Energy Conversion and Management 52 (2011) 1439–1448

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Energy Conversion and Management

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A model for analysis and design of H2O–LiBr absorption heat pumps

Bahador Bakhtiari ⇑, Louis Fradette, Robert Legros, Jean Paris ⇑École Polytechnique Montréal, Department of Chemical Engineering, QC, Canada

a r t i c l e i n f o

Article history:Received 7 November 2009Received in revised form 21 September2010Accepted 30 September 2010Available online 28 October 2010

Keywords:Absorption heat pumpH2O–LiBrModelingExperimental results

0196-8904/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.enconman.2010.09.037

⇑ Corresponding authors. Present address: NaturatENERGY, 1615 Lionel-Boulet, C.P. 4800, Varennes, QC652 0214 (B. Bakhtiari).

E-mail addresses: bahador.bakhtiari@nrcan.gc.capolymtl.ca (J. Paris).

a b s t r a c t

An experimental and simulation analysis of a laboratory single-stage H2O–LiBr absorption heat pumpwith a cooling capacity of 14 kW has been performed. Design characteristics of the machine are givenand experimental results obtained from the variation of the five most influential parameters are pre-sented. The machine performance, as described by the coefficient of performance (COP) and coolingcapacity was then measured at different flow rates and temperatures of the external cool and hot waterloops and for different temperatures of produced chilled water. A design and dimensioning model ofH2O–LiBr absorption heat pumps was developed. First, the steady-state simulation results of the modelwere compared with experimental measurements. Close agreement between experimental and simula-tion results was found. Results also show that the heat pump can adequately operate over a wide rangeof generator input energy and chilled water temperature; the cooling water flow rate and temperaturesignificantly affect the performance of the machine. Finally, the capability of the model is illustratedby dimensioning an absorption heat pump implemented in a Kraft process.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Absorption heat pumps (AHP) have been used since the late19th century and a large body of scientific and technical literaturehas been devoted to the fundamental principles, engineering de-sign and application of those devices [1–3]. Due to volatile energyprices and environmental concerns, these systems have receivedmore attention in the past two decades. AHPs supplied with wasteenergy or water heated through solar collectors are attractive op-tions, but only if they are correctly implemented. Such devicesare environmentally friendly since they use working fluids whichdo not cause ozone depletion. For the majority of AHPs used inindustrial applications, H2O–LiBr is the working fluid pair of choicesince it is not toxic, has a high enthalpy of vaporization and doesnot require a rectification step.

AHP chillers working at low driving temperatures are suitablefor trigeneration (cold, heat, and power production simulta-neously) and solar cooling applications. They commonly have beenused in air conditioning and it has been shown that they can beeffectively integrated to load shifting during summer peak electric-ity demand. However, they are rarely commercially available witha small cooling capacity.

ll rights reserved.

l Resources Canada, Canme-, Canada J3X 1S6. Tel.: +1 450

(B. Bakhtiari), jean.paris@

Single effect AHPs have been investigated in the past [4–7].Many parameters can affect the performance of AHP systems andseveral studies have been reported in the literature [8–11]. Math-ematical models of various complexity have been developed fordifferent purposes, such as single simulation of absorption system,evaluation of potential working fluids, optimization and design[5,6,10,12,13]. Some of those models were validated against exper-imental results with good agreement. However, most of them arerestricted to a specific system and are empirically derived and insome cases overly simplified.

In order to characterize the performance of the AHP and give anexperimental dimension, a prototype of 33 kW AHP was builtthrough an international collaboration [14–16]. In a previousstudy, to determine limits of operation of this prototype and tocharacterize the performance of the machine, 16 selected experi-ments based on a partial fractional design with seven variableswas performed [14]; those variables were the temperature andflow rate of chilled, cooling and hot water as well as the internalsolution mass flow rate. The respective effects of the independentvariables on the COP and the heat fluxes in the main four heatexchangers were computed. The variations of COP were very large(from 0.1 to 0.75); while some results were close to the design COPof 0.75, others were out of bound. The temperature of chilled, cool-ing and hot water and, the flow rate of cooling water and hot waterwere found to be the most influential operating parameters.

