How is it calculated?

Kremser, solute-free solvent: fraction left φ = (E − 1)/(E^(N+1) − 1) → N = ln((E − 1)/φ + 1)/ln E − 1. With E < 1 even infinite stages remove at most E × 100%.

Extraction / Stripping Stages Calculator (Kremser)

Understanding the Kremser extraction and stripping stages calculator — concept and principle

The Kremser equation gives the number of ideal stages needed in a countercurrent cascade (liquid–liquid extraction, gas absorption or stripping) to remove a chosen fraction of a solute. It needs only two numbers: the extraction (or stripping) factor E and the fraction of solute you want removed. It is a quick tool for sizing a mixer-settler train, an absorber or a stripping column before detailed design.

Each added countercurrent stage cuts the solute left behind; 5 stages pass the 95% target.

How it is calculated

With a solute-free entering solvent, the fraction of solute left in the treated stream is

φ = (E − 1) ÷ (E^(N+1) − 1)

Solving for N: N = ln[(E − 1)/φ + 1] ÷ ln E − 1, with φ = 1 − (removal % ÷ 100).

When E = 1 the formula becomes φ = 1/(N + 1), so N = 1/φ − 1.

The extraction factor is E = m × S/F, where m is the distribution ratio (solute concentration in solvent ÷ in feed at equilibrium) and S/F the solvent-to-feed flow ratio. For stripping, E = K × V/L.

The principle

In each ideal stage the two phases leave in equilibrium. If the equilibrium line is straight and flow rates are constant, the stage-by-stage balance forms a geometric series in E, and summing that series gives the closed-form Kremser result. E compares the solvent's capacity to carry solute with the feed's: E > 1 means the solvent can take everything, so almost complete removal is possible with enough stages; E < 1 means removal can never exceed E × 100% however many stages you add.

Worked example

Inputs: E = 1.5, removal 95%.
φ = 1 − 0.95 = 0.05.
(E − 1)/φ + 1 = 0.5 ÷ 0.05 + 1 = 11.
N = ln 11 ÷ ln 1.5 − 1 = 2.3979 ÷ 0.4055 − 1 = 4.914 ideal stages.

How to read the result

Round up: 5 ideal stages give φ = 0.5 ÷ (1.5⁶ − 1) = 0.048, or about 95.2% removal. Raising E reduces the stage count quickly: for 95% removal, E = 2 needs about 3.4 stages and E = 1 needs 19. Real equipment reaches only part of equilibrium, so divide by a stage efficiency to estimate actual units.

Common mistakes

Using a target above E × 100% when E < 1; no number of stages can reach it and the result has no meaning.
Mixing mass ratios and mole ratios in the distribution coefficient and flow ratio.
Ignoring solute already present in the entering solvent, which the solute-free form here does not include.

Keep in mind: The Kremser equation assumes a linear equilibrium, constant flow rates, immiscible phases and ideal stages. Concentrated or non-linear systems need stage-by-stage or rigorous calculation and expert review.

Frequently asked questions

Is the extraction factor the same as the absorption factor?

They are the same idea from different sides: A = L/(KV) for absorption, S = KV/L for stripping, and E = mS/F for extraction.

Why might N not be a whole number?

The formula is continuous; a fractional result means you need the next whole stage.

What if the entering solvent already contains solute?

The general Kremser form then uses the feed concentration that would be in equilibrium with the entering solvent; this calculator assumes it is zero.

Sources: A. Kremser, National Petroleum News 22 (1930) · J. D. Seader, E. J. Henley and D. K. Roper, Separation Process Principles, Wiley · R. E. Treybal, Mass-Transfer Operations, McGraw-Hill

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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