3. pressure loss in the wellbore

8/16/2019 3. Pressure Loss in the Wellbore

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Pressure Loss in the Wellbore


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Lecture Outcomes

At the end of this lecture, students should be able to:

• Identify the major components of pressure losses in the

wellbore

• Explain the origin and applicability of common industry

multiphase flow correlations

• Define slip and liquid holdup


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Introduction

• !or the "ast majority of wells, the major part of

pressure loss in the production system is the

wellbore

• #articular care must be therefore be ta$en to

understand and model this pressure drop

correctly%


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Introduction

• #ressure loss in the wellbore may also be called

&outflow' or tubing performance or "ertical lift

performance ()*#+

• It is used in conjunction with pressure drop in

the reser"oir or &inflow' performance relationship

(I#+ for well performance prediction (flowrates

and pressures+


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Introduction

Note that it may be incorporated into reservoir models as vertical lift

performance (VLP) curves or tubing hydraulic tables

!igure -: I# and )*# cur"es


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Wellbore Fluid Fundamentals

• !low up the wellbore can be laminar or turbulent, single or multiphase,

"ertical or inclined

• .ultiphase flow is complex and cannot be described completely by

equations

• .odels rely on correlations to allow calculation of pressure loss

• /he dominant component is hydrostatic head (gra"ity pressure loss+

• /he secondary component is resistance to flow (friction pressure loss+

• /he minor component is $inetic energy change (acceleration pressure

loss+


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!igure 0: A schematic of a wellbore


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1oted that the top and the bottom of the wellbore are often called &nodes':

• /he top nodes is the depth of the wellhead (where the pressure is termed

well head or tubing pressure 2 #wh or 34# or /4#+

• /he bottom node is the depth of the reser"oir (or well face+, usually chosen

as top perforations or top open hole (2 #wf+%

• #wf stands for pressure at the well face and not flowing pressure (at 5ero

flow, #wf 2 static reser"oir pressure, #+% /his is usually chosen as the

solution node for well performance prediction (i%e% inflow and outflowintersection+



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6uidelines for magnitudes of these pressure components

are as follows:

• !or oils, acceleration term is usually negligible andgra"ity term is a minimum of 789 of the total

• !or low 6 oils (or high water cut wells+, gas "olumes

are small and the gra"ity term is typically ;


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Gravity Term

!or most wells, this is dominant pressure loss component and

therefore is must be calculated correctly%

?alculation of the gra"ity term requires:

• determination of oil, water and gas densities at element (#a" , /a"+

• calculation of phase "olumes and areas at element (#a" , /a"+• calculation of mixture density at element (#a" , /a"+

where:

@mix 2 lbBcuftC 4/)D 2 ft /)DC

#gra"ity 2 psiC


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• /he abo"e calculation assumes that the liquid and gas phases areflowing at the same "elocity in the wellbore%

• In reality the gas phase will mo"e faster due to buoyancy forces,

gi"ing rise to a slip velocity :

• slip "elocity 2 gas "elocity liquid "elocity

• /he consequence of slip is a change in the areas of each phase(the effecti"e liquid area increases+%

• /he slipcorrected liquid area is termed liquid holdup (4*+:

Gravity Term


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• /he correction from 9* to 4* by accounting for slip is determined by

multiphase flow correlations

• 1ote that the noslip density represents the minimum # gra"ity case

and is a useful diagnostic

• Flip is determined by finding the "elocities of each phase which is

dependent on flow distribution

• Determination of slip is highly complex and depends on a number of

parameters

• /hese parameters are often grouped together in the form of flow regime

maps

Gravity Term


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Exercise

?onsider two cases of the same amount of gas (089+ distributed

differently in the liquid phase

• In which case would the slip be highest and why?

• hich fluid parameter is most influential in determining thedistribution?


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Multiphase FlowCorrelations

Most oil wellswould be inbubble fowtowards the

bottom o the

wellbore andmove to slug

fow towards themiddle and top o

the wellbore.Slug fow is

usually thedominant fow

regime.


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Flow Regime Map

• !low regime maps use combinations of dimensionless groups for

the gas and liquid phases% /hese are plotted on the x and y axes

respecti"ely and the intersection determines the flow regime%

• /he boundaries between the flow regimes are found experimentally%


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Flow Regime Map

Note the primary fluid parameters of importance are liquid density

and gas-liquid interfacial tension.

#ractical implications of these grouped parameters are:

-% 4igh interfacial tension fluids (biodegraded oils+ will support large

bubble si5es ( slug flow+∴

0% *ow interfacial tension fluids ("olatile oils+ cannot support large

bubbles ( mist flow+∴

G% /he correct determination of gasliquid interfacial tension is criticalH


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Selection For Flow Correlations

• Applying the appropriate holdup correlation depends on flow regime

detection and the emphasis of the experimental wor$ performed in

deri"ing the correlation%

• 6eneral comments on the origin and applicability of common

industry correlations are as follows:

Fancher-Brown (!"#$ %o-slip correlation. &ood as a diagnosticsince this give the minimum possiblegravity pressure loss

&ri'th-allis (!"$ Bubble fow correlation. )dopted by

*agedorn-Brown and others todetermine bubble-slug fow boundary

+uns and ,os (!"$ omprehensive wor including fowregime map and derivation o holdupcorrelations or each. Best in mist fow

regime


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4agedornrown(original -;>J+ ?ombined the results of 6riffith3allis, 4agedornrown and Duns and os with "elocity determinedboundaries% ?an gi"e discontinuities%

eggs and rill(-;JG+

?orrelation deri"ed for hori5ontal flow and thenmodified for angle for de"iated wells% 6ood for pipelinesbut usually o"erpredicts for wells%

ontinue..


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• Fince most oil wells are in slug flow (with some bubble flow towards

the bottom of the wellbore+, 4agedornrown (modified+ would be

the best choice% .ost commercially de"eloped correlations for oil

wells use 4agedornrown as the basis%

•!ancher rown is a no slip correlation and is a useful diagnosticsince it will predict the minimum #wf (slip will increase #wf+% If a

measured gauge pressure in the wellbore is less than !ancher

rown then a data measurement or #)/ problem exists%

• eggs K rill is good for surface flowlines and pipelines but is not

recommended for oil wells, de"iated or otherwise%

• Duns and os is recommended for wet gas or gascondensate wells

that are dominant in mist flow% /he 6ray correlation, not mentioned

abo"e, is appropriate for dry gas wells%


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Friction Term

• /he main dependencies of frictional pressure loss are mixture"elocity (or flowrate+, pipe diameter and "iscosity% It is "ery sensiti"e

to gas "olumes since this directly affects "elocities%

• 1ote that it is in"ersely proportional to diameter to the fifth power%

• /he equation for friction pressure loss (per unit length+ is as follows:


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Friction Term

• !riction factor (f+ is correlated to !eynolds number (e+ and tubing

roughness (L+ from the .oody Diagram (de"eloped for single phase

flow+%

• 1ote that for laminar flow (e M 0888+, the friction factor 2 >=Be

• /ubing roughness (granularity of the tubing inside wall+ is onlyrele"ant in turbulent flow% In laminar flow, roughness has no effect%


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Friction Term

/ypical "alues of roughness (L+ are as follows:

• Ftainless steel B -G9 ?r 8%8888> in

• .ild steel 8%888> in

• ?orroded tubingBcast iron 8%8- in

• "or turbulent conditions in multiphase flow , the frictional loss term is

influenced by slip%

• )arious authors ha"e modified the friction term for bubble, slug and

mist flow%• A twophase eynolds number is used accounting for gas and liquid

"iscosities%


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Acceleration Term

• /his results from $inetic energy losses due to the rate of change of "elocity%

• It is usually only significant at the top of the wellbore with low flowing

pressures and large gas "olumes%

• 6enerally this is negligible for most oil wells%


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uestion !!

Than" #ou

3. pressure loss in the wellbore

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