Grace Robert. Advanced Blowout and Well Control
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266
Advanced Blowout
and
Well
Control
Figure
S.8
-
Calculated Open Flow Potential Test
Williford Energy Company
-
Rainwater
No.
2-1
4
In
this
instance,
the Orkiszewski method was modified and
utilized to predict the multiphase behavior.’ The well was successklly
controlled.
The technique used
in
the Williford Energy example is very
conservative
in
that
it determines the multiphase kill rate required to
control the shut in bottomhole pressure
of
1995 psi. Analysis of Figure
5.9 indicates that the static bottomhole pressure will not be reached
in
the
blowout for more
than
100
hours. The flowing bottomhole pressure when
the kill procedure begins is only
434
psi and is only 1500 psi
approximately
20
minutes after the flowing bottomhole pressure
has
been
exceeded.
Of
course, in
this
case the kill operation is finished in just over
10 minutes. Including
all
these variables is more complex but well within
the capabilities
of
modem computing technology. Based on
this
more
complex analysis, the kill rate using 10.7-ppg mud was determined
to
be
10 bpm.
Fluid
Qwamics
in Well Control
261
Figure
5.9
-
Boitom Hole
Pressure
Build
Up
Test
Williford Energy Compary
-
Rainwater
No.
2-14
The model is further complicated by the fact that the Calculated
Open Flow Potential curve (COFP) presented
as
Figure
5.8
is
a
very
optimistic evaluation
of
sustained productive capacity.
An
Actual Open
Flow Potential curve (AOFP) based on
sustained
production would be
more appropriate for modeling actual kill requirements. A kill procedure
based on the
COFP
is
the more conservative approach. An
AOFP
curve
more accurately reflects the
effect
of
the pressure draw
down
in
the
reservoir
in
the vicinity
of
the wellbore.
THE
MOMENTUM
KILL
The Momentum Kill is a procedure where
two
fluids collide and
the one with the greater momentum
wins.
If the greater momentum
belongs to the fluid from the blowout, the blowout continues. If the
greater momentum belongs
to
the kill fluid, the well
is
controlled. The
technology of the Momentum
Kill
procedure is the newest and least
understood of well control procedures. However, the technique itself
is
not new.
In
the late fifties and early sixties, the air drillers
of
eastern
Oklahoma
thought nothing
of
pulling
into
the surface pipe to mud up an
268
air-drilled hole in an effort
to
avoid the hazards associated with the
introduction of mud to the Atoka Shale.
Momentum Kill concepts are best illustrated by Figures 5.10 and
5.1 1. Figure
5.10
illustrates
a
situation
in
which the outcome would never
be
in
doubt. The most fundamental reasoning would conclude
that
the
occupant
of
the
car
is
in
greater peril than the occupant of the truck.
It
is
most likely that the momentum
of
the truck will prevail and the direction
of
the car will be reversed. Conceptually, fluid dynamics are not
as
easy.
However, consider the guys
in
Figure 5.1 1. They have forgotten the fire
and turned their attention to each other. Obviously, the one with the least
momentum is destined for a bath.
Advanced
Blowout
and
Well
Control
I
Figure
5.
IO
The dynamics
of
a blowout are very much the same as
those illustrated
in
Figure 5.11. The fluid flowing from the blowout
exhibits
a
definable quantity
of
momentum. Therefore, if the kill fluid is
introduced
at a
greater momentum, the flow from the blowout is reversed
when the fluids collide. The governing physical principles are not
significantly different from those governing the collision of
two
trains,
two
cars or two men. The
mass
with the greatest momentum will win the
encounter.
Fluid
Dynamics
in
Well
Control
269
~~~
Figure
5.11
Newton’s Second Law states that the net force acting on a given
mass is proportional to the time rate
of
change of linear momentum of that
mass.
In
other words, the net external force acting on the fluid
within
a
prescribed control volume equals the time rate
of
change
of
momentum of
the fluid within the control volume plus the net rate
of
momentum
transport out of the surfaces of the control volume.
Consider the following development with all units being basic:
Momentum:
mv
M=--
gc
and the
mass
rate of
flow:
0=pVA=pq
and,
from
the conservation
of
mass:
pA
=
piviA,
(5.14)
(5.15)
(5.16)
Where:
m
=Mass,
lb,
270
Advanced
Blowout
and
Well
Control
ft
V
=
Velocity,
-
SeC
I'm
*
fr
=
Gravitational constant,
=
Density,
-
Ibf
-
sec2
gc
P
I'm
3'
3'
=
Volume rate
of
flow,
-
sec
Q
'bm
w
=
Mass
rate
of
flow,
-
sec
i
A
All variables are at standard conditions unless noted with a subscript,
i.
The momentum
of
the kill fluid is easy
to
compute because it is
essentially
an
incompressible liquid. The momentum
of
the
kill
fluid is
given by Equation
5.14:
=
Conditions at
any
point
=
Cross sectional flow area,
ft2
Substituting
results in the momentum
of
the kill fluid, Equation
5.17:
FluidDynamics
in
Well
Control
271
(5.17)
Since the formation fluids are compressible or partially
so,
the
Consider the
following
momentum
is
more difficult to determine.
development of an expression for the momentum of a compressible fluid.
From the conservation
of
mass,
Equation
5.16:
And, for
a
gas, the
mass
rate of flow from Equation
5.15
is
Substituting into the momentum equation gives
the
momentum
of
the
gas
as:
Rearranging the equation for the conservation of
mass
gives an
expression for the velocity
of
the gas,
vi
,
at any location
as
follows:
From the Ideal
Gas
Law
an
expression for
pi,
the density
of
the
gas at any point in the
flow
stream,
is
given by Quation
5.18:
272
Advanced
Blowout
and
Well
Control
',Ma<
zi
TR
Pi
=
(5.18)
Where:
sg
Ma
=
Specific gravity
of
the
gas
=
Molecular weight
of
air
1%
fr2
=
Pressure at point
i,
-
e
zi
T
R
=
Units
conversion constant
Substituting results in
an
expression for
vi,
the velocity
of
the gas
=
Compressibility factor
at
point
i
=
Temperature at point
i,
"Rankine
at
point
i
as
follows:
(5.19)
Making the final substitution gives the
final
expression for the
momentum
of
the
gas:
(5.20)
In
this
development,
all
units are
BASIC!
That
means
that
these
equations
can
be used in any system
as
long
as
the variables are entered in
their basic units.
In
the English system, the
units
would be pounds, feet
and seconds.
In
the metric system, the units would
be
grams, centimeters
and seconds. Of course, the
units
conversion constants would have
to
be
changed accordmgly.
Consider the example at the Pioneer Production Company
Martin
NO
1-7:
Fluid
Dynamics
in
Well
Control
273
Examule
5.6
Given:
Figure 5.12
Bottomhole pressure,
Volume rate
of
flow,
Specific gravity,
Flowing surface pressure,
Kill-mud density,
Tubing
OD
Tubing
ID
Casing
ID
Temperature at 4,000 feet,
Flowing pressure
at
4,000
fxt,e
Compressibility factor:
at 4,000 feet,
zi
Required:
=
5000psi
=
10mmscfpd
=
0.60
=
14.65 psia
=
15PPg
=
2
318 inches
=
1.995 inches
=
4.892 inches
=
58OORankine
=
317.6 psia
=
1.00
Determine the momentum of the
gas
at 4,000 feet and the rate at
which the kill mud will have
to
be pumped in order for the
momentum
of
the kill mud to
ex&
the momentum of the
gas
and kill the well.
274
Advanced
Blowout
and
Well
Control
\
]I
L
T
i
-
8-Z/ByCSG
AT
E.000
FT:
I
-
END
OF
TUBING
AT
4.000
Ff.
Figure
5.12
-
Pioneer Production
Company
-Martin
No.
1-7
Solution:
The momentum
of
the
gas
at
4,000
feet
can
be
calculated
from
Equation
5.20
as
follows:
Fluid
L?ynamics
in
Well
Control
215
Substituting and in
the proper
units,
lbm
fr'
=
0.0458
-
3'
=
115.74
-
sec
=
1.00
=
580
'Rankine
=
1544
=
0.60
=
28.97
P
-
lbf
"R-lb,
lbf
=
45734
2
P
4l-
P
=
32.2
Ibf
-sec2
=
0.1305
ft'
[(0.0458)(1
15.74)]2(1.00)(580)(1544)
(0.60)(28.97)(45734)(32.2)(
0.1
305)
M=
M
=
7.53
lbf
The
rate at
which
the
kill
mud must
be
pumped can
be
determined
by re-arranging Equation
5.17,
substituting
in
the proper
units
and solving
for
the
volume
rate
of
flow
as
follows:
Where:
M
=7.53
lbf