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In the present study, a dual-pressure organic Rankine cycle (DORC) driven by geothermal hot water for electricity production is developed, investigated and optimized from the energy, exergy and exergoeconomic viewpoint. A parametric study is conducted to determine the effect of high-stage pressure and low-stage pressure variation on the system thermodynamic and exergoeconomic performance. The DORC is further optimized to obtain maximum exergy efficiency optimized design (EEOD case) and minimum product cost optimized design (PCOD case). The exergy efficiency and unit cost of power produced for the optimization of EEOD case and PCOD case are 33.03% and 3.059 cent/kWh, which are 0.3% and 17.4% improvement over base case, respectively. The PCOD case proved to be the best, with respect to minimum unit cost of power produced and net power output over the base case and EEOD case.

In recent years, the utilization of low-grade heat sources such as geothermal, biomass, solar and power and industrial process waste heat, are becoming more and more attractive as a sustainable approach towards ameliorating environmental issues, such as air pollution, acid rain, global warming and ozone layer depletion caused by greenhouse gas emission from fossil fuel combustion. It is also considered a potential solution to reducing the energy shortage being experienced due to the rapid growth in population and economic activities around the world. Organic Rankine cycle (ORC) is widely used and considered a promising heat-to-power conversion technology that uses lower boiling temperature working fluids, which makes it suitable, flexible and efficient for converting a wide range of heat source temperature to useful power output [

Geothermal energy is a low-medium grade heat source, which is attracting growing attention for power generation due to concern about environmental pollution problems from fossil fuel consumption. The advantage of geothermal energy over other renewable energy like wind and solar energies, is that its availability is all year round and, independent of time of day or seasons. The utilization of geothermal energy is increasing worldwide, in 2016 the total install generating capacity was 12.7 GW with annual electricity generation of 80.9 terawatt-hour (TWh) in 2015, accounting for 3% global electricity production [_{3}H_{2}O) which produces two vapour-components at variable temperature, the ORC uses pure organic working fluids with specific evaporation temperature and better matching characteristic with the geothermal fluid, therefore resulting in higher thermodynamic and exergy efficiencies.

Several Scholars have conducted studies on suitable technology options for low-grade heat source utilization such as geothermal, in which ORC is considered the best technology for heat recovery, with cycle modification capable of achieving higher performance [

There exist in public domain several researches comparing performance of different ORC layouts and system optimization of the DORC. However, a few studies have investigated the exergoeconomic performance of the DORC system with optimization towards optimal system exergy efficiency and minimum product total cost design. Even though DORC systems produces better performance compared with the conventional SORC, their much higher specific investment cost due to their complex configurations consisting of two evaporation processes, two turbine expansion processes and two pumping processes, might be a drawback. Therefore, it is essential to investigate the thermoeconomic and exergoeconomic performance of DORC applications.

The present study, investigates the exergoeconomic optimization of dual-pressure ORC using geothermal heat source. Thermodynamic and thermoeconomic analysis was performed to determine the system first and second law efficiencies, as well as the exergy unit cost rate for each stream. Parametric analysis was also conducted to determine the influence of the high-stage and low-stage pressures, working fluids mass flow and heat source temperature on the system overall exergy efficiency and product unit cost. In addition, optimization was performed to obtain optimal decision parameters to attain maximum exergy efficiency optimized design (EEOS case) and minimum product cost optimized design (PCOD case). Finally, to design a cost-efficient system the exergoeconomic parameters like the exergoeconomic factor and cost of exergy destruction were determined for each component in order to identify potential opportunities for system improvement.

high-stage pressure. The compressed fluid from the HP pump (state 5) flows through the preheater 2, absorbing heat before entering the HP evaporator (state 6). The vaporized fluid (state 7) is then superheated before exiting the superheater (state 8) to undergo expansion in the HP turbine. The working fluid leaving the HP turbine (state 9) mixes with the fluid stream from the LP evaporator (state 4) and then flows to the LP turbine inlet (state 10) where it undergoes second turbine expansion. The LP turbine exhaust vapour (state 11) is condensed in the condenser into liquid (state 1) by the cooling water entering (state 12) and leaving (state 13) the condenser. The liquid working fluid (state 1) is then pumped to the preheater 1 and the entire cycle is completed. The geothermal hot water is the heat source that have been used to drive the ORC system. It is a medium-temperature heat source with maximum temperature of 150˚C at 2525 kPa pressure.

The geothermal resource from the geothermal well (state 14) enters the superheater and exits (state 15) into the HP evaporator where the working fluid is superheated and vaporize, respectively. The hot water streams from HP evaporator (state 16) preheats the high pressure (HP) working fluid in the Preheater 2, then leaves to vaporize (state 17) the low pressure (LP) working fluid. The remaining enthalpy in the hot water leaving (state 18) the LP evaporator is used to preheat the working fluid in preheater 1, and finally delivered back to the geothermal well (state 19). It is worth noting that, the working fluid pressure leaving the LP evaporator (state 4) is equal to the HP turbine exhaust vapour pressure (state 9).

