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Applied Thermal Engineering 91 (2015) 654e670

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

A review of absorption heat transformers

W. Rivera a, *, R. Best a, M.J. Cardoso b, R.J. Romero c

a Instituto de Energías Renovables, Universidad Nacional Autonoma de Mexico, Privada Xochicalco S/N, Colonia Centro, 62580, Temixco, Mor., Mexicob Instituto de Investigaciones El�ectricas, Av. Reforma 113, Col. Palmira, 62490, Cuernavaca, Mor., Mexicoc Centro de Investigaci�on en Ingeniería y Ciencias Aplicadas, Universidad Aut�onoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, 62209,Cuernavaca, Mor., Mexico

h i g h l i g h t s

� We review heat transformer systems in papers that were mainly published in specialized journals.� We cover single stage, advanced systems, applications and new working pairs.� 168 references were classified and cited.� Tables were provided mentioning the author, the working pairs and the relevant implications.� Conclusions were provided for the state of the art of heat transformers.

a r t i c l e i n f o

Article history:Received 23 January 2015Accepted 11 August 2015Available online 20 August 2015

Keywords:Absorption heat transformersHeat pumpsEnergy savingWater-lithium bromideAlternative working fluids

* Corresponding author.E-mail address: [email protected] (W. Rivera).

http://dx.doi.org/10.1016/j.applthermaleng.2015.08.021359-4311/© 2015 Elsevier Ltd. All rights reserved.

a b s t r a c t

In this paper, a review of the performance and development of absorption heat transformers is pre-sented. The review covers the current state of theoretical and experimental studies of single andadvanced systems, operating with conventional or alternative mixtures. It also includes their applica-tions, such as waste heat recovery from industrial processes, cogeneration systems and seawater desa-lination and distillation among others. A bibliographic review has been done based on internationaljournals, dating back from 1986 to date. The review does not intend to be exhaustive, but to reflect themost important research that has been published concerning these technologies.

© 2015 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6552. Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655

2.1. Single-stage heat transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6552.1.1. Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6552.1.2. SSHT operating with water/lithium bromide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6562.1.3. SSHT operating with alternative mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6562.1.4. Conclusions of SSHT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657

2.2. Advanced absorption heat transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6572.2.1. Description of advanced systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6582.2.2. Advanced AHT operating with water/lithium bromide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6582.2.3. Advanced AHT operating with alternative mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6592.2.4. Conclusions of AAHT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660

2.3. Heat transformers applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6602.3.1. Water purification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6602.3.2. Energy recover from industrial processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6612.3.3. Other applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662

1

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W. Rivera et al. / Applied Thermal Engineering 91 (2015) 654e670 655

2.3.4. Conclusions of heat transformers applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6623. Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

3.1. Single stage heat transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6633.1.1. SSHT operating with water/lithium bromide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6633.1.2. SSHT operating with alternative mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6633.1.3. Conclusions of SSHT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664

3.2. Advanced absorption heat transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6653.2.1. Conclusions of AAHT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665

3.3. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6653.3.1. Small scale application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6653.3.2. Industrial applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6663.3.3. Conclusions of applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667

1. Introduction

Energy is an essential element for economic development andsocial progress in all countries. Without adequate and secure sup-plies of energy, objectives of economic and social development areunlikely to be met. Currently, crude oil, natural gas (NG) and coalaccount for about 90% of the world's commercial energy produc-tion. The rest is provided by a variety of sources which includenuclear power, geothermal energy and renewable resources.

Although in the last months, the cost of energy has beenreduced considerably due to an oversupply, it is not clear that theprices of oil and natural gas will remain low in the upcoming years.In addition to, the use of fossil fuels continues to cause an increasein the emission and release of CO2 into the atmosphere. It is notsurprising then, that many countries are investing importantamounts in the development of equipment to facilitate the recoveryand efficient use of energy.

Some of the most interesting devices for energy savings, whichconsume negligible amounts of primary energy, are heat-drivenabsorption heat-pump systems. These and especially absorptionheat transformers are some of the most promising devices forupgrading industrial waste heat and heat from geothermal andsolar sources to higher temperature levels. Moreover, heat trans-formers can be used in cogeneration systems, for seawater desali-nation and distillation among other applications.

T

ABEV

GECO

HE

PQEV

QCO QGE

QAB

Fig. 1. Pressure against temperature diagram for a single-stage heat transformer.

Absorption heat transformers (AHT) are devices for increasingthe temperatures of moderately heat sources to more useful levels.Typically, with single-stage systems up to half of the heat supplycould be increased in temperature while the rest is discharged tothe atmosphere at lower temperature.

Currently, two bibliographic reviews about heat transformershave been published in international journals. Parham et al. [1]published a comprehensive review of 99 references of single andadvanced absorption heat transformers and their applications indifferent industrial processes reporting, for some cases, economicaspects. Donellan [2] analyzed 106 references on the vapor ab-sorption heat transformers emphasizing in optimization studies,alternate cycle configurations, some studies of working fluids andindustrial application case studies.

The present paper is a comprehensive bibliographic review ofthe state of the art of AHT. The review covers the current state oftheoretical and experimental studies of single and advanced sys-tems, operating with conventional or alternative mixtures. It alsoincludes their applications, such as waste heat recovery from in-dustrial processes, cogeneration systems, seawater desalinationand distillation, among others. The bibliographic review was donebased on international journals, dating back from 1986 to date. Thereview covers 158 studies related on absorption heat transformers.It does not intend to be exhaustive, but to reflect the most impor-tant research that has been published concerning thesetechnologies.

2. Theoretical studies

This section presents everything in reference to theoreticalstudies regarding heat transformers including the description andresearch of themain cycles, either single-effect or advanced, as wellas the use of conventional and alternative mixtures and theirpossible applications.

2.1. Single-stage heat transformers

2.1.1. DescriptionA single-stage heat transformer (SSHT) basically consists of an

evaporator (EV), a condenser (CO), a generator (GE), an absorber(AB) and a heat exchanger (HE) or also called economizer as shownin Fig. 1. Waste heat is added at intermediate temperature to thegenerator (QGE) to vaporize the refrigerant from the weak solution(low absorbent concentration). The vaporized refrigerant goes tothe condenser where it is condensed delivering an amount of heat(QCO) at low ambient temperature. The refrigerant leaving the

W. Rivera et al. / Applied Thermal Engineering 91 (2015) 654e670656

condenser is pumped to the evaporator where it is evaporated bymeans of a quantity of waste heat at intermediate temperature(QEV). After this, the refrigerant vapor goes to the absorber where itis absorbed by the solution with high concentration of absorbentcoming from the generator, delivering an amount of heat at highertemperature (QAB). Finally, the solution with low concentration ofabsorbent returns to the generator, preheating the solution in theeconomizer starting the cycle again.

Some theoretical studies of SSHT independent of the usedmixtures have been carried out by diverse authors. The optimalperformance of an AHT was investigated by Chen [3,4]. He pro-posed a general expression related to the rate of heat pumping, thecoefficient of performance (COP), and the overall heat transfer areaof the heat transformer to optimize the main performance pa-rameters of the AHT. Chen [5] also carried out a thermodynamicanalysis of the performance of a solar absorption heat transformer(SAHT) to determine the maximum COP. The author reported thatthe results may serve as a good guide for the evaluation and opti-mization of existing SAHT. Bhardwaj et al. [6] carried out a finitetime optimization of an irreversible AHT. The parametric studyprovided the variation of the maximum heating load, COP, workingfluid temperatures and heat transfer rate between the system andits thermal reservoirs with operating variables. The performance ofthe generalized irreversible four-heat-reservoir AHTcyclewith heatresistances, heat leak and internal irreversibility was analyzed andoptimized using finite-time thermodynamics by Qin et al. [7]. Basedon the same generalized irreversible heat transformer, Qin et al.[8,9] proposed a generalized heat transfer law to optimize theperformance of the system. Based on an endoreversible absorptionheat transformer cycle, Qin et al. [10] and Sun et al. [11] developedmodels which could be used to provide some guidance for theoptimal design of absorption heat transformers, and Wu and Chen[12] carried out a parametric optimum design of an irreversibleheat transformer based on the thermo-economic approach.

