Thermodynamic Analysis and Optimization of Multi-Generation System

This project focuses on the thermodynamic analysis and optimization of a multi-generation system designed to produce domestic heating, cooling, electricity, and desalinated water. A parabolic solar collector, using molten salt as the working fluid, drives a Rankine cycle to generate electricity, which in turn powers a reverse osmosis desalination unit. A water-ammonia absorption chiller provides cooling. The analysis, conducted using Engineering Equation Solver (EES) software, includes energy and exergy assessments, along with a parametric sensitivity analysis of factors such as ambient temperature, solar radiation, and mass flow rates. The optimization goals are to maximize the energy and exergy efficiency of the system and its components. The project includes the EES code, equations, and input parameters used in the analysis.

Equations
C pref = 0.5195
m ref = 1
T 1 = T 2
P 1 = P 2
m 3 = m 7 + m 4
m 3 · X 3 = m 7 · X 7 · m 4 · X 4
Q gen = m 7 · h 7 + m 4 · h 4 – m 3 · h 3
m 3 = m 7 · 1 – X 4
X 3 – X 4
m 4 = m 7 · 1 – X 3
X 3 – X 4
CR = m 3
m 7
E ex = 0.7
T 5 = E ex – T 2 + ( 1 – E ex ) · T 4
h 3 = h 2 + m 4
m 2
· ( h 8 – h 2 )
Q abs = m 10 · h 10 + m 6 · h 6 – m 1 · h 1
Q cond = m 7 · ( h 7 – h 8 )
Q eav p = m 7 · ( h 10 – h 9 )
Q eav p = m water · C pwater · ( T 11 – T 12 )
Q gen = m s · C pmsalt · ( T 18 – T 19 )
Q abs = m water · C pwater · ( T 16 – T 15 )

Q cond = m water · C pwater · ( T 14 – T 13 )
T 19 = T 20
h 19 = h ( 'Steam ' , T = T 19 , P = P 19 )
s 19 = s ( 'Steam ' , T = T 19 , P = P 19 )
h 20 = h ( 'Steam ' , T = T 20 , P = P 20 )
s 20 = s ( 'Steam ' , T = T 20 , P = P 20 )
COP = Q eav p
Q gen
COP = T 10
T 12 – T 10
· T 19 – T 12
T 19
h 15 = h ( 'Steam ' , T = T 15 , P = P 15 )
s 15 = s ( 'Steam ' , T = T 15 , P = P 15 )
h 16 = h ( 'Steam ' , T = T 16 , P = P 16 )
s 16 = s ( 'Steam ' , T = T 16 , P = P 16 )
effs = 0.8
Aa = 1
G b = 158.5
T 20 = 50
m s = 1
C pmsalt = 10
Q s = A a · G b
Q u = effs · Q s
Q u = m s · C pmsalt · ( T 21 – T 18 )

T 17 = T 21
P 17 = P 21
s 17 = s ( 'CaCl2' , T = T 17 , P = P 17 )
Qu = Qb
m water = 1
C pwater = 999.7
Q b = m water · C pwater · ( T 22 – T 23 )
P 17 = T 17 · P 18
T 18
P 22 = 600
T 22abs = T 22 + 459.6
T 23 = 80
T 24 = T 23 – 5 [f]
T 24abs = T 24 + 459.6
efft = 0.9
effp = 0.8
P 24 = P 23
P 25 = P 22
Wdotcycle SI = 1000
Wdotcycle Eng = Wdotcycle SI · 3413 [(Btu/hr)/kW]
h 22 = h ( 'Steam ' , T = T 22 , P = P 22 )
s 22 = s ( 'Steam ' , T = T 22 , P = P 22 )

s 23 = s 22
h 23 = h 22 – efft · ( h 22 – h 23s )
h 23s = h ( 'Steam ' , T = T 23 , s = s 22 )
x 23 = x ( 'Steam ' , T = T 23 , h = h 23 )
P 23 = P ( 'Steam ' , T = T 23 , x = x 23 )
h 24 = h ( 'Steam ' , T = T 24 , x = 0 )
h 24s = h ( 'Steam ' , T = T 24 , P = P 24 )
s 24 = s ( 'Steam ' , T = T 24 , h = h 24 )
s 25 = s 24
h 25s = h ( 'Steam ' , P = P22 , s = s 24 )
q c = h 23 – h 24
h 25 = h 24 + h 25s – h 24
effp
w net = h 22 – h 23 – ( h 25 – h 24 )
Q b = h 22 – h 25
h th = w net
Q b
h max = 1 – T 24abs
T 22abs
Wdotcycle max,Eng = Q b · m · h max
Wdotcycle max,SI = Wdotcycle max,Eng
3413 [(Btu/hr)/kW]
T 26 = 25
T 26 = T 27

T 27 = T 28
i = 1.8
M = 0.599
R nacl = 0.08206
T inK = T 26 – 32
1.8 + 273.15
P 28,atm = i · M · R nacl · TinK
P 28 = P 28,atm · 14.7
P 26 = 14.6959
P 27 = P 26
Q pump = 100
m 27 = 63.9 · Q pump
m 28 = m 27 · 0.965

