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

Gas Lift

Production Technology Lecture 11c - Unloading Valve Opening, Closing and PTRO Calculation Recommended Texts: Handout

and

Artificial A ifi i l Lift Lif Methods, M h d Kermit E. Brown, Volume 2a PennWell Publishing Co, Tulsa, OK, 1980 Akim Kabir Senior Lecturer Department of Petroleum Engineering Curtin University of Technology

Aug 2008 Section 3 – Opening and Closing and Ptro Calc.

Slide 1

Gas Lift

Analogy gy Between Pressure Regulator g / Gas Lift Valve Diaphragm/ p g Atmospheric Bellows Spring

St Stem

Upst ea Upstream /Casing

Stem Tip Upstream Downstream Port Downstream/Tubing

Pressure Regulator Section 3 – Opening and Closing and Ptro Calc.

Spring Operated Gas Lift Valve Slide 2

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IPO G/L Valve Behavior In an IPO valve, valve high pressure nitrogen in the dome exerts pressure on the inside of the bellows. This causes the bellows to extend down and pushes the ball on the seat.

Section 3 – Opening and Closing and Ptro Calc.

Nitrogen pressure

Slide 3

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IPO G/L Valve Behavior

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

Section 3 – Opening and Closing and Ptro Calc.

Slide 4

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IPO G/L Valve Behavior

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

Section 3 – Opening and Closing and Ptro Calc.

Slide 5

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IPO G/L Valve Behavior

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

Section 3 – Opening and Closing and Ptro Calc.

Slide 6

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IPO G/L Valve Behavior

Pd

Ab

Section 3 – Opening and Closing and Ptro Calc.

Slide 7

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IPO G/L Valve Behavior The valve is in the closed position now. What does it take to open this valve?

Pd

Let’s look first at the forces trying to close the valve.

Closing force = Pd xAb where:

Ab

Pd = nitrogen pressure Ab = area of the bellows

Section 3 – Opening and Closing and Ptro Calc.

Slide 8

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Now the opening forces:

IPO G/L Valve Behavior

Opening force = Pt x Ap + Pc(Ab - Ap) where: Pt = tubing pressure Pc = casing pressure Ap = port area Ab = bellows area The casing pressure only acts on this area when the valve is closed

Pc Ap

Ap

Pt

Ab Section 3 – Opening and Closing and Ptro Calc.

Slide 9

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IPO G/L Valve Behavior The solution: The valve begins to open when the opening forces exceeds the closing force:

Pd

Pt x Ap + Pc(Ab - Ap) >= Pd x Ab For a given Pd we could solve for Pc Pc, the pressure at which the valve should open. Or, for a design case of Pc and Pt, we could solve for the correct Pd Pd. Section 3 – Opening and Closing and Ptro Calc.

Ab Pc A Ap Pt

Slide 10

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IPO G/L Valve Opening Pressure Calculation The valve begins to come open when the opening forces starts to exceed closing force. Pd (Ab) =< Pt (Ap) + Pc(Ab - Ap)

Pd

O Opening i Pressure: P Pc >= (Pd(Ab) – Pt(Ap)) /(Ab-Ap) or Pvo = Pc >= (Pd – Pt (R)) / (1-R)

Ab

Where R = Ap/Ab

Pc

or

Ap

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

Pt

T.E.F = Tubing ub g Effect ect Factor acto Section 3 – Opening and Closing and Ptro Calc.

Slide 11

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IPO G/L Valve Closing Pressure Calculation

Pd

Ab Pc Ap Pt

Section 3 – Opening and Closing and Ptro Calc.

Slide 12

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IPO G/L Valve Closing Pressure Calculation When the valve is about to close the pressure acts t underneath d th the th portt is i Pc

Pd

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

Ab

Pc (Ab) = Pd/(1-R) – Pt(T.E.F.)

WHEN THE VALVE IS OPEN TO CLOSE IT…..

Pvc = Pc = (Pd – Pc (R) / (1 (1-R) R) Where R = Ap/Ab Pc

or

Ap p

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

Pt

C.E.F = Casing Effect Factor Section 3 – Opening and Closing and Ptro Calc.

Slide 17

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PPO G/L Valve Closing Pressure Calculation

Pd

Ab

Pc

Ap p

Pt Section 3 – Opening and Closing and Ptro Calc.

Slide 18

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PPO G/L Valve Closing Pressure Calculation When the valve is about to close the pressure acting underneath the port is Pt Pd

Pd (Ab) >= Pt (Ap) + Pt(Ab - Ap) Closing Pressure: Pvc = Pt = Pd or Pc

Pc

Pvo = Pt >= Pd/(1-R) – Pc(C.E.F.)

WHEN THE VALVE IS OPEN TO CLOSE IT…..

Pt

Pvc = Pt temp. correction (Charles’ (C a es Law) a ) T2 Z2 V2 = V1 x ---- x ---T1 Z1

Section 3 – Opening and Closing and Ptro Calc.

Slide 25

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V l Volume Stored S d Wi Within hi a C Conduit d i C Calculation l l i To find the volume of gas contained under specific well conditions): P x Tb Vb = V x ---------------Z x Pb x T Where: Vb = gas volume at base conditions V = capacity of conduit in cubic feet P = average pressure within conduit Tb= temperature base in degrees Rankin Z = compressibility factor for average pressure and temperature in a conduit Pb= pressure base (14.73 psi) T = average g temperature p in the conduit in degrees g Rankin

Section 3 – Opening and Closing and Ptro Calc.

Slide 26

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Calculations for Gas Injection Pressure at Depth Gas injection pressure at depth 0.01875 x S.G. x D TxZ

P@D = P@Se Where:

e = 2.71828 P@D = Pressure at depth, psia P@S = Pressure at surface, psia S.G. = Gas Specific Gravity D = Depth, feet T = Average Temp Degrees R Z = Average Compressibility for T and average pressure

Section 3 – Opening and Closing and Ptro Calc.

Slide 27

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Calculation for Gas Inj. Inj Pressure at Depth “Rule “R l off th thumb” b” Equation E ti based b d on S.G. S G off 0.65, 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, psia P@S = Pressure at surface, psia D = Depth, feet

Section 3 – Opening and Closing and Ptro Calc.

Slide 28

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A [in2]

d [ft] dx

Section 3 – Opening and Closing and Ptro Calc.

Slide 29

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Volumetric 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 across the th orifice ifi

Section 3 – Opening and Closing and Ptro Calc.

Slide 30

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



 k  k 1/ k 2/ k 2g   Fdu   Fdu  k 1  Qgsc  155.5Cd  A p1  g T1 



where Qgsc = Cd = A = P1 = P2 = g = k= T1= Fcf Fdu

gas flow rate at standard conditions (14.7 psia and 60 oF)., Mscf/D discharge coefficient (determined experimentally), dimensionless, area of opening, sq in., upstream p ppressure, ppsia, downstream pressure, psia acceleration due to gravity, ft/sec2 ratio of specific heats, dimensionless upstream temperature, oR k / k 1  2  =critical flow pressure ratio =  k  1  =ratio ti off downstream d t pressure// upstream t pressure, consistent i t t units, it Fdu = Fcf if Fdu< Fcf and Fdu = p2/p1 ≥ Fcf

Section 3 – Opening and Closing and Ptro Calc.

Slide 31

Gas Lift

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



 k  2/ k  k 1/ k 2g   Fdu   Fdu  k 1  Qgsc  155.5Cd  A p1  g T1 



Z factor not included in the equation

C gT  0.0544  g TgD  Q gc Q ga  C gT



where CgT = TgD = Qga = Qgc =

approximate correction factor for gas gravity and temp, dimensionless, gas temperature at valve depth, oR actual volumetric ggas rate,, Mscf/D,, and chart volumetric gas rate, Mscf/D.

Section 3 – Opening and Closing and Ptro Calc.

Slide 32

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

Section 3 – Opening and Closing and Ptro Calc.

Slide 33

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Class Exercise #1 A pressure operated valve (IPO) is located at 6000’. Pressure in the dome is 700 psi & tubing pressure is 500 psi at 6000’. Ab = 1 sq. in Ap = 0.1 sq. in

F=PXA Pd

1) Find Pc required to open the valve at depth

WHEN THE VALVE IS CLOSED TO OPEN IT…..

Pc

2) C Calculate l l t ttubing bi effect ff t factor and tubing effect

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

or

Pc

Pvo= Pc >= Pd/(1-R) – Pt(T.E.F.)

3) Calculate spread of the valve SPREAD = Opening – Closing pressure

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

Pd

WHEN THE VALVE IS OPEN TO CLOSE IT…..

Pvc = Pd >=Pc

Pt

Pt Injection Pressure Operated Valve

A Assume z=0.9 0 9 att Pavg & Tavg Section 3 – Opening and Closing and Ptro Calc.

Slide 34

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Gas Passage Response of IPO Valves

Section 3 – Opening and Closing and Ptro Calc.

Slide 35

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Gas Passage Response of PPO Valves

Section 3 – Opening and Closing and Ptro Calc.

Slide 36