaatt ttrraannssffeerrrreedd ffrroomm tthhee wweeaakk ttoo tthhee ssttrroonngg ssoolluuttiioonn iiss eexxpprreesssseedd iinn tteerrmmss ooff tthheepprrooppeerrttiieess ooff tthhee wweeaakk ssoolluuttiioonn::

((22..1177)) ( ) ( )Q Cp M T T Cp M T TEXWE ST= − = −. . . .8 8 9 7 10 13

wwhheerree

( )Cp x Cp x CpWE WE a WE w= + −. .1

aanndd

((22..1188)) Cp a b T c T d T e Tab b b b= + + + +. . . .2 3 4

((22..1199)) Cp f g T h Twb b= + +. . 2

ffoorr tthhee tteemmppeerraattuurree rraannggee

2252

3208 9< =+

<TT T

b

TThhee ccooeeffffiicciieennttss ffoorr tthhee aabboovvee rreellaattiioonnssaarree ggiivveenn iinn TTaabbllee 22..33


WWiitthh PPhhiigghh==99..773311 bbaarrss aanndd xxSSTT==00..44332288,, aa SSiimmppssoonn’’ss rruullee iitteerraattiioonn oonn eeqq.. ((aa11)) eevvaalluuaatteess tthheessaattuurraattiioonn tteemmppeerraattuurree ooff tthhee ssttrroonngg ssoolluuttiioonn aatt ppooiinntt 1100..

eeqq.. ((aa11)) ggiivveess:: TT1100eeqq==334477..0044 KK {{1144}}

WWiitthh xxSSTT==00..44332288 aanndd PPhhiigghh== bbaarrss,,eeqq.. ((bb11)) ggiivveess:: hh1100eeqq== 9999..5588 kkJJ//kkgg {{1155}}

TThhee hheeaatt eexxcchhaannggeedd wwiitthhiinn tthhee ssoolluuttiioonn iiss::QQEEXX==hh1100eeqq..mm77 --QQ1133==11119911..7711 kkJJ//kkgg {{1166}}

TThhiiss hheeaatt mmuusstt bbee eeqquuaall ttoo tthhee qquuaannttiittyy eexxpprreesssseedd bbyy eeqq.. ((22..1177))::

AAssssuummiinngg TT99==TT77,, TT88==337733..1155 KK tthhee bbuullkk tteemmppeerraattuurree ooff tthhee wweeaakk ssoolluuttiioonn iiss ggiivveenn bbyy::TTbb==((TT88++TT99))//22==333355..6655 KK

eeqq.. ((22..1188)) ggiivveess:: CCppaa == 44..99330033 kkJJ//kkgg KKeeqq.. ((22..1199)) ggiivveess:: CCppww == 44..11881122 kkJJ//kkgg KK

aannddeeqq.. ((22..1177)) ggiivveess:: QQEEXXtteesstt==11442277..3377 kkJJ//kkgg

IItteerraattiioonnss bbeettwweeeenn QQEEXX aanndd QQEEXXtteesstt ccoonnvveerrggee ggiivviinngg::TT99==331100..7755 KK

TTaabbllee 22..33CCpp ffoorr tthhee ppuurree ccoommppoonneenntt

CCooeeffff.. AAmmmmoonniiaa CCooeeffff WWaatteerraa 1199..557777557766 ff 55..550088779988bb --00..2255229977 gg 88..2244447766xx1100--33

cc 11..553366xx1100--33 hh 11..2277557766xx1100--55

dd 44..11xx1100--99

ee 44..995555xx1100--1133


22..44..66 GGeenneerraattoorr

EEaarrlliieerr iinn tthhiiss cchhaapptteerr,, iitt wwaass sshhoowwnn ggrraapphhiiccaallllyy tthhee wwaayy bbyy wwhhiicchh tthhee aabbssoorrppttiioonn rreeffrriiggeerraattiioonnccyyccllee iiss ooppttiimmiisseedd ttoo aa ppaarrttiiccuullaarr ggeenneerraattoorr’’ss tteemmppeerraattuurree TT88

oopptt..

TThhiiss ooppttiimmuumm tteemmppeerraattuurree iiss ccaallccuullaatteedd bbyy eeqq.. ((22..22)) aanndd ((22..44)) aanndd iitt iiss sseett aass tthhee ggeenneerraattoorr’’ssooppeerraattiinngg tteemmppeerraattuurree uunnlleessss aa ddiiffffeerreenntt tteemmppeerraattuurree TT88 iiss ddeessiirreedd.. TThheenn tthhee ccoonncceennttrraattiioonn xxWWEE

ooff tthhee wweeaakk ssoolluuttiioonn iiss ddeetteerrmmiinneedd bbyy aa PPHHIIGGHH--TT88--xxWWEE rreellaattiioonnsshhiipp,, AAPPPPEENNDDIIXX AA..

TThhee bbuullkk ssoolluuttiioonn iinn tthhee ggeenneerraattoorr iiss aa mmiixxttuurree ooff tthhee iinnccoommiinngg ssttrroonngg ssoolluuttiioonn,, tthhee rreettuurrnneeddlliiqquuiidd ffrroomm tthhee ddiissttiillllaattiioonn ccoolluummnn aanndd tthhee oouuttggooiinngg wweeaakk ssoolluuttiioonn.. TThhee ccoonncceennttrraattiioonn ooff tthhiissmmiixxttuurree ddeeppeennddss oonn tthhee ccoonnssttrruuccttiioonn ooff tthhee ggeenneerraattoorr.. FFoorr eexxaammppllee iiff tthhee mmiixxttuurree rreemmaaiinnss ffoorraa lloonngg ttiimmee iinn tthhee ggeenneerraattoorr,, iittss ccoonncceennttrraattiioonn wwiillll bbee cclloossee ttoo tthhee wweeaakk ssoolluuttiioonn.. IInn tthhiissssiimmuullaattiioonn pprroocceedduurree,, iitt iiss aassssuummeedd tthhaatt tthhee ccoonncceennttrraattiioonn ooff tthhee bbuullkk ssoolluuttiioonn iiss tthhee aavveerraaggee

bbeettwweeeenn tthhee ssttrroonngg aanndd wweeaakk ssoolluuttiioonnss:: xx x

b

WE ST

=+2

TThhiiss ssoolluuttiioonn iiss ssaattuurraatteedd aanndd iittss tteemmppeerraattuurree TTbb iiss ccaallccuullaatteedd bbyy tthhee PPHHIIGGHH--TTbb--xxbb rreellaattiioonnsshhiipp..TThhee vvaappoouurr iinn eeqquuiilliibbrriiuumm wwiitthh tthhiiss bbuullkk lliiqquuiidd--mmiixxttuurree hhaass aa ccoonncceennttrraattiioonn yy1111 ggiivveenn bbyy::

( )

( )( )ya x

a x

T b

T b

111 1

=+ −

.

.

wwhheerree

αα((TT)) == tthhee rreellaattiivvee vvoollaattiilliittyy bbeettwweeeenn wwaatteerr aanndd aammmmoonniiaa aatt tthhee pprreevvaaiilliinngg tteemmppeerraattuurree

TThhee vvaalluueess ooff αα((TT)) aarree ttaakkeenn ffrroomm tthhee ppuubblliiccaattiioonn bbyy SSccaattcchhaarrdd eett aall.. [[SS11]] aanndd hhaavvee bbeeeennmmooddeelllleedd iinnttoo FFoouurriieerr eeqquuaattiioonnss ffoorr tthhee wwhhoollee rraannggee ooff ccoonncceennttrraattiioonnss aanndd tteemmppeerraattuurreess.. TThheeeeqquuaattiioonnss aanndd ccooeeffffiicciieennttss ooff tthhee TT--xx--yy rroouuttiinnee aarree ddeessccrriibbeedd iinn AAPPPPEENNDDIIXX CC..


