GAS LAWS APPLIED TO GAS LIFT - espexpert.com

© Schlumberger

GAS LAWS APPLIED TO GAS

LIFT

© Schlumberger

GAS CALCULATIONS RELATED TO

GAS LIFT SYSTEMS

• Gas injection pressure at depth

• Gas volume stored within a conduit

• Temperature effect on bellows-charged dome pressure

• Volumetric gas throughput of a choke or GL Valve port

© Schlumberger

GAS PRESSURE AT DEPTH

S.G. x L

53.34 x T x Z

P@L = P@S x e

Where: e = 2.71828

P@L = Pressure at depth, psia

P@S = Pressure at surface, psia

S.G. = Gas Specific Gravity

L = Depth, feet

T = Average Temp Degrees R

Z = Average Compressibility for T

and average pressure

© Schlumberger

COMPRESSIBILITY FACTOR

PV = ZnRT

P = Pressure, psia

V = Volume of Gas, ft3

N = Number Moles Gas

R = Gas Constant, 10.72

T = Temperature, Deg R

Z = Compressibility Factor

© Schlumberger

GAS 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@L = P@S + (2.3 x P@S x L )

100 1000

Where: P@L = Pressure at depth, psia

P@S = Pressure at surface, psia

L = Depth, feet

© Schlumberger

GAS PRESSURE AT DEPTH

0

2000

6000

8000

10000

12000

14000

4000

1000 2000

DE

PT

H F

TT

VD

TUBING PRESSURE

CASING PRESSURE

1500500 2500

DRAWDOWN

3000 3500

FBHP SIBHP

© Schlumberger

GAS VOLUME STORED WITHIN A

CONDUIT

Internal capacity of a single circular conduit

Q(ft3/100ft.) = 0.5454 di2

Q(barrels/100ft.) = 0.009714 di2

Annular capacity of a tubing string inside casing

Q(ft3/100ft.) = 0.5454 di2 - do2

Q(barrels/100ft.) = 0.009714 di2 - do2

Where: di = inside diameter in inches

do = outside diameter in inches

© Schlumberger

GAS VOLUME STORED WITHIN A

CONDUIT

To find the volume of gas contained under specific

well conditions):

P x Tb

b = V x ----------------

Z x Pb x T

Where: b = 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 temperature in the conduit in degrees Rankin

© Schlumberger

TEMPERATURE EFFECT ON

BELLOWS CHARGED DOME

Major Advantages of Nitrogen

•Availability

•Non-explosive

•Non- corrosive

•Predictable compressibility

•Predictable temperature effect

© Schlumberger

TEMPERATURE EFFECT ON

BELLOWS CHARGED DOME

P2 = P1 X Tc

Where: P1 = Pressure at initial temperature

P2 = Pressure resulting from change of temperature

Tc = Temperature correction factor

and

1 + 0.00215 x (T2 - 60)

Tc = --------------------------------

1 + 0.00215 x (T1 - 60)

Where : T1 = Initial temperature, Deg F

T2 = Present temperature, Deg F

© Schlumberger

© Schlumberger

VOLUMETRIC GAS THROUGHPUT

OF A CHOKE OR A GAS LIFT VALVE

Equation based on Thornhill-Craver Studies

Since this is a complex equation a chart is used

to provide a means of quickly obtaining

an approximate gas passage rate for a given

port size

© Schlumberger

THORNHILL-CRAVER

Assume Q = 650 mscf/day

Pt = 750 psi

Pc = 1000 psi

Port Size Required = ?

Q = P C K

650 = 1000 x C x 0.41

C = 1.59

Use 3/16 inch port

© Schlumberger

GAS PASSAGE THROUGH ORIFICE

VALVE

ORIFICE VALVE PERFORMANCE CURVE

PRESSURE

GA

S R

AT

E

CRITICAL FLOW SUBCRITICAL FLOW

© Schlumberger

GAS PASSAGE THROUGH ORIFICE

VALVE

RDO-5 Orifice Valve, 24/64" Port, Cd = 0.86

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00 1400.00 1600.00 1800.00 2000.00

Downstream Pressure (psig)

Ga

s F

low

rate

(m

ms

cf/

d)

Calculated Flowrate Measured Flowrate

Calculated Flowrate Measured Flowrate

Calculated Flowrate Measured Flowrate

Calculated Flowrate Measured Flowrate

© Schlumberger

GAS PASSAGE THROUGH

UNLOADING VALVE

UNLOADING VALVE PERFORMANCE CURVE

PRESSURE

GA

S R

AT

E Orifice Flow

Throttling Flow

© Schlumberger

INFLOW, OUTFLOW, FLOW

CORRELATIONS and NODAL

ANALYSIS

© Schlumberger

SUCCESSFUL DESIGN DEPENDS

UPON PREDICTION OF FLOWRATE

© Schlumberger

INJECTION GAS

PRODUCED FLUID

WELL

INFLOW (IPR)

WELL OUTFLOW

RELATIONSHIP (TPC)

SURFACE PRESSURE

SANDFACE

PRESSURE

BHFP

RESERVOIR

PRESSURE

BOTTOM HOLE PRESSURE AS A FUNCTION OF FLOW RATE

PRODUCTION AS A FUNCTION OF BOTTOM HOLE PRESSURE

© Schlumberger

WELL & RESERVOIR INFLOW PERFORMANCE

•Inflow performance relationship (IPR)

•Productivity Index (PI)

•Reservoir Pressure (Pr)

© Schlumberger

WELL & RESERVOIR INFLOW PERFORMANCE

PRODUCTIVITY INDEX

The relationship between well inflow rate and pressure

drawdown can be expressed in the form of a Productivity

Index, denoted „PI‟ or „J‟, where:

q

q = J(Pws - Pwf) or J = ------------------

Pws - Pwf

kh(Pav - Pwf)

qo = -----------------------------------

141.2 oBo.[ln(re/rw) - 3/4]

© Schlumberger

WELL & RESERVOIR INFLOW PERFORMANCE

FACTORS AFFECTING PI

1. Phase behaviour•Bubble point pressure

•Dew point pressure

2. Relative permeability behaviour•Ratio of effective permeability to a particular fluid (oil, gas or

water) to the absolute permeability of the rock

3. Oil viscosity•Viscosity decreases with pressure decrease to Pb

•Viscosity increases as gas comes out of solution

4. Oil formation volume factor (bo)

•As pressure is decreased the liquid will expand

•As gas comes out of solution oil will shrink

© Schlumberger

AS RATE INCREASES IS NO LONGER STRAIGHT LINE

• Increased gas sat. Near wellbore - rel. Perm. Effects

• Laminar > turbulent flow

• Exceeds critical flow of sand face

WELL & RESERVOIR INFLOW PERFORMANCE

© Schlumberger

WELL & RESERVOIR INFLOW PERFORMANCE

VOGEL

Dimensionless reference curve based on the following

equation:

Q/Qmax = 1 - 0.2(Pwf/Pws) - 0.8(Pwf/Pws)2

where: Q = the liquid production rate, stb/d

Qmax = the maximum liquid rate for 100% drawdown

Pwf = bottom hole flowing pressure, psi

Pws = the reservoir pressure, psi

© Schlumberger

Dimensionless Inflow Performance Relationship Curve for Solution

Gas Drive Reservoir (after Vogel)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Q/Qmax

Pb

hf/P

bh

s

© Schlumberger

© Schlumberger

Combined Vogel: PR > PB

0

500

1000

1500

2000

2500

0 1000 2000 3000 4000

Q (bpd)

Pw

f (p

si)

COMBINED IPR (STRAIGHT LINE PI AND VOGEL)

Straight line PI above Pb

Vogel below Pb

© Schlumberger

INJECTION GAS

PRODUCED FLUID

WELL

INFLOW (IPR)

WELL OUTFLOW

RELATIONSHIP (TPC)

SURFACE PRESSURE

SANDFACE

PRESSURE

BHFP

RESERVOIR

PRESSURE

BOTTOM HOLE PRESSURE AS A FUNCTION OF FLOW RATE

PRODUCTION AS A FUNCTION OF BOTTOM HOLE PRESSURE

© Schlumberger

OUTFLOW PERFORMANCE AND MULTIPHASE FLOW

Vertical flowing gradients

Horizontal flowing gradients

• Select correct tubing size

• Predict when artificial lift will be required

• Design artificial lift systems

• Determine BHFP

• Determine PI

• Predict maximum and/or optimum flow rate

• Determine maximum depth of injection

© Schlumberger

FACTORS EFFECTING TPC

Tubing Performance Curve is a function of

physical properties not inflow

• Tubing ID

• Wall roughness

• Inclination

• Liquid / gas density

• Liquid / gas viscosity

• Liquid / gas velocity

• Well depth / line lengths

• Surface pressure

• Water cut

• GOR

• Liquid surface tension

• Flowrate

© Schlumberger

PRESSURE LOSS IN WELLBORE

© Schlumberger

• System described by a energy balance expression

• Mass energy per unit mass in = energy out

• (+ - exchange with surroundings)

• For wellbore- pressure Calc. for length of pipe

• Integrated each section

• Pressure conveniently divided into three terms

ZP/Z

PRESSURE LOSS IN WELLBORE

© Schlumberger

PRESSURE LOSS IN WELLBORE

P/Ztotal = g/gccos + fv2/2gcd + v/gc[P/Z]

TOTAL

PRESSURE

DIFFERENCE

GRAVITY

TERM

ACCELERATION

TERM

FRICTION

TERM

© Schlumberger

• Correcting weight of fluid

• Dominant term

• Single phase simple

• Multiphase complex

g/gccos

GRAVITY

TERM

© Schlumberger

• Increases with rate

• Proportional to velocity

• Proportional to relative roughness

• Laminar vs turbulent flow

• Effective viscosity

• Effective mixture density

fv2/2gcd

FRICTION

TERM

© Schlumberger

• Expansion of fluid as pressure decreases

• Smallest term

• Often ignored

• Need to account in high rate

v/gc[P/Z]

ACCELERATION

TERM

© Schlumberger

NEAR SANDFACE

GRAVITY

FRICTION

ACCELERATION

NEAR SURFACE

GRAVITY

FRICTION

ACCELERATION

© Schlumberger

OUTFLOW PERFORMANCE AND

MULTIPHASE FLOW

• Multi-phase flow

• Holdup

• Superficial velocities

• Slip

• Flow regimes

• Flow maps

© Schlumberger

FLOW REGIMES

• Based on observations

• Different flow patterns

– Proportion of phases

– Flow velocity

– Viscosities

– Interfacial tension

© Schlumberger

FLOW REGIMES

© Schlumberger

CORRELATIONS

• Babson (1934)

• Gilbert (1939 / 1952)

• Poettmann & Carpenter (1952)

• Duns & Ros

• Hagedorn & Brown

• Orkiszewski

• Fancher & Brown

• Beggs &Brill

• Duckler Flannigan

• Gray

• Mechanistic

• Proprietary

© Schlumberger

Vertical Multi-Phase Flowing

Gradients

© Schlumberger

Horizontal Multi-Phase Flowing

Gradients

© Schlumberger

NODAL ANALYSIS

© Schlumberger

Pe

_

PrPwfsPwf

Pdr

Pur

Pusv

Pdsv

Pwh

Pdsc Psep

DP1 = Pr - Pwfs = Loss in Porous MediumDP2 = Pwfs - Pwf = Loss across CompletionDP3 = Pur - Pdr = Loss across RestrictionDP4 = Pusv - Pdsv = Loss across Safety ValveDP5 = Pwh - Pdsc = Loss across Surface ChokeDP6 = Pdsc - Psep = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in TubingDP8 = Pwh - Psep = Total Loss in Flowline

Possible Pressure Losses in Complete Production System

Bottom

Hole

Restriction

Safety

Valve

Surface

Choke

Separator

NODAL ANALYSIS

© Schlumberger

GAS INJECTION RATE (Qg)

THEORETICAL

OPTIMUM

GAS INJ. RATE

OPTIMUM GAS INJ. RATE

WITH SYSTEM CONSTRAINTS

UNSTABLE GAS

INJ. RATE

PR

OD

UC

TIO

N R

AT

E (

Qra

te)

FIND STABLE & OPTIMUM POINT OF INJECTION

© Schlumberger

• Select correct tubing size

• Predict when artificial lift will be required

• Design artificial lift systems

• Determine BHFP

• Determine PI

• Predict maximum and/or optimum flow rate

• Determine maximum depth of injection

NODAL ANALYSIS