A cryogenic propellant depot constantly leaks heat in from sunlight and the surrounding structure. That heat boils a small amount of liquid propellant into vapor, which must be vented (boil-off) — unless an on-site ISRU plant (electrolysing water ice into propellant) is producing new liquid faster than it's being lost.
Q_leak = Q_base · shield_factor / (1 + 0.09·N_MLI) [W]
m_boil = max(0, Q_leak − P_cryo) / L_v [kg/s]
m_net = m_ISRU − m_boil [kg/day]
tank(t+dt) = clamp(tank(t) + m_net·dt, 0, capacity)
- MLI layers — each extra multi-layer-insulation blanket layer adds a radiation barrier; effective heat leak falls with diminishing returns, per the empirical layer-density curves used on real cryogenic stages.
- Sun shield — a deployable parasol that blocks ~85% of direct solar heating when facing the sun; stowing it (for maneuvering or launch) exposes the tank to full solar flux.
- Cryocooler power — active refrigeration intercepts heat before it boils propellant; modeled here at unit efficiency for clarity (real cryocoolers have a coefficient of performance well below 1, so this is an optimistic simplification).
- ISRU production rate — propellant manufactured locally (e.g. electrolysing lunar or asteroid water ice into LOX/LH2, or the Sabatier reaction for methane) instead of launched from Earth. This is the resource-utilization lever: a high enough production rate can outrun boil-off entirely, letting the depot fill even with a leaky tank.
- L_v (latent heat of vaporization) differs by propellant — since m_boil = Q/L_v, the propellant with the lowest L_v boils off fastest per watt of heat leak. Of the three modeled here, LOX has the lowest L_v (213 kJ/kg vs LH2's 446 and CH4's 511), so LOX is actually the quickest to boil off per watt, not hydrogen — hydrogen's very low density and low boiling point make it hard to insulate and store in absolute terms, but per watt of heat that does leak in, it is LOX that turns into vapor fastest.
Real-world relevance: this is the core trade study behind every proposed cislunar or Mars propellant depot — NASA and commercial architectures all live or die on whether local resource production can keep ahead of unavoidable cryogenic boil-off.
Drag the tank view to pan, and scroll (or pinch) to zoom in on the insulation layers and vapor plume.