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In this paper the SOFC-GT-Kalina (solid oxide fuel cell, gas turbine, and Kalina cycle) integrated system is proposed. The system uses Kalina cycle as the bottoming cycle to recovery the waste heat from the gas turbine to generate power. Kalina cycle uses ammonia-water mixture as the work fluid which has sliding-temperature boiling characteristics. By comparing with the SOFC-GT-ST (solid oxide fuel cell, gas turbine, and steam turbine cycle) system as the reference system, the systems are simulated by Aspen Plus through analyzing the overall system performance. Electrical and exergy efficiency of the proposed system are 74.41% and 71.93%, and electrical and exergy efficiency of the reference system are 71.45% and 69.07%, proving the superiority of Kalina cycle for waste heat recovery. In addition, the exergy losses of each component are studied, and the detail performance analysis of the proposed system is presented, consisting of thermal analysis, exergy analysis and EUD (Energy-utilization diagram) analysis, which intuitively disclosed the causes of exergy loss. Additionally, it was revealed that there exists an optimal current density at 350 mA/cm2 for power and power density.

Now, distributed power systems are more and more popular, because it can reduce losses during transmission and distribution of power; in addition, it can flexibly adjust to user demand change. As a kind of modular power generation device, SOFC is suitable for distributed power generation. SOFC has a lot of advantages, for example it can directly convert chemical energy of fuel into electricity with little pollution, which is different from the traditional power generation mode being limited by Carnot cycle efficiency. In addition, because of its high operating temperature, its high-temperature exhaust gas (about 650˚C - 1000˚C) can be used to drive combined cycle [

The concept of SOFC-GT integrated system has been proposed for many years. Ali Volkan Akkaya etc. [_{2} for operation on natural gas. The authors [_{2} emission. Paper [_{2} capture in existing IGCC power plants utilizing high percentage(up to 70%) biomass co-gasification [

Kalina cycle is put forward to improve Rankine cycle; it can be used as bottom cycle to recover the waste heat from the gas turbine to generate power. Kalina cycle uses ammonia-water mixture as the working fluid which has sliding-temperature boiling characteristics. On the other hand, due to the boiling point of ammonia is much lower than water, it can be easily gasified at low temperature [

As can be seen, in Kalina cycle temperature match can be improved, which can improve the heat exchange process. Previous studies have combined the first law of thermodynamics, the second law of thermodynamics, parameter optimization, system economics analysis, artificial neural network analysis, EES engineering equation solver, genetic algorithm, etc., having guiding significance for further study. But little research has been found to use Kalina cycle to recover SOFC-GT waste heat as well as do comprehensive performance analysis of the SOFC-GT-Kalina system. The objective of the study is to present a thermodynamic analysis of SOFC-GT-Kalina cycle based on the first and second law of thermodynamics, as well as the comparison with SOFC-GT-ST system, at the same time, using EUD analysis method to disclose the nature of exergy loss.

pressure gas (13) flow into GT and generate electricity there. The exhaust gas from GT (14) is sequentially used to preheat the air, and then (15) flow into Kalina cycle or Rankine cycle for further heat recovery, in this way to realize the cascade utilization of energy and improve the efficiency of the overall system.

The basic Kalina cycle (KC) is similar with Rankine cycle (RC), mainly consisting of HRSG, turbine and condenser, the main difference is that Kalina cycle uses a distillation subsystem to solve the condensation problem of ammonia-water mixture.

In the proposed system, KC uses ammonia-water mixture as working fluid. The saturated working fluid (NH_{3}/H_{2}O) is boosted through high-pressure pump (01), then turns into superheated gas (02) in an ammonia generator which can generate power in AT. Exhaust steam (03) from AT is cooled by regenerator, and mixes with rich aqueous solution (014) from the bottom of the distillation to form the basic solution (05), then condensed completely to saturated liquid (06) through the low-pressure condenser and boosted through low-pressure pump (08). Stream (08) flows into the Sep, a surge (09) after being heated by regenerator (010) flows into the distillation, then separated into rich ammonia solution (011) and rich aqueous solution (012); Another surge mixes with the rich ammonia solution (011) to form working solution (016), then through high-pressure condenser is condensed into saturated working solution (NH_{3}∙H_{2}O), in this way to complete the cycle.