2.1.2. SSHT operating with water/lithium bromideEisa et al. [13] published the thermodynamic design data for an

AHT operating with H2O/LiBr reporting tables of possible combi-nations of operating temperatures, concentrations, flow ratios (FR)and COP. The authors found that the maximum COP was close to0.5. A graphical exergy study on a SSHT was carried out by Ji andIshida [14]. The results showed that the exergy losses in the pre-mixing process in the absorber was very large, reason why theauthors proposed a multiple-compartment absorber in close-to-equilibrium operation, in order to reduce that exergy losses.Based on the second law of thermodynamics an analysis was con-ducted byWang et al. [15] to study the effects of diverse parameterson the COP and irreversibility of the cycle. Zebbar et al. [16]developed a mathematical model for an AHT operating accordingto the endoreversible cycle. The model was used to find out theoptimal operating parameters using an alleged structural analysis.It was concluded that for the same thermal powers and heattransfer parameters, an increase on the first and second law effi-ciencies equal to 10% and 5.3%, respectively, could be achieved. Guoet al. [17] developed a mathematical model of a vertical falling filmabsorber to analyze the performance of AHT under design and off-design conditions. The results showed that the COP and exergyefficiency were significantly higher under off-design conditionscompared with the use of previous operation strategies.

2.1.3. SSHT operating with alternative mixturesTo date, the H2O/LiBr has been the most used mixture in AHT,

even though it possesses some well-known disadvantages. For thisreason, several studies have been carried out in order to findalternative mixtures to be used in heat transformers.

George and Murthy carried out diverse studies on the perfor-mance of AHT operating with R21/dimethyl formamide (DMF) andR21/dimethylether tetraethylene glycol (DMETEG) pairs. Theyfound that the COPs using R21/DMF increased from 0.45 to 0.498and using R21/DMETEG from 0.41 to 0.442 when the mass transfereffectiveness in the absorber increased from 0.3 to 0.9 [18]. Theyalso found that the COPs operating with R21/DMF increased from0.445 to 0.479 andwith R21/DMETEG from 0.391 to 0.425 when themass transfer effectiveness in the generator increased from 0.3 to0.9 [19], and the COPs using R21/DMF varied from 0.417 to 0.509and using R21/DMETEG from 0.405 to 0.446 when the heatexchanger effectiveness varied from 0.3 to 0.9 [20]. In all the casesthe generator and condenser temperatures where 90 �C and 30 �C,respectively. Also they studied the effect of the evaporator andgenerator temperatures on the system performance and found thatthe COP increases with the increment of both temperatures, espe-cially when the higher temperature of the heat sourcewas suppliedto the generator [21]. In the four studies carried out by these au-thors, the system operating with R21/DMF achieved higher COPsthan the system operating with R21/DMETEG. A series of papersabout the thermodynamic design data of AHT operating withdifferent mixtures were published by diverse authors. Best et al.[22] utilized ammonia/water, Grover et al. [23] water/lithiumchloride, Best et al. [24] ammonia/lithium nitrate, Patil et al. [25]water/lithium iodide, Best et al. [26] ammonia/sodium thiocya-nate, Best and Rivera [27] water/Carrol™ (where Carrol is a mixtureof LiBr and ethylene glycol [(CH2OH)2] in the ratio 1:4.5 by weight),and Rivera and Romero [28] water/ternary hydroxides. From theanalysis of these papers for an specific condition of 60 �C of the heatsource the COP were 0.453, 0.443, 0.432, 0.422, 0.32 and 0.279 forwater/lithium bromide, water/Carrol, water/ternary hydroxides,water/lithium iodide, ammonia/sodium thyocianate and ammonia/lithium nitrate, respectively. So, from this similar studies it can beconcluded that the highest COP were obtained with mixtures usingwater as refrigerant. However, it was also observed that the highestgross temperature lifts (GTL) up to 60 �Cwere obtainedmainly withmixtures using ammonia as refrigerant. Stephan and Seher [29]reported the results of a SSHT operating with the NH3/H2Omixture. The results showed that a COP and a GTL as high as 0.35and 40 �C, could be obtained, respectively. Kriplani et al. [30] pre-sented a comparative performance study of a SSHT operating withH2O/LiBr, R21/DMF, R22/DMF and R22/DMETEG as working fluids.It was found that for similar operating conditions the mixture withthe higher COPs, between 0.48 and 0.60 was R21/DMF followed byH2O/LiBr with COPs between 0.48 and 0.53, and the mixture withthe lower COPs, between 0.35 and 0.44 was R/22/DMF. Ciambelliand Tufano [31e33] developed a model for an AHT operating withthe water/sulfuric mixture. The results showed that the mixturewas particularly suited for heat source temperatures higher than100 �C. The maximum COP was almost 0.5. Tyagi et al. [34] studiedthe theoretical performance characteristics of SSHT usingammonia/1,4 butaneidol, ammonia/2,3butaneidol, ammonia/trie-thylenglycol dimethyl ether (TEG-DME) and sulphur dioxide/dimethylacetamide (SO2/DMA). For a heat source temperature of60 �C, a condenser temperature of 30 �C and a Dx ¼ 16% the COPwere 0.593, 0.541, 0.503, 0.498 and 0.487 for the mixtures NH3/H2O, SO2/DMA, NH3/1,4 butadeinol, NH3/2,3 butadeinol and NH3/TEG-DME, respectively. A comparative study of different workingfluid combinations with R22 as refrigerant and six absorbents,namely, dimethyl formamide (DMF), dimethyl acetamide (DMA),methyl-2-pyrrolidone (NMP), dimethylether diethylene glycol(DMEDEG), dimethylether tetraethylene glycol (DMETEG) anddimethylether triethylene glycol (DMETrEG), in a vapor absorptionheat transformer was carried out by Fatouh and Murthy [35]. It wasfound that the DMA and NMP were preferable solvents for R22 to

T

P

AEEV

GECO

HE1

ABAE

QEV

QGE

QAB

QAE

QAE

QCO

Fig. 3. Pressure against temperature diagram for a double-stage heat transformer.


obtain high heat delivery temperatures, low circulation ratios andhigh COP which were around 0.4. Zhuo and Machielsen [36]compared the performance of an AHT using the working pair tri-fluoroethanol/pyrrolidone (TFE/Pyr) with the H2O/LiBr. The resultsshowed that the useful heat and the COPs were up to 20% higherwith the working pair H2O/LiBr than with TFE/Pyr. However due tocorrosion problems the H2O/LiBr could only operate at tempera-tures up to 150 �C, while the alternative mixture could operate upto 200 �C. Ismail [37] studied the performance of AHT operatingwith the ammonia/water mixture. COP values as high as 0.45 wereobtained at low GTL and heat exchanger effectiveness close to 0.9.Yin et al. [38] compared the theoretical performance of an AHToperating with H2O/LiBr, TFE (2,2,2-trifluoroethanol)/NMP (N-methy1-2-pyrrolidone), TFE/E181 (dimethylether tetra/ethyleneglycol) and TFE/Pyr. The results showed that the COPs were higherwith the mixture H2O/LiBr than those with the other mixtures,however, they found that with TFE/NMP, TFE/E181 and TFE/Pyr thesystem could operate up to 200 �C, instead of the 150 �C with theH2O/LiBr. Bourouis et al. [39] compared the performance of an SSHToperating with the H2O/(LiBr þ LiI þ LiNO3 þ LiCl) and H2O/LiBrmixtures. The multi-component salt mixture showed a consider-ably higher solubility and less corrosive than the H2O/LiBr mixture.The COP for the multicomponent salt were almost constant withthe increase of the condenser temperature, while the COP withH2O/LiBr decreased considerably. The maximum COP with theproposed mixture was 0.51. Zhang and Hu [40] reported the per-formance simulation of an SSHT using a new working paircomposed of ionic liquids, water/1-ethyl-3-methylimidazoliumdimethylphosphate (H2O/EMIM-DMP) and compared the resultswith the mixtures water/lithium bromide and water/tri-fluoroethanol (TFE) þ tetraethylenglycol dimethylether (E181). Theresults indicated that when generation, evaporation, condensingand absorption temperatures were 90 �C, 90 �C, 35 �C and 130 �C,the COP using H2O/LiBr, H2O/EMIM-DMP and TFE/E181 as workingpairs were 0.494, 0.481 and 0.458, respectively. Jernqvist et al. [41]proposed different efficiencies to evaluate heat transformers

T

AB1EV1

GE1CO1

HE1

AB2EV2

GE2CO2

HE2

P

QAB1QAB2

QAB1QEV1

QCO1

QCO2

QGE1

Fig. 2. Pressure against temperature diagram for a two-stage heat transformer.

operating with the H2O/NaOH pair. The maximum COP obtainedwith the mixture was 0.48.

2.1.4. Conclusions of SSHTFrom the bibliographic review related to SSHT operating with

the mixture of H2O/LiBr, it can be observed that most works havefocused on the analysis of these systems from the point of view ofthe first and second laws of thermodynamics, in an attempt to findthe optimum conditions to achieve the highest COP and exergyefficiencies, as well as the lowest irreversibilities. For this mixturethe highest COPs were close to 0.5 with maximum GTL values of50 �C.

