Thermoeconomic analysis of an integrated multi-effect desalination thermal vapor compression (MED-TVC) system with a trigeneration system using triple-pressure HRSG

Abstract

In this research, thermoeconomic analysis of a multi-effect desalination thermal vapor compression (MED-TVC) system integrated with a trigeneration system with a gas turbine prime mover is carried out. The integrated system comprises of a compressor, a combustion chamber, a gas turbine, a triple-pressure (low, medium and high pressures) heat recovery steam generator (HRSG) system, an absorption chiller cycle (ACC), and a multi-effect desalination (MED) system. Low pressure steam produced in the HRSG is used to drive absorption chiller cycle, medium pressure is used in desalination system and high pressure superheated steam is used for heating purposes. For thermodynamic and thermoeconomic analysis of the proposed integrated system, Engineering Equation Solver (EES) is used by employing mass, energy, exergy, and cost balance equations for each component of system. The results of the modeling showed that with the new design, the exergy efficiency in the base design will increase to 57.5%. In addition, thermoeconomic analysis revealed that the net power, heating, fresh water and cooling have the highest production cost, respectively.

Appendices

Appendix 1: Energy balance equations for different components

Gas turbine cycle:

To calculate the compressor efficiency (η _comp ), following relation can be used [39]:

$$ {\eta}_{comp}=1-\left(0.04+\frac{r_{comp}-1}{150}\right), $$

(28)

where, r _comp is the compressor pressure ratio. The net consumed compressor power is calculated as follows:

$$ {\overset{\cdotp }{W}}_{comp}={\overset{\cdotp }{m}}_{air}\left(1+{\omega}_1\right)\left({h}_2-{h}_1\right) $$

(29)

where, ω is the humidity ratio.

Applying energy balance equation on the combustion chamber, the input heat of the proposed integrated system can be calculated as follows:

$$ {\dot{Q}}_{in}={\dot{m}}_{air}\left(1+\lambda \right)\left({h}_3-{h}_2\right), $$

(30)

where, λ is the fuel to air ratio.

The gas turbine isentropic efficiency can be obtained from the following relation [39]:

$$ {\eta}_t=\mathsf{1}-\left(\mathsf{0.03}+\frac{r_t-1}{180}\right). $$

(31)

To calculate the output power of turbine, following relation is taken into account:

$$ {\dot{W}}_t={\dot{m}}_{\mathrm{gas}}\left({h}_{\mathsf{3}}-{h}_{\mathsf{4}}\right). $$

(32)

After conducting the above mentioned mathematical manipulation, the net output power of the gas turbine cycle can be calculated as follows:

$$ {\dot{W}}_{net}={\dot{W}}_t-{\dot{W}}_{comp}. $$

(33)

HRSG:

Figure 22 illustrates the HRSG temperature profile. Pinch point is the difference between the exhaust gas temperature from the evaporator (economizer side) and the saturated liquid temperature. Triple-pressure heat recovery generator has three pinch points. The difference in the temperature of the outlet water from the economizer (T _w2, T _w4 and T _w6) and the saturated temperature (T _sat, LP , T _sat, MP and T _sat, HP ) is called the approach point, which its value depends on the economizer arrangement. In this study, the values of approach points (AP _LP , AP _MP and AP _HP ) are assumed 5^° C

Fig. 22

Temperature profile in HRSG

The feed water enters to LP economizer with temperature of T _w1 and is heated to T _w2 by extracting heat of the flue gas. The T _w2 is calculated as follows:

$$ {T}_{w2}={T}_{sat, LP}-{AP}_{LP}. $$

(34)

Similarly, T _w4 and T _w6 are calculated:

$$ {T}_{w4}={T}_{sat, MP}-{AP}_{MP}, $$

(35)

$$ {T}_{w6}={T}_{sat, HP}-{AP}_{HP}, $$

(36)

where, T _sat, LP , T _sat, MP and T _sat, HP are saturated steam temperatures of low pressure, medium pressure and high pressure streams.

