Absorption Factor

If you learn one number in absorption, learn this one. The absorption factor $A = L/(mV)$ is the ratio of the slope of the operating line to the slope of the equilibrium line, and it decides whether a column can do its job before any question of height or trays arises. The numerator is the solvent's capacity to carry solute away; the denominator is the gas's capacity to hand it over. Everything else is detail.

The threshold at $A = 1$ is absolute rather than economic. Below it the solvent reaches equilibrium with the incoming gas before it has absorbed everything on offer, so some fraction of the feed leaves untouched — and the fraction is fixed by $A$ alone, not by the size of the column. This is the origin of the minimum liquid rate: the solvent flow at which the exit liquid would be exactly in equilibrium with the inlet gas, requiring infinite stages to approach. Real columns are designed at 1.2 to 1.5 times that minimum, which typically puts $A$ between 1.2 and 2.0.

Above that window the economics turn around. More solvent absorbs more readily and shortens the column, but the solvent has to be pumped, cooled, and above all REGENERATED, and regeneration duty is usually the dominant operating cost of the entire plant. Doubling $A$ from 2 to 4 might save a metre or two of packing while doubling the reboiler load in the stripper for the next thirty years. The optimum sits where the capital saved on height stops covering the energy spent on circulation, and in most plants that lands close to $A = 1.4$.

Three cautions on the terms. $L$ and $V$ must be MOLAR flows, not mass or volumetric ones, because $m$ is the slope of an equilibrium line drawn in mole fractions — mixing bases here is a common and silent error. Both should strictly be the solute-free carrier flows, though in a dilute system the difference is negligible. And $m$ moves with temperature and total pressure: absorption is exothermic, so a column running hot has a larger $m$ and a smaller $A$ than its design sheet claims, which is one reason absorbers that worked in winter start missing specification in July. The same group inverted, $1/A$, is the stripping factor, and a stripper is designed by requiring THAT to exceed 1 instead — which is why a solvent chosen to absorb easily is by construction difficult to regenerate.