# A Comparative Exergoeconomic Analysis of Waste Heat Recovery from a Gas Turbine-Modular Helium Reactor via Organic Rankine Cycles

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## Abstract

**:**

## 1. Introduction

## 2. Configurations of GT-MHR/ORC Combined Cycles

- The combined cycles operate in a steady-state condition.
- Pressure drops through pipes are negligible.
- Isentropic efficiencies for the turbines and pumps in the ORCs are 80% and 85%, respectively.
- Changes in kinetic and potential energies are neglected.
- The effectiveness of the intercooler, the recuperator and the precooler is considered to be 90%.

**Figure 1.**Schematics of the (

**a**) gas turbine modular helium reactor (GT-MHR)/simple organic Rankine cycle (SORC), (

**b**) GT-MHR/ORC with an internal heat exchanger (HORC) and (

**c**) GT-MHR/regenerative organic Rankine cycle (RORC) combined cycles.

## 3. Exergoeconomic Analysis

#### 3.1. Application of SPECO Method to the System

#### 3.1.1. Modeling

_{D}is the exergy destruction rate in the component, Ė

_{Q}is the exergy rate associated with a heat transfer rate and Ė

_{W}is the exergy rate associated with mechanical power.

_{ph}= (h − h

_{0}) − T

_{0}(s − s

_{0})

_{i}and e

_{ch,i}are the mole fraction and specific chemical exergy of working fluid, i, through a component, respectively.

Parameters | Value |
---|---|

P_{0} (kPa) | 100 |

PR_{C} | 1.5–5 |

600 | |

T_{0} (°C) | 25 |

T_{1} (°C) | 700–900 |

T_{C} (°C) | 40 |

T_{E} (°C) | 80–120 |

∆T_{E} (°C) | 2–10 |

∆T_{Sup} (°C) | 0–15 |

η_{P} (%) | 85 |

η_{T} (%) | 80 |

Effectiveness (for IC, R, PC) (%) | 90 |

∆P_{RC} (kPa) | 100 |

∆P_{E}, ∆P_{IC}, ∆P_{PC} (kPa) | 40 |

∆P_{R,HP} (kPa) | 80 |

∆P_{R,LP} (kPa) | 50 |

#### 3.1.2. Defining the Fuel and Product for Each Component

#### 3.1.3. Cost Balances

_{k}). The prediction of the capital investment cost is significant in an economic analysis. In this regard, using vendor quotations or consulting with cost engineers is probably the most precise method. In consulting with cost engineers, after each design modification, the necessary thermodynamic data is submitted to the cost engineer to determine the new purchased-equipment costs. For simplicity, however, in the present work, the cost functions available in the literature are used assuming that the cost values provided by the cost engineer are in agreement with the corresponding values calculated from the cost functions [19]. The cost functions for different components are functions of the parameters important to the component, i.e., the pressure ratio in compressor or turbine and the heat transfer area in heat exchangers. Considering the recuperator, the evaporator, the precooler and the intercooler as heat exchangers, equations for calculating the capital investment of the components can be expressed as described below [12,20].

_{Pump}= 3540Ẇ

_{P}

^{0.71}

_{Condenser}= 1773 ṁ

_{steam}

_{th}(based on data for the year 2003) and $8/MWh, respectively [8,21]. To convert the capital investment into the cost per time unit, one can write [12]:

_{k}= Z

_{k}.CRF.φ / (N × 3600)

_{j}= c

_{j}Ė

_{j}

_{F,k}), the average cost per unit exergy of product (c

_{P,k}), the cost flow rate associated with the exergy destruction (Ċ

_{D}) and the exergoeconomic factor (f

_{k}). Mathematically, exergoeconomic parameters are expressed as [19]:

_{D,k}= c

_{F,k}Ė

_{D,k}

_{k}, suggests purchasing a less expensive component at the expense of exergy destruction (fuel) cost.

