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Performance analysis of a novel cascade absorption refrigeration for low-grade waste heat recovery Sheng Yang, Yifan Wang, Jun Gao, Zhien Zhang, Zhiqiang Liu, and Abdul-Ghani Olabi ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.8b00397 • Publication Date (Web): 29 May 2018 Downloaded from http://pubs.acs.org on May 29, 2018

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is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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ACS Sustainable Chemistry & Engineering

1 2 3

Performance analysis of a novel cascade absorption refrigeration for low-grade

4

waste heat recovery

5 6

Sheng Yanga, Yifan Wangb, Jun Gaoc, Zhien Zhangd*, Zhiqiang Liua*, Abdul Ghani

7

Olabie

8

a

9

South Rd., Changsha 410083, P. R. China

School of Energy Science and Engineering, Central South University, 932 Lushan

10

b

11

Rd., Piscataway, NJ 08854, USA

12

c

13

Science and Technology, 579 Qianwangang Rd., Qingdao 266590, P. R. China

14

d

15

Technology, 69 Hongguang Ave., Chongqing 400054, P. R. China

16

e

17

McLachlan Building, Paisley PA1 2BE, United Kingdom

Department of Chemical and Biochemical Engineering, Rutgers University, 98 Brett

College of Chemical and Environmental Engineering, Shandong University of

School of Chemistry and Chemical Engineering, Chongqing University of

School of Engineering and Computing, University of the West of Scotland, D163a,

18 19

*Corresponding authors:

20

Professor Zhiqiang Liu, Ph.D.

21

School of Energy Science and Engineering

22

Center South University 1

ACS Paragon Plus Environment

ACS Sustainable Chemistry & Engineering 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

932 Lushan South Rd.

2

Changsha, 410083, P. R. China.

3

Email: [email protected]

4 5

Zhien Zhang, Ph.D.

6

School of Chemistry and Chemical Engineering

7

Chongqing University of Technology

8

69 Hongguang Ave.

9

Chongqing 400054, P. R. China

10

Email: [email protected]

2


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1

Abstract

2

Absorption refrigeration (AR) systems have been extensively used for utilizing

3

waste heat from the industrial plants. In this paper, a novel cascade absorption

4

refrigeration (NCAR) is proposed to produce -40 oC cold energy via using low-grade

5

waste heat. The developed sytem consists of NH3/H2O AR cycle and LiBr/H2O AR

6

cycle. A simulation study is conducted, based on the revised model built in Aspen Plus.

7

The impacts of feed concentration, generator temperature, low-pressure part pressure,

8

high-pressure part pressure, and concentration range are investigated to offer guidance

9

for NCAR designs. In addition, the developed NCAR aims to obtain a highest

10

coefficiency of performance (COP). The maximum of COP is 0.19 and the exergy

11

efficiency of NCAR reaches 9.71%. The economic performance of NCAR is

12

compared with the industrial application. The results indicate that NCAR has an

13

excellent adaptability. This present work proposes a novel method for producing

14

low-temperature cold energy from low-grade waste heat.

15

Keywords: NCAR; Waste heat recovery; Ammonia; Lithium bromide; Absorption

16

refrigeration; Performance analysis

3



1

Introduction

2

Currently there is an rising demand for refrigeration under the conditions of low

3

evaporation temperatures, especially for storing medical materials, rapid freezing,

4

high heat-flux electronics, etc.1,

5

absorption or compression refrigeration systems to obtain a refrigeration temperature

6

below -20

7

sustainable development and conservation through waste heat recovery and renewable

8

energy has attracted much attention focusing on usage of the absorption refrigeration

9

(AR).4, 5

2

But, it is hard for the conventional single-stage

o

C with acceptable performance and economic benefits.3 Energy

10

AR system is a common type of heat recovery technology. It is often referred as

11

the “future” technology that is significant to energy utilization in 21st century based

12

on International Energy Agency (IEA).6 ARs are devices for producing cold energy by

13

heat-driven methods. The typical work pairs of AR include LiBr/H2O and NH3/H2O,

14

which could effectively recover around half of waste heat and reuse it in industries.7

15

Generally, the waste heat includes three types according to temperature levels:

16

low temperature waste heat less than 300 oC, medium temperature waste heat in the

17

temperature range of 300 oC and 600 oC, and high temperature waste heat higher than

18

600 oC. There is lot of low-grade temperature waste heat produced in the various

19

chemical processes. It is also hard to be utilized because of its various forms,

20

temperature limitations and environment and process restriction.8

21

As plotted in Figure 1, a single-stage AR has a condenser, an absorber, an

22

evaporator, a generator, and a heat exchanger (or economizer). Waste heat is added to 4


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1

the generator for vaporizing the refrigerant in the lean solutions. The vaporized

2

refrigerant passes to the condenser in which it is condensed delivering a certain

3

amount of heat. Then, it is expanded to the evaporator and is evaporated to produce

4

cold energy. Then, the refrigerant vapor flows into the absorber, which is absorbed in

5

the solutions from the generator, delivering a certain amount of heat. Finally, the rich

6

solution from the absorber is heated by the solution coming from the generator in

7

SHX, and flows back to the generator for the recycling use.

8 QC

QG Condenser

Generator

SHX

QE

QA Evaporator

Absorber

9 10 11

Figure 1. Diagram of a basic AR

12

Several studies have been carried out in various areas of industrial waste heat

13

recovery to produce cold energy and absorption system working fluids based on

14

thermodynamic analysis. Fukuta et al. proposed a compression/absorption hybrid

15

refrigeration system to recover waste heat and discussed the feasibility of the

16

proposed system.9 Kang et al. studied absorption and vapor compression combination 5



to

recover

waste

heat.

Four

different

advanced

Page 6 of 55

1

cycles

hybrid

GAX

2

(generator-absorber heat exchanger) cycles were reported and discussed.10

3

Fernández-Seara et al. developed a novel cascade system consisting of a CO2

4

compression system and an NH3/H2O absorption system. The performance of the

5

proposed system to produce cooling energy differs from -50 oC to -30 oC was

6

reported.11 Xu et al. reported a novel absorption–compression cascade refrigeration

7

system and discussed the cooling energy temperature, which showed a good

8

performance. The presented system could generate low-temperature refrigerant

9

(below - 170 oC).12 Garimella et al. proposed a novel absorption–compression system

10

in cascade with a LiBr/H2O absorption cycle and a subcritical CO2 vapor compression

11

cycle.13 Boman et al., developed a method to compare absorption heat pump working

12

pairs and screen working pairs for adsorption heat pumps based on thermodynamic

13

and transport characteristics.14, 15 Yang et al. proposed a low-grade waste heat driven

14

cascade absorption heat pump system and conducted an economic evaluation based

15

on thermodynamic analysis.16, 17 Mortazavi et al. built and tested a compact plate and

16

frame generator for low grade solar and waste heat driven absorption systems.18 The

17

cascade refrigeration system was used to generate -40 oC cooling energy. However,

18

few studies have reported the utilization of low-grade waste heat and proposed new

19

methods to use this kind of energy more efficiently in the systems of hybrid

20

refrigeration.

21

In this work, a novel cascade absorption refrigeration (NCAR) is proposed to use

22

low-grade waste heat for generating -40 oC cold energy. NCAR overcomes the limits 6


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1

of refrigeration temperature, which differs from conventional single-stage absorption

2

or compression refrigeration systems. NCAR consists of two cycles: NH3/H2O and

3

LiBr/H2O AR cycles. The model of NCAR was constructed and revised based on the

4

two cycles, its thermodynamic performance was evaluated and analyzed. The design

5

of NCAR was based on those analyses, aiming to achieve a maximal COP. In addition,

6

to further investigate the proposed system, technical analysis, economic analysis and

7

exergy analysis were carried out, and exergy destruction saving mechanism was

8

elucidated.

9 10

Process description

11

NCAR consists of two cycles, i.e. LiBr/H2O AR cycle and NH3/H2O AR cycle as

12

depicted in Figure 2. The LiBr/H2O AR cycle includes an evaporator, an absorber, a

13

generator, a condenser, and a heat exchanger. In this cycle, the low-pressure parts are

14

evaporator and absorber, while the high-pressure parts are condenser and generator.

15

The difference between these two cycles is that the solution to absorb refrigerant in

16

the NH3/H2O AR cycle is a lean solution, while it is a concentrated solution in the

17

LiBr/H2O AR cycle. The refrigerants of LiBr/H2O and NH3/H2O AR cycle are water

18

and ammonia, respectively. It is noticed that the range of temperature and pressure in

19

NH3/H2O AR cycle are both higher than those in LiBr/H2O AR cycle.

7



1 2

Figure 2. P-T diagram for NCAR

3 4

Figure 3 is the schematic diagram of NCAR used in this work. As can be seen

5

from the figure, the low-grade waste heat includes low temperature part and high

6

temperature part. Ts is a critical temperature between low temperature part and high

7

temperature part. On the basis of the principle of energy cascade utilization, low

8

temperature part and high temperature part are the heat sources of LiBr/H2O and

9

NH3/H2O AR cycles, respectively. The LiBr/H2O AR cycle produces cooling water

10

(QE1) is fed to NH3/H2O AR cycle for process intensification. The NH3/H2O AR cycle

11

produces cold energy (QE2) of high quality.

8


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1 2

Figure 3. Schematic of NCAR

3

A process diagram of NCAR is depicted in Figure 4. In the NH3/H2O AR cycle,

4

the concentrated NH3 solution is fed into the lower portion of the NH3 generator. The

5

diluted NH3 solution leaves from the bottom side of the column, while NH3 leaves

6

from the top side. Meanwhile, the column is heated using the waste heat from high

7

temperature part (QG2), and the condenser is cooled using the chilled water (QG1),

8

which is produced by the LiBr/H2O AR cycle. NH3 from the top side of the column is

9

condensed to liquid NH3, which is then evaporated into gaseous NH3 in the evaporator

10

to generate cold energy. NH3 gas is then fed into the NH3 absorber. The diluted NH3

11

solution flows into the NH3 absorber from the NH3 storage. The NH3 gas is absorbed

12

by the diluted NH3 solution within the NH3 absorber. Meanwhile, the absorber is

13

cooled using the chilled water from the NH3 condenser. Finally, the concentrated NH3

14

solution from the NH3 absorber flows into the NH3 generator.

15

In the AR cycle of LiBr/H2O, the diluted LiBr solution is fed into the LiBr

16

generator. The concentrated LiBr leaves the bottom side of the generator, while the

17

water steam leaves from the top. The LiBr generator is heated by low temperature part

18

of the waste heat (QG1) and water steam from the top of the LiBr generator is cooled

19

inside the water condenser. Water flows to the NH3 absorption refrigeration process

20

through the water valves. The chilled water is evaporated to steam producing cold 9



1

energy, and then, the steam flows back into the LiBr absorber. Furthermore, the

2

solution of concentrated LiBr from the bottom side of the LiBr generator enters the

3

LiBr absorber from the LiBr storage. The steam is then absorbed by the concentrated

4

LiBr solution within the LiBr absorber. Finally, the dilute LiBr flows back into the

5

LiBr generator.

6

Figure 4. Process flowchart of NCAR

7 8 9 10 11

Mathematical and exergy analysis model The developed model is based on the global mass and energy balance formulas. The following assumptions are made as follows19, 20:

12

1) The pump work is negligible in the whole system.

13

2) Heat loss to the environment and pressure loss in the devices are negligible.

14

3) Solutions from generators and absorbers are assumed to be under the

15

equilibrium conditions at the generator and absorber temperatures,

16

respectively.

17 18

4) Solutions flow via a non-isothermal process inside the absorbers and generators owing to various concentrations of the inlet and outlet solutions. 10


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1 2 3

5) The liquid from the condenser and the vapor from the evaporator are assumed to be saturated.