Similarly, from Fig. 22, we have:

$$ {T}_{w3}={T}_{w2}, $$

(37)

$$ {T}_{w5}={T}_{w4}. $$

(38)

The flue gas entered HRSG with the temperatures of T_4, g3, T_4, g5 and T_4, g7 are calculated from the Eqs. (39–41):

$$ {T}_{4,g3}={T}_{sat, HP}+{PP}_{HP}, $$

(39)

$$ {T}_{4,g5}={T}_{sat, MP}+{PP}_{MP}, $$

(40)

$$ {T}_{4,g7}={T}_{sat, LP}+{PP}_{LP}. $$

(41)

Applying energy balance equations for the economizers of HRSG, feed water mass flow rate (or heating mass flow rate) and also T _4, g4 and T _4, g6 can be obtained as follows:

$$ {\dot{m}}_{heating}\times \left({h}_{w,1}-{h}_{w,2}\right)+{\dot{m}}_g\times \left({h}_{4,g7}-{h}_{4,g8}\right)=0, $$

(42)

$$ {\dot{m}}_{heating}\times \left({h}_{w,3}-{h}_{w,4}\right)+{\dot{m}}_g\times \left({h}_{4,g5}-{h}_{4,g6}\right)=0, $$

(43)

$$ {\dot{m}}_{heating}\times \left({h}_{w,5}-{h}_{w,6}\right)+{\dot{m}}_g\times \left({h}_{4,g3}-{h}_{4,g4}\right)=0. $$

(44)

The mas flow rate of absorption chiller, desalination system and T _4, g2 are obtained from the following relations:

$$ {\dot{m}}_{cooling}\times \left({h}_{\left( water,{T}_{sat, LP,x=0}\right)}-{h}_{\left( water,{T}_{sat, LP,x=1}\right)}\right)+{\dot{m}}_g\times \left({h}_{4,g6}-{h}_{4,g7}\right)=0, $$

(45)

$$ {\dot{m}}_{desalination}\times \left({h}_{\left( water,{T}_{sat, MP,x=0}\right)}-{h}_{\left( water,{T}_{sat, MP,x=1}\right)}\right)+{\dot{m}}_g\times \left({h}_{4,g4}-{h}_{4,g5}\right)=0, $$

(46)

$$ {\dot{m}}_{heating}\times \left({h}_{\left( water,{T}_{sat, HP,x=0}\right)}-{h}_{\left( water,{T}_{sat, HP,x=1}\right)}\right)+{\dot{m}}_g\times \left({h}_{4,g2}-{h}_{4,g3}\right)=0. $$

(47)

Now, energy balance is applied to HP superheater of the HRSG for calculating the temperature of the superheated process steam:

$$ {\dot{m}}_{heating}\times \left({h}_{\left( water,{T}_{sat, HP,x=1}\right)}-{h}_{w,7}\right)+{\dot{m}}_g\times \left({h}_{4,g1}-{h}_{4,g2}\right)=0. $$

(48)

The amount of heating capacity produced in the system is calculated as below:

$$ {Q}_{heating}={\dot{m}}_{heating}\times \left({h}_{w,7}-{h}_{w,1}\right). $$

(49)

Absorption chiller cycle:

For thermodynamic analysis of the absorption chiller cycle, the energy balance equation for each component of system can be applied using Eqs. (1, 2). These employed equations are given below:

• Evaporator:

$$ {\dot{Q}}_{evap}={\dot{m}}_{13}\left({h}_{16}-{h}_{13}\right). $$

(50)

• Absorber:

$$ {\dot{m}}_{18}{x}_{18}={\dot{m}}_{17}{x}_{17}, $$

(51)

$$ {\dot{Q}}_{abs}={\dot{m}}_{18}{h}_{18}-{\dot{m}}_{17}{h}_{17}-{\dot{m}}_{16}{h}_{16}. $$

(52)

• Pump

$$ {\dot{W}}_{pump}={\dot{m}}_{18}{v}_{18}\left({P}_{18}-{P}_{21}\right). $$

(53)

