criteria for gas-lift stability
TRANSCRIPT
-
8/10/2019 Criteria for Gas-Lift Stability
1/5
Criteria for Gas-Lift
Stability
a ~ a l d
Ashelm SPE U.
of
Trondheim
Summary
Severe flow instability (heading
or
annulus heading) is known from operations of gas-lift systems. Here, two simple
stability criteria are developed and compared with reported field data. The stability problems experienced for the cases examined
would have been identified with these criteria and corrected at the design stage.
Introduction
The currently used principles for gas-lift design were established
during the early 1950's.
1-3
They provide relations between
(1)
gas
injection pressure and the most efficient point of injection and (2)
gas injection rate and the production rate to be expected. From these
relations, standardized procedures for gas-lift design have been
worked out.
4
Works on application and optimization of the
procedures have provided further insight into the interrelations be
tween gas-lift design and economic performance.
5-8
Often-unstated assumptions of gas-lift design are that it will be
possible to inject gas at a constant downhole rate and that the
resultant production rate will be stable. This is not necessarily true;
severe flow instability is well known in the actual operation of gas
lift systems.
Variations in pressure and flow rate are observed in
all
multiphase
flow systems, even in pumping wells, because of redistribution of
gas and liquids. They cause relatively small short-duration pressure
and flow changes. Alone, this has little effect on the continuity of
production. In a gas-lift system, however, it may trigger system
instabilities.
API9 recommends that, for the sizing of pipes receiving gas
lifted production, a surge factor
of
40 to 50% should be added
to the estimated steady-state flow rate, compared with 20% for
naturally flowing wells.
9
Intended as guidelines for cases where
more definite information is lacking, these numbers may indicate
something about the uncertainties concerning the flow instabilities
during gas lift.
Bertuzzi
et al.
2 observed that when the lift-gas input rate was
reduced below a certain minimum, violent heading would occur
and the liquid production would eventually cease. They postulated
that
a
sudden drop in pressure in the tubing brought about a sudden
surge of gas into the tubing. The volume of gas surging into the
tubing is dependent on the pressure and volume
of
gas in the an
nular space.
If
the pressure in the annular space dropped too much,
gas ceased to flow into the tubing. More recently, gas-lift insta
bilities have led to shutdowns of wells in the Claymore field.
10
This was amended by replacement of the downhole injection valve
by a fixed orifice.
Flow instabilities have also been observed and analyzed for simple
air-lift pumps. 11,12 This
is
related to gas-lift instability. However,
the inflow mechanisms of a gas-lift system are considerably more
complicated than for an air-lift pump. Besides, the friction damp
ening will be much larger in a gas-lift system because of order-of
magnitude-larger flow length. Thus, the dominating mechanisms
of instability will be quite different.
During the last few years, attempts have been made to under
stand and to quantify gas-lift instabilities with numerical techniques.
One approach is to make a dynamic numerical model of the gas
lift system, assuming that instabilities that occur when the model
is run on a computer represent physical flow instabilities, as
Grupping et al. did. 13,14 This succeeds in demonstrating unstable
flow behavior by numerical means. The other approach is to apply
linear stability analyses directly on a mathematical model of the
flow system. Fitremann and Vedrines
l5
performed linear stability
analyses for a gas-lift system. The results after low-pressure sim
plifications were shown to correspond to small-scale laboratory ex
periments. No field data comparisons were attempted.
Copyright 1988
SOCiety of
Petroleum Engineers
1452
In the current work, two simple criteria are developed providing
causal relationships between gas-lift design parameters and flow
stability. The criteria developed do not substitute the more advanced
approaches of unstable flow behavior, but they may provide a prac
tical method for the design of stable gas-lift systems.
Mechanisms of Gas-Lift Instabili ty. Fig. 1 shows an abstraction
of
a gas-lift system. t is assumed that the high-pressure lift gas
enters the surface inlet of the gas conduit (surface piping and
casing/tubing annulus, or dedicated lift string) at a constant rate.
The lift gas will flow through the gas conduit and enter the tubing
through a subsurface injection port. The gas inflow rate into the
tubing is governed by the pressure difference across this port, be
tween the gas conduit and the tubing. By conventional gas-lift
design, constant inflow of lift gas is assumed. As mentioned, the
tubing pressure may show temporary variations, causing temporary
variations in the gas inflow rate. The question addressed here is
how the gas-lift system will respond to this.
f an increase
of
gas inflow causes increased pressure difference
between the gas conduit and the tubing, then the gas inflow to the
tubing will increase further. This positive feedback leads to unstable
flow behavior, as described by Bertuzzi et at 2 If an increased flow
of gas causes decreased pressure difference between the gas conduit
and the tubing, gas flow will decrease. Under this condition, the
gas-lift system will be stabilized by negative feedback.
