# Modeling of a Combined Kalina and Organic Rankine Cycle System for Waste Heat Recovery from Biogas Engine

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Description

#### 2.1. CHP Engine

#### 2.2. Combined KC and ORC

## 3. Mathematical Method

#### 3.1. General Equations

#### 3.2. The Kalina Cycle

#### 3.3. The Rankine Cycle

#### 3.4. Economic Estimation

## 4. Results and Discussion

^{®}Professional software program by determining the optimum ratio of the ammonia–water mixture for the KC as well as the optimum working fluid for the ORC. In Table 6, the best performing cycle’s thermodynamical results obtained using the simulation program are shown.

#### 4.1. The Optimization of the Single KC with Different Mass Fractions of Working Fluids

#### 4.2. Optimization of ORC with Different Working Fluids with HEX and No HEX

#### 4.3. Result Comparison of Combined Best Performed KC and ORC with R123 Working Fluid

#### 4.4. Economical Result

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | area (m^{2}) |

ASHRAE | American society of heating, refrigerating and air-conditioning engineers |

CF | capacity factor |

CHP | combined heat and power |

CRF | capital recovery factor |

EPC | electrical performance capacity (%) |

$\dot{E}$ | exergy flow (kW) |

GT | gas turbine |

GWP | global warming potential |

h | enthalpy (kJ/kg) |

i | interest rate (%) |

HEX | heat exchanger |

HTR | high temperature recuperator |

KC | Kalina Cycle |

LHV | low heating value (kJ/kg) |

LMTD | logarithmic mean temperature difference |

LTR | low temperature recuperator |

MEP | biogas engine electrical power (kW) |

MPC | biogas engine mechanical performance capability (%) |

$\dot{m}$ | mass flow rate (kg/s) |

N | lifetime (year) |

NOE | number of engines |

n | annual operation time (hour) |

ODP | ozone depletion potential |

ORC | Organic Rankine Cycle |

$\dot{Q}$ | heat flow (kW) |

P | pressure (bar) |

PB | payback period (year) |

PEC | purchased equipment cost ($) |

RC | Rankine cycle |

s | entropy (kJ/kgK) |

${T}_{0}$ | ambient temperature (°C) |

T | temperature (°C) |

TIT | turbine inlet temperature (°C) |

TPC | thermal performance capacity |

TIP | turbine inlet pressure (bar) |

U | heat transfer coefficient (kW/m^{2}K) |

$\dot{W}$ | power (kW) |

X | ammonia-water mass fraction ratio (%) |

Greek Letters | |

$\psi $ | specific exergy (kJ/kg) |

$\epsilon $ | exergetic efficiency (%) |

$\u03f5$ | burner effectiveness (%) |

$\eta $ | thermal efficiency (%) |

ϕ | maintenance factor |

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**Figure 2.**Combined cogeneration cycle including KC and ORC for recovering waste heat of exhaust gas and jacket water of the engine (pipes 1–13 KC, pipes 14–21 ORC, pipes 22–24 KC cooling water, pipes 25–27 ORC cooling water, pipes 28–30 water heating, pipes 31–33 flue gas and pipes 34–36 jacket water).

**Figure 3.**Temperature-entropy (T-s) diagram of the combined system (the blue lines indicate constant pressure and purple lines indicate constant enthalpy).

**Figure 4.**Temperature-Entropy diagram of working fluids (

**a**) R123, (

**b**) R124, (

**c**) Ammonia-water and (

**d**) R236ea respectively (the blue lines indicate constant pressure and purple lines indicate constant enthalpy).

**Figure 5.**Effect of turbine inlet temperature for different pressures and mixing ratio of working fluid on net power of the Kalina Cycle.

**Figure 7.**Effect of turbine inlet temperature, pressure and mixing ratio of working fluid on the net thermal efficiency of Kalina Cycle.

**Figure 8.**Effect of turbine inlet temperature, turbine inlet pressure and mixing ratio of working fluid on exergy efficiency of KC.

**Figure 10.**Effects of turbine inlet temperature and pressure on ORC exergy efficiency for various working fluids.

**Figure 11.**For various working fluids, the effect of turbine inlet temperature and pressure on the net thermal efficiency of the ORC.

**Figure 12.**The sequence of TIT and TIP on net power, exergy efficiency and energy efficiency of combined KC and ORC.

**Figure 13.**The effect of turbine inlet temperature and pressure on the combined KC, ORC, and Jacket Water Heating’s (Cogeneration) net thermal efficiency and exergy efficiency.

Parameter | Value | Unit |
---|---|---|

${T}_{jacketw;in}$ | 70 | °C |

${T}_{jacketw;out}$ | 86 | °C |

${\eta}_{{pump}_{ORC}}$ | 80 | % |

${\eta}_{{pump}_{KC}}$ | 80 | % |

${\eta}_{{turbine}_{ORC}}$ | 82 | % |

${\eta}_{{turbine}_{KC}}$ | 82 | % |

${T}_{coldw;in}$ | 20 | °C |

${T}_{KC;exg,in}$ | 450 | °C |

${T}_{KC;exg,out}$ | 120 | °C |

${P}_{KC;tur,in}$ | 90 | Bar |

${P}_{KC;tur,out}$ | 10.5 | Bar |

${P}_{ORCC,R123;tur,in}$ | 35 | Bar |

${P}_{ORCC,R123;tur,out}$ | 1 | Bar |

${P}_{ORCC,R124;tur,in}$ | 35 | Bar |

${P}_{ORCC,R124;tur,out}$ | 4 | Bar |

${P}_{ORCC;R236tur,in}$ | 33 | Bar |

${P}_{ORCC;R236tur,out}$ | 2 | Bar |

MPC | 40.6 | % |

EPC | 39.3 | % |

TPC | 37.2 | % |

MEP | 600 | kWe |

NOE | 2 | piece |

${\dot{m}}_{exhaust}$ | 2 | Kg/s |

${T}_{exhaust,out}$ | 450 | °C |

Fluid | Formula | Critical Pressure (bar) | Critical Temperature (°C) | Destruction Temperature (°C) | GWP | ODP | ASHRAE |
---|---|---|---|---|---|---|---|

R123 | CHClCF3 | 36.61 | 183.68 | 326.85 | 77 | 0.018 | B |

R124 | CHClFCF3 | 36.20 | 122.00 | 196.85 | 527 | 0.022 | A1 |

R236ea | CF3CHFCF2 | 34.20 | 139.29 | 138.85 | 1200 | 0.000 | Unknown |

Components | Mass and Energy | Exergy |
---|---|---|

Evaporator | ${\dot{m}}_{31}={\dot{m}}_{32}={\dot{m}}_{exg}$ ${\dot{m}}_{4}={\dot{m}}_{5}={\dot{m}}_{KC;mix}$ ${\dot{Q}}_{eva}={\dot{m}}_{KC;mix}({h}_{5}-{h}_{4})$ | ${\dot{E}}_{eva,dest}={\dot{m}}_{exg}\left({\psi}_{31}-{\psi}_{32}\right)-{\dot{m}}_{KC;mix}\left({\psi}_{5}-{\psi}_{4}\right)$ ${\epsilon}_{eva}=\frac{{\dot{m}}_{KC;mix}({\psi}_{5}-{\psi}_{4})}{{\dot{m}}_{exg}({\psi}_{31}-{\psi}_{32})}$ |

Turbine | ${\dot{m}}_{6}={\dot{m}}_{7}={\dot{m}}_{KC;mix}-{\dot{m}}_{8}={\dot{m}}_{a}$ ${\dot{W}}_{KC;tur}={\dot{m}}_{a}\left({h}_{6}-{h}_{7}\right)$ ${\eta}_{KC;tur}=\frac{{\dot{W}}_{KC;tur}}{{\dot{W}}_{KC;tur,s}}$ | ${\dot{W}}_{KC;tur,rev}={\dot{m}}_{a}\left({\psi}_{6}-{\psi}_{7}\right)$ ${\dot{E}}_{KC;tur,dest}={\dot{W}}_{KC;tur,rev}-{\dot{W}}_{KC;tur}$ ${\epsilon}_{t}=\frac{{\dot{W}}_{KC;tur}}{{\dot{W}}_{KC;tur,rev}}$ |