In the reference system, RC uses water as working fluid, and produces high pressure (01) and high temperature steam (02) which can generate power in ST.

The parameters and structural size involved in the process simulationis according to the tubular designed by Siemens-Westinghouse, as shown in

We also need to make some assumptions for calculation as follows:

1) Considering the velocity of the fluid flow through the relevant components, heat losses from system to environment are negligible; 2) Temperature and pressure inside the battery are almost uniform, all the battery cells within the stack are in the same state; 3) Due to the high temperature and low pressure, the reaction gas can be regard as ideal compressible gas; 4) Because of good sealing, the mass loss of each component is ignored; 5) The dynamic performance of the system is not considered in this paper, all reactions are in equilibrium state, and SOFC works under steady-state operation; 6) The process is relatively short through the cell stack, the mass and pressure loss in it are negligible. These assumptions may have certain error effect on the absolute values of the calculation results, but do not affect the understanding of the system law.

To evaluate the performance of the system, the first law and the second law method can be used. For the first law perspective, performance indicators mainly include: current density, voltage, power, electrical efficiency and power density. For the second law perspective, performance indicators mainly include: exergy losses and exergy efficiency. The formulas in this paper are based on the classical formulas in the literature [

Parameter | Size |
---|---|

Battery length | 150 cm |

Battery outer diameter | 2.2 cm |

Cell reaction area | 260 cm^{2} |

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

Fuel inlet temperature/˚C | 25 | Air inlet temperature/˚C | 25 |

Fuel inlet pressure/bar | 1 | Air inlet pressure/bar | 1 |

Steam/carbon ratio | 2.5 | DC-AC conversion efficiency/% | 98 |

SOFC heat loss/% | 2 | SOFC operating pressure/bar | 10 |

Compressor polytropic efficiency/% | 85 | Turbine polytropic efficiency/% | 85 |

Compressor mechanical efficiency/% | 99 | Turbine mechanical efficiency/% | 99 |

The current density model of SOFC can be defined as Equation (1):

I = n × F × 4 q CH 4 N c e l l × A c e l l (1)

where: n―Electrons number transferred of each Oxygen atom in the electrochemical reaction, taking 2; F―Faraday constant, 96,485 C/mol; q CH 4 ―me- thane molar flow rate, mol/s; N_{cell}―number of cells; A_{cell}―single-cell area, m^{2}.

Firstly, select the reference voltage, and then by calculating the influence of pressure, temperature, gas pressure on voltage at other non-reference state to calculate voltage value.

Δ V p ( mV ) = C × 1 log ( p / p r e f ) (2)

where: Δ V p ( m V ) ―The influence of operating pressure on the voltage, mV; C_{1} = 76; p―The SOFC operating pressure, bar; P_{ref}―Reference pressure, 1 bar.

Δ V T ( mV ) = K × ( T − T r e f ) × I (3)

where: V T ―The operating temperature on voltage, mV; K = 8; T―The SOFC operating temperature, ˚C; P_{ref}― Reference temperature, 1000˚C.

Δ V a n ( mV ) = 172 × log ( p H 2 / p H 2 O ) / ( p H 2 / p H 2 O ) r e f (4)

where: Δ V a n ―The influence of hydrogen and water vapor partial pressure on the voltage, mV; p H 2 / p H 2 O ―Pressure ratio of hydrogen and water vapor;

( p H 2 / p H 2 O ) r e f ―Pressure ratio of hydrogen and water vapor at reference condition, taking 0.15.

Δ V c a t ( mV ) = 92 × log ( p O 2 / ( p O 2 ) r e f ) (5)

where: Δ V c a t ―The influence of the oxygen partial pressure in cathode on voltage, mV; p O 2 ―The average oxygen partial pressure in cathode, bar; ( p O 2 ) r e f ―Oxygen partial pressure at reference condition, taking 0.164.

In summary, the SOFC voltage can be obtained as the Equation (6) below:

V S O F C = ( V r e f + Δ V p + Δ V T + Δ V c a t + Δ V a n ) / 1000 (6)

where: V S O F C ―The SOFC voltage, V.

