Page 331 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

298 Reservoir Engineering

Since the volume of water injected to fill-up is equal to the volume of gas
displaced by the oil bank as the initial gas saturation, S,, is reduced to the
trapped-gas saturation, S, a material balance for r*, is:

(5-233)

At interference, rd = d/*, and Equation 5-233 can be used to compute the
volume of water required to reach interference. Usually, fill-up occurs in a
relatively short time after interference, and the volume of water injected at fill-
up is:

W, = 2d24hS, (5-234)
At fill-up, r,is obtained by:

(5235)

After interference, the equation in Table 5-44 for the 5-spot pattern can be used
to estimate injectivity Additional details of estimating injectivity can be found
in several good texts on this subject [197,254,278].
Monitorlng Injectivity. Injection well performance can be analyzed and monitored
by several means. During and after a period of injection, the pressure transient
methods discussed earlier can be used. Additionally, several bookkeeping
methods of monitoring injection rates and pressures are quite useful.
Hearn [314] recently proposed a method to analyze injection well pressure
and rate data. Permeability is obtained from the slope of a plot of Ap/q, versus
the logarithm of cumulative water injected. However, the method can only be
used during the initial injection period. After fill-up, Ap/q, the reciprocal of
injectivity index, will cease to be a function of cumulative water injected unless
the well experiences damage or is stimulated. In these cases, the plots suggested
by Hall [315] are convenient for analysis of the data.
A Hall plot is a graph of cumulative pressure-time versus cumulative water
injection. Such plots are useful in observing injection well plugging or any
beneficial results of stimulation procedures. An improvement in injectivity is
indicated if the slope decreases, whereas plugging is suspected if the slope
steepens. Figure 5-172 shows an improvement in water injectivity that resulted
from a surfactant treatment [316].
The reciprocal of the Hall plot slope is the injectivity index in bbl/D/psi.
Effective pressures are obtained by subtracting the static reservoir pressure from
the flowing bottomhole pressures [315]:
-
effective pressure - P, - p = (p, + 0.45D - Apt) - jj (5-236)

where pd is the wellhead pressure, 0.45 is the hydrostatic pressure gradient in
psi/ft, D is the depth to the mid-point of the reservoir, and Apt is the pressure
drop in the tubing. Although the Hall method assumes that only the wellhead
pressure changes with cumulative water injected, the effective pressure drop