Performance improvement and optimizing an innovative dual-loop RC–ORC heat recovery system with nano-working fluids

Abstract

The application of nanofluids to increase the heat transfer rate in heat exchangers of a proposed dual-loop RC–ORCheat recovery system (RC with water and ORC with R141b working fluids) is investigated here. The effects of adding nanoparticles into working fluids of a heat recovery system with two RC and ORC loops and its performance, has not been studied so far. Appropriate single-phase/two-phase heat transfer coefficients have been used for nanofluids in the system modeling by extracting their properties from available experimental data. Performance evaluation criterion (PEC) was also applied to assess and compare the performance of nanofluids in the proposed system. Optimization of the proposed system with exergy efficiency and payback period as objective functions for various nanofluids (working fluids mixed with four nanoparticles Al₂O₃, CuO, Cu, TiO₂) with various volume fraction (0.5, 1, and 2%) which satisfied PEC > 1 provided a Pareto front. The selected optimum point from Pareto front by TOPSIS method showed that the proposed dual loop RC–ORC system with water/Cu nanofluid (with volume percent of 2% for the RC loop) and 141b/Cu nanofluid (with a volume percent of 0.5% for the ORC loop) had the most suitable performance (higher thermal and exergy efficiencies and lower payback period). Under these conditions, the thermal efficiency, the exergy efficiency, the turbine power output and the annual net profit of the proposed RC–ORC system increased by (4.4%), (17.2%), (15.4%) and (15.6%) respectively.

Appendices

Appendix A: governing equations for modeling the dual loop RC–ORC system

Modeling (energy)

Governing energy equations for pumps, turbines and heat exchanger of the integrated RC-ORC-GE system are listed in Table 12.

Table 12 Governing energy equations for heat exchangers, turbine and pumps of the integrated RC–ORC–GE system

Modeling (exergy)

Exergy is defined as the maximum work attainable during a process from one specific state to the dead state as following:

$$ \dot{E}_{{\text{X}}} = \left( {h - h_{{{\text{amb}}}} } \right) - T_{{{\text{amb}}}} \left( {s - s_{{{\text{amb}}}} } \right) $$

(18)

The equipment exergy destruction rates in the above Rankine–Organic Rankine system are also listed in Table 13:

Table 13 Relations for estimation of destruction rate of exergy for the studied RC–ORC system

$$ \dot{E}_{{{\text{X}},{\text{Des}}}} = \dot{E}_{{{\text{X}},{\text{mass}},{\text{in}}}} - \dot{E}_{{{\text{X}},{\text{mass}},{\text{out}}}} + \dot{E}_{{{\text{X}},{\text{heat}}}} - \dot{E}_{{{\text{X}},{\text{work}}}} $$

(19)

The exergy efficiency and the total exergy destruction rate of the system are expressed by Eqs. (20)–(22) [33]:

$$ \dot{E}_{{{\text{Des}},{\text{Total}}}} = \sum\limits_{i = 1}^{i = k} {\dot{E}_{{{\text{Des}},{\text{i}}}} } $$

(20)

$$ \dot{E}_{{{\text{Des}},{\text{RC}} - {\text{ORC}}}} = \dot{E}_{{{\text{Des}},{\text{Pumps}}}} + \dot{E}_{{{\text{Des}},{\text{HRSG}}/{\text{Vapor}}\;{\text{Generator}}/{\text{Preheater}}}} + \dot{E}_{{{\text{Des}},{\text{Turbine}}/{\text{Expander}}}} + \dot{E}_{{{\text{Des}},{\text{Condenser}}}} $$

(21)

$$ \eta_{{{\text{ex}}}} = 1 - \frac{{\dot{E}_{{{\text{Des}},{\text{Total}}}} }}{{\dot{E}_{{{\text{Supplied}}}} }} $$

(22)

Modeling (economic)

The following sections cover the estimation of annual income, annual net profit, payback period, the operational cost and the equipment investment cost:

Investment cost

The cost functions with their constant coefficients for equipment investment cost are presented in Tables 14 and 15 respectively.

Table 14 Relations for equipment’s investment cost [33]

Table 15 Constants of Eq. (5) in Table 14 [33]

The annual investment cost are estimated by the Eq. (24):

$$ C_{{{\text{Inv}}}} = \sum\limits_{i = 1}^{i = k} {C_{{{\text{Inv}},\text{K}}} } = C_{{{\text{Inv}},{\text{Expander}}/{\text{Turbine}}/{\text{Pumps}}}} + C_{{{\text{Inv}},{\text{Superheater}}/{\text{Evaporator}}/{\text{Preheater}}/{\text{HRSG}}/{\text{Condenser}}}} $$

(23)

$$ C_{{{\text{Inv}}.{\text{ann}}}} = CRF \times C_{{{\text{Inv}}}} $$

(24)

$$ CRF = \left( {\frac{{i\left( {1 + i} \right)^{\text{n}} }}{{\left( {1 + i} \right)^{\text{n}} - 1}}} \right) $$

(25)

The yearly maintenance cost was assumed to be 6% of the capital cost.

