Analysis of Development Methods for Gravel Envelope Wells - 2
The basic feature of the mathematical models of each of these systems
are similar. There is a completed well of radius a, a filter pack of radius b, and
assumed hydraulic conductivities in the filter pack and formation of k1 and
k2 respectively (Figure 6). It is assumed that
k1 greatly exceeds k2. Typical values of k1 and
k2 are 10,000 gpd/ ft2 and 100 gpd/ ft2 respectively,
giving a ratio k2/k1 of order 0.01. This ratio may vary from 0.1
to 0.001 but, as will be shown, results obtained generally show a great insensitivity to
the ratio k2/k1.
Figure 6
The basis for assessment of the development methods will be the
magnitude of scouring velocity induced at the filter pack/ formation interface by
development flow circulation. This circulation fluid velocity has two components. One
is the radial to the well axis, the other tangential or parallel to the well axis.
Tangential fluid velocity at the filter pack/ formation interface is primarily
responsible for scouring wall cake. The radial component of this velocity removes the
material from the well.
This report considers each technique, its model, and results in turn.
Conclusions are drawn with respect to the applicability of the results presented and
relative usefulness of development methods considered. A comparison of the different
techniques is made for typical practical applications.
Details of all mathematical models are given in Appendix A.
Basic models for each of the five well development techniques and
computational results from the models are presented in this section.
The purpose of jetting is to provide a high energy flow through the
filter pack to the wall cake at the formation. This is considered to occur either by
flow through the motionless pack or by physical displacement of the pack material by the
jet. Mathematical modeling of either mode of operation is difficult. In the first case,
even though it is assumed that the pack will not move, the flow will not obey the Darcy
equations for flow in porous media. In these equations velocity is directly proportional
to pressure gradient. However, for very strong pressure gradients, the velocity produced
is less than would be predicted by the Darcy equations. This implies that their use here
will give a favorable representation of the jetting flow.
In the second case, where filter pack is presumed to be displaced by
the jet and move with the flow, equations describing the motion of the combined
pack-fluid motion are extraordinarily difficult to solve. Furthermore, it is not clear
how to predict the boundary that will form between the pack material that moves and that
which does not. It is apparent that any evaluation of this mode of jetting action must
be performed through use of a laboratory test model.
In the following mathematical analysis it is assumed first that the
pack material does not move and that any flushing of the wall cake must occur solely by
jet flow. A mathematical model of this operation is developed and its efficiency
evaluated. Subsequently, a laboratory test model will be described. This model has
been used to determine when the jet does move the pack material, and provides visual
evidence of the mechanisms involved. Each model will be discussed in turn.
Back |
R & D Home |
Next