Space Velocity

Space velocity is space time turned upside down, and the inversion is not laziness — it is what makes the number useful on a datasheet. A space time of 1800 seconds and a space velocity of 2 h⁻¹ are the same fact, but the second says it in the form a catalyst vendor and a plant operator both think in: this bed processes two of its own volumes of feed every hour.

The abbreviations matter because two of them are the same quantity and one is not. LHSV is liquid hourly space velocity and GHSV is gas hourly space velocity; both are volumetric feed rate divided by bed volume, and both are genuine reciprocal times. WHSV — weight hourly space velocity — is mass of feed per mass of catalyst per hour. It is also in reciprocal hours dimensionally, but it is a different quantity, and converting between WHSV and LHSV needs the feed density and the catalyst bulk density. Comparing them directly is a common and expensive confusion.

Two conventions have to be nailed down before any two space velocities can be compared. First, the reference state of the feed: a gas flow measured at 1 atm and 0 °C occupies a very different volume from the same moles hot in the reactor, and GHSV is conventionally quoted at standard conditions, so a number computed from an operating flow will not match a vendor's. Second, which volume goes in the denominator — the catalyst bed, the whole vessel including freeboard and supports, or the tube volume in a multitubular reactor. These can differ by a factor of two, and neither convention is wrong, only unstated.

Space velocity connects to everything else on these pages through the Damköhler number, since $\mathrm{Da} = k\tau = k/\mathrm{SV}$. That relation is the reason a doubled throughput at fixed vessel size costs conversion, and how much: halving $\tau$ halves $\mathrm{Da}$, and the conversion curve does the rest. It is also the reason a bed that is losing activity — $k$ falling as the catalyst ages — can be held at constant conversion for a while by cutting the space velocity, which is exactly what a plant does before it schedules a change-out.