TThhee mmiinniimmuumm wweeaakk ssoolluuttiioonn tteemmppeerraattuurree iiss wwhheenn TT88==TT1100eeqq==334477..1111 KKTThhee ddeessiiggnn iiss ffoorr aa tteemmppeerraattuurree TT88==110000ooCC==337733..1155 KK {{1177}}WWiitthh TT88==337733..1155 KK aanndd PPHHIIGGHH==99..773311 bbaarrss,, aa SSiimmppssoonn’’ss rruullee iitteerraattiioonn oonn eeqq.. ((aa11)) eevvaalluuaatteess tthheessaattuurraattiioonn ccoonncceennttrraattiioonn ooff tthhee wweeaakk ssoolluuttiioonn aatt ppooiinntt 88..

eeqq.. ((aa11)) ggiivveess:: xxWWEE==00..33004444 {{1188}}

WWiitthh xxWWEE==00..33004444 aanndd PPHHIIGGHH==99..773311 bbaarrss,,eeqq.. ((bb11)) ggiivveess:: hh88==224466..8888 kkJJ//kkgg {{1199}}

TThhee mmaassss rraattee ooff tthhee wweeaakk ssoolluuttiioonn iiff ggiivveenn bbyy ((ff--11)) wwhheerree ff iiss tthhee mmaassss rraattee ooff tthhee ssttrroonnggssoolluuttiioonn ggiivveenn bbyy eeqq ((22..66))..TThhuuss mm88==44..33331155 kkgg//ss {{2200}}

TThhee ggeenneerraattoorr’’ss bbuullkk ssoolluuttiioonn ccoonncceennttrraattiioonn iiss xxbb==00..33668866aanndd xx1122== 00..33668866 {{2211}}

WWiitthh xx1122==xxbb==00..33668866 aanndd PPHHIIGGHH==99..773311 bbaarrss,,eeqq.. ((bb11)) ggiivveess:: hh1122==116655..7722 kkJJ//kkgg {{2222}}


WWiitthh xxbb==00..33668866 aanndd PPHHIIGGHH==99..773311 bbaarrss,, aa SSiimmppssoonn’’ss rruullee iitteerraattiioonn oonn eeqq.. ((aa11)) eevvaalluuaatteess tthheessaattuurraattiioonn tteemmppeerraattuurree ooff tthhee wweeaakk ssoolluuttiioonn aatt ppooiinntt 1111..

eeqq.. ((aa11)) ggiivveess:: TT1111==335599..7799 KK

WWiitthh TT1111==335599..7799 KK aanndd xxbb==00..33668866,,eeqq.. ((cc11)) ggiivveess:: yy1111==00..99660022 {{2233}}

TThhee aassssuummppttiioonn tthhaatt xx1122==xxSSTT lleeaaddss ttoo TT1122==TT1111

WWiitthh yy1111==00..99660011 aanndd PPHHIIGGHH==99..773311 bbaarrss..eeqq.. ((bb33)) ggiivveess:: hh1111==11448844..9900 kkJJ//kkgg {{2244}}


22..44..77 DDiissttiillllaattiioonn CCoolluummnn

TThhee eeqquuaattiioonnss uusseedd ffoorr tthhee ssiimmuullaattiioonn ooff tthhee ddiissttiillllaattiioonn ccoolluummnn aarree pprreesseenntteedd iinn sseeccttiioonn22..22..22..55


TThhee vvaappoouurr ccoonncceennttrraattiioonn ooff ssttrreeaamm 11 iiss tthhee ssaammee aass tthhee ccoonncceennttrraattiioonn ooff tthhee ccoonnddeennssaattee ooffssttrreeaamm 33,, TThhuuss::

yy11==xx33==00..9999005511 {{2255}}

TThhee ccoonncceennttrraattiioonn ooff tthhee lliiqquuiidd aatt ppooiinntt 11 iiss ccaallccuullaatteedd iitteerraattiivveellyy..AAssssuummee aa lliiqquuiidd ccoonncceennttrraattiioonn xx11==00..55

WWiitthh xx11==00..55 aanndd PPHHIIGGHH==99..773311,, aa SSiimmppssoonn’’ss rruullee iitteerraattiioonn oonn eeqq.. ((aa11)) eevvaalluuaatteess tthhee ssaattuurraattiioonntteemmppeerraattuurree ooff tthhee lliiqquuiidd iinn eeqquuiilliibbrriiuumm wwiitthh tthhee vvaappoouurr aatt ppooiinntt 11..

eeqq.. ((aa11)) ggiivveess:: TT11==333311..006633 KK

WWiitthh xx11==00..55 aanndd TT11==333311..006633 KK,,eeqq.. ((cc11)) ggiivveess:: yy11tteesstt==00..9999337744

TThhee ccoonncceennttrraattiioonn ooff xx11 iiss aaddjjuusstteedd iitteerraattiivveellyy uunnttiill yy11== yy11tteesstt==00..9999005511

TThhee iitteerraattiioonnss ccoonnvveerrggee,, ggiivviinngg tthhee ffoolllloowwiinngg rreessuullttss::xx11==00..449911TT11==333366..449977 KK

WWiitthh TT11==333366..449977 KK aanndd yy11== 00..9999005511eeqq.. ((bb33)) ggiivveess:: hh11==11339955..1166 kkJJ//kkgg {{2266}}

TThhee hheeaatt rreejjeecctteedd ffrroomm tthhee ddiissttiillllaattiioonn ccoolluummnn iiss ggiivveenn bbyy eeqq ((22..1100)).. TThhuuss::eeqq.. ((22..1100)) ggiivveess:: QQDD//mm11==5577..3311 kkJJ//kkgg {{2277}}eeqq.. ((22..1122)) ggiivveess:: RReefflluuxx==mmRR== 00..112222 kkgg//ss {{2288}}


22..44..88.. MMaassss aanndd hheeaatt ffllooww rraatteess

TThhee hheeaatt eeffffeeccttss aarree ccaallccuullaatteedd ppeerr kkgg//ss ooff rreeffrriiggeerraanntt.. TThheerreeffoorree tthhee mmaassss ffllooww rraatteess aanndd ttoottaallhheeaatt wwiitthhiinn eeaacchh ccoommppoonneenntt aarree ddeetteerrmmiinneedd aass ffoolllloowwss::

•• tthhee mmaassss rraattee ooff tthhee mmiixxttuurree aatt tthhee ssttrreeaammss 33,, 55,, 66,, 44 aanndd 1155 iiss sseett eeqquuaall ttoo MM11==11kkgg//ss•• tthhee mmaassss rraattee ooff tthhee vvaappoouurr ffrroomm tthhee ggeenneerraattoorr ttoo tthhee ddiissttiillllaattiioonn ccoolluummnn,, ssttrreeaamm 1111::

M My xy x11 1

1 12

11 12

=−−

•• tthhee mmaassss rraattee ooff tthhee rreettuurrnniinngg lliiqquuiidd rreettuurrnniinngg ttoo tthhee ggeenneerraattoorr ffrroomm tthhee ddiissttiillllaattiioonnccoolluummnn.. ssttrreeaamm 1122::

M My yy x12 1

1 11

11 12

=−−

•• tthhee mmaassss rraattee ooff tthhee wweeaakk ssoolluuttiioonn ffrroomm tthhee ggeenneerraattoorr ttoo tthhee aabbssoorrbbeerr,, ssttrreeaamm 88::

M My x

x x

ST

ST WE8 11=

−−

•• tthhee mmaassss rraattee ooff tthhee ssttrroonngg ssoolluuttiioonn ttoo tthhee ggeenneerraattoorr ffrroomm tthhee aabbssoorrbbeerr,, ssttrreeaamm 77:: M M M7 1 8= +

•• tthhee mmaassss rraattee ooff tthhee mmiixxttuurree aatt tthhee ssttrreeaammss 1133 aanndd 1100 iiss sseett eeqquuaall ttoo MM77

•• tthhee mmaassss ooff mmiixxttuurree aatt tthhee ssttrreeaamm 99 iiss sseett eeqquuaall ttoo MM88

