Pressure Loss Correlations Introduction In the flow of fluids inside pipes, there are three pressure loss components: •
Friction
•
Hydrostatic
•
Kinetic energy
Of these three, kinetic energy losses are frequently much smaller than the others, and are usually ignored in all practical situations. All the pressure pressure loss procedures calculate calculate the Hydrostatic Hydrostatic ressure !ifference !ifference and Friction Friction ressure "oss components indi#idually, indi#idually, and then add $or su%tract& them to o%tain the total pressure loss. 'here are many pu%lished correlations for calculating pressure losses. 'hese fall into the two %road categories of (single phase flow( and (multi)phase flow(.
Single Phase 'here e*ist many single)phase correlations that were deri#ed for different operating conditions or from la%oratory e*periments. +enerally speaking, they only account for the friction component, i.e. they are applica%le to horiontal flow. 'ypical 'ypical e*amples are : For Gas : anhandle, -odified anhandle, eymouth and Fanning For Liquid : Fanning Howe#er, these these correlations can also %e used for #ertical or inclined flow, pro#ided the hydrostatic pressure drop is accounted for, in addition to the friction component. A As s a result, e#en though a particular correlation may ha#e %een de#eloped for flow in a horiontal pipe, incorporation of the hydrostatic pressure drop allows that correlation to %e used for flow in a #ertical pipe. 'his adaptation is rigorous, and has %een implemented into all the correlations used in /irtuell. 0e#ertheless, for identification purposes, the correlation1s name has %een kept unchanged. 'hus, as an e *ample anhandle was originally de#eloped for horiontal flow, %ut its implementation in this program allows it to %e u sed for all directions of flow.
Single Phase Friction Component 'here are two distinct types of correlations for calculating friction pressure loss $ f &. &. 'he first type, adopted %y the A+A $American $American +as Association&, includes anhandle, -odified anhandle and eymouth. 'hese correlations are for single)phase gas only. 'hey incorporate a simplified friction factor and a flow efficiency. 'hey all ha#e a similar format as follows:
where: 2,34upstream and downstream pressures respecti#ely $psia& 54gas flow rate $ft678d 9 ',& 4pipeline efficiency factor 4reference pressure $psia& $2;.<= psia& '4reference temperature, $>& $=3? >& +4gas gra#ity !4inside diameter of pipe $inch& 'a4a#erage flowing temperature $>& @a4a#erage gas compressi%ility factor "4pipe length $miles& 4 constants 'he other type of correlation is %ased on the definition of the friction factor $-oody or Fanning& and is gi#en %y the Fanning equation:
where: f 4pressure 4pressure loss due to friction effects, $l%f 8ft3& 8ft3& f4Fanning friction factor $function of >eynolds num%er& 4density, $l%m8ft7& #4a#erage #elocity, $ft8s& "4length of pipe section, $ft& gc 4 con#ersion factor $73.3 $l% mft&8$l% f s3&& s3&& !4inside diameter of pipe, $ft& 'his correlation can %e used either for single)phase gas $Fanning +as& or for single)phase liquid $Fanning ) "iquid&.
Single-Phase friction factor (f) 'he single)phase friction factor can %e o%tained from the hen $2BCB& equation, which is representati#e of the Fanning friction factor chart.
where: f 4 friction factor k 4 a%solute roughness $in& k8! 4 relati#e roughness $unitless& >e 4 >eynold1s num%er 'he single)phase friction factor clearly depends on the >eynold1s num%er, which which is a function of the fluid density, #iscosity, #elocity and pipe diameter. 'he friction factor is #alid for single)phase gas or liquid flow, as their #ery different properties are taken into account in the definition of >eynold1s num%er.
where: 4 density, l%m8ft7 # 4 #elocity, ft8s ! 4 diameter, ft 4 #iscosity, l%8ftDs Eince #iscosity is usually measured in (centipoise(, and 2 cp 4 2; l%8ftDs, the >eynolds num%er can %e rewritten for #iscosity in centipoise.
>eference: hen, 0. H., (An *plicit quation for Friction Factor in ipe,( Ind. ng. hem. Fund. $2BCB&.
Single Phase Hydrostatic Component Hydrostatic pressure difference d ifference HH can %e applied to all correlations %y simply adding it to the friction compon component ent.. 'he 'he hydrost hydrostati atic c pressu pressure re drop drop $ HH& is defined, for all situations, as follows: HH 4 gh where: 4density of the fluid g4acceleration of gra#ity h4#ertical ele#ation $can %e positi#e or negati#e& For a liquid, liquid, the density density $ & is constant, constant, and the the a%o#e equation is easily e#aluated. For a gas, the density #aries with pressure. 'herefore, to e#aluate the h ydrostatic pressure loss8gain, the pipe $or well%ore& is su%di#ided into a sufficient num%er of segments, such that the density in each segment can %e assumed to %e constant. 0ote that this is equi#alent to a multi)step ullender and Emith calculation.
Single Phase Correlations Single Phase Gas
Liquid
Corr Co rrel elat atio ions ns
Vertic rtical al
Hori Horizo zont ntal al
Fanning-Gas
*
*
Vertic rtical al
Hori Horizo zont ntal al
Fanning-Liquid
Panhandle
*
*
Modified Panhandle
*
*
Weymouth
*
*
Mechanistic
*
*
*
*
*
*
ultiphase -ultiphase pressure loss calculations parallel single phase pressure loss calculations. ssentially, ssentially, each multiphase correlation makes its own particular modifications to the hydrostatic pressure difference and the friction pressure loss calculations, in order to make them applica%le to multiphase situations. 'he friction pressure pressure loss is modified modified in se#eral ways, ways, %y adGusting the friction factor $f&, the density density $ & and #elocity $#& to account for multiphase mi*ture properties. In the A+A type equations $anhandle, -odified anhandle and eymouth&, it is the flow efficiency that is modified. 'he hydrostatic pressure difference calculation is modified %y defining a mi*ture density. 'his 'his is determined %y a calculation of in)situ liquid holdup. Eome correlations determine holdup %ased on defined flow patterns. Eome correlations $Flanigan& ignore the pressure reco#ery in downhill flow, in which case, the #ertical ele#ation is defined as the sum of the uphill segments, and not the (net ele#ation change(. 'he multiphase pressure loss correlations used in this software are of two types. •
'he first type $Flanigan, -odified Flaniganand eymouth $-ultiphase&& is %ased on a com%ination of the A+A equations for gas flow in pipelines and the Flanigan multiphase corrections. 'hese equations can %e used for gas) liquid multiphase flow or for single)phase gas flow. 'hey A00O' %e used for single)phase liquid flow.
Important 0ote: 'hese three correlations can gi#e erroneous results if the pipe descri%ed de#iates su%stantially $more than 2? degrees& from the horiontal. For this reason, these correlations are only a#aila%le on the ipe and omparison pages. •
'he second type $eggs and rill, Hagedorn and rown, +ray& is the set of correlations %ased on the Fanning friction pressure loss equation. 'hese can %e used for either gas)liquid multiphase flow, single)phase gas or single)phase liquid, %ecause in single)phase mode, they re#ert to the Fanning equation, which is equally applica%le to either gas or liquid. eggs and rill is a multipurpose correlation deri#ed from la%oratory data for #ertical, horiontal, inclined uphill and downhill flow of gas)water mi*tures. +ray is %ased on field data for #ertical gas wells producing
condensate and water. Hagedorn and rown was deri#ed from field data for flowing #ertical oil wells.
Important 0ote: 'he +ray and Hagedorn and rown correlations were deri#ed for #ertical wells and may not apply to horiontal pipes. elow is a summary of the correlations a#aila%le in this program and the connection %etween the single) phase and multiphase forms. 0ote that each correlation has %een adapted to calculate %oth a hydrostatic and a friction component.
Procedure $'he phrases (pressure loss,( (pressure drop,( and (pressure difference( are used %y different people %ut mean the same thing&. In F.A.E.'. /irtuell, the pressure loss calculations for #ertical, inclined or horiontal pipes follow the same procedure: 2. 'otal ressure "oss 4 Hydrostatic ressure !ifference J Friction ressure "oss. 'he total pressure loss, as well as each indi#idual component can %e either positi#e or negati#e, depending on the direction of calculation, the direction of flow and the direction of ele#ation change. 3. Eu%di#ide the pipe length into segments so that the total pressure loss per segment is less than twenty $3?& psi. -a*imum num%er of segments is twenty $3?&. 7. For each segment assume constant fluid properties appropriate to the pressure and temperature of that segment. ;. alculate the 'otal ressure "oss in that segment as in step 2. =. Knowing the pressure at the inlet of that segment, add to $or su%tract from& it the 'otal ressure "oss determined in step ; to o%tain the pressure at the outlet. <. 'he outlet pressure from step = %ecomes the inlet pressure for the adGacent segment. C. >epeat steps 7 to < until the full length of the pipe has %een tra#ersed. !"#$: As discussed under Hydrostatic ressure !ifference and Friction ressure "oss, the hydrostatic pressure difference is positi#e in the direction of the earth1s gra#itational pull, whereas the friction pressure loss is always positi#e in the direction of flow.
Single Phase Flo% 'he most generally applica%le single phase equation for calculating Friction ressure "oss is the Fanning equation. It utilies friction factor charts $Knudsen and Kat, 2B=&, which are functions of >eynold1s num%er and relati#e pipe roughness. 'hese charts are also often referred to as the -oody charts. F.A.E.'. /irtuell uses the equation form of the Fanning friction factor as pu%lished %y hen, 2BCB. 'he calculation of Hydrostatic ressure !ifference is different for a gas than for a liquid, %ecause gas is compressi%le and its density #aries with pressure and temperature, whereas for a liquid a constant density can %e safely assumed. +enerally it is easier to calculate pressure drops for single)phase flow than it is for multiphase flow. 'here are se#eral single)phase correlations that are a#aila%le:
•
•
•
•
Fanning L the Fanning correlation is di#ided into two s u% categories Fanning "iquid and Fanning +as. 'he Fanning +as correlation is also known as the -ulti)step ullender and Emith when applied for #ertical well%ores. anhandle L the anhandle correlation was de#eloped originally for single)phase flow of gas through horiontal pipes. In other words, the hydrostatic pressure difference is not taken into account. e ha#e applied the standard hydrostatic head equation to the #ertical ele#ation of the pipe to account for the #ertical component of pressure drop. 'hus our implementation of the anhandle equation includes O'H horiontal and #ertical flow components, and this equation can %e used for horiontal, uphill and downhill flow. -odified anhandle L the -odified anhandle correlation is a #ariation of the anhandle correlation that was found to %e %etter suited to some transportation systems. 'hus, it also originally did not account for #ertical flow. e ha#e applied the standard hydrostatic head equation to account for the #ertical component of pressure drop. Hence our implementation of the -odified anhandle equation includes O'H horiontal and #ertical flow components, and this equation can %e used for horiontal, uphill and downhill flow. eymouth L the eymouth correlation is of the same form as the anhandle and the -odified anhandle equations. It was originally de#eloped for short pipelines and gathering systems. As a result, it only accounts for horiontal flow and not for hydrostatic pressure drop. e ha#e applied the standard hydrostatic head equation to account for the #ertical component of pressure drop. 'hus, our implementation of the eymouth equation includes O'H horiontal and #ertical flow components, and this equation can %e used for horiontal, uphill and downhill flow.
In our software, for cases that in#ol#e a single phase, the +ray, the Hagedorn and rown and the eggs and rill correlations re#ert to the Fanning single)phase correlations. For e *ample, if the +ray correlation was selected %ut there was only gas in the system, the Fanning +as correlation would %e used. For cases where there is a single phase, the Flanigan and -odified Flanigan correlations de#ol#e to the single) phase anhandle and -odified anhandle correlations respecti#ely. 'he eymouth $-ultiphase& correlation de#lo#es to the single)phase eymouth correlation.
&eferences Knudsen, M. +. and !. ". Kat $2B=&. Fluid !ynamics and Heat 'ransfer, -c+raw)Hill ook o., Inc., 0ew Nork. hen, 0. H., (An *plicit quation for Friction Factor in ipe,( Ind. ng. hem. Fund. $2BCB&.
Panhandle Correlation 'he original anhandle correlation $+as rocessors Euppliers Association, 2B?& was de#eloped for single)phase gas flow in horiontal pipes. As such, only the pressure drop due to friction was taken into account %y the anhandle equation. Howe#er, we ha#e applied the standard equation for calculating hydrostatic head to the #ertical component of the pipe, and thus our anhandle correlation accounts for horiontal, inclined and #ertical pipes. 'he anhandle correlation can only %e used for single)phase gas flow. 'he Fanning "iquid correlation should %e used for single)phase liquid flow.
Panhandle - Friction Pressure Loss 'he anhandle correlation can %e written as follows:
where:
'he anhandle equation incorporates a simplified representation of the friction factor, which is %uilt into the equation. 'o account for real life situations, the flow efficiency factor, , was included in the equation. 'his flow efficiency generally ranges from ?. to ?.B=. Although we recognie that a common default for the flow efficiency is ?.B3, our software defaults to 4 ?.=, as our e*perience has shown this to %e more appropriate $-attar and @aoral, 2B;&.
