Page 290 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Reserve Estimates 25’7

Material Balance

If a field development program has been well planned and executed, enough
information should be available to calculate reserves by the material balance
equation. The material balance equation is derived on the assumption that the
reservoir is a homogeneous vessel with uniform porosity, permeability, and fluid
properties. The equation accounts for all quantities of materials that enter or
leave the vessel. The simplest form of the equation is that initial volume is equal
to the volume remaining plus the volume removed. As material is withdrawn
from a constant-volume reservoir the pressure declines and remaining material
expands to fill the reservoir. Laboratory PVT analysis of the reservoir fluid
defines the change in volume per unit pressure drop. Knowing the amount of
fluid withdrawn from the reservoir and the drop in pressure one can calculate
the corresponding volume of fluid at the original reservoir pressure. The
calculated reservoir size should remain constant as fluid is withdrawn and
pressure drops. If the calculated reservoir size changes constantly in one
direction as the field is produced the assumed production mechanism is
probably wrong. Calculations should be repeated assuming different mechanisms
until one is found that yields a constant reservoir size. Since Schilthuis E2491
developed the original material balance equation in 1936 it has been rearranged
to solve almost any unknown. The most frequently used forms of the equation
are for these types of recovery mechanisms [272]:

1. Oil reservoir with gas cap and active water drive.
2. Oil reservoir with gas cap and no active water drive.
3. Initially undersaturated oil reservoir with active water drive: A. Above
bubble point. B. Below bubble point.
4. Initially undersaturated oil reservoir with no active water drive: A. Above
bubble point. B. Below bubble point.
5. Gas reservoir with active water drive.
6. Gas reservoir with no active water drive.
The material balance equation, when combined with reIiable relative per-
meability data, can be used to predict future reservoir performance. Many times,
reservoirs do not conform to the assumptions made in the material balance
equation. Few reservoirs are homogeneous and no reservoirs respond instan-
taneously to changes in pressure. The precision with which reserves can be
calculated or predicted with the material balance equation is affected by the
quality of data available and the degree of agreement between the assumptions
made in the equation and the actual reservoir conditions.

Model Studies
Predicting reservoir performance with the Tarner [250] or the Muskat [251]
method is a long and tedious process and, even with a programmable calculator,
the process takes several hours. To resolve the problems caused by the assump-
tions inherent in the material balance equation, a reservoir would have to be
broken up into parts small enough to be considered homogeneous. The material
balance equation would then have to be calculated for each part and for each
increment of production. This would entail thousands of calculations performed
thousands of times and would drastically limit the number of reservoir simula-
tions an engineer could run. Fortunately, computers have cut the required time
to a few minutes. Numerical simulators divide the reservoir up into discreet