TThhee eenntthhaallppiieess ooff tthhee mmiixxttuurreess aatt tthhee nnuummeerraallss aarree eevvaalluuaatteedd eeiitthheerr tthhrroouugghh aa ssaattuurraatteeddmmiixxttuurree eeqquuaattiioonn oorr tthhrroouugghh aa ppsseeuuddoo--tteemmppeerraattuurree oorr ppsseeuuddoo--pprreessssuurree pprroocceedduurree.. TThheenn tthheettoottaall hheeaatt ccaarrrriieedd bbyy tthhee fflluuiidd aatt aa ppaarrttiiccuullaarr ““jj”” ppooiinntt iiss QQjj==hhjj..MMjj

TThhee hheeaatt bbaallaannccee wwiitthhiinn eeaacchh ccoommppoonneenntt iiss aass ffoolllloowwss::•• GGeenneerraattoorr ((QQiinn)):: QQ88++QQ1111--QQ1122--QQ1100

•• AAbbssoorrbbeerr:: QQ66++QQ99--QQ77

•• CCoonnddeennsseerr:: QQ11--QQ33

•• PPuummpp:: WWPP eeqq.. ((22..1144))•• DDeefflleeggmmaattoorr QQDD eeqq.. ((22..1100))•• RReeffrriiggeerraattiioonn eeffffeecctt ((RR..EE..)):: QQ55--QQ44

aanndd tthhee ccooeeffffiicciieenntt ooff ppeerrffoorrmmaannccee iiss::

COPQ Q

Q Q Q Q WR E

Q WP in P

=−

+ − − +=

+5 4

8 11 12 10

. .

TThhee ssiimmuullaattiioonn pprrooggrraamm iiss sshhoowwnn iinn aa ffllooww--cchhaarrtt ffoorrmm iinn FFiigguurree 22..2299..


TThhee mmaassss fflluuxxeess aarree aass ffoolllloowwss::mm11==11..00 kkgg//ss {{2299}}


FFrroomm {{2211}},, {{2233}},, {{2255}},, {{2299}} m my yy x12 1

1 11

11 12

=−−

. ==00..00551122 kkgg//ss {{3300}}

FFrroomm {{2211}},, {{2233}},, {{2255}},, {{2299}} m my xy x11 1

1 12

11 12

=−−

. ==11..00551122 kkgg//ss {{3311}}

TThhee hheeaatt fflluuxxeess aarree aass ffoolllloowwss::FFrroomm {{2255}},, {{2266}} QQ11==11339955..1166 kkWW {{3322}}FFrroomm {{33}},, {{2299}} QQ33==111100..1111 kkWW {{3333}}FFrroomm {{77}},, {{2299}} QQ66==11229911..0011 kkWW {{3344}}FFrroomm {{1100}},, {{1111}} QQ77==--666655..9922 kkWW {{3355}}FFrroomm {{1188}},, {{1199}} QQ88==11006699..4400 kkWW {{3366}}FFrroomm {{1166}},, {{3366}} QQ99==--112222..3311 kkWW {{3377}}FFrroomm {{1111}},, {{1155}} QQ1100==553300..9911 kkWW {{3388}}FFrroomm {{2233}},, {{3311}} QQ1111==11557700..9966 kkWW {{3399}}FFrroomm {{2211}},, {{3300}} QQ1122==88..448899 kkWW {{4400}}

TThheerreeffoorree tthhee hheeaatt eeffffeeccttss oonn tthhee ccoommppoonneennttss aarree aass ffoolllloowwss::FFrroomm {{3366}},, {{3388}},, {{3399}},, {{4400}} QQiinn==22009911..00kkWWFFrroomm {{3344}},, {{3355}},, {{3366}} QQAABBSS==11883344..66kkWWFFrroomm {{3322}},, {{3333}} QQCCOONN==11228855..0055 kkWWFFrroomm {{3377}} QQDDIISSTT==115577..33 kkWWFFrroomm {{1122}} WWPP==55..113366 kkWW

TThhee rreeffrriiggeerraattiioonn eeffffeecctt aanndd tthhee CCOOPP ooff tthhee ppllaanntt aarree::FFrroomm {{88}} RR..EE..==11118800..99 kkWWFFrroomm {{88}},, {{1122}},, {{3366}},, {{3388}},, {{3399}},, {{4400}} CCOOPP==00..556633

TThhee ccoommpplleettee ssiimmuullaatteedd ppeerrffoorrmmaannccee ooff tthhee ppllaanntt iiss pprreesseenntteedd iinn TTaabblleess 22..44 ttoo 22..77

TTaabbllee 22..44PPoossiittiioonn PPrreessssuurree TTeemmppeerraattuurree MMaassss ffllooww rraattee SSpp.. HHeeaatt HHeeaatt CCoonncceennttrraattiioonn

BBaarr ooCC kkgg//ss kkJJ//kkgg kkWW11 99..7733 6633..44 11..00 11339955..22 11339955..22 00..99990055

RR** 99..7733 2255..00 00..112222 111100..11 1133..55 00..9999005533 99..7733 2255..00 11..00 111100..11 111100..11 00..9999005544 99..7733 --00..77 11..00 --1111..44 --1111..44 00..9999005555 22..2200 --1122..00 11..00 11116699..55 11116699..55 00..9999005566 22..2200 2233..00 11..00 11229911..00 11229911..00 00..9999005577 22..2200 2255..00 55..333322 --112244..99 --666655..8855 00..44333388 99..7733 110000..00 44..333322 224466..99 11006699..3366 00..33005599 99..7733 3377..77 44..333322 --112222..33 00..330055

1100 99..7733 7733..99 55..3333 9999..9911 553300..99 00..4433331111 99..7733 8866..66 11..005511 11448855..00 11556611..00 00..9966001122 99..7733 8866..66 00..005511 116655..77 88..55 00..3366991155 22..2200 --1155..00 11..00 --1111..44 00..999900


RR** iinnddiiccaatteess tthhee ppoossiittiioonn ooff tthhee rreefflluuxx iinn tthhee ddeefflleeggmmaattoorr

TThhee ppllaanntt iiss ssiizzeedd aaccccoorrddiinngg ttoo tthhee hheeaatt eeffffeeccttss pprreesseenntteedd iinn TTaabblleess 22..66 aanndd 22..77

TTaabbllee 22..55RReeffrriiggeerraattiioonn ccaappaacciittyy kkWW 11118800..99IInnppuutt hheeaatt ttoo ggeenneerraattoorr kkWW 22009911..00WWoorrkk ddoonnee bbyy tthhee ppuummpp kkWW 55..113366

HHeeaatt rreejjeecctteedd ffrroomm tthhee ccoonnddeennsseerr kkWW 11228855..0055HHeeaatt rreejjeecctteedd ffrroomm tthhee ddeefflleeggmmaattoorr kkWW 115577..33HHeeaatt rreejjeecctteedd ffrroomm tthhee aabbssoorrbbeerr kkWW 11883344..66

RReeffrriiggeerraattiioonn EEffffeecctt kkJJ//kkgg 11118800..6666CCooeeffffiicciieenntt ooff ppeerrffoorrmmaannccee 00..556633


BBaarr ooCC kkgg//ss xx 110033 kkJJ//kkgg kkWW11 99..7733 6633..44 00..884477 11339955..22 11..118822 00..99990055RR 99..7733 2255..00 00..110044 111100..11 00..00112233 00..9999005533 99..7733 2255..00 00..884477 111100..11 00..009933 00..9999005544 99..7733 --00..77 00..884477 --1111..44 --00..00009966 00..9999005555 22..2200 --1122..00 00..884477 11116699..55 00..999911 00..9999005566 22..2200 2233..00 00..884477 11229911..00 11..009933 00..9999005577 22..2200 2255..00 44..551155 --112244..99 --00..556644 00..44333388 99..7733 110000..00 33..666688 224466..99 00..990066 00..33005599 99..7733 3377..77 33..666688 --00..110033 00..330055

1100 99..7733 7733..99 44..551155 9999..9911 00..445511 00..4433331111 99..7733 8866..66 00..889900 11448855..00 11..332299 00..9966001122 99..7733 8866..66 00..00443344 116655..77 00..00007722 00..3366991155 22..2200 --1155..00 00..884477 --1111..44 00..999900