• Heat exchanger

$$ {\dot{m}}_{21}{h}_{21}+{\dot{m}}_8{h}_8={\dot{m}}_{22}{h}_{22}+{\dot{m}}_7{h}_7. $$

(54)

• Generator

$$ {\dot{m}}_8{x}_8={\dot{m}}_7{x}_7, $$

(55)

$$ {\dot{Q}}_{gen}={\dot{m}}_8{h}_8+{\dot{m}}_9{h}_9-{\dot{m}}_7{h}_7. $$

(56)

• Condenser

$$ {\dot{Q}}_{cond}={\dot{m}}_{12}\left({h}_{12}-{h}_9\right). $$

(57)

The amount of cooling capacity of the chiller is equal to the evaporator load:

$$ {\dot{Q}}_{cooling}=-{\dot{Q}}_{evap}={\dot{m}}_{13}\left({h}_{13}-{h}_{16}\right). $$

(58)

MED-TVC desalination plant system:

MED system is divided into five sub-systems and mass and energy balances are applied for each of them as follows:

• Steam ejector and desuperheater:

$$ R=\frac{{\dot{m}}_{24}}{{\dot{m}}_{25}}, $$

(59)

$$ {h}_{26}=\frac{Rh_{24}+{h}_{25}}{1+R}, $$

(60)

$$ {R}_1=\frac{{\dot{m}}_{63}}{{\dot{m}}_{24}+{\dot{m}}_{25}}, $$

(61)

$$ {R}_1=\frac{h_{26}-{h}_{27}}{h_{27}-{h}_{63}}, $$

(62)

$$ {\dot{m}}_{63}={\dot{m}}_{24}{R}_1\left(1+\frac{1}{R}\right), $$

(63)

where, ${\dot{\mathrm{m}}}_{24}$, ${\dot{\mathrm{m}}}_{25}$ and ${\dot{\mathrm{m}}}_{63}$ are the mass flow rates of the ejector motive steam, withdrawn vapor from nth effect by steam ejector and water consumed in desuperheater, respectively.

• Effects 1,…,N:

In order to have a more efficient operational condition, it is assumed that the temperature difference of all effects is the same [25]:

$$ \varDelta {T}_{effect}=\left(\frac{T_s-T(N)}{N}\right), $$

(64)

where,

$$ {T}_1={T}_s-\varDelta T, $$

(65)

$$ T\left(i+1\right)=T(i)-\varDelta T,\kern1.75em i=1,2,\dots, N-1 $$

(66)

In this study, the mass flow rates of steam, brine and feed water of the ith effect are denoted by D(i), B(i) and f(i), respectively. In addition, the latent heat and the specific heat capacities of water in the ith effect are specified by L(i) and Cp(i), respectively. With these regards, the mass and energy balances for the effects of 1,…,N will be as follows [40]:

✓ Effects 1, 2 and 3:

$$ \left({\dot{m}}_{24}+{\dot{m}}_{25}+{\dot{m}}_{63}\right){L}_{24}=f(i){Cp}_f\left(T(1)-{T}_f(1)\right)+D(1)L(1), $$

(67)

$$ \left(D(1)-{D}_r(1)\right)L(1)+B(1){Cp}_B\varDelta T=f(2){Cp}_f\left(T(2)-{T}_f(2)\right)+D(2)L(2), $$

(68)

$$ \left(D(2)-{D}_r(2)\right)L(2)+B(2){Cp}_B\varDelta T=f(3){Cp}_f\left(T(3)-{T}_f(3)\right)+D(3)L(3), $$

(69)

✓ Effects 4,…,N:

$$ \left(D\left(i-1\right)-{D}_r\left(i-1\right)\right)L\left(i-1\right)+B\left(i-1\right){Cp}_B\varDelta T=f(i){Cp}_f\left(T(i)-{T}_f(i)\right)+D(i)L(i),\kern0.5em \mathrm{i}=4,\dots, N. $$

(70)

