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Hi Maha,
If you're conducting an activity analysis, then emissions of each pollutant are calculated simply by multiplying an emissions factor by total energy.
Emissions factors are added from LEAP's Technology and Environmental Database (which you can view by selecting the 'Technology Database' view in LEAP). You're free to add any emission factors that you want, although most modelers stick to the IPCC Tier 1 emission factors for combustible fuels. For each fuel, IPCC Tier 1 factors contain data on the mass of each gas emitted per unit of fuel energy consumed.
Total energy is calculated by multiplying the Activity Level for each process by that process' Final Energy Intensity, which is expressed as energy per unit of activity.
While there are no particularly mysterious parts of this calculation, its important to make sure that when you compare LEAP's results to your own Excel calculations, you're comparing 'like to like'. I can't speculate about any differences between your LEAP model and spreadsheet, but I would recommend that you carefully examine any intermediate results of the calculation in LEAP (using the Results view, or the Elaboration tab in Analysis view) to make sure you're understanding exactly what LEAP is doing.
Good luck,
Taylor