Operating cost

Electricity consumption of fans and pumps which are estimated by Eq. (26) are the system operating cost.

$$ C_{{{\text{op}}}} = \left( {\dot{W}_{{{\text{Pump}}}} + \dot{W}_{{{\text{Fan}},{\text{Cond}}}} } \right) \times \left( {C_{{{\text{elec}},{\text{B}}}} } \right) \times H $$

(26)

Income and salvage value

Selling electricity income and the salvage value are obtained by the following equations respectively:

$$ I_{{{\text{e}},{\text{s}}}} = \left( {\dot{W}_{{{\text{Turb}}}} } \right) \times C_{{{\text{elec}},\,{\text{s}}}} \times H $$

(27)

$$ \begin{aligned} C_{{{\text{SV}}}} = & \sum\limits_{r = 1}^{n} {\left( {SV_{{\text{r}}} \times \gamma \left( {i,n} \right)} \right)} \\ SV = & 0.2 \times C_{{{\text{Inv}},{\text{ann}}}} \\ \gamma \left( {i,n} \right) = & \frac{i}{{\left( {1 + i} \right)^{\text{n}} - 1}} \\ \end{aligned} $$

(28)

Payback period

Payback period is computed by Eq. (29):

$$ - \left( {\sum\limits_{k} {C_{{{\text{Inv}},{\text{k}}}} } } \right) - C_{{{\text{op}}}} \left( {\frac{{\left( {1 + i} \right)^{p} - 1}}{{i\left( {1 + i} \right)^{p} }}} \right) + \left( {C_{{{\text{SV}}}} + I_{{{\text{e}},{\text{s}}}} } \right)\left( {\frac{i}{{\left( {1 + i} \right)^{p} }}} \right) = 0 $$

(29)

Annual profit (AP)

Annual profit is defined as the difference between income and all costs of the system as is expressed in Eq. (30):

$$ AP = \left( {C_{{{\text{SV}}}} + I_{{{\text{e}},{\text{s}}}} } \right) - \left( {C_{{{\text{Inv}},{\text{ann}}}} + C_{{{\text{ma}},{\text{ann}}}} + C_{{{\text{op}}}} } \right) $$

(30)

Heat transfer coefficients

The single/two-phase flow heat transfer coefficients are listed in Tables 16 and 17.

Table 16 Condenser convection heat transfer coefficient [33]

Table 17 Condenser, economizer, superheater and preheater convection heat transfer coefficient in [33]

Chen correlation is used for two-phase forced convective and nucleate boiling processes. For two-phase flow in inner pipe of condenser, Dobson and Chato correlation is used for Reynolds number lower than 35,000 while Boyko and Kruzhilin correlation is utilized for higher Reynolds number.

The allowed variations of decision variables and constrains in optimization

Decision variables with their variation range for the studied system are presented in Table 18.

Table 18 The allowed variations of decision variables for optimization of the studied system [33]

The following constraints are also applied in the system optimization:

• (1) The gas engine exhaust temperature must be higher than its dew point temperature (to avoid stack corrosion)

• (2) To prevent the back pressure phenomenon, the pressure drop in the gas side of HRSG should be lower than 0.045 bar.

• (3) The system power loss which is computed from Eq. (30), should be lower than a determined value $\left( { \prec 3\% } \right)$:

  $$ \Delta W\left( {kW} \right) = \dot{m}_{\text{g}} c_{\text{P,g}} \eta_{\text{GE}} T_{\text{GE}} \left( {\left( {\frac{{P_{\text{atm}} }}{{P_{\text{GE}} }}} \right)^{{{\raise0.7ex\hbox{${\gamma - 1}$} \!\mathord{\left/ {\vphantom {{\gamma - 1} \gamma }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\gamma $}}}} - \left( {\frac{{P_{\text{atm}} + \Delta P}}{{P_{\text{GE}} }}} \right)^{{{\raise0.7ex\hbox{${\gamma - 1}$} \!\mathord{\left/ {\vphantom {{\gamma - 1} \gamma }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\gamma $}}}} } \right) $$

  (31)