In the present study, those preliminary results were used to de-sign an experimental plan aimed at measuring the performance ofthe machine under different operating conditions using the fivepreviously identified dominant parameters. In parallel, a design

Nomenclature

A surface area (m2)D tube diameter (m)F fouling factor (m2 �C/kW)k thermal conductivity (kW/m2 �C)h enthalpy (kJ/kg)LMTD log mean temperature difference (�C)m mass flow (L/min)P pressure (bar)Q heat capacity (kW)T temperature (�C)U overall heat transfer coefficient (kW/m2 �C)un uncertaintyX concentration of LiBr (%)

Greek symbolsa heat transfer coefficient (kw/m2 �C)C fluid mass flow rate per unit length per one side of the

exchanger tube (kg/s m)e heat exchanger effectiveness

AbbreviationsAb absorberAct actualAHP absorption heat pump

Con condenserCOP coefficient of performanceEva evaporatorExp experimentalGen generatorRTD resistance temperature detectorSHX solution heat exchangerSim simulationTheo theoretical

Subscriptsa absorberc condensere evaporatoreq equilibriumg generatorin inletout outletref refrigerantsat saturationsol solutionst strong solutionw waterwe weak solution

1440 B. Bakhtiari et al. / Energy Conversion and Management 52 (2011) 1439–1448

and dimensioning model of the absorption cycle was developed.Experimental results were then used to validate the model. Thismodel requires minimal information about the working fluid andcharacteristics of the heat exchangers, and it is suitable for rapidand reliable simulation of an existing absorption cycle, evaluationand comparison of different working fluids and design and dimen-sioning of new AHPs. Finally, the model is used for dimensioningan AHP implemented in an actual Kraft process.

2. Experimental setup

2.1. Absorption machine

The prototype under study is a single effect AHP unit illustratedin Figs. 1 and 2 [15]. It consists of four main heat exchangers: con-denser, generator, absorber and evaporator and a fifth auxiliaryheat exchanger placed between the generator and the absorber,the solution heat exchanger SHX. The four main exchangers areof shell-and-tube type with horizontal tube bundles and a pres-sure-loss free arrangement for the distribution of the working solu-tion and refrigerant. The solution heat exchanger is a commerciallyavailable plate heat exchanger. The working pair is H2O–LiBr, inwhich water is the refrigerant and an aqueous lithium bromidesolution is the absorbent. In addition to the main working fluid, asurfactant additive, Octyl alcohol (2-ethyl-1-hexanol), is used toact as a heat transfer enhancer on the solution side. The prototypeis designed to offer good controllability with a high coefficient ofperformance (COP), in a compact design. To minimize pressuredrops and prevent leakage problems, condenser and generator, aswell as evaporator and absorber are placed together in a single ves-sel. The machine was designed for cooling purposes, either for theproduction of chilled water for air-conditioning systems with anevaporator temperature (Te,out) of 6–12 �C, or for the supply of cool-ing to radiant ceilings with an evaporator temperature of 15–18 �C.Table 1 presents the design specification of the absorption ma-chine. The absorber and condenser are water-cooled. The coolingwater is heated in nominal conditions from 27 to 40.4 �C (Ta,in to

Tc,out). It is connected in series: first the absorber is cooled and thenthe condenser. Series arrangements of the condenser and absorberallows for easy operation since a single pump can be used withoutthe control problem associated with a parallel design. It is also abetter configuration to avoid crystallization in the system. Duringthe experiments, the temperature level of the outlet cooling water(Tc,out) could be raised to 44 �C. This temperature is sufficient for aheat pump supplying a low-temperature heating systems such asthose used for floor heating. The hot water (Tg,in) is supplied at95 �C, making the machine suitable for use in cogeneration unitsdriven by engines or fuel cells, or in solar-assisted heating andair-conditioning systems. A centrifugal pump is used for the waterrecirculation in the evaporator. The solution pump is a gear pumpthat operates with a magnetic drive. The advantage of this type ofpump is the seal free drive that provides a hermetically enclosedenvironment without emission. Flow rates of recirculated waterand solution circuit are controlled by diaphragm valves bypassingthe pumps. Ball valves just before and after the pumps were builtin for maintenance. Both valves can be closed and the pump can bereplaced without losing solution or water. There is a bypass be-tween the evaporator recirculation pipe and the solution circuitjust before the solution enters the generator. Normally this bypassis closed and is used only in case of emergency to dilute the solu-tion in the solution loop.

2.2. Power station

The power station provides constant conditions at the desiredtemperatures and flow rates in the external circuits. It consists ofthree independent water loops that are connected to the heatpump. Fig. 3 shows these external loops providing the heat sourcesand sinks required by the prototype. The hot water loop is con-nected to the generator and supplies the driving energy. Threeheaters of 10 kW heating capacity each, heat the water to a set-point temperature. The power of the heaters is controlled by thegenerator inlet temperature. The cooling water loop cools the ab-sorber and condenser. It is connected in series: the absorber is

Fig. 1. Schematic of the prototype chiller built at Polytechnique Montreal.

Fig. 2. Schematic of the absorption heat pump.

Table 1Design specification of the absorption machine.

