Thermodynamic analysis of three combined power and refrigeration ‎Systems based on a demand

Document Type: Original Article

Authors

1 K.N. Toosi University of Technology

2 K. N. Toosi University of Technology

Abstract

Three combined power and refrigeration system are introduced to compare and analyze for a defined demand and same fuel consumption based on thermodynamic parameters in a 24 hours period. Gas turbine and/or steam turbine are used for power generation and also ejector refrigeration cycle is used to produce cooling. These three systems are named as GER, SER and GSER. The results of three systems are compared and it’s shown that SER has so much lower cogeneration efficiency than two other systems. GSER produces 284 MWhr per year more power than GER with the same fuel consumption that can easily cover the additional capital cost of the system. Moreover, exergy efficiency of GSER is 12% higher than GER and its cogeneration efficiency is 8% higher than GER too. So, between these three systems we would recommend GSER because of better performance like higher exergy and energy efficiency and also better conformity with our demand

Keywords

Main Subjects


1. Introduction

Many researchers have been done on combined power and refrigeration cycle to improve energy efficiency and performance of systems. A combined cycle was proposed by Xu, Goswami and Bhagwat in 2000 (Xu, Goswami, & Bhagwat, 2000). Goswami worked on combined power and cooling system with some other researchers both theoretically and experimentally (Goswami, Vijayaraghavan, Lu, & Tamm, 2004; Hasan, Goswami, & Vijayaraghavan, 2002; Martin & Goswami, 2006; Sadrameli & Goswami, 2007; Tamm, Goswami, Lu, & Hasan, 2004; Vidal, Best, Rivero, & Cervantes, 2006; Vijayaraghavan & Goswami, 2006). A combined power and cooling cycle was introduced by Zheng et al. based on the Kalina cycle (Zheng, Chen, Qi, & Jin, 2006). They used a rectifier which could obtain a higher concentration ammonia-water vapor for refrigeration. Also, a condenser and an evaporator were used between the rectifier and the second absorber. Liu and Zhang presented an ammonia-water cycle for a cogeneration system (Liu & Zhang, 2007). They used a splitting/absorption unit into the cogeneration system. An ammonia–water system for the power and refrigeration system was presented by Zhang and Lior (N. Zhang & N. J. I. J. o. R. Lior, 2007). The plant operated in a parallel combined cycle mode with an ammonia–water Rankine cycle and an ammonia refrigeration cycle, interconnected by absorption, separation and heat transfer processes. Zhang and Lior also presented several novel combined refrigeration and power systems using ammonia–water as working fluid and summarized some guidelines for integration of refrigeration and power systems to produce higher energy and exergy efficiencies (N. Zhang & N. J. J. o. E. R. T. Lior, 2007). Wang et al. also proposed a combined refrigeration and power system which combined Rankine cycle and absorption refrigeration cycle (Wang, Dai, & Gao, 2008). Although much research has been carried out on the combined power and refrigeration cycle, most of them have combined the Rankine cycle or Kalina cycle with the absorption refrigeration cycle, and little attention has been paid to the combination of Rankine cycle and the ejector refrigeration cycle. Alexis in 2007 studied a combined power and refrigeration cycle with ejector refrigeration cycle (Alexis, 2007). This cycle used extraction steam from steam turbine in conventional Rankine cycle to heat the working fluid in an independent steam ejector refrigeration cycle.   The ejector refrigeration cycle which many studies have been devoted to, has many advantages such as less movable parts and low operating, installation and maintenance cost except for the relatively low performance (Li & Groll, 2005; Pianthong et al., 2007; Sankarlal & Mani, 2007; R. Yapıcı, Ersoy, & management, 2005; R. Yapıcı, Yetişen, & Management, 2007; R. J. E. C. Yapıcı & Management, 2008). In addition, the ejector refrigeration cycle has the possibility of using a wide range of refrigerants with the system. Wang et al. in 2009 presented a combined power and ejector refrigeration cycle which used steam extraction turbine between HRVG and ejector (Wang, Dai, & Sun, 2009). Ameri et al. in 2010 presented a tri-generation system based on a gas turbine and ejector refrigeration which power and refrigeration cycles were independent (Ameri, Behbahaninia, & Tanha, 2010). Many other studies are done about different cogeneration and tri-generation systems with different approaches to upgrade these system performances by using thermodynamic and economic analysis and also optimization methods (Ghorbani, Mafi, Amidpour, MOUSAVI, & Salehi, 2013; Ghorbani, Shirmohammadi, & Mehrpooya, 2018; Ghorbani, Shirmohammadi, Mehrpooya, & Mafi, 2018; Mohammadi, Ahmadi, et al., 2017; Mohammadi, Kasaeian, Pourfayaz, & Ahmadi, 2017; Niasar et al., 2017).