For the purpose of system analysis, each component of the DORC is considered a control volume in which mass and energy conservation principles, as well as the second law of thermodynamics are applied. The EES software developed by Ibrahim and Klein [

The following simplified assumptions are further employed in modelling of the ORC:

· The ORC system operates at steady-state condition.

· Pressure drops in all heat exchangers and pipes are negligible.

· Dry and isentropic working fluid at the turbine inlets are superheated vapor.

· Pinch point temperature difference at the heat exchanger is 10˚C.

· Changes in potential and kinetic are negligible.

The mass and energy conservation, as well as exergy balance relations for each system component are represented as [

∑ m ˙ i n = ∑ m ˙ o u t (1)

∑ m ˙ i n h i n + Q ˙ c v − ∑ m ˙ o u t h o u t − W ˙ c v = 0 (2)

∑ E ˙ i n − ∑ E ˙ o u t + ∑ E ˙ h e a t + ∑ W ˙ J − E ˙ D , J = 0 (3)

Neglecting the potential and kinetic exergies, the total exergy ( E ˙ ) is considered as the sum of the physical and chemical components expressed as [

E ˙ = E ˙ p h + E ˙ c h (4)

The physical exergy quantifies the maximum obtainable useful work when the system state changes due to variation in pressure and temperature from the specific state ( T , P ) to reference state ( T 0 , P 0 ). The specific physical and chemical exergies are expressed as follow:

E ˙ p h = m ˙ [ ( h − h 0 ) − T 0 ( s − s 0 ) ] (5)

E ˙ c h = m ˙ [ ∑ i = 1 n X i e x c h , i + R T 0 ∑ i = 1 n X i L n ( X i ) ] (6)

In the exergy analysis of a system, the product exergy ( E ˙ p ) and fuel exergy ( E ˙ f ) of both the system components and the entire system are calculated separately. For each system component the exergy destruction is defined as the difference between the product and fuel exergies:

E ˙ D , J = E ˙ f , J + E ˙ p , J (7)

The ORC performance evaluates the system energy utilization factor, defined in terms of the thermal efficiency and exergy efficiency.

Thermal efficiency is the ratio of the net power output to the input energy from the geothermal heat source [

η t h e r m a l = W n e t / Q i n (8)

where,

W ˙ n e t = W ˙ H P _ t u r b + W ˙ L P _ t u r b − W ˙ p u m p 1 − W ˙ p u m p 2 (9)

Q ˙ i n = m ˙ 14 ( h 14 − h 19 ) (10)

The exergy efficiency is expressed as follows

η e x e r g y = ( W n e t + E r e f ) / E ˙ i n (11)

where,

E ˙ i n = E ˙ 14 − E ˙ 19 (12)

The overall system efficiency, η s y s , and the heat recovery effectiveness, ϕ , of the ORC are calculated as follows:

η s y s = Q i n / m ˙ 14 ( h 14 − h 0 ) (13)

ϕ = W n e t / m ˙ 14 ( h 14 − h 0 ) (14)

where, h 0 is specific heat enthalpy of heat source water at ambient temperature.

The energy and exergy relations for each component of the ORC system is shown in

Exergoeconomic analysis is an approach that combines exergy and economic analyses in order to facilitate better design and more cost-efficient systems. The

Components | Organic Rankine Cycle | |
---|---|---|

Energy equations | Exergy equation | |

Pump 1 | η P u m p 1 = w s w A = h 2 s − h 1 h 2 − h 1 W P u m p 1 = m ˙ 1 ( h 2 − h 1 ) | E ˙ 1 + W ˙ p u m p 1 − E ˙ 2 = E ˙ D e s t r u c t i o n |

Pump 2 | η P u m p 2 = w s w A = h 5 s − h 3 b h 5 − h 3 b W P u m p 2 = m ˙ 5 ( h 5 − h 3 b ) | E ˙ 3 b + W ˙ p u m p 2 − E ˙ 5 = E ˙ D e s t r u c t i o n |

Condenser | m ˙ c o o l i n g ( h 13 − h 12 ) = m ˙ 11 ( h 11 − h 1 ) Q ˙ E c o n = m ˙ 11 ( h 11 − h 1 ) | E ˙ 11 + E ˙ 12 − E ˙ 1 − E ˙ 13 = E ˙ D e s t r u c t i o n |