The steam is only withdrawn in the Nth effect (inlet of steam ejector), so:

$$ i\ne n\kern0.5em \to \kern0.5em {D}_r(i)=0, $$

(71)

$$ B(i)=\sum \limits_{i=1}^Nf(i)-\sum \limits_{i=1}^ND(i)\kern0.75em ,\kern0.5em i=1,2,\dots, N. $$

(72)

• Feed water heater:

The energy balance for feed-water heater can be expressed as follows:

$$ \sum \limits_{i=1}^{N-1}D(i)\left({h}_f(i)-{h}_f(N)\right)+{\dot{m}}_{24}\times \left[{h}_{f24}\left({R}_1+\frac{1+{R}_1}{R}\right)-\frac{h_{f24}}{R}-{h}_{fN}\left({R}_1+\frac{R_1}{R}\right)\right]=\left(f(1)+f(2)+f(3)\right){Cp}_f\left({T}_f(1)-{T}_f\right). $$

(73)

• Condenser:

The mass and energy balance equations for the condenser can be written as follows:

$$ {T}_f=T(N)-\varDelta {T}_{\min, cond}, $$

(74)

$$ {\dot{m}}_{57}=F+ Rej, $$

(75)

$$ \left(D(N)-{D}_r(N)\right)L(N)=\left(F+ Rej\right){Cp}_{sw}\left({T}_f-{T}_{sw}\right), $$

(76)

where, ${\dot{m}}_{57}$ , F, and Rej are the mass flow rates of condenser cooling water, feed water MED and the rejected water from desalination system, respectively. D(N) is the total rate of the exhaust steam of the Nth effect, D _r (N) is the rate of the withdrawn steam from the effect N and T _f and T _sw are the feed water and seawater temperatures, respectively.

Gained-Output-Ratio (GOR) is another important parameter in thermal desalination plants which is defined as the ratio between the mass flow rate of produced fresh water and that of the consumed motive steam:

$$ GOR=\frac{{\dot{m}}_{61}\ }{{\dot{m}}_{24}}. $$

(77)

The MED-TVC plant duty can be obtained from the following relation:

$$ {\dot{Q}}_{desalination}={\dot{m}}_{61}\left({h}_{61}-{h}_{sw}\right). $$

(78)

The overall thermal efficiency of system can be defined as the ratio of output energies of the system (cooling, heating, power and fresh water) to the input energy supplied to the system:

$$ {\eta}_{system}=\frac{{\dot{\mathrm{W}}}_{net}+{\dot{Q}}_{heating}+{\dot{Q}}_{cooling}+{\dot{Q}}_{desalination}}{{\dot{\mathrm{m}}}_{fuel}\times LHV}, $$

(79)

where, LHV is the lower heating value of the fuel.

Appendix 2: Exergy relations

The chemical exergy is obtained by combining the combustion gases in accordance with Eq. (80). The fixed values in the numerator are the exergy of the elements substituted from Ref. [32].

$$ {\dot{E}}^{CH}={\dot{\mathrm{m}}}_{gas}\times \left(\frac{\begin{array}{l}639\times {Y}_{N_2}\times 3951\times {Y}_{O_2}+14176\times {Y}_{CO_2}+8636\times {Y}_{H_2O}+8.3143\times {T}_0\times \\ {}\left({Y}_{N_2}\times \mathit{\ln}\left({Y}_{N_2}\right)+{Y}_{O_2}\times \mathit{\ln}\left({Y}_{O_2}\right)+{Y}_{CO_2}\times \mathit{\ln}\left({Y}_{CO_2}\right)+{Y}_{H_2O}\times \mathit{\ln}\left({Y}_{H_2O}\right)\right)\times \left({Y}_{N_2}+{Y}_{O_2}+{Y}_{H_2O}\right)+ diff\times (45)\end{array}}{M_{mix}}\right). $$

(80)

