There are two ways it can be done, but only one it is really done on industrial scale.
The old way was that you could pre-brew the coffee for a few seconds. Large portion of caffeine extracts *very* fast. If you then remove the coffee and move it to fresh water, the resulting coffee will have significantly less caffeine and still taste like a weak coffee.
Caffeine sensitive people still do this with [tea](https://www.thespruceeats.com/how-to-naturally-decaffeinate-tea-765280). But I have never heard anyone actually doing it with coffee after industrial decaf became a thing.
These days, on industrial scale, they flush the coffee with a solvent, like alcohol / acetone or compressed CO2. The CO2 extraction being the latest and greatest. It binds the caffeine, but little else. When you then remove the solvent, you’re left with coffee with less caffeine.
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