With respect to the SSHT operating with alternative mixtures,many binary and even ternary options instead of the H2O/LiBrmixture have been analyzed. However, the only ones with COPshigher than 0.5 were: the R21/DMF mixture with COPs of up to 0.6[30] and the NH3/H2O and SO2/DMAmixtures with maximum COPsof 0.593 and 0.541, respectively [34]. Zhuo and Machielsen [36] andYin et al. [38] found that with the TFE/Pyr, TFE/NMP and TFE/E181mixtures it is possible to operate the SSHT at temperatures of up to200 �C instead of the 150 �C, which can be achieved for systemsusing the H2O/LiBr mixture due to crystallization problems. Inrespect to the GTL it was found that the mixtures that use ammoniaas a refrigerant can reach a GTL of up to 60 �C instead of the 50 �Cobtained with the H2O/LiBr mixture [22,24,26]. Finally, Best andRivera [27] and Bourouis et al. [39] reported that the ternarymixture H2O/Carrol™ and the quaternary mixture H2O/(LiBr þ LiI þ LiNO3þLiCl) have a higher solubility and are less cor-rosive than the H2O/LiBr mixture.

2.2. Advanced absorption heat transformers

Advanced adsorption heat transformers (AAHT) refer to thosesystems that use more components than SSHT in order to achievehigher COP or GTL. Two-stage heat transformers and double-absorption heat transformers are some examples of advancedsystems.

Fig. 4. Pressure against temperature diagram for a triple-absorption heat transformer.


2.2.1. Description of advanced systemsTwo-stage heat transformers (TSHT) basically consist of two

SSHT, which can be coupled in three different ways as shown inFig. 2. The first way is by connecting the absorber of the first stageto the evaporator of the second stage, so the heat delivered by theabsorber allows the evaporation of the working fluid in the secondstage (QAB1 ¼ QEV2). The second way is by coupling the absorber ofthe first stage to the generator of the second (QAB1 ¼ QGE2). Thethird way is by splitting the heat delivered by the absorber of thefirst stage between the generator and the evaporator of the secondstage (QAB1 ¼ QEV2þQGE2).

Double-absorption heat transformers (DAHT) basically consistof a generator (GE), a condenser (CO), an evaporator (EV), anabsorber (AB), an absorber-evaporator (AE) and a heat exchanger oreconomizer as shown in Fig. 3. A heat source is supplied to thegenerator (QGE) to separate the working fluid at an intermediatetemperature TGE. The vaporized working fluid is condensed in thecondenser at a lower temperature TCO. Then the condensed work-ing fluid is split into two streams. One of them is pumped into theevaporator where it is vaporized at an intermediate temperatureTEV and pressure PEV. The other one is pumped at a higher pressurePAB and vaporized in the absorber-evaporator by an amount ofavailable heat QAE. The vaporized working fluid is absorbed in theabsorber, at a higher temperature TAB, by the high concentration

ABEV

GECO

HE

QEV

QCO QGE

QAB

Fig. 5. Schematic diagram of an ejector-absorption heat transformer.

solution XGE coming from the generator. The diluted solution at anintermediate concentration XAB is split into two streams. One goesto the generator preheating the high concentration solutionthrough the heat exchanger. The other is fed to the absorber-evaporator absorbing the vaporized working fluid coming fromthe evaporator and delivering an amount of heat QAE. Finally, thediluted solution at a low concentration XAE leaving the absorber-evaporator goes to the generator starting the cycle again.

Besides the double-absorption and the two-stage absorptionheat transformers, there are also triple-absorption heat trans-formers (THAT), which are similar to the double absorption sys-tems, but with an additional stage at higher temperature as can beseen in Fig. 4.

2.2.2. Advanced AHT operating with water/lithium bromideA couple of studies on the thermodynamic analysis on single

and advanced AHT operating with H2O/LiBr were performed byRivera et al. [42,43]. The results showed that SSHT systemswere thesimplest andmost efficient, since they achieved a maximum COP of0.48, while the maximum COPs were 0.32 and 0.31 for the DAHTand TSHT, respectively. However, the highest GTLs were obtainedwith the TSHT, followed by the DAHT and finally the SSHT,achieving GTL values of 80 �C, 75 �C and 50 �C, respectively. Theauthors concluded that because DAHT could achieve similar COPand GTL than TSHT, the former seemed to be a better alternativesince they require less components and are less expensive. Ji andIshida [44] proposed the modification of a conventional TSHToperating with H2O/LiBr by utilizing the sensible and latent heatexchange-modes in the generators and absorbers. The resultsshowed that with the modifications the GTL can be improved by10.7 �C and the exergy efficiency can be increased from 48.14 to54.95%, however, the COP decreased from 0.314 to 0.293. Based onthe performance analysis of the SSHT, DAHT and TSHT a newejection-absorption heat transformer (EAHT) with H2O/LiBr waspresented and analyzed by Shi et al. [45], (see Fig. 5). The proposedsystem incorporates an ejector at the entrance of the absorber inorder to increase the pressure and temperature of the component.Compared with a conventional SSHT, the delivered useful temper-ature for the EAHT increased 5% and the exergy efficiency increased2.7%, however, the COP decreased 0.4% for the discussed conditions.Donnellan et al. [46] studied a TAHT operating with H2O/LiBr. Theresults showed that the generator was the source of the greatest


exergy destruction in the cycle, followed by the two absor-bereevaporators. GTL as high as 140 �C could be obtained with theproposed systems but with COPs not higher than 0.2. Donnellanet al. [47] modeled a THAT using H2O/LiBr in order to determine theoptimum number and locations of internal heat exchange unitswithin the system. It was found that the conventional design of theTAHT does not employ heat exchangers effectively and by rear-ranging these components the system COPs could be increased by11.7%. Strategically adding one or two extra heat exchangers theCOPs were increased by 16.4% and 18.8%, respectively. Wang et al.[48] reported the optimization design of the large temperature lift/drop multi-stage vertical absorption temperature transformeroperating with H2O/LiBr, the results showed that the minimumtotal multiplication of the heat transfer coefficient by the heattransfer area was obtained when entransy dissipation per trans-ferred heat was uniformly distributed in the four basic components.The authors did not report values of the COP neither GTL for theproposed system. Based on first and second law of thermodynamicsFartaj [49], and Martínez and Rivera [50] analyzed a DAHT oper-ating with H2O/LiBr. The authors concluded that second law anal-ysis offers an alternative view of cycle performance and provides aninsight that the first law analysis cannot. Also it was found that thegenerator was the component with the highest irreversibilitiescontributing to about 40% of the total exergy destruction in thewhole system. The thermodynamic performance of a new type ofDAHT operating with H2O/LiBr was studied by Zhao et al. [51,52]and Hao et al. [53]. In the proposed cycle the strong solutioncoming from the generator was split into two streams instead of theweak solution coming from the absorber as it was previously pro-posed by other authors [42,43]. The GTL with the new proposedconfiguration was between 5 �C and 10 �C higher than those withprevious DAHT, but the COP decreased about 0.01 when comparedwith the other configurations.

2.2.3. Advanced AHT operating with alternative mixturesBesides the published studies about the modeling of advanced

absorption heat transformers (AAHT) operating with the H2O/LiBrmixture, there have been several studies related with the devel-opment of AAHT operating with alternative mixtures. Ziegler andAlefeld [54] reported a method by which the COP of advancedabsorption cycles could be calculated easily if the efficiencies ofsingle-stage systems are known. Also compared the performance ofAAHT operating with the working pairs H2O/LiBr and NH3/H2O.They found that the COP for a DAHTwere 0.31 and 0.27 for the H2O/LiBr and NH3/H2O, respectively. The theoretical performance ofSSHT and DAHT using water/ammonia as binary mixture was

Fig. 6. Double-effect absorption heat transformer, Zhao et al., 2005.

studied by Stephan and Seher [55] and Tyagi [56]. The resultshowed that the highest COP was 0.35 with GTL of 60 �C. Ciambelliand Tufano [57e59] analyzed the performance of single and AAHToperating with the water/sulfuric acid mixture. The results showedthat with the two-stage configuration a COP of 0.35 and GTL of75 �C could be achieved, while with the double-absorptionconfiguration the COP and GTL were 0.32 and 65 �C, respectively.Iyoki and Uemura [60] compared the performance of a TSHToperating with H2O/(LiBe þ ZnCl2 þ CaBr2) and the conventionalH2O/LiBr mixture. At similar conditions, the highest COP with thealternative mixturewas 0.32 instead of the 0.34 obtained with H2O/LiBr, however, the proposed mixture has a wider range of operatingconditions than the H2O/LiBr mixture. High-temperature absorp-tion heat transformers operating with Alkitrate as the working pairwere investigated by Zhuo andMachielsen [61]. The results of SSHT,DAHT and TSHT were reported and compared with H2O/LiBr cycles.The COP of Alkitrate cycles were practically the same than thosewith H2O/LiBr cycles, under the same operating conditions. It wasconcluded that Alkitrate was especially useful for operating at hightemperatures, of up to 260 �C, however, the proposed mixture wasnot recommended at condenser temperatures lower than 50 �C dueto solubility problems. Single and advanced heat transformersoperating with the water/Carrol mixture were analyzed by Bestet al. [62] and Romero et al. [63]. For a condenser temperature of30 �C and a generator temperature of 80 �C, the highest COPs were0.49, 0.32 and 0.31 for the SSHT, DAHT and TSHT respectively. Thehighest GTL for SSHT was almost 60 �C, while for TSHT and DAHTwere around 105 �C. A thermodynamic study of a DAHT operatingwith the water/calcium chloride mixture was carried out byBarrag�an et al. [64]. GTLs up to 40 �C were achieved with COP closeto 0.3. Rivera et al. [65] compared the performance of SSHT, TSHTand DAHT operating with the water/lithium bromide and the wa-ter/Carrol mixtures. Similar tendencies and values of the COPs wereobtained in general for both mixtures, however, at specific condi-tions the gross temperature lifts with the H2O/Carrol were up to15 �C higher than those obtained with H2O/LiBr. A mathematicalmodel was developed by Scott et al. [66] of a multi-compartmentH2O/NaOH AHT. In the proposed system the generator and evapo-rator were divided in different sections to operate at differenttemperatures. The results showed that COPs as high 0.495 could beobtained with the proposed system. A self-regenerated AHT with agenerator-absorber heat exchanger (GAX) cycle using the neworganic working pair 2,2,2-trifluoroethanol (TFE)/N-methylpyr-olidone (NMP) was proposed by Shiming et al. [67]. Some of themost important features of the proposed mixture were the absenceof crystallization and the low working pressures; however, it hadthe disadvantage or requiring rectification. The COPs of the systemvaried between 0.17 and 0.21. Wang et al. [68] compared the per-formance of a TSHT operating with H2O/LiBr, with TFE/NMP andwith H2O/LiBr in the bottom cycle and TFE/NMP in the high cycle.The highest COP and GTL for the system operating with H2O/LiBr inboth cycles were 0.3 and 80 �C, respectively. Although themaximum COP for the system operating with H2O/LiBr and TFE/NMP was 0.25, the GTL was 90 �C, and the maximum absorbertemperature was 40 �C higher than that attained with H2O/LiBr.Zhao et al. [69,70] reported the thermodynamic performance of anew cycle named double-effect absorption heat transformer(DEAHT) using TFE/E181 as the working fluid. This system is acombination of a double-stage and double-absorption systems (seeFig. 6). The results showed that, when the temperature in the high-pressure generator exceeds 100 �C and the GTL was 30 �C, the COPof the systemwas about 0.58, which was larger than the 0.48 of theSSHT, however, this increase was still less than 0.64 of the DEAHTusing H2O/LiBr as the working fluid. S€ozen et al. [71e73] developedmathematical models of an ejector-absorption heat transformer

Fig. 7. COP against GTL for the different heat transformer configurations.


(EAHT) operating with the NH3/H2O mixture. Under the sameoperating conditions, the COP and exergy COP were improved by14% and 30% respectively, by using the ejector when compared toan AHT without an ejector. Romero et al. [74] modeled an experi-mental TSHT operating with a ternary mixture of hydroxides basedin sodium, potassium and cesium. The results showed that it waspossible to achieve a GTL of 72 �C with a COP of 0.32. Barrag�an et al.[75] modeled a single and DAHT operating with the mixtures H2O/CaCl2 and H2O/LiCl. The maximum COPs were 0.49 and 0.44 for theH2O/ClCa2 and H2O/LiCl, respectively. The GTLs reported werelower than 50 �C for both mixtures. A thermodynamic study of aSSHT and a DAHT using new working pairs composed of ionic liq-uids (1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF4]) and 1-butyl-3-methylimidazolium tetrafluoroborate([bmim][BF4])) as absorbent and 2,2,2-trifluoroethanol (TFE) asrefrigerant was carried out by Ayou et al. [76]. The maximumvaluesof the COP for the DAHT operating with the proposed mixtureswere between 0.24 and 0.26 which were lower than those obtainedwith the H2O/LiBr mixture which were about 0.32; however, it wasshown than the mixtures TFE/([bmim][BF4]) and TFE/([emim][BF4]) could achieve GTLs up to 15 �C higher than those obtainedwith the H2O/LiBr mixture.

2.2.4. Conclusions of AAHTAs can be seen from the bibliographic review there are several

studies regarding the development of new heat transformers cy-cles. They have all focused on obtaining higher COPs or GTLs andcentered in both the use of the H2O/LiBr and alternative mixtures.With respect to advanced cycles operating with the H2O/LiBr theyhave mainly focused in double-absorption, two-stage, triple-stage,ejection-absorption and double-effect absorption heat trans-formers. Of all the heat transformers analyzed, the DEAHT are theones with the higher COP of up to 0.64, however their GTLs are thelowest of approximately 30 �C [69,70]. The SSHT reach COP valuesclose to 0.5 with a GTL of 40 �C. The TSHT reach COP values of 0.32with GTL values of up to 80 �C, while with the DAHT, COP values of0.31 and maximum GTLs of 75 �C [42,43]. The TAHT systems reachGTLs of up to 140 �C, but COPs no higher than 0.2 [46]. With theejection-absorption heat transformers 5% higher GTLs were ob-tained, but 4% lower COPs with respect to the SSHT under the sameoperating conditions [45]. Rivera et al. [42,43] and Ciambelli andTufano [57e59] concluded that the DAHT seemed to be a betteralternative than TSHT since similar COP and GTL could be achievedwith both systems.

With respect to the AAHT operating with alternative mixtures,from the bibliographic review it can be seen that there have beenmany mixtures analyzed, but with none one of them COP higherwere obtained than those obtained with the H2O/LiBr mixture.However, regarding the GTL Rivera et al. [65] and Ayou et al. [76]analyzed the mixtures H2O/Carrol, TFE/([bmim][BF4]) and TFE/([emim][BF4]), respectively, and found that GTL up to 15 �C highercould be obtained with those mixtures than those with the H2O/LiBr mixture. Besides, Wang et al. [68] found that a TSHT operatingwith H2O/LiBr in the bottom cycle and TFE/NMP in the top cyclecould reach absorber temperatures up to 40 �C higher than thoseobtained with the same system but utilizing H2O/LiBr in both cy-cles. In regard to solubilities, Iyoky and Uemura [60] reported thatthe mixture H2O/(LiBe þ ZnCl2 þ CaBr2) has a wider range ofoperating conditions in a TSHT than the H2O/LiBr mixture. Zhuoand Machielsen [61] reported that for DAHT and TSHT the COP ofAlkitrate cycles were practically the same than those of H2O/LiBrcycles, under the same operating conditions. However, they foundthat Alkitrate was especially useful for operating at high tempera-tures, up to 260 �C, but the proposed mixture was not recom-mended at condenser temperatures lower than 50 �C because ofsolubility problems. Finally, Fig. 7 shows the zones of COP againstGTL for the different heat transformer configurations.

2.3. Heat transformers applications

Heat transformers can be used for different application such as:distillation in chemical plants, desalination or water purification,evaporation and waste heat recovery from industrial processes,among others.