When using the first law of thermodynamic to evaluate the combined system, we use SOFC power, SOFC electrical efficiency, electrical efficiency of the overall system, total power etc. as the evaluation indexes.

Since the electrochemical reaction occurs in the cell stack, and the whole system is assumed to be adiabatic, therefore the total power generation of the fuel cell can be shown as the Equation (7):

W D C = V S O F C × I (7)

SOFC electrical efficiency can be defined as Equation (8):

η S O F C = W D C × 0.92 m f × L H V f × 100 % (8)

where: 0.92―DC/AC conversion efficiency; LHV_{f}―Low heat value of fuel, kJ/kg.

The electrical efficiency of proposed and reference system can be defined as Equation (9) and (10):

η p r o − s = ( W S O F C + W G T + W A T − W A C − W F C − W L P − W H P ) / ( m f × L H V f ) × 100 % (9)

η r e f − s = ( W S O F C + W G T + W S T − W A C − W F C − W P U M P ) / ( m f × L H V f ) × 100 % (10)

With doing the second law of thermodynamics analysis, exergy efficiency and exergy loss is always used to evaluate the thermodynamic perfection degree of devices. For the total system, as Equation (11):

∑ k ( E i n ) k = ∑ j ( E o u t ) j + ∑ i W i + I η e x = E x g a i n / E x p a y ≤ 100 % (11)

where: E_{in}―Input exergy, E_{out}―Output exergy, W_{i}―Power, I―System exergy loss.

Exergy efficiency and exergy loss for compressor, turbine, heat exchanger and SOFC are shown as Equations (12)-(15):

η e x , C = E x g a i n / E x p a y = ( E x o u t − E x i n ) / W C E x L , C = E x i n − E x o u t + W C (12)

η e x , T = W n e t / ( E x i n − E x o u t ) E x L , T = E x i n − E x o u t − W n e t (13)

η e x , H E = E x g a i n E x p a y = exergygainedbycoldfluid exergypaiedbyhotfluid E x L , H E = ∑ E x i n − ∑ E x o u t (14)

E x a n , i n + E x c a , i n = E x a n , o u t + E x c a , o u t + W S O F C + E x L , S O F C (15)

In this paper, we use Aspen Plus for simulation, and select more reasonable basic parameters for a specific condition analysis. In this paper, the simulation fuel of the SOFC inlet includes 97% of CH_{4} and 3% of N_{2}. GT exhaust gas temperature is 680.2 K. The ammonia-water mass concentration is 70% and AT pressure ratio is 24 as the specific conditions. By Simulation we can get thermodynamic parameters at each working point of the proposed system in

For comparing the two systems, firstly we need to specify the external heat source and cooling water conditions which are exactly the same. When keeping former SOFC-GT under the same operating conditions, make comparison between the performances of the two systems, in order to verify Kalina superiority.