LiBr/H2O AR cycle model

4

At a steady state, the input mass is equal to the output value in every unit, and

5

each component follows mass balance in all units. The work pair consists of LiBr and

6

H2O. In this cycle, two independent mass balance governing equations are used.21

7

The governing equations of the proposed model can be expressed by:

8

Generator：

9

m1 = m2 + m3

(1)

10

m1 x1= m3 x3

(2)

11

Absorber：

12

m9 = m5 + m8

(3)

13

m9 x9= m5 x5

(4)

14

The input and output values of the heat exchanger, valve and pump follow

15

energy balance. The energy of the absorber, generator, condenser and evaporator are

16

kept balanced with external energy.

17

Generator：

18

QG1 = m2 h2 + m3 h3 - m1 h1

19

Absorber：

20

QA1 = m9 h9 - m5 h5 – m8 h8

21

Condenser：

22

QC1 = m6 h6 - m2 h2

(5)

(6)

(7) 11



Page 12 of 55

1

Evaporator：

2

QV1 = m8 h8 – m7 h7

3

Heat exchanger and throttling valve：

4

m4 h4 - m3 h3 = m1 h1 – m10 h10

(9)

5

m6 h6 = m7 h7

(10)

6

m4 h4 = m5 h5

(11)

7 8 9

(8)

NH3/H2O AR cycle model Similarly, the mass and energy balance of the NH3/H2O AR cycle are demonstrated in Eqs. (12) - (22) at steady state.

10

Generator:

11

m11 = m12 + m13

(12)

12

m11 x11= m12 + m13 x13

(13)

13

Absorber：

14

m19 = m18 + m15

(14)

15

m19 x19= m18 + m15 x15

(15)

16

The energy balance can be calculated by:

17

Generator：

18

QG2 = m12 h12 + m13 h13 - m11 h11

19

Absorber：

20

QA2 = m19 h19 - m15 h15 – m18 h18

21

Condenser：

22

QC2 = m16 h16 - m12 h12

(16)

(17)

(18) 12


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1

Evaporator：

2

QE2 = m18 h18 - m17 h17

3

Heat exchanger and throttling valve：

4

m14 h14 - m13 h13 = m11 h11 – m20 h20

(20)

5

m16 h16 = m17 h17

(21)

6

m15 h15 = m14 h14

(22)

7

(19)

Exergy analysis model

8

Exergy analysis helps to accurately demonstrate the intensity of irreversibility for

9

each component and the refrigeration system. In addition, it is able to identify the

10

location of the irreversibility in the system. The definitions of the exergy destruction

11

and its percentages of each component in NCAR are referred to the previous

12

work.22-24

13

The physical exergy of each stream in NCAR can be calculated by:

14

Ex = m [(h-h0) - T0(s-s0)]

(23)

15

in which the subscript “0” stands for the reference state. The reference temperature T0

16

and reference pressure P0 are 25 oC and 101.325 kPa, respectively.25

17

The exergy destruction percentanges ϕ of each component in NCAR are:

18

In the generator:

19

 T  Ex2 + Ex3 − Ex1 − QG1 1 − 0   TG1  ϕG1 = 2 T QGi (1 − 0 ) ∑ TGi i =1

(24)

13



1

 T  Ex12 + Ex13 − Ex11 − QG2 1− 0   TG2  ϕG2 = 2  T  QGi 1− 0  ∑ i =1  TGi 

2

In the condenser:

3

ϕC1 =

4

ϕC2 =

5

In the valve:

6

ϕV 1 =

7

ϕV 2 =

8

ϕV 3 =

9

ϕV 4 =

Page 14 of 55

(25)

Ex6 − Ex2 + ∆Exwater 2  T  QGi 1− 0  ∑ i =1  TGi 

(26)

Ex16 − Ex12 +∆Excooling water (27)

 T  QGi 1− 0  ∑ i=1  TGi  2

Ex7 − Ex6  T  QGi 1 − 0  ∑ i =1  TGi 

(28)

2

Ex5 − Ex4 2  T  QGi 1 − 0  ∑ i =1  TGi 

(29)

Ex17 − Ex16  T  QGi 1− 0  ∑ i=1  TGi 

(30)

2

Ex15 − Ex14  T  QGi 1 − 0  ∑ i =1  TGi 

(31)

2

10

In the evaporator:

11

ϕE1 =

Ex8 + Ex16 + Ex19 − Ex7 − Ex12 − Ex18 − Ex15 2  T  QGi 1− 0  ∑ i =1  TGi 

14


(32)

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Ex18 − Ex17 +∆Excold energy

1

ϕE2 =

2

In the absorber:

3

ϕA1 =

4

ϕ A2 =

5

In the pump:

6

ϕP1 =

7

ϕP1 =

8

The exergy efficiency of NCAR can be calculated by:

9

T0 −1) TE 2 η= 2  T0  2 Q  + ∑WEi ∑ Gi 1 − i =1  TGi  i=1

(33)

 T  QGi 1− 0  ∑ i=1  TGi  2

Ex9 − Ex8 − Ex5 +∆Exwater 2  T  QGi 1− 0  ∑ i=1  TGi 

(34)

Ex19 − Ex18 − Ex15 + ∆Excooling water

(35)

 T  QGi 1− 0  ∑ i =1  TGi  2

Ex10 − Ex9 + WE1 2  T  QGi 1− 0  ∑ i =1  TGi 

(36)

Ex10 − Ex9 +WE2 2  T  QGi 1− 0  ∑ i =1  TGi 

(37)

QE 2 (

(38)

10 11

Thermodynamic analysis

12

The numerical analysis of NCAR was developed in the software of Aspen Plus.

13

The NCAR includes LiBr/H2O and NH3/H2O AR cycles. ELECNRTL was chose for

14

the property method to simulate NCAR.26 The electrolyte parameter pair of LiBr/H2O

15

solution and the binary parameter of NH3/H2O solution were obtained from LiBr/H2O 15



Page 16 of 55

1

and NH3/H2O vapor-liquid equilibrium data, respectively.27, 28 The revised results of

2

electrolyte parameters and the regressed binary parameters of NH3/H2O are shown

3

respectively in Tables 1 and 2. Table 1 Electrolyte properties of the LiBr/H2O solution

4

Parameter

Component i Component j Value (SI units)

GMELCC/1

H2 O

(Li+, Br-)

7.17

GMELCC/1

(Li+, Br-)

H2 O

-1.417

GMELCD/1

H2 O

(Li+, Br-)

-4803.40

GMELCD/1

(Li+, Br-)

H2 O

-854.73

5

Table 2 Binary parameters of the NH3/H2O solution

6

Item Value

Component i Component j NH3

H2 O

Aij

Aji

Bij

Bji

Cij

0.71 4.83 -782.28 -1584.41 0.20

7

In order to ensure that the thermodynamic model created is accurate, a

8

comparison against experimental data should be conducted.29 The LiBr/H2O model is

9

compared with the model of Ebrahimi et al.30 The NH3/H2O model is compared to the

10

work of Ouadha and EI-Gotni.31 The comparison and deviations of NCAR are

11

presented in Table 3. As can be seen, the deviation of LiBr/H2O AR cycle is 0.6% and

12

the NH3/H2O cycle is 0.3%. Thus, it can be obtained that the built models are very

13

accurate.

14

Table 3 Comparison of LiBr/H2O AR cycle and NH3/H2O AR cycle model with Ref.30,

15

31

16


Page 17 of 55 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Type

Parameter

Generator

LiBr/H2O

AR

Reference

Present

Data

Deviation

data

study

type

(%)

84.8

84.8

Input

-

39.8

39.8

Input

-

35.5

35.5

Input

-

8.6

8.6

Input

0.7755

0.7701

Output

100

100

Input

40

40

Input

25

25

Input

-5

-5

Input

0.5488

0.5503

Output

Symbol

TG1 o

temperature

( C)

Condenser

TC1

temperature

(oC)

Absorber

TA1 o

temperature

( C)

Evaporator

TE1

temperature

o

( C)

Coefficient of COP1

0.6

performance Generator

TG2 o

temperature

( C)

NH3/

Condenser

TC2

H2 O

temperature

(oC)

AR

Absorber

TA2

temperature

(oC)

Evaporator

TE2

temperature

o

( C)

Coefficient of COP2 performance 17


0.3


1 2 3

Page 18 of 55

Performance parameters In this paper, the COP32, circulation ratio33, and concentration range34 are utilized as the performance parameters to evaluate NCAR.

4

The COP of the AR is equal to the heat load in the generator per unit heat load in

5

the evaporator. In this study, the generator heat load is supplied by the low-grade

6

waste heat that is belonged to the consumption of the system. The expression of COP

7

can be calculated by:

8

9

COP =

QE QG

(39)

where QE and QG denote respectively the heat loads of evaporator and generator.

10

The circulation ratio is a significant design and optimization parameter, which is

11

directly relevant to the size and cost of the system components. It is the ratio of the

12

mass flow rate of the solution feeding into generator to the refrigerant leaving the

13

generator.

14

The circulation ratios of LiBr/H2O AR and NH3/H2O AR are written as:

m1 m2

(40)

m11 m12

(41)

15

f1 =

16

f2 =

17 18 19

The concentration range is the input and output solution concentration difference of the generator. In the NH3/H2O AR cycle, it can be defined as: △x2 = x11 – x13

(42)

20

A higher COP means a higher energy utilization efficiency and better performance.

21

f has an inverse relationship with △x. A higher f is a higher solution flow rate recycle 18


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1

generate per mass unit refrigerant resulting in higher energy consumption. Thus, it is

2

an obstacle to improve the performance of absorption refrigeration.

3

Thermodynamic analysis of LiBr/H2O AR

4

Generator temperature, feed concentration (generator), low-pressure part

5

pressure and high-pressure part pressure are important parameters affecting the

6

LiBr/H2O AR cycle35,

7

pressure were respectively 4.4 kPa and 0.93 kPa. The feed concentration was 0.515 in

8

the cycle. The generator temperature as a function of COP and circulation ratio is

9

plotted in Figure 5. When the pressure and composition of feed concentration were

10

constant, increasing the temperature of generator improves the vapor fraction. The

11

mass flow rate ratio of the rich solution leaving the generator to the refrigerant

12

produced by the generator is depressed. As a consequence, the f decreases and heat

13

loads of generator and evaporator increases while increasing the generator

14

temperature. Meanwhile, the increasing ratio of evaporator is higher than that of the

15

generator. Therefore, the COP is correlated with the generator temperature.

36

. The high-pressure part pressure and low-pressure part

16

The temperature of generator remains at 80 oC. The pressures of high-pressure

17

part and low-pressure part were 4.4 kPa and 0.93 kPa, respectively. Under the

18

conditions, a study was carried out to study the effect of feed concentration in the

19

LiBr/H2O AR cycle. Figure 6 shows the correlation between the feed concentration,

20

COP and circulation ratio. The pressures (high-pressure part and low-pressure part)

21

and feed temperature were constant. While increasing the feed concentration, the feed

22

bubbling point temperature is increased. A decrease in the vapor fraction could 19



1

increase the mass flow ratios of solution leaving generator and refrigerant. In addition,

2

the circulation ratio is positively correlated with the feed concentration. On the other

3

hand, with an increment of the feed concentration, heat loads of generator and

4

evaporator are reduced. The decreasing ratio of the evaporator is higher than that of

5

the generator. Therefore, the COP shows an inverse relationship with the feed

6

concentration.

7 8

Figure 5. COP and circulation ratio versus generator temperature

9 10

Figure 7 shows condenser temperature and feed temperature versus

11

high-pressure part pressure, when generator temperature is 80 oC, the pressure of

12

low-pressure part is 0.93 kPa and feed concentration is 0.515. The rise of

13

high-pressure part pressure suggests increasing the condenser pressure. The

14

composition remains unchanged in the condenser. With an increase of the

15

high-pressure part pressure, the refrigerant temperature and the condenser temperature 20


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1

increase.

2 3

Figure 6. COP and circulation ratio versus generator feed concentration

4 5 6

Figure 7. Feed temperature and condenser temperature versus high-pressure part pressure

7 21



1

Thermodynamic analysis of NH3/H2O AR

2

Concentration range, feed concentration of generator, high-pressure part pressure

3

and low-pressure part pressure are four important design parameters of NH3/H2O AR

4

cycle.37-39 The pressure of high-pressure part was set at 612.2 kPa, the pressure of

5

low-pressure part was 72 kPa, the generator feed concentration was 0.372, and the

6

refrigerant flow rate was a constant.