Working fluid H2O–LiBr

Cooling capacity (Qe) 14 kWChilled water temperature in/out (Te,in/Te,out) 21.7/15 �CFlow rate (me,in) 30 L/min

Driving heat capacity (Qg) 18.6 kWHot water temperature in/out (Tg,in/Tg,out) 95/81.7 �CFlow rate (mg,in) 20 L/min

Rejected heat capacity (Qa + Qc) 32.6 kWCooling water temperature in/out (Ta,in/Tc,out) 27/40.4 �CFlow rate (ma,in) 35 L/minCOP 0.75

B. Bakhtiari et al. / Energy Conversion and Management 52 (2011) 1439–1448 1441

cooled first and then the condenser. Normally the loop is con-nected to an external cooling tower. For the purpose of theseexperiments, the cooling tower is simulated by a plate heat ex-

changer connected to the water network of the laboratory. Waterfrom the network is constantly running through the heat exchan-ger. Its flow rate is controlled by a manual valve. A three-way valveon the side of the cooling water loop is used to control the absorberinlet temperature. The chilled water loop simulates the user de-mand for cooling. The user could be, for example, a house thatneeds cooling to compensate for loads generated by occupantsand by solar radiation. These loads are simulated by two heatersof 10 kW heating capacity each. The working principle is the sameas for the hot water loop. Three centrifugal pumps are used forwater recirculation in the power station. The flow is controlledby a control gate valve placed at the discharge of each pump. Theflow rates of each water loop can be adjusted by slider valves.

2.3. Measurement equipment and data acquisition

The prototype is computer-monitored and -controlled by meansof a Labview program [17]. It is equipped with 23 sensors to record

Fig. 3. Schematic of the power station system.

1442 B. Bakhtiari et al. / Energy Conversion and Management 52 (2011) 1439–1448

all process pressures, temperatures and flow rates as presented inFigs. 2 and 3. On the cooling machine itself, there are eight resis-tance temperature detectors (RTD) to measure eight internalstream temperatures. Two flow meters measure the volume flowrates of the recirculation loop at the evaporator and in the solutioncircuit. The flow meter in the solution circuit can also measure thedensity of the solution rich in water (weak solution). Two pressuresensors measure the pressure in the absorber and in the condenser.Furthermore, there are three sight glasses in the circuit to providevisual observation during the experiments and one sight glass oneach of the four main heat exchangers. There are eight additionalRTD temperature detectors in the power station to measure theeight external stream temperatures at the inlet and outlet of eachmain heat exchanger. Three flow meters are installed to measurethe volume flow rates of the three external water loops. Tenmanometers in the external loops indicate the water pressure dur-ing the experiments, but the data is not registered. These modulesreceive and send signals from and to the measuring instrumentsand communicate with the data acquisition program. This programcontrols the pumps and heaters and saves the experimental data atselected time intervals.

Real time operating variables and certain calculated parametersare constantly displayed on the monitor during the experiments.The calculated parameters are saved together with the measuredexperimental data in a worksheet. Calculated parameters are theloads of the four main heat exchangers, the COP, the concentrationof the weak and strong solutions and the solution recirculationflow rate. The COP for cooling and heating are calculated as follows[1]:

COPcooling ¼Qe

Q gð1Þ

and

COPheating ¼Q a þ Q c

Qgð2Þ

3. Model development

An analytical model to simulate a single stage AHP with H2O–LiBr was developed; its purpose is to assist in the design anddimensioning of those thermal machines. In this model, each com-

ponent is treated as a control volume with its own inputs and out-puts. The performance of the cycle is described by mass balanceson water and LiBr and energy balances for each machine elementand, by overall energy balance and heat transfer equations be-tween the internal and external streams. Solutions in the generatorand absorber are considered to be in equilibrium with refrigerantvapor at the same temperature and pressure. Major assumptionsmade to simplify the simulation and analysis are: steady-stateoperation, negligible heat losses and heat gains between the sys-tem and its environment, negligible work input to all internalpumps as compared to input energy to the generator and negligiblepressure losses in the equipment and pipes. The empirical equa-tions of enthalpies, temperatures, concentrations and vapour pres-sures of the H2O–LiBr working pair given by McNeely are used [18].The IAPWS-IF 97 equations has been used for calculating the ther-modynamic properties of water and steam [19]. The boiling tem-perature of saturated aqueous lithium bromide solution iscalculated as a function of the saturated temperature of the vaporand concentration of the solution proposed by Feuerecker et al.[20].

The heat transfer rate between the internal and externalstreams in the generator is given by,

Qg ¼ UgAgLMTDg ð3Þ

where Ag is the total heat transfer surface area in the generator, Ug isthe overall heat transfer coefficient for the generator and LMTDg isthe logarithmic mean temperature difference defined as:

LMTDg ¼ðTg;in � T4Þ � ðTg;out � T7Þ

ln Tg;in�T4

Tg;out�T7

ð4Þ

Prediction of heat transfer coefficients is affected by many uncer-tainties and unexpected results often arise in practice [7]. For thepurpose of this simulation, the user can choose between averageoverall heat transfer coefficients for each heat exchanger calculatedfrom experimental results if they are available, and heat transfercoefficients calculated from correlations. The overall heat transfercoefficient for the generator is determined from the sum of heattransfer resistances based on the outside surface of the tube as:

Ug ¼1

DoutDin

h i1

ag;in

h iþ Dout

2k

� �ln Dout

Din

h iþ 1

ag;outþ Dout

Din

h iFin þ Fout

ð5Þ

B. Bakhtiari et al. / Energy Conversion and Management 52 (2011) 1439–1448 1443

For this equation, the value of the fouling factors (Fi and Fo) for theoutside and inside surfaces of the tube can be assumed as0.09 m2 �C/kW [21]. A correlation for copper thermal conductivity,k, was developed by integrating table information provided by Hol-man [22], resulting in:

k ¼ �3e� 7T3 þ 0:0002T2 � 0:0832T þ 385:99 ð6Þ

The internal heat transfer coefficient between hot water andthe generator tube surface (ag,in) is determined using the Gni-elinski correlation [23]. If steam is used as the driving energyfor the generator, the correlation presented by Agrawal for thecondensation of vapours flowing inside a cylindrical tube is used[24].

There are few available published data for the generator exter-nal heat transfer coefficient (ag,out). A new correlation for ag,out wasproduced for the purpose of this work by integrating experimentalresults published by Wang et al. [25], resulting in:

ag;out ¼ 5554:3C0:236 ð7Þ

Fig. 4. Block diagram of the simulation program.

The definition of C used here is the total mass flow rate of the inter-nal fluid (LiBr solution in this case) per unit length of wetted tube(only one side of each tube is wetted).

Equations analogous to Eqs. (3)–(5) are applied to the absorber,condenser and evaporator. The Gnielinski correlation [23] is usedfor all internal heat transfer coefficients. The external heat transfercoefficient for the condenser is computed by a correlation for lam-inar evaporating films proposed by Holman [22]; in the case of theevaporator the corresponding correlation developed by Rohesnowet al. [26] was used. The external heat transfer coefficient for theabsorber is based on the correlation presented by Hoffmann et al.[27].

The SHX is characterized by using a solution heat exchangereffectiveness (eSHX) defined by Eq. (8).

eSHX ¼T4 � T5

T4 � T2ð8Þ

Table 2Modalities for the input variables.

Te,out (�C) Ta,in (�C) Tg,in (�C) ma,in (L/min) mg,in (L/min)

Min 6 20 65 15 10Nominal 15 27 95 35 20Max 16 40 110 43 35Increment 2 4 5 5 5

The entire set of non-linear equations is solved with the Gauss–Newton method.

The model has two different fields of applications. It can be usedeither to analyze the performance of an existing machine undervarious operating conditions or to design and dimension a newone. The organigram of the model in the simulation and analysismode is shown in Fig. 4. Results from the simulation were vali-dated by experimental results generated on the laboratory proto-type and by results from the literature [1,7]. Mass and energybalance equations for a single stage AHP used in the model are gi-ven in Appendix A.

The core of the model is unchanged when it is used for designand dimensioning purposes. However, user input data and outputvalues are different. The user must, in that case, define externaltemperatures and mass flow rates, concentration of the strongsolution (xst) and solution heat exchanger effectiveness (eSHX) as in-put data. The model calculates all the internal temperatures, pres-sures and mass flow rates as well as heat transfer coefficients forthe heat exchangers as output values. The heat exchangers surfaceareas are also calculated as design values. The usefulness of themodel is presented in the following sections, first, as a tool to pre-dict the operating parameters of an existing AHP and second, as atool for design and dimensioning of an AHP for a particular indus-trial application.

4. Model validation and experimental work

4.1. Experimental plan

Five sets of experiments were conducted to measure the perfor-mance of the machine under different operating conditions. It fo-cused on the effect of variations in the five dominant variables asidentified in the study presented earlier [14] on the performanceof the heat pump. Each of those variables was varied over a giveninterval in a stepwise fashion by a predetermined increment, othervariables remaining constant at their median value. The results byJahnke et al. [14] provided guidance to chose the modalities so thateach variable would span the practical range of operation for a sin-gle effect AHP (Table 2). After each temperature or flow ratechange, steady state was considered as being achieved when all re-corded variables remained constant for about 20 min. A method forestimating the uncertainty on experimental results by Kline andMcClintock [28] was used; it is summarized in Appendix B.

4.2. Results

Fig. 5 shows the variation of the COP and cooling capacity of theabsorption heat pump as a function of the temperature of the heatsource to the generator (Tg,in). The uncertainty bar for the experi-mental data is also displayed in this figure, considering (1% T)and (2% m) as the uncertainties for the temperature sensors andflow meters, respectively. Computed uncertainties are 10.3% forthe COP and 2.9% for the cooling capacity in the experiments.

0.0

0.2

0.4

0.6

0.8

60 70 80 90 100 110Generator inlet temperature [°C] (Tg,in)

CO

P

2

6

10

14

18

22

Coo

ling

capa

city

[kW

]

COP (Exp)

COP (Sim A)

COP (Sim B)

Cooling capacity (Exp)

Cooling capacity (Sim A)

Cooling capacity (SimB)

Fig. 5. Variation of the COP and cooling capacity with generator inlet temperature(Tg,in).

1444 B. Bakhtiari et al. / Energy Conversion and Management 52 (2011) 1439–1448

The range of relative uncertainty being predictably constant in allexperiments, it is not presented in the following figures. The exper-imental COP is almost constant close to the design COP with a max-imum value of 0.76 at Tg,in = 90 �C. The capacity varies almostlinearly starting from a low value of 5.2 kW up to 16.5 kW. The factthat the capacity is increasing while the COP remains constantindicates that there are several factors with opposite effects thatvary as the heat source temperature changes.

The performance of the heat pump is strongly affected bychanges in the internal and external temperatures. The COP wouldbe expected to increase with increasing generator temperature. Atthe same time, the evaporator temperature is increased which re-sults in a decrease of the COP. This negative effect seems to balancethe beneficial effect of the high temperature of the generator inlet.Two pairs of simulated COP and cooling capacity results are alsopresented in Fig. 5. In pair A, the model uses average overall heattransfer coefficients calculated from experimental results. In pairB, the model calculates heat transfer coefficients using the correla-tions presented earlier. In general, there is a good agreement be-tween measured and calculated COP and cooling capacity byboth methods. Since similar behavior was observed in the otherexperiments; simulation results based on values of U computedfrom the correlations are not presented in the following figures.

Table 3 presents experimental data and model predictions for aset of experiments in which the effect of generator inlet tempera-ture on the performance of the AHP is studied. It also shows thegood agreement between measured and predicted values. Massflow rates for the three external loops were those in Table 1, i.e. de-sign values.

Values of overall heat transfer coefficients calculated fromexperimental results, designated ‘‘experimental” and those com-

Table 3Effect of generator inlet temperature (Tg,in) on the performance of AHP.

Exp/Sim Independent variables (input) Process variables (outp

Temperature (�C)

Tg,in Ta,in Te,out Tg,out Te,in

Exp 1 70.1 26.9 14.8 63.2 18.3Sim 1 70.1 26.9 14.8 62.5 18.7Exp 2 79.9 26.8 14.9 70.2 19.8Sim 2 79.9 26.8 14.9 70.2 19.9Exp 3 89.9 27.1 15.2 78.5 21.0Sim 3 89.9 27.1 15.2 78.1 21.3Exp 4 100.1 27.2 15.1 85.4 22.4Sim 4 100.1 27.2 15.1 86.2 22.2Exp 5 109.7 26.8 14.9 93.4 22.8Sim 5 109.7 26.8 14.9 93.7 23.0

puted from a correlation designated ‘‘correlations” for the differentheat exchangers are presented in Table 4. As expected in generalthe experimentally computed ones are lower than the ones com-puted from correlations. The biggest difference between the twosets is in the case of the generator where the external heat transfercoefficient is calculated using the new correlation (Eq. (7)). Thiscan be explained by the fact that the operating range of this partic-ular heat exchanger was outside the range of literature data [25]used to obtain this correlation, thus requiring an extrapolation. Agood agreement between calculated COP by both methods(Fig. 5) was observed which shows that the COP is relatively insen-sitive to change in U while the capacity is more sensitive to thosecoefficients. It should be noted that the same behavior was ob-served by Herold et al. [1].

The variation of the COP and cooling capacity with chilled watertemperature (Te,out) is shown in Fig. 6. The COP varies very littleover the experimental range of chilled water temperature (6 –16 �C). This variation has a stronger effect on the cooling capacitywhich increases from 9.2 kW at 6 �C to 14.3 kW at 16 �C. It causestemperature effects in the system that balance the increasedcapacity and the COP remains almost constant. The COPs predictedby the model and measured are almost identical. The difference be-tween measured and predicted cooling capacities at lower chilledwater temperature can be explained by the fact that average valuesof overall heat transfer coefficients for each heat exchangers areused for the simulation. Those average valued may differ fromthe actual heat transfer coefficients in the case of low generator in-let temperatures.

As shown in Fig. 7, cooling water temperature (Ta,in) has thestrongest effect on the cooling capacity of the heat pump. Thereis good agreement between experiments and simulations. Thecooling capacity increases significantly as cooling water tempera-ture decreases. In an actual implementation, low cooling watertemperature can be achieved using a wet cooling tower, whilehigher cooling water temperature can be obtained with dry coolingtowers. Once again, the COP varies only slightly in the range of0.78–0.7 with cooling water temperature between 20 �C and32 �C as the combined effects of temperature and capacity changestend to cancel each other. At higher cooling water temperatures,the COP drops to 0.53. This is due to the fact that the rate of de-crease of the evaporator load becomes larger than that of the otherheat exchangers at the higher cooling water temperature.

Fig. 8 shows that the generator water flow rate (mg,in) has littleeffect on the performance of the heat pump. The COP is almost con-stant in the range of flow rates which indicates that the hot waterside is not the dominant factor in controlling heat transfer coeffi-cient of the generator. The cooling capacity is improved slightlyby high generator flow rate. The effect of cooling water flow rate(ma,in) on the cycle performance is plotted in Fig. 9. The cooling

ut) Calculated values

Heat load (kW) COP

Tc,out Ta,out/Tc,in Gen Ab Eva Con

33.9 30.2 9.7 8.1 7.3 8.9 0.7534.7 30.6 10.6 8.9 8.1 9.8 0.7736.6 31.6 13.5 11.6 10.2 12.1 0.7636.8 31.6 13.5 11.8 10.5 12.2 0.7738.7 32.8 15.9 13.8 12.1 14.2 0.7639.0 33.0 16.5 14.4 12.7 14.8 0.7741.9 35.0 20.4 18.9 15.2 16.7 0.7441.1 34.6 19.4 18.2 14.9 16.1 0.7743.1 35.7 22.8 21.5 16.5 17.8 0.7343.1 35.6 22.3 21.4 16.9 17.8 0.76

Table 4Overall heat transfer coefficients of the various heat exchangers.

Unit Overall heat transfer coefficient (kW/m2 K)

Correlations Experimental

Gen 1–1.15 0.7Ab 0.4–0.65 0.52Eva 1.62–1.65 1.11Con 2.3–2.4 1.75SHX �0.2 0.2

0

0.2

0.4

0.6

0.8

6 8 10 12 14 16

Chilled water temperature [°C] (Te,in)

CO

P

Coo

ling

capa

city

[kW

]

COP (Exp)

COP (Sim)

Cooling capacity (Exp)

Cooling capacity (Sim)2

6

10

14

18

22

Fig. 6. Variation of the COP and cooling capacity with chilled water temperature(Te,out).

0.2

0.4

0.6

0.8

20 25 30 35 40Cooling water temperature [°C] (Ta,in)

CO

P

Coo

ling

capa

city

[kW

]

COP (Exp)

COP (Sim)

Cooling capacity (Exp)

Cooling capacity (Sim)2

6

10

14

18

22

Fig. 7. Variation of the COP and cooling capacity with cooling water temperature(Ta,in).

0

0.2

0.4

0.6

0.8

Generator flow rate [L/min] (mg,in)

CO

P

2

6

10

14

18

22

Coo

ling

capa

city

[kW

]

COP (Exp)

COP (Sim)

Cooling capacity (Exp)

Cooling capacity (Sim)

10 14 18 22 26 30 34

Fig. 8. Variation of the COP and cooling capacity with generator flow rate (mg,in).

15 20 25 30 35 40Cooling water flow rate [l/min] (ma,in)

CO

P

Coo

ling

capa

city

[kW

]

COP (Exp)COP (Sim)Cooling capacity (Exp)Cooling capacity (Sim)

00.10.20.30.40.50.60.70.80.9

46810121416182022

Fig. 9. Variation of the COP and cooling capacity with cooling water flow rate(ma,in).

B. Bakhtiari et al. / Energy Conversion and Management 52 (2011) 1439–1448 1445

capacity and the COP are improved by high cooling water flowrates. It indicates that the cooling water side is the dominant factorin the heat transfer coefficients of the absorber and condenser.

It is worth mentioning that, in this study higher cooling capac-ities and better COPs are obtained, in comparison with the results

presented by Jahnke et al. [14]. Table 5 presents selected experi-mental results (4 runs among 16) presented in [14]. The higherperformance observed in our study can be explained by the differ-ent experimental conditions of the two studies. In [14], the AHPwas operated at conditions close its operating limits with morethan one variable being kept at its extremum. In our study, the per-formance of the heat pump is observed with only one variablebeing varied over a given interval, all other variables being keptconstant at their design value. In comparison with the design per-formance, experiment J1 from Table 5 has the same COP but lowercooling capacity. It can be explained by its low generator inlet tem-perature (Tg,in); as discussed in the previous sections. On the otherhand, experiment J4 has the lowest performance of those pre-sented. It is because of combining the negative effects of high cool-ing water temperature (Ta,in), low generator inlet temperature(Tg,in) and very low cooling water and generator flow rates (ma,in

and mg,in) at the same time.

