pipeline hydraulics analysis: study case

7/25/2019 Pipeline Hydraulics Analysis: Study case

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Pipeline Engineering: Part I- Hydraulic AnalysisWith Case Study

Dr. Ramadan O. Saied and Dr. F.M. ShuaeibMechanical Engineering Department

Faculty of EngineeringGaryounis University !engha"i #ibya $ GS%#&'(

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presented in this article are either derived form their first principles or are ell non fluidmechanics euations. n this article fluid energy euations are first derived. hen practicaleuations are formulated to calculate the pipeline system parameters such as pressure lossesflo rate and the poer reuirements. %ump performance characteristics are presented. %umpsystem characteristics are then presented and discussed. &nalysis of methods of increasing the

pipeline capacity is presented. Optimum pipeline diameter procedure is highlighted. &comprehensive case study to illustrate the most important pipeline hydraulics is presented.herefore this article serves as a good theoretical bacground to engineers ho deal ithpipeline problems and also beneficial for maintenance engineers and operation engineers hodeal ith pipeline problems.

Key words %ipeline %ump System characteristics %ressure drop Fluid mechanics.

'"0" I$GJKC$I&n etensive netor of underground pipelines are eisting in every city and country to

transport ater seage and crude oil petroleum products $such as gasoline diesel or getfuel( natural gas and many other liuids and gases. npant pipelines are also used etensivelyin most industrial or municipal plants for processing ater seage chemicals food productsetc. Despite the long history and idespread applications of pipelines pipeline engineeringhas not emerged as a separate engineering discipline or field as for eample have highayengineering . he fragmentation of pipeline engineering can be seen from the numberof different euations used to predict the pressure drop along pipelines that carry differentfluids such as ater and oil. et all these fluids are incompressible etonian fluids hichshould be and can be treated by the same euations. he fragmentation of the pipeline fieldhas implied the diffusion of the noledge and transfer of manpoer from one pipeline toanother thereby creating and artificial barrier to technology transfer and ob mobility

$%rofessional development(. here is a strong need to unify the treatment of different types ofpipelines by using a common approach so that the net generation of engineers can beeducated to understand a broad range of pipelines for a ide variety of applications. n thisarticle pipeline is considered to be a common technology or a single transportation mode thathas different applications. he euations used are all developed from basic hydraulicprinciples hich are ell published in tet boos. herefore this article is considered to bebeneficial for engineers ho need to perform uic estimation of pipeline components such aspipeline si"e and pumps. he article also provides comprehensive approaches on ho tomanipulate the various pipeline parameters ith a clear vision.

2"0" FASIC CCEP$S L PIPE LMW

2"'" Energy Gelati!ns N!r Pipe-Pu#p Syste#s: onsider Figure $( hich shos a systemconsisting of a pump and a pipe. Energy balance beteen crosssections $( and $( gives

($

hHZP

g

UZ

P

g

Ul

+++=++

here U is the average velocity $ ms( % is the pressure $ m ( is the elevation $ m( is the energy supplied by the pump per unit eight of fluid floing $m( h f is the head loss


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due to friction and separation $m( g is the gravitational acceleration $ m s(.

2"2" Energy M!ss in Pipes: he frictional head loss $hf( or energy loss due to friction in apipeline can be conveniently epressed in terms of the velocity head $U g( by

($

Q

dg

lf

g

U

d

lfhf ==

here l is the length of the pipe $m( d is the diameter of the pipe $m(f is the friction factor is the flo rate $ms(.

he friction factor $f( depends ither the flo is laminar or turbulent. For laminar flo

Figure $( Energy change $!alance(

(-$Re

=f

here Re is the Reynolds number defined as

($

Re dv

Q

v

Ud

==

is the volume flo rate $m s( and is the inematic viscosity $ m s (.For turbulent flo the friction factor $f( depends on both Reynolds number and the relativeroughness $d( here $( is the absolute roughness of the pipe. Several relations for thefriction factor $f( as a function of $Re( and $d( are available and . One of the mostcommonly used relations is the olebroo euation

($Re

.