7 8

Figure 8. COP and circulation ratio versus concentration range

22


Page 22 of 55

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1 2

Figure 9. Generator temperature and feed temperature versus concentration range

3 4 5

Figure 8 shows the COP and circulation ratio versus the concentration range.

6

Figure 9 depicts the generator temperature and feed temperature versus the

7

concentration range. The increase in the concentration range indicates a larger

8

concentration difference between the solution entering the generator and the solution

9

leaving the generator. The mass flow ratio of solution leaving generator and

10

refrigerant reduces as increasing the concentration range. Thus, the circulation ratio

11

reduces while increasing the concentration range. For the single-stage AR, the

12

concentration should be higher than 0.06, the singe-stage AR would not be

13

economically beneficiary otherwise.40

14

The temperature at the bottom of the generator increases when increasing the

15

concentration range with unchanged composition, pressure and temperature of 23



1

generator feed. The temperature of energy consumed in generator increases, while the

2

amount of energy consumption in the generator decreases. The change of

3

concentration range has no influence on evaporator. It is indicated that COP increases,

4

with the increase of concentration range. Meanwhile, the NH3 exchanger recovers

5

more energy with an increment in concentration range, resulting in an increase of feed

6

temperature.

7 8

Figure 10. COP and feed temperature versus feed concentration

9 10

The pressures of high-pressure part and low-pressure part were 612.2 kPa, and

11

72 kPa. The feed range was 0.08, and the refrigerant flow rate was a constant. Figure

12

10 demonstrates the correlation between the feed concentration, the COP and feed

13

temperature. The heat load of the generator decreases, the load of evaporator stands

14

constant, and the NH3 exchanger recovers little energy, when the feed concentration

15

increases. Thus, in the COP shows the same tendency as the feed concentration 24


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1

changes and the feed temperature having the opposite tendency.

2

Based on the analysis, it can be obtained that feed concentration, generator

3

temperature, low-pressure part pressure and high-pressure part pressure are the design

4

parameters for LiBr/H2O AR cycle and feed concentration, concentration range,

5

low-pressure part pressure and high-pressure part pressure are the design parameters

6

for NH3/H2O AR cycle. In the LiBr/H2O AR cycle, feed concentration determines the

7

absorber temperature, generator temperature determines the energy consumption

8

grade, the pressure of high-pressure part determines the condenser temperature, and

9

the pressure of low-pressure part determines the evaporator temperature. In the

10

NH3/H2O AR cycle, concentration range determines the energy consumption grade in

11

generator and other parameters are similar to LiBr/H2O AR cycle. It is noticed that

12

low-pressure part pressure influences the absorber temperature both in LiBr/H2O AR

13

and NH3/H2O AR cycles.

14 15 16 17 18

NCAR design and analysis The design purpose of NCAR is generating -40 oC cold energy. The constraint of NCAR is shown as Table 4. Table 4 Design constraints of NCAR Component

Value Unit

△TG1

10

o

Temperature difference of LiBr evaporator △TE1

5

o

Temperature difference of LiBr condenser

10

o

Temperature difference of LiBr generator

△TC1

25


C C C


Page 26 of 55

Temperature difference of LiBr absorber

△TA1

10

o

Temperature difference of NH3 condenser

△TG2

5

o

Temperature difference of NH3 absorber

△TA2

5

o

Temperature difference of NH3 generator

△TE2

10

o

Temperature of water

TW

25

o

C C C C C

1 2

NCAR design

3

The mass balance and energy balance of NCAR were simulated using Aspen

4

Plus.40-42 In order to study COP of the NCAR system, the low-grade waste heat

5

capacity was set as a constant including high temperature part and low temperature

6

part. The cooling water temperature generated by the LiBr/H2O AR cycle is TC1. The

7

low-pressure part pressure in LiBr/H2O AR and NH3/H2O AR cycles are determined,

8

according to bubble point of the refrigerant. It is assumed that the total low-grade

9

waste heat energy is Q. The hot outlet-cold inlet temperature difference of LiBr

10

exchanger and NH3 exchanger are both 10 oC.

11

The disadvantage of the LiBr-H2O pair is that it cannot produce a below-zero

12

degree coolant. It also has a risk of crystallization at high temperatures when the

13

concentration of LiBr solution is high. While, the advantage of the NH3-H2O pair is

14

that it can produce a below-zero degree coolant, but the COP is smaller than

15

LiBr-H2O pair. The limit of NH3/H2O AR design is solubility.

16

Energy constraint：

17

QG 2 =

150 − TS ×Q 150 − 90

(43) 26


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TS − 90 ×Q 150 − 90

1

QG 1 =

2

QE1 ≥ QC2 + QA2

3

Temperature constraint：

4

Ts ≥TG2 +∆TG2

(46)

5

TG1 +∆TG1 ≤ 90

(47)

6

TC1 ≥TW +∆TC1

(48)

7

TA1 ≥TW +∆TA1

(49)

8

TC2 ≥ TE1 +∆TC2

(50)

9

TA2 ≥ TE1 +∆TA2

(51)

(44) (45)

10

where QG1, QG2, QE1, QC2 and QA2 denote the heat load of generator duty of LiBr/H2O

11

AR cycle, generator heat load of NH3/H2O AR cycle, evaporator duty of LiBr/H2O

12

AR cycle, condenser duty of NH3/H2O AR cycle, and absorber duty of NH3/H2O AR

13

cycle, respectively. TG1, TC1, and TE1 are respectively the temperatures of generator,

14

condenser, and evaporator in LiBr/H2O AR cycle. TG2, TA2, and TC2 are respectively

15

the temperatures of generator, absorber, and condenser in the NH3/H2O AR cycle.