5. Application to design

The model will now be used to calculate the design and operat-ing parameters of an AHP to be implemented in a Kraft process. TheKraft process is a paper pulp-making technology by which woodchips are transformed into paper pulp [29]. The core of the Kraftprocess is a chemical delignification step in which chemical attackis employed to degrade and solubilise the lignin which binds to-gether the fibres in wood in chemical reactors called digesters.The fibres are separated from the residual digesting liquor, theblack liquor, in a series of counter current washers. The black li-quor is then concentrated in a series of evaporators and burnedin recovery boilers to utilize its energy content and recover thespent reactants which are regenerated. The clean pulp is bleached,dried to about 90% solids, cut in sheets and baled for shipment tocustomers. A simplified schematic of the complete Kraft processis given in Fig. 10. Supporting data for this study were taken fromthe work by Bakhtiari et al. [30], in which implementation of AHPsin a Kraft pulping process was studied using a new methodologyfor the optimal integration of those devices in a process [31]. It pro-vides systematic guidelines for the proper selection of heat sourcesand sinks to maximize the benefit derived from heat pumping,while respecting both process constraints and operating require-ments of the AHP. Economic evaluation of AHPs, comparison ofAHPs with the conventional heat pumps and the correspondinggreenhouse gas emissions avoided are presented in a series of pub-lication elsewhere [3,30–32]. A simple case has been chosen toillustrate the capability of the model in the design mode.

Bakhtiari et al. [30] showed that in the Kraft process, there is avery large amount of energy at low temperatures which has thepotential to be upgraded and recovered. In the selected example,

Table 6Properties of the selected streams [30].

Stream Tin (�C) Tout (�C) Flow (kg/s) Heat load (kW)

Bleaching alkalineeffluents

56.1 44 27.8 961

Hot water 57 76 19 2229LP steam 144 144 0.63 1268

Digester

Unbleachedpulp

Washer

WashedPulp

BleachingChemicals Bleaching

BleachedPulp

MarketPulp

Drying

Evaporators

Strong BlackLiquor

Recausticizing Plant

RecoveredChemicals

CookingChemicals

Steam

Biomass &Bunker oil

WoodChips

Weak BlackLiquor

BoilerRecovery Boiler

Fig. 10. Schematic representation of the Kraft process.

Table 5Selected experimental results from Jahnke et al. [14].

Exp Independent variables (Input) Calculated values

Temperature (�C) Flow rate (L/min) Heat load (kW) COP

Tg,in Ta,in Te,out mg,in ma,in me,out Gen Ab Eva Con

J1 75 26.8 14.8 37.9 40.3 44.7 13.3 12.0 10.0 10.7 0.75J2 110 26.4 15 4.8 39.2 15.0 14.1 12.9 9.8 10.7 0.70J3 110 26.5 15 4.9 10.9 44.5 8.2 7.1 4.1 4.9 0.50J4 75.4 34 25 6.9 13.2 43.5 3.6 2.7 0.3 0.9 0.09

40% 50%

60%

70%

0 20 40 60 80 100 150 200120

Concentration x =

Pure Wate

r

Pres

sure

[kPa

]

Temperature [°C]

Crystal

lizati

on line

0.5

1

2

5

10

20

50

100

200

Fig. 11. The proposed AHP in LiBr/H2O equilibrium diagram.

1446 B. Bakhtiari et al. / Energy Conversion and Management 52 (2011) 1439–1448

the particular objective of the heat pump is to upgrade the lowtemperature heat load from the effluent of the pulp bleaching plantto a higher temperature level. Hot water from the power plant wasselected as the proper above the pinch point. Low pressure steam

Table 7Design parameters for the single stage AHP.

Description Unit

InputQ kWInside diameter of tube mmOutside diameter of tube mmLength of the unit mNumber of tubes in the vertical direction per passNumber of passesFouling factor m2 �C/kW

ComputedPressure kPaU kW/m2 �CLMTD �CCalculated Surface area m2

Total number of tubesNumber of tubes in the horizontal direction per pass

(LP) at 345 kPa was used as the driving energy for the generator.Table 6 presents the properties of the selected streams.

The model calculates the design parameters of the heat pump ina steady-state operation. It was assumed that the four heatexchangers are shell-and-tube, and eSHX and xst are respectively0.7 and 59%, that safely is far from the crystallization zone. Thebleaching alkaline effluents are cooled in the evaporator from56.1 �C (Te,in) to 44 �C (Te,out), using 0.63 kg/s LP steam as the driv-ing energy in the generator (Tg,in = Tg,out = 144 �C). Condenser andabsorber release the useful energy above the pinch point to in-crease the temperature of 19 kg/s of hot water from 57 �C (Ta,in)to 77 �C (Tc,out). The design and dimensioning parameters are pre-sented in Table 7 as the input and calculated values. For each heatexchanger, the total surface area required is calculated and thenumber of tubes is obtained for the given values of the physicaldimensions of each unit. Fig. 11 presents the cycle in the phase dia-