In the present study, time dependent analysis is done for three systems. Three combined power and refrigeration systems which use a micro-gas turbine, an extraction steam turbine and ejector refrigeration is presented. Also, R141 is used as working fluid in the cycle. These three cogeneration systems are analyzed for specified power and cooling demand and results are compared with each other to select the best one.

2. System Description

The schematic of GSER is shown in Fig. 1. Air at atmospheric pressure is compressed in compressor and it passes through the recuperator. The air temperature increases in this stage. The fuel, i.e. natural gas, is injected into the combustion chamber and ignition occurs. The hot flue gas passes through turbine blades and produces power. The flue gases pass through the recuperator and enter generator.

 

 

Figure 1. Schematic diagram of GSER

 

Figure 2. Schematic diagram of SER

 

Figure 3. Schematic diagram of GER

 


These hot gases increase the temperature of R141b as the working fluid of the next cycle. The extraction turbine and ejector play important roles in this combined cycle. The HRVG is a device in which high pressure and temperature vapor is generated by absorbing heat from flue gases of gas turbine. The high pressure and temperature vapor is expanded through the turbine to generate power. The extracted vapor from the turbine enters the ejector as the primary vapor. The very high velocity vapor at the exit of the nozzle produces a high vacuum at the inlet of the mixing chamber and entrains secondary vapor into the chamber from the evaporator. The stream out of the ejector mixed with turbine exhaust is cooled at the preheater and enters the condenser where it condenses from vapor to liquid by rejecting heat to the surroundings. Some of the working fluid leaving the condenser enters the evaporator after passing through the throttle valve, and the other part flows to the pump. The high pressure working fluid is heated at the preheater before entering heat recovery vapor generator to be vaporized again. The working fluid with low pressure and temperature from the valve is vaporized at the evaporator, providing a cooling effect for cooling user such as a cold-storage room. SER and GER are two other cogeneration systems that we want to compare them with GSER. These two systems are presented in Fig. 2 and Fig. 3. R141b is selected as the working fluid as a low-pressure, nontoxic, nonflammable and non-corrosive refrigerant.

Table 1 contains the main assumptions made for the simulation of the system. Moreover, there is a cooling demand that is presented for a typical day in Fig. 4.

3. Mathematical Model

In the present work, there are some assumptions for exergy calculation, ejector and the whole cycle performance simulation that are the same as J. Wang’s work in 2009 (Wang et al., 2009). A computer program has been developed to calculate all necessary parameters. The parameters for the gas turbine cycle are presented as it follows:

   
   
 

(3)

 

(4)

 

The energy balance at the mixing point of the ejector is presented as it follows:

 

(5)

At the mixing section of the ejector yields, mass conservation is written as follows:

 

(6)

The entrainment ratio is written as:

 

(7)

From the conservation law for energy, the basic equations in the components are presented for evaporator, turbine and pump.

 

(8)

 

(9)

 

(10)

The system performance is evaluated as equation (11) and (13). The thermal efficiency is presented as the useful energy output divided by the total energy input, given by:

 

(11)

Where Wnet is the turbine power output, Qe is the refrigeration output and Qin is the total heat input from the boiler.

 

Table 1. Main assumptions for the combined cycle

Environment temperature (˚C)

31

Environment pressure (MPa)

0.10135

Steam turbine inlet pressure (MPa)

1.251

Steam turbine inlet temperature (˚C)

130

Steam turbine extraction pressure (MPa)

0.283

Isentropic efficiency of steam turbine (%)

85

Combustion chamber efficiency (%)

100

Pinch point temperature difference (˚C)

40

Approach point temperature difference (˚C)

5

Isentropic efficiency of gas turbine (%)

85

Isentropic efficiency of compressor (%)

85

Pressure ratio of compressor

10

Generator efficiency (%)

98

Condenser temperature (˚C)

36

Evaporator temperature (˚C)

8

 

 

 

 

 

 

 

 

 

 

 

Figure 4. Hourly cooling demand variations in a day

 

Figure 5. Effect of motive fluid temperature on entrainment ratio

 


 

The physical exergy can be calculated as:

 

(12)

Exergy efficiency is defined as the summation of exergy of the network and the refrigeration divided by the exergy of the heat source.

 

(13)

 

Ein is the exergy of the heat source fluid.

