Analysis of Calculations

Pump energy per day (J) = ΔP*M / ρ

Water pump

Pressure change (ΔP) = 2937700 N/m²
Fluid density (ρ)= 1000 kg/m³
Mass water per day = 4.4519 Nm³ water, based on one mole of water per mole of hydrogen and a fluid being 1000th the volume of a gas.

So pump energy required per day = 13.078 MJ
Small pump efficiency around 60% so actual energy required = 21.79 MJ

Heating energy required per day (J)= Moles*C_p*ΔT

Water heater

Water heat capacity (C_p) = 75.291 J/moleK
Moles = 198609.73
Temperature change (ΔT) = 80 K
So heating energy required = 1.05 MJ

Electrolysis

Energy required for electrolysis (Kwh) = 4.6*V_H2/(2.778*10^-7)
Normalised volume of hydrogen per day (V_H2)= 4451.91 Nm³

So energy required in electrolysis per day (MJ)= 73723.58 MJ
However the electrolysis unit operated on DC current and the energy loses due to AC to DC conversion is 0.03% .
so the actual electrolysis energy per day = 76003.69 MJ

Hydrogen compression

The compression of hydrogen cannot be achieved in one stage due to the temperature rises in the polytropic compression from 30 bar to 200 bar absolute. Therefore an inlet temperature of 250 °C and exit temperature of 250 °C is assumed per stage. Using these values to get a temperature ratio that equates to pressure in the following equation:

Required pressure ratio is P₂/P₁ = (T₂/T₁)^{(1.4 / (1.4-1))}
So the pressure ratio = 1.86

Therefore Number of stages (N) = Log(P_out/P_in)/Log(Pressure ratio)
Number of stages = 3.05 ~ 3 stages

Compression energy per day(kJ) = Moles*1.4*8.314*T₁/(0.4)*N*(P_ratio ^(0.4/1.4)-1))

Mole = 198.61 kmoles
Temperature inlet = 298 K

Number of stages (N) = 3
Pressure ratio = 1.86

Energy required for compression per day = 1022.62 MJ
However compressor is assumed to be 86% efficient
Therefore actual energy requirement is 1189.09 MJ

Hydrogen loss in storage

Volume lost in storage/day = D* Area_wall / e
Area_wall = 53.41 m²
Wall thickness (e) = 154 mm
Actual Diffusion (D) at 80 °C= Do*exp(-Ud / kT)
Diffusion at standardised conditions (Do)= 2.4*10^-6 m²/s & 4.8*10^-4 m²/s at 200 bar
Activation energy of diffusion (Ud) = 0.21 eV
Bolzmann constant (k) = 8.61442*10^-5 eV/K
Temperature (T) = 298 K
So D = 5.04*10^-8 m²/s at 200 bar & 25 °C

Volume lost = 1.7 m³/day per tank
Total lost = 5.09 m³/day