According to the recently developed SAE J2601 filling standard for compressed hy

Question

According to the recently developed SAE J2601 filling standard for compressed hydrogen tanks at
70MPa

For a given filling of hydrogen to a desired pressure of 70MPa, the following information is known:

· There are 2 equal tanks connected in parallel as shown (in reality the two tanks are slightly
different but for simplicity we assume that they have the same dimensions)
· The height of each tank is 100cm
· The diameter of each of the cylindrical tanks is 50cm
· The supply pressure is 1000 bar and can be assumed constant during the filling process
· The ambient temperature conditions varies between -20 and 50ºC
· The initial pressure of the hydrogen in the two tanks is 72bar
· The valve coefficient C_valve is 2e-5 kg/(s*Pa^0.5)
· The initial temperature of hydrogen in the tank as well as the wall temperature of the tank can
be considered equal to the ambient temperature
· The average total convective heat transfer coefficient for heat losses from the tank surface can
be assumed constant as, U_conv=40 W/m^2*K (Heat loss=Tank Surface Area·U_conv·DT)
· Assume that the initial temperature of hydrogen in the tank equals the ambient temperature

1) Estimate the supply temperature the hydrogen needs to be cooled to at the inlet of the tank
system in order to avoid exceeding a temperature of 85ºC (the temperature in the tank will rise
during filling!) and a pressure of 85.7 MPa in the tanks at any time during the filling process.
Do the calculation for an ambient temperature of 7ºC and repeat it at 45ºC.

2) At the found required cooling at the tank inlet in 1) at 7ºC ambient temperature, calculate the
filling time to achieve a pressure of 70 MPa (700 bar) in the two composite tanks (tank initial
temperature is the same as the ambient temperature).

3) Is there a risk of overpressure in the tank if the tanks are placed in direct sunlight and the hydrogen
in the tanks is heated to 75ºC during the Summer-period?

4) Estimate the total energy loss in the filling process assuming that the hydrogen is initially delivered
at 30bar when supplied to the filling station (the estimate can be made in multiple
ways – one way is to assume ideal isentropic or isothermal compression - but be sure to state
your exact assumptions!).

5) Under which circumstances would there be a risk of overfilling the tank?

How do I solve this ODE's?

Explanation / Answer

1)   the supply temperature   = (273.15 + 85) * 85.7/45

                                             = 682.076 K

2) filling time to achieve a pressure = (85.7/70) * 6.76

                                                         = 8.276 s

3) Yes, there is a risk of overpressure in the tank if the tanks are placed in direct sunlight due to excess pressure tank can explode .

4) the total energy loss in the filling process = P(V2 - V1)

                                                                        = 70 * 106 * 0.67

                                                                        = 46.9 * 106 J

5) Under excess heating would there be a risk of overfilling the tank .

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