EES codes
{Absorbtion Refridgeration}
C_pref = 0.5194898251637
m_ref = 1
T_1= T_2 { In the pumping process no heat is added}
P_1 = P_2 { In the pump no pressure was devleoped.}
m_3 = m_7 + m_4
m_3* X_3 = ((m_7*X_7)* (m_4*X_4))
Q_gen = ((m_7 * h_7) + (m_4 * h_4) - (m_3 *h_3))
m_3 = (m_7*((1-X_4)/(X_3-X_4)))
m_4 = (m_7*((1-X_3)/(X_3-X_4)))
CR = ( m_3/m_7)
E_ex = 0.7
T_5 = (E_ex-T_2 +((1-E_ex)*T_4))
h_3= (h_2 +((m_4/m_2) * (h_8-h_2)))
Q_abs = ((m_10 * h_10)+(m_6*h_6)-(m_1*h_1))
Q_cond = m_7 * (h_7-h_8)
Q_eavp = m_7* (h_10-h_9)
Q_eavp = m_water * C_pwater *(T_11- T_12)
Q_gen = m_s * C_pmsalt *(T_18- T_19)
Q_abs = m_water * C_pwater * (T_16-T_15)
Q_cond =m_water * C_pwater * (T_14-T_13)
T_19 = T_20
h[19]=Enthalpy(Steam,T=T[19],P=P[19])
s[19]=Entropy(Steam,T=T[19],P=P[19])
h[20]=Enthalpy(Steam,T=T[20],P=P[20])
s[20]=Entropy(Steam,T=T[20],P=P[20])
COP = Q_eavp / Q_gen
COP = ((T_10) / (T_12- T_10)) * ((T_19 -T_12)/(T_19))
h[15]=Enthalpy(Steam,T=T[15],P=P[15])
s[15]=Entropy(Steam,T=T[15],P=P[15])
h[16]=Enthalpy(Steam,T=T[16],P=P[16])
s[16]=Entropy(Steam,T=T[16],P=P[16])

{Solar collector}
effs=0.8 { Efficency of the solar collector}
A_a = 1 { Area of Aperture}
G_b = 158.499165314 {Solar beam Radiation}
T_20 = 50
m_s= 1 {Mass flow rate of molten salt}
C_pmsalt = 10 { Specific Heat capacity of fluid}
Q_s = A_a * G_b
Q_u = effs * Q_s
Q_u = (m_s * C_pmsalt ) * (T_21 - T_18)
T_17 = T_21
P_17 = P_21
s[17] = Entropy (CaCl2,T=T[17],P=P[17])
{Boiler} { Assume that the heat collected by the solar collector was directly feed to the
boiler input. There is no losses during the transmission}
Q_u = Q_b
m_water = 1
C_pwater = 999.6895003323
Q_b = m_water * C_pwater * ( T_22 - T_23)
P_17 = (T_17 * P_18)/ ( T_18)
{Rankine Cycle}
P_22 = 600
T_22abs = T_22 + 459.6
T_23 = 80
T_24 = T_23 - 5 [f]
T_24abs = T_24 +459.6
efft = 0.9
effp = 0.8
P_24 = P_23
P_25 = P_22
Wdotcycle_SI= 1000

Wdotcycle_Eng = Wdotcycle_SI*3413 [(Btu/hr)/kW] "[Btu/hr]"
h[22]=Enthalpy(Steam,T=T[22],P=P[22])
s[22]=Entropy(Steam,T=T[22],P=P[22])
s[23] = s[22]
h_23 = h_22 - efft*(h_22 - h_23s)
h_23s = Enthalpy(Steam, T= T_23, s= s[22])
x_23 =quality(Steam, T=T_23, h=h_23)
p_23 = pressure(steam, T=T_23, x=x_23)
h_24 = Enthalpy(Steam, T= T_24, x=0)
h_24s = Enthalpy(Steam, T= T_24,P=P_24)
s_24 = Entropy(Steam, T=T_24,h=h_24)
s_25=s_24
h_25s = Enthalpy(Steam, P=P22,s= s_24)
q_c = h_23-h_24 {Specific Heat Transfer}
h_25 = h_24+ (h_25s-h_24)/effp
w_net = (h_22 - h_23) - (h_25 - h_24)
q_b = h_22 - h_25
eta_th = w_net / q_b
eta_max = 1 - ((T_24abs)/(T_22abs)) {CARNOT}
Wdotcycle_max_Eng = q_b*m_dot*eta_max
Wdotcycle_max_SI = Wdotcycle_max_Eng/3413 [(Btu/hr)/kW]
T_26= 25
T_26 = T_27
T_27 = T_28
{Reverse osmosis}
i = 1.8 {van 't Hoff factor for NaCl}
M= 0.599 {Molarity of a NaCl = 0.599 mol/L}
R_nacl = 0.08206 {R value for NaCl =0.08206 L atm / mol K}
T_inK = ((( T_26 - 32)/1.8) + 273.15)
P_28_atm = (i* M* R_nacl* TinK)
P_28 = (P_28_atm * 14.695950253958822)
P_26 = 14.6959 {Assume that there is no pressure rice in pump, the pump only creatres the
flow of water.}
P_27 = P_26
Q_pump = 100 {Assume the discharge rate of the pump was 100 lpm}

m_27 = 63.9* Q_pump
m_28 = m_27 *0.965 {Assue the contamination of the sea water as 3.5 %}