Lecture11c_Basic Gaslift Sec 3 - Opening and Closing and TRO Pressure Calculation

Gas Lift

Production TechnologyProduction TechnologyLecture 11c - Unloading Valve Opening, Closing and

P CalculationPTRO CalculationRecommended Texts: Handout and

A ifi i l Lif M h dArtificial Lift Methods, Kermit E. Brown, Volume 2a PennWell Publishing Co, Tulsa, OK, 1980

Akim Kabir

Senior Lecturer

Department of Petroleum Engineering

Curtin University of Technology

Slide 1Section 3 Opening and Closing and Ptro Calc.

Aug 2008

Gas Lift

Analogy Between Pressure Regulator / Gas Lift Valvegy g

Diaphragm/p gAtmospheric Bellows

Spring

St Upstream Stem

Stem TipUpstream

Upst ea/Casing

Port

DownstreamUpstream

Downstream/Tubing


Pressure Regulator Spring Operated Gas Lift Valve

Gas Lift

IPO G/L Valve BehaviorIPO G/L Valve Behavior

In an IPO valve high pressure

Nitrogen

In an IPO valve, high pressure nitrogen in the dome exerts pressure on the inside of the bellows. This causes the bellows Nitrogen

pressureto extend down and pushes the ball on the seat.


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G fGas from the casing tries to get into the valve. The pressure acts on the outside of the bellows, trying to compress the bellows.trying to compress the bellows.


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Fl id f th d tiFluid from the production tubing tries to force the stem off the seat.


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When the valve opens gas moves through the valve and out the nose.


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PdPd

Ab


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The valve is in theThe valve is in the closed position now. What does it take to open this valve? Pdvalve?Lets look first at the forces trying to close the valve.

Pd

Closing force = Pd xAb

Abwhere:Pd = nitrogen pressure

Ab = area of the bellows


Gas Lift


Opening force = Pt x Ap +

Now the opening forces:

Opening force = Pt x Ap + Pc(Ab - Ap)where:Pt = tubing pressurePc = casing pressureAp = port areaAp port areaAb = bellows area

The casing pressure

Pc

The casing pressure only acts on this area when the valve is closed

ApPt

closed

Ap

Slide 9Section 3 Opening and Closing and Ptro Calc.Ab

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IPO G/L Valve BehaviorIPO G/L Valve BehaviorThe solution:

The valve begins to open when the opening forces exceeds the Pdforces exceeds the closing force:

Pt x Ap + Pc(Ab - Ap)

Pd

>= Pd x Ab

For a given Pd we could solve for Pc the

Absolve for Pc, the pressure at which the valve should open.

Pc

AOr, for a design case of Pc and Pt, we could solve for the correct Pd

ApPt


solve for the correct Pd.

Gas Lift

IPO G/L Valve Opening Pressure CalculationThe valve begins to come open when the opening forces starts to exceed

IPO G/L Valve Opening Pressure Calculation

closing force.

Pd (Ab) =< Pt (Ap) + Pc(Ab - Ap)

O i PPd

Opening Pressure:

Pc >= (Pd(Ab) Pt(Ap)) /(Ab-Ap)

oror

Pvo = Pc >= (Pd Pt (R)) / (1-R)

Where R = Ap/AbAb

Where R = Ap/Ab

or

Pvo = Pc >= Pd/(1-R) Pt(T E F)

Pc

ApPvo Pc > Pd/(1 R) Pt(T.E.F)Where T.E.F = R/(1-R)

T.E.F = Tubing Effect Factor

ApPt


ub g ect acto

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IPO G/L Valve Closing Pressure CalculationIPO G/L Valve Closing Pressure Calculation

Pd

Ab

Pc

ApAp

Pt


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IPO G/L Valve Closing Pressure Calculation

When the valve is about to close the t d th th t i

IPO G/L Valve Closing Pressure Calculation

pressure acts underneath the port is Pc

Pd (Ab) > = Pc (Ap) + Pc(Ab - Ap) Pd( ) ( ) ( )or

Pd (Ab) >= Pc (Ab)

or

Pc (Ab)

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Valve Opening & Closing Pressures (IPO)

F = P X AF = P X A

WHEN THE VALVE IS CLOSEDWHEN THE VALVE IS CLOSEDTO OPEN IT..TO OPEN IT..

PdPd PdPd

Pc (1Pc (1--Ap/Ab)+Pt (Ap/Ab)Ap/Ab)+Pt (Ap/Ab) >= PdPc Pc

or

Pvo= Pc >= Pd/(1-R) Pt(T.E.F.)

WHEN THE VALVE IS OPENWHEN THE VALVE IS OPENTO CLOSE IT.. TO CLOSE IT.. Pvc = Pc

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Spread & Tubing Effect of the IPO Valves

Spread = Valve Opening Pressure Valve Closing Pressure

T.E. = Pt x T.E.F.