WWiitthh tthhee uussee ooff tthhee ooppttiimmiissaattiioonn ccuurrvveess ooff FFiigguurree 22..55 tthhee TT1155 == --1155ooCC,, TTSS == 2255ooCC ppaaiirr ggiivveessTT88

oopptt == 8800..4444ooCC

TThhee mmaaxxiimmuumm ppeerrffoorrmmaannccee ppllaanntt wwoouulldd hhaavvee tthhee wwoorrkkiinngg ppaarraammeetteerrss aass iinnddiiccaatteedd iinn TTaabblleess22..88 aanndd 22..99

TThhee mmaaxxiimmuumm CCOOPP vvaalluuee pprreeddiicctteedd bbyy tthhee ooppttiimmiissaattiioonn ccuurrvveess iiss CCOOPPmmaaxx==00..662200


bbaarr ooCC KKgg//ss kkJJ//kkgg kkWW

11 99..7733 6633..44 11..00 11339955..1166 11339955..1166 00..9999005500RR 99..7733 2255..00 00..006611 111100..1111 66..8877 00..999900550033 99..7733 2255..00 11..00 111100..1111 111100..1111 00..999900550044 99..7733 --00..7755 11..00 --1111..4444 --1111..4444 00..999900550055 22..22 --1122..00 11..00 11116699..4466 11116699..4466 00..999900550066 22..22 2233..00 11..00 11229911..0011 11229911..0011 00..999900550077 22..22 2255..00 1177..556666 --112244..9900 --22119944..0011 00..44333388 99..7733 8800..44 1166..556666 113300..9933 22116688..9911 00..44000099 99..7733 2266..66 1166..556666 --11775577..3388 00..440000

1100 99..7733 7733..99 1177..556666 9999..5588 11774499..1166 00..4433331111 99..7733 7777..11 1100..225544 11444400..2244 11447777..9966 00..9977661122 99..7733 7777..11 2255..44 111155..11 22..99 00..4433331155 22..22 --1155..00 11..00 --1111..4411 00..9999




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[B10] Bosnjakovic FTECHNICAL THERMODYNAMICSTranslated by P L Blackshear Jr, Third Edition 1965, Holt, Rinehart and Winston

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[K5] Keizer CABSORPTION REFRIGERATION MACHINESPh D Thesis, Delft University of Technology, 1982

[K7] Kelly S WGLOBAL PHASE OUT OF FULLY HALOGENATED CHLOROFLUOROCARBONSUNDER THE TERMS OF THE MONTREAL PROTOCOL - POTENTIALREPLACEMENT AND THEIR CURRENT STATUSASHRAE-FRIGAIR 90 Conference, CSIR Conference Center Pretoria, April 1990

[K10] Krauss M R et Stephan KENTHALPY- CONCENTRATION CHARTInstitute international Du Froid (1991)

[L1] Lazzarin R MAN EXPERIMENTAL ANALYSIS OF A SOLAR ASSISTED ABSORPTION HEATPUMP WITH SEASONAL STORAGEInternational Journal of Energy Research, Vol 12, 1988, pp 631-646

[M1] Macintire H JREFRIGERATION ENGINEERINGJohn Wiley & Sons, Inc New York 1937

[M10] Morrison NINTRODUCTION TO FOURIER ANALYSISJohn Wiley & Sons, Inc 1994, pp 37-45

REFERENCES 67

[N3] Nielsen C HDISTILLATION IN PRACTICEReinhold Publishing CorporationNew York, Chapman & Hall, Ltd, London 1956 pp 41-71(Physical design features of plate columns, by Geddes R L )

[R2] Raber B F and Hutchinson F WREFRIGERATION AND AIR-CONDITIONING ENGINEERINGNew York, John Wiley & Sons Inc

[R4] Renz M and Steimle FCOMPARISON OF THERMODYNAMIC PROPERTIES OF WORKING FLUIDS FORABSORPTION SYSTEMSScience et technique du froid, part 3 1982 pp 61-67

[R6] Rose A and EDISTILLATIONThechnique of Organic Chemistry Vol IV Interscience Publishers Inc N Y 1951

[S1] Scatchard G, Epstein L F, Warburton J, Cody P JTHERMODYNAMIC PROPERTIES SATURATED LIQUID AND VAPOUR OFAMMONIA-WATER MIXTURESJournal of the ASRE, 1947 pp 413-419, pp 446-452

[S10] Smith M V BROBUST DESIGN OF TRIPLE FLUID REFRIGERATION SYSTEMSS A Refrigeration and Airconditioning, Nov 1991, vol7 No 6 pp 27-31

[S11] Stierlin HCOME BACK OF THE ABSORPTION REFRIGERATIONProceedings of the XIth International Congress of Refrigeration pp 643-652 Progress inRefrigeration Science and Technology Vol I

[S13] Stoecker W F and Reed L DEFFECT OF OPERATING TEMERATURES ON THE COEFFICIENT OFPERFORMANCE OF AQUA-AMMONIA REFRIGERATING SYSTEMSASHRAE-Trans 77 (1971) pp 163-170

[S14] Szucs LNEW PUMPING METHOD IN ABSORPTION REFRIGERATIONProceedings of the XIth International Congress of Refrigeration Progress in RefrigerationScience and Technology Vol I

[T2] Threlkeld J LTHERMAL ENVIRONMENTAL ENGINEERINGII edition, Prentice-Hall Inc, Englewood Cliffs, New Jersey

[T6] Tyagi K P and Rao K SCHOICE OF ABSORBENT-REFRIGERANT MIXTURESEnergy research, Vol 8, 361-368 (1984)

[V2] Vicatos GABSORPTION REFRIGERATION USING WASTE HEATNational Energy Council, CSIR Pretoria, 1989, report No EV8

[V3] Vicatos G and Grysagoridis JA GRAPHIACL ANALYSIS FOR THE OPTIMISATION OF ABSORPTIONREFRIGERATIONInternational Congress of refrigeration FRIGAIR 94, Durban, South Africa

[W2] Wood B D

REFERENCES 68

APPLICATIONS OF THERMODYNAMICS,II edition, Addison-Wesley Publishing Company

[W3] Woolrich W RHANDBOOK OF REFRIGERATING ENGINEERING4 edition vol 1 1965, Westport connecticut The AVI Publishing Co Inc

[Y1] Young SDISTILLATION PRINCIPLES AND PROCESSES,MacMillan And Co, Ltd St Martin's Street London 1922

[Z1] Zellhoefer G F, Copley M J, Marvel C SHYDROGEN BONDS INVOLVING THE C-H LINK THE SOLUBILITY OFHALOFORMS IN DONOR SOLVENTSThe Jurnal of the American Chemical Society Vol 60 Part 1, 1938 pp 1337-1343

[Z2] Zellhoefer G F, Copley M JTHE HEATS OF MIXING OF HALOFORMS AND POLYETHYLENE GLYCOLEATHERSThe Journal of the American Chemical Society Vol 60 Part 1, 1938 pp 1343-1345

AAPPPPEENNDDIICCEESS 6699

APPENDICES


ROUTINESROUTINES

The routines used in the procedure to analyse the properties of the saturated fluid and its vapour,are polynomials modelled from the experimental data of Scatchard et al. [S1] and from the linesof the enthalpy-concentration diagram [K10]. The experimental data has provided thepolynomials for the pressure-temperature-concentration (P-T-x) relation and the polynomials forthe temperature-liquid-vapour concentrations (T-x-y) relation. The enthalpy-concentrationdiagram has provided the polynomials for the enthalpies of the liquid and vapour concentrations.

These routines are classified in three main categories:

1. those using the P-T-x relation for the saturated solution to evaluate the pressure, or thetemperature, or the concentration of the solution.

• Routine A.1: to evaluate the pressure, if the temperature and concentration areknown

• Routine A.2: to evaluate the temperature, it the pressure and concentration areknown

• Routine A.3: to evaluate the concentration, if the temperature and pressure areknown

2. those evaluating the specific enthalpies of the liquid and vapour mixtures.