## 4. Results and Discussion

#### 4.1. Exergoeconomic Analysis

State No. | GT-MHR/SORC | GT-MHR/HORC | GT-MHR/RORC | |||

Ċ ($/s) | c ($/GJ) | Ċ ($/s) | c ($/GJ) | Ċ ($/s) | c ($/GJ) | |

1 | 17.17 | 11.83 | 17.15 | 11.83 | 17.20 | 11.83 |

2 | 10.55 | 11.83 | 10.53 | 11.83 | 10.59 | 11.83 |

3 | 7.428 | 11.83 | 7.419 | 11.83 | 7.444 | 11.83 |

4 | 7.016 | 11.83 | 7.015 | 11.83 | 7.046 | 11.83 |

5 | 6.936 | 11.83 | 6.927 | 11.83 | 6.953 | 11.83 |

6 | 8.565 | 12.15 | 8.558 | 12.15 | 8.582 | 12.15 |

7 | 8.347 | 12.15 | 8.338 | 12.15 | 8.362 | 12.15 |

8 | 10.05 | 12.39 | 10.04 | 12.39 | 10.06 | 12.39 |

9 | 13.18 | 12.56 | 13.17 | 12.56 | 13.22 | 12.56 |

10 | 0.010 | 32.46 | 0.0009 | 18.5 | 0.0008 | 18.05 |

11 | 0.434 | 18.36 | 0.010 | 32.61 | 0.001 | 24.10 |

12 | 0.045 | 18.36 | 0.021 | 36.05 | 0.007 | 24.22 |

13 | 0.0009 | 18.36 | 0.438 | 18.50 | 0.016 | 28.98 |

14 | 0 | 0 | 0.046 | 18.50 | 0.427 | 18.05 |

15 | 0.085 | 72.86 | 0.039 | 18.50 | 0.006 | 18.05 |

16 | 0 | 0 | 0 | 0 | 0.042 | 18.05 |

17 | 0.222 | 59.80 | 0.093 | 66.88 | 0 | 0 |

18 | 0 | 0 | 0 | 0 | 0.098 | 64.10 |

19 | 0.050 | 47.9 | 0.224 | 59.69 | 0 | 0 |

20 | - | - | 0 | 0 | 0.224 | 59.56 |

21 | - | - | 0.044 | 45.52 | 0 | 0 |

22 | - | - | - | - | 0.046 | 50.73 |

Nuclear fuel | 2.424 | 4.040 | 2.422 | 4.036 | 2.422 | 4.036 |

Ẇ_{T} | 6.843 | 12.56 | 6.843 | 12.55 | 6.837 | 12.56 |

Ẇ_{C,HP} | 1.695 | 12.56 | 1.695 | 12.55 | 1.692 | 12.56 |

Ẇ_{C,LP} | 1.622 | 12.56 | 1.624 | 12.55 | 1.622 | 12.56 |

Ẇ_{T,ORC} | 0.458 | 26.68 | 0.461 | 26.89 | 0.449 | 26.21 |

Ẇ_{P,ORC} | 0.0085 | 26.68 | 0.0085 | 26.89 | 0.0006 | 26.21 |

Ẇ_{P2,ORC} | - | - | - | - | 0.008 | 26.21 |

Component | GT-MHR/SORC | GT-MHR/HORC | GT-MHR/RORC | |||||||||

Ė_{D} | ε | Ċ_{D} | f | Ė_{D} | ε | Ċ_{D} | f | Ė_{D} | ε | Ċ_{D} | f | |

(kW) | (%) | ($/s) | (%) | (kW) | (%) | ($/s) | (%) | (kW) | (%) | ($/s) | (%) | |

Reactor core | 198,088 | 87.99 | 1.874 | 45.51 | 198,122 | 87.98 | 1.874 | 45.52 | 197,980 | 88.02 | 1.874 | 45.51 |

Turbine | 14,868 | 97.34 | 0.176 | 55.40 | 14,878 | 97.34 | 0.176 | 55.37 | 14,837 | 97.35 | 0.176 | 55.54 |

Recuperator | 25,397 | 90.37 | 0.301 | 4.262 | 25,315 | 90.38 | 0.299 | 4.275 | 25,605 | 90.36 | 0.303 | 4.238 |

