Analysis of Development Methods for Gravel Envelope Wells - 10
For this case it is possible to estimate the magnitude of the
tangential velocity at the filter pack/ formation interface. If we assume that the
flow out between the swabs divides equally into an upflow and a downflow, and that
vertical velocity distribution in the filter pack is uniform, then the estimated
tangential velocity ve is given by
since all flow must pass through the annular area comprising the gravel envelope. From
equations (4) and (5) it is possible to show that
This relationship is presented in Figure 16
jointly with the tangential velocity to scaling velocity ratio as derived from the
mathematical model given in Appendix A.
Figure 16 demonstrates that the dependence of the mathematically
predicted tangential velocity on the ratios of b/a and L/a is very close to that
estimated in equation (6) above. However, peak tangential velocities are found to be
less than the estimated values. This can be ascribed to non-uniformity in the velocity
distribution, as is apparent from the fact that the mathematically predicted value
becomes a smaller fraction of the estimate as b/a increases except for increasing L/a.
Results in Figure 16 can therefore be used
to evaluate peak tangential velocities for any practical ratio of b/a and L/a.
Figure 16
In this section we compare the methods as applied to a 14-inch
diameter well with 7-inch filter pack, giving a dimensional ratio b/a = 2.0. Hydraulic
conductivity of the filter pack is assumed to be 10000 gpd/ ft2 and the
formation 100 gpd/ ft2, giving a ratio k2/k1 = 0.01,
which is within the range used in the computations. We consider each development method
in turn.
Consider first a well with filter pack particle size distribution
that does not permit any filter pack material to pass through the screen, restricting
pack motion. In this case assume three jets each ½-inch in diameter and operating
at 104 gpm at 250 psi, providing jet velocity of 190 ft/sec (Zdener and Allred 1979).
The ratio T/c = 28. Using formulae given in Appendix A, the peak tangential velocity at
the filter pack/ formation interface cannot exceed 0.003 ft/sec.
Jet development is essentially useless in this configuration.
Results indicate that for any practical thickness of filter pack (>2 inches) in a
situation where pack motion is impossible, jet development is inappropriate since
velocities generated at the interface of the filter pack and formation are too small to
be of much use.
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