Stability Criteria
In Appendices A and B, first-order stability analyses for gas-lift
systems are performed. This gives two explicit stability criteria.
The first quantifies stabilization as a result of the inflow responses
of reservoir fluid and lift gas; the second quantifies stabilization
caused by depletion
of
the gas conduit pressure.
Inflow Response. If the inflow rate of the heavier reservoir fluids
is more sensitive to pressure than the lift-gas flow rate, then the
average density of the flowing fluid mixture will increase in response
to a decrease in tubing pressure. This causes the tubing pressure
to increase again, which stabilizes the flow. Appendix A shows that
stabilization by the inflow response requires (Criterion 1
Pgse gqgs}
I
=
> 1 1)
qLse EAj)2
By this criterion, stability is promoted by a high flow rate of lift
gas, a high productivity index, and a small injection port.
Pressure-Depletion Response. f he first criterion is not fulfilled,
a decrease in the tubing pressure will cause the gas flow rate to
increase more than the liquid flow rate. This will cause a decreasing
tubing pressure, but will also deplete the gas conduit pressure. If
the gas conduit pressure depletes faster than the tubing pressure,
then the pressure difference between the gas conduit and tubing
will decrease, and so will the lift-gas rate. This stabilizes the flow.
Appendix B shows that stability corresponds to Criterion 2:
Journal of Petroleum Technology, November 1988
-
8/10/2019 Criteria for Gas-Lift Stability
2/5
By this criterion, stability is promoted by a small gas conduit
volume, a high gas flow rate, and a high inflow-response ratio. A
high tubing pressure, provided by higher wellhead backpressure,
will be stabilizing
if
the downhole gas injection volume is main
tained constant.
Relationships
to
xisting
Recommendations
and
Models
Some
of
the above considerations can be recognized in existing
design rules. API
4
recommends that the size
of
the injection port
be chosen so that a pressure differential of 690 kPa [100 psi] is
established across the injection port. For many gas-lift installations,
this will secure a stable inflow-response ratio:
F1 > l.
Bertuzzi et at
2
observed that the use
of
an auxiliary, small
diameter lift-gas string, would stabilize wells that were unstable
when injected through the casing/tubing annulus. Criterion 2 shows
that stability can always be achieved by choice of a sufficiently small
gas-lift conduit.
On the basis
of
experience and numerical simulation, Grupping
et
at
14 stated that gas-lift stabilization should be based on the
principle that the choking effect exercised at the surface injection
orifice, relative to that of the downhole orifice, should be de
creased.
By
the current model, this conclusion can
be
derived from
Criterion 1
Fitremann and Yedrines
15
observed that the pressure drop at the
gas injection point has a strong stabilizing effect. This again corre
sponds to Criterion 1, expressed most clearly by Eq. A-9.
In
the pressure-depletion-response analyses, Appendix B, the
Sffects
of
inertia and friction danIpening in the tubing are neglected.
These second-order effects are included by Fitremann and Ye
drines in their model and presumably also by Grupping et al 13
Fitremann and Yedrines' analysis showed that waves of three prin
cipal modes may establish
in
the tubing. The higher-frequency waves
are danIpened by flow friction; the lowest frequency is undampened.
The lowest frequency is the continuity wave, created by a change
in the inflow-mixture density.
By neglecting inertia and friction, the current analysis is based
on the assumption that the higher-frequency waves are sufficiently
dampened in a field-scale installation, so they can be neglected.
The field cases analyzed below appear to support this assumption.
Examination
of Reported Field
ases
Data on gas-lift instability are scarce in the literature. The cases
reported by DeMoss and Tiemann 10 and by Bertuzzi et al
2
are
primarily studies of stable gas-lift performance. However, they
contain enough information to examine the stability criteria, de
veloped above vs. actual gas-lift performance.
DeMoss and Tiemann report that Well C-2 in the Claymore field
turned out to be unstable when gas-lifted. The instability caused
.--- - - - Production
rr======= ift
gas
Tubing
Gas
condui t (annulus o r
dedica ted s t r i ng
Downhole choke
Reservoi r
Fig. 1-Gas-lift system.
pressure surges and prevented injection from the lower injection
port. Stability was later achieved by replacing the bottomhole in
jection valves by two fixed 9.5-mm [2r64-in.] orifices. Well C-6
showed a considerably lower productivity index than Well C-2;
therefore, stability problems were expected. Well C-6 was therefore
equipped initially with fixed 9.5-mm F%4-in.] downhole orifices.
With this arrangement, the well gave no stability problems.
The data reported for the Claymore wells are listed in the first
two columns of Table
1
The production and injection rates and
the pressure at the injection point are the design parameters reported
for the system:The effective injection port size for the valve type
originally installed in Well C-2 was estimated from the performance
chart given. A tubing-pressure-controlling feature
of
the valve ap
parently did not work and was neglected. Table 2 lists the estimated
fluid properties and downhole flow rates (volumetric flow rates at
gas injection conditions).
Bertuzzi et al
's
data were collected from an experimental well.
In Cases 1 through 4 the gas was injected through a small-diameter
auxiliary string. In these cases, no stability problems were experi-
TABLE 1-DATA REPORTED
Claymore Claymore Bertuzzi et al.
Bertuzzi et al. Bertuzzi et al.
Well C-2 Well C-6
Case 2 Case 7
Case 12
Vertical depth to injection port,
It [m)
7,600 [2317) 7,865 [2397) 4,500 [1372)
3,810 [1161) 3,810 [1161)
Tubing 10,' in. [mm)
4.78 [121.4) 4.78 [121.4) 1.995 [50.7) 1.995 [50.7)
1.995 [50.7)
Tubing 00, ' in. [mm)
5.51 [140.0) 5.51 [140.0) 2.375 [60.3) 2.375 [60.3)
CaSing
10,'
in. [mm) 8.7 [221) 8.7 [221) 5 [127)
5 [127)
Gas-string
10,
in. [mm) 0.824 [20.9)
Liquid production rate, BID
[m
3
/s
14,000 [0.0258) 12,000 [0.0221) 374 [0.000688)
541 [0.000995) 541 [0.00114)
Gas injection rate, MscflD [std m
3
/d 11,200 [3.67) 12,000 [2.87) 68.3 [0.0224) 192.3 [0.0630) 507.9 [0.1664)
WOR, 1t3 lt
3
0.025 0.04
306
105
18.8
Nominal injection port size, in. [mm) 0.91 23) 24/64 [9.53 14/64 [5.6 14/64 [5.6
Orifice efficiency factor
0.9
0.9 0.9 0.9
0.9
Injection-gas specific gravity
0.81 0.81
0.668 0.668 0.668
Oil specific gravity
0.884 0.884 0.846 0.846
0.846
Water specific gravity 1.07 1.07 1.07
Formation gaslliquid ratio, 1t3 lt
3
,0
13
11.2 29.1
67.5
Temperature at injection port, OF [K)
172 351)
172 351) 166 348) 162 346) 162 346)
Pressure at injection port, psi [kPa) 1,610 [11
100)
1,600 [11
030)
1,035 7140) 590 4070) 600 [4140)
Productivity index, BID-psi [m 3/s Pal
26 [6.94x10-
9
) 14.4 [3.84x10-
9
) 1.88 [5.02x10-
1O
) 1.88 [5.02x10-
1O
) 1.88 [5.02x10-
1O
)
Values from tubing tables based on nominal diameters given
....
Two valves/orifices are used for the Claymore wells. The equivalen t port size for the valves
in
Well C-2 is estimated from valve performance curve given. 10
Journal of Petroleum Technology, November 1988
1453
-
8/10/2019 Criteria for Gas-Lift Stability
3/5
TABLE
2 ESTIMATED
FLUID PARAMETER AND FLOW RATES. IN SI UNITS AS APPLIED IN THE CALCULATIONS
Claymore
Well C-2
z
factor of injected gas
0.79
FVF of injected gas
0.00877
Downhole density of injected gas, kglm 3
113
Downhole density of reservoir fluid mix,
kg/m
3
884
Downhole fluid (oil, gas, water) rate, m
3
/s
0.0258
Downhole gas injection rate, m
3
/s
0.0322
enced. Case 2 examined here is the lowest-flow case. According
to our stability criteria, this would be the least stable.
For
Bertuzzi et ai. s Cases 5 through 18, the gas was injected
into the annulus. The well was equipped with a 5.6-mm
[1 4-in.]
downhole orifice. They reported that liquid production could be
varied only over a range of about 10 percent by varying the input
gas rates. f the gas input rate was reduced below the minimum,
heading would occur and the flow would eventually cease. Cases
7 and
12
are examined here. Case
12
had the highest reported liquid
production and should be stable. In Case 7, the liquid production
is about
13
% lower than for Case 12; it should therefore be at least
on the border of instability. .
