Chp 02 v3 Choke Performance

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


• 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


• 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


• The performance of CD as a function of Reynolds number and beta

is illustrated by Crane (1957)

9


• 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


• 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


• 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 =


• 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


• 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


• 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)


( )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


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• 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


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( )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


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( ) ( )

( ) ( )

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,


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

−+=−

Chp 02 v3 Choke Performance

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