27



1 2

Figure 11. Design procedure for NCAR

3 4

Based on the LiBr/H2O AR cycle and NH3/H2O cycle analysis, a design

5

procedure has been developed and is illustrated in Figure 11 for NCAR design. The

6

first step is to calculate QG1 and QG2. The second step is to design NCAR, according

7

to the input conditions. The energy constraint is based on a decision-oriented test. If

8

the cooling water generated by LiBr/H2O AR cycle is able to enhance NH3/H2O AR

9

cycle, the test is passed. Otherwise, NCAR is re-designed. Next, two temperature

10 11 12

constraints are tested. NCAR will only be designed, when all the constraints are met. COP is based on the first law of thermodynamics to estimate AR performance. In this section, COP is the criteria for NCAR design. The objective function is given by:

28


Page 28 of 55

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Max COP =

1

QE 2

(52)

2

∑ QGi i =1

2

The final design results using low-grade waste heat to generate -40 oC cold

3

energy are based on Eq. (52). The simulation results of LiBr/H2O AR and NH3/H2O

4

AR cycles are summarized in Table 5 and Table 6, under the condition that Ts equals

5

127.5 oC and TC1 equals 5 oC. This means that the low-grade waste heat above 127.5

6

o

7

LiBr/H2O AR cycle. The COP of NH3/H2O AR cycle is 0.49. The COP of LiBr/H2O

8

AR cycle is 0.83. Thus, the COP of NCAR is 0.19. The stream NOs are corresponding

9

to Fig. 4.

C is used by NH3/H2O AR cycle and the heat below 127.5 oC is consumed by

Table 5 The modeling results of LiBr/H2O AR cycle

10

Stream NO.

1

2

3

4

5

6

7

8

9

10

49.1

80.0

80.0

40.0

40.0

30.4

5.0

5.0

30.0

30.0

4.4

4.4

4.4

4.4

0.93

4.4

0.93

0.93

0.93

4.4

H2 O

0.485

1

0.353

0.353

0.353

1

1

1

0.485

0.485

Li+

0.041

0

0.052

0.052

0.052

0

0

0

0.041

0.041

Br-

0.474

0

0.595

0.595

0.595

0

0

0

0.474

0.474

Temperature o

C

Pressure KPa Mass Fraction

11 12

Table 6 The modeling results of NH3/H2O AR cycle 29



Stream NO.

11

12

13

71.0

64.4

14

Page 30 of 55

15

16

17

18

19

20

117.5 20.4

20.5

10.0

-40.1

-40.1

10.1

10.5

612. 2

612.2 612.2

72

612.2 72

72

72

612.2

Temperature o

C

Pressure kPa 612.2 Mass Fraction H2O

0.628

0

0.861 0.861

0.861

trace

trace

trace

0.628

0.628

NH3

0.372

1

0.139 0.139

0.139

1

1

1

0.372

0.372

1 2

Technical analysis

3

The performance of NCAR was studied by changing the initial values of the

4

system. The COP values of NCAR were plotted while changing LiBr condenser

5

temperature keeping low-grade waste heat and cooling water temperature constant.

6

This plotting is studied with the variation of LiBr condenser temperature from 5 to 15

7

o

8

condenser temperature, while the Ts increases. The temperature of LiBr condenser

9

should be kept as low as possible for a better COP.

C. As shown in Figure 12, the COP of NCAR drops with the decrease of LiBr

30


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1 2

Figure 12. LiBr condenser temperature versus the COP of NCAR and Ts

3 4

Figure 13. Cold energy temperature versus the COP of NCAR

5

It was also noted that the cold energy temperature is another important parameter

6

for NCAR. The temperature of cold energy implies the product “quality” of NCAR.

7

The correlation of COP and cold energy temperature is shown in Figure 13. This 31



1

correlation is studied the cold energy temperature between -60 oC and -10 oC. With

2

the increase of cold energy temperature, the COP increases fast, then slows down. At

3

a -10 oC cold energy temperature the COP is 0.23 and at a -60 oC cold energy

4

temperature the COP is 0.13.

5

Exergy analysis

6

COP is a performance parameter of NCAR, however, it cannot estimate the

7

potential of the substance to cause change.43 Therefore, an exergy analysis is also

8

conducted for NCAR. Exergy analysis is on the basis of the second law of

9

thermodynamics and returns to Maxwell and Gibbs.44

10

11 12

Figure 14. Exergy flow diagram of NCAR

13

Figure 14 shows the exergy flow diagram of NCAR for low-grade waste heat to

14

generate -40 oC cold energy at the condition of Ts = 127.5 oC, TC1 = 5 oC and COP = 32


Page 32 of 55

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1

0.19. The exergy destruction is result from the irreversibility of thermal exergy

2

transfer caused by concentration gradient, pressure gradient, external force, and

3

temperature gradient. Due to the concentration gradient, external force, and

4

temperature gradient, the exergy destruction of the generator occupies a big part. The

5

irreversibility of the valves results in the exergy destruction because of pressure

6

gradient. The flow of the streams in LiBr AR is larger than that in NH3 AR. Thus, the

7

loop of LiBr AR occupies the more exergy destruction than the loop of NH3 AR. It

8

can be seen that LiBr generator, NH3 generator and condenser, V2, V3, and V1 cause

9

almost half of NCAR irreversibility. The exergy destruction in NH3/H2O AR cycle is

10

less than that in LiBr/H2O AR cycle. The exergy efficiency of NCAR is 9.71%.

11

Therefore, to reduce irreversibility is to firstly optimize LiBr/H2O AR cycle, on the

12

view of subsystem. Reducing irreversibility is prior to optimizing generators and

13

valves, on the view of component.

14

Economic analysis

15

An understanding of process economic is therefore critical in process design. For

16

economic analysis, NCAR is compared to the vapor compression refrigeration (VCR),

17

which is the most widely used refrigeration method in industry. The cost of unit cold

18

energy and process initial investment are conducted comparison in this section. Table

19

8 shows the basic parameters for the economic analysis.

