Research methodology

Research methodology

Research methodology to find out the optimal performance of the ORC system combined with the absorption refrigeration is presented the each step relation in Figure 10.

Figure 10 Schematics diagram of the research process.

Start

Review paper of the ORC system Review paper of the absorption refrigeration

The mathematical modeling of the absorption refrigeration The mathematical modeling of the ORC

system

Comparison results the simulation and

experiment of the ORC system Comparison results of the simulation and experiment of the absorption

refrigeration

Comparison results of the energy and exergy efficiencies in stages of the each model

Economic analysis of the energy and exergy costings in the terms of LEC and LExC values

Comparison results of the economics Conclusions

Thesis examination

The integrated models of the ORC system combined with the absorption refrigeration

Energy efficiency analysis of the ORC system combined with the absorption

refrigeration

Exergy efficiency analysis of the ORC system combined with the absorption

refrigeration

Study the theory of the ORC system and the absorption refrigeration Study the theory of the ORC system and the absorption refrigeration are reviewed to the main advantaged points of the various refrigerant types used in the absorption refrigeration system.

Mathematical modeling of the ORC system

Mathematical modeling of the ORC system is used to analyze the ORC performance. In this research, the ORC mathematical model is analyzed and created.

The properties of working fluid according from the Refprop program are used. The energy and exergy simulation steps of the ORC system are shown in Figure 11 and Figure 12, respectively. And the initial conditions of the system are:

 The working fluid of the ORC system is R-245fa,

 Hot water temperature entering to the boiler of the ORC system (THW,i) is 80- 120 ^oC,

 Hot water temperature different and working fluid in boiler (∆THW-ref) is 3 ^oC,

 Water temperature different inlet and outlet of boiler (∆THW) is 15 ^oC,

 The cooling water temperature entering to the condenser is constants (TCW,i) 32

oC,

 Cooling water difference inlet and outlet in condenser (∆TCW) is 5 ^oC,

 Cooling temperature different and working fluid of condenser (∆TCW-ref) is 3 ^oC,

 Temperature of ambient is considered to be (TAbm) 28 ^oC,

 Isentropic efficiency of expander (^ɳS,Exp) is 85 %,

 Isentropic efficiency of pump (ɳ_S,P) is 85 %,

 Efficiency of generator(^ɳG) is 85 %,

 Superheating (SH) is 10 ^oC,

 Sub cooling (SC) is 5 ^oC.

21

Figure 11 Energy diagram mathematical modeling of the ORC system.

Start T_HW,i,T_CW,i

Condenser T1 = Tc – SC

h1 = f(T1) n = f(T1) S1 = f(T1)

Temperature TB = THW,i – ∆THW – ∆THW-ref

TC = TCW,i + ∆TCW + ∆TCW-ref

Pressure PH = f(TB) PL = f(TC)

Boiler T3 = f(TB + SH)

h2' = f(TB) h3' = f(TB) h3 = f(TH,TB + SH)

S3 = f(PH,TB) Refrigerant

S_2s = S₁ h_2s = f(P_H,S_2s) h₂ = f(h_2s – h₁) / h_SP

T₂ = f(P_H,h₂)

Mass

ṁref = ṁ1= ṁ2= ṁ3= ṁ4

ṁref = QB / (h3–h2s)

Heat pump

₂ = f(T₂) H = f(P_H / g) / 1000

Expander S_4s = S₃ T₄ = f(P_L,T_B + SH)

h_4s = f(P_L,T_B) h₄ = h₃ – h_Exp (h₃ – h_4s)

S₄ = f(P_L,h₄) Vapor quality

Sf,c = f(Tc) S_g,c = f(T_c) Sfg = Sg,c – Sf,c

qv₄ = (S₄ – S_f,c) / S_fg Energy balance

QB = ^ṁref (h3 – h2) QC = ^ṁref (h4 – h1) W_P = (P_H – P_L) ^ṁ_ref ν₁ / h_sp

W_Exp = ^ṁ_ref (h₃ – h₄)

Energy efficiency of the ORC system h_ORC = ((W_Exp– W_P) / Q_B) × 100

End

Refrigerant, ∆T_HW-ref, T_CW-ref, T_0, SH, SC, h_SP,h_Exp

Figure 12 Exergy diagram mathematical modeling of the ORC system.