• Routine B.1: to evaluate the enthalpy of the liquid for the whole range ofconcentrations and pressures

• Routine B.2: to evaluate the enthalpy of the vapour for the whole range ofpressures and for vapour concentrations from 0<y<0.9 and from 0.9<y<1.0

3. those using the temperature-concentration-activity (T-x-α) relation to evaluate theconcentration of the vapour mixture

• Routine C.1


APPENDIX AA.1A.1 THE P-T-THE P-T-xx RELATION RELATION

The (P-T-x) relation is the key to solving the equilibrium properties of any binary saturatedmixture. Attempts have been made in the past to demonstrate graphically this relation for thewater-ammonia solution [B13, R1], by plotting the natural logarithm of the pressure over thesolution, against the inverse of its temperature. These graphs without exception wereapproximated as straight lines for all concentrations of the mixture, including the pure substances.This is far from an accurate representation of the P-T-x relation, as it is well known that thesaturation pressures of both water and ammonia plotted in this way are not straight lines.According to the data published by Scatchard et al. [S1] the graphical representation of the P-T-xrelation is shown in Figure A.1

This data is used to form an empirical equation eq. (a1) relating the pressures, temperatures andconcentrations (P-T-x relation), for solutions in equilibrium with their vapours.

eq. (a1) Ln P Fa Fb T FcT

Fd T Fe Ln Tx x x x x( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )= + +

+ +

1 2

wwhheerree FFaa,,......,, FFee aarree ppoollyynnoommiiaall ffuunnccttiioonnss ooff tthhee ccoonncceennttrraattiioonn xx,, ooff tthhee ffoorrmm

F a xii

i==∑

0

9

TThhee ccooeeffffiicciieennttss ααii ooff tthhee ppoollyynnoommiiaallss FFaa ........ FFee aarree ggiivveenn iinn tthhee TTaabbllee TT..11

AAAA....2222 RRRROOOOUUUUTTTTIIIINNNNEEEE PPPP----TTTT----xxxx ((((xxxx----PPPP aaaarrrreeee kkkknnnnoooowwwwnnnn))))UUssiinngg SSiimmppssoonn’’ss rruullee,, tthhee tteemmppeerraattuurree ooff tthhee ssaattuurraatteedd ssoolluuttiioonn iiss iitteerraattiivveellyy ccaallccuullaatteedd ffrroomm tthheePP--TT--xx rreellaattiioonn wwiitthhiinn aann aaccccuurraaccyy ooff 00..0011ooCC..

T Tg

gP

P1 0= − ( )

( )'

wwhheerree g Ln P Fa Fb T FcT

Fd T Fe Ln TP x x x x x( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )= − + +

+ +

1 2

TTaabbllee TT 11FFaa FFbb FFcc FFdd FFee

αααα0000 4488..110000116600 --00..000055118899 --66888855..447755993322 00..000000000066 --44..881144112200

αααα1111 5533117799..776633774499 3388..111100443300 --886611330011..991111007722 --00..002211990000 --1100447744..550066993388

αααα2222 --11665555333388..776688000000 --11009977..990066221111 2299772222008877..227700118811 00..660055777700 332211000033..112277444499

αααα3333 1155229966669922..339922000000 1100003344..445522550088 --227788449922551133..224477774488 --55..550055556688 --22995599880044..771144556699

αααα4444 --6699777744007700..112233000000 --4455775522..772233667700 11227722332211774466..002277331100 2255..110099000011 1133449988886655..992299999977

αααα5555 118811660033774400..221122000000 111199223355..006655003311 --33330088556655660011..773377338800 --6655..448888996699 --3355114411774422..998822009977

αααα6666 --228822117766885522..228844000000 --118855442211..771122334444 55113355445588888822..336622664400 110011..885544664400 5544661133113366..666600003300

αααα7777 225588771122337755..557766775566 116699999933..442255668899 --44770055330044443333..227755886600 --9933..330088226600 --5500007744223311..006699553366

αααα8888 --112299005500117744..776622117722 --8844771188..222266663344 22334466559900004477..889999449900 4466..442266995522 2244997755889933..661122222277

αααα9999 2266999900445566..441133447700 1177668899..552222008899 --449900886666331100..003333883333 --99..667711666655 --55222222664488..446600882266


aanndd g Fb FcT

Fd TFe

TP x x x

x' ( )( ) ( ) ( ) ( )

( )= − −

+ +

1

22

Figure A. 1

AAAA....3333 RRRROOOOUUUUTTTTIIIINNNNEEEE PPPP----TTTT----xxxx ((((TTTT----PPPP aaaarrrreeee kkkknnnnoooowwwwnnnn))))

UUssiinngg SSiimmppssoonn’’ss rruullee,, tthhee ccoonncceennttrraattiioonn ooff tthhee ssaattuurraatteedd ssoolluuttiioonn iiss iitteerraattiivveellyy ccaallccuullaatteedd ffrroomm tthheePP--TT--xx rreellaattiioonn wwiitthhiinn aaccccuurraaccyy ooff 1100--55..

x xg

gP

P1 0

1

= − ( )

( )'

wwhheerree gg((PP)) iiss ddeeffiinneedd iinn ppaarraaggrraapphh AA..22

aanndd g Fa Fb T FcT

Fd T Fe Ln TP x x x x x121

' ' ' ( ) ' ' ( ) ' ( )( ) ( ) ( ) ( ) ( ) ( )= − + +

+ +

wwhheerree tthhee FFaa’’............FFee’’ ffuunnccttiioonnss aarree tthhee ffiirrsstt ddeerriivvaattiivveess ooff tthhee FFaa ........ FFee ffuunnccttiioonnss ddeessccrriibbeedd iinnppaarraaggrraapphh AA..11::

F ia xii

i'==

−∑1

91

The P-T-x relationship

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

2.0 2.5 3.0 3.5 4.0 4.5 5.0

1000/T [T=K]

Ln(

P)

[P

=bar

]

experimental [S1] modeled

x = 0

x = 1 .

0

x = 0 .2


APPENDIX BBBBB....1111 EEEENNNNTTTTHHHHAAAALLLLPPPPYYYY OOOOFFFF TTTTHHHHEEEE SSSSAAAATTTTUUUURRRRAAAATTTTEEEEDDDD LLLLIIIIQQQQUUUUIIIIDDDD

TThhee eenntthhaallppyy ooff tthhee ssaattuurraatteedd lliiqquuiidd iiss eevvaalluuaatteedd ffoorr aallll ccoonncceennttrraattiioonnss ((iinncclluuddiinngg tthhee ppuurreessuubbssttaanncceess)) aanndd ffoorr pprreessssuurreess wwiitthhiinn tthhee rraannggee ooff 00..0055bbaarrss aanndd 3300..00bbaarrss.. TThhee FFoouurriieerr eeqquuaattiioonn eeqq..((bb11)) iiss ddeevveellooppeedd aaccccoorrddiinngg ttoo MMoorrrriissoonn [[MM1100]],, bbyy ttaakkiinngg 2200 sstteeppss bbeettwweeeenn xx==00..00 aanndd xx==11..00 TThheeiinnddeeppeennddeenntt ppaarraammeetteerrss aarree tthhee ccoonncceennttrraattiioonn ““xx”” aanndd tthhee pprreessssuurree ““PP”” ooff wwhhiicchh tthhee pprreessssuurree iiss aatteemmppeerraattuurree ddeeppeennddaanntt ffuunnccttiioonn iittsseellff..

eeqq.. ((bb11)) h

A A nx

k

kx P

P n Pk

n

k

( , )

( ) ( ) .cos

=+

=

−

∑01

1

2 22

2

π

wwhheerree tthhee ccooeeffffiicciieennttss AA00((PP)),, ............,, AAnn((PP)) aarree ffuunnccttiioonnss ooff pprreessssuurree ooff tthhee ffoorrmm::

eq. (b2) A a b PcP

dP

e Ln Pn P n nn n

n( ) . . ( )= + + + +2 for n=0 to k-1

wwhheerree

kk iiss tthhee nnuummbbeerr ooff sstteeppss wwiitthhiinn tthhee ccoonncceennttrraattiioonn rraannggee.. IInn tthhiiss ccaassee kk==2200 aanndd xxkk==2200xx

TThhee ccooeeffffiicciieennttss aann,, ........,, eenn ooff tthhee pprreessssuurree ddeeppeennddeenntt ffuunnccttiioonnss AAnn((PP)) aarree ggiivveenn iinn TTaabbllee TT22..