Superheater | m ˙ 14 ( h 14 − h 15 ) = m ˙ 8 ( h 8 − h 7 ) Q ˙ S u p e r H = m ˙ 8 ( h 8 − h 7 ) | E ˙ 14 + E ˙ 7 − E ˙ 15 − E ˙ 8 = E ˙ D e s t r u c t i o n |

HP Evaporator | m ˙ 15 ( h 15 − h 16 ) = m ˙ 6 ( h 7 − h 6 ) Q ˙ H P _ E v a p = m ˙ 6 ( h 7 − h 6 ) | E ˙ 15 + E ˙ 6 − E ˙ 7 − E ˙ 16 = E ˙ D e s t r u c t i o n |

HP Turbine | η H P _ t u r b = w A w s = h 8 − h 9 h 8 − h 9 s W H P _ t u r b = m ˙ 8 ( h 8 − h 9 ) | E ˙ 8 − W ˙ H P _ t u r b − E ˙ 9 = E ˙ D e s t r u c t i o n |

Preheater 1 | m ˙ 18 ( h 18 − h 19 ) = m ˙ 3 ( h 3 − h 2 ) Q ˙ p r e H 1 = m ˙ 3 ( h 3 − h 2 ) | E ˙ 18 + E ˙ 2 − E ˙ 19 − E ˙ 3 = E ˙ D e s t r u c t i o n |

LP Evaporator | m ˙ 17 ( h 17 − h 18 ) = m ˙ 4 ( h 4 − h 3 a ) Q ˙ L P _ E v a p = m ˙ 4 ( h 4 − h 3 a ) | E ˙ 17 + E ˙ 3 a − E ˙ 18 − E ˙ 4 = E ˙ D e s t r u c t i o n |

LP Turbine | η L P _ t u r b = w A w s = h 10 − h 11 h 10 − h 11 s W L P _ t u r b = m ˙ 10 ( h 10 − h 11 ) | E ˙ 10 − W ˙ L P _ t u r b − E ˙ 11 = E ˙ D e s t r u c t i o n |

Preheater 2 | m ˙ 16 ( h 16 − h 17 ) = m ˙ 5 ( h 6 − h 5 ) Q ˙ p r e H 2 = m ˙ 5 ( h 6 − h 5 ) | E ˙ 16 + E ˙ 5 − E ˙ 17 − E ˙ 6 = E ˙ D e s t r u c t i o n |

analysis provides information about the cost formation process and cost of unit exergy of each stream. This analysis is conducted through the formation of cost balance equations and auxiliary equations for each component expressed in the form [

∑ C ˙ i , J + C ˙ q , J + Z ˙ J = ∑ C ˙ e , J + C ˙ w , J (15)

where,

C ˙ = c E ˙ (16)

In the equations above, C ˙ is the cost rate of exergy ($⁄hr) and c is the cost of unit exergy of each stream ($⁄GJ). Also, C q and C w represent the heat transfer rate of each component and the work associated costs, respectively.

The cost balance equation for the entire system is usually formulated as follow [

C ˙ P , t o t a l = C ˙ f , t o t a l + Z ˙ t o t a l (17)

where, C ˙ P denotes total product related costs, C ˙ f is the fuel cost rate and Z ˙ is the total costs related to capital investment and operation and maintenance.

The Investment cost rate ( Z ˙ J ) of J^{th} component is defined as the sum of the capital investment ( Z ˙ J C I ) and operation and maintenance costs ( Z ˙ J O M ).

Z ˙ J = Z ˙ J C I + Z ˙ J O M (18)

The annual levelized capital investment cost is computed as [

Z ˙ J = ( C R F / τ ) Z J + ( y J / τ ) Z J + ω J E ˙ P , J + R J / τ (19)

where Z J is the capital cost for J component, and is calculated with relations as expressed in Appendix A. CRF denotes the capital recovery factor given as:

C R F = i r ( 1 + i r ) n / ( ( 1 + i r ) n − 1 ) (20)

where, i r is the interest rate, and n is the number of useful years the plant is in operation.

In Equation (19), τ is the annual hours of plant operation, y J is the fixed cost and ω J is the variable cost relating to operation and maintenance.

The term R J refers to all other costs independent from investment cost and operation and maintenance costs. The first term in Equation (19) is much larger than the two last terms, therefore the two last terms can be neglected.

