Analysis of Development Methods for Gravel Envelope Wells - 8
Computations of the solution obtained in this way gives the tangential
velocity distribution presented in Figure 14. This figure
includes a schematic of the flow field expected in the filter pack. It is interesting to
note that, for a short swabbing stroke, results obtained for k2/k1
= 0.001 and b/a = 1.5 give a tangential velocity ratio vt/v* = 3.0, agreeing
well with results obtained for line swabbing, even though separate methods were employed.
This is a satisfying check on the computation.
Figure 14
For b/a = 2.0 the peak velocity is reduced to 1.5 v*, or 50% of that
for b/a = 1.5. (See point X in Figure 14.) The solution
shown in Figure 14 represents peak velocities to be expected
from rocker beam swabbing. This would be repeated with each uphaul of the beam.
Complete reversal will not occur because of the foot valve. Peak radial velocities
induced by the swab motion are shown in Figure 13. These
are also cyclic with the swab motion.
In this method of development, flow is injected into the well below a
swab-equipped drill pipe (Figure 3). The injected flow must
bypass the swab through the gravel envelope or enter the formation. The mathematical
model for this operation is almost identical to that for line swabbing but with the
pressure drop reversed. Head provided by the pump at the surface will control head
difference across the swab when the swab is stationary.
There is a basic difference from line swabbing. Sections of the well
above and below the swab will be subjected to a pressure excess over the original static
pressure in the well. Consequently, the well will act as a recharge well.
Recharge potential of the well will be controlled by the hydraulic
conductivity of the wall cake and increase in static pressure. For a given head drop
across the swab the effect of this recharge will not modify the magnitude of the
tangential velocity profile because recharge flow is always radial. There remains the
question, of course, of how much head is used in radial flow and how much is used to
flush the filter pack. It seems reasonable to assume that the head difference between
the pumping head and overflow is used for flushing and head difference between the
overflow and the original static for recharge. The line swab results in
Figure 14 utilizing the head difference between the overflow
and pumping levels minus the head losses in the delivery pipe are used to determine the
flushing velocities.
If the swab is placed in motion by hauling the drill pipe then some
modification of the previous analysis is required. On an up motion of the swab the
tangential velocity in the filter pack will be reduced and may come to zero. The latter
occurs when the speed of the haul, multiplied by the area of the swab, exactly matches
the flow delivered by the pump. On the down stroke flushing effectiveness is enhanced
since the effective flow rate will be that delivered by the pump added to that induced
by the swab motion. A numerical comparison of the two cases is made in section 3.
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