Page 398 - Fundamentals of Reservoir Engineering

NATURAL WATER INFLUX 333

9.6 APPLICATION OF INFLUX CALCULATION TECHNIQUES TO STEAM SOAKING

The method of predicting aquifer performance, using the unsteady state theory of Hurst
and van Everdingen presented in the previous section, is not necessarily restricted in
use to the description of reservoir-aquifer systems. The same technique can be used to
predict fluid influx in any system which has the same geometry as the reservoir-aquifer
model described in this chapter. As an example, the method will be used to determine
the oil producing rate during the early, transient phase of a steam soak cycle. This
subject was discussed in Chapter 6, sec. 4, in which an expression was derived for the
PI ratio increase during the later stabilized flow part of the cycle. Immediately upon
opening the well on production, however, there will be a period when transient flow
conditions prevail, that is, before the effect of the boundary of the drainage volume has
been felt.

The initial situation is shown in fig. 9.21, in which, after injecting several thousand tons
of steam, a hot zone of radius r h is created around the well in which the temperature is
T s, the condensing steam temperature at the prevailing reservoir pressure.

cold hot

T , µ oc
T s
r
µ oh

r w r h r

Fig. 9.21 Conditions prior to production in a steam soak cycle

The radius of the hot zone can be calculated using the technique of Marx and
7
Langenheim , which allows for heat losses to both cap and base rock during the steam
injection. This simplified description of the temperature distribution is justified by the
8
experimental findings of Niko and Troost , which indicate that the dominant factor in the
production cycle is the total amount of heat injected into the formation, the additional oil
production being largely independent of the way in which the temperature is
distributed.

The overall geometry of this system is the same as for an aquifer producing into a
reservoir, only on a smaller scale. During the transient flow period there will be an
influx of cold oil into the heated region which can be described using the water influx
calculation procedures al ready developed in this chapter.

If the transient period is divided into small, equal time steps of length ∆t, then it is
th
required to calculate the average oil rate q during the n time step and, assuming
n
steady state flow at all times within the small volume of the hot zone close to the well,
then