Components | Organic Rankine cycle | |
---|---|---|

Cost equations | Auxiliary equation | |

Pump 1 | C ˙ 1 + C ˙ w , p u m p 1 + Z ˙ p u m p 1 = C ˙ 2 | |

Condenser | C ˙ 11 + C ˙ 12 + Z ˙ c o n d = C ˙ 1 + C ˙ 13 | c 11 = c 1 ; c 12 = 0 |

Preheater 1 | C ˙ 2 + C ˙ 18 + Z ˙ p r e H 1 = C ˙ 3 + C ˙ 19 | c 2 = c 3 ; c 3 a = c 3 |

LP Turbine | C ˙ 10 + Z ˙ L P _ t u r b = C ˙ 11 + C ˙ w , L P _ t u r b | c 11 = c 10 c w , L P _ t u r b = c w , p u m p 1 |

LP Evaporator | C ˙ 3 a + C ˙ 17 + Z ˙ L P _ e v a p = C ˙ 4 + C ˙ 18 | c 3 a = c 4 ; c 3 a = c 3 b |

Preheater 2 | C ˙ 5 + C ˙ 16 + Z ˙ p r e H 2 = C ˙ 6 + C ˙ 17 | c 5 = c 6 |

Pump 2 | C ˙ 3 b + C ˙ w , p u m p 2 + Z ˙ p u m p 2 = C ˙ 5 | C ˙ w , p u m p 2 = C ˙ w , p u m p 2 |

HP Turbine | C ˙ 8 + Z ˙ H P _ t u r b = C ˙ 9 + C ˙ w , H P _ t u r b | c 9 = c 8 ; c w , H P _ t u r b = c w , p u m p 2 |

HP Evaporator | C ˙ 6 + C ˙ 15 + Z ˙ H P _ e v a p = C ˙ 7 + C ˙ 16 | c 6 = c 7 |

Superheater | C ˙ 7 + C ˙ 14 + Z ˙ S u p e r H = C ˙ 8 + C ˙ 15 | c 7 = c 8 |

Mixer | C ˙ 4 + C ˙ 9 + Z ˙ m i x e r = C ˙ 10 | |

Separator | C ˙ 3 = C ˙ 3 a + C ˙ 3 b | c 3 a = c 3 b |

of the ORC system.

Exergoeconomic FactorsThe exergoeconomic factor ( f J ), and the cost of exergy destruction are very important exergoeconomic parameters that are used for evaluating the economic performance of the entire system and each component.

· Exergoeconomic factor (f_{J}):

Exergoeconomic factor ( f J ) defines the proportion of capital investment and operation and maintenance costs in the exergy destruction and exergy loss related costs for each component [

f J = Z ˙ J / [ Z ˙ J + ( C ˙ D , J + C ˙ L , J ) ] (21)

· Cost of exergy destruction:

The cost of exergy destruction is often referred to as a hidden cost, as it does not appear in the cost balance equation of the components. The cost of exergy destruction, cost of product and cost of fuel can be expressed as follows [

C ˙ D , J = c f , J E ˙ D , J (22)

C ˙ P , J = c p , J E ˙ P , J (23)

C ˙ F , J = c f , J E ˙ F , J (24)

where c f and c p denotes average cost per unit fuel and the cost per unit product for each component.

The thermodynamic model developed for the DORC system being investigated is first validated against available public literature [

The Input data and assumptions made for the parametric study of the DORC system is listed in

The thermodynamic properties, exergy rate E ˙ , exergy cost rate C ˙ [$/hr] and cost rate of unit exergy c[$/GJ] at each stream for the developed model of the DORC system based on the input conditions listed in

Parameters | Working fluid-Isobutane | ||
---|---|---|---|

Present Work | Manente et al. [ | Relative error [%] | |

T S a t _ H P [˚C] | 113.40 | 113.30 | +0.088 |

T S a t _ L P [˚C] | 76.57 | 76.60 | −0.039 |

P H P [KPa] | 2525 | 2530 | −0.198 |

P L P [KPa] | 1230 | 1230 | 0.0 |

m ˙ H P [Kg/s] | 62.90 | 62.90 | 0.0 |

m ˙ L P [Kg/s] | 32.74 | 32.80 | −0.183 |

η t h [%] | 10.59 | 10.22 | +3.493 |

η s y s [%] | 7.026 | 7.066 | −0.569 |

W n e t [KW] | 3859 | 3871 | −0.310 |

Parameters | Values |
---|---|

Ambient Temperature, T a m b | 20 [˚C] |

Ambient Pressure, P a m b | 101 [kPa] |

Geothermal Water Temperature, T 14 | 150 [˚C] |

Geothermal Water Pressure, P 14 | 2525 [kPa] |

Geothermal water mass flow rate, m ˙ 14 | 45 [Kg/s] |

Pinch point temperature difference in the evaporator, Δ T E v a p | 10 [˚C] |

Cooling water entry temperature, T 12 | 25 [˚C] |

Condensation temperature, T c o n d | 29 [˚C] |

Pinch point temperature difference in the condenser, Δ T c o n d | 10 [˚C] |

Turbine efficiency, η t u r b | 85 [%] |

Pump efficiency, η p u m p | 70 [%] |

Annual operating hours, τ | 8000 [hr./year] |

Interest rate, i r | 15 [%] |

Plant years of operation, n | 20 years |

efficiency of 99.87%.

After the condenser, the next components with significant contribution to the cycle exergy destruction rate are the HP evaporator, LP turbine and preheater 1, with exergy efficiencies of 99.91%, 98.92% and 99.98%, respectively.

The DORC base case exergoeconomic parameters are presented in

State | Working Fluid | T [˚C] | P [KPa] | m ˙ [Kg/s] | E ˙ e x [MW] | C ˙ [$/h] | c [$/GJ] |
---|---|---|---|---|---|---|---|

1 | Isobutane | 39.00 | 517 | 43.34 | 8.238 | 154.40 | 5.205 |

2 | Isobutane | 39.67 | 1250 | 43.34 | 8.322 | 161.40 | 5.389 |

3 | Isobutane | 76.57 | 1250 | 43.34 | 12.371 | 188.30 | 4.229 |

4 | Isobutane | 76.57 | 1250 | 14.48 | 7.658 | 86.42 | 3.135 |

5 | Isobutane | 78.19 | 2525 | 28.87 | 8.347 | 135.70 | 4.517 |

6 | Isobutane | 113.3 | 2525 | 28.87 | 11.407 | 158.10 | 3.850 |

7 | Isobutane | 113.3 | 2525 | 28.87 | 16.176 | 190.00 | 3.263 |

8 | Isobutane | 114.3 | 2525 | 28.87 | 16.278 | 194.50 | 3.319 |

9 | Isobutane | 82.45 | 1250 | 28.87 | 15.646 | 186.90 | 3.319 |

10 | Isobutane | 80.48 | 1250 | 43.34 | 23.303 | 436.70 | 5.205 |

11 | Isobutane | 52.42 | 517 | 43.34 | 21.979 | 411.90 | 5.205 |

12 | Water | 25.00 | 101 | 877.30 | 17.108 | 0 | 0 |

13 | Water | 29.00 | 101 | 877.30 | 30.809 | 264.60 | 2.386 |

14 | Water | 150.00 | 2525 | 45.00 | 23.345 | 115.40 | 1.373 |

15 | Water | 149.40 | 2525 | 45.00 | 23.243 | 114.90 | 1.373 |

16 | Water | 123.30 | 2525 | 45.00 | 18.460 | 91.24 | 1.373 |

17 | Water | 106.30 | 2525 | 45.00 | 15.391 | 76.07 | 1.373 |

18 | Water | 86.57 | 2525 | 45.00 | 11.854 | 58.59 | 1.373 |

19 | Water | 63.69 | 2525 | 45.00 | 7.792 | 38.51 | 1.373 |

Components | Exergy Parameters | |||
---|---|---|---|---|

E ˙ p [KW] | E ˙ f [KPa] | E ˙ D [KW] | ε [%] | |

HP Turbine | 626.1^{a} | 632.4 | 6.229 | 99.02 |

LP Turbine | 1310.0 | 1325.0 | 14.270 | 98.92 |

Condenser | 30,809.0 | 30,849.0 | 39.110 | 99.87 |

LP Pump 1 | 8322.0 | 8323.0 | 1.637 | 99.98 |

Preheater 1 | 12,371.0 | 12,384.0 | 12.59 | 99.90 |

LP Evaporator | 7658.0 | 7669.0 | 11.470 | 99.85 |

HP Pump 2 | 8347.0 | 8349.0 | 1.884 | 99.98 |

Preheater 2 | 11,407.0 | 11,416.0 | 8.323 | 99.93 |

HP Evaporator | 16,176.0 | 16,191.0 | 14.640 | 99.91 |

Superheater | 16,278.0 | 16,279.0 | 0.4564 | 100.00 |

Components | Exergoeconomic Parameters | |||||
---|---|---|---|---|---|---|

c p [$/GJ] | c f [$/GJ] | C ˙ D [$/hr] | Z ˙ J [$/hr] | Z ˙ J + C ˙ D , J [$/hr] | f [%] | |