Start T_HW,i,T_CW,i

Condenser T₁ = Tc – SC

h₁ = f(T₁) n = f(T₁) S1 = f(T1)

Temperature T_B = T_HW,i – ∆T_HW – ∆T_HW-ref

T_C = T_CW,i + ∆T_CW + ∆T_CW-ref Pressure

P_H = f(T_B) PL = f(TC)

Boiler T₃ = f(T_B + SH)

h_2' = f(T_B) h3' = f(TB) h3 = f(TH,TB + SH)

S3 = f(PH,TB) Refrigerant

S_2s = S₁ h_2s = f(P_H,S_2s) h₂ = f(h_2s – h₁) / h_SP

T₂ = f(P_H,h₂)

Mass

ṁref = ṁ1= ṁ2= ṁ3= ṁ4

ṁ_ref = QB / (h3–h2s)

Heat pump

₂ = f(T₂) H = f(PH / g) / 1000

Expander S_4s = S₃ T₄ = f(P_L,T_B + SH)

h_4s = f(P_L,T_B) h4 = h3 – hExp (h3 – h4s)

S4 = f(PL,h4) Vapor quality

S_f,c = f(T_c) Sg,c = f(Tc) Sfg = Sg,c – Sf,c

qv4 = (S4 – Sf,c) / Sfg

Exergy balance

ĖB = ṁ_ref (h₃ – h₂ – T₀ [S₃ – S₂])

ĖC = ṁ_ref (h4 – h1 – T0 [S4 – S1])

ĖP = ṁ_ref (h2 – h1 – T0 [S2 – S1])

ĖExp = ṁref (h3 – h4 – T0 [S3 – S4])

Ė_B = QB (1– [T0 / THW,i])

Exergy efficiency of the ORC system

ψ_EX-ORC = ((^Ė_Exp– ^Ė_P) / ^Ė_B) × 100 End

Refrigerant, ∆THW-ref, TCW-ref, T0, SH, SC, h_SP,h_Exp

23 Comparison results of the simulation and experiment of the ORC

Comparison results of the simulation and experiment are analyzed the suitable enhancement model of the ORC system. Which the research experiment analyzed of the ORC system, size 20 kWe using the working fluid was R-245fa (Chaiyat and Kiatsiriroat, 2015). Thus, it was similar to the mathematical model of simulations. Which the experiments results of the ORC system was shown in Table 1 below:

Table 1 Testing results of the R-245fa ORC system at varying inlet hot water temperature (Chaiyat and Kiatsiriroat, 2015).

Description Uni

t

State 1 State 2 State 3 State 4 Hot water inlet (THW,i) °C 116.00 107.80 97.00 88.90

Hot water outlet (THW,o) °C 89.80 81.00 75.00 77.80

Heat source capacity (QB) kW 243.20 248.20 203.40 188.30 Cool water inlet (TCW,i) °C 28.00 28.00 28.00 28.00 Cool water outlet (TCW,o) °C 35.00 35.00 35.00 35.00 Condenser temperature (T_C) °C 37.00 37.00 37.00 37.00 Heat sink capacity (QC) kW 219.00 215.60 210.90 211.00 Expander inlet pressure (PHigh) kPa 1097.10 1120.00 1074.00 811.30 Expander inlet temperature (T1) °C 93.70 94.60 92.80 85.70 Expander outlet pressure (PLow) kPa 227.41 227.40 227.00 239.30 Expander outlet temperature (T2) °C 75.00 70.60 70.60 59.50

Refrigerant pump power (WP) kW 1.78 1.90 1.19 1.24

Oil pump power (WOP) kW 1.40 1.40 1.40 1.40

Lift temperature (THW,i - TCW,i) °C 88.00 79.80 69.00 58.80

Cycle power (WORC) kW 21.50 21.36 16.70 9.00

Cycle efficiency (h_ORC) % 8.73 8.49 8.11 4.71

Mathematical modeling of the absorption refrigeration

Mathematical modeling of the absorption refrigeration is developed. The energy and exergy steps for simulation are shown in Figure 13 and Figure 14, respectively. Moreover, the working pairs of the water-lithium bromide solution (H2O- LiBr) and the ammonia-water solution (NH3-H2O) also programed and developed.