Evaporator | 11,436 | 67.10 | 0.153 | 8.339 | 11,035 | 67.64 | 0.131 | 9.154 | 10,591 | 68.57 | 0.125 | 8.997 |

Precooler | 5599 | 17.22 | 0.066 | 6.760 | 6054 | 18.65 | 0.072 | 6.281 | 6324 | 19.41 | 0.075 | 6.048 |

LP compressor | 10,536 | 91.84 | 0.132 | 5.180 | 10,541 | 91.85 | 0.132 | 5.181 | 10,520 | 91.86 | 0.132 | 5.186 |

Intercooler | 14,226 | 20.68 | 0.173 | 2.180 | 14,368 | 20.71 | 0.175 | 2.158 | 14,354 | 20.76 | 0.174 | 2.166 |

HP compressor | 10,830 | 91.98 | 0.136 | 5.119 | 10,835 | 91.98 | 0.136 | 5.120 | 10,815 | 91.98 | 0.136 | 5.125 |

ORC turbine | 4014 | 81.05 | 0.074 | 48.56 | 4013 | 81.03 | 0.074 | 48.37 | 6221 | 81.41 | 0.112 | 38.07 |

Condenser | 1369 | 43.29 | 0.025 | 18.59 | 1081 | 46.91 | 0.020 | 22.54 | 1352 | 40.25 | 0.024 | 17.98 |

Pump | 320 | 85.43 | 0.009 | 10.36 | 45.85 | 85.43 | 0.001 | 44.19 | 3.084 | 85.46 | 0 | 64.02 |

Pump 2 | - | - | - | - | - | - | - | - | 43.87 | 85.88 | 0.001 | 45.69 |

IHE | - | - | - | - | 135 | 66.15 | 0.002 | 56.32 | - | - | - | - |

OFOF | - | - | - | - | - | - | - | - | 78 | 78.73 | 0.002 | - |

Overall | 296,683 | 49.61 | 3.101 | 38.1 | 296,425 | 49.58 | 3.092 | 38.22 | 298,724 | 49.56 | 3.134 | 37.85 |

_{D}among the other components in all three combined cycles. The f value of this component is almost 45.5% and indicates that the exergy destruction cost in this component dominates the owning and operating cost. Furthermore, the reactor core has the highest value of exergy destruction in combined cycles.

_{D}. The very low value of f for this component indicates that the exergy destruction cost rate of the recuperator is significantly higher than the owning and operating cost rate for it. Thus, selecting more expensive components will be helpful in improving the exergoeconomic performance. This can be performed through increasing the heat transfer area. The relatively higher value of exergy destruction in the recuperator is mainly due to the temperature differences between the recuperator streams.

_{D}and the very low value of f for the HP and LP compressors suggest that greater capital investments are appropriate, i.e., higher values of the pressure ratio and isentropic efficiency.

_{D}associated with these components are the lowest of the combined cycles.

#### 4.2. Parametric Study

_{C}, the turbine inlet temperature, T

_{1}, and the temperature of the evaporator, T

_{E}. The important exergoeconomic parameters are: the unit cost of electricity produced by the ORC turbine, c

_{W,T,ORC}, and the total exergy destruction cost rate, Ċ

_{D,total}.

**Figure 2.**The effects of T

_{1}on the (

**a**) unit cost of electricity produced by the ORC turbine and (

**b**) the total exergy destruction cost rate.

_{1}increases both the Ẇ

_{T,ORC}and Ċ

_{W,T,ORC}. However, these variations are such that the net effect is an increase in c

_{W,T,ORC}, as shown in Figure 2a. Furthermore, this figure shows that the GT-MHR/RORC has the lowest c

_{W,T,ORC}.

_{1}decreases Ċ

_{D,total}. This is mainly due to a considerable decrease in the reactor core exergy destruction cost, which constitutes about 60% of the total exergy destruction cost (see Table 3). This trend is the same in all three combined cycles.

_{1}is recommended.

_{W,T,ORC}and Ċ

_{D,total}with the compressor pressure ratio are shown in Figure 3.

