Multi-objective Optimization of Cogeneration of Power and Heat in a Combined Gas Turbine and Organic Rankine Cycle

Abstract

A multi-objective optimization method of cogeneration of power and heat in a combined gas turbine and organic Rankine cycle (ORC) is conducted to achieve the best system design parameters from both thermodynamic and economic aspects by utilizing nondominated sorting genetic algorithm-II (NSGA-II). Exergy efficiency and total cost rate of the system have been considered as objective functions. The cogeneration system consists of a gas turbine (GT) and an organic Rankine cycle (ORC) in which the two cycles are connected through a single-pressure heat recovery steam generator (HRSG). In order to optimize the system, air compressor pressure ratio, air compressor isentropic efficiency, air preheater outlet temperature, turbine inlet temperature, isentropic efficiency of the gas turbine, pinch point temperature of HRSG, pinch point temperature of evaporator, evaporator temperature, and condenser temperature have been selected as decision variables. Optimization results indicate that exergy efficiency of the cycle increases from 51.41% at base case to 55.6% while more than 9.15% reduction is achieved in the total cost rate of the cycle. Also by applying multi-objective optimization, the exergo-economic factor has reached from 10.68 to 27.40.

Appendix A: Purchase Equipments Cost (PEC)

Governing relations of the purchase equipment cost (PEC) for the system components of GT-HRSG/ORC are as follows:

The cost of equipment purchase of the gas turbine cycle (Bejan and Moran 1996):

Air compressor

$$ {\mathrm{PEC}}_{\mathrm{AC}}=\left(\frac{71.10\ {\dot{m}}_{\mathrm{a}}}{0.9-{\eta}_{\mathrm{sc}}}\right)\ \left({\frac{P_2}{P_1}}_1\right)\ln \frac{P_2}{P_1} $$

(A.1)

Air preheater

$$\begin{array}{l}{\mathrm{PEC}}_{\mathrm{APH}}=4122{\left(\frac{{\dot{m}}_{\mathrm{g}}\left(h_5-h_6\right)}{U\mathrm{\Delta }{T}_{\mathrm{lm}.\mathrm{aph}}}\right)}^{0.6}\\ U=18W/\left(m^{2}K\right)\end{array}$$

(A.2)

Combustion chamber

$$ {\mathrm{PEC}}_{\mathrm{CC}}=\frac{46.08\ {\dot{m}}_{\mathrm{a}}}{0.995-\left(\frac{P_4}{P_3}\right)}\left[1+\exp \left(0.018\ {T}_4-26.4\right)\right] $$

(A.3)

Gas turbine

$$ {\displaystyle \begin{array}{l}{\mathrm{PEC}}_{\mathrm{GT}}=\left(\frac{479.34\ {\dot{m}}_{\mathrm{g}}}{0.92-{\eta}_{\mathrm{sc}}}\right)\ln \left(\frac{P_4}{P_5}\right)\\ {}\left[1+\exp \left(0.036\ {T}_4-54.4\right)\right]\kern0.5em \end{array}} $$

(A.4)

Heat recovery steam generator

$$ {\displaystyle \begin{array}{l}{\mathrm{PEC}}_{\mathrm{HRSG}}=6570\ \left[{\left(\frac{{\dot{Q}}_{\mathrm{ec}}}{\Delta {T}_{\mathrm{lm},\mathrm{ec}}}\right)}^{0.8}+{\left(\frac{{\dot{Q}}_{\mathrm{ev}}}{\Delta {T}_{\mathrm{lm},\mathrm{ev}}}\right)}^{0.8}\right]+\\ {}21276{\dot{m}}_{\mathrm{w}}+1184.4{{\dot{m}}_{\mathrm{g}}}^{1.2}\end{array}} $$

(A.5)

Organic Rankine cycle equipment purchase costs:

Pump (Baghernejad and Yaghoubi 2011)

$$ {\mathrm{P}\mathrm{EC}}_{\mathrm{P}}=3540\ {\left({\dot{W}}_{\mathrm{P}}\right)}^{0.71}\kern1.5em $$

(A.6)

Evaporator (Sayyaadi and Nejatolahi 2011)

$$ {\mathrm{PEC}}_{\mathrm{Eva}}=309.143\ \left({A}_{\mathrm{Eva}}\right)+231.915\kern0.5em $$

(A.7)

Turbine (Pierobon et al. 2013)

$$ {\mathrm{PEC}}_{\mathrm{T}}=6000\ \left({{\dot{W}}_{\mathrm{T}}}^{0.7}\right)\kern2em $$

(A.8)

Condenser (Baghernejad and Yaghoubi 2011)

$$ {\mathrm{PEC}}_{\mathrm{Cond}}=1773\ {\dot{m}}_{\mathrm{Steam}}\kern1.75em $$

(A.9)

Internal heat exchanger (Quoilin et al. 2011)

$$ {\mathrm{PEC}}_{\mathrm{IHE}}=1.3\ \left(190+310\ {A}_{\mathrm{IHE}}\right)\kern1.25em $$

(A.10)

The following formula is used to convert the cost of purchasing equipment from the base year to the reference year (Bejan and Moran 1996):

$$\begin{array}{l}\text{Cost}\mathrm{at}\text{reference year}=\\ \text{original Cost}\frac{{\mathit{CI}}_{\text{reference year}}}{{\mathit{CI}}_{\text{original year}}}\end{array}$$

(A.11)

Here CI is the cost index which their values are given in Table A.1 from 1990 to 2013. In the present work to calculate cost index, Marshall and Swift index is used (Sayyaadi and Nejatolahi 2011).

Table A.1 Marshall and Swift cost index at various years

It is noted that the cost of the gas turbine cycle components is based on 1995, cost of pump and condenser is based on 2011, cost of evaporator is based on 2006, cost of organic Rankine cycle turbine is based on 2013, and cost of internal heat exchanger is based on 2010 in which all the costs have been converted to the equivalent expenses in 2013 by the cost index.