Page 172 - Well Logging and Formation Evaluation

162 Well Logging and Formation Evaluation

time the GOR will drop back once most of the free gas has been produced.
Some of the free gas may move to the crest of the structure and form a
secondary gas cap.
Where the producing GOR in wells has become high, the oil rate
can be improved by injecting water into the reservoir. This will have the
effect of raising reservoir pressure, causing some free gas to redissolve,
and also help displace oil to the wells. However, where water break-
through occurs in the producing wells, the overall effect on production
may be negative.

11.3 MATERIAL BALANCE

Material balance treats a reservoir like a tank, with areal and depth pres-
sure equilibrium. For undersaturated oil reservoirs (i.e., those for which
the pressure remains above the bubble point), oil is produced by the
expansion of the liquid phases and connate water, the shrinkage of the
pore volume, and the influx of water from the aquifer. When the reservoir
pressure drops from its initial value P i to P, the formation volume oil
factor increases from B oi to B o.
If the produced oil volume at standard conditions is N p (with initial
volume N), the volume removed from the reservoir at downhole condi-
tions must be N p *B o. The expansion of the oil in place must be N*B oi -
N*B o. The initial pore volume equals N*B oi /(1 - S w), where S w is the
water saturation. If the compressibility of the water is C w, and that of the
pores is Cf, the composite compressibility C is given by:

C = ( C w * S wc + f - S w ). (11.3.1)
C ) (1

From material balance it must be true that produced volume (at reservoir
conditions) = expansion of oil in reservoir + expansion of pore volume +
water influx (W). Hence:

)
*
N p * B o = N * ( B oi - B o + N B oi * C * ( P i - P) + W. (11.3.2)
Porespace compressibility can be measured in the lab as part of a
special core analysis (SCAL) program. Typical values range from
-5
-5
about 15*10 l/bar for a low-porosity rock to 5*10 l/bar for a high-
porosity rock. Water compressibility varies with pressure, temperature,
salinity, and amount of dissolved gas. An approximate value to use is
-5
4.35*10 l/bar.