 The working fluid of absorption refrigeration are H2O-LiBr solution and NH3-H2O solution,

 Maximum flow ratio (FR) for starting is lower that 20 (Chaiyat and Kiatsiriroat, 2011),

 Water temperature different of generator of working flow is 3 ^oC,

 The water temperature different of working fluid at condenser is 3 ^oC,

 The water temperature different of working fluid at adsorbate is 3 ^oC,

 The water temperatures outlet of absorbate are equally the water temperature inlet of condenser, the water temperature different inlet and outlet of condenser, absorbate, evaporator and generator is 5 ^oC,

 Temperature of ambient is considered to be 28 ^oC,

 Isentropic efficiency of pump is 85% and

The properties of the thermodynamic H2O-LiBr solution are not the program to calculate, that this research develop the program to useful the mathematical modeling of the absorption refrigeration. Which the equation of the mathematical is referent of the experiment of the research various as shown in Table 2 below:

Table 2 Properties of the thermodynamic H2O-LiBr solution.

Variable Equation Source

Enthalpy ^{4 n}

0 n

2 4 n

0 n

4 n

0 AnX T B X T C X

h^



^



^



ASHRAE (2009)

Solution temperature ^{3 n}

0 n

ref 3 n

0 BnX T A X

T ^



^



ASHRAE (2009)

25

Variable Equation Source

Refrigerant

temperature ^ref D (D2 4E[C log(P)])^0.5 T 2E







 



 







 





 ₂

ref

ref T

E T

C D log(P)

ASHRAE (2009)

Density

] (T)m d

(T)m d (T)m d (T)[1 m)

(T,

2 2

1.5 1 0

0







ρ ρ

[X/100]) M (1

(X/100) m

S









 ⁴

0 i

i ji

j(T) C T

d

Khairulin et al., (2006)

Isobaric specific heat C_P A₀ A₁X(B₀ B₁X) Kaita (2001)

Entropy



 

 ³

0 i

3

0 j

i j ijxT b

s Feuerecker

(1993)

Figure 13 Energy diagram mathematical modeling of the absorption refrigeration.

Heat exchanger C_P8 = f(X_8, T₈)

T₆ = T₅ CP6 = f(X6, T6) Q_max = (ṁ C_P)_min (T₈ – T₆)

Qact = Qmax εHX

T9 = T8 – [Qmax / (ṁ CP)8] T₇ = T₆ – [Q_max / (ṁ C_P)₆]

h9 = f(X9 + T9) h₇ = f(X₇ + T₇) Start

Condenser T₂ = T_C – SC

h2 = f(T2,PH) h₃ = h₂ Tmin = f(X,Tc)

Temperature T_A = T_CW,I + ∆T_CW TC = TCW,I + ∆TCW + ∆TCW-ref

T_E = T_CW,E,i – ∆T_CW,E – ∆T_CW-ref TG = T4 – ∆TR-245fa – ∆TR-245fa-ref

Pressure PH = f(TC) PL = f(TE)

Generator T₁ = T_G T8 = TG

H₁ = f(T_1,P_H) X8 = X9 = X10

h8 = f(X8,T8) Evaporator

T4 = TE + SH h4 = f(T4) X4 = X1 = X2 = X3

Absorber T₅ = T_A X₅ = X₆ = X₇ h5 = f(X5 + T5) Mass balance

ṁ₄ = QE / (h4 – h3)

ṁ₄ = ṁ₁ = ṁ₂ = ṁ₃ ṁ₄ = ṁ₄ (X₁ – X₇) / (X₇ – X₈)

