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Choke Valve Performance
1
Choke Valves
• Choke valves are utilized to regulate the well
production
• Choke valves can be classified as
– Fixed Choke Valve: these valves has certain bore size that
cannot be modified
– Positive Choke Valve: these valves has a bore size that can
be modified if the valve trim is replaced (require the well
shut-in by a secondary valve)
– Variable Choke Valve: the bore size of these valves can be
varied from a handle or hydraulic/pneumatic actuator
2
Positive Choke Valve
3
Variable Choke
4
Choke valves
• Subsurface Safety Valves
– Subsurface safety valve (SSV) is a control device used to
shut off production from the well in an emergency
situation
– SSV opening and closing may be controlled at the surface
or directly by subsurface well conditions
• Surface controlled subsurface safety valve (SCSSV) devices is
controlled by supplying pressure in a hydraulic line
• Subsurface controlled subsurface safety valve (SSCSV) are
operated directly by the well pressure (close when the well is
flowing outsider its normal production regime)
5
• The choke performance fluid can be approximated as done in flow through
restrictions,
• For incompressible fluid, Bernoulli equation applied to this case leads,
Choke Valve – Incompressible Fluid
( ) ( )2222
2
1112
1
2
1vgzpvgzp ρρρρ ++=++ ( ) ( )222
2
112
1
2
1vpvp ρρ +=+
1
1
v
p
2
2
v
p1d 2d
6
Choke Valve – Incompressible Fluid
• From continuity equation
• Replacing in the previous equation
• Yielding,
( ) ( ) 2
1
212211 vA
AvvAvA =⇒=
( )
−=−
2
2
1
22
2212
vA
Avpp
ρ
( )
−=−
2
1
22
221 12 A
Avpp
ρ
7
( )
2
1
4
1
2
21222
1
2
−
−==
d
d
ppAvAqideal
ρ
Choke Valve – Incompressible Fluid
• Experimentally has been found that the previous equation does not
predict the differential pressure for a given flow rate accurately.
Therefore, the following modification is carried out
• “CD” is known as valve discharge coefficient while the ratio of the
diameter is known as beta factor (β)
• Valve discharge coefficient is a function of valve Reynolds number
and the beta factor8
1
2
d
d=β
Choke diameter
Pipe diameter
( ) 2
1
212
2
14
1
2
2
1
−
−
=⇒=ρpp
A
d
d
CqC
q
q DD
ideal
Choke Valve – Incompressible Fluid
• The performance of CD as a function of Reynolds number and beta
is illustrated by Crane (1957)
9
Choke Valve – Incompressible Fluid
• Guo and Ghalambor (2005) proposed the following correlation,
which provide accurate results for Reynolds number above 104
• For incompressible fluid, the valve Reynolds number is calculated
as,
• While this equation for compressible fluid is written as,
10
( )[ ]4Relog025.03167.0
6.0−++= VDC β
β
2
477.1Re
d
q
µρ
=3
,,,ft
lbcPindbpdq ==== ρµ
2
,g3
1020Re
d
Q scg
µ
γ×= ,,,, cPindscfdQ scg === µ
Choke Valve – Incompressible Fluid
• The term “C” is the valve capacity factor and it is defined as
• In field units
( ) 2
1
212
2
−=
ρpp
CAq
[ ]
1 2
14β−
= DCC
( ) 2
1
2
2 10286
∆=
ρp
CAq ( )2
1
2
2 68.8078
∆=
ρp
dCq
indinAft
lbpsipbpdq ====∆= 2
2
3,,,, ρ
11
Incompressible Choke Performance
• The performance of choke valve is analyzed in regions
12
Incompressible Choke Performance
• Three operating regions are then observed:
– Normal flow region: the flow rate is proportional to the square
root of the pressure differential
– Semi-critical flow region: the flow rate does not shows a linear
relationship with the square pressure drop as observed in the
normal flow region
– Limit flow or choke flow: the flow rate remains constant in spite
of further increment of pressure drop. This means that the vena
contracta has reached the maximum evaporation rate and the
mean velocity is close to the sound velocity
13
Compressible Choke Performance
• Bernoulli equation does not apply for compressible fluids so that
the previous equation cannot be used for predicting the choke
performance for compressible fluids
• Therefore, let’s write the energy balance equation
• Let’s assume that there is no heat or work done in the valve
• Replacing terms
• We assume that there is not change of height
14
WQHEE PK&&&&& +=∆+∆+∆
0=∆+∆+∆ HEE PK&&&
( ) ( ) ( ) ( ) 022
1212
2
1
2
2 =−+−+
− hhmzzgmvv
m &&&
( ) ( ) ( ) 022
12
2
1
2
2 =−+− hhvv
Compressible Choke Performance
• From the continuity equation, we know
• Thus, the previous equation can be reduced as,
• The following relationship is obtained under the assumption of
ideal gas
• Leading
• From thermodynamic relationship, we know the following
relationship for ideal gas
15
( )21
2
2
2hh
v−=
small very 112 vvv ⇒>>
( )2121 TTChh p −=−
( ) ( )21
2
2 2 TTCv p −=
RC p1−
=κκ
V
P
C
Ck =
Compressible Choke Performance
• The velocity is given as,
• From ideal gas equation,
• Yielding,
• For an isentropic expansion,
16
( ) ( )21
2
21
2TTRv −
−=κκ
ρp
MWRTm
pVMWRTRT
MW
mpV =⇒=⇒=
( )
−
−=
2
2
1
12
21
2
ρρκκ ppMWv
