Analysis of Development Methods for Gravel Envelope Wells   -   6

Consider the swab at rest with the well at equilibrium. Moving the swab upwards causes the well to flow at a rate that matches the flow generated by the swab. If there is D feet of screen below the swab, then at the filter pack/formation interface radius b )and assuming no leakage past the swab) we must have a radial inflow velocity v_r given by

2 b Dv_r = a²U

so that the inflow velocity is

              (1)

where   a     is the radius of the well
           U     is the velocity of the swab.

This radial velocity will gradually decrease as D increases due to the rising swab. It is conceivable that the aquifer may not produce flow at the rate induced. If not, then pressure in the well below the swab will continue to drop and may even reach vapor pressure, forming a vapor cavity behind the swab. The magnitude of pressure drop is controlled by the productive capability of the aquifer, leakage past the swab and bypass flow through the filter pack about the swab. This pressure drop will gradually decrease with time since more well surface area capable of producing is exposed as the swab rises. Maximum well production clearly cannot exceed the equivalent flow produced by the swab motion, so that a maximum value for the production velocity component is that given above in equation (1).

The pressure rise above the swab as the swab lifts water in the well above the static point will continue to increase until limited by one of two effects. The well will overflow as water reaches the surface, or a level will be attained where the head is sufficient to cause flow into the aquifer and bypass around the swab at a rate that exactly matches the flow produced by the swab motion. This bypass through the filter pack will flush drilling debris and wall cake from the filter pack/ formation interface and deposit it in the well behind the swab.

Swab-induced flow can be modeled mathematically by ignoring the top and bottom aquifer boundaries and by considering the flow in a system of coordinates moving with the swab. Basic parameters controlling the solution are the ratio of filter pack to well radii b/a, ratio of hydraulic conductivities k2/k1, and the distance up or down the well from the swab in terms of well radii (z/a). Results are given in terms of multiples of a scaling velocity v* which is defined by

V* = k₁H/ a               (2)

where   H     is the head difference across the swab
            k₁    is the hydraulic conductivity of the filter pack
            a      is the well radius

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