ṁ₈ = ṁ₉ = ṁ₁₀ ṁ₇ = ṁ₁ + ṁ₈

ṁ₇ = ṁ₆= ṁ₅

Solution pump

∆P = (PH – PL)

₂= f( X5, ∆P) n₅ = 1 / ₂

Coefficient of performance COP_AB = [Q_E / (Q_G + W_P)]

End Heating capacity

QG = ^ṁ1 h1 + ^ṁ8 h7 – ^ṁ7 h7

Q_C = ṁ₁ h₁ – ṁ₂ h₂ QE = ṁ₄ h4 – ṁ₃ h3

Q_A = ṁ₄ h₄ + ṁ₁₀ h₁₀ – ṁ₅ h₅

ṁ₇ = ṁ₁ + ṁ₈

WP = ^ṁ4ν₅ (PH – PL) / ^ɳS,P

TR-245fa, TCW,i, εHX

H₂O-Libr, NH₃-H₂O, SH,SC, ^ɳ_S,P

27

Figure 14 Exergy diagram mathematical modeling of the absorption refrigeration.

Heat exchanger CP8 = f(X8, T8)

T6 = T5

CP6 = f(X6, T6) Qmax = (ṁ CP)min (T8 – T6)

Qact = Qmax εHX

T9 = T8 – [Qmax / (ṁ CP)8] T7 = T6 – [Qmax / (^ṁ CP)6]

h9 = f(X9 + T9) h7 = f(X7 + T7) Start

Condenser T2 = TC – SC

h2 = f(T2,PH) h3 = h2

Tmin = f(X,Tc)

Temperature TA = TCW,I + ∆TCW

TC = TCW,I + ∆TCW + ∆TCW-ref

TE = TCW,E,i – ∆TCW,E – ∆TCW-ref

TG = T4 – ∆TR-245fa – ∆TR-245fa-ref

Pressure PH = f(TC) PL = f(TE)

Generator T1 = TG

T8 = TG

H1 = f(T1,PH) X8 = X9 = X10

h8 = f(X8,T8) Evaporator

T4 = TE + SH h4 = f(T4) X4 = X1 = X2 = X3

Absorber T5 = TA

X5 = X6 = X7

h5 = f(X5 + T5) Mass balance

ṁ₄ = QE / (h4 – h3)

ṁ4 = ṁ1 = ṁ2 = ṁ3 ṁ₄ = ṁ₄ (X1 – X7) / (X7 – X8)

ṁ8 = ṁ9 = ṁ10 ṁ₇ = ṁ₁ + ṁ₈

ṁ₇ = ^ṁ6= ^ṁ5

Solution pump

∆P = (PH – PL)

2= f( X5, ∆P) n₅ = 1 / ₂ TR-245fa, TCW,i, εHX

H2O-Libr, NH3-H2O, SH,SC, ^ɳS,P

End Exergy balance

ĖG = ṁ7 (h7 – T0 S7) – ṁ8 (h8 – T0 S8) – ṁ1 (h1 – T0 S1) + QG (1–[T0/TG])

Ė_C = ṁ_ref (h1– h2) – T0 (S1 – S2)

Ė_E = ṁ_ref (h4– h3) – T0 (S4 – S3) + QE (1–[T0/TE])

Ė_A = ^ṁref (h4 – T0 S4) + ^ṁ10 (h10 – T0 S10) – ^ṁ5 (h5 – T0 S5)

ĖS,P = ṁref (h6 – h5) – T0 (S6 – S5)

Ė_HX = ṁ_ref (h6 – h7) – T0 (S6 – S7) + ṁ_ref (h8 – h9) – T0 (S8 –S9) Exergy coefficient of performance

COPEX-AB = [ĖE / (ĖG + ĖSP)]

Comparison results of the simulation and experiment of the absorption refrigeration

Comparison the simulation and experiment are assessed the suitable enhancement model of the absorption refrigeration system.

The integrated models of the ORC system and the absorption refrigeration The integrated models of the ORC system and the absorption refrigeration are designed, which the combined units have been presented 3 models, as shown in Figures 15-17. The first model presents the absorption system as the ORC condenser, the second model represents technique for reducing working fluid temperature leaving the ORC expander and the third model shows the absorption system combined with the cooling tower to reducing temperature working fluid at the ORC condenser.

29

Figure 15 Schematic of the ORC combined with absorption refrigeration 1.

From the above cycle, the combined energy and exergy efficiencies could be defined by equations below:

h_Overall = (WExp + QE / [QB + WP + WSP]) equation 57

_Overall = (^ĖExp+^ĖE / [^ĖB+ ^ĖP + ^ĖSP]) equation 58 1

4 Refrigerant

pump (WP)

Expander (WExp)

Alternator

Grid line Boiler (QB,TB)

3

2 THW,i

THW,o

(WExp,e)

Generator

(QG,TG) Condenser

(QC,TC)

Evaporator (QE,TE) Absorber

(QA,TA)

PRV

Heat exchanger

Solution pump (WSP)

TXV 1

3

4 8

9 10

7 6 5

TCW,E,i

TCW,E,o

TCW,C,i

TCW,C,o

TCW,A,i

TCW,A,o

3' 2'

2

Figure 16 Schematic of the ORC combined with absorption refrigeration 2.

From the above cycle, the combined energy and exergy efficiencies could be defined by equations below:

h _Overall = (WExp + QE / [QB + WP + WSP]) equation 59

 Overall = (^ĖExp+^ĖE / [^ĖB + ^ĖP + ^ĖSP]) equation 60

1

4 Refrigerant

pump (W_P)

Expander (W_Exp)

Alternator Grid line Boiler (Q_B,T_B)

Condenser (QC,TC)

3

2 T_HW,i T_HW,o

(W_Exp,e)

TCW,i T_CW,o

Generator

(QG,TG) Condenser

(QC,TC)

Evaporator (Q_E,T_E) Absorber

(Q_A,T_A)

PRV

Heat exchanger

Solution pump (W_SP)

TXV 1

3

4 8

9 10

7 6

5

T_CW,E,i TCW,E,o

T_CW,C,i

TCW,C,o

T_CW,A,i T_CW,A,o 2' 3'

2 5

31

Figure 17 Schematic of the ORC combined with absorption refrigeration 3.

From the above cycle, the combined energy and exergy efficiencies could be defined by equations below:

h_Overall = (WExp / [QB + WP + WSP]) equation 61

Overall = (^ĖExp / [^ĖB + ^ĖP + ^ĖSP]) equation 62

1

4 Refrigerant

pump (WP)

Expander (W_Exp)

Alternator

Grid line Boiler (QB,TB)

Condenser (QC,TC)

3

2 THW,i

THW,o

(WExp,e)

TCW,i TCW,o

Generator

(QG,TG) Condenser

(QC,TC)

Evaporator (QE,TE) Absorber

(QA,TA)

PRV

Heat exchanger

Solution

pump (WSP)

TXV 1

3

4 8

9 10

7 6 5

TCW,E,i

TCW,E,o

TCW,C,i TCW,C,o

TCW,A,i

TCW,A,o

2' 3'

2 5

Energy and exergy efficiency analyzes of the ORC system combined with the absorption refrigeration

Energy and exergy efficiencies of the ORC system combined with the absorption refrigeration are determined the energy efficiency and exergy efficiency of the each models.

Comparison results of the energy and exergy efficiencies

Comparison results of the energy and exergy efficiencies are analyzed the suitable enhancement models of the ORC combined with the absorption refrigeration.

Economic analysis of the ORC combined with the absorption refrigeration Economic analyses, energy electricity cost, exergy electricity cost, energy and exergy costings are to carry out the ORC-absorption power output.

Comparison results of the economic results of the energy and exergy costings Comparison of the energy and exergy costings are assessed of the electricity per unit price of the ORC system combined with the absorption refrigeration.

Chapter 4