Hydrogen Tank Fast Fill at 70 MPa: Precooling, Real-Gas Heating and State of Charge (2D Schematic)

Presets

Live readouts

Graphs

Tank pressure and target ramp against time

Gas, wall and inlet temperature against time

State of charge and mass flow against time

End state of charge and peak gas temperature against precooling temperature

Numerical checks

running...

How to use

The fill starts by itself and repeats after a rest (switch off the restart box to keep the final state). Watch the gas temperature curve against the red 85 C limit and the state of charge at the end. Try: (1) No precooling - the fill is stopped by the temperature limit at about 70 percent charge; (2) Mild cooling, 0 C and compare the end state of charge with -40 C (the sweep graph shows the whole trend); (3) Cooler before the valve to see Joule-Thomson reheating; (4) slow the ramp and see the gas lose more heat to the wall; (5) change the tank size or the ambient temperature. The settled pressure in the readout is what the driver sees after the tank cools. Hover a part for its numbers. Space pauses, R starts a new fill.

The science

Why the tank heats up. Filling a closed tank is an open-system energy balance. For a gas zone of mass m and temperature T with inflow enthalpy h_in and heat flow to the wall Q:

d(m u)/dt = ṁ h_in - hA (T - T_w), m c_v dT/dt = ṁ (h_in - c_v T) - hA (T - T_w)

Incoming gas carries flow work, so even gas at -40 C ends up much hotter than it started: the tank is compressing its own contents. The wall (a polymer liner inside a carbon-fibre shell, with low thermal conductivity) soaks up only a little heat in the few minutes of a fill:

C_w dT_w/dt = hA (T - T_w) - h_oA_o (T_w - T_amb)

Real hydrogen. At 70 MPa hydrogen is far from ideal. The Abel-Noble equation p (v - b) = R T with b = 7.69 × 10^-3 m³/kg describes it to about 1 percent. For this law the internal energy depends only on temperature and the enthalpy is

u = c_v T, h = c_p T + b p, density ρ = 1 / (R T/p + b)

Joule-Thomson heating. Unlike most gases, hydrogen warms when throttled at room temperature. Since h is conserved across a valve, T₂ = T₁ + b (p₁ - p₂)/c_p: a 50 MPa drop adds about 27 K. If the dispenser chiller sits before the control valve (the checkbox), the cold gas is partly reheated.

State of charge is the density relative to the nominal value at 70 MPa and 15 C, ρ_ref = 40.5 kg/m³ in this model (the commonly quoted figure is 40.2). After the fill the gas cools to ambient at constant mass: the pressure falls (Gay-Lussac effect) and the state of charge is unchanged. A hot fill that stops at 70 MPa therefore ends with a lower state of charge than a cold one.

Pressure ramp. Dispensers follow an average pressure ramp rate (APRR). The mass flow is set by a proportional controller tracking p_target(t) = p₀ + APRR t, limited by the nozzle. The fill stops at the target pressure, the target state of charge or the temperature limit (85 C for Type IV tanks), whichever comes first.

Checks (run in the page). (1) the Abel-Noble density at 70 MPa and 15 C against the reference value; (2) an adiabatic ideal-gas fill integrated step by step against its closed form m_f c_v T_f = m₀ c_v T₀ + (m_f - m₀) c_p T_in; (3) the first-law closure of the real fill; (4) a physical bound: wall heat transfer can only lower the peak gas temperature.

Simplifications. The gas is a single well-mixed zone (real tanks stratify, with a hot top near the inlet jet in a horizontal tank); constant c_p (about 14.3 kJ/kg/K, a few percent variation over the range); a fixed internal heat-transfer coefficient and one lumped wall node instead of liner plus composite layers; a simple pressure-tracking controller instead of the full SAE J2601 lookup tables; the area is that of a cylinder with length 3 times its diameter. The page is educational and does not implement any station protocol.