20

Table 8 Basic parameters of the economic analysis45 Item

Value

Capacity (kW)

1000 33



Electricity price ($/kWh)

0.11

Cooling water price ($/GJ)

0.35

Medium-pressure steam ($/GJ)

14.19

Project life of VCR (y)

15

Project life of NCAR (y)

10

Page 34 of 55

1 2

VCR and NCAR are driven by steam turbine generator and low-grade waste heat,

3

respectively. The energy supply and refrigerant schematic diagram of VCR and

4

NCAR is shown in Figure 15. The power consumption of VCR includes the power

5

consumption of cooling unit, cooling pump, chilled water pump, and cooling tower

6

fan. The power consumption of NCAR includes the power consumptions of chilled

7

water pump, cooling pump, cooling tower fan, solution pump, refrigerant pump and

8

vacuum pump. The investment of NCAR consists of the investment of NH3 AR and

9

LiBr AR. The cost of unit cold energy and process initial investment of VCR and

10

NCAR are formulated as follows: sf

11

I  B ZR,VCR = ZR,VCR ×  R,VCR  B I  R,VCR 

(53)

12

CR,VCR = α × ZR,VCR

(54)

13

Cp,VCR =

14

I  B ZR, NCAR = ZR,NCAR ×  R,NCAR  B I  R,NCAR 

Cw × ( Nin + Nlb + Nlf ) + CR, VCR Q0

(55)

sf

(56)

34


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1

CR, NCAR = α × ZR, NCAR

2

Cp, NCAR =

α=

3

(57)

Cw × ( Ng + Na + N0 + Nlb + Nlf ) + CR, NCAR Q0

i 1 − (1 + i)−n

(58)

(59)

4

where ZR,VCR and ZR,NCAR represent investment of VCR and NCAR, which includes

5

equipment purchase, design and installation cost, land and building cost, etc.;

6

and

7

IR,VCR and IR,NCAR represent the scale of VCR and NCAR, respectively;

8

B IR,NCAR represent the reference scale of VCR and NCAR, respectively; Cp, VCR and Cp,

9

NCAR

B ZR,VCR

B ZR,NCAR represent the reference investment of VCR and NCAR, respectively; B IR,VCR and

represent the cost of unit cold energy of VCR and NCAR, respectively; CR, VCR

10

and CR, NCAR represent the process initial investment of VCR and NCAR, respectively;

11

Cw is electricity price; Nin represents cooling unit power consumption; Nlb represents

12

chilled water pump power consumption and cooling pump power consumption; Nlf

13

represents cooling tower fan power consumption; Ng represents solution pump power

14

consumption; Na represents refrigerant pump power consumption; N0 represents

15

vacuum pump power consumption; i represents annual interest rate; and n represents

16

project life.

35



1 2 3

Figure 15. Energy supply and refrigeration schematic diagram of VCR and NCAR

4 5 6

Figure 16. Investment comparison between VCR and NCAR with different scales

7 8

The investments of VCR and NCAR are calculated by Eq. (53) and Eq. (56)

9

according to the benchmarks46-48. Investments of VCR and NCAR with varying scale 36


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1

are presented in Figure 16. It indicates that the investments of VAR and NCAR

2

increase with the increment in the scale. With the scale varying from 200 kW to 1800

3

kW, the investment of VCR increases from 0.98×105 USD to 3.7×105 USD while

4

the investment of NCAR increases from 1.0×105 USD to 3.8×105 USD. The

5

investment of NCAR is slighly higher than that of VCR. Besides, the increase ratio of

6

NCAR investment is also bit bigger than that of VCR.

7 8 9

Figure 17. Cost of unit cold energy comparison between VCR and NCAR varying with scale

10 11

The cost of unit cold energy of VCR and NCAR are calculated by Eq. (55) and Eq.

12

(58), which are based on Eqs. (53), (54), (56), (57), and (59). The comparison results

13

of cost of unit cold energy between VCR and NCAR varying with scale are shown in

14

Figure 17. As can be seen, with the increase of the scale, the cost of unit cold energy

15

decreases. Particularly for the NCAR, the decreasing rate is relative large. With the 37



1

scale increasing from 200 kW to 1800 kW, the cost of unit cold energy of VCR

2

decreases from 18.6 USD/GJ to 14.8 USD/GJ while the cost of unit cold energy of

3

NCAR decreases from 11.8 USD/GJ to 6.7 USD/GJ. The NCAR shows a better

4

performance on the cost of unit cold energy than that of the VCR. While the scale

5

increases, the ratio of the cost of unit cold energy of NCAR to that of VCR deceases.

6

It indicates that the cost advantage becomes more obvious as the increment in the

7

scale.

8 9

Conclusion

10

NCAR is proposed to generate -40 oC cold energy by using low-grade waste heat.

11

This study provides an innovative and efficient method for producing high quality

12

cold energy by the low-grade waste heat. Regarding the characteristics of NCAR, two

13

subsystems are analyzed separately. The design parameters for NCAR are analyzed in

14

details. NCAR is designed to achieve a maximal COP. The technical analysis, exergy

15

analysis, and economic analysis are conducted. The following conclusions can be

16

obtained:

17

1. The COP of the designed NCAR is 0.19.

18

2. The exergy efficiency of NCAR is 9.71%. It needs to be pointed out that

19

reducing irreversibility is the first optimizing LiBr/H2O AR cycle in terms of

20

subsystem. Reducing irreversibility is prior to optimizing generators and

21

valves in terms of component.

22

3. The economic analysis shows that the investment of NCAR is not dominant, 38


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1

but the operating cost shows a better performance compared with the VCR.

2

4. The varying rate of NCAR is larger than VCR in investment and cost of unit

3 4 5

cold energy. 5. The advantage of NCAR becomes more obvious in cost of unit cold energy as the scale increases.

6

39



1

Notes

2

The authors declare no competing financial interest.

3 4

Acknowledgements

5

The authors would like to thank the financial support from the China NSF

6

project (NO. 51676209), and Collaborative Innovation Center of Building Energy

7

Conservation and Environmental Control.

8

40


Page 40 of 55

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1

Nomenclature

AR

absorption refrigeration

COP

coefficient of performance (-)

NCAR

novel cascade absorption refrigeration

VCR

vapor compression refrigeration

IEA

International Energy Agency

GAX

generator absorber heat exchange

m&

mass flow rate (kg/s)

x

concentration (-)

& Q G

generator duty (kW)

& Q A

absorber duty (kW)

& Q C

condenser duty (kW)

& Q V

evaporator duty (kW)

h

enthalpy (kJ/kg)

W

power rate (kW)

f

circulation ratio (-)

△x

concentration range (-)

△T

temperature difference (oC)

Greek symbol

ϕ

exergy destruction percentage

41



η

exergy efficiency

1

42


Page 42 of 55

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1

Appendix

2

The ELECNRTL property method is the most versatile electrolyte property

3

method. It can handle very low and very high concentrations. And it can handle

4

aqueous and mixed solvent systems.