Panhandle - Hydrostatic Pressure 'ifference 'he original anhandle equation only accounted for f . Howe#er, %y applying the hydrostatic head calculations the anhandle correlation has %een adapted for #ertical and inclined pipes. 'he hydrostatic head is calculated %y:
!omenclature ! 4 pipe inside diameter $inch& 4 anhandle8eymouth efficiency factor + 4 gas gra#ity g 4 gra#itational acceleration $73.3 ft8s3& gc 4 con#ersion factor $73.3 $l% mft&8$l% f s3&& " 4 length $mile& 4 reference pressure for standard conditions $psia& 2 4upstream pressure $psia& 3 4 downstream pressure $psia& HH 4 pressure change due to hydrostatic head $psi& 5+ 4 gas flow rate at standard condition $ft78d& ' 4 reference temperature for standard conditions $>ankin& 'a 4 a#erage temperature $>ankin& @a 4 a#erage compressi%ility factor 4 ele#ation change $ft& + 4 gas density $l%8ft7&
&eferences +as rocessors Euppliers Association, Field ngineering !ata ook, /ol. 3, 2?th ed., 'ulsa $2BB;& -attar, ". and @aoral, K., (+as ipeline fficiencies and ressure +radient ur#es,( M' ;)7=)B7 $2B;&
Fanning Correlation 'he Fanning friction factor pressure loss $ f & can %e com%ined with the hydrostatic pressure difference $ HH& to gi#e the total pressure loss. 'he Fanning +as orrelation $-ulti)step ullender and Emith& is the name used in this document to refer to the calculation of the hydrostatic pressure difference $ HH& and the friction pressure loss $ f & for single)phase gas flow, using the following standard equations. 'his formulation for pressure drop is applica%le to pipes of all inclinations. hen applied to a #ertical well%ore it is equi#alent to the ullender and Emith method. Howe#er, it is implemented as a multi) segment procedure instead of a 3 segment calculation.
Fanning Gas - Friction Pressure Loss 'he Fanning equation is widely thought to %e the most generally applica%le single phase equation for calculating friction pressure loss. It utilies friction factor charts $Knudsen and Kat, 2B=&, which are functions of >eynold1s num%er and relati#e pipe roughness. 'hese charts are also often referred to as the -oody charts. e use the equation form of the Fanning friction factor as pu%lished %y hen, 2BCB.
'he method for calculating the Fanning Friction factor is the same for single)phase gas or single)phase liquid. •
>oughness
•
Flow fficiency
Fanning Gas - Hydrostatic Pressure 'ifference 'he calculation of hydrostatic head is different for a gas than for a liquid, %ecause gas is compressi%le and its density #aries with pressure and temperature, whereas for a liquid a constant density can %e safely assumed. ither way the hydrostatic pressure difference is gi#en %y:
Eince + #aries with pressure, the calculation must %e done sequentially in small steps to allow the density to #ary with pressure.
Fanning Liquid Correlation 'he Fanning friction factor pressure loss $ f & can %e com%ined with the hydrostatic pressure difference $ HH& to gi#e the total pressure loss. 'he Fanning "iquid orrelation is the name used in this program to refer to the calculation of the hydrostatic pressure difference $ HH& and the friction pressure loss $ f & for single)phase liquid flow, using the following standard equations.
Fanning Liquid - Friction Pressure Loss 'he Fanning equation is widely thought to %e the most generally applica%le single)phase equation for calculating friction pressure loss. It utilies friction factor charts $Knudsen and Kat, 2B=&, which are functions of >eynold1s num%er and relati#e pipe roughness. 'hese charts are also often referred to as the -oody charts. e use the equation form of the Fanning friction factor as pu%lished %y hen $2BCB&.
'he method for calculating the Fanning friction factor is the same for single)phase gas or single)phase liquid.
Fanning Liquid - Hydrostatic Pressure 'ifference 'he calculation of hydrostatic head is different for a gas than for a liquid, %ecause gas is compressi%le and its density #aries with pressure and temperature, whereas for a liquid a constant density can %e safely assumed. For liquid, the hydrostatic pressure difference is gi#en %y:
Eince
does not #ary with pressure, a constant #alue can %e used for the entire length of the pipe.
!omenclature ! 4 pipe inside diameter $inch& f 4 Fanning friction factor g 4 gra#itational acceleration $73.3 ft8s3& gc 4 con#ersion factor $73.3 $l% mDft&8$l% f Ds3&& k8! 4 relati#e roughness $unitless& " 4 length $ft& HH 4 pressure change due to hydrostatic head $psi& f 4 pressure change due to friciton $psi& >e 4 >eynold1s num%er / 4 #elocity $ft8s& 4 ele#ation change + 4 gas density $l%8ft7&
&eferences hen, 0. H., (An *plicit quation for Friction Factor in ipe,( Ind. ng. hem. Fund. $2BCB&. ullender, -. H. and >. /. Emith $2B=<&. ractical Eolution of +as)Flow quations for ells and ipelines with "arge 'emperature +radients, 'rans., AI-, 3?C, 32)3C. +as rocessors and Euppliers Association, ngineering !ata ook. /ol. 3, Eect. 2C, 2?th ed., 2BB;. Knudsen, M. +. and !. ". Kat $2B=&. Fluid !ynamics and Heat 'ransfer, -c+raw)Hill ook o., Inc., 0ew Nork.
eymouth Correlation 'his correlation is similar in its form to the anhandle and the -odified anhandle correlations. It was designed for single)phase gas flow in pipelines. As such, it calculates only the pressure drop due to friction. Howe#er, we ha#e applied the standard equation for calculating hydrostatic head to the #ertical component of the pipe, and thus our eymouth correlation accounts for HO>I@O0'A", I0"I0! and />'IA" pipes. 'he eymouth equation can only %e used for single)phase gas flow. 'he Fanning "iquid correlation should %e used for single)phase liquid flow.
eymouth Friction Pressure Loss 'he pressure drop due to friction is gi#en %y:
where:
'he eymouth equation incorporates a simplified representation of the friction factor, which is %uilt into the equation. 'o account for real life situations, the flow efficiency factor, , was included in the equation. 'he flow efficiency generally used is 2. Our software defaults to this #alue as well $-attar and @aoral, 2B;&.
eymouth Hydrostatic Pressure 'ifference 'he original eymouth equation only accounted for f . Howe#er, %y applying the hydrostatic head calculations, the eymouth equation has %een adapted for #ertical and inclined pipes. 'he hydrostatic head is calculated %y:
!omenclature ! 4 pipe inside diameter $inch& 4 anhandle8eymouth efficiency factor + 4 gas gra#ity g 4 gra#itational acceleration $73.3 ft8s3& gc 4 con#ersion factor $73.3 $l% mft&8$l% f s3&& " 4 length $mile& 4 reference pressure for standard conditions $psia& 2 4upstream pressure $psia& 3 4 downstream pressure $psia& HH 4 pressure change due to hydrostatic head $psi& 5+ 4 gas flow rate at standard conditions, ',, ft78d ' 4 reference temperature for standard conditions $>ankin& 'a 4 a#erage temperature $>ankin& @a 4 a#erage compressi%ility factor 4 ele#ation change $ft& + 4 gas density $l%8ft7&
&eferences +as rocessors Euppliers Association, Field ngineering !ata ook, /ol. 3, 2?th ed., 'ulsa $2BB;&. -attar, ". and @aoral, K., (+as ipeline fficiencies and ressure gradient ur#es.( M' ;)7=)B7 $2B;&.
ultiphase Flo% 'he presence of multiple phases greatly complicates pressure drop calculations. 'his is due to the fact that the properties of each fluid present must %e taken into account. Also, the interactions %etween each phase ha#e to %e considered. -i*ture properties must %e used, and therefore the gas and liquid in)situ #olume fractions throughout the pipe need to %e determined. In general, all multiphase correlations are essentially two phase and not three phase. Accordingly, the oil and water phases are com%ined, and treated as a pseudo single liquid phase, while gas is considered a separate phase. 'he following is a list of general concepts inherent to multiphase flow. lick on each of them for a %rief o#er#iew.