2.3.1. Water purificationThe integration of a water purification system and a heat

transformer operating with the H2O/LiBr was modeled by Siqueirosand Romero [77], by Romero et al. [78] and by Contreras-Valenzuelaet al. [79]. The results showed that the proposed system was notonly capable to produce purified water but also to increase thesystem COP more than 120%, for some specific conditions, byrecycling part of the energy from a water purification system.Escobar et al. [80] integrated the model of a helical double-pipevertical evaporator into the thermodynamic model proposed bythe previous authors in order to design physically this component.Romero and Rodriguez [81] developed a modeled of an AHT forwater purification (AHTWP) in order to optimize its performance. Itwas found that with heat source temperatures between 65 �C and80 �C it was possible to obtain absorber temperatures higher than105 �C for water distillation, achieving COPs from 0.30 to 0.43. Also,for AHTWP mathematical models using artificial neural networkshave been developed to predict the COP [82] and to find the optimaloperating conditions [83]. Gomri [84] developed a model of a flatplate solar collectors, an SSHT and a desalination system used toprovide a beach house located in Skikda with drinking water. Theresults showed that thewater productivity varied between 0.64 l/h/m2 and 0.62 l/h/m2 depending on the operating conditions. Gomri[85] carried out a comparative study from the first and second lawof thermodynamics between SSHT and DAHT operating with H2O/LiBr for seawater desalination. The results showed that when in-termediate heat source temperature was supplied from 74 �C to96 �C the maximum energy efficiencies were between 0.799 and0.833, and from 1.276 to 1.308 for the SSHT and DSHT, respectively,while the exergy efficiencies varied from 46.9% to 54.1% for theSSHT and from 58.5% to 60.8% for the DSHT. Srinivas et al. [86]developed a mathematical model of an AHT coupled to a multi-effect desalination system operating with diverse working pairs.The results showed that the system operating with the H2O/

30 oC

85 oC

heat transformer

Solar Pond

Steam at 125 oC

water to be heatedcooling water

hea ng water

Fig. 8. Schematic diagram of a heat transformer coupled to a solar pond.


(LiClþ LiNO3) mixture achieved the highest COPwhich was close to0.5 and the lowest values of the energy consumed to produce 1 m3/h of distilled water, which varied between 128 and 134 kWh/m3.Rivera et al. [87] carried out and energy and exergy analysis of aheat transformer for water purification increasing the heat sourcetemperature operating with the H2O/LiBr mixture. The resultsshowed that the highest irreversibilities occurred in the absorbercontributing with more than 30% of the irreversibilities of theentire system, followed by the auxiliary condenser with about 25%.The highest COP was almost 0.5. Alternative AHT configurationsintegrated with water desalination systems were studied by Par-ham et al. [88]. It was shown that applying different modifications,the COP of the AHT could be increased to achieve values close to0.55 and consequently increasing the productivity of the desali-nation system. The maximum rate of distilled pure water reachedwas 0.2435 kg/s. Ju�arez-Romero et al. [89] developed a dynamicmodel which described the heat and mass transfer of a horizontalpipe absorber applied to an AHT operating with H2O/LiBr used forwater purification. The authors concluded that the model could beused to optimize the performance of the system. A thermodynamicanalysis of six different configurations of TAHT utilizing H2O/LiBrintegrated to a water desalination system was conducted by Kha-mooshi [90]. It was shown that modified configurations of TAHTscould increase the freshwater productivity compared to conven-tional systems. The results indicated that the optimized amount ofdistilled water produced was 0.1307 kg/s when a heat load of1200 kWwas supply to the heat transformer with a maximum COPof 0.25. The performance analysis on a new multi-effect distillationcombined with an open H2O/LiBr absorption heat transformer(OAHT) driven by waste heat was carried out by Zhang et al. [91].The results indicated that combined with OAHT, the waste heat at70 �C could be elevated to 125 �C producing steam at 120 �C in theabsorber, which was able to drive a four-effect distiller to producedistilled water. For a single-effect and four-effect distiller, the COPswere 1.02 and 1.03, respectively, performance ratios (amount ofdistilled water to the amount of motive stem) were 2.19 and 5.72,respectively. They concluded that the four-effect distillation systemcombined with an OAHT was the most efficient.

2.3.2. Energy recover from industrial processesEisa et al. [92] analyzed the theoretical performance of an AHT

assisting a distillation system. The authors concluded that a heattransformer could replace mechanical vapor compression by heatpumps in the distillation process with energy savings between 10%and 60%. Tufano [93] analyzed the performance of single and TSHTused to save energy in a distillation column and found that a steamsaving factor as high as 0.4 could be obtained in distillation pro-cesses by the integration of AHT. Rivera et al. [94] reported thetheoretical analysis of the use of SSHT and DAHToperating with theH2O/LiBr mixture coupled to a butane and pentane distillationcolumn in a Mexican refinery. The results showed that it wastheoretically possible to reduce the energy consumed in the re-boiler between 26 and 43% by the use of an SSHT at some specificconditions, and between 28 and 33% with a DAHT, for a wide rangeof operating conditions. Aly et al. [95] analyzed the application ofAHT for energy conservation in the oleochemical industry. The heattransformer used 314 kWof vapor, which was condensed in a dumpcondenser and discharged. The analysis showed that the AHT couldrecover up to half of the energy achieving a GTL of 34 �C, producingsteam at 3 bar which could be fully reused in the plant. The eco-nomic analysis showed that a payback period less than 18 monthscould be achieved based on a steam cost of 14.25$/GJ, an installedequipment cost of 535$/kW, annual operation time of 7200 h, and aheat transformer efficiency of 0.45. Rivera et al. [96] proposed thedesign of a mobile pilot-plant for the production of

environmentally clean steam. The unit consisted of an SSHTcoupled to a mechanical vapor recompression system with anominal output capacity of 260 kg/h of saturated steam at 3 barabsolute pressure for a liquid feed at a temperature of 80 �C and aCOP of 0.48. Another application to produce steam by means ofSSHT and DAHT using H2O/LiBr was analyzed by Horuz and Kurt[97]. It was concluded that absorber temperatures as high as 130 �Cand 160 �C with could be obtained with SSHT and DSHT, respec-tively, when heat was supplied to the evaporator and generator attemperatures of 90 �C. The maximum COPs were 0.482 and 0.377with the SSHT and DAHT, respectively.

The same authors [98] analyzed a theoretical application of theAHT system in a textile company which produces hot water at90 �C. The study considered to produce useful heat at 120 �C to bereused in the industrial process. It was shown that, by applyingdifferent modifications in the industrial process, the COP could beincreased by 14.1%, the heat transfer at the absorber by 158.5% andthe hot process water produced by 3.59% compared to the basicAHT system. Jeday et al. [99] evaluated an AHT utilizing waste heatfrom an industrial sulfuric acid plant. The system produced su-perheated steam at 180 �C fromwaste heat at 106 �C. A COP close to0.45 was obtained. The authors concluded that from the economicpoint of view the heat transformers are a good alternative to beused in industrial process to save energy. A detailed graphicalexergy study based on the energy-utilization diagram was appliedby Ishida and Ji [100] to humid air turbine cycle incorporated with amodified TSHT. Compared to a conventional AHT cycle, the overallcycle efficiency was increased by 2% and the specific work wasincreased by 7.3%. The exergy and exergo-economic optimization ofa cogeneration pulp and paper mill plant including the use of aDAHTwas carried out by Cort�es and Rivera [101]. Heat coming fromthe evaporator of the paper mill plant at temperatures between70 �C and 80 �C was supplied to the DAHT to produce useful heat attemperatures between 90 �C and 120 �C to be supplied to thecogeneration plant and force plant boilers, saving about the 25% ofthe natural gas consumed by the plant. The improved CO2 capturesystem with heat recovery based on the use of an AHT and a flashevaporator (FE) was analyzed by Zhang et al. [102]. Compared withthe base CO2 capture system of 3000 t/dCO2, capture capacity froma 660MWcoal-fired power unit, the AHT-FE-aided capture systemreduced the heat consumption from 3.873 GJ/tCO2 to 3.772 GJ/tCO2,


and the corresponding energy saving was 26.2%. The economicanalysis showed that the annual profit would be 2.94million RMBYuan. The payback period of the AHT-FE-aided capture system wasapproximately 2.4 years. Donnellan et al. [103] reported the eco-nomic evaluation of a TAHT in a small Irish oil refinery, examiningvarious different natural gas price scenarios. The TAHT was capableof increasing the temperature of supplied heat by up to 140 �C witha COP of 0.14 corresponding to approximately 4.5 MW of energysaved. The results showed that at the present gas price, the capitalcost of the (conventional) equipment was too high to make itfinancially attractive for the current industrial example, with anextremely high predicted payback period. However, a return tonatural gas price levels observed in 2008 and 2009 would make theunit economically viable with a payback period of 5 years or less.Scott et al. [104] investigated the technical and economic feasibilityof incorporating an absorption heat transformer to increase theenergy efficiency of an evaporation-crystallization plant in a sugarmill, having an intake capacity of 17.5 kton of sugar beets per day.The authors proposed the use of an open multi-compartment AHTfor different steam temperatures. The results of the simulationsrevealed that the total amount of live steam used in the evaporationplant could be reduced by 11.8e16.4%, depending on the temper-ature level allowable in the crystallization plant. The authors re-ported that the payback period of this type of investment variedfrom 1.8 to 4.7 depending of the energy cost and with an annualoperation time of 8000 h/year.

