There are 4 major types of Evaporative Emissions from the fuel system of a car, these are:
- Diurnal: Evaporation caused by the fuel tank being heated by the sun
- Running Losses: Heat from the engine and exhaust system causes fuel vaporisation
- Heat Soak: Once an engine is stopped heat from the engine and exhaust system causes fuel vaporisation
- Refuelling: there are always fuel vapours in the fuel tank, when you refuel these vapours are displaced by liquid fuel (and generally vented into the atmosphere).
The amount of Evaporative Emissions created by a fuel depends on the given fuels Reid Vapour Pressure (RVP). RVP is a measure of a fuels volatility, or put simply, how easily a fuel vaporises. In the summer you want fuel with a lower RVP to avoid losses and more specifically to avoid Vapour Lock, in the winter you want fuel with a higher RVP so that vaporisation occurs more easily when trying to start your vehicle, you want the fuel to vaporise as it’s entering the combustion chamber/cylinder so that it will burn.
Interestingly the EPA in the USA regulates the RVP of fuels sold depending on the time of year. This also occurs in other countries but I haven’t found any other references to link to.
You are asking about “leaking vapours” which means the first 3 forms of Evaporative Emissions are relevant, but we can probably discount the 4th as, aside from some methods of minimising refuelling vapour emission, these vapours are still deliberately vented to atmosphere in most/all cars so it can’t really be defined as “leaking”.
If you are interested in Refuelling Emissions Kristy Welsh did some calculations in 2008 to estimate how much Refuelling Loss would occur over a year for an “average American”, her initial answer is “about an 1/8th of a gallon”, she then goes on to multiply by a factor of 10 (just in case you think it’s way too low) and the answer is a little over a gallon or about 3.8 litres per year.
None of this answers the question of an estimate for loss from a fuel system leaking vapours and I’m afraid I can’t find anything that does answer the question. There is an EPA document here which gives a lot of the information required to answer some parts of the question, but aside from being a very a large document, it only deals with stationary Liquid Storage Tanks so does not take into account extra evaporation caused by slosh, nor does it deal with Running Losses or Heat Soak.
I don’t think Diurnal Evaporation could cause anywhere near the same losses as Refuelling. These both operate on a similar principal, the sun must heat and expand the vapour enough for it to escape from the tank through emissions control hoses. If you assume Kristy Welsh is correct with her refuel losses estimate then losses from Diurnal Evaporation should be small enough to discount, particularly when talking about measuring fuel economy.
The other two forms of loss, Running Losses and Heat Soak are much more difficult to estimate. They usually occur in what is a closed system, unless there is a leak. I’m afraid I can provide no evidence but experience that these don’t cause enough loss to be measurable when dealing with fuel economy.
If a damaged/malfunctioning EVAP valve is causing a measurable difference in fuel economy there are 2 more likely reasons for this than Evaporative Emissions
- (the less likely option) The vehicles ECU has detected a fault and has put itself into a safer mode that over-fuels the car somewhat.
- (the more likely option) The leaky valve is causing a leak in your air intake and your engine is sucking in air that has not been measured by the ECU (MAP/MAF/some other air flow measurer). The ECU puts in enough fuel for the amount of air it thinks is in the system, this isn’t enough fuel and it makes the engine run lean. Running lean makes the engine detonate (also called knock/ping/pink) This triggers a knock sensor which in turn puts the ECU into an mode where it over-fuels the engine deliberately in order to stop the knocking.
The outcome is the same, the ECU is deliberately over-fuelling the engine so as to avoid any damage being done.
Of course, this is just my opinion that’s based on a couple of facts supplied. When your mechanic replaces the EVAP valve I’m sure he (or she) will run a full diagnostics test on your vehicle and a simple fault clear will probably sort the problem out.
(I'm not an expert on any of this so please feel free to edit this answer and improve it)