gas laws applied to gas lift - espexpert.com
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© 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
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