No. | Temperature | Pressure | Mass flow | LHV |
---|---|---|---|---|

[K] | [bar] | [kg/s] | [kJ/kg] | |

FUEL | 298.1 | 1 | 0.059 | 47,466.59 |

0 | 520.3 | 10 | 0.059 | 47,466.59 |

1 | 1019.5 | 10 | 0.443 | 8219.40 |

6 | 1173.2 | 10 | 0.25 | 2165.22 |

AIR | 298.1 | 1 | 1.523 | 0.00 |

7 | 635.9 | 10 | 1.523 | 0.00 |

8 | 925.7 | 10 | 1.523 | 0.00 |

11 | 1173.2 | 10 | 1.332 | 0.00 |

13 | 1435.7 | 10 | 1.582 | 0.02 |

14 | 935.7 | 1 | 1.582 | 0.02 |

15 | 680.2 | 1 | 1.582 | 0.02 |

16 | 343.1 | 1 | 1.582 | 0.02 |

NH_{3}∙H_{2}O | 298.15 | 9 | 0.242 | 13,022.53 |

01 | 299.10 | 72 | 0.242 | 13,022.53 |

02 | 649.10 | 72 | 0.242 | 13,022.53 |

03 | 373.70 | 3 | 0.242 | 13,022.53 |

06 | 291.10 | 3 | 0.369 | 9554.07 |

010 | 370.77 | 9 | 0.258 | 9554.07 |

011 | 370.78 | 9 | 0.132 | 15,939.16 |

012 | 370.78 | 9 | 0.127 | 2921.50 |

016 | 337.98 | 9 | 0.242 | 13,022.03 |

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

SOFC current density/A/m^{2} | 2393.9 | SOFC operating voltage/V | 0.714 |

SOFC operating temperature/K | 1173 | SOFC electrical power/kW | 1510.15 |

After burner temperature/K | 1273 | SOFC electrical efficiency/% | 53.74 |

Fuel compressor power/kW | 33.03 | GT power/kW | 1016.41 |

Air compressor power/kW | 537.06 | AT power/kW | 139.88 |

High-pressure pump power/kW | 2.61 | ST power/kW | 105.34 |

Low-pressure pump power/kW | 0.34 | Input exergy/kW | 2908.36 |

Total net power of the proposed system/kW | 2092.076 | Total net power of the reference system/kW | 2008.858 |

Total electrical efficiency of the proposed system/% | 74.414 | Total electrical efficiency of the reference system/% | 71.454 |

Total exergy efficiency of the proposed system/% | 71.933 | Total exergy efficiency of the reference system/% | 69.072 |

for 136.26 kW, accounting for 16.72%. Gas turbine exergy loss is 71.07 kW, accounting for 8.72%. Energy loss of ammonia generator is 45.34 kW, accounting for 5.56%, and its exergy efficiency can get 80.9%. As for the small temperature difference, it can reduce the damage caused by heat transfer irreversible. Exhaust gas temperature is controlled at 70˚C, its energy destruction is 17.71 kW, accounted for a small proportion. We can see from the result that a lot of measures can be taken to increase system utilization, SOFC’s exergy loss can be reduced by improving the interior materials or selecting the appropriate operating temperature and operating pressure; The maximum loss of combustor is mainly combustion irreversible loss, it can be reduced by choosing a suitable air, fuel flow; Energy loss of heat exchanger also have great controllability, selecting an appropriate heat exchanger temperature difference can reduce its exergy loss; To take full advantage of exhaust heat in the exhaust gas, when ensuring the temperature above the dew point, we can use it to a situation temperature as low as possible, thus reducing the exergy taken away by exhaust gas.

By energy analysis we can find out the weaknesses in the system energy use, system performance can be optimized by improving the performance of SOFC, optimizing heat exchanger arrangement, minimizing the temperature difference.

As can be seen from

We can also see from

electrical efficiency. Electrical efficiency of SOFC changes from 49.92% to 53.715%; as can be seen from

^{2} and then decrease. SOFC efficiency decreases mainly because of power increasing (AC and FC) and energy input caused by increasing fuel and air flow rate. We generally expect to make SOFC run at the left of peak, at the same time trade-off between power, efficiency, voltage. There exists an optimal current density at 350 mA/cm^{2}.

As can be seen from

In the Kalina cycle when the cooling tower is used as cold source, condensation temperature is greatly affected by ambient temperature. So it’s necessary to study the impact of condensation temperature on system performance.

Kalina cycle uses the binary mixture NH_{3}/H_{2}O as working fluid which has the characteristics of change temperature in evaporation. At ambient pressure conditions the boiling point of NH_{3} is 240 K, and the boiling point of H_{2}O is 373.34 K, while in the evaporation process, the mixture concentration decreases which can lead to an increasing of the boiling point. Since the Kalina cycle is operating at higher pressures, as basis for calculation, the thermo-physical properties of NH_{3}/H_{2}O at higher pressures and temperatures are required. We refer to the ASPEN PLUS simulation results in our calculation. Ammonia mixture should be fully condensed into a liquid before entering the solution pump, when the condensing pressure is determined, the bubble point and dew point of different concentrations ammonia at condensing pressure is required in order to guide us to determine the condensed water temperature, as shown in

In order to reveal the internal phenomena of the main processes of the proposed system, EUD method which was proposed by Ishida, was adopted in this study.

