Qcw = Cp,H2O · ( Tcw,out – Tcw,in) Eq 4.5.3-18
The first term on the right hand side of Eq 4.5.3-15 is the internal heat generation, the second term the total heat loss to the ambient, and the third term the auxiliary cooling demand. The overall thermal capacity Ct and resistance Rt for the electrolyzer, and the UA-product for the cooling water heat exchanger are the constants that need to be determined analytically or empirically prior to solving the thermal equations. It should be noted that the thermal model presented here is on a per stack basis. In Type 160, UA is given as a function of electrolyzer current:
UAHX = h1 + h2 · Iely Eq 4.5.3-19
4.5.3.4 Additional information
Type 160 is also described in an EES-based executable program distributed with TRNSYS 16: %TRNSYS16%\Documentation\HydrogenSystemsDocumentation.exe
4.5.3.5
External data file
Type 160 reads the electrolyzer performance data from a data file. An example is provided in "Examples\Data Files". The data file should have the following information:
<Nb of electrolyzers>
<No of the electrolyzer>, <Name of electrolyzer>
The parameters that must be provided are described here below: No Parameter Units Description
1 r1 Ω m² Ohmic resistance (Eq 4.5.3-5) 2 r2 Ω m² / °C Ohmic resistance (Eq 4.5.3-5)
3 s1 V Overvoltage on electrodes (Eq 4.5.3-6) 4 t1 m² / A Overvoltage on electrodes (Eq 4.5.3-7) 5 t2 m² °C / A Overvoltage on electrodes (Eq 4.5.3-7) 6 t3 m² °C² / A Overvoltage on electrodes (Eq 4.5.3-7) 7 a1 mA / cm Faraday efficiency (Eq 4.5.3-8)
8 a2 0..1 Faraday efficiency (Eq 4.5.3-8)
9 h1 W / °C Convective heat transfer coefficient (Eq 4.5.3-19) 10 h2 W / °C per A Convective heat transfer coefficient (Eq 4.5.3-19)
EXAMPLE 2
1,Alkaline Electrolyzer PHOEBUS (KFA)
8.05031E-05 -2.50410E-07 0.1849 -0.10015 8.4242 247.2663 250.0 0.96 7.0 0.020 2,GHW Electrolyzer (p=30 bar) (Munich Airport)
1.997990E-05 0.0 0.2113 0.01984 0.0 0.0 250.0 0.96 7.0 0.0200
4.5.3.6 References
1. Ulleberg Ø. (2002) Modeling of advanced alkaline electrolyzers: a system simulation approach. Int. J. Hydrogen Energy 28(1): 7-19.
2. Ulleberg Ø. (1998) Stand-Alone Power Systems for the Future: Optimal Design, Operation & Control of Solar-Hydrogen Energy Systems. PhD thesis, Norwegian University of Science and Technology, Trondheim.
3. Rousar I. (1989) Fundamentals of electrochemical reactors. In Electrochemical Reactors: Their Science and Technology Part A, Ismail M. I. (Eds), Elsevier Science, Amsterdam.
4. GriesshaberW. and Sick F. (1991) Simulation of Hydrogen-Oxygen-Systems with PV for the Self-Sufficient Solar House (in German). FhG-ISE, Freiburg im Breisgau.
5. Havre K., Borg P. and Tømmerberg K. (1995) Modeling and control of pressurized electrolyzer for operation in stand alone power systems. In Proceedings of 2nd Nordic Symposium on Hydrogen and Fuel Cells for Energy Storage, January 19-20, Helsinki, Lund P. D. (Ed.), pp. 63-78.
6. Vanhanen J. (1996) On the Performance Improvements of Small-Scale Photovoltaic- Hydrogen Energy Systems. Ph.D. thesis, Helsinki University of Technology, Espoo, Finland. 7. Hug W., Divisek J., Mergel J., Seeger W. and Steeb H. (1992) Highly efficient advanced
4.5.4
Type 164: Compressed gas storage
Type 164 is a compressed gas storage model. The model calculates the pressure in the storage based on either the ideal gas law, or van der Waals equation of state for real gases [1,2].
4.5.4.1 Mathematical reference
The pressure gas storage model described below, referred to as Type 164, was originally developed by Griesshaber and Sick [3]. However, the model has been modified to also include van der Waals equation of state for real gases (PMODE=2, while PMODE=1 uses the ideal gas law).
According to the van der Waals equation of state, the pressure p of a real gas in a storage tank can be calculated from:
p = n · R · Tgas
Vol – n · b – a · n2
Vol 2 Eq 4.5.4-1
Where n denotes the number of moles of gas, R is the universal gas constant, Vol is the volume of the storage tank, and Tgas is the temperature of the gas. The second term (comprising the constant a ) account for the intermolecular attraction forces, while b accounts for the volume occupied by the gas molecules.
Note that the ideal gas law is obtained by setting a and b to 0:
p Vol = n R Tgas Eq 4.5.4-2
In the Van der Waals equation, a and b are defined as
a = 27 · R 2 · Tcr2 64 · pcr` Eq 4.5.4-3 b = R · Tcr 8 · pcr` Eq 4.5.4-4
Where Tcr and pcr are respectively the critical temperature and pressure of the substance.
The model simply performs a mass (or moles) balance of gas entering and leaving the storage and calculates the pressure corresponding to the resulting mass of Hydrogen in the tank.
If the pressure rises beyond a fixed level, the excess of Hydrogen is dumped.
4.5.4.2 Additional information
Type 164 is also described in an EES-based executable program distributed with TRNSYS 16: %TRNSYS16%\Documentation\HydrogenSystemsDocumentation.exe
4.5.4.3 References
1. C¸ engel Y. A. and Boles M. A. (1989) Thermodynamics - An Engineering Approach. 1 edn, McGraw-Hill, London.
2. Ulleberg Ø. (1998) Stand-Alone Power Systems for the Future: Optimal Design, Operation & Control of Solar-Hydrogen Energy Systems. PhD thesis, Norwegian University of Science and Technology, Trondheim.
3. GriesshaberW. and Sick F. (1991) Simulation of Hydrogen-Oxygen-Systems with PV for the Self-Sufficient Solar House (in German). FhG-ISE, Freiburg im Breisgau, Germany.
4.5.5
Type 167: Multistage compressor
Type 167 is a multi-stage polytropic compressor model. The model calculates the work and cooling need for a polytropic compressor of 1 to 5 stages; [1, 2]. This manual uses a 2-stage compressor as an example.
4.5.5.1 Thermodynamic model
This model is based on an ideal gas model in a quasi-equilibrium compression process. A quasi- equilibrium process is a process in which all states through which the system passes may be considered equilibrium states. A polytropic process, is a quasi- equilibrium process which describes the relationship between pressure and volume during a compression. It can be expressed as:
(p V) N = constant Eq 4.5.5-1
where p and V are the pressure and volume of the ideal gas, respectively, and the value of N is a constant for the particular prosess.