The chemical exergy of LiBr-H₂O solution can be obtained from the following relation [41]:

$$ {\dot{\mathrm{E}}}^{\mathrm{CH}}={\dot{\mathrm{m}}}_{\mathrm{LiBr}/{\mathrm{H}}_2\mathrm{O}}\times \left(\frac{{\overline{\mathrm{Y}}}_{{\mathrm{H}}_2\mathrm{O}}\times {\upvarepsilon}_{{\mathrm{H}}_2\mathrm{O}}+{\overline{\mathrm{Y}}}_{\mathrm{LiBr}}\times {\upvarepsilon}_{\mathrm{LiBr}}+\overline{\mathrm{R}}\times {\mathrm{T}}_0\times \left({\overline{\mathrm{Y}}}_{{\mathrm{H}}_2\mathrm{O}}\times \ln \left({\mathrm{a}}_{{\mathrm{H}}_2\mathrm{O}}\right)+{\overline{\mathrm{Y}}}_{\mathrm{LiBr}}\times \ln \left({\mathrm{a}}_{\mathrm{LiBr}}\right)\right)}{{\mathrm{M}}_{\mathrm{sol}}}\right). $$

(81)

where, ${\upvarepsilon}_{{\mathrm{H}}_2\mathrm{O}}=0.9\frac{\mathrm{kJ}}{\mathrm{kg}}$ and ${\upvarepsilon}_{\mathrm{LiBr}}=101.6\frac{\mathrm{kJ}}{\mathrm{kg}}$. ${\mathrm{a}}_{{\mathrm{H}}_2\mathrm{O}}$ and a_LiBr coefficients are obtained from Ref. [41].

Also, chemical exergy of seawater can be obtained from the following equation [21]:

$$ {\dot{E}}^{CH}=-{\dot{m}}_{sw}\times \frac{\overline{R}\times {T}_0\times \left({X}_{\frac{W}{s}}\times \mathit{\ln}\left({X}_{\frac{W}{s}}\right)+X\frac{s}{W}\times \mathit{\ln}\left({X}_{\frac{s}{W}}\right)\right)}{M_{sw}}. $$

(82)

For one stream, we have:

$$ {\dot{E}}_{sw}={\dot{E}}_Q+{\dot{m}}_i{e}_i-{\dot{m}}_e{e}_e-{\dot{E}}_D. $$

(83)

The exergy destruction of each component in the proposed multigeneration system can be obtained from the following relationships.

• For compressor:

$$ {\dot{E}}_{D, comp}={\dot{E}}_1+{\dot{E}}_2+{\dot{W}}_{comp}. $$

(84)

• For combustion chamber:

$$ {\dot{E}}_{D, cc}={\dot{E}}_2+{\dot{E}}_F+{\dot{E}}_3. $$

(85)

• For turbine:

$$ {\dot{E}}_{D,t}={\dot{E}}_3+{\dot{E}}_4+{\dot{W}}_t. $$

(86)

• For HRSG:

$$ {\dot{E}}_{D, HRSG}={\dot{E}}_{W1}+{\dot{E}}_{D, in, LP, evap}+{\dot{E}}_{D, in, MP, evap}+{\dot{E}}_4-{\dot{E}}_{W3}-{\dot{E}}_{W5}-{\dot{E}}_{W7}-{\dot{E}}_{4,g8}. $$

(87)

• For absorption chiller:

$$ {\dot{E}}_{D, chiller}={\dot{E}}_5+{\dot{E}}_{10}+{\dot{E}}_{14}+{\dot{E}}_{19}-{\dot{E}}_6-{\dot{E}}_{11}-{\dot{E}}_{15}-{\dot{E}}_{20}. $$

(88)

• For desalination system:

$$ {\dot{E}}_{D, desalination}={\dot{E}}_{24}+{\dot{E}}_{23}+{\dot{E}}_{57}+{\dot{E}}_{Rej}-{\dot{E}}_{54}-{\dot{E}}_{61}. $$

(89)

The total exergy destruction rate of system can be expressed as follows:

$$ {\dot{E}}_{D, total}=\sum \limits_{i=1}^n{\dot{E}}_{D,i}. $$

(90)

Appendix 3

Table 10 is listed the cost flow rate, cost balance equations and auxiliary equations for the proposed multigeneration system.

Table 10 Cost balance and auxiliary equations for components of the proposed MG system