Liquids-general (Chapter 12)

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Chapter 12 - Liquids - General

• Determining the viscosity of crude

• Chart gives API gravity of blends quickly

• Liquid gravity and density conversion chart

• Nomograph for calculating viscosities of liquid hydrocarbons at high pressure• Calculate viscosity of a blend

• Calculate gravity of a blend

• Convert viscosity units

• Convert specific gravity to API gravity

• Calculate bulk modulus

• Viscosities of hydrocarbon liquids

• Nomograph for calculating viscosity of slurries

• Nomograph for calculating velocity of liquids in pipes

• Nomograph for calculating velocity of compressible fluids in pipes

• Nomograph for calculating velocity of liquids in pipes

• Derivation of base ultrasonic flo equations• !o fast does oil move in a pipe line"

• #stimate the volume of a pipe line per linear foot using the inside diameter

• $hat is the linefill of a given pipe in barrels per mile"

• #stimate leakage amount through small holes in a pipe line

• %able gives velocity heads for various pipe diameters and different rates of discharge

Determining the Viscosity of Crude

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If the viscosity of a gas&saturated crude oil at the saturation 'bubble&point( pressure is knon) using

this nomograph you can quickly estimate the viscosities at higher pressures*

Example. +ind the viscosity at ,)-.. psia for a crude oil hen its viscosity is /. cp at the saturation

pressure of 0)-.. psia* notice that ,-.. psia is /)... psi above the saturation pressure* Connecting/)... on the pressure difference scale 'left( ith /. on the curved scale for viscosity at the bubble&

point pressure) the intersection ith the scale on the right at ,1 cp is the desired value*

Chart Gives API Gravity of Blends Quickly



API gravity of a crude oil blend may be readily estimated from the gravity of the components and

their percentage composition* It is a simple procedure to use these curves to find the resulting APIgravity of the blend*

Example. If you blend a 0,2 API pitch '3.4( ith a /32 API cutting stock ',.4() the resulting fuel

oil has an API gravity of --2 as read from the nomograph* Calculated result from gravity tables

ould be --*02

API* 5esults found using this nomograph checked out ithin 02 API over the range of gravities and percentage of components '0( and '-( in the nomograph belo* #stimates from the nomograph are

used on the assumption that volumes of blends are additive and that no light components flash off in

blending*

Liquid Gravity and Density Conversion Chart

%his line chart provides an easy method for converting units of liquid gravity and density* Dra a

hori6ontal line perpendicular to the scale line through a knon value and read the equivalent value on

any other scale*



omogra!h for Calculating Viscosities of Liquid "ydrocar#ons at "ighPressure

Lockhart and Lenior developed a graphical correlation shoing the effect of pressure on viscosity of

liquid hydrocarbons* %his correlation is shon in +igure 0 hich is based primarily on data of !erseyand !opkins)- including pure hydrocarbons) lubricating oils) bright stocks) and distillates* Data from

5eference 0 have also been included*



%o use the nomograph) the characteri6ation factor of $atson) 7 ) and the viscosity of the liquid at

atmospheric pressure are required*

%he accuracy of the correlation decreases as pressures increases*

Example. $hat is the viscosity of an oil at 8),.. psia) if its characteri6ation factor is 00*1 and its

viscosity at atmospheric conditions is 9. centipoises"

#nter 8),.. psia in the pressure scale to the viscosity line of 9. and proceed hori6ontally to middle

reference scale* +ollo the curve lines to intersect the vertical line dran at 7 : 00*1 and read theratio of viscosity on the e;treme left scale at -*3* %he viscosity of the oil is '-*3('9.( : -/,

centiposes*



Figure 1. Isothermal effect of pressure on viscosities of liquid hydrocarbons at lo reduced

temperatures* '5eproduced by permission Petroleum Refiner ) Vol* ,.) No* / page -.9) copyright0930) <ulf Publishing Co*) !ouston(

Source

Lockhart) +* =* and Lenoir) =* >*) Petroleum Refiner ) ,.) No* /) -.9 '0930(

References

0* <reist) and others) =* Chem. Physics) -9) ?00 '0981(*

-* !ersey) >*D*) and !opkins) 5* +*) Viscosity of Lubricants Under Pressure) A@>#) 098,*

Calculate Viscosity of a Blend

Viscosity is not an additive function of percentage composition* %he viscosity of a blend of productscan be calculated ith the folloing equation

hereVb : viscosity of blend

< : volume 'gals) gpm) bBd) etc*(

V : viscosity in @@

Example.

