criteria for gas-lift stability

8/10/2019 Criteria for Gas-Lift Stability

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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


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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


1453


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



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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

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criteria for gas-lift stability

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