( )
−
−=
2
1
1
2
1
12
2 11
2
ρρ
ρκκ
p
ppMWv
κ
κκ
ρρ
=⇒=
2
1
2
12211
p
pVpVp
Compressible Choke Performance
• The velocity is given as,
• The gas mass flow rate is calculated as,
• Replacing,
17
( )
−
−=
−κ
ρκκ
11
1
2
1
12
2 11
2
p
ppMWv
222 uAmg ρ=
−
−=
−κ
ρκκ
11
1
2
1
12 1
1
2
p
ppMWv
−
−=
−κ
ρκκ
ρ
11
1
2
1
122 1
1
2
p
ppMWAmg
Compressible Choke Performance
• Using the isentropic relationship again, the previous equation can
be written
• Since we know that
• This equation can be written as,
18
( )( )
−
−=
+κκ
ρκκ
11
1
2
2
1
2112
1
2
p
p
p
ppMWAmg
scg
g
scgscgscgg
mQQm
,
,,, ρρ =⇒=
( )( )
−
−=
+κκ
ρκκ
ρ
11
1
2
2
1
211
,
2,
1
2
p
p
p
ppMWC
AQ D
scg
scg
idealscgDscg
idealscg
scg
D QCQQ
QC −
−
=⇒= ,,
,
,
Compressible Choke Performance• Further mathematical manipulation leads to the following equation
• The sudden expansion of the gas downstream of the valve cause a
variation of the temperature. If the process is assumed isentropic,
the temperature variation can be calculated as,
19
( )( )( )
−
−=
+κκ
γκκ
11
1
2
2
1
2
1
12,1
1248p
p
p
p
TCpAQ
g
Dscg
RTpsiappindinAdMscfQ scg deg;,;;; 121
2
2
2
, =====
( ) ( )( )( )
−
−=
+κκ
γκκ
11
1
2
2
1
2
1
1
2
2,1
177.980p
p
p
p
TCpdQ
g
Dscg
κκ 1
1
2
2
1
1
2
−
=
p
p
z
z
T
T
Compressible Choke Performance• Plotting the previous equation is obtained that,
20
criticalp
p
1
2
Compressible Choke Performance• The previous results implies that if you gradually lower the
downstream pressure keeping the upstream pressure constant for a fixed choke opening, the flow rate will go from zero to certain maximum
• The pressure ratio at the maximum flow rate is known as critical ratio
• If you keep reducing the downstream pressure even further than critical ratio, the flow rate will remains constant at the maximum value
• The critical ratio is obtained by solving the following equation,
• Gas velocity in the choke reaches the speed of sound. Therefore, this is referred as sonic flow condition
21
( )1
1
2
12 1
20
−
+
=
⇒=
k
k
critical
g
kp
p
ppd
dm
• Tangren et al (1949) performed the first investigation on the effect
of gas/liquid mixture in the choke and restriction performance
• They showed that the critical pressure ratio is affected by the
presence of gas and the choke performance resemble the
performance of a choke handling compressible
Multiphase Performance Choke Performance
Critical pressure ratio
Choke Flow
Sub Critical or
Sub-sonic
22
• Based on this early research, several empirical correlations have
been formulated. Most of these correlation has the following form,
• This equation provides the choke upstream pressure assuming that
the valve operates under choke flow condition (sonic flow)
Multiphase Performance Choke Performance
( )n
m
S
qGLRCp =1
in 1/64 size, choke
bpd rate, liquid
scf/stb ratio, liquid-gas producing
(welhead) pressure valveupstream 1
=
=
=
=
S
q
GLR
p
psig 1 =p
psia 1 =p
23
• Subcritical and critical performance under two-phase
conditions has been modeled using different approaches
– Homogenous Model or Frozen Flow Model: it is assumed that
the phases flow through the choke as a homogenous mixture
with no flashing of gas from the oil phase
– General Homogenous Model: this model assumes a that a gas
and liquid mixture is flowing in thermodynamic equilibrium
(flashing of gas from oil is included)
– Empirical or Semi-empirical models: this models describe
relationship of the entrainment of one phase in the other based
on single-component approach
– Heterogeneous Flow Model: gas and liquid phase flowing
separately and without one phase being entrained in the other
Multiphase Performance Choke Performance
24
• Homogenous Model –SubCritical Flow:
• This model assume that both liquid and gas behave as
incompressible fluids
• The two-phase pressure drop is calculated assuming that mixture is
flowing at certain mixture velocity
• Density, volumetric flow rate and non-slip fractions are calculated
based on the upstream pressure
Multiphase Performance Choke Performance
25
( )2
1
2
2 68.8078
∆=
m
m
pdCq
ρ
GgLLm λρλρρ +=
gLm qqq +=
• Sachdeva’s Model:
• Sachdeva proposes the following equation for predicting the critical
pressure ratio
• where
• This is a implicit equation that can be solved using numerical
method
Multiphase Performance Choke Performance
26
( ) ( )
( ) ( )
1
2
21
11
21
11
11
11
1
2
1
21
11
1
−
−+
−++
−
−−+
−=
κκ
υυ
υυ
κκ
υυ
κκ
g
l
g
l
g
cl
c
x
xn
x
xnn
x
yx
y
( )( )CxCx
CCxn
V
VP
11
1
11
−+−
+= ( ) κυυ1
12
−= cgg y
• Sachdeva’s Model:
• If we define
• The criteria for critical flow is given as,
– Choke Flow
– Subcritical Flow
• The mass flux for subcritical flow is calculated as,
Multiphase Performance Choke Performance
27
critical
cp
py
=
1
2
=
1
2
p
pya
ca yy ≤
ca yy >
( ) ( ) ( )( ) ( )5.0
21112
2122,1
11288
−
−+
−−= gg
l
mcDg yxyx
pgCAm υυκκ
ρρ
( ) lg
m
xyx υυρ
κ1
1
11
2
11
−+=−