Page 264 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Material Balance and Volumetric Analysis 233

A plot of p/z versus GP may not be a straight line for several reasons: an
unexpected water drive may exist, average reservoir pressure may be inaccurate,
or the reservoir pore volume may be changing unpredictably as a result of
abnormally high reservoir pressures [ 1971. A water drive reduces relative
permeability to gas and increases pressure at abandonment [ 1801. For reservoirs
at moderate to high pressure in the absence of a water drive, the recovery
efficiency under pressure depletion may range from about 80% to more than
90%; a water drive can reduce recovery to about 60%. To maximize efficiency,
water-bearing zones should not be perforated if the water is movable, and
production should be at a high rate since water entry is time dependent [180j.

Material Balance Equations in Oil or Combination Reservoirs

When discovered, a reservoir may contain oil, gas, and water that can be
intermingled or segregated into zones. As described earlier, recovery may be
caused by solution gas drive, water drive, gas cap drive, or a combination of
these mechanisms. A general material balance equation should be capable of
handling any type of fluid distribution and any drive mechanism.
From the compressibilities given in the first section, water and formation
compressibilities are less significant where there is appreciable gas saturation
such as in gas reservoirs, gas cap reservoirs, and in undersaturated reservoirs
below the bubble point. Because of this and because of the complications they
would introduce in already complex equations, water and formation com-
pressibilities are generally neglected, except in undersaturated reservoirs pro-
ducing above the bubble point. Gas in solution in the formation is small and
also generally neglected. One general material balance equation, the Schilthuis
equation, is a volumetric balance stating that the sum of the volume changes
in oil, gas, and water must be zero because the reservoir volume is constant.

oil zone gas cap water cumulative oil
[expansion] + [expansion] + [influx] = [zoneproduction]

NmB, (B, - B, )
N(B,-B,)+ +We = N,B,
B,

cumdtive gas cap cumdtive water 1
+ [ gas production ] + [ production

+ N,(R, - RJBg + BwWp (5-148)
All symbols have been defined earlier. Rearranging terms, Equation 5-148 can
be written:

Material balance equations are often expressed in terms of the initial oil in
place, N: