Page 254 - Fundamentals of Reservoir Engineering

OILWELL TESTING 191

t ( p − p ) 0.000264 4kt

S = 1.151 log t +∆ + ws(LIN) wf − log ×
t ∆ m γφ µ cr 2
w

in which m is the slope of the buildup. Finally, evaluating this latter equation for the
specific value of ∆t = 1 hour, and assuming that t >> ∆t gives

(p − p ) k
S = 1.151 ws(LIN) 1 -hr wf − log + 3.23 (7.52)
m φµ cr 2
w

in which p WS(LIN) 1-hr is the hypothetical closed-in pressure read from the extrapolated
linear buildup trend at ∆t = 1 hour as shown in fig. 7.18.

It should be noted in connection with the determination of the permeability from the
buildup plot that k is in fact, the average effective permeability of the formation being
tested, thus for the simultaneous flow of oil and water in a homogeneous reservoir

( )
k = k (abs ) × k ro S w (7.53)

in which ( ) is the average relative permeability representative for the flow of oil in
ro S
k
w
the entire formation and is a function of the thickness averaged water saturation
prevailing at the time of the survey. It has been assumed until now that reservoirs are
perfectly homogeneous. In a test conducted in an inhomogeneous, stratified reservoir,
however, providing the different layers in the reservoir are in pressure communication,
the measured permeability will be representative of the average for the entire layered
system for the current water saturation distribution. The concept of averaged (relative)
permeability functions which account for both stratification and water saturation
distribution will be described in detail in Chapter 10. The permeability measured from
the buildup, or for that matter from any well test, is therefore the most useful parameter
for assessing the well's productive capacity since it is measured under in-situ flow
conditions. Problems occur in stratified reservoirs when the separate sands are not in
pressure communication since the individual layers will be depleted at different rates.
This leads to pressure differentials between the layers in the wellbore, resulting in
crossflow.

It is also important to note that in the subtraction of equ. (7.48) from equ. (7.51) to
determine the skin factor, the p D (t D) functions in each equation disappear leading to an
unambiguous determination of S. If this were not the case then one could have little
confidence in the calculated value of S since the evaluation of p D (t D) at the time of
closure may require a knowledge of the geometry of the drainage area and degree of
well asymmetry with respect to the boundary. This point is made at this stage to
contrast this method of determining the skin factor with the method which will be
described in sec. 7.8, for multi-rate flow tests, in which the calculation of S does rely on
the correct determination of the dimensionless pressure functions throughout the test.

Figure 7.19 shows the effect of the flowing time on the Horner buildup plot. For an

initial well test in a reservoir, if the flowing period prior to the buildup is short, then p D