It varies according to the particular geologic formation. The natural gas you are asking about is called "gas shale" and the rock it is found in is called shale (formed from clay), but is often considered marl (formed from a mixture of clay and carbonate) or can have a high carbonate content (sometimes called a carbonate mudstone). It also sometimes contains dolomite and siltstone. There are generalized numbers of the amount of gas that is expected to be recovered from each major shale formation, but these numbers are very general, and geologic formations are not homogenous, even shale, so there is a large amount of variability from place to place within the same area. It also has a lot to do with how well the company that is doing the drilling does in designing and drilling the well. A poorly drilled well may recover nothing while a properly designed and drilled well may have superlative performance.
Here are some numbers that you can use as general guidelines. These are expressed in standard cubic feet per ton, which is a standard that was developed by the coal bed methane industry before anyone started drilling shale gas. It is useful for comparing shales, but requires some work to convert to cubic feet per acre:
Barnett Shale: 300-350 scf/ton
Fayetteville Shale: 60-220 scf/ton
Haynesville Shale: 100-330 scf/ton
Marcellus Shale: 60-100 scf/ton
Woodford Shale: 200-300 scf/ton
New Albany Shale: 40-80 scf/ton
Here are some other numbers that may guide you:
Barnett Shale (Texas) is assessed at 327 Trillion cubic feet original gas in place
Average EUR (Estimated Ultimate Recovery) for a Barnett well is 2.1 Billion cubic feet
Average well spacing for a Barnett well is 60-160 acres
Woodford Shale (Oklahoma) is assessed at 23 Trillion cubic feet original gas in place
Average EUR for a Woodford well is 3.5 Billion cubic feet
Average well spacing for the Woodford is 640 acres (one square mile)
Haynesville Shale (Louisiana and Texas) has 717 Trillion cubic feet original gas in place
Average EUR for Haynesville is 6 Billion cubic feet
Average well spacing for Haynesville is 40-560 acres
Marcellus Shale (Pennsylvania, Ohio, West Virginia) is assessed at 1,500 Trillion cubic feet original gas in place
Average EUR for Marcellus is 3.6 Billion cubic feet
Average spacing for Marcellus is 40-160 acres
Fayetteville Shale (Arkansas) is assessed at 52 Trillion cubic feet original gas in place
Average EUR for Fayetteville is 2.3 Billion cubic feet
Average spacing for Fayetteville is 80-160 acres
Of course not all "fracking" is related to gas shale. Some of it is in tight sands or tight carbonates. Some of it has been done in almost every type of rock formation with low porosity or permeability since about 1960, and sometimes the frac job improved the well, and sometimes it didn't. In anything other than gas shales there is really no way to estimate the number you are requesting, as the gas is not "in place" meaning it is not in the same place where it was generated as it is in shales. Migrated natural gas has been the most typical target of natural gas drilling for many decades, and finding the biggest reservoir with the most gas was what determined the amount of gas recovered per well. Usually in those types of gas fields the wells in one part of the field recovered most of the gas and the others recovered much smaller amounts, because they were all draining the same reservoir. In a shale it is all the same reservoir, but the gas cannot move freely inside the reservoir, which is why they frac it. Fracing it creates pathways in the reservoir for the gas to escape.
http://www.ugcenter.com/ PS Natural gas does not come from "vegetation", instead most of it forms from remains of plankton, with some input from woody materials that are carried into lakes and oceans from land. Most of the organic material that sources natural gas (other than that in coal bed methane) is deposited marine environments or sometimes fresh water lakes and forms either by catagenesis (a process of heat), or by biogenesis from methane forming bacteria.