Absorber Evaporator Condenser Generator

1213 961 1016 126813.84 13.84 13.84 13.8415.87 15.87 15.87 15.876.096 6.096 6.096 6.0968 8 12 124 4 1 29E�6 9E�6 9E�6 9E�06

8.3 8.3 54.5 54.50.8 2.3 2.1 119.5 5.6 11.4 15.377.7 74.6 42.4 82.9256 256 144 2888 8 12 12

B. Bakhtiari et al. / Energy Conversion and Management 52 (2011) 1439–1448 1447

gram of the binary solution. It shows that the desired temperaturelift can be accomplished in a single effect machine, with reasonabletemperatures, pressures and concentrations. Mass flow rate andconcentration of the weak solution are calculated at 3.9 kg/s and53%; respectively. A typical value of 1.76 is obtained for theCOPheating.

6. Conclusion

In this work, a single-stage H2O–LiBr absorption chiller of14 kW was experimentally characterized and modeled. The ma-chine performance, as described by cooling capacity and COP weremeasured at different temperatures of chilled, cooling and hotwater and, different flow rates of cooling and hot water.

The results have shown that an AHP has almost a constant COPover a large hot water inlet temperature which makes such a de-vice well suited for trigeneration or solar cooling applications.The COP is primarily influenced by the cooling stream temperatureand flow rate. The heat pump cooling capacity is more sensitive tocooling stream and generator inlet temperature than it is to chilledstream temperature.

A model for analysis and design of H2O–LiBr absorption has alsobeen developed. Good agreement of the experimental and simula-tion results was observed. The model has the capability to useeither actual heat transfer coefficients computed experimentallyor to estimate them by theoretical or empirical correlations. Themodel is capable of quick and reliable simulation and can be usedas an aid to design of absorption cycles. It is shown how the devel-oped model can be linked to the AHP implementation methodol-ogy for the design of an AHP to be implemented in an existingprocess. The design parameters are presented.

The development of economic data to complement the techni-cal design capability of the model would constitute a very valuabletool for the optimal design of AHPs. It would assist engineeringwork for the implementation of such machines in industrialprocesses.

Acknowledgements

Max Siegel research intern and Keyvan Agha Bararpour MScstudent, contributed to the experimental work presented and tothe developing the thermodynamic model; their contributionsare acknowledged. This work was supported by research grantsfrom the Natural Science and Engineering Research Council ofCanada.

Appendix A

A.1. Energy equations

Condenser

Q c ¼ mcðhc;out � hc;inÞ ¼ mref ðh7 � h8Þ ¼ UcAcLMTDc ðA:1Þ

LMTDc ¼ðTc;in � T8Þ � ðTc;out � T8Þ

ln Tc;in�T8Tc;out�T8

ðA:2Þ

Evaporator

Q e ¼ meðhe;in � he;outÞ ¼ mref ðh10 � h9Þ ¼ UeAeLMTDe ðA:3Þ

LMTDe ¼ðTe;in � T10Þ � ðTe;out � T9Þ

ln Te;in�T10Te;out�T9

ðA:4Þ

Generator

Qg ¼ mgðhg;in � hg;outÞ ¼ mref h7 þmsth4 �mweh3

¼ UgAgLMTDg ðA:5Þ

LMTDg ¼ðTg;in � T4Þ � ðTg;out � T7Þ

ln Tg;in�T4

Tg;out�T7

ðA:6Þ

Absorber

Qa ¼ maðha;out � hg;inÞ ¼ mref h10 þmsth6 �mweh10

¼ UaAaLMTDa ðA:7Þ

LMTDa ¼ðT6 � Ta;outÞ � ðT1 � Ta;inÞ

ln T6�Ta;outT1�Ta;in

ðA:8Þ

Solution heat exchanger

QSHX ¼ mweðh3 � h2Þ ¼ mstðh4 � h5Þ ¼ USHXASHXLMTDSHX ðA:9Þ

Overall

Qg þ Qe ¼ Q a þ Q c ðA:10Þ

A.2. Mass balances

mwe ¼ mst þmref ðA:11Þ

xwemwe ¼ xstmst ðA:12Þ

Appendix B

B.1. Uncertainty analysis

Kline and McClintock method for estimating the uncertainty inexperimental results is based on specifications of the uncertaintiesin the primary experimental measurements.

If F is a given function of m independent variables y1, y2, . . . , ym,

F ¼ Fðy1; y2; . . . ; ymÞ ðB:1Þ

And un1, un2, . . . , unm are the related uncertainties of the inde-pendent variables then the uncertainty in the result (unF) is givenas:

unF ¼@F@y1

un1

� �2

þ @F@y2

un2

� �2

þ � � � þ @F@yn

unn

� �2" #0:5

ðB:2Þ

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