(T.E.= Tubing Effect)


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PPO G/L Valve BehaviorPPO G/L Valve Behavior

PdPd

Casing pressure is ti d th b ll f Pcacting under the ball of

the stem tip.

Pc


Gas Lift

PPO G/L Valve Opening Pressure CalculationThe valve begins to open when the opening forces start to exceed

PPO G/L Valve Opening Pressure Calculation

p gclosing force:

Pd (Ab) = (Pd(Ab) Pc(Ap)) /(Ab-Ap)Ap)

or

Pvo = Pt >= (Pd Pc (R) / (1-R)

Ab

Pvo Pt (Pd Pc (R) / (1 R)

Where R = Ap/Ab

or Pc Ap

Pvo = Pt >= Pd/(1-R) Pc(C.E.F)

Where C.E.F = R/(1-R)Pt

p


C.E.F = Casing Effect FactorPt

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PPO G/L Valve Closing Pressure CalculationPPO G/L Valve Closing Pressure Calculation

Pd

Ab

Pc Ap

Pt

p


Pt

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PPO G/L Valve Closing Pressure Calculation

When the valve is about to close

PPO G/L Valve Closing Pressure Calculation

When the valve is about to close the pressure acting underneath the port is Pt

Pd (Ab) >= Pt (Ap) + Pt(Ab Ap)Pd

Pd (Ab) >= Pt (Ap) + Pt(Ab - Ap)

Closing Pressure:

Pvc = Pt

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Valve Opening & Closing Pressures (PPO)

F = P X AF = P X A

p g g ( )

WHEN THE VALVE IS CLOSEDWHEN THE VALVE IS CLOSEDTO OPEN IT..TO OPEN IT..

PdPd PdPd

Pt (1Pt (1--Ap/Ab)+Pc (Ap/Ab)Ap/Ab)+Pc (Ap/Ab) >= Pd

orPc PcPvo = Pt >= Pd/(1-R) Pc(C.E.F.)

WHEN THE VALVE IS OPENWHEN THE VALVE IS OPENTO CLOSE IT.. TO CLOSE IT.. PtPt

Pvc = Pt

Gas Lift

Test Rack Opening Pressure Calculation (IPO)Test Rack Opening Pressure Calculation (IPO)Valve opening equation (IPO):

Pd = Pd/(1-R) Pt x R/(1-R) Valves are usually set in the workshop in a test rack with external pressure (Ptro) applied into the casing side while Pt is zero and valve temperature is at 60oF. pp g t pNitrogen is normally charged into the dome of the valvesTest Rack Opening Pressure is:

Pd @60Fd @60FPtro = -------------------------

(1 - (Ap/Ab))

Pd@d thPd@depth Ptro = ------------------------- ; [ Pd@60F = Pd/ Ct]

Ct x (1 - (Ap/Ab))

This equation can be applied for all type of valvesThis equation can be applied for all type of valvesCt =1+0.00215 X (T@D- 60)Ct = N2 Temperature Correction FactorT@D = Temperature at Valve Depth, oF


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Test RackTest Rack


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Gas Calculations for Gas Lift SystemGas Calculations for Gas Lift System

Temperature effect on dome pressure Temperature correction for gas volumetricTemperature correction for gas volumetric

throughput Gas volume stored within a conduit Gas injection pressure at depth Volumetric gas throughput of a choke or G.L.Volumetric gas throughput of a choke or G.L.

Valve port


Gas Lift

Temperature Effect on Dome Pressure Major Advantages of Nitrogen :

* Availability * Non-explosive* Non- corrosive * Predictable compressibility* Predictable temperature effect* Predictable temperature effect

From non-ideal (real) gas law:

P2 = P1/(Z1T1/Z2T2) {assume dome volume constant}2 1 ( 1 1 2 2) { }

Where: The initial conditions are labelled with subscript 1 and present condition with subscript 2

If the present conditions are at 60 F, Ct = 1+0.00215(T1 60) =Z1T1/Z2T2If the present conditions are at 60 F, Ct 1 0.00215(T1 60) Z1T1/Z2T2

P2 = P1/CtIf the present temperature is not at 60F, apply the following equation to determine P2p p , pp y g q 2

P2 = P1 X Tc

Where: Tc = Temperature correction factorWhere: Tc Temperature correction factor1 + 0.00215 x (T2 - 60)

Tc = --------------------------------1 + 0.00215 x (T1 - 60)


Where : T1 = Initial temperature, Deg FT2 = Present temperature, Deg F

Gas Lift

Temperature Correction for Volumetric Throughput

Based on equation of state for real gasPV = n ZRT

For real gas For real gas P1V1 P2V2

-------- = --------Z1T1 Z2T2

If P1 = P2 i.e. same pressure => temp. correction (Charles Law)(C a es a )

T2 Z2V2 = V1 x ---- x ----

T1 Z1T1 Z1


Gas Lift

V l S d Wi hi C d i C l l iVolume Stored Within a Conduit Calculation

To find the volume of gas contained under specificwell conditions):