2.3.3. Other applicationsIn addition to the heat transformer applications previously

described, AHT have been proposed for other uses such as to in-crease the temperature of the useful heat produced by solar pondsas it is shown in Fig. 8. In regard to this, a thermodynamic study ofan AHT coupled to a solar pond was reported by Murugesan et al.[105]. The heat transformer used R134a as refrigerant and organicfluids DMAC and DMETEG as absorbents. The results showed that,for a high temperature lift, R134a/DMAC had superior performancecompared to R134a/DMETEG. For both mixtures the COP variedfrom 0.1 to 0.34, while the GTL varied from 10 �C to 30 �C. Math-ematical models of SSHTand AAHToperatingwith the H2O/LiBr andH2O/Carrol mixtures were developed by Rivera et al. [106] tosimulate the performance of these systems coupled to a solar pond.The results showed that the SSHT and DAHT were the mostpromising configuration to be coupled to solar ponds. With SSHT itwas possible to increase solar pond's temperature up to 50 �C with

Fig. 9. Coefficients of performance against GTL in different industrial processes.

COPs of about 0.48, and with DAHT up to 100 �C with COP of 0.33.S€ozen [107] developed a mathematical model for that purpose andfound that the maximum upgrading of solar pond's temperature bythe heat transformer was obtained at 51.5 �C and gross temperaturelift at 93.5 �C with COP of about 0.4. The maximum temperature ofthe useful heat produced by the AHT was approximately 150 �C.Sencan et al. [108] proposed the use of an SSHT operating withaqueous ternary hydroxide fluid to upgrade the heat deliver by asolar pond. According to the authors COP close to 0.5 and GTL up to70 �C could be achieved.

2.3.4. Conclusions of heat transformers applicationsFrom the bibliographic review of this section, it was found that

there are several theoretical studies based on the first and secondlaws of thermodynamics regarding the use of heat transformers forwater purification. These studies cover the use of SSHT as well asDAHT, TSHT, and OAHT all of them operating with an H2O/LiBrmixture and obtaining, depending on the heat transformer used,COPs between 0.25 and 0.5. According to Romero and Rodriguez[81] it is possible to produce distilled water when heat is suppliedto a heat transformer at temperatures starting at 65 �C. Srinivaset al. [86] published the only study that did not use H2O/LiBr; theypropose a multiple effect desalinization system integrated to anSSHT operating with an H2O/(LiCl þ LiNO3) mixture, with a highestCOP of about 0.5 and with energy consumption between 128 and124 kWh/m3 to produce 1 m3/h of distilled water.

With respect to energy recovery in industrial processes, severaltheoretical studies have been conducted regarding the use of one-stage or advanced heat transformers in industries such as: distil-lation, sugar mill, textile, chemical, oleochemical, and in a cogen-eration of pulp and paper mill plants. Depending on the applicationand the type of transformer used, the energy saving in the differentindustries varied between 10% and 60%. The payback periods in anevaporation-crystallization plant in a sugar mill varied from 1.8 to4.7 years [104], in oleochemical industries less than 18months [95],in a coal-fired power industry approximately 2.4 years [102], and inan oil refinery less than 5 years at the natural gas price levelsobserved in 2008 and 2009 [103].

Other applications have exclusively focused in theoreticalstudies for the use of single-stage or advanced AHT systems to raisethe temperature of solar ponds. According to Rivera et al. [106]using the H2O/Carrol mixture with SSHT, it was possible to in-crease the solar pond's temperature up to 50 �C with COPs of about

Fig. 10. Photograph of the heat transformer developed by Rivera et al. [118].


0.48, and DAHTs of up to 100 �C with COPs of 0.33. Using a water/ternary hydroxides mixture with a SSHT [108] the temperatureincreased up to 70 �C with a COP of 0.5.

Fig. 9 shows the coefficients of performance against grosstemperature lifts for the diverse industrial processes analyzed.

3. Experimental studies

The following section presents everything in reference toexperimental studies regarding heat transformers including thedescription and research of the main cycles, either single-effect oradvanced, as well as the use of conventional and alternative mix-tures and their possible applications.

3.1. Single stage heat transformers

3.1.1. SSHT operating with water/lithium bromideEnergy and exergy analysis of an experimental SSHT of 500 W

capacity operating with the H2O/LiBr mixture were carried out byRivera et al. [109]. The GTLs varied from 22 �C to 27.5 �C, and thehighest COP of 0.45 was achieved at the highest solution concen-tration of 59%. It was observed that in general the absorberaccounted with more than half of the total irreversibility in thesystem. In order to reduce the irreversibility reported by Riveraet al. [109], Colorado et al. [110] developed a model based on directand inverse artificial neural networks. It was shown that by usingthe proposed methodology the total irreversibility could bereduced up to 14%. An experimental study was performed byOlarte-Cort�es et al. [111] on a graphite disk absorber coupled to anAHT operating with H2O/LiBr. According to the authors, thegraphite was used in order to eliminate the corrosion problems inthe absorber. The authors reported that the heat transfer coefficientvaried from 0.62 to 1.53 kW/m2 K. The heat transfer coefficientswere similar than those reported by Kim et al. [112] utilizing avertical absorber of concentric tubes made of stainless steel, butlower than those reported by Deng and Ma [113] using an absorberof horizontal tubes made of cooper, both operating with the samemixture. The analysis of effective wetting area of a horizontalgenerator for an absorption heat transformer operating with H2O/LiBr was carried out by Lazcano-V�eliz et al. [114]. They analyzed thewetting area and falling film behavior of the mixture on a bank ofsixteen horizontal tubes. The results showed the distribution ofabsorbent mixture, along the tubes of the bank at different massflow rates per unit length (0.006e0.034 kg/m s). The most regularfilm distribution of the mixture, through the tubes of the bank, wasobtained with the flow of 0.025 kg/m s, which gave the best resultsof heat transfer efficiency, with values between 80 and 98%. Maet al. [115] studied the heat transfer and thermodynamic perfor-mance of a H2O/LiBr AHT with vapor absorption inside verticalspiral tubes. The available COP in the experiments was higher than0.4. The heat and mass transfer coefficients of the absorberincreased with the increase of the flow rate of LiBr solution, up to400 W/m2/K and 0.013 kg/m2/s at waste heat temperature of 90 �C.

In order to improve the performance of the systems operatingwith the H2O/LiBr mixture, some studies have been carried out onthe use of additives, Rivera and Cerezo [116,117] reported the re-sults of an experimental study of the use of 1-octanol and 2-ethyl-1-hexanol as additives in the performance of an SSHT operatingwith H2O/LiBr. It was concluded that the 1-octanol additive in-creases slightly the absorber temperature and the COP, however,the 2-ethyl-l-hexanol increases considerably the performance ofthe system. Absorber temperatures up to 7 �C higher and COP up to40% higher were obtained by using this additive than those ob-tained without additive.