 

(14)

Since the heat source fluid is finally exhausted into the environment, the calculation of the exergy input is based on the difference between its initial state and the environment state. Ee is the exergy associated with the refrigeration output, which is calculated as the

 

 

working fluid exergy difference across the evaporator.

 

(15)

4. Results and Discussion

The simulation of the combined GSER, GER and SER is carried out using a simulation program written in Matlab by present authors. Moreover, thermodynamics properties of R141b were calculated by using EES database.

The thermodynamic analysis of GSER is done and the results are brought in comparison with SER and GER with the same fuel consumption based on the assumptions.

Table 2 shows the thermodynamic properties of the cycle states for GSER. The results of thermodynamic analysis of GER and SER for their states are shown in table 3 and 4. In Table 5 the analysis results of three systems are brought together.

 

 

 

Figure 6. Hourly fuel consumption variations of the systems

 

Figure 7. Hourly extraction ratio variations of the systems

 


Fig. 5 shows the effect of generator temperature on the entrainment ratio. It’s clear that entrainment ratio increases with generator temperature until 90˚C. For the generator temperature more than it, entrainment ratio doesn’t increase anymore. So 90˚C is the optimum temperature for steam turbine extraction. Fig. 6 shows the fuel consumption of three systems. It’s constant for GER, but the others are time dependent. The minimum fuel consumption for GER and GSER is at noon when the cooling demand is high. The three systems have the same average of fuel consumption.

Fig. 7 shows the extraction ratio of GSER and SER. The extraction ratio is calculated based on our time dependent demand. As shown in the figure, the maximum extraction is at noon, because of the maximum cooling demand. GSER has higher extraction ratio, because its steam turbine size is smaller and in order to achieve the cooling demand, more extraction ratio is needed. 

Fig. 8 shows the produced cooling by GSER and the two other systems in comparison. SER produced the same cooling as GSER that is equal to the demand. But the produced cooling by GER is constant and produces the maximum of demand. So, there is useless produced cooling at the most hours of the day.

Fig. 9 shows the produced power by GSER and the two other systems in comparison. As it’s clear in the figure, the maximum produced power is for GSER and the minimum is for SER that is less than our demand. We should consider that SER is just recommended for using low temperature heat sources, because of low boiling temperature of the working fluid. So, Sources like geothermal and solar energy and also low temperature waste heat, can produce power in this cycle.

Fig. 10 shows the cogeneration efficiency of the GSER and two other systems in comparison. GSER and GER cogeneration efficiency is more than SER.

 

 

 

 

Figure 8. Hourly produced cooling variations of the systems

 

Figure 9. Hourly produced power variations of the systems

 


 

Figure 10. Hourly cogeneration efficiency variations of the systems

 

 

Figure 11. Hourly exergy efficiency variations of the systems

 

Table 2. Thermodynamic properties of GER states

 

State

s (kJ kg-1 K-1)

h (kJ kg-1)

P (kPa)

T (˚C)

Ė̇ (kW)

g1

5.715

304.6

101.35

31

0.000

g2

5.808

644.7

1014

362.5

279.5

g3

6.225

958.3

978.8

649.4

446.9

g4

6.791

1603

912.1

1200

886.1

g5

6.904

1014

112.6

698.4

317.3

g6

6.544

705.5

107.6

419.6

135.7

g7

6.072

437

103.4

162.1

21.73

1

1.02

338.1

538.5

90

38.91

2

1.083

324.7

116.1

64.15

7.009

3

1.026

305.9

116.1

41

5.016

4

0.2962

80.31

116.1

36

0.08274

5

0.2962

80.31

116.1

36

0.02006

6

0.2962

78.75

39.93

8

-0.4951

7

1.021

282.6

39.93

8

-5.976

8

0.2962

80.31

116.1

36

0.06268

9

0.2962

80.7

538.5

36

0.4652

10

0.3748

105.5

538.5

56.78

1.388


 

The maximum efficiency is for GSER and the other two systems work with lower cogeneration efficiency.

Fig. 11 shows the exergy efficiency of GSER and two other systems. GSER has less efficiency than SER but more than GER. The maximum exergy efficiency is at 2:00 a.m. that cooling demand is minimized. It's because the exergy efficiency of cooling cycle is low.

5. Conclusion

Three cogeneration systems are introduced to cover our power and cooling demand and also analyzed to select the best one. The results

show that GSER is the best choice for our demand. Because GER produces enough power and cooling with the same fuel consumption based on our demand and it has lower capital cost, this system is a good choice too. But production of 284 MWhr per year more power than GER can easily cover the higher capital cost and can produce income after the additional capital cost payback date. SER has much lower efficiency, but because of working in low temperature, it’s a good choice for low temperature heat sources, such as low temperature waste heat. Moreover, exergy and cogeneration performances of GSER are more than GER. These reasons can approve the great performance of GSER for our demand.

