pseudo steady-state plunger lift model

Gas Well Deliquification Workshop

Sheraton Hotel, Denver, Colorado

February 19 – 22, 2012

Pseudo Steady-State Plunger Lift Model

Kees Veeken

Shell E&P Europe (NAM B.V.)

Feb. 19 – 22, 2012 2012 Gas Well Deliquification Workshop

Denver, Colorado

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Contents

• Reasons

• Assumptions and equations

• Observations

• Conclusions


Denver, Colorado

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Reasons

• Selection and justification of (high cost) deliquification

measures based on comparison of incremental

production and cost profiles

• Outflow models for production forecasting “easily”

constructed for steady-state techniques such as

velocity string, foam, gas lift and downhole pump

• More complicated for transient techniques such as

plunger lift and intermittent production (plunger-less

lift)


Denver, Colorado

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Production Forecast

• Need to calculate average capacity (Qcap) as function of

reservoir pressure (Pres), and minimum achievable

reservoir pressure (Pmin) to compare plunger lift

against alternatives

– Pmin dictates incremental reserves

– Qcap governs time to recover those reserves

– Combination determines discounted incremental reserves and

costs for economics

• To date plunger modeling has focused mostly on

understanding and optimizing plunger cycle, rather

than capturing associated production performance


Denver, Colorado

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Production Performance – Prolific

Pmin dictates incremental reserves

Qcap governs time to recover reserves

Combi determines discounted reserves

Pmin

Compression

Pmin

Orginal

1 bara = 14.5 psia, 1e3 m3/d = 35.31 Mscf/d


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Production Performance – Poor

Production forecast follows

when combined with reservoir model

Pmin

Compression

Pmin

Orginal



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Well Model – Three Curves

Inflow – Forcheimer Pres

2 – FBHP2 = A.Q + F.Q2

Back Pressure Curve (Pres

2 – FBHP2)n = Q/Cres Cres=1/A @ n=1

Outflow – Cullender & Smith FBHP2 = B.FTHP2 + C.Q2

Liquid Loading Rate – Turner Qmin = TC.FTHP0.5.ID2/[(FTHT+273).Z]

Qcap = {[A2+4(C+F).(Pres2-B.FTHP2)]0.5-A}/2(C+F)

Pmin2 = B.FTHP2 + A.Qmin+ (C+F).Qmin

2



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Outflow Model – Approximation OK

LGR Bwet Cwet 20 1.37 0.0124 100 1.9 0.0144 500 4.5 0.026

Transition from “dry” gas well to “wet” gas well takes time

E.g. Q=100e3 m3/d, LGR=100 m3/e6m3, 4” ID 4 bar/hr



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Compression: Qcap Benefit, Pmin Benefit



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Velocity String: Qcap Penalty, Pmin Benefit



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Nomenclature

• Pres = reservoir pressure

• Pmin = minimum achievable Pres

• Qcap = average well capacity

• Q = gas rate

• Qmin = minimum stable gas rate

• FTHP = flowing wellhead press.

• FBHP = flowing bottom hole pr.

• A = Darcy inflow resistance

• F = non-Darcy inflow resistance

• B = hydrostatic outflow

parameter

• C = friction outflow parameter

• TC = liquid loading parameter

• LGR = liquid to gas ratio

• Vup = average upward plunger

velocity

• Vdown = average downward

plunger velocity

• Toff = shut-in period

• DP = liquid load + plunger friction

• P = pressure buildup during

shut-in period

• Vt = tubing volume

• Va = annulus volume

• F = plunger frequency

Plunger Lift Cycle

Feb. 27 - Mar. 2, 2011 2011 Gas Well Deliquification Workshop Denver, Colorado

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• Cartoon depicts Fekete Virtuewell plunger model

Plunger moves up and down tubing at given velocities Vup and Vdown

Qmin ~ FTHP.ID2.Vup, Toff > Tdown

On

= U

p

Afte

r F

low

Off

=

Plu

ng

er

Do

wn

+ B

uild

up

Pe

rio

d

Picture

Fekete

James MacDonald

Plunger Lift Cycle


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• ON (UP) – AFTER FLOW – OFF (BUILDUP)

Qmin is delivered by reservoir inflow Q plus blow down of annulus

volume if Q < Qmin

Up & Start Buildup

Q = {[A2+4.(C+F).(Pres2-(B0.5.THP+DP)2)]0.5-A}/2.(C+F)

After Flow

Q = {[A2+4.(C+F).(Pres2-(B0.5.THP+DP/2)2)]0.5-A}/2.(C+F)

Plunger Lift Cycle


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• ON (UP) – AFTER FLOW – OFF (BUILDUP)

Pressure buildup ∆P during Off period is just sufficient to generate

required annulus decompression volume

Difference between Qcap and Qmin is delivered

by annulus decompression volume Va x ∆P

P = (Pres-B0.5.FTHP-DP).[1-EXP(-c*Toff-0.3*c2*Toff

2)]

where

c = 1e3*Q/[(Va+Vt).(Pres-B0.5.FTHP-DP)]

and

Q = {[A2+4.(C+F).(Pres2-(B0.5.THP+DP)2)]0.5-A}/2.(C+F)


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Plunger Lift – No Annulus Support

Qcap penalty due to DP and Toff

Pmin benefit



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Plunger Lift – Annulus Support

Qcap penalty Pmin benefit



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Plunger Modeling

• Liquid load x plunger frequency F equals produced

liquid volume LGR x Qcap

• Calculate maximum Qcap, F, Toff and ∆P by varying DP

• Calculate maximum Qcap, F, ∆P and DP as function of

reservoir pressure Pres

• Show impact of inflow performance, annulus volume,

liquid production, inflow performance and wellhead

pressure

• Ignore complexity and transient nature of plunger

cycle, including plunger friction, plunger by-pass,

annulus friction and varying plunger velocity !


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0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0

5

10

15

20

0 5 10 15 20 25

T off

(d)

Q (e

3 m

3 /d

),

P (b

ara)

, F (

1/d

)

Liquid Load - DP (bara)

Gas Rate Frequency Buildup Toff

Vary Liquid Load DP to Maximize Qcap


Small Annulus Volume – Va=4 m3


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Large Annulus Volume – Va=100 m3


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Medium Annulus Volume – Va=20 m3


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Vary LGR @ Pres=62 bara


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Frequency, liquid load and

associated capacity loss

increase as LGR increases


Vary LGR @ Pres=40 bara


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Pmin increases as LGR increases


Vary A @ FTHP=25 bara


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Before Qmin = 46.9 e3m3/d

After Qmin = 31.7 e3m3/d (68%)

Plunger causes

deferment in

prolific wells


Vary A @ FTHP=5 bara


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Before Qmin = 19.2 e3m3/d

After Qmin = 6.3 e3m3/d (33%)

Plunger

most effective

at low FTHP



Denver, Colorado

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Observations

• Gas rate shows broad maximum Vs liquid load

• Suggests that plunger settings are quite forgiving

Parameter Pmin Benefit Qcap Penalty

Annulus Volume Increases (Decreases)

LGR Decreases Increases

Inflow Resistance Increases Decreases

FTHP Decreases (Increases)

Vup Decreases @ low Va

Vdown Decreases


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Conclusions

• Need pseudo steady-state plunger model to rank

plunger against alternative techniques

• Capture plunger performance by using simplest of

inflow and outflow models

• Make crude assumptions in the process

• Need to validate model against field results

• Plunger best suited for poor inflow and low liquid-gas

ratio

• Plunger performance benefits from significant annulus

volume and low wellhead pressure


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Denver, Colorado

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pseudo steady-state plunger lift model

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