5

The ELECNRTL model uses the infinite dilution aqueous solution as the

6

reference state for ions. It adopts the Born equation to account for the transformation

7

of the reference state of ions from the infinite dilution mixed solvent solution to the

8

infinite dilution aqueous solution.

9

The excess Gibbs free energy calculated as:

10

11 12

∑X G τ ∑X G

  X + ∑ Xc ∑ a c a'  ∑ X a'' k kB k  a''   ∑ X jGja,c'aτ ja,c'a  Xc'  j +∑ Xa ∑  a c'  ∑ X c''  ∑ XkGka,c'a  c''  k

GmE,lc = ∑ XB RT B

j

 ∑ X jGjc,a'cτ jc,a'c  j   ∑ Xk Gkc,a'c  k (A-1)

where j and k can be any ion form (a, c, or B). The molecule activity coefficient:

∑X G τ = ∑X G j

ln γ

lc B

jB jB

j

k

kB

k

13

jB jB

j

 ∑k XkGkB'τkB' X B' GBB'  +∑ τ BB' − B' ∑ X k GkB'  ∑k XkGkB' k 

    

 ∑k XkGkc,a'cτ kc,a'c  XcGBc,a'c  Xa +∑∑ τ Bc,a'c − c a' ∑ X a'' ∑ X k Gkc,a'c  ∑k XkGkc,a'c  '' k  a  ∑k XkGka,c'aτka,c'a  X aGBa,c'a  +∑∑ τ Bc,c'a − Xk Gka,c'a  a' c ∑ X c'' ∑ X k Gka,c'a  ∑ '' k k   c Xc'

14

The cation activity coefficient: 43


(A-2)


1

2

3

4

  ∑ XkG ' τ '  ∑k XkGkBτkB  kc,a c kc,a c X BGcB  1  X a'  k lc ln γ c = ∑ +∑  τ cB − zc X k Gkc,a'c X k GkB  a'  ∑ X a''  B' ∑ X k GkB  ∑ ∑ '' k k    a  k (A-3)    X kGka,c'aτ ka,c'a  ∑ X G  X '  a ca,c'a   +∑∑ c  τ ca,c'a − k  ' a c  ∑ X c''  ∑ X k Gka,c'a  ∑k XkGka,c'a  '' k   c  The anions activity coefficient:

  ∑ Xk G ' τ '  ∑k XkGkBτ kB  ka,c a ka,c a X BmGaB  1  Xc'  k lc ln γ a = ∑ +∑  τ aB − za X kGka,c'a X kGkB  B ∑ X k GkB  ∑ ∑ c'  ∑ X c''  '' k k    c  k (A-4)    Xk Gkc,a'cτ kc,a'c  ∑ X G X '   c ac,a'c   +∑∑ a  τ ac,a'c − k  Xk Gkc,a'c  c a'  ∑ X a''  ∑ X k Gkc,a'c  ∑ '' k   a  k where:

∑X G = ∑X

ca , B

a

5

GcB

a

∑X G = ∑X

ca , B

c

GaB

c

αBc = αcB

(A-6)

c'

c'

7

(A-5)

a'

a'

6

∑X G = ∑X

αBa = αaB

B,ca

a

a

(A-7)

a'

a'

8

Page 44 of 55

∑X G = ∑X c

B,ca

c

c'

(A-8)

c'

9

τ cB = −

ln GcB

10

τaB = −

ln GaB

11

τBa,ca =τaB −τca.B +τB,ca

(A-9)

αcB

(A-10)

αcB

(A-11) 44


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1

τBc,ac =τcB −τca.B +τB,ca

(A-12)

2

Each type of electrolyte NRTL parameter consists of both the

3

nonrandomness factor, α, and energy parameters, τ. The temperature dependency

4

relations of the electrolyte NRTL parameters are:

5

Molecule-Molecule Binary Parameters:

6

τij = Aij +

Bij

T

+ Fij ln (T ) + GijT

(A-13)

7 8

αij = Cij + Dij (T − 273.15K)

9

Electrolyte-Molecule Pair Parameters:

(A-14)

10

(T ref −T )  T τca,B = Cca,B + + Eca,B  + ln  ref T T  T

  

(A-15)

11

(T ref −T )  T τB,ca = CB,ca + + EB,ca  + ln  ref T T  T

  

(A-16)

12

Electrolyte-Electrolyte Pair Parameters:

13

For the electrolyte-electrolyte pair parameters, the two electrolytes must

Dca,B

DB,ca

14

share either one common cation or one common anion:

15

(T ref −T )  T τca' ,c''a = Cca' ,c''a + + Ec'a,c''a  + ln  ref T T  T

  

(A-17)

16

(T ref −T )  T = Cca' ,ca'' + + Eca' ,ca''  + ln  ref T T  T

  

(A-18)

Dc'a,c''a

17 18

τca ,ca '

''

Dca' ,ca''

where: T ref = 298.15 K

(A-19) 45



Page 46 of 55

1

Table A.1 Electrolyte-Molecule Pair parameters

2

Parameter name

Symbol

NO. of elements

Cca,B

1

CB,ca

1

Dca,B

1

Temperature

DB,ca

1

Temperature

GMELCC

GMELCD

3

Units

Table A.2 Molecule-Molecule Pair parameters Parameter name

Symbol

NRTL/1

Aij

NRTL/2

Bij

NRTL/3

Cij

Units

Temperature

4 5

Aij and Bij are unsymmetrical. That is, Aij may not be equal to Aji, etc. The binary

6

parameters Aij, Bij and Cij can be determined from VLE and/or LLE data regression.

7

Typically, recommended Cij values for different types of mixtures are 0.3, 0.2, or 0.47.

8

46


Page 47 of 55 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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