Analysis of Development Methods for Gravel Envelope Wells - 7
Speed of the swab enters the problem in two ways. As noted above, it
controls the magnitude of the head difference across the swab. It also enters in the
form of a dimensionless parameter
R = aSU/ 2k1
where U is swab velocity
S is the specific storativity of the filter pack
In general, S is small* so that the parameter R will usually be in
the range of 0.1 - 0.001. In the particular case when R = 0.1 and the ratio of filter
pack radius to well radius is 1.5, distribution of tangential (along the well) velocity
at the formation/ filter pack interface is given in Figure 13.
Peak tangential velocity at the interface of the formation and pack is found to be
2.9 v*.
Figure 13
In the case when R = aSU/ 2k1 = 0.001, the magnitude of the
peak tangential velocity at the interface increases slightly to 3.0 v*. The solution
appears to be relatively insensitive to R in the range of practical interest.
The results above were developed relative to a coordinate frame
moving with the swab. To reduce these results to a fixed reference frame, the variable
z, the distance from the swab, must be replaced by z - Ut. This means that at a fixed
point in the well the velocity experienced will be similar to that shown in
Figure 13 as if the well axis were time. Tangential velocity
at the formation/ filter pack interface will be experienced for a time of approximately
2a/U, which will be relatively short for common well sizes and swabbing speeds.
Radial velocity is also developed by the swab bypass flow. There
will be flow into the formation ahead of the moving swab, and flow out of the formation
behind it. This flow velocity is also scaled by v*, and a graph of radial velocity,
vr/v*, as a function of distance ahead of and behind the swab is given in
Figure 13. The magnitude of this radial velocity will not be
high, relative to the peak tangential component of velocity along the well.
Nevertheless, behind the swab it will form a steady inflow into the well which will
carry drilling debris along with it.
In summary, line swabbing is a two-stage process involving production
inflow generated by the swan displacement followed by high velocity tangential motion in
the filter pack coupled with a more uniform radial well inflow. Repeated applications
of the process will be effective in clearing drilling debris and wall cake from the
borehole.
In this method, of well development the swab is oscillated up and
down in the screen section. The exact modeling of this technique is extraordinarily
difficult. The problems arise from having to satisfy a condition on the swab surface
that is being accelerated then decelerated continuously. In the previous case a simple
change in coordinates was sufficient to enable a solution to be found. Here we look for
a solution that has a periodic nature, with frequency f 
The results (Appendix
A) involve numerical computations that are very time-consuming even with a digital
computer. However, a simplification is possible by noting that the basic parameter of
the solution is a2S 
/k1. This has a very small magnitude and the solution is
equivalent to a motionless swab with a steady pressure drop across it. The oscillatory
solution therefore is of the form of this steady state solution multiplied by cos
t.
· See Bear (1979)
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