P x TbVb = V x ----------------

Z x Pb x T

Where: Vb = gas volume at base conditionsV = capacity of conduit in cubic feetP = average pressure within conduitTb= temperature base in degrees RankinZ = compressibility factor for average pressure andZ = compressibility factor for average pressure and temperature in a conduitPb= pressure base (14.73 psi)T = average temperature in the conduit in degrees Rankin


g p g

Gas Lift

Calculations for Gas Injection Pressure at Depth

Gas injection pressure at depth

Calculations for Gas Injection Pressure at Depth

0.01875 x S.G. x DT x Z

Where: e = 2.71828

P@D = P@Se

P@D = Pressure at depth, psiaP@S = Pressure at surface, psiaS.G. = Gas Specific GravityS.G. Gas Specific GravityD = Depth, feetT = Average Temp Degrees RZ = Average Compressibility for TZ = Average Compressibility for T

and average pressure


Gas Lift

Calculation for Gas Inj Pressure at Depth

R l f th b E ti b d S G f 0 65

Calculation for Gas Inj. Pressure at Depth

Rule of thumb Equation based on S.G. of 0.65,a geothermal gradient at 1.60F/100ft and a surface temperature of 700F

P@D = P@S + (2.3 x P@S x D )100 1000

Where:P@D = Pressure at depth, psiaP@S = Pressure at surface, psiaP@S Pressure at surface, psiaD = Depth, feet


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A [in2]

d [ft]dx [ft]


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Volumetric Gas Throughput of a ChokeVolumetric Gas Throughput of a Choke

Equation based on Thornhill-Craver Studies

Since this equation is so complex it is much easier to use the chart attached to your class exercise.OR

Use the software program Ccgas a free ware from Camco for calculation of gas flow rate

th ifiacross the orifice


Gas Lift

Thornhill Craver Equation: Qg Throughput of a Choke q Qg g p

/1/21

2 FFkkg kkdu

kdu

11

15.155T

kg

pACQg

dudu

dgsc g

whereQgsc = gas flow rate at standard conditions (14.7 psia and 60 oF)., Mscf/DCd = discharge coefficient (determined experimentally), dimensionless,A = area of opening, sq in.,P1 = upstream pressure, psia,1 p p pP2 = downstream pressure, psiag = acceleration due to gravity, ft/sec2k= ratio of specific heats, dimensionless

1k/k1k

2

T1= upstream temperature, oR

Fcf =critical flow pressure ratio =F ti f d t / t i t t it


Fdu =ratio of downstream pressure/ upstream pressure, consistent units,Fdu = Fcf if Fdu< Fcf and Fdu = p2/p1 Fcf

Gas Lift

Thornhill Craver Equation: Qg Throughput of a Choke q Qg g p

/1/21

2 FFkkg kkdu

kdu

11

15.155T

kg

pACQg

dudu

dgsc g

Z factor not included in the equation TC 05440gcQQ

gDggT TC 0544.0gT

ga CQ

wherewhereCgT = approximate correction factor for gas gravity and temp, dimensionless,TgD = gas temperature at valve depth, oRQga = actual volumetric gas rate, Mscf/D, and


Qga g , ,Qgc = chart volumetric gas rate, Mscf/D.

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Class Exercise #1A pressure operated valve (IPO) is located at 6000. Pressure in the dome is

Class Exercise #1

Pressure in the dome is 700 psi & tubing pressure is 500 psi at 6000.

Ab = 1 sq. in

F = P X AF = P X A

WHEN THE VALVE IS CLOSEDWHEN THE VALVE IS CLOSEDPdPd PdPdAp = 0.1 sq. in1) Find Pc required to open the valve at depth

2) C l l t t bi ff t

WHEN THE VALVE IS CLOSEDWHEN THE VALVE IS CLOSEDTO OPEN IT..TO OPEN IT..Pc (1Pc (1--Ap/Ab)+Pt (Ap/Ab)Ap/Ab)+Pt (Ap/Ab) >= PdPc

PdPd

Pc

PdPd

or2) Calculate tubing effect factor and tubing effect

3) Calculate spread of the valve WHEN THE VALVE IS WHEN THE VALVE IS

OPENOPEN

Pvo= Pc >= Pd/(1-R) Pt(T.E.F.)

SPREAD = Opening Closing pressure

OPENOPENTO CLOSE IT.. TO CLOSE IT.. Pvc = Pd >=PcPvc = Pd >=Pc

PtPt PtPtT.E. = Pt x T.E.F.Injection Pressure Operated ValveInjection Pressure Operated Valve

PtPt PtPt

A 0 9 t P & T


Assume z=0.9 at Pavg & Tavg

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Gas Passage Response of IPO ValvesGas Passage Response of IPO Valves


Gas Lift

Gas Passage Response of PPO ValvesGas Passage Response of PPO Valves


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Lecture11c_Basic Gaslift Sec 3 - Opening and Closing and TRO Pressure Calculation

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