•
Euperficial /elocities, /sl, /sg
•
-i*ture /elocity, /m
•
"iquid Holdup ffect
•
Input /olume Fraction, "
•
In)situ /olume Fraction, "
•
-i*ture /iscosity,
•
0o Elip /iscosity,
•
-i*ture !ensity,
•
0o Elip !ensity,
•
Eurface 'ension,
ultiphase Flo% Correlations -any of the pu%lished multiphase flow correlations are applica%le for (#ertical flow( only, while others apply for (horiontal flow( only. Other than the eggs and rill correlation, there are not many correlations that were de#eloped for the whole spectrum of flow situations that can %e encountered in oil and gas operations namely uphill, downhill, horiontal, inclined and #ertical flow. Howe#er, we ha#e adapted all of the correlations $as appropriate& so that they apply to all flow situations. 'he following is a list of the multiphase flow correlations that are a#aila%le. 2.
+ray: 'he +ray orrelation $2BC& was de#eloped for #ertical flow in wet gas wells. e ha#e modified it so that it applies to flow in all directions %y calculating the hydrostatic pressure difference using only the #ertical ele#ation of the pipe segment and the friction pressure loss %ased on the total pipe length.
3.
Hagedorn and rown: 'he Hagedorn and rown orrelation $2B<;& was de#eloped for #ertical flow in oil wells. e ha#e also modified it so that it applies to flow in all directions %y calculating the hydrostatic pressure difference using only the #ertical ele#ation of the pipe segment and the friction pressure loss %ased on the total pipe length.
7.
eggs and rill: 'he eggs and rill orrelation $2BC7& is one of the few pu%lished correlations capa%le of handling all of the flow directions. It was de#eloped using sections of pipe that could %e inclined at any angle.
;.
Flanigan: 'he Flanigan orrelation $2B=& is an e*tention of the anhandle single)phase correlation to multiphase flow. It incorporates a correction for multiphase Flow fficiency, and a calculation of hydrostatic pressure difference to account for uphill flow. 'here is no hydrostatic pressure reco#ery for downhill flow. In this software, the Flanigan multiphase correlation is also applied to the -odified anhandle and eymouth correlations. It is recommended that this correlation not %e used %eyond J8) 2? degrees from the horiontal.
=.
-odified)Flanigan: 'he -odified Flanigan orrelation is an e*tention of the -odified anhandle single)phase equation to multiphase flow. It incorporates the Flanigan correction of the Flow
fficiency for multiphase flow and a calculation of hydrostatic pressure difference to account for uphill flow. 'here is no hydrostatic pressure reco#ery for downhill flow. In this software, the Flanigan multiphase correlation is also applied to the anhandle and eymouth correlations. It is recommended that this correlation not %e used %eyond J8) 2? degrees from the horiontal. <.
eymouth $-ultiphase&: 'he eymouth $-ultiphase& is an e*tension of the eymouth single) phase equation to multiphase flow. It incorporates the Flanigan correction of the Flow fficiency for multiphase flow and a calculation of hydrostatic pressure difference to account for uphill flow. 'here is no hydrostatic pressure reco#ery for downhill flow. In this software, the Flanigan correlation is also applied to the anhandle and -odified anhandle correlations. It is recommended that this correlation not %e used %eyond J8) 2? degrees from the horiontal.
ach of these correlations was de#eloped for it1s own unique set of e*perimental conditions, and accordingly, results will #ary %etween them.
Single Phase Gas In the case of single)phase gas, the a#aila%le correlations are the anhandle, -odified anhandle, eymouth and Fanning +as. 'hese correlations were de#eloped for ho riontal pipes, %ut ha#e %een adapted to #ertical and inclined flow %y including the hydrostatic pressure component. In #ertical flow situations, the Fanning +as is equi#alent to a multi)step ullender and Emith calculation.
Single Phase Liquid In the case of single)phase liquid, the a#aila%le correlation is the Fanning "iquid. It has %een implemented to apply to horiontal, inclined and #ertical wells. For multiphase flow in essentially horiontal pipes, the a#aila%le correlations are eggs and rill, +ray, Hagedorn and rown, Flanigan, -odified)Flanigan and eymouth $-ultiphase&. All of these correlations are accessi%le on the ipe page and the omparison page.
ultiphase Flo% For multiphase flow in essentially #ertical wells, the a#aila%le correlations are eggs and rill, +ray, and Hagedorn and rown. If used for single)phase flow, these three correlations de#ol#e to the Fanning +as or Fanning "iquid correlation. hen switching from multiphase flow to single)phase flow, the correlation will default to the Fanning. hen switching from single)phase flow to multiphase flow, the correlation will default to the eggs and rill. Important !otes •
•
'he Flanigan, -odified)Flanigan and eymouth $-ultiphase& correlations can gi#e erroneous results if the pipe descri%ed de#iates su%stantially $more than 2? degrees& from the horiontal. 'he +ray and Hagedorn and rown correlations were deri#ed for #ertical wells and may not apply to horiontal pipes. In our software, the +ray, the Hagedorn and rown and the eggs and rill correlations re#ert to the appropriate single)phase Fanning correlation $Fanning "iquid or Fanning +as. 'he Flanigan, -odified)Flanigan and eymouth $-ultiphase& re#ert to the anhandle, -odified anhandle and eymouth respecti#ely. Howe#er, they may not %e used for single)phase liquid flow.
Eingle hase P -ultiphase orrelations
Multiphase
Gas Correlations
Vertical
Liquid
Horizontal
Vertical
Horizontal
Fanning-Gas *
Fanning-Liquid Panhandle Modified Panhandle Weymouth *
Beggs & Brill
*
*
*
*
Gray
*
Hagedorn & Brown *
Flanigan
*
ModifiedFlanigan
*
Weymouth Multi!hase" *
Mechanistic Model
*
*
*
Petalas * +,i, echanistic odel 'etermine Flo% Pattern 'o determine a flow pattern, we do the following: •
egin with one flow pattern and test for sta%ility.
•
heck the ne*t pattern.
•
uild Flow attern -ap.
$ample Flo% Pattern ap
'ispersed .u//le Flo% *ists if
where
and if
Stratified Flo% *ists if flow is downward or horiontal $ ?& alculate
$dimensionless liquid height&
-omentum alance quations:
where
and f + from standard methods where
f " from
where f s" from standard methods where
f i from
where
Qse "ochhart)-artinelli arameters
where
where
+eometric /aria%les:
Eol#e for h "8! iterati#ely. Etratified flow e*ists if
$0ote: when cos ?.?3 then cos 4 ?.?3& where
and
$0ote: when cos ?.?3 then cos 4 ?.?3& Etratified smooth #ersus Etratified a#y if
where and
then ha#e Etratified Emooth, else ha#e Etratified a#y.