HP Turbine | 9.979 | 3.319 | 0.07441 | 14.940 | 15.010 | 99.50 |

LP Turbine | 9.979 | 5.205 | 0.26730 | 22.250 | 22.520 | 98.81 |

Condenser | 2.386 | 2.319 | 0.32640 | 7.139 | 7.465 | 95.63 |

LP Pump 1 | 5.389 | 5.254 | 0.03096 | 4.003 | 4.034 | 99.23 |

Preheater 1 | 4.229 | 4.072 | 0.18450 | 6.831 | 7.016 | 97.37 |

LP Evaporator | 3.135 | 2.912 | 0.12020 | 6.024 | 6.144 | 98.04 |

HP Pump 2 | 4.517 | 4.305 | 0.02919 | 6.349 | 6.378 | 99.54 |

Preheater 2 | 3.850 | 3.672 | 0.11000 | 7.208 | 7.318 | 98.50 |

HP Evaporator | 3.263 | 3.118 | 0.16440 | 8.240 | 8.404 | 98.04 |

Superheater | 3.319 | 3.251 | 0.00534 | 3.968 | 3.968 | 99.87 |

using cheaper turbine. The next components with the highest Z ˙ + C ˙ D value are the HP turbine, HP evaporator and condenser in descending order, respectively. In the same manner, in HP turbine the capital investment cost Z ˙ L P _ t u r b value dominates the contribution associated with exergy destruction C ˙ D , H P _ t u r b .

This implies, lowering the value of Z ˙ + C ˙ D in the HP turbine would come by choosing turbine with lower capital investment cost.

Other components are observed to follow similar trend. The high value off for these components indicates that the capital investment cost Z ˙ , is larger than the cost rate associated with exergy destruction C ˙ D . Therefore, any further reduction in the value of Z ˙ + C ˙ D parameter can be achieved by lowering the capital investment cost of the components.

Comparing the processes involving compression in the pump, expansion in the turbines and heat transfer in the superheater, evaporators and preheaters, the LP pump1 and superheater are observed to have lower value of rate of exergy destruction E ˙ D than other components in the DORC. The superheater and LP pump1 also appears to have lower value of Z ˙ + C ˙ D compare to other components of the cycle, in which superheater has the lowest value of Z ˙ + C ˙ D , which is understandable considering the degree (1˚C) of superheating in the base case. Therefore, the LP pump1 and superheater are considered the cheapest components in the cycle with minimum values of Z ˙ + C ˙ D and having no significant effect on the exergoeconomic performance of the cycle given any changes in the component. It is also observed that all the components where heat transfer process occur except in the superheater, have high rate of exergy destruction E ˙ D with corresponding high cost associated with exergy destruction C ˙ D .

In this section, an investigation on the effect of operating parameters on the cycle thermodynamic and exergoeconomic performance is undertaken.

Thermal efficiency:

cycle is determined by Q ˙ H P E and Q ˙ p r e H 1 , in which the value of Q ˙ H P E dominants the value of Q ˙ T o t a l , which decreases at first and then increases afterwards. Therefore, causing thermal efficiency η t h to increase as the value of P L P increases. The highest η t h is observed within the range 2450 kPa < P H P < 2750 kPa and 1400 kPa < P L P < 1600 kPa (see

Net power output:

As P L P increases while P H P is held constant, the value of W ˙ H P _ t u r b decreases (

If the P L P is increased while P H P is kept constant, the values of C ˙ 10 , C ˙ 11 , Z ˙ L P _ t u r b and C ˙ D , L P _ t u r b showing similar trend, increasing steadily as P L P increases. The value of C ˙ 8 increases, the Z ˙ H P _ t u r b show a declining trend, while the parameter C ˙ D , H P _ t u r b ascend at first and then descend afterward. The C ˙ 6 , C ˙ 7 and HP evaporator cost rate associate with exergy destruction C ˙ D , H P _ E v a p show slight increase and the parameter Z ˙ H P _ E v a p remains unchanged. It is obvious that changes in these component parameters can significantly influences the overall exergoeconomic performance of the DORC system.

In the case of P H P increasing and P L P constant, the C ˙ D shows a descending trend for the LP turbine and HP evaporator and an increasing trend for HP turbine. These components account for up to half of the value of the overall cost rate associated with exergy destruction, C ˙ D , o v e r a l l , therefore affecting the behavior of C ˙ D , o v e r a l l .

is increased and P L P is constant. This indicate that C ˙ D , L P _ t u r b , C ˙ D , H P _ e v a p and other components with descending trend have stronger influence on the behavior of C ˙ D , o v e r a l l . The Z ˙ o v e r a l l trend is observed to first increase and then decrease as P H P is increased and P L P held constant (

If P L P is increased and P H P is held constant, the value of C ˙ D for components with significant influence on the behavior of C ˙ D , o v e r a l l such as the LP turbine and HP evaporator show an increasing trend.

This results in the ascending trend of C ˙ D , o v e r a l l as P L P increases. In the other hand, the Z ˙ o v e r a l l parameter have similar behavior as previous, increasing at first and then decreasing. C ˙ D , o v e r a l l + Z ˙ o v e r a l l also takes a similar trend due to the dominant influence of Z ˙ . The f o v e r a l l parameter show increasing trend with increase in P L P , reflecting the dominance of Z ˙ o v e r a l l in the C ˙ D , o v e r a l l + Z ˙ o v e r a l l parameter.

The DORC system optimization is considered in this section to determine the optimal design (working conditions) from the viewpoint of the exergy efficiency optimal design (EEOD), and the minimum unit cost of product cost optimal design (PCOD) using the direct search method in EES software. Six decision parameters with the range of variation shown below were considered to optimize the system:

2200 kPa ≤ P H P ≤ 2750 kPa

900 kPa ≤ P L P ≤ 1600 kPa

1 ˚ C ≤ Δ T S H ≤ 10 ˚ C

25 ˚ C ≤ T c o n d , o u t ≤ 29 ˚ C

1 ˚ C ≤ Δ T c o n d , p p ≤ 10 ˚ C

5 ˚ C ≤ Δ T E v a p , p p ≤ 15 ˚ C

The results of the optimization presented in

Parameters | Optimization | ||
---|---|---|---|

Base case | EEOD | PCOD | |

P H P [Pa] | 2525 | 2481 | 2590 |

P L P [Pa] | 1250 | 1200 | 1059 |

Δ T S H [C] | 1 | 1 | 1 |

Δ T E v a p _ p p [C] | 10 | 10 | 5 |

Δ T c o n d _ p p [C] | 10 | 5 | 6.66 |

η e x [%] | 32.93 | 33.03 | 33 |

η t h [%] | 10.6 | 11.3 | 10.82 |

W n e t [kW] | 1741 | 1939 | 1991 |

c w , t u r b | 3.592 | 3.507 | 3.059 |

θ [%] | 66.39 | 69.38 | 74.39 |

η s y s [%] | 7.039 | 7.841 | 8.05 |

m ˙ c o o l i n g [kg/s] | 877.3 | 909.7 | 692.9 |

m ˙ H P [kg/s] | 28.87 | 29.43 | 33.56 |

m ˙ L P [kg/s] | 14.48 | 14.5 | 14.58 |

design (PCOD) case, the c w , t u r b parameteris 3.059 cent/kWh, which is 17.4% and 14.64% lower than the base case and EEOD case, respectively. The net power output in the PCOD case is 1991 kW, which is 12.55% and 2.6% higher than base case and the EEOD case, respectively. It is apparent from

In

The HP evaporator, LP turbine and condenser are observed to have the highest value of cost rate associated with exergy destruction C ˙ D , and the HP turbine and superheater having the lowest value. The components in

Components | Rate of exergy destruction | Cost rate of exergy destruction | Cost rate of Investment | C ˙ D , J + Z ˙ J ($⁄hr) | Exergoeconomic factors | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

E ˙ D , J (KW) | C ˙ D , J ($⁄hr) | Z ˙ J ($⁄hr) | Base case | EEOD | PCOD | f (%) | |||||||||

Base case | EEOD | PCOD | Base case | EEOD | PCOD | Base case | EEOD | PCOD | Base case | EEOD | PCOD | ||||

HP Evaporator | 14.640 | 15.580 | 14.200 | 0.16440 | 0.17080 | 0.13400 | 8.240 | 8.273 | 10.230 | 8.404 | 8.444 | 10.360 | 98.04 | 97.98 | 98.71 |

LP Turbine | 14.270 | 16.250 | 14.320 | 0.26730 | 0.30710 | 0.19280 | 22.250 | 23.550 | 22.250 | 22.520 | 23.860 | 22.440 | 98.81 | 98.71 | 99.14 |

Preheater 2 | 8.323 | 8.780 | 8.836 | 0.11000 | 011340 | 0.09258 | 7.208 | 7.260 | 10.270 | 7.318 | 7.373 | 10.360 | 98.50 | 98.46 | 99.11 |

HP Pump 2 | 1.884 | 1.928 | 2.567 | 0.02919 | 0.02927 | 0.03147 | 6.349 | 6.338 | 7.437 | 6.378 | 6.367 | 7.469 | 99.54 | 99.54 | 99.58 |

Preheater 1 | 12.590 | 14.370 | 7.501 | 0.18450 | 0.20600 | 0.08467 | 6.831 | 6.946 | 8.588 | 7.016 | 7.152 | 8.673 | 97.37 | 97.12 | 99.02 |

LP Evaporator | 11.470 | 11.840 | 9.752 | 0.12020 | 0.12120 | 0.08335 | 6.024 | 5.976 | 7.036 | 6.144 | 6.098 | 7.120 | 98.04 | 98.01 | 98.83 |

HP Turbine | 6.229 | 6.636 | 9.138 | 0.07441 | 0.07745 | 0.09285 | 14.940 | 15.470 | 18.400 | 15.010 | 15.540 | 18.500 | 99.50 | 99.50 | 99.50 |

LP Pump 1 | 1.637 | 1.700 | 1.478 | 0.03096 | 0.03242 | 0.02011 | 4.003 | 3.888 | 3.683 | 4.034 | 3.920 | 3.703 | 99.23 | 99.17 | 99.46 |

Superheater | 0.456 | 0.469 | 0.520 | 0.00534 | 0.00536 | 0.00518 | 3.963 | 3.956 | 3.881 | 3.968 | 3.962 | 3.886 | 99.87 | 99.86 | 99.87 |

Condenser | 39.110 | 24.910 | 35.070 | 0.32640 | 0.20960 | 0.25110 | 7.139 | 8.880 | 8.392 | 7.465 | 9.090 | 8.643 | 95.63 | 97.69 | 97.09 |

Total | 110.609 | 102.463 | 103.382 | 1.313 | 1.273 | 0.988 | 86.950 | 90.530 | 100.20 | 88.260 | 91.810 | 101.20 | 98.45 | 98.61 | 99.03 |

Z ˙ + C ˙ D , effort to select components with low capital investment cost and operating and maintenance cost might be employed.

This work investigates the thermodynamic, exergoeconomicand optimization of the dual-pressure organic Rankine cycle (DORC) for the utilization of medium temperature geothermal source for power production. Since several literatures [

It is observed that the condenser have the highest rate of exergy destroyed, E ˙ D compared to the other components, which is due to exergy lost to cooling water in the condenser. To minimize this loses in the condenser, hence improve system performance, further investigations may be performed on how to utilize some energy in the LP turbine exit stream for absorption cooling or domestic water heating before entering the condenser.

The authors acknowledge the support of Department of Mechanical Engineering, Faculty of Engineering, Cross River University of Technology, Calabar, Nigeria.

The authors declare no conflicts of interest regarding the publication of this paper.

Igbong, D., Nyong, O., Enyia, J., Oluwadare, B. and Mafel, O. (2021) Exergoeconomic Evaluation and Optimization of Dual Pressure Organic Rankine Cycle (ORC) for Geothermal Heat Source Utilization. Journal of Power and Energy Engineering, 9, 19-40. https://doi.org/10.4236/jpee.2021.99002

The equations for calculating the equipment purchase cost for the turbine, pumps and heat exchangers are expressed as follows [

Z t u r b = C P , t u r b ( F M , t u r b F P , t u r b ) (A.1)

Z p u m p = C P , p u m p ( B 1 , p u m p + B 2 , p u m p F M , p u m p F P , p u m p ) (A.2)

Z H X = C P , H X ( B 1 , H X + B 2 , H X F M , H X F P , H X ) (A.3)

where C P refers to component bare module cost and can be calculated as follows:

log C P , x = K 1 , x + K 2 , x log Y + K 3 , x ( log Y 2 ) (A.4)

where Y in Equation (A.4) indicates the capacity of the turbine and pump, or the area in the case of the heat exchanger. K 1 , K 2 and K 3 are coefficients of equipment cost given in TableA1. F M is the material factor, and B 1 and B 2 are constants given in TableA1. F P is the pressure factor and can be obtained as follows:

log F P , x = C 1 , x + C 2 , x log ( 10 P − 1 ) + C 3 , x ( log ( 10 P − 1 ) ) 2 (A.5)

C 1 , C 2 and C 3 are constants given in TableA1. The Marshall and Swift equipment cost indices [

C 2021 * = C o r i g i n a l cos t C I M . S 2021 C I M . S r e f e r e n c e y e a r (A.6)

The LMTD method has been adopted in the present study to calculate the heat exchange area. The heat transfer rate in heat exchanger can be expressed as [

Q = U k A k Δ T m e a n (A.7)

X | Y | K 1 | K 2 | K 3 | B 1 | B 2 | C 1 | C 2 | C 3 | F M |
---|---|---|---|---|---|---|---|---|---|---|

Turbine | W ˙ t u r b | 2.2476 | 1.4965 | −0.1618 | 0 | 1 | 0 | 0 | 0 | 3.4 |

Pump | W ˙ p u m p | 3.3892 | 0.0536 | 0.1538 | 1.89 | 1.35 | −0.3935 | 0.3957 | −0.0023 | 1.6 |

Heat exchanger | A H X | 4.3247 | −0.3030 | 0.1634 | 1.63 | 1.66 | 0.0388 | −0.1127 | 0.0818 | 1 |

Components | Overall heat transfer coefficient, U_{k} (kW/(m^{2} K)) |
---|---|

Evaporator | 0.9 |

Condenser | 1.1 |

Heat exchanger | 1.0 |

where Δ T m e a n is the logarithmic mean temperature difference between the working fluid and the coolant, and U k is the overall heat transfer coefficient given in TableA2.