<0 : 0.)... bbls

<- : -.)... bbls

</ : 8)... bblsV0 : ,8 @@

V- : 8. @@V/ : /? @@



Vb : ,3*, @@

Calculate Gravity of a Blend

%he gravity of a blend of liquids may be calculated directly by a ratio of the gravity of each

component in the blend*

#;ample* Assume a blend consisting of the folloing

Convert Viscosity $nits

Convert @@ to centistokes 'c@(

vsus : .*-- vsus '&0/8 B vsus( here vsus 0..E

vsus : .*--3 vsus '&098 B vsus( here vsus less than or equal to 0..E

Convert centistokes 'c@( to centipoise 'cP(

cP : vcs ; density) gmBcm/

@@ : cs ; ,*33?/) if cs 8..) @@ : cs ; ,*3/,?

Convert %!ecific Gravity to API Gravity

API : 0,0*8 B s3. & 0/0*8 here s : specific gravity F 3.2+

s3. : ,0,*8 B 'API3. G 0/0*8(



Calculate Bulk &odulus

%he bulk modulus) 7) of a liquid is the reciprocal of its compressibility* %he bulk modulus for ateris 7 : /..)... psi* %he compressibility factors for most liquids can be found in Chapters 00*-*0 and

00*-*- of the API Manual of Petroleum Measurement Standards* %he folloing relation) knon asthe A5CH formula) can be used to calculate the bulk modulus for crude oil

7 : 0*-13'0.3( G 0/*88p & ,*0--'0.,(%0B- & ,*8/'0./(API & 0.*89API- G /*--1% APIE

here7 : adiabatic bulk moduls) psi

p : average pressure in the line) psig

API : API gravity% : absolute temperature) 25

E5eprinted ith permission +luid +lo Consultants) %ulsa) H7*



Viscosities of "ydrocar#on Liquids



omogra!h for Calculating Viscosity of %lurries

%he nomogram is based on the !atschek equation for estimating the viscosity of slurries in an

aqueous suspension*

: B '0 & ;.*///(

here

: viscosity of slurry) centipoises

: viscosity of ater at the temperature of the slurry) centipoises; : volume fraction of dry solids in the slurry

%he nomograph '+igure 0( shos a scale calibrated in terms of the temperature of the ater instead of

its viscosity* %hus) the actual ater viscosity value is not needed*

#;ample* $hat is the viscosity of a slurry having a volume fraction of solids of .*.3 at a temperatureof /9oC"

Connect % : /92C ith ; : .*.3 and read m : 0*0 centipoises on the middle scale*

Source

Davis) D* @*) Brit. Chem. En.) ,) 9) ,?1 '0989(*



Figure 1. Viscosity of slurries '5eproduced by permission) British Chemical Enineerin ) Vol* ,)

page ,?1) copyright 0989*(



omogra!h for Calculating Velocity of Liquids in Pi!es

%he mean velocity of any liquid floing in a pipe of circular cross section can be calculated from the

folloing formula

v : 01/*/q B d- : .*,.1J B d-: .*.8.9$ B d- !

here

v : average fluid velocity) ftBsec

d : inside diameter of pipe) in*q : rate of flo) cubic ftBsec

J : rate of flo) galBmin

$ : rate of flo) lbBhr

! : fluid density) lbBcubic ft

%he Nomograph for Calculating Velocity of Liquids in Pipes can be used to calculate the liquidvelocity hen the rate of flo is in cubic ft) gallons or thousands of lb* Conversely) knon the flo

rate and velocity) the pipe diameter may be calculated*

Example. $hat is the velocity of fuel oil at 3.o+ floing through a -&in* schedule ,. pipe at a rate of,8)... lbBhr* %he oil density is 83*.- lbBga*

Connect ith !ar" or Read

$ : ,8 ! : 83*.- J : 0.. cubic ftBsec

J : 0.. d : -&in* schedule ,. v : 0. ftBsec

Source

"lo# of "luids $hrouh Val%es& "ittins& and Pi!e) %echnical Paper No* ,0.) /&?) Crane Company)

Chicago) Illinois '098?(*

omogra!h for Calculating Velocity of Com!ressi#le 'luids in Pi!e



%he mean velocity of a compressible fluid in a pipe can be computed by the folloing formula)

hich is obtained after dividing the rate of flo in appropriate units by the cross&sectional area of the pipe

Example. @team at 3.. psig and 18.2+ is to flo through a schedule 1. pipe at a rate of /.)... lbBhr*+ind the pipe if the velocity is to be limited to 1)... ftBmin*

If a ,&in* schