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Separation Theory
Stokes' law relates buoyancy forces to drag forces(8):
nr = 4.146 doil2 (goil - gwater)/µwater
where:
nr = rising velocity of oil (ft/hr),
doil = diameter of oil droplet (thousandths of an inch),
goil = specific gravity of oil,
gwater = specific gravity of water,
µwater = viscosity of water, (cp).
The above equation is for Reynolds number less
than 1.85. This will typically be the case for wellbore flow.
Stokes' law suggests that for any given set of conditions, if
a downward flow of water is kept below a certain velocity, then
oil will still gravitate upward through the column. Also, over
time, oil droplets will tend to coalesce together, increasing
their diameter, and increasing their rising velocity.
Figure 1 shows a pumping system situated in a wellbore with intakes
above and below the production perforations. A water flow gets
pulled down to the bottom intake and an oil concentrate stream
is produced to surface through the top intake.
There are several things that enhance this phenomenon of wellbore
gravity separation. Downhole video(9) has shown that oil typically
enters the wellbore in streams or as large droplets not as the
tight emulsion that is seen at surface. Given normal reservoir
characteristics (non-stratified), it can be assumed that the vast
majority of the oil enters the wellbore through the upper portion
of the perforations. Also, a zero velocity zone exists at some
point along the perforation face above which all fluid is pulled
up to the top intake and below which water is pulled down to the
bottom intake. Not only does this ensure that all oil is produced
up and to surface but it can also set up a small beneficial reverse
coning effect(10-11).
These are obviously some pretty optimistic assumptions. Some oil
may enter the wellbore below the zero velocity zone and be mm
size droplets in a homogeneous solution travelling down with the
water at too high a velocity for any relative upward movement.
Given this possibility it is necessary to configure a separation
chamber within the wellbore. This "separation chamber"
would provide for low velocities and long residence times to allow
for oil droplet coalescence and net upward velocity.
The above configuration can be constructed with two reciprocating
rod pumps connected by sucker rod. The top pump is a small bore
pump to produce an oil rich stream to surface. The bottom pump
is typically larger bore to pull the water down and dispose of
it to a zone in the same wellbore. Small bore tubing is run between
the two pumps to create the separation chamber. One of the major
advantages of a reciprocating rod pump design over other forms
of artificial lift for wellbore gravity separation is the 50%
dead time on the downstroke. During this dead time no water is
pulled down to the bottom pump and oil droplet coalescence and
upward velocity is maximized.
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