TTaabbllee TT 22nn aann bbnn ccnn ddnn eenn00 --55773377..665577119988226666 224433..6688880077885555551144 554455..6677555544443300116655 --2266..4400223366337755338888 44770088..662299551144338811 44442255..66992299550033330011 66..22445544883311117799668811 2244..221100005566776633335533 --..885599114422443333337799 336611..224499882266665599441122 33332255..22773322775599994455 11..88999911992277778866660022 5555..112277444433667777227777 --22..994422662288889988664499 --55..66221199775577116600889933 555555..8866881144115566773355 22..11882255559955552299551166 --1155..6622662200552222550033 11..77446622444411554400007744 --3311..666688339977889999666644 668811..5588887777116633000044 22..11448866000033889966111188 66..00668866776688550033447777 --..551144333355337733003366 --66..99550033331111556666227755 222244..0099773322332200440044 ..22338811779955225555552299 44..88221166007799440066004422 --..227700117700882233009955 11..9966000055774477112299001166 331188..3344558800552233884411 --44..228855558822889933778833 2299..337733661188555500448844 --11..660077005500220011000033 2255..99999900223399002200888877 113322..2299882233112233669944 --11..663366440066880022001111 55..222222444422996600117755 --..006611000022669922662244 88..0099888822224422223366777788 117788..9955442244004444556655 --33..663399000022998877449977 2255..330022554422114411664488 --11..3388778822449966992288 1199..22667766665511779955119999 7700..008877444411778800331155 --44..222244774400449977665544 1199..446633335566007733990055 --11..009944667722006655772299 2233..8888999911446666889944221100 111177..6666662299662222110022 --33..558866776655110033556666 2244..112200664411331166880033 --11..668899001144551177339977 1199..7722882211337722117711661111 5599..113344442200669966224411 --11..335588445500553311997777 66..33775511116633771199117777 --..440088550066448833334477 44..334466777799448888664477331122 110011..5500770066550033667733 --..885599115588554422331199 99..44009900771111552288552244 --..774466999988776688882222 --11..7766442233441188771111221133 5522..333344660066440044116688 --11..337700008855662277009922 22..33660022225522885522558855 --..113366223344335544888866 --..2266558877558888992222551144 7788..443399000000118811665544 --11..445577440044888844889977 1122..3388442200330000888899 --..775577995533997700669922 88..551133994411337711000022661155 3399..117766220044552211885588 --..774455005577882299888877 55..66226622000077333355661155 --..228833773355008877339977 22..886644667700331177883366991166 7711..223388333344994466661177 ..00663366776644664455776677 66..559988443355660044779999 --..446622222255445555999988 ..229944770011002266558811551177 3333..222211445588447788334444 --..006611002277995599000088 44..33664422669922991111336688 --..226699440066557711999911 ..8888557700776666553344991188 5544..889955772200663322228888 --..557777224466775500885511 1133..004488883399555522888844 --..887700663311664488995533 66..990044668899222255997744221199 2299..441122332255335544994422 ..00998877115566557766009933 44..55332233771188558877991188 --..223311556699223377330022 22..11990011006644448877228888


BBBB....2222 EEEENNNNTTTTHHHHAAAALLLLPPPPYYYY OOOOFFFF TTTTHHHHEEEE SSSSAAAATTTTUUUURRRRAAAATTTTEEEEDDDD VVVVAAAAPPPPOOOOUUUURRRRTThhee eenntthhaallppyy ooff tthhee ssaattuurraatteedd vvaappoouurr iiss eevvaalluuaatteedd ffoorr tthhee ssaammee pprreessssuurree aass tthhaatt ffoorr iittss lliiqquuiidd.. TThheevvaappoouurr ccoonncceennttrraattiioonnss aarree ssuubbddiivviiddeedd iinnttoo ttwwoo rraannggeess::•• 00..000000<<yy<<00..990000•• 00..990000<<yy<<11..000000IInn tthhee ffiirrsstt rraannggee ooff ccoonncceennttrraattiioonnss tthheerree aarree 1100 kk--sstteeppss..

eeqq.. ((bb33)) h

A A nyk

kx P

P n Pk

n

k

( , )

( ) ( ) .cos

.=+

=

−

∑01

1

2 22

20 874972

πyykk==1100xx

tthhee ccooeeffffiicciieennttss AA00((PP)),, ............,, AAnn((PP)) ooff eeqq.. ((bb33)) aarree ffuunnccttiioonnss ooff pprreessssuurree ooff tthhee ffoorrmm::

eq. (b4) A a b Pc

P

d

Pe Ln Pn P n n

n nn( ) . . ( )= + + + +2 for n=0 to k-1

TThhee ccooeeffffiicciieennttss aann,, ........,, eenn ffoorr tthhee pprreessssuurree ddeeppeennddeenntt ffuunnccttiioonnss AAnn((PP)) ooff eeqq.. ((bb44)) aarree ggiivveenn iinn TTaabblleeTT33..

IInn tthhee sseeccoonndd rraannggee ooff ccoonncceennttrraattiioonnss tthheerree aarree 2200 kk--sstteeppss..

eeqq.. ((bb55)) h

A A nxk

kx P

P n Pk

n

k

( , )

( ) ( ) .cos

=+

=

−

∑01

1

2 22

2

π

wwhheerree tthhee ccooeeffffiicciieennttss AA00((PP)),, ............,, AAnn((PP)) ooff eeqq.. ((bb55)) aarree ffuunnccttiioonnss ooff pprreessssuurree ooff tthhee ffoorrmm::

eq. (b6) A a b PcP

dP

e Ln Pn P n nn n

n( ) . . ( )= + + + +2 for n=0 to k-1

TThhee ccooeeffffiicciieennttss aann,, ..........,, eenn ffoorr tthhee pprreessssuurree ddeeppeennddeenntt ffuunnccttiioonnss AAnn((PP)) ooff eeqq.. ((bb66)) aarree ggiivveenn iinn TTaabblleeTT44..

TTaabbllee TT 33nn aann bbnn ccnn ddnn eenn00 22339955..99338800776666999922 ..22220077339977885566112288 1100..111100990000770099772211 --..6633222200221199118811 5522..11774477224455008844666611 226688..99442288558877999955 --..008833992299444433444488 --..007755330000001100228866 ..00009900883377771166774433 ..9922118866881155668888229922 --44..336644000011116611550088 --..009966884466882200338822 --..001166660099776699008877 --..000022559933334411116611 --..33555533332288997700006633 3322..776655224400445588117788 --..004499118844661177221155 ..55221166000044551188889911 --..0033883377557755992277 ..7766550022227755110033991144 --11..009977883377334499332266 --..001199660055555555773388 --..4422774488332277110011 ..00228899009966991188666688 --..55005588882244445500001155 1144..994477887799331188772233 ..00001100559900333388331111 ..11229977119900773366555577 --..001111229977440044660099 ..2277880011223311448855118866 --11..111111663377008888772299 --..008899667755553344555511 ..22331155227799220033662277 --..001188444411332211997744 ..2222996655115511330022117777 1100..339944663399550099116699 ..00448866229966441155222244 --..333300339933334444001166 ..00117777333377330055330066 --..22887799004488004499994488 --..990033223322333399665511 --..007700005599993355663366 ..11224444662222224499114444 --..001100006611007799008855 ..1122551111112222337777449999 99..44110022224433222277889988 ..00776688449977995500118877 --..4466772200222299006611 ..00229911221166223311556611 --..339922779900889966448866


