Page 90 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 29

can be checked against the volumetric estimate obtained as described in secs. 1.2 and
1.3. This technique of matching the observed production pressure history by building a
suitable mathematical model, albeit in this case a very simple one, equ. (1.35), and
using the model to predict future performance is one which is fundamental to the
subject of Reservoir Engineering.

b) Water drive reservoirs

If the reduction in reservoir pressure leads to an expansion of the adjacent aquifer
water, and consequent influx into the reservoir, the material balance equation must
then be modified as

Production = GIIP − Unproduced Gas
(sc) (sc) (sc) (1.40)
G
G p = G − − W E
e
E i

where, in this case, the hydrocarbon pore volume at the lower pressure is reduced by
the amount W e, which is the cumulative amount of water influx resulting from the
pressure drop. The equation assumes that there is no difference between surface and
reservoir volumes of water and again neglects the effects of connate water expansion
and pore volume reduction.

If some of the water influx has been produced it can be accounted for by subtracting
this volume, W p, from the influx, W e, on the right hand side of the equation. With some
slight algebraic manipulation equ. (1.40) can be expressed as

p p G p WE
i
e
= i 1− 1− (1.41)
Z Z i G G
where W e E i /G represents the fraction of the initial hydrocarbon pore volume flooded
by water and is, therefore, always less than unity. When compared to the depletion
material balance, equ. (1.35), it can be seen that the effect of the water influx is to
maintain the reservoir pressure at a higher level for a given cumulative gas production.
In addition, equ. (1.41) is non-linear, unlike equ. (1.35), which complicates both history
matching and prediction. Typical plots of this equation, for different aquifer strengths,
are shown in fig. 1.11.

During the history matching phase, a separate part of the mathematical model must be
designed to calculate the cumulative water influx corresponding to a given total
pressure drop in the reservoir; this part of the history match being described as "aquifer
fitting". For an aquifer whose dimensions are of the same order of magnitude as the
reservoir itself the following simple model can be used