+nnular ist Flo% alculate
$dimensionless liquid height&
-omentum alance quations
where
and
$2& from standard methods where
from standard methods where
f i from
$3& Qse "ochhart)-artinelli arameters
where
where
+eometric /aria%les:
Eol#e for
iterati#ely.
Annular -ist Flow e*ists if
where
from
Eol#e iterati#ely for
.u//le Flo% u%%le flow e*ists if
$7&
where: 2 4 ?.= 4 2.7 d% 4 Cmm
$;& In addition, transition to %u%%le flow from intermittent flow occurs when
where:
$see Intermittent flow for additional definitions&.
Intermittent Flo% Intermittent flow e*ists if
where:
If " R 2, " 4 " and:
where
is from standard methods where:
for f m S 2, f m 4 2 where
is from standard methods where:
if
2.
If
and
then Elug Flow
3.
If
and
then longated u%%le Flow
7.
Froth Flow
If none of the transition criteria for intermittent flow are met, then the flow pattern is designated as Froth, implying a transitional state %etween the other flow regimes.
Footnotes
2.
, where: /E+ $ft8s&,
"
$c&,
$dyn8cm&
$l%8ft7&,
+
"
$l%8ft7&,
3.
, where:
$l%8ft7&, / $ft8s&, ! $ft&,
$dyn8cm&
7.
, where: $l%8ft7&,
"
$l%8ft7&, $dyn8cm&
+
;.
, where: $l%8ft7&,
"
+
$l%8ft7&,
$dyn8cm&
=.
, where: ! $ft&,
$l%8ft7&,
"
+
$l%8ft7&,
<.
$dyn8cm&
, where: $l%8ft7&,
"
!omenclature A 4 cross sectional area ? 4 #elocity distri%ution coefficient ! 4 pipe internal diameter 4 in situ #olume fraction F 4 liquid fraction entrained g 4 acceleration due to gra#ity h" 4 height of liquid $stratified flow& " 4 length 4 pressure >e 4 >eynolds num%er
+
$l%8ft7&,
$dyn8cm&
E 4 contact perimeter /E+ 4 superficial gas #elocity /E" 4 superficial liquid #elocity 4 liquid film thickness 4 pipe roughness 4 pressure gradient weighting factor $intermittent flow& 4 Angle of inclination 4 #iscosity 4 density 4 interfacial $surface& tension 4 shear stress 4 dimensionless quantity
Su/scripts % 4 relating to the gas %u%%le c 4 relating to the gas core F 4 relating to the liquid film d% 4 relating to dispersed %u%%les + 4 relating to gas phase i 4 relating to interface " 4 relating to liquid phase m 4 relating to mi*ture E+ 4 %ased on superficial gas #elocity s 4 relating to liquid slug E" 4 %ased on superficial liquid #elocity w" 4 relating to wall)liquid interface w+ 4 relating to wall)gas interface ? 4 #elocity distri%ution coefficient
&eferences •
•
•
etalas, 0., Ai, K.: (A -echanistic -odel for -ultiphase Flow in ipes,( M. et. 'ech. $Mune 3???&, ;7)==. etalas, 0., Ai, K.: (!e#elopment and 'esting of a 0ew -echanistic -odel for -ultiphase Flow in ipes,( AE- 2BB< Fluids ngineering !i#ision onference $2BB<&, F!)/ol 37<, 2=7)2=B. +ome, ".. et al.: (Qnified -echanistic -odel for Eteady)Etate 'wo)hase Flow,( etalas, 0., Ai, K.: (A -echanistic -odel for -ultiphase Flow in ipes,( E Mournal $Eeptem%er 3???&, 77B)7=?.
.eggs +nd .rill Correlation For multiphase flow, many of the pu%lished correlations are applica%le for (#ertical flow( only, while others apply for (horiontal flow( only. 0ot many correlations apply to the whole spectrum of flow situations that may %e encountered in oil and gas operations, namely uphill, downhill, horiontal, inclined and #ertical flow. 'he eggs and rill $2BC7& correlation, is one of the few pu%lished correlations capa%le of handling all these flow directions. It was de#eloped using 2( and 2)283( sections of pipe that could %e inclined at any angle from the horiontal.
'he eggs and rill multiphase correlation deals with %oth the friction pressure loss and the hydrostatic pressure difference. First the appropriate flow regime for the particular com%ination of gas and liquid rates $Eegregated, Intermittent or !istri%uted& is determined. 'he liquid holdup, and hence, the in)situ density of the gas)liquid mi*ture is then calculated according to the appropriate flow regime, to o%tain the hydrostatic pressure difference. A two)phase friction factor is calculated %ased on the (input( gas)liquid ratio and the Fanning friction factor. From this the friction pressure loss is calculated using (input( gas)liquid mi*ture properties. If only a single)phase fluid is flowing, the eggs and rill multi)phase correlation de#ol#es to the Fanning +as or Fanning "iquid correlation. Eee Also: ressure !rop orrelations, -ultiphase Flow orrelations
Flo% Pattern ap Qnlike the +ray or the Hagedorn and rown correlations, the eggs and rill correlation requires that a flow pattern %e determined. Eince the original flow pattern map was created, it has %een modified. e ha#e used this modified flow pattern map for our calculations. 'he transition lines for the modified correlation are defined as follows:
'he flow type can then %e readily determined either from a representati#e flow pattern map or according to the following conditions, where
. E+>+A'! flow if and Or
and I0'>-I''0' flow if or
and and
!IE'>IQ'! flow
if
and
or
and
'>A0EI'IO0 flow
if
and
Hydrostatic Pressure 'ifference Once the flow type has %een determined then the liquid holdup can %e calculated. eggs and rill di#ided the liquid holdup calculation into two parts. First the liquid holdup for horiontal flow, "$?&, is determined, and then this holdup is modified for inclined flow. "$?& must %e " and therefore when "$?& is smaller than ", "$?& is assigned a #alue of ". 'here is a separate "$?& for each flow type. E+>+A'!
I0'>-I''0'
!IE'>IQ'!
I/.'>A0EI'IO0
here
Once the horiontal in situ liquid #olume fraction is determined, the actual liquid #olume fraction is o%tained %y multiplying "$?& %y an inclination factor, $ &. i.e.
where
is a function of flow type, the direction of inclination of the pipe $uphill flow or downhill flow&, the liquid #elocity num%er $0#l&, and the mi*ture Froude 0um%er $Frm&. 0#l is defined as:
For QHI"" flow: E+>+A'!
I0'>-I''0'
!IE'>IQ'!
For !O0HI"" flow: I, II, III. A"" flow types
0ote:
must always %e ?. 'herefore, if a negati#e #alue is calculated for ,
4 ?.
Once the liquid holdup $"$ && is calculated, it is used to calculate the mi*ture density $ m&. 'he mi*ture density is, in turn, used to calculate the pressure change due to the hydrostatic head of the #ertical component of the pipe or well.
.eggs and .rill - Friction Pressure Loss 'he first step to calculating the pressure drop due to friction is to calculate the empirical parameter E. 'he #alue of E is go#erned %y the following conditions: if 2 S y S 2.3, then
otherwise,
where:
0ote: Ee#ere insta%ilities ha#e %een o%ser#ed when these e quations are used as pu%lished. Our implementation has modified them so that the insta%ilities ha#e %een eliminated. A ratio of friction factors is then defined as follows:
is the no)slip friction factor. e use the Fanning friction factor, calculated using the hen equation. 'he no)slip >eynolds 0um%er is also used, and it is defined as follows:
Finally, the e*pression for the pressure loss due to friction is:
!omenclature " 4 liquid input #olume fraction ! 4 inside pipe diameter $ft& "$?& 4 horiontal liquid holdup "$ & 4 inclined liquid holdup f tp 4 two phase friction factor
f 0E 4 no)slip friction factor Fr m 4 Froude -i*ture 0um%er g 4 gra#itational acceleration $73.3 ft8s3& gc 4 con#ersion factor $73.3 $l% mDft&8$l% f Ds3&& " 4 length of pipe $ft& 0#l 4 liquid #elocity num%er /m 4 mi*ture #elocity $ft8s& /sl 4 superficial liquid #elocity $ft8s& 4 ele#ation change $ft& 0E 4 no)slip #iscosity $cp& 4 angle of inclination from the horiontal $degrees& " 4 liquid density $l%8ft7& 0E 4 no)slip density $l%8ft7& m 4 mi*ture density $l%8ft7& 4 gas8liquid surface tension $dynes8cm&
&eference eggs, H. !., and rill, M.., (A Etudy of 'wo)hase Flow in Inclined ipes,( M',
Flanigan Correlation 'he Flanigan correlation is an e*tension of the anhandle single)phase correlation to multiphase flow. It was de#eloped to account for the additional pressure loss caused %y the presence of liquids. 'he correlation is empirical and is %ased on studies of small amounts of condensate in gas lines. 'o account for liquids, Flanigan de#eloped a relationship for the Flow fficiency term of the anhandle equation as a function of liquid to gas ratio. Eince the anhandle equation applied to essentially horiontal flow, Flanigan also de#eloped a liquid holdup factor to account for the hydrostatic pressure difference in upward inclined flow. For downhill, there is no hydrostatic pressure reco#ery. As noted pre#iously, the Flanigan correlation was de#eloped for essentially horiontal flow. onsequently, it is not applica%le in #ertical flow situations such as #ertical well%ores. 'herefore, the Flanigan correlation is only a#aila%le on the ipe and omparison pages. are should %e taken when applying the Flanigan correlation to situations other than essentially horiontal flow. 'he effects of using the Flanigan correlation can %e in#estigated using the omparison module. In this program , the Flanigan correlation has %een applied to the anhandle, -odified anhandle and eymouth correlations in the same way, %y adGusting the hydrostatic pressure difference using the Flanigan holdup factor and %y using the appropriate efficiency $& for multiphase flow.
Flanigan - Hydrostatic Pressure 'ifference hen calculating the pressure losses due to hydrostatic effects the Flanigan correlation ignores downhill flow. 'he hydrostatic head caused % y the liquid content is calculated as follows:
where: hi 4 the #ertical (rises( of the indi#idual sections of the pipeline $ft& " 4 Flanigan holdup factor $in)situ liquid #olume fraction&
'he Flanigan holdup factor is calculated using the following equation.
Flanigan Friction Pressure Loss In the Flanigan correlation, the friction pressure drop calculation accounts for liquids %y adGusting the anhandle8eymouth efficiency $& according to the following plot.
0otice that when there is mostly gas $the liquid to gas ratio is #ery small&, the anhandle efficiency is around ?.= $close to the single)phase default for gas& and as the quantity of liquids increases, the efficiency decreases.
odified-Flanigan Correlation 'he -odified)Flanigan is equi#alent to the Flanigan correlation applied to the -odified anhandle single) phase correlation. 'he Flanigan correlation was de#eloped as a method to account for the additional pressure loss caused %y the presence of liquids. 'he correlation is empirical and is %ased on studies of small amounts of condensate in gas lines. 'o account for liquids, Flanigan de#eloped a relationship for the Flow fficiency term of the anhandle equation as a function of liquid to gas ratio. In addition, Flanigan de#eloped a liquid holdup factor to account for the hydrostatic pressure difference in upward inclined flow. For downhill, there is no hydrostatic pressure reco#ery. As noted pre#iously, the Flanigan correlation was de#eloped for essentially horiontal flow. onsequently, it is not applica%le in #ertical flow situations such as #ertical well%ores. 'herefore, the Flanigan correlation, and hence the -odified)Flanigan correlation, is only a#aila%le on the ipe and omparison pages. are should %e taken when applying the -odified)Flanigan correlation to situations other than essentially horiontal flow. 'he effects of using the -odified)Flanigan correlation can %e in#estigated using the omparison module.
In this program , the Flanigan correlation has %een applied to the anhandle, -odified anhandle and eymouth correlations in the same way, %y adGusting the hydrostatic pressure difference using the Flanigan holdup factor and %y using the appropriate efficiency $& for multiphase flow.
odified-Flanigan - Hydrostatic Pressure 'ifference hen calculating the pressure losses due to hydrostatic effects the Flanigan correlation ignores downhill flow. 'he hydrostatic head caused % y the liquid content is calculated as follows:
where: hi 4 the #ertical (rises( of the indi#idual sections of the pipeline $ft& " 4 Flanigan holdup factor $in)situ liquid #olume fraction& 'he Flanigan holdup factor is calculated using the following equation.
odified-Flanigan Friction Pressure Loss In the Flanigan correlation, the friction pressure drop calculation accounts for liquids %y adGusting the anhandle8eymouth efficiency $& according to the following plot. 'he plot has %een normalied for the -odified)Flanigan correlation, so that when there is mostly gas, the efficiency is around ?.? $close to the single)phase default for gas&
0otice that as the quantity of liquids increases, the efficiency decreases.
!omenclature 4 anhandle8eymouth efficiency " 4 Flanigan holdup factor $in)situ liquid #olume fraction& g 4 gra#itational acceleration $73.3 ft8s3& gc 4 con#ersion factor $73.3 $l% mDft&8$l% f Ds3&& hi 4 the #ertical (rises( of the indi#idual sections of the pipeline $ft& HH 4 pressure loss due to hydrostatic head $psi& f 4 pressure change due to friction $psi& /sg 4 superficial gas #elocity $ft8s& "
4 liquid density $l%8ft7&
&eference Flanigan, O., (ffect of Qphill Flow on ressure !rop in !esign of 'wo)hase +athering Eystems(, OP+M, /ol. =<, 0o. 2?, p. 273, -arch $2B=&.