3.1.2. SSHT operating with alternative mixturesAs it was mentioned in Section 2.1.3, currently the H2O/LiBr

mixture has been the most used mixture in AHT but it has somemajor disadvantages, reason why different mixtures have beenproposed or used. Rivera et al. [118] developed a SSHT of 500 Wcapacity operating with the H2O/Carrol mixture (see Fig. 10). TheCOPs were in the range 0.1e0.2 while the highest GTL was 52 �C.The authors commented that COP values were low because of thelow capacity of the facility and the high of the heat losses. Riveraet al. [119] compared the performance of a SSHT operating withH2O/LiBr and the H2O/Carrol mixtures. For both mixtures the COPvaried between 0.3 and 0.4, however, the GTL values were higherfor the system operating with the H2O/Carrol than those obtainedwith H2O/LiBr. The highest GTL with H2O/LiBr was 43 �C, while withthe H2O/Carrol the highest GTL was 52 �C. The authors consideredthat because the H2O/Carrol mixture has higher solubility thanH2O/LiBr and high GTL, the alternative mixture seemed to be abetter alternative mixture to be used in AHT. Similar conclusionswere reported by Silva-Sotelo and Romero [120] comparing thesame mixtures in a TSHT. Ibarra-Bahena [121] reported the exper-imental evaluation of a SSHT built with commercial plate heat ex-changers operating with the H2O/Carrol mixture. The heat powerswere measured from 0.99 to 1.35 kW for the generator,0.97e1.33 kW for the condenser, 0.99e1.35 kW for the evaporatorand 0.69e0.81 kW for the absorber. The experimental GTLs variedfrom18.5 to 22.2 �C, while the COPs varied from0.30 to 0.35. Ibarra-Bahena et al. [122] analyzed the effectiveness of a plate heatexchanger used as an economizer integrated into an experimentalSSHT operating with the H2O/Carrol mixture. The economizereffectiveness ranged from 0.69 to 0.71. The results showed that atlow absorber temperatures, the COPs were almost the same fordifferent economizer effectiveness, however, at absorber temper-atures higher than 135 �C, the COPs, with economizer effectivenessof 0.7 and 0.9, were almost twice than those obtained without theeconomizer. Pataskar et al. [123] carried out an experimentalevaluation of a small AHT operating with H2O/LiBr, H2O/LiBr þ LiCl(1:1 by weight), and H2O/LiCl. It was demonstrated that under thesame operating conditions the maximum COP for the H2O/LiBrmixture was 0.26, for the H2O/LiBr þ LiCl was 0.31 and for the H2O/LiCl the COP was 0.38. Bokelmann and Steimle [124] presented areport on an experimental research to discover new working fluidsfor sorption plants. Some of the most important results for heattransformer applications were presented in the form of graphs ortables and the suitability of the new working fluids was comparedwith some well-known working couples. The mixtures analyzedwere TFE-Chi, TFE-DTG, TFE-EP, TFE-ICh, TFE-MP, TFE-NMP, TFE-Pyr, TFE-TEG, HFIP-NMP and PFPA-DTG. The authors found thatthe mixtures TFE-NMP and TFE-Pyr were specially promising inspite of the higher cost and lower heat transfer coefficients whencompared with traditional mixtures. George and Srinivasa [125]evaluated an SSHT of 3 kW heating capacity operating with R21/DMF. Heat source temperature and condensing temperature werevaried in the ranges 50e70 �C and 20e40 �C, respectively. Heatdelivery temperatures up to 85 �C and temperature lifts up to 20 �Cwere achieved. The COP ranged from 0.2 to 0.35, whereas exergeticefficiencies between of 0.3 and 0.4 were obtained. Barragan et al.[126] reported the experimental results of the performance of aSSHT operating with the H2O/LiCl mixture. The results showed thatGTLs higher than 30 �C could be obtained with a COP of 0.45. Thesame authors [127] reported experimental results with the binarymixtures H2O/CaCl2 [128], H2O/MgCl2 and with the ternary mix-tures H2O/LiCl þ ZnCl2 and H2O/CaCl2 þ ZnCl2 [129]. With the H2O/CaCl2 the highest GTL was 19 �C and the COP was 0.45, while withthe H2O/CaCl2 the highest GTL was 0.18 and the COP was 0.273.Regarding to the ternary mixtures, the H2O/LiCl þ ZnCl2 solution

Fig. 11. Photograph of the two-stage heat transformed developed by Romero et al.[135].


showed in general better performance than the H2O/CaCl2 þ ZnCl2mixture. The highest GTL obtained with the former solution was37.5, while the COP was 0.28. Stephan et al. [130] built a pilot plantand developed a model to simulate the dynamics of a heat trans-former working with the mixture H2O/NaOH. The results showedthat COPs as high as 0.49 could be obtained. Xiao et al. [131] carriedout a vaporeliquid equilibrium study of an absorption heat trans-former working with HFC-32/DMF. The authors reported that ac-cording to its thermodynamic properties the mixture could be analternative be used in AHT but they did not report its use. Thesolubility of R134a in DMEDEG and DMETrEG was measured byZehioua et al. [132] using the “static-analytic” method at

Fig. 12. Schematic diagram of the experimental set up developed by Alonso et al. [137].

temperatures between (303 and 353) K. The study remarked thepossibility of the use of those mixtures as working fluids in AHT.

3.1.3. Conclusions of SSHTExperimental studies of SSHT operating with the H2O/LiBr

mixture have been carried out from the point of view of the firstand second law of thermodynamics [109], the development of newcomponents [111e115], and the use of additives in order to improvethe performance of the system. Regarding the latter ones it wasfound that using 2-ethyl-l-hexanol considerably increases theperformance of the system, since absorber temperatures up to 7 �Chigher and COPs up to 40% higher were obtained by using thisadditive compared to those obtained without additive [116,117].

Regarding the study of new mixtures, from the many thermo-dynamically analyzed, it was reported that the TFE/NMP, TFE/Pyr,and HFC-32/DMF were specially promising compared to traditionalmixtures; however, there are no reports of the operation of heattransformers using thesemixtures [124]. There is a report of the useof other mixtures like H2O/CaCl2 [128], H2O/MgCl2 and H2O/LiCl/þZnCl2 [129], and R21/DMF [125], but the results are not comparedwith the H2O/BrLi mixture and from their analysis it is not clear ifthey represent and advantage over its use. Of all the mixturesanalyzed, the only ones obtaining better results when compared tothe H2O/LiBr mixture under the same operating conditions werethe H2O/Carrol, H2O/LiBr þ LiCl, and H2O/LiCl mixtures. It was re-ported that an AHT operating with H2O/LiCl achieved COPs up to31% higher than those obtained with the H2O/BrLi mixture [123],and although with the H2O/Carrol mixture the COPs were similar to

Fig. 13. Photograph of the experimental heat transformer for water purificationdeveloped by Huicochea and Siqueiros [141,142].

Fig. 15. Photograph of the experimental heat transformer for water purificationdeveloped by Meza et al. [150].


those obtained with the H2O/LiBr mixture, the GTLs were up to 7 �Chigher [118].

3.2. Advanced absorption heat transformers

In regards to experimental studies of AAHT, a novel multi-compartment AHT for different steam temperatures was pro-posed by Scott et al. [133]. Both the absorber and generator werepartitioned in a number of compartments according with the steamtemperature levels. The authors reported values of the experi-mental heat transfer coefficients for the but the authors did notreport values of the COP. Silva-Sotelo et al. [134] and Romero et al.[135] reported the results of a TSHT built with compact heat ex-changers of 1 kW capacity controlled by flow ratio operating withthe H2O/Carrol mixture (see Fig. 11). The waste heat energy wasadded at the system at 70 �C achieving 128 �C in the secondabsorber with a COP of 0.326. Eriksson and Jernqvist [136] reportedthe preliminary results of a heat transformer with self-circulationoperating with the mixture H2O/NaOH. The self-circulation wasreached according to the thermosiphon principle. The pressuredifference in the apparatus was achieved through a difference inhydrostatic pressures. The COPs achieved were around 0.26 whenthe heat was supplied to the generator at 83 �C, to the evaporator at107 �C and the useful heat produced in the absorber at 125 �C.Alonso et al. [137] carried out an experimental study of an inno-vative AHT using partially miscible working mixtures. The systemoperated with the n-heptane/DMFmixture. Gross temperature liftsof 8 �C were achieved with COPs between 0.3 and 0.4 (see Fig. 12).An experimental study of an innovative absorption-demixing heattransformer (ADHT) operating n-heptane/DMF and cyclohexane/DMSO was carried out by Alonso et al. [138]. The system base itsperformance in the use of partially miscible working mixtures.Gross temperature lifts as high as 50 �C were obtained with COPbetween 0.27 and 0.42.

3.2.1. Conclusions of AAHTThe experimental works seen in this section regarding the study

of advanced heat transformers are few when compared to theworks reported on single-stage heat transformers. The studies havebasically focused on multi-compartment heat transformers [133],two-stage [134,135], self-circulation [136], using partially miscibleworking mixtures [137], and absorption demixing [138]. Due to bigdifferences among them in terms of their configuration, fluids used,and scarcity of reported data, a comparison among then to

Fig. 14. Photograph of the experimental set up of the absorption heat transformercoupled distillation system developed by Sekar and Saravanan [147].

determine the best one, is not possible. In all the cases the COPsvaried between 0.2 and 0.42.

3.3. Applications

3.3.1. Small scale applicationIn regards to absorption heat transformer applications. First and

second law of thermodynamics were used by Rivera et al. [139] toanalyze the performance of an experimental AHT used for waterpurification of 700W capacity operating with the H2O/LiBr mixturebuilt mainly in stainless steel. The heat was supplied to thegenerator and evaporator at about 80 �C, and the heat was deliv-ered from the absorber to the water purification system at about100 �C. The COPs varied between 0.23 and 0.33, while de ECOPsvaried from 0.15 to 0.24, and the water purification between 400and 800 mL/h. Huicochea et al. [140] presented the results of theexperimental tests applied to a portable water purification systemintegrated to an AHT of about 1 kW of capacity operating with theH2O/LiBr mixture. The heat transformer operated with waste heattemperatures from 68 �C to 78 �C achieving COP values between 0.1and 0.3, and the distilled water quality varied between 200 and500mL/h. Huicochea and Siqueiros [141,142] reported the results ofan SSHT of about 700 W capacity using the H2O/LiBr mixture (seeFig. 13). The authors reported that typical COP values could byincreased by means of heat recycling from the water purificationsystem to the AHT. The maximum COP was 0.432, obtaining amaximum of 684 mL/h of distilled water for a generation andevaporation temperatures about 70 �C and absorber temperaturesaround 110 �C. With the previous results, Hern�andez et al. [143]developed a model based on artificial neural networks to deter-mine on-line the optimum system operating conditions. The errorpropagation on COP was reported by Colorado et al. [144].Hern�andez and Colorado [145] determined the uncertainty of theCOP for the same system, and Escobar et al. [146] carried out on-line COP estimations in order to analyze and modify in real timethe system operating conditions. An AHT working with H2O/LiBrsolution, coupled with a seawater distillation systemwas evaluatedby Sekar and Saravanan [147] (see Fig. 14). The heat was supplied tothe generator and evaporator between 60 �C and 80 �C. The heatinput to the generator was fixed to 5 kW. The results showed thatthe COPs varied between 0.3 and 0.38 obtaining a maximumdistillate flow rate of 4.1 kg/h. The analysis of the behavior of an


experimental absorption heat transformer for water purification fordifferent mass flux rates in the generator was carried out by Hui-cochea et al. [141,148]. The results showed that the system irre-versibilities increased, while the COP and the ECOP decreased withan increment of the mass flow of hot water supplied to thegenerator. Also, it was shown that the system performanceimproved when the production of purified water increased due tothe increment of the heat recycled to the generator and evaporator.The COP varied from 0.16 to 0.26. Huicochea et al. [149] studied thepotential of a novel cogeneration system consisting of a 5 kWproton exchange membrane fuel cell (PEMFC) and an AHT. Thedissipation heat resulting from the operation of the PEMFC wasused to feed the AHT, which was integrated to a water purificationsystem. Therefore, the proposed system would produce electricity,heat and distilled water. The results showed that experimentalvalues of COP of the AHT and the overall cogeneration efficiencyachieved values of 0.256 and 0.571, respectively. An experimentalstudy of an AHToperating with H2O/LiBr for water purificationwithsingle-effect evaporation was carried out by Meza et al. [150] (seeFig. 15). The maximum heat recovered from the distillation processwas of 541Wwith a flowof distilled water of 888mL/h and a COP of0.391, reaching a useful heat of 1157 W.

G�omez-Arias et al. [151] reported a study for steam generationusing a H2O/Carrol SSHT. The experimental evaluation was carriedout with plate heat exchangers acting as generator in horizontaland vertical position. The results showed that the heat exchangersin vertical positions were better than horizontal positions since theevaporation take place at lower length of the heat exchanger. Theauthors did not report the COP of the system. A new concept of aclosed drying system with superheated steam provided from anAHT was proposed by Nomura and Nobuya [152]. The heat trans-former was driven directly by heat from a solar collector. It wasconcluded that the system would be useful for industries wherehigh temperature drying (over 100 �C) is required. A TSHT of about1 kW of capacity was designed and constructed by Currie andPritchard [153] to investigate the potential for dehumidifying andreheating a simulated dryer exhaust stream to make it suitable for

Fig. 16. Photograph of the industrial-scale absorption heat transformer developed byMa et al. [157].

recycling to the dryer inlet. The performance data for the heattransformer indicated that an airstream could be reheated to atemperature of 160 �C, using a lithium bromide solution of 68% w/w, with a circulation ratio (LiBr: steam flow) of 14.8 with a COPclose to 0.2. Temperature lifts between 50 and 70 �C were possiblein the reheat columnwhen using a low circulation ratio and a highLiBr concentration. The results of a 10 kW experimental AHToperating with H2O/NaOH with self-circulation (obtained accord-ing to the thermosiphon principle), installed on a pulp and papermill were reported by Abrahamsson et al. [154]. The heat trans-former used steam at 100 �C in both the generator and evaporatorand the absorber produced steam at 123 �C. The authors did notreported the COP but they estimated that was very low due to thehigh heat losses and the low capacity of the facility. Rivera [155]carried out an experimental evaluation of a single-stage heattransformer of 1 kW of capacity operating with the H2O/Carrolmixture to demonstrate the feasibility of these systems to increasethe temperature of the heat obtained from the solar ponds. GTLs ashigh as 50 �C were obtained and the maximum temperature of theuseful heat produced by the heat transformer was 132 �C. The COPsfor the unit were in the range 0.14e0.36.

3.3.2. Industrial applicationsAbrahamsson et al. [154] reported the results of a heat trans-

former plant, delivering 100 kW, designed and installed in a majorpulp and paper mill in Swedish. The unit was directly incorporatedwith one of the evaporation plants of the mill. The AHT wasdesigned to be operated with vapor supply at a temperature rangeof 87e100 �C and to produce steam at a temperature range of110e135 �C with the working pair H2O/NaOH. Because of the plantwas still in the first test period the authors did not report the COP,but they performed an economic evaluation to determine theeconomic feasibility of incorporating an AHT in this type of evap-oration plant. They found that assuming an installation cost of theAHT of 410 $ kW�1 and considering a COP of 0.45 the paybackperiod was 3.1 years. Mostofizadeh and Kulick [156] developed apilot plant of 100 kWand then built a 4 MWheat transformer plantdenominated TRAXX (currently known as double absorption)operating with the H2O/LiBr mixture to recover heat from an in-dustrial process. The pilot plant of 100 kW was used as a prototypeto produce clean steam upgrading the heat from 80 �C to 121 �Cwith and average COP of 0.52. The 4 MW plant was fed with steamfrom a counterpressure turbine at 80 �C, and the useful heat pro-duced was given up into the steam distribution system at about141 �C achieving a GTL around 60 �C. The experimental COPwas notreported for this plant but the authors estimated that considering aCOP around 0.45 the payback period of the heat transformer wouldbe 2.4 years. Ma et al. [157] reported the test results of the firstindustrial-scale absorption heat transformer equipment in China,to recover the waste heat released from mixture of steam andorganic vapor at 98 �C in the coacervation section, of a syntheticrubber plant of Yanshan Petrochemical Corporation, Beijing, China(see Fig. 16). The recovered heat was used to heat hot water from 95to 110 �C, feeding it back to the coagulator as the supplementaryheating source. The AHT system operated with the H2O/LiBrmixturewith a power capacity of 5000 kW. The results showed thatthe mean COP was 0.47, the gross temperature lift of 25 �C and thepayback period was 2 years.

3.3.3. Conclusions of applicationsAs seen in the “Small scale applications of AHT” section, most of

the applications have centered either in water purification or invapor production. In regards to water purification, several pro-totypes have been developed with capacities that vary from 700 Wto 5000 W and with COPs that vary between 0.15 and 0.43, and


purified water capacities that varied between 0.6 and 1.6 kg/h foreach kW of power supplied to the heat transformer. Since theprototypes were small, none of the cases reported payback periods.Another one of the main applications of heat transformers is invapor production. In these cases, due to the small capacity of theprototypes, variations in the capacities were between 1 kW and10 kW of exit power. The different authors reported COPs between0.1 and 0.2, but concluded that at higher power, the COPs couldincrease their values close to 0.4.

There are few works reported in the literature in relation toindustrial applications regarding the use of heat transformers.When mentioned, they have been used in vapor production, in thepulp and paper industry, and in the petrochemical industry. TheCOPs have varied between 0.45 and 0.47 and the payback periodsbetween 2 and 3.1 years.

Regarding the payback periods, it is important to mention thatin the articles published by Aly et al. [95] in 1993, Abrahamssonet al. [154] in 1995, and Scott et al. [66] in 1999 when the price ofnatural gas was similar to the current one (varying between 2.3 and3.0 dollars per Mbtu), the payback periods were lower than 18months, 3.1 years, and between 1.8 and 4.7 years, respectively,which were very attractive. In the study conducted by Ma et al.[157] in 2003, the price of natural gas was around 5 dollars with apayback period of 2 years, and comparing it to the current priceswill make it less than four years. In 2014 Donellan et al. [103]published an article stating that if the prices of natural gas werethe same as they were in 2008 (between 9 and 11 dollars), thepayback period of the installation of a heat transformer would beless than 5 years.

From the above mentioned, it becomes clear that even with thedecrease in fuel prices in the last months, the use of heat trans-formers in industrial processes for the recovery of energy is stillappealing.

Moreover, it is worth mentioning that energy saving is impor-tant not only from an economic, but also from an environmentalpoint of view, since energy saving also implies a reduction in CO2emissions, one of the main causes of global warming and all itsconsequences. All of the above makes us believe that heat trans-formers will have an even bigger impact in the near future.

Acknowledgements

The authors thank the projects SENER-CONACyT 117914, CON-ACyT 154301 and CONACyT Sabatical Year for the economic supportgiven for the development of this study.

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