.-log

+=

fdf

he Moody chart offers a direct and easy ay to obtain the friction factor. Energy loss occursalso due to separation across the pipe fittings such as valves bends unctions etc. hisseparation loss $or minor loss( $h s( can also be epressed in terms of the velocity head as

($

g

Qdg

KUKhs ==

here the value of the coefficient $( depends on the nature of the fitting.

he total energy hl hf hs OOOO""$(


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2"&" Energy Mine and Hydraulic rade Mine: he changes of energy, and its transformationfrom one form to another can be represented graphically. n Figure $( for eample the floof a liuid from reservoir $&( to $!( is assisted by a pump. &t the surface of reservoir $&( thefluid has no velocity and is at atmospheric pressure $hich is taen as "ero gage pressure( so

that the total energy per unit eight is represented by the height $ &( of the surface above thedatum. he entrance loss is

g

U

for sharp edged entrance. &s the fluid flos in the pipe

there is a continuous loss of energy due to friction and the energy line ill slope donards.&t $( the pump ill supply energy $( to the fluid. he energy line falls again due tofriction and separation losses $loss in bends and eit loss( in the delivery pipe until the fluidflos into reservoir $!( here the energy is represented by the height of the surface above thedatum. he height at any section of the energy line $E#( above datum represents the totalenergy at that section. he height of the hydraulic grade line $G#( above the pipelinerepresents the pressure head at that section. f the pipeline rises above the G# the pressureat that section is belo the atmospheric pressure. Under reduced pressure air or other gases

may form and interrupt the flo. t is to be noticed that if the velocity head is negligiblysmall the E# and the G# coincides.he pump head $( hich is the energy supplied by the pump to the fluid is

st hl OOOOOOO""$(here st is the elevation deference !&he poer gained by the fluid is then

% $att( OOOOOOO"" $(

here is the specific eight of the fluid in m $ g and is the density in gm(.he shaft poer $S%( hich is the poer input to the pump shaft is greater than the fluidpoer $%( due to the hydraulic and mechanical losses inside the pump. he pump overall

efficiency $ ( is defined as S% OOOOOOO".$(

2"4" Pu#p perN!r#anceCharacteristic curves:he variation of the pump head $( shaft poer $S%( and efficiency $(ith the flo rate $( at constant speed $( are non as the pump characteristic curves orperformance curves. he shape of these curves depends on the type of the pump. hecharacteristic curves are of considerable practical importance. he pump should operate near itsbest efficiency point $bep(. he shape of the poer curve is important to assure safe operationof the pump. n case Figure $( an electric motor used to drive such a pump may be safelyrated at the maimum poer. n case for hich the poer is continuously rising rating the

motor for maimum poer ould mean over rating hile a smaller motor rated ust for the$bep( may be in dangerof being overloaded should the pump be operated by mistae at a florate greater than that corresponding to the $bep( .


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Figure $( %ump and pipe system

a. Effect of speed on the characteristic curves: he similarity las state that fordynamically similar points on the characteristic curves of a pump is proportional to isproportional to and onstant.

hese relations could be used to predict the characteristic curves of a pump running at a givenspeed $( from the non curves at speed $ (. onsider point $( in Figure $( on the

non characteristic curve $ at (. he corresponding point $( on the characteristiccurve at speed $( is defined by

QQ

!!

=

=

HH !! !"# !$ OOOO.$(

otice that the line oining ..etc is non as isoefficiency curve since allthe points on this curve have the same efficiency. he euation of the isoefficiency curve is

($

Q

Q

HH

!

!=

his euation is for a parabolic curve passing through the origin.

& classic problem is to find out the speed at hich the pump should run to meet a given duty.onsider a pump hose curve at speed $ ( is shon in Figure $(. his pump isreuired to meet the duty $S( i.e. to deliver a flo rate $ s( at a head $s(. otice that point$S( does not lie on the curve at speed . he solution of this problem is to change thespeed of the pump such that the characteristic curve at the ne speed passes ith point $S(.