Gray Correlation 'he +ray correlation was de#eloped %y H.. +ray $+ray, 2BC&, specifically for wet gas wells. Although this correlation was de#eloped for #ertical flow, we ha#e implemented it in %oth #ertical, and inclined pipe pressure drop calculations. 'o correct the pressure drop for situations with a horiontal component, the hydrostatic head has only %een applied to the #ertical component of the pipe while friction is applied to the entire length of pipe. First, the in)situ liquid #olume fraction is calculated. 'he in)situ liquid #olume fraction is then used to calculate the mi*ture density, which is in turn used to calculate the hydrostatic pressure difference. 'he input gas liquid mi*ture properties are used to calculate an (effecti#e( roughness of the pipe. 'his effecti#e roughness is then used in conGunction with a constant >eynolds 0um%er of to calculate the Fanning friction factor. 'he pressure difference due to friction is calculated using the Fanning friction pressure loss equation. For a more detailed look at each step, make a selection from the following list:
Gray - Hydrostatic Pressure 'ifference 'he +ray correlation uses three dimensionless num%ers, in com%ination, to predict the in situ liquid #olume fraction. 'hese three dimensionless num%ers are:
where:
'hey are then com%ined as follows:
where:
Once the liquid holdup $"& is calculated it is used to calculate the mi*ture density $ m&. 'he mi*ture density is, in turn, used to calculate the pressure change due to the hydrostatic head of the #ertical component of the pipe or well.
0ote: For the equations found in the +ray correlation, is gi#en in l%f 8s3. e ha#e implemented them using with units of dynes8cm and ha#e con#erted the equations %y multiplying %y ?.??33?;<3. $?.??33?;<3dynes8cm 4 2l%f 8s3&
Gray - Friction Pressure Loss 'he +ray orrelation assumes that the effecti#e roughness of the pipe $ke& is dependent on the #alue of >#. 'he conditions are as follows: if
then
if
then
where:
'he effecti#e roughness $ke& must %e larger than or equal to 3.CC
2?)=.
'he relati#e roughness of the pipe is then calculated %y di#iding the effecti#e roughness %y the diameter of the pipe. 'he Fanning friction factor is o%tained using the hen equation and assuming a >eynolds 0um%er $>e& of 2?C. Finally, the e*pression for the friction pressure loss is:
0ote: 'he original pu%lication contained a misprint $?.???C instead of ?.??C&. Also, the surface tension $ & is gi#en in units of l% f 8s3. e used a con#ersion factor of ?.??33?;<3 dynes8cm 4 2 l% f 8s3.
!omenclature " 4 liquid input #olume fraction ! 4 inside pipe diameter $ft& " 4 in)situ liquid #olume fraction $liquid holdup& f tp 4 two)phase friction factor g 4 gra#itational acceleration $73.3 ft8s3& gc 4 con#ersion factor $73.3 $l% mft&8$l% f s3&& k 4 a%solute roughness of the pipe $in& ke 4 effecti#e roughness $in& " 4 length of pipe $ft& HH 4 pressure change due to hydrostatic head $psi& f 4 pressure change due to friction $psi& /sl 4 superficial liquid #elocity $ft8s& /sg 4 superficial gas #elocity $ft8s& /m 4 mi*ture #elocity $ft8s& 4 ele#ation change $ft& + 4 gas density $l%8ft7& " 4 liquid density $l%8ft7& 0E 4 no)slip density $l%8ft7& m 4 mi*ture density $l%8ft7& 4 gas 8 liquid surface tension $l% f 8s3&
&eference American etroleum Institute,AI -anual 2;, (Eu%surface ontrolled Eu%surface Eafety /al#e Eiing omputer rogram (, Appendi* , Eecond d., Man. $2BC&
Hagedorn and .ro%n Correlation *perimental data o%tained from a 2=??ft deep, instrumented #ertical well was used in the de#elopment of the Hagedorn and rown correlation. ressures were measured for flow in tu%ing sies that ranged from 2 ( to 2 T( O!. A wide range of liquid rates and gas8liquid ratios were used. As with the +ray correlation, our software will calculate pressure drops for horiontal and inclined flow using the Hagedorn
and rown correlation, although the correlation was de#eloped strictly for #ertical wells. 'he software uses only the #ertical depth to calculate the pressure loss due to hydrostatic head, and the entire pipe length to calculate friction. 'he Hagedorn and rown method has %een modified for the u%%le Flow regime $conomides et al, 2BB;&. If %u%%le flow e*ists the +riffith correlation is used to calculate the in)situ #olume fraction. In this case the +riffith correlation is also used to calculate the pressure drop due to friction. If %u%%le flow does not e*ist then the original Hagedorn and rown correlation is used to calculate the in)situ liquid #olume fraction. Once the in)situ #olume fraction is determined, it is compared with the input #olume fraction. If the in)situ #olume fraction is smaller than the input #olume fraction, the in)situ fraction is set to equal the input fraction $" 4 "&. 0e*t, the mi*ture density is calculated using the in)situ #olume fraction and used to calculate the hydrostatic pressure difference. 'he pressure difference due to friction is calculated using a com%ination of (in)situ( and (input( gas)liquid mi*ture properties. For further details on any of these steps select a topic from the following list:
Hagedorn and .ro%n - Hydrostatic Pressure 'ifference 'he Hagedorn and rown correlation uses four dimensionless parameters to correlate liquid holdup. 'hese four parameters are:
/arious com%inations of these parameters are then plotted against each other to determine the liquid holdup. For the purposes of program ming, these cur#es were con#erted into e quations. 'he first cur#e pro#ides a #alue for 0 ". 'his 0" #alue is then used to calculate a dimensionless group, o%tained from a plot of of num%ers,
#s
. Finally, the third cur#e is a plot of
.
can then %e
#s. another dimensionless group
. 'herefore, the in)situ liquid #olume fraction, which is denoted % y ", is calculated %y:
'he hydrostatic head is once again calculated %y the standard equation:
where:
Hagedorn and .ro%n - Friction Pressure Loss 'he friction factor is calculated using the hen equation and a >eynolds num%er equal to:
0ote: In the Hagedorn and rown correlation the mi*ture #iscosity is gi#en %y:
'he pressure loss due to friction is then gi#en %y:
where:
-odifications e ha#e implemented two modifications to the original Hagedorn and rown orrelation. 'he first modification is simply the replacement of the liquid holdup #alue with the (no)slip( $input& liquid #olume fraction if the calculated liquid holdup is less than the (no)slip( liquid #olume fraction. if then 'he second modification in#ol#es the use of the +riffith correlation $2B<2& for the %u%%le flow regime. u%%le flow e*ists if
where:
If the calculated #alue of " is less than ?.27 then " is set to ?.27. If the flow regime is found to %e %u%%le flow then the +riffith correlation is applied, otherwise the original Hagedorn and rown correlation is used.
#he Griffith Correlation (odification to the Hagedorn and .ro%n Correlation) In the +riffith correlation the liquid holdup is gi#en % y:
where:/s 4 ?. ft8s 'he in)situ liquid #elocity is gi#en %y:
'he hydrostatic head is then calculated the standard way. 'he pressure drop due to friction is also affected %y the use of the +riffith correlation %ecause " enters into the calculation of the >eynolds 0um%er #ia the in)situ liquid #elocity. 'he >eynolds 0um%er is calculated using the following format:
'he single phase liquid density, in)situ liquid #elocity and liquid #iscosity are used to calculate the >eynolds 0um%er. 'his is unlike the maGority of multiphase correlations, which usually define the >eynolds 0um%er in terms of mi*ture properties not single phase liquid properties. 'he >eynolds num%er is then used to calculate the friction factor using the hen equation. Finally, the friction pressure loss is calculated as follows:
'he liquid density and the in)situ liquid #elocity are used to calculate the pressure drop due to friction.
!omenclature " 4 input liquid #olume fraction + 4 input gas #olume fraction ! 4 inside pipe diameter $ft& " 4 in)situ liquid #olume fraction $liquid holdup& f 4 Fanning friction factor g 4 gra#itational acceleration $73.3 ft8s3& gc 4 con#ersion factor $73.3 $l% mft&8$l% f s3&&
" 4 length of calculation segment $ft& HH 4 pressure change due to hydrostatic head $psi& f 4 pressure change due to friction $psi& /sl 4 superficial liquid #elocity $ft8s& /sg 4 superficial gas #elocity $ft8s& /m 4 mi*ture #elocity $ft8s& /" 4 in)situ liquid #elocity $ft8s& 4 ele#ation change $ft& "4 liquid #iscosity $cp& m 4 mi*ture #iscosity $cp& + 4 gas #iscosity $cp& + 4 gas density $l%8ft7& " 4 liquid density $l%8ft7& 0E 4 no)slip density $l%8ft7& m 4 mi*ture density $l%8ft7& f4 $l%8ft7& 4 gas 8 liquid surface tension $dynes8cm&
&eferences •
•
conomides, -.M. et al, etroleum roduction Eystems. 0ew Mersey: rentice Hall Inc., 2BB;. Hagedorn, A.>., rown, K.., (*perimental Etudy of ressure +radients Occurring !uring ontinuous 'wo)hase Flow in Emall !iameter /ertical onduits(, M', p.;C=, April. $2B<=&
#urner Correlation >. +. 'urner, -. +. Hu%%ard and A. !ukler first presented the 'urner correlation at the E +as 'echnology Eymposium held in Omaha, 0e%raska, Eeptem%er 23 and 27, 2B<. 'he correlation $E paper 32B& calculates the minimum gas flow rate required to lift liquids out of a well%ore and is often referred to as 'he "iquid "ift quation or ritical Flow >ate alculation for "ifting "iquids. In F.A.E.'. /irtuwell, this correlation is used to test for sta%le well%ore flow.
#heoretical .ac0ground 'he 'urner correlation assumes free flowing liquid in the well%ore forms droplets suspended in the gas stream. 'wo forces act on these droplets. 'he first is the force of gra#ity pulling the droplets down a nd the second is drag force due to flowing gas pushing the droplets upward. If the #elocity of the gas is sufficient, the drops are carried to surface. If not, they fall and accumulate in the well%ore. 'he correlation was de#eloped from droplet theory. 'he theoretical calculations were then compared to field data and a 3?U fudge factor was %uilt)in. 'he correlation is generally #ery a ccurate and was formulated using easily o%tained oilfield data. onsequently, it has %een widely accepted in the petroleum industry. 'he model was #erified to a%out 27? %%l8--scf. 'he 'urner correlation was formulated for free water production and free condensate production in the well%ore. 'he calculation of minimum gas #elocity for each follows:
From the minimum gas #elocity, the minimum gas flow rate required to lift free liquids can then %e calculated using:
where: A 4 cross)sectional area of flow $ft3& + 4 gas gra#ity k 4 calculation #aria%le 4 pressure $psia& qg 4 gas flow rate $--scfd& ' 4 temperature $>& #g 4 minimum gas #elocity required to lift liquids $ft8s& @ 4 compressi%ility factor $supercompressi%ility&
+pplication of the #urner Correlation 'here are two ways to calculate the liquid lift rate in F.A.E.'. /irtuwell. First of all, the "iquid "ift page may %e used. 'his requires the entry of pressure, temperature and tu%ing I!s to calculate the corresponding gas rates to lift water and condensate. As well, a liquid lift rate is calculated in conGunction with each 'u%ing erformance ur#e on the +as AOF8' page. It is represented on the tu%ing performance cur#e %y a circle listing the num%er identifying the tu%ing performance cur#e. 'o the right of the liquid lift rate, the tu%ing performance cur#e is a solid green line. 'o the left, it is a dotted red line. 'he solid green line represents sta%le flow, i.e. the well%ore will lift liquids continuously. 'he dotted red line represents unsta%le flow. If the 'u%ing erformance ur#e is a dotted red line o#er the entire range of flow rates represented, the circled num%er is placed in the middle of the cur#e solely for identification. 'he calculated liquid lift rates for each tu%ing performance cur#e are ta%ulated in the "iquid "ift module. 'he 'urner correlation incorporates separate equations for water and condensate. 'he liquid lift rate calculated on the +as AOF8' pages will %e the rate associated with the hea#iest liquid in the well%ore. For e*ample, if the flow through the well%ore includes gas, condensate and water, the liquid lift rate will %e calculated for water. If there is no liquid flow in the well%ore, the liquid lift rate is also calculated for water. Important !otes •
If %oth condensate and water are present, use the 'urner correlation for water to Gudge %eha#iour of a system.
•
It is #ery important to note that the 'urner correlation utilies the cross)sectional area of the f low path when calculating liquid lift rates. For e*ample, if the flow path is through the tu%ing, the minimum gas rate to lift water and condensate will %e calculated using the tu%ing inside diameter. hen the tu%ing depth is higher in the well%ore than the mid)point of perforations $-& in a #ertical well, the 'urner correlation does not consider the rate required to lift liquids %etween the - and the end of the tu%ing. Qltimately, the liquid lift rate calculations are %ased on the inside diameter $I!& of the tu%ing or the area of the annulus and not on the casing I! unless flow is up the (casing only(.
inimum Gas &ate to Lift Condensate 'his is the minimum gas rate at which condensate will %e lifted continuously. 'his rate is calculated %ased on the 'urner correlation. First the required gas #elocity is found:
where: + 4 gas gra#ity k 4 calculation #aria%le 4 pressure $psia& ' 4 temperature $>& #g 4 minimum gas #elocity required to lift liquids $ft8s& 4 compressi%ility factor $supercompressi%ility& 'his leads to an e*pression for the 'urner calculated gas rate:
where: A 4 cross)sectional area of flow $ft3& qg 4 gas flow rate -cfd $2?7m78d& As pressure increases, so does the minimum gas rate to lift water or condensate. 'herefore, to determine the minimum gas rate to lift water or condensate in a well%ore, it is recommended that the highest pressure in the well%ore %e used. 'his is typically the flowing sandface pressure. In his original work, 'urner $2B
inimum Gas &ate to Lift ater 'his is the minimum gas rate at which water will %e lifted continuously. 'his rate is calculated %ased on the 'urner correlation. First the required gas #elocity is found:
