Material balance is used in petroleum engineering to estimate the amount of
available fluid (usually natural gas) in a reservoir (also known as a pool).
The simplest material balances are just simple plots with obvious relationships.
The most commonly used plot for a gas material balance is a 'P/Z Plot'. The
name, however, is misleading. This type of plot has cumulative gas production on the
X axis, and (pressure / compressability factor) on the Y axis. For each pressure test
done on a natural gas well, a point is plotted at the cumulative production of that
well to date, and the pressure yielded from the test divided by the compressability
factor of the gas (which is determined from a number of gas properties, such as the CO2
concentration, the gas gravity, and the average reservoir temperature). When this
has been done for all the wells believed to be producing from the same gas reservoir, a
linear relationship is usually easily visible. A least squares best fit line is
usually fit over the data, and where the best fit line intersects the X axis (when
the pressure is 0), that reading from the X axis is your IGIP (initial gas in place).
However, in the case of a connected reservoir or a waterdrive reservoir, the pressure
in your reservoir is not constant with time, and therefore time must be factored into
the material balance. You can use time to determine the artificial pressure of a reservoir
over a number of years, and plotting that line on a P/Z plot will reveal your /actual/
P/Z plot (which, in the case of a simple reservoir, will follow your best-fit line
exactly, if done right).
Pressure-Transient Analysis, Rate-Transient Analysis, Decline Analysis, and
Volumetric calculations are other popular methods for determining the gas in place
in a reservoir. They'll all tend to give different but similar results for any good
set of data.