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Cracked gases usually are quenched after cracking reactions.

Why for lighter gases like ethane, indirect quenching is used,

But for cracking of heavier naphtha or gas oil, most cooling is performed by direct quench.

I understand that cracked heavy gas oil contain a larger amount of fuel oil and vice versa but why.

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Not only fuel but consider the properties of each gas, cracked gases when cooled usually turn to an organic fluid, so to extract that excess water you just need to cool those things to room temperature. Direct quenching in lighter gases will mean you need more energy to get rid of the water.

You can go ahead and try to design direct quenching of light gases and heavy gases in Hysys, then try to size them (yeah keep a constant flow for both) and you can see which is the cheaper option.

Direct quenching is more efficient because "there is no better area of contact than the medium itself" but if separating them is tough you tend to move away from it.

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Cat crackers in the US do not quench gas-oil products except incidentally by the steam stripping of the catalyst. Hot gas oil and hot catalyst are combined and quickly cracked, then the vapor products are separated from the catalyst in the reactor Some directly and some by steam stripping. All product and steam goes to vapor recovery. Catalyst goes to the regenerator where small remaining amounts of hydrocarbon and coke are burned to reheat the catalyst.

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