**Figure 3.**The effects of PR

_{C}on the (

**a**) unit cost of electricity produced by the ORC turbine and (

**b**) the total exergy destruction cost rate.

_{T,ORC}and Ċ

_{W,T,ORC}have a minimum value with respect to the PR

_{C}. As a result, c

_{W,T,ORC}is minimized at a particular value of PR

_{C}, as shown in Figure 3a.

_{C}increases, the exergy destruction and its associated cost decreases for some components and increases for others. The net effect is shown in Figure 3b.

_{E}on important exergoeconomic parameters for three considered combined cycles.

**Figure 4.**The effects of T

_{E}on the (

**a**) unit cost of electricity produced by the ORC turbine and (

**b**) the total exergy destruction cost rate.

_{E}on c

_{W,T,ORC}is similar to that for PR

_{C}. However, in this case, the minimum occurs at high evaporator temperatures.

_{E}, as shown in Figure 4b. The reason for this is that, as T

_{E}increases, the enthalpy drops of the working fluids across the ORC turbines increase, while their mass flow rates decrease. However, the net effect is the maximization of the produced power and, consequently, the exergy efficiency of ORC at the mentioned value of T

_{E}. Maximum exergy efficiency means minimum exergy destruction and its associated costs.

_{C}and the T

_{E}have optimum values from the exergoeconomic viewpoint and a lower or a higher value of these parameters results in a higher unit cost of electricity produced by the ORC turbine.

## 5. Conclusions

## Nomenclature

A | heat transfer area (m ^{2}) |

c | cost per unit exergy ($/kJ) |

Ċ | cost rate ($/s) |

e | specific exergy (kJ/kg) |

Ė | exergy rate (kW) |

f | exergoeconomic factor |

h | specific enthalpy (kJ/kg) |

IHE | internal heat exchanger |

ṁ | mass flow rate (kg/s) |

OFOF | open feed organic fluid |

P | pressure (bar, kPa) |

PR_{C} | compressor pressure Ratio |

heat transfer rate (kW) | |

R | gas constant (kJ/kg K) |

s | specific entropy (kJ/kg K) |

T | temperature (°C, K) |

Ẇ | electrical power (kW) |

X | mole fraction |

Z | capital cost of a component ($) |

Ż | capital cost rate ($/s) |

## Greek letters

η | isentropic efficiency |

ε | exergy efficiency |

∆T_{E} | pinch point temperature difference in the evaporator |

∆T_{Sup} | degree of superheat at the inlet to the ORC turbine |

## Subscripts

0 | dead (environmental) state |

1, 2, 3, … | cycle locations |

C | condenser |

ch | chemical exergy |

D | destruction |

e | outlet |

E | evaporator |

F | fuel |

HE | heat exchanger |

HP | high pressure |

IC | intercooler |

i | inlet |

j | j-th stream |

k | k-th component |

L | loss |

LP | low pressure |

P | pump, product |

PC | precooler |

ph | physical exergy |

q | heat |

R | recuperator |

RC | reactor core |

T | turbine |

w | power |

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Shokati, N.; Mohammadkhani, F.; Yari, M.; Mahmoudi, S.M.S.; Rosen, M.A. A Comparative Exergoeconomic Analysis of Waste Heat Recovery from a Gas Turbine-Modular Helium Reactor via Organic Rankine Cycles. *Sustainability* **2014**, *6*, 2474-2489.
https://doi.org/10.3390/su6052474

**AMA Style**

Shokati N, Mohammadkhani F, Yari M, Mahmoudi SMS, Rosen MA. A Comparative Exergoeconomic Analysis of Waste Heat Recovery from a Gas Turbine-Modular Helium Reactor via Organic Rankine Cycles. *Sustainability*. 2014; 6(5):2474-2489.
https://doi.org/10.3390/su6052474

**Chicago/Turabian Style**

Shokati, Naser, Farzad Mohammadkhani, Mortaza Yari, Seyed M. S. Mahmoudi, and Marc A. Rosen. 2014. "A Comparative Exergoeconomic Analysis of Waste Heat Recovery from a Gas Turbine-Modular Helium Reactor via Organic Rankine Cycles" *Sustainability* 6, no. 5: 2474-2489.
https://doi.org/10.3390/su6052474