The data reported by Bertuzzi et ai are listed in the three last
columns of Table
1.
Table 2 lists the estimated fluid properties and
downhole flow rates (volumetric flow rates at gas injection con
ditions).
For
both Bertuzzi
et ai. s
data and the Claymore cases,
0.9 was used for the orifice efficiency factor.
Table 3 summarizes the stability criteria calculated for the cases
examined. As seen, the estimates correspond nicely to observed
behavior. A discrepancy occurs for Bertuzzi
et ai. s
Case 12, which
was reported as stable but is predicted to be unstable. This is a case
of
high flow rate in a small tubing with significant, but not suffi
cient, stabilization by conduit pressure depletion (F2
=0.83).
It is
possible that tubing-flow friction dampening, which is neglected
in the criteria development, may smooth out the flow variations
in this case. However, there may also be other explanations.
onclusions
On the basis of limited comparison with reported field data, the
theoretically founded criteria appear to identify potentially unstable
wells and to provide quantitative guidelines for stabilization. The
stability problems experienced for the cases examined would have
been identified with these criteria and corrected at the design stage.
omenclature
Ai = injection port size, m
2
[ft2]
AI
=
tubing flow area, m
2
[ft2]
Bfi = FVF of reservoir fluids at injection point
Bg
= FVF
of
gas at injection point
D = vertical depth to injection point, m [ft]
E =
orifice efficiency factor, here assumed to equal 0.9
F
1
F
2
= stability criteria
g = acceleration of gravity, m/s2 [ft/sec
2
]
J = productivity index, std m
3
/s Pa [scf/sec'psi]
M = gas molecular weight
Pei
=
gas conduit pressure at the injection point, Pa [psi]
PR = reservoir average pressure, Pa [psi]
Claymore Bertuzzi et a/. Bertuzzi at al
Bertuzzi at al
Well C-6
Case 2
Case 7
Case 12
0.79 0.9 0.92 0.92
0.00882 0.0154 0.0274
0.0270
112
52.9 29.7
30.2
884 9 593 377
0.0221 0.000807 0.00179 0.00323
0.00254 0.000345 0.00173 0.00449
Pt
= tubing pressure, Pa [psi]
Ptf
= tubing-head flowing pressure, Pa [psi]
Pti = tubing flowing pressure at gas injection point, Pa
[psi]
Pwf
= bottornhole flowing pressure, Pa [psi]
::"Pj = friction loss, Pa [psi]
qfi = flow rate of reservoir fluids at injection point, m
3
/s
[ft
3
/sec]
qgi = flow rate of lift gas at injection point, m
3
/s [ft
3
/sec]
qgse
= flow rate of lift gas at standard conditions, std m
3
/s
[scf/sec]
qLse = flow rate of liquids at standard conditions, std m
3
/s
[scf/sec]
R
=
universal gas constant, Nm/kmol' K [ft-Ibf/gmol'
OF]
t
= time, seconds
rei = conduit gas flowing temperature at the injection
point, K reF]
Tti = tubing fluid flowing temperature at the injection
point, K [OF]
v =
flow velocity, m/s [ft/sec]
Ve
=
gas conduit volume, m
3
[ft3]
VI = tubing volume downstream of gas injection point,
m
3
[ft3]
Wei = mass injection rate
of
gas into conduit volume, kg/s
[Ibm/sec]
wti =
mass injection rate of gas into tubing, kg/s [Ibm/sec]
z = gas z factor
o = small perturbation of steady state
Pa
=
tubing-averaged fluid density, kg/m3 [lbm/ft3]
Pfi = reservoir fluid density at injection point, kg/m3
[lbm/ft3]
Pgi = lift-gas density at the injection point, kg/m
3
[lbm/ft3]
Pgsc = lift-gas density at standard surface conditions,
kg/std m
3
[lbm/sct]
Pi
= mixture density of reservoir fluids and lift gas at
injection point, kg/std m
3
[Ibm/sct]
References
I. Poettmann, F.H. and Carpenter, P.G.: Multiphase Flow
of
Gas, Oil,
and Water Through Vertical Flow Strings with Application to the Design
of Gas-Lift Installations,
Drill Prod. Prac.,
API (1952) 257-317.
2. Bertuzzi, A.F. Welchon, J.K., and Poettmann, F.H.: Description
and Analysis
of
an Efficient Continuous-Flow Gas-Lift Installation,
Trans.,
AIME (1953) 198, 271-78.
TABLE 3 RESULTS
Predicted Observed
WelllCase Behavior Behavior
Well C-2
0.06 0.76 Unstable Unstable
Well C-2 after valves replaced
by
20 /
64
-in. orifices
1.9 Stable Stable
Well C-6 0.76 2.7 Stable Stable
Bertuzzi et a/. Case 2 5.2
Stable
Stable
Bertuzzi et a/. Case 7 0.09 0.28 Unstable Unstable
(?)
Bertuzzi
et a/.
Case 12 0.55 0.83 Unstable Stable (?)
1454
Journal of Petroleum Technology, November 1988
-
8/10/2019 Criteria for Gas-Lift Stability
4/5
3. Gilbert, W.E.: Flowing and Gas-Lift Well Performance , Drill.
Prod. Prac., API (1954) 126.
4 Gas Lift, Vocational Training Series, Prod. Dept. API,
6.
5. Blann, J.R., Brown, J.S., and DuFresne, L.P.: Improving Gas-Lift
Performance in a Large North African Oil Field, JPT(Sept.
1980)
1486-92.
6. Kanu,
E.P.,
Mach,
J.,
and Brown, K.E. : Economic Approach to Oil
Production and Gas Allocation
in
Continuous
Gas
Lift, JPT (Oct.
1981
1887-92.
7. Clegg, J.D.: Discussion
of
Economic Approach to Oil Production and
Gas Allocation in Continuous Gas
Lift,
JPT(Feb. 1982) 301-02.
8. Blann, J.R. and Williams, J.D.: Determining the Most Profitable Gas
Injection Pressure for a Gas Lift Installation, JPT (Aug. 1984 1305-11.
9.
API RP
14E, Design and Installation
of
Offshore Production Platform
Piping Systems, API (1984).
10. DeMoss, E.E. and Tiemann, W.D.:
Gas
Lift Increases High-Volume
Production From Claymore Field,
JPT
(April 1982) 696-702.
11. Hjalmars, S.:
The
Origin
of
Instability in Airlift Pumps, Trans.,
Appl. Mech., ASME (1973) 41, 399-404.
12. Apazidis, N.: Influence of Bubble Expansion and Relative Velocity
of he Performance and Stability
of
an Airlift Pump, Inti. J. Multiphase
Flow (1985) 11, No.4, 459-79.
13. Grupping,
A.W.,
Luca,
C.W.F.,
and Vermeulen, F.D.: Heading
Action Analyzed for Stabilization, Oil
Gas
J. (July 30, 1984 47-51.
14. Grupping, A.W., Luca,
C.W.F.,
and Vermeulen, F.D. : These
Methods Can Eliminate
or
Control Annulus Heading, Oil Gas J.
(July 30, 1984) 186-92.
15. Fitremann, J.M. and Vedrines, P.: Non Steady Gas-Liquid Flow in
Pipes and Gas-Lifted Wells, Proc., Second Inti. Conference on Multi
Phase Flow, London (June 19-21, 1985) 245-62.
Appendix A Inflow
Response
A decrease in the downhole tubing pressure will cause increased
flow of both reservoir fluid and lift gas. I f he flow
of
gas increases
relatively more than the flow of liquid, the density of the fluid
mixture decreases. This reduces the static head and the flow friction
and thus may accentuate instabilities. On the other hand, if the
density increases in response to decreasing pressure, both the static
head and the flow friction will increase and the system will be stabi
lized by negative feedback. Thus, a criterion for stability becomes
OPi
F,
l
A-8)
qft (
EA
i)2
or, equivalently, in terms of pressures,
2Pt In(p Ipt )
F = I CI I > 1
A-9)
PR-Pwj
It is convenient to express the criterion in terms of surface flow
rates:
Fl = P g s c g q ~ s c
_ _
>
1
(A-tO)
qLsc (EAJ2
ppendix
B Pressure D epletlon Response
Suppose that the system is unstable by the criterion derived in Ap
pendix A. Then a decrease in tubing pressure will cause increased
inflow of lift gas. However, the increased inflow of lift gas will
also deplete the gas conduit pressure. I f
the gas conduit pressure
depletes faster than the tubing pressure, the gas flow rate will soon
reverse to stabilize the flow:
aqg/at 1
(B-2)
Pci
-apti
1at
The change of gas conduit pressure is expressed by the general
gas equation:
apci zciRTci
- -=O(Wc i -W l i ) - - -
B-3)
at
VcM
1455
-
8/10/2019 Criteria for Gas-Lift Stability
5/5