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Figure $( %umpcharacteristics curve

Figure $( Effect of speedon pump characteristics

Figure $( Determination ofthe speed to meet certain duty.

he reuired speed $( can be determined as follos %lot the isoefficiency curve passing ith point $S( by the folloing euation

QQ

HH

s

s =

Find out the point of intersection $&(. %oint $S( and $&( are dynamically similar points and thus

Q

Q

%

s=

2"%" Pu#p Q Syste# characteristicsa" &yste' curve:onsider the pump and pipe system of Figure $(. Recall euation $( forthe pump head the pump head is given by

H # Hst( hlhe energy loss $hf( consists of the frictional loss $h f( and the separation loss $hs(. From Es.

and

QKQKKQdg

KQ

dg

flhhh sfl

($

=+=

+=+=

and H # Hst ( KQ" OOOOOO"R(

his relation is called system characteristic or system curve $Hst( is the static head and theconstant $K( depends on the characteristics of the pipeline. n order to maintain a flo rate$Q( in this specific system the energy $ H ( hich must be supplied to the system is givenby E..

he system curve Figure $( is a parabola. t must be remembered that if the pipe system isin any ay modified or additional losses are introduced $such as partially closing a valve( ane different parabola ill result because the value of $K( ill be changed.

"Pu'p operating point:onsider again the pump and pipe system shon in Figure $(. hecharacteristic of the pipeline is shon in Figure $(. he pump has its on characteristic.Figure $( shos the pump and system characteristics. he point of intersection of the tocharacteristics is called $the operating point(. &t this point the head generated by the pumpis eactly the energy reuired to maintain the flo in the pipeline. his is the single point in


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the pump characteristic at hich the pump could operate hen inserted in the pipeline of theshon characteristic.

C. Capacity control:%ump matching means the process of selecting a pump to operate inconunction ith a given piping system so that it delivers the reuired flo rate and in thesame time is operating at $or near( its best efficiency point. he point on the system

characteristic hich corresponds to the reuired flo rate is non as the $duty reuired(.hus for correct matching the operating point should coincide ith the duty reuired.Even if the matching is correct it may be reuired to change the flo rate for some practicalreasons. hree methods are commonly used to control the pump capacity.i(. hrottling %artially closing the valve shifts the system curve until the ne operating pointsatisfies the reuired flo rate $See Figure (. hrottling astes poer due to the loss ofenergy in the valve and the considerable drop of efficiency.ii(.Speed variation &s mentioned in section ..b the speed of the pump could be changedsuch that the operating point coincides ith the duty reuired Figure $(. his entails verylittle or no poer loss but the pump drive should be variable speed.iii(. !ypuss n this method for capacity control the ecess capacity is bypassed bac to the

suction sump. t is commonly used ith aial flo pumps.

Figure $( System characteristics. Figure $( %ump and system characteristics.

Figure $( apacity control by throttling. Figure $( apacity control by speed.D.Parallel and series operation of pu'ps: t is sometimes necessary to use more than onepump in conunction ith a given pipe system. he pumps could be arranged in series or inparallel Figure $(. Figure $( shos the combined characteristics for to identical pumpsoperating in series and in parallel against to pipe systems $S ( and $S(. For clarity systemsith no static head are used. For S the single pump ill operate at & the to pumps


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connected in series ill operate at ! and hen connected in parallel at . Similarly for S thecorresponding operating points ill be D for a single pump E for parallel operation and F forseries operation. t can be seen that for Sparallel operation yields higher flo rate than seriesoperation hile for Sseries operation gives higher flo rate. his shos that the choice ofseries or parallel connection depends upon the shape of the pump characteristic and the system

characteristic.

Figure $( Series and parallel connections. Figure $( Series and parallel operation ofto identical pumps.

2"(" Hydraulic Analysis !N Pipeline Ll!T Rcase studyU

onsider the pipeline shon in Figure $( hich is for a real case ith little modification tofully illustrate the pipeline hydraulic theory. From the preliminary process and mechanicaldesign the pipeline outer diameter is do .mm $&ppro. si"e( and inner diameter d i.mm $thicness t . mm( and laid over the surveyed terrain shon in Figure $(. hedesign flo rate is mhr density gm and inematic viscosity . centistoes$orresponds to local crude oil( . he length of the pipeline is . m and the euivalentroughness of the selected pipe is . mm. he items discussed in this case study are thepressure reuired to move the fluid at a prescribed flo rate through a pipeline the maimumcapacity $flo rate( of the pipeline methods of increasing the capacity and the optimum traceand si"e of the pipeline.

a. Hydraulic gradient and 'a!i'u' capacity: &pplying energy euation beteen the headend $point l( and a point at a distance l and neglecting minor losses

h !ZgUPZgUP f!

!!

+++=++

Since U Ul and denoting the pressure gradient PVby h the folloing relation can beobtained.

l&Q

dg)

lf

g

U

d

lfh !

!!f! ===


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here S dg)

Qf

OOOO$(

&is the pressure gradient and is constant for a given pipeline. he pressure head hlat head end$( reuired to move the liuid at a flo rate Qthrough pipeline of diameter dlaid over a giventerrain can be determined as follos. Using E. $( the gradient &is calculated. & line ith a

slope corresponding to this gradient is dran from tail end $( to head end hich is shon asline Xin the figure. f this line intersects the ground profile then the hydraulic grade line $G#(must be displaced parallel to itself until it touches the ground profile line Iin the figure. heinitial pressure head hlis the above ground section of the ordinate at the head end $(. t isrecommended for safety to increase hlby m" he point M is called a critical point. hisis here the pressure head is least. otice that the $G#( beteen Yand is steeper thanbeteen and Y. onseuently if there is no throttling at the tail end flo is free beyondthe critical point and fluid ill arrive at atmospheric pressure at the tail end tan. f throttling isapplied at the tail end the fluid ill have a pressure head h2at the end point. &nother criticalpoint as far as pipe strength is concerned may be valley point; * . t is necessary to calculatethe pressure head h * and find out hether pressure dose not eceed the maimum alloableoperating pressure of the pipeline.

Figure $( ydraulic gradient of a pipeline laid over undulating terrain

herefore the -.-

RenumberReynolds ===vd

Q

v

Ud

i

Relative roughness di .

From Moody chartf . and From E. $ ( S dg)

Qf !

.

h . . & m $ m is the elevation difference (


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&s shon in the figure the obtained $G#( $line X( enters the ground and therefore it should bedisplaced parallel to itself until it ill be tangent to ground profile at point M. &ccordingly h$ m. For safety let us augment this by m giving h$ m. he pressure delivered bythe pump installed at point $( should then be %g hl m.

*a!i'u' capacity of the pipeline&ssuming that pumping is concentrated at the head end $( the greatest flo rate through thepipeline can be determined by the folloing procedure. #et us plot on the above groundprofile at point $( the pressure head h'a!corresponding to the maimum alloable operatingpressure of the pipe $see Figure (. 'oining this point ith the tail end point $( $or ithcritical point M( the $G#( hose slope corresponds to the maimum feasible pressuregradient &'a! is obtained. From the obtained value of &'a! the maimum flo rate Q'a!. isobtained as follos.For this particular case study an empirical relation is derived for the friction factor as afunction of the Reynolds number $using the selected pipe(. Other empirical formulae hichare ell documented in literature can also transformed to the derived euation using curve

fitting procedures f a Re b OOOOOOOO""$(here a and b are constants characteristic of the actual value of relative roughness andthe Re range involved. For selected pipe type in this study the curve fit euation ith thevalues of the constants are determined as

f . Re .

ntroducing this into E. e obtain S . o.. d. OOOOOOOO" R(

and Q # .S. di. . OOOOOOOO" $(

Substituting in $( the graphically determined value of S S ma e can calculate mathe maimum liuid flo rate of the pipeline if the only pump station is at the head end of thepipeline. Furthermore the maimum capacity of the previous pipeline can be determined. f&% standard line pipe made of steel is used $maimum stress Mm(. Selectedsafety factor is .. henhe alloable stress a . Mm.

+he 'a!i'u' allowale internal pressure:he pressure can be determined from simplemechanics calculation of the pipeline pressure asshon in Figure $ (

'*d

tP all

-

-

..

. ===

Figure $ (From the relation % g h

'h .-

.

ma =

=

#et us reduce this value by m for safety hence h'a! m. %lotting h'a!at point $( and


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oining ith point $( e obtain the G# $#ine in Figure (.he maimum gradient

.

-ma

=

=&

From euation $(

ma. . m

s m s the design flo rate of mhr.b. Increasing the capacity of pipelines

&ny pipeline design should consider the possible future epansion. o illustrate this issue eill consider that the designed pipeline has been already installed and e ant to eplore thepossibility of increasing its capacity. herefore it is reuired to increase the flo rate throughthe designed pipeline to a value higher than its maimum capacity ma. Often this can beachieved by letting the pipeline stay as it is and by. #aying a second one alongside $double line( or by.. nstalling one or several intermediate pumping stations $booster stations( along theeisting pipeline.

1- .oule line: he double line is called $looped( it may be of to types a ne line of thesame length as old one but usually of different diameter $complete loop( or a ne line shorterthan old one but of the same diameter $partial loop(.

omplete loophe to lines are independent. he si"e of the ne line is chosen so as to deliver Q'a!under the original input pressure h'a!. Oing to the identity of trace and of input andoutput pressures the pressure gradient of the ne line is the same as the maimum feasiblegradient Sma of the eisting line. he tas in hand is then to determine the si"e of the pipereuired to deliver under the pressure gradient &'a!.From E.$(

($. .

ma

-.

--.

&Qd = %artial loop

f the ne line is to have the same diameter as the eisting one and ma the length ofthe ne line is less than that of the eisting one. he ne line is usually laid beginning ateither the tail or head end of the old line. Figure $( illustrates the method to determine thelength of the ne line.For the single line S Sma$since l ma( and from E.$(

dQ& ..

.

-. =

n the double section each line delivers and

dQ&

....

($ -. =

Dividing the first euation by the second and solving for S S2 . S OOOOOOOOO"$(

he length l!can then be obtained by tracing a pressure traverse of slope &"forard from pointAand another one of slope &$bacard from point . he point of intersection determines thelength l!. alculation of l!can be also performed as follos

H # &'a!l # &$/l0l!1 (&"l!


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hen ($

ma

&&

&&ll!

=

ontinuing on the previous case study and putting numerical values. #et the capacity of thepipeline need to be increased to mhr by building a ne line. So hat ill be thediameter of the ne line for complete loop and the length of the ne line for partial loop

For complete loop2 mhr .msFrom e. $(

(.$(.$(.$. .-. --.

=d .mFor partial loop

.(.$(-

$(.$-.

..

.

== &

Form e. $( S2 . . .he length of the ne line $E. (

m

..

..l x -

==

. m

he pressure traverse of the loop is shon in Figure $(.

Figure $( %ressure traverse of looped line

2. 2ooster pu'p stations:Each pump station delivers the liuid at the maimum alloablepressure $ecept usually the last one(. he slope of the pressure traverse hich is lieiseeual in all sectionsdepends on the flo rate . he first pump station is installed at head end$(. & pressure traverse of slope eual to the pressure gradient is to be dran starting fromh'a!plotted at & until it intersects the ground profile this is here the first booster station is


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to be installed. o h'a! is plotted again at this point and the construction is repeated until thelast booster station ill deliver the liuid to or beyond the delivery end $( $See Figure(.aing numerical values let the capacity of the previous pipeline be increased to m hr byinstalling booster stations. t is reuired to find the location of the booster stations along thepipeline.

Z' m

hr . m

sFrom E.$( S .

he maimum alloable discharge head is m.%erforming the construction noing & and h'a! it becomes apparent $Figure ( that atstation $( a discharge head h'a! ould be ecessive. he discharge head reuired can befound by tracing a pressure traverse bacard from point $( in hich case the head inuestion is the height difference at point $( beteen the ground profile and the pressuretraverse. he discharge head reuired is m.Figure illustrates the construction of the pressure traverse and indicates the location of thebooster pump stations.

Figure $( %ressure traverse ith booster stations

c. Optimum trace and size of pipelines:

&s this paper is concerned ith the hydraulic analysis only the pipeline trace and si"e issuesare not considered. oever a brief overvie on the method of determines the pipeline traceand pipe si"e is given hereunder.n the absence of arguments to the contrary the economically optimal trace for a pipeline isthe straight line oining the to end points. &rguments to the contrary include the folloing

. he straight trace ould traverse country here laying the pipeline ould be toocostly $samp lae roc etc.(.


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. t ould penetrate the safety "ones of obects designated by other authorities$!uildings defense establishments( or intersect main roads railroads etc.

. Deviation from the straight trace ould entail a substantial saving by avoiding damage to crops and the tying don of valuable land.. t is to be preferred to lay a line along a road or railroad as this ill reduce laying

costs and facilitate and accelerate repairs.

Optimum pipe si"e is that si"e permitting transport of liuid at loest cost. f the annual florate may be considered constant then the optimum pipe si"e for the line can be determinedby the folloing consideration. ost of transport is a sum of to components depreciationplus interest on the investment $to be called depreciation for short( and operating plusmaintenance cost. ncreasing pipe si"e ill increase first cost and decrease operating cost.Figure $( shos plots of depreciation & operating cost ! and total cost v. pipe si"e for agiven flo rate. Optimum pipe si"e dopt is seen to belong to the minimum of the curve f$d(.he total annual cost of transportation is & & ! !

ere depreciation &lis &l $al ad(.l. "here alis a cost component independent of pipe si"e e.g. ditch cutting and supervision a dis the cost component depending on pipe si"e $pipe price transportation to the site eldingpainting insulation testing etc( " is the annual depreciation rate of the ready to operatepipeline and lis the length of the pipeline. he annual depreciation of a pump station is

&2 %. b ."here pump station output % g h b is unit first cost of the station " 2is the annualdepreciation rate of the pump station s the overall efficiency of the installation.he annual operating cost is F' %.c.e.fhere cis operating time per year eis specific poer consumption $ '( for electric motor

and g' for internal combustion engines( f is the price of electric poer or fuel.he annual cost of maintenance F2 may be considered constant.

&"0" CCMKSIS

From the previous study the folloing points can be concluded he special pipeline hydraulic issues are illustrated and discussed in a comprehensivemanner ith illustrative case studies. Methods of pipeline capacity control and capacity increase are presented and discussedusing the case studies. & brief pipeline trace and si"e cost study is highlighted and it is recommended that further

analysis is provided. his or is a useful tool for pipeline engineers particularly those ho deal ith pipelinehydraulics programming pacages.


15/15

Figure $( Fied and operating cost of transportation.

GELEGECES

enry #iu $( %ipeline Engineering #S %U!#SERS US&.

Douglass '.F. Gasiore and Saffield &.'. $( Fluid Mechanics %M& %ublishing nc. Massachusetts '.Ranald . Gilies $( heory and %roblems of Fluid Mechanics andydraulics ndEdition Schaums Outline Series McGR# !oo ompany. /Bz /3 {x3 .. w[/B-/ 1Q2J1Q23 j^1_:I JB?1 =]31Zydraulic nstitute Standards for centrifugal rotary and reciprocating pumps Fourteenth edition $( leveland Ohio US&.%revies proect eperience of the authors at the &rabian Gulf Oil o. $&GOO(!engha"i #ibya GS%#&'.estaay .R. and #oomis &.. ameron ydraulic Data Siteenth edition%ublished by GRESO##R&D US&.

rocer S. $( %iping andboo Fifth Edition McGR# !OO OM%&. !yron S. Gottfried $( Spreadsheet ools for Engineers Ecel ersion McGR# !OO OM%&. urveEpert . urve Fitting System for indos. opyright $c( Daniel yams eb site http.ebicom.netdhyamscvpt.htm.

pipeline hydraulics analysis: study case

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