I wasn't aware of the gas making water vapor. I'll have to look that up as I'm wondering what takes place to make that happen.
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When you burn any hydrocarbon fuel, the hydrogen combines with oxygen to produce H2O (water). The carbon combines with oxygen to produce CO2. The only difference between the fuels is how much hydrogen VS carbon it contains. Methane (natural gas) is CH4, so 4 hydrogen atoms for 1 carbon. Propane is C3H8, butane is C4H10, octane is C8H18, and so on. Real fuels are never as pure as a single component, so it's a little more complicated than that but as the chain gets longer, the ratio approaches 2 hydrogen for 1 carbon.
Because the combustion is hot, the H2O will be steam. I think to clean the deposited carbon out of an engine, you need liquid water to enter the combustion chamber, soak into the carbon, then flash to steam, exploding the carbon away from whatever it is deposited on. I don't think water vapor entering the intake or steam produced during combustion does much to clean the carbon deposits. That's just my theory, I don't have any hard evidence for it.
The other aspect of burning natural gas or LPG, is that it is already a gas. In order to burn gasoline, it has to evaporate first to combine with air. If liquid gas enters the cylinder, it may not evaporate in time to burn properly, thus leaving deposits behind. In an environment lacking oxygen, the hydrogen will burn off leaving the carbon behind. Any liquid fuel entering the cylinder has the opportunity to create a localized area that is fuel-rich (lacking oxygen) and thus not burn well. A lot of the engineering in gasoline fuel injection and diesel injection is getting the fuel to completely mix with the air. That is much simpler if you start with a fuel that is already a vapor.