TTaabbllee TT 44nn aann bbnn ccnn ddnn eenn00 4488773355..668800661122005533 --2255..6655330044110022660077 7755..005577117755555577115511 --..333322667755991122225577 11229977..5500110077997744443311 55773388..77999922440055665588 1122..447788110022009933228877 112288..6600440066559955442299 --1111..2200224477330044997722 114444..992233887788000022006622 ..00001144445588222211003388 ..00000033224433554499882277 --..000022000055776600995566 ..00000011446600117755227711 --..000022330022885511111133 --664400..33116655009999554488 --44..331199224411559999228855 99..55881111110066662200337788 ..55449933449911889933446611 5566..11008877991199000099113344 --..000000551188006644666633 ..0000000099551188116611667711 ..00000033115522112233880099 --..00000000445577773300555522 --..00000022555511775555118855 559944..9966660022887700441199 --..774400882299117788881122 --1144..1100005588443333773311 ..55009977996677991144007788 --2255..991100004444003366112266 --..000066995544337700886622 --..000000446677222222112299 ..00004499449966228844998899 --..000000227799773377337722 ..0000553377552233119911004477 --226633..33331122118811991199 ..00445511666677004444667722 1188..880000990022443355666633 --11..001133884444339988009977 2299..11339922770022115511221188 --..000011331166550066447755 --..000000117733559933334444 ..00001122002288333311669922 --..00000000662255887777114488 ..0000116666883355223366221199 223355..4444005566664444445555 --..771188997744992222442211 --11..222266664422999966999966 ..11002266994499992200115544 --44..881188770022664466880055

1100 ..000044664466660044000033 ..00000011440055447755886688 --..000033118811440000445511 ..00000022116633556600880066 --..0000224466115566330099441111 --9900..4488997788880099991122 33..22556666110000111177222222 --1166..99440011000011115544 ..99662233883333770077887722 --1199..00886611884477667711441122 --..000011550099557733442211 ..00000011223377990022332277 ..000011558877443322888822 --..000000115511440033116688 --..0000002288776677884433221133 8888..558822330088338800009966 --33..002211112233339955331133 2200..559922006611663355338866 --11..1111556699228877440033 2255..0066335500447766664466881144 ..00000044331155774400889922 ..0000000066779999884477006644 --..000011116688227766111133 ..0000000077332233221155007722 --..0000004466884411991122551155 --2211..7744665511227755778855 22..88554477554422552211887766 --1177..6633114433882288774455 ..99336677884466663311228833 --2222..33662255113355883322551166 ..00001155440000662288773311 ..00000000663322447722001133 --..000011222288777700008855 ..0000000088551144776644667788 --..0000007755886699118844331177 3333..551199550011440077997777 --11..990011009900551100110066 1133..559900553399000000002277 --..772255665555334422775511 1177..3333778855557700004422991188 --..000000338855449977003333 --..000000112277882200333311 ..00000022661155004422226611 ..0000000000118899996611117766 ..000000990044337766442222221199 1111..555511447733118866442266 ..66664444883344229977223355 --55..336666224422665544778888 ..33113344660044224488993388 --55..666611776677113300331188


APPENDIX CCCCC....1111 VVVVAAAAPPPPOOOOUUUURRRR MMMMIIIIXXXXTTTTUUUURRRREEEE CCCCOOOONNNNCCCCEEEENNNNTTTTRRRRAAAATTTTIIIIOOOONNNNTThhee ccoonncceennttrraattiioonn ooff tthhee vvaappoouurr mmiixxttuurree iiss rreellaatteedd ttoo tthhee ccoonncceennttrraattiioonn ooff tthhee ssaattuurraatteedd lliiqquuiidd aannddttoo tthhee aaccttiivviittyy ccooeeffffiicciieenntt αα bbyy eeqq.. ((cc11))

eq. (c1) yxx

=+ −

.( )αα1 1

TThhee aaccttiivviittyy ccooeeffffiicciieennttss aarree oobbttaaiinneedd ffrroomm tthhee ddaattaa ppuubblliisshheedd bbyy SSccaattcchhaarrdd eett aall [[SS11]] aanndd hhaavveebbeeeenn rreellaatteedd ttoo tthhee ccoonncceennttrraattiioonn ooff tthhee lliiqquuiidd xx aanndd iittss ssaattuurraattiioonn tteemmppeerraattuurree ““TT”” bbyy aa ddoouubblleeFFoouurriieerr eeqquuaattiioonn eeqq.. ((cc22)) aanndd eeqq.. ((cc33))..

eq. (c2) LnB B m

Tl

l

ml

m

l

( )cos .( ) ( )

απ

=+

=

−

∑01

1

2 22

2l = 0, ..., 43

wwhheerree

eq. (c3) BA A n

xk

km

nk

n

k

( )

( ) ( ) cos .=

+

=

−

∑01

1

2 22

2

πk = 0, ..., 10

aanndd Tt

l =+ 6010

((tt == FF)) xxkk==1100..xx

TThhee AA((nn)) aanndd BB((mm)) ccooeeffffiicciieennttss aarree ggiivveenn iinn TTaabbllee TT55..


TTaabbllee TT 55AA00 AA11 AA22 AA33 AA44 AA55 AA66 AA77 AA88 AA99

BB00 77998899..996600998866 --998866..00006644448822 --332211..66440044008833 2277..66666600887799 --4477..7777446622558866 --2244..33007788553399 --1100..99112277119977 --1122..00771188006699 1122..3311771166776633 --2266..0055885555993366BB11 22332255..999944552255 --665511..99665577446622 --2222..3344339922770011 --2288..2222775533990033 1100..44229999440055 --2211..0088666677447733 --44..005511667722002266 44..113355553300330055 --1111..2222999999880077 1155..9922888822881144BB22 442299..33775588559933 --113344..44445599110066 --1100..3388887766113311 --44..771144004466551166 --66..110011330033337711 --1133..7755115522228833 99..332222773300442299 --44..227777660011443344 88..337755333311668855 --22..007788004422771166BB33 333399..66110077995599 --9922..0022550055669922 --11..550000337766884422 --44..555588333333119977 --11..228833884422993377 --88..440011558844339977 --00..9911552222331166 --22..116655885599006644 00..115599007711557788 11..338855661122332255BB44 112244..44779955332255 --3366..7700552266002266 --11..663377002299994422 --33..221144333388999988 --33..668844223399220077 --88..113377551144337744 11..003333889988554433 --22..447788227744118877 33..227733553377449933 11..221111334477113344BB55 112255..88116655228877 --3377..5599446622995566 --11..4422339966333399 --22..000077223311002299 00..110022997777552266 --22..448833113355880099 11..113366661155009977 00..002288994499222222 --00..003366448899775555 11..887788002211111155BB66 5544..4466889999117755 --1177..4488770000990033 --11..660077998833669977 --00..117700441199008866 --22..004477008866774433 --11..776655003300776622 --00..229911229944662288 --00..3322444400009944 00..221177114466660011 22..4477223300442266BB77 5599..4488004433552222 --1199..4433889999001199 --22..884422448899113355 11..119999666644668855 --00..330055222222550077 22..446699113355992233 --00..007711554499339966 11..665577883311556699 --00..664433002255005566 11..551177555577550033BB88 2266..66116655555588 --88..883388881166116655 --22..666611229977668866 11..994422559955117766 --11..222288880077999955 11..885522223311551122 --00..116655777799888899 00..223322441188229966 00..116611221100111188 00..118811444433884466BB99 3366..1111331122992288 --1111..4433887766667777 --11..995555006611557777 11..664444003300225511 00..227777779944110066 11..669911330099886611 00..440099776666666644 --00..116611553377999988 --00..003300994411448866 --00..44889922118822

BB1100 1199..5533112233002277 --66..774499772277558844 --00..449900663366227733 11..115522776677110077 00..338866333300778855 00..005533229966334466 00..446622999911778811 --00..552266880088888844 00..228877666677332266 --00..991111001177992222BB1111 2277..4444001166668855 --88..224499446699887733 00..225566332266447733 00..550022330055331199 00..883333444477448844 --00..223311666677992299 --00..550077337744666622 --00..113377002277779944 --00..331188440066440088 --00..111133666688559999BB1122 1144..6622778866779933 --44..551111330022551155 00..110011003355662277 00..992233883377880044 00..449911002222330011 --00..006666446655331133 --00..449977550000330044 --00..229955990077994422 --00..554488110055667777 --00..666677990022771188BB1133 2200..3355441155229922 --55..009977440011111144 --00..119922888877111199 00..770000998844335544 --00..224488997744997799 --00..229977663344773355 --00..664455007711119911 --00..224488663300227744 --00..228899552288332288 --00..229900333344338822BB1144 1111..1133116633664477 --33..336666229944552211 --00..448800331100883322 00..558866117722883399 --00..002233337777002299 00..330066557700440022 --00..000088223322992244 --00..339944333344668811 --00..0099993388220099 --00..334499881199004433BB1155 1155..6622666611669977 --44..443399888833993388 --00..330088337766445588 --00..115566227755775555 --00..110022111100993344 00..119922991144448888 --00..667722772277774499 --00..009933445577777766 00..002211773355669933 00..7755444466665566BB1166 77..660000449911666644 --33..222244336699114466 --00..773300440077554444 00..0011553322220011 00..009911331100447799 00..773344333355113377 --00..114444550044449944 00..227777998866333399 00..225588777722005544 00..333388116633229944BB1177 1111..4444111133119977 --33..662244992233772244 --00..997799001199114433 --00..111188666677558833 --00..229977441111884499 00..339922776688445599 --00..229966005588889955 --00..007722226600229966 00..556699336622227799 00..777700118899887711BB1188 66..119966558833007777 --22..5533889966441188 --00..993388227755554444 --00..111155113300772299 --00..223377228899004411 00..330077448888884466 00..1166229977775577 --00..224433997744770077 00..774444225533442299 00..441199339933559999BB1199 99..7788442266114444 --33..4466005577551111 --00..339988337755772299 --00..336666442277990033 --00..005533003377661144 00..005511113333994477 --00..117788667766883311 00..110088332277001133 00..5544668844554433 00..661111990055332233BB2200 66..009911114477663344 --11..998899776666991144 --00..111144117777992233 --00..224466442277441133 --00..223388447733776633 --00..110088224444770055 --00..446600337766888822 00..002255441166779977 00..223388338844661188 00..442222556677992222BB2211 88..776655000055557755 --22..333366558800999933 --00..116666774400663377 00..115577443300775511 --00..223322119966552266 00..007777558822774477 --00..441122559900770055 --00..115566667733113355 00..004499886699778877 00..221177448855440022BB2222 55..551100779988886677 --00..992255223311664411 00..001144228800002233 00..332266117722220099 --00..447755884444334455 --00..331122334499009999 --00..446666336655669988 --00..555566442200333322 00..111177771111338866 00..006677008855779922BB2233 77..998833449900774411 --11..773322999933335599 00..1122663399888855 00..112266115566007722 00..005511889900997733 --00..002200667733885588 --00..336611554444448822 --00..333355442233335566 --00..223377661100225544 --00..008888443344774444BB2244 55..331155006655110066 --00..775533888899770066 00..335533221122882222 00..008833885500991155 --00..115544440055338822 --00..332200339933997777 --00..6677337711331144 --00..3366994488221177 --00..224411669911111111 00..113377112277888833BB2255 77..0000009922665599 --11..550055557766448822 00..004499000011113366 00..229955221100772244 --00..000088330044112277 00..116622000066550055 --00..330022003399881199 --00..227744772288009999 --00..229999661155887799 --00..1122778855995588BB2266 44..333377228877221166 --00..664400992200661177 --00..008877998833880066 00..119977663322990011 --00..339966447722118833 --00..222233223311661199 --00..338899553344449944 --00..449922668800115555 00..110077993311441133 00..117733339955441177BB2277 66..002211887755336611 --11..661166559922991133 --00..004444334433116633 --00..0022003311330099 --00..006666773322110088 --00..007777443300885599 --00..22664400227788 --00..111133448888880066 00..115500771188226666 00..222266774499440055BB2288 33..883300447711991122 --11..119999331100006644 --00..000066118833226666 --00..226633886644118855 --00..227700339977000055 --00..118866004499882233 --00..332244883344006666 00..000055113388003388 00..119900552299664411 00..4433225533881188BB2299 55..551155991122770077 --11..775566660099779999 --00..2299339900229911 --00..115599119966991144 --00..333399775522007788 --00..001166447777992233 --00..229911446677885533 --00..001155110055995577 00..221166556644224411 00..661100337722667788BB3300 33..006666998811775588 --11..112288779933880055 --00..5566445599552233 --00..005533229955668888 --00..447777554422661188 --00..007799110055330033 --00..009933333399777755 --00..000033557777334488 00..444455003300991188 00..443355448899113366BB3311 44..994400662277881166 --11..447788443399225577 --00..338811996633668811 --00..330000994400883333 --00..441122997766005577 --00..224422339944996633 --00..222244887722556622 00..002244334488226622 00..339999995544449955 00..661100999955992211BB3322 22..886600001177336699 --11..331166886600223344 --00..110022337799332211 --00..119966996633778833 --00..003377115544333311 00..0077224499444477 00..000033662211999966 00..004455666600992255 00..113355889944440033 00..229999112233664488BB3333 44..884422557755778833 --11..445533111133887799 00..000044224488551144 --00..110022115500115544 --00..221166555566770077 --00..009911661100660044 --00..119977881122009911 00..001155229999221133 00..118877559900554466 00..440022550077110099BB3344 22..773300884499994466 --00..777777663366662255 --00..115555222299116644 00..332288006600668877 00..006644228811005599 00..220055441188999933 --00..002255994433111133 --00..119999339955333322 --00..001166009966887799 --00..116666446622002299BB3355 44..557744332299006699 --00..884411558844889933 --00..000044773399668833 00..119999333355990044 --00..001188771100996655 --00..002288221166005577 --00..2255774444771177 --00..223388225555886633 --00..111100779933881188 --00..114444553399333311BB3366 22..887755667700441199 --00..773333552277991177 00..119999998811333399 00..223355118899004466 00..220011332266554499 00..116688228855994433 --00..003377885588995511 --00..008822776622889977 --00..223322113344666655 --00..442200775577669922BB3377 44..668800447722778866 --11..118899225544555555 00..220077225533111166 00..119977228822112299 00..118800009944669977 00..116644006688556633 --00..119966669900881133 --00..114455448800223333 --00..228855006622116611 --00..221155999955993322BB3388 22..883311884477558888 --00..660000880033991133 00..005511885544117711 00..225599005544332266 00..001144220099440033 00..112244771177559966 --00..113388882299338833 --00..118844881122556655 --00..118888779955552277 --00..229988663344884499BB3399 33..996611225500991166 --11..007766335533667722 --00..004488111166006666 00..116688335599110033 00..004488774488332277 00..119911337777227799 --00..004422111100000088 --00..007733447722009977 --00..112233660044224499 --00..222222112211445588BB4400 22..556600775533888811 --00..889922225599228899 --00..004477996688225588 --00..002211889911886611 00..000088774433667711 00..113322885588004455 --00..001199772211118833 --00..111155667744224477 --00..002200997722111155 --00..002288664411446611BB4411 33..991188333399113388 --11..771144558888774422 --00..222288778800990033 --00..006688668899888855 00..220011884477777744 00..335522111111338833 00..112244113388442255 00..009966332244333322 00..007722229911332266 00..008800004477990099BB4422 22..221199225500555511 --11..111111887711557733 --00..4400770055447777 --00..007799667755009999 --00..007766555500111111 00..114466990077661133 00..000011226611227744 00..008877118866774499 00..228855882277557733 00..2288330055550033


FFiigguurree CC 11 TThhee rreeccoonnssttrruucctteedd eenntthhaallppyy--ccoonncceennttrraattiioonn ddiiaaggrraamm uussiinngg tthhee eeqquuaattiioonnss iinnAAPPPPEENNDDIICCEESS AA,, BB aanndd CC

design of absorption refrigeration (george vicatos)

Documents

oocc ttoo

oocc aannddffrroomm

oocc rreessppeeccttiivveellyy