LHEX | ${\dot{m}}_{2}={\dot{m}}_{3}={\dot{m}}_{34}={\dot{m}}_{35}={\dot{m}}_{KC}$ ${\dot{Q}}_{LHEX}={\dot{m}}_{KC;}\left({h}_{3}-{h}_{2}\right)$ | ${\dot{E}}_{LHEX,dest}={\dot{m}}_{34}\left({\psi}_{34}-{\psi}_{35}\right)-{\dot{m}}_{2}\left({\psi}_{3}-{\psi}_{2}\right)$ ${\epsilon}_{LHEX}=\frac{{\dot{m}}_{2}\left({\psi}_{3}-{\psi}_{2}\right)}{{\dot{m}}_{34}\left({\psi}_{34}-{\psi}_{35}\right)}$ |

HHEX | ${\dot{m}}_{3}={\dot{m}}_{4}={\dot{m}}_{KC}$ ${\dot{m}}_{8}={\dot{m}}_{9}={\dot{m}}_{KC}-{\dot{m}}_{6}={\dot{m}}_{s}$ ${\dot{Q}}_{HHEX}={\dot{m}}_{KC}\left({h}_{4}-{h}_{3}\right)$ | ${\dot{E}}_{HHEX,dest}={\dot{m}}_{s}\left({\psi}_{8}-{\psi}_{9}\right)-{\dot{m}}_{KC}\left({\psi}_{4}-{\psi}_{3}\right)$ ${\epsilon}_{HHEX}=\frac{{\dot{m}}_{KC;mix}\left({\psi}_{4}-{\psi}_{3}\right)}{{\dot{m}}_{s}\left({\psi}_{8}-{\psi}_{9}\right)}$ |

Condenser | ${\dot{m}}_{13}={\dot{m}}_{1}={\dot{m}}_{KC,mix}$ ${\dot{m}}_{23}={\dot{m}}_{24}={\dot{m}}_{cond}$ ${\dot{Q}}_{KC;cond}={\dot{m}}_{KC,mix}\left({h}_{13}-{h}_{1}\right)$ | ${\dot{E}}_{cond,dest}={\dot{m}}_{KC,mix}\left({\psi}_{13}-{\psi}_{1}\right)-{\dot{m}}_{cond}\left({\psi}_{24}-{\psi}_{23}\right)$ ${\epsilon}_{KC;cond}=\frac{{\dot{m}}_{cond}\left({\psi}_{24}-{\psi}_{23}\right)}{{\dot{m}}_{KC,mix}\left({\psi}_{13}-{\psi}_{1}\right)}$ |

Pump | ${\dot{m}}_{1}={\dot{m}}_{2}={\dot{m}}_{KC;mix}$ ${\dot{W}}_{KC;pump}={\dot{m}}_{KC;mix}\left({h}_{2}-{h}_{1}\right)$ ${\eta}_{KC;pump}=\frac{{\dot{W}}_{KC;pump,s}}{{\dot{W}}_{KC;pump}}$ | ${\dot{W}}_{KC;pump,rev}={\dot{m}}_{KC;mix}\left({\psi}_{2}-{\psi}_{1}\right)$ ${\dot{E}}_{KC;pump,dest}={\dot{W}}_{KC;pump}-{\dot{W}}_{KC;pump,rev}$ ${\epsilon}_{KC;pump}=\frac{{\dot{W}}_{KC;pump,rev}}{{\dot{W}}_{KC;pump}}$ |

**Table 4.**The cost equations of each equipment used in the Kalina and Rankine Cycles [27].

Rankine Cycle | |

System Component | Purchased Equipment Cost (PEC) |

Preheater | $130{\left({A}_{prh}/0.093\right)}^{0.78}$ |

Evaporator | $130{\left({A}_{eva}/0.093\right)}^{0.78}$ |

Superheater | $130{\left({A}_{sph}/0.093\right)}^{0.78}$ |

Turbine | $6000{\left({\dot{W}}_{RC;tur}\right)}^{0.7}$ |

Condenser | $588{\left({A}_{RC;cond}\right)}^{0.8}$ |

Pump | $3540{\left({\dot{W}}_{RC;pump}\right)}^{0.7}$ |

Kalina Cycle | |

System Component | Purchased Equipment Cost (PEC) |

Turbine | $4405{\left({\dot{W}}_{KC;tur}\right)}^{0.7}$ |

Condenser | $1397{\left({A}_{KC;cond}\right)}^{0.89}$ |

Pump | $1120{\left({\dot{W}}_{KC;pump}\right)}^{0.8}$ |

LTR | $2681{\left({A}_{KC;ltr}\right)}^{0.59}$ |

HTR | $2681{\left({A}_{KC;htr}\right)}^{0.59}$ |

Evaporator | $1397{\left({A}_{KC;cond}\right)}^{0.89}$ |

**Table 5.**Constraints economical estimation [27].

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

Operation time in one year $\left(n\right)$ | hour | 7680 |

Rate of interest $\left(i\right)$ | % | 15 |

Factor of maintenance $\left(\varphi \right)$ | % | 6 |

Activity lifetime $\left(N\right)$ | year | 15 |

Factor of capacity (FC) | - | 0.89 |

Number | Component | Pressure | Temperature | Enthalpy | Mass Flow | Energy Flow | Density | Entropy | Exergy |
---|---|---|---|---|---|---|---|---|---|

bar | °C | kJ/kg | kg/s | kW | kg/m³ | kJ/kgK | kJ/kg | ||

1 | Pump KC in | 10.50 | 30.04 | 372.50 | 0.35 | 131.29 | 640.88 | 1.77 | 203.52 |

2 | Pump KC out | 90.00 | 32.38 | 387.95 | 0.35 | 136.73 | 644.60 | 1.78 | 216.02 |

3 | L HEX KC out | 89.95 | 85.19 | 650.21 | 0.35 | 229.17 | 563.30 | 2.57 | 248.05 |

4 | Evaporator KC in | 88.95 | 85.18 | 650.21 | 0.35 | 229.17 | 563.14 | 2.57 | 247.91 |

5 | Evaporator KC out | 88.95 | 430.00 | 2703.95 | 0.35 | 953.02 | 27.18 | 7.03 | 1003.64 |

6 | Turbine KC in | 90.00 | 88.95 | 430.00 | 2703.95 | 0.35 | 953.02 | 7.03 | 1003.64 |

7 | Turbine KC out | 10.50 | 220.84 | 2199.76 | 0.35 | 775.31 | 4.47 | 7.18 | 453.64 |

8 | Separator KC out | 88.95 | 128.60 | 908.56 | 0.00 | 0.00 | 460.16 | 3.25 | 308.69 |

9 | H HEX KC out | 87.95 | 127.95 | 908.56 | 0.00 | 0.00 | 445.84 | 3.25 | 308.53 |

13 | Condenser KC in | 10.50 | 220.84 | 2199.76 | 0.35 | 775.31 | 4.47 | 7.18 | 453.64 |

31 | Evaporator KC Gas in | 1.20 | 450.00 | 488.24 | 2.00 | 976.48 | 0.57 | 7.98 | 202.11 |

32 | Evaporator KC Gas out | 1.20 | 120.00 | 126.31 | 2.00 | 252.62 | 1.04 | 7.31 | 34.07 |

23 | Water Condenser KC in | 2.00 | 15.01 | 63.20 | 15.41 | 973.77 | 0.22 | 0.16 | |

24 | Water Condenser KC out | 1.50 | 25.01 | 105.00 | 15.41 | 1617.79 | 997.07 | 0.37 | 0.40 |

14 | Pump ORC in | 1.00 | 27.46 | 227.65 | 0.85 | 193.32 | 1457.58 | 1.10 | 0.15 |

15 | Pump ORC out | 35.10 | 29.23 | 230.57 | 0.85 | 195.79 | 1463.08 | 1.10 | 2.51 |

21 | HEX ORC in | 35.05 | 38.00 | 239.54 | 0.85 | 203.41 | 1441.01 | 1.13 | 2.96 |

11 | Evaporator ORC in | 35.05 | 180.17 | 415.30 | 0.85 | 352.66 | 780.89 | 1.58 | 45.66 |

10 | Superheater ORC in | 35.05 | 180.98 | 455.15 | 0.85 | 386.50 | 361.94 | 1.67 | 59.96 |

19 | Turbine ORC in | 35.00 | 185.00 | 469.44 | 0.85 | 398.63 | 288.45 | 1.70 | 65.11 |

20 | Turbine ORC out | 1.00 | 55.09 | 417.66 | 0.85 | 354.67 | 5.79 | 1.73 | 6.98 |

17 | Preheater ORC out | 1.00 | 42.61 | 408.70 | 0.85 | 347.05 | 6.04 | 1.70 | 6.10 |

26 | Water Condenser ORC in | 2.00 | 15.01 | 63.20 | 4.60 | 290.60 | 999.15 | 0.22 | 0.16 |

27 | Water Condenser ORC out | 1.50 | 23.01 | 96.64 | 4.60 | 444.33 | 997.56 | 0.34 | 0.23 |

Cycle | Component | Exergy Inlet (kW) | Exergy Outlet (kW) | Exergy Destruction (kW) | Exergy Efficiency (%) |
---|---|---|---|---|---|

Kalina | Pump | 77.19 | 76.14 | 1.05 | 98.64 |

L HEX | 506.50 | 500.45 | 6.06 | 98.80 | |

Evaporator | 491.59 | 421.89 | 69.70 | 85.82 | |

Separator | 353.74 | 353.74 | 0.00 | 100.00 | |

Turbine | 353.74 | 334.04 | 19.70 | 94.43 | |

H HEX | 87.43 | 87.38 | 0.05 | 99.94 | |

Condenser | 162.41 | 77.83 | 84.58 | 47.92 | |

ORC R123 | Pump | 16.06 | 15.65 | 0.42 | 97.41 |

Evaporator | 166.34 | 142.45 | 23.89 | 85.64 | |

Preheater | 128.07 | 127.84 | 0.23 | 99.82 | |

Superheater | 175.13 | 92.24 | 82.88 | 52.67 | |

Turbine | 61.73 | 58.36 | 3.37 | 94.53 | |

Condenser | 24.75 | 15 | 9.74 | 60.63 |

**Table 8.**ORC and KC Equipment costs [26].

Part | ORC (PEC)-DOLLAR | Part | KC (PEC)-DOLLAR |
---|---|---|---|

Pump | $6572.92 | Pump | $4352.45 |

Recuperator | $3870.87 | LTR | $12,763.80 |

Preheater | $1556.91 | HTR | $14,705.62 |

Evaporator | $9663.83 | Evaporator | $9239.20 |

Superheater | $630.67 | Turbine | $163,151.63 |

Turbine | $85,827.57 | Condenser | $20,993.74 |

Condenser | $1478.87 |

**Table 9.**Combined Cycle payback period [26].

Acceptions-Maximum Point | ||||||||
---|---|---|---|---|---|---|---|---|

n (Plantlife) | N (Annual Operation Time | i (Interest Rate) | Operation and Maintenance Factor | Electrical Sale Value | Maintenance Operation Cost | Purchased Equipment Cost (PEC) | OVERALL NET POWER | Payback Period |

Year | Hour | - | - | $/kWh | $ | $ | kW | Years |

15 year | 7680 year/h | 0.12 | mf = 1.06 | KALİNA + ORC | KALİNA + ORC | |||

15.00 | 7680.00 | 0.15 | 1.060 | 0.07 | 2008.85 | 334,807.63 | 211.04 | 4.29 |

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**MDPI and ACS Style**

Öksel, C.; Koç, A.
Modeling of a Combined Kalina and Organic Rankine Cycle System for Waste Heat Recovery from Biogas Engine. *Sustainability* **2022**, *14*, 7135.
https://doi.org/10.3390/su14127135

**AMA Style**

Öksel C, Koç A.
Modeling of a Combined Kalina and Organic Rankine Cycle System for Waste Heat Recovery from Biogas Engine. *Sustainability*. 2022; 14(12):7135.
https://doi.org/10.3390/su14127135

**Chicago/Turabian Style**

Öksel, Cem, and Ali Koç.
2022. "Modeling of a Combined Kalina and Organic Rankine Cycle System for Waste Heat Recovery from Biogas Engine" *Sustainability* 14, no. 12: 7135.
https://doi.org/10.3390/su14127135