 

Table 3. Thermodynamic properties of GSER states

 

State

s (kJ kg-1 K-1)

h (kJ kg-1)

P (kPa)

T (˚C)

Ė̇ (kW)

g1

5.715

304.6

101.4

31.0

0

g2

5.808

644.7

1014

362.5

276.5

g3

6.225

958.3

978.8

649.4

442.2

g4

6.791

1603.0

912.1

1200

876.7

g5

6.904

1014.0

112.6

698.4

314.0

g6

6.544

705.5

107.6

419.6

134.3

g7

5.852

349.9

102

76.0

3.278

s1

1.033

362.0

1251

130

70.05

s2

1.076

343.4

283.1

90

17.99

s3

1.061

317.3

116.1

55.1

2.318

s4

1.095

328.7

116.1

69.0

5.024

s5

1.083

324.5

116.1

64.0

7.105

s6

1.026

305.9

116.1

41.0

5.290

s7

0.296

80.3

116.1

36.0

0.08725

s8

0.296

80.3

116.1

36.0

0.01346

s9

0.302

80.3

39.9

8.0

-0.3573

s10

1.021

282.6

39.9

8.0

-4.011

s11

0.296

80.3

116.1

36.0

0.07379

s12

0.296

80.7

1251

36.0

0.5476

s13

0.367

102.8

1251

54.6

1.420

s14

1.020

356.6

1251

130.

68.29

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4. Thermodynamic properties of SER states

 

State

s (kJ kg-1 K-1)

h (kJ kg-1)

P (kPa)

T (˚C)

Ė̇ (kW)

1

1.033

362.0

1251.00

130.0

131.9

2

1.076

343.4

283.10

90.0

18.06

3

1.061

317.3

116.10

55.1

7.066

4

1.095

328.7

116.10

69.0

5.045

5

1.074

321.5

116.10

60.2

11.76

6

1.026

305.9

116.10

41.0

9.244

7

0.296

80.3

116.10

36.0

0.1520

8

0.296

80.3

116.10

36.0

0.01400

9

0.302

80.3

39.93

8.0

-0.3590

10

1.021

282.6

39.93

8.0

-4.027

11

0.296

80.3

116.10

36.0

0.1390

12

0.296

80.7

1251.00

36.0

1.031

13

0.351

97.8

1251.00

50.5

1.789

14

1.025

358.7

1251.00

130.0

129.9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5. Results of simulation for three cycles

 

6:00

12:00

18:00

24:00

Time

42

67

57

26

Cooling demand (kW)      

0.53

0.86

0.72

0.33

GSER

 

Extraction Ratio

0.28

0.45

0.38

0.18

SER

X

X

X

X

GER

42.00

67.33

57.00

26.00

GSER

 

 

Produced cooling (kW)

42.00

67.33

57.00

26.00

SER

67.33

67.33

67.33

67.33

GER

255.8

245.6

249.7

262.2

GSER

 

Power (kW)

85.3

75.1

79.3

91.8

SER

221.2

221.2

221.2

221.2

GER

605

598

601

610

GSER

 

Fuel Consumption (kW)

605

598

601

610

SER

604

604

604

604

GER

0.49

0.52

0.51

0.47

GSER

 

Cogeneration Efficiency

0.21

0.24

0.23

0.19

SER

0.48

0.48

0.48

0.48

GER

0.48

0.46

0.47

0.49

GSER

 

Exergy Efficiency

0.68

0.62

0.65

0.72

SER

0.41

0.41

0.41

0.41

GER

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Nomenclature

C                      Velocity (m s-1)

E                      Exergy (kW)

h                      Enthalpy (kJ kg-1)

LHV                 Low Heating Value (kJ kg-1)

m                     Mass Rate (kg s-1)

Q                      Heat Transfer Rate (kW)

s                       Entropy (kJ kg-1 K-1)

T                      Temperature (K)

W                     Power (kW)

Greek letters

η                      Efficiency

ω                      Entrainment Ratio

Subscripts

CC                    Combustion Chamber

d                      Diffuser

e                       Evaporator

ex                     Exergy

g                      Heat Recovery Steam

Generator

gt                     Gas Turbine

m                     Mixture

n                      Nozzle

p                      Pump

s                       Isentropic

st                     Steam Turbine

th                     Thermal

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