When doing EUD analysis for a thermodynamic process, there exists two processes respectively called “energy donor” and “energy acceptor”. The x-coordinate in the EUD diagram is energy change, and the y-coordinate is energy level A, which is a dimensionless criteria, the ratio of the exergy change ΔE and energy change ΔH in the thermal process. The area between Aed and Aea curves represents the exergy destruction in the energy transfer process.

As can be seen from the horizontal of

_{ea,AC} A_{ea,FC} A_{ed,GT} and A_{ed,AT}, respectively. As can

be seen from the horizontal of

The SOFC-GT-Kalina integrated system is put forward in this paper. By energetic and exergetic performance analysis, the following conclusions can be drawn:

1) By comparison, under the given condition, electrical and exergy efficiency of the proposed system are 74.41% and 71.93%, while those of the reference system are 74.45% and 69.07%, proving the superiority of Kalina cycle for waste heat recovery.

2) The largest exergy destruction occurs in the SOFC, followed by the after-burner, ammonia steam generator and GT. By using Kalina cycle for fully using of waste heat, the exergy destruction of exhaust gas is small.

3) There exists an optimal SOFC current density at 350 mA/cm^{2}. Within a certain range by increasing compression ratio, air flow is conducive to system performance.

4) When other conditions remain unchanged, increasing the ammonia flow can increase the exergy destruction of ammonia generator; it has little effect on ammonia steam turbine exergy destruction.

5) With the increase of ammonia concentration, the condensation temperature should be decreased in order to achieve higher thermal efficiency. In addition, when the AT inlet pressure keeps constant, the thermal efficiency decrease with the condensation temperature.

The Project Supported by National Natural Science Foundation of China No. 51274224.

Zhao, H.B., Hou, X. and Yang, Q. (2018) Thermodynamic Study and Exergetic Analysis of the Integrated SOFC-GT-Kalina Power Cycle. Energy and Power Engineering, 10, 43-64. https://doi.org/10.4236/epe.2018.102004

I: Current of the SOFC (A)

F: Faraday’s constant (96,485.3 C/mol)

p: SOFC operating pressure (bar)

pref: Reference pressure (1 bar)

T: SOFC operating temperature (˚C)

T_{ref}: Reference pressure (1000˚C)

P H 2 : Partial pressures for hydrogen (bar)

P H 2 O : Partial pressures for water vapor (bar)

P O 2 : Average oxygen partial pressure in cathode(bar)

V_{SOFC}: SOFC voltage (V)

V_{ref}: reference voltage

WDC: SOFC DC power

WAC: SOFC AC power

η S O F C : SOFC electrical efficiency

η : Electrical efficiency

W: Electrical power

η e x : Exergy efficiency

Ex_{gain}: Exergy benefits

Ex_{pay}: Exergy cost

Ex_{L}: Exergy loss

EUD: Energy-utilization diagram

A: Energy level

q CH 4 : Mole flow rate (mol/s)

A_{cell}: The active area of one single cell (m^{2})

N_{ce}_{ll}: The total numbers of the cell

m_{f}: Fuel flow rate (kg/s)

LHVf: Low heat value of fuel (kJ/kg)

x: Ammonia mass concentration (%)

Δ V p : Influence of operating pressure on the voltage (mV)

Δ V T : Influence of operating temperature on the voltage (mV)

Δ E : Exergy change (kJ/mol)

Δ H : Enthalpy change (kJ/mol)

KCS: Kalina cycle system

ICE: Internal combustion engine

SOFC: Solid oxide fuel cell

RC: Rankine cycle

ST: Steam turbine

GT: Gas turbine

HE: Heat exchanger

AT: Ammonia steam turbine

pro-s: The proposed system

ref-s: The reference system

HRSG: Heat recovery steam generator

HP: High-pressure pump

LP: Low-pressure pump

CW: Cooling water

HE: heat exchanger

AB: After-burner

an: SOFC anode

ca: SOFC cathode

AC: Air compressor

FC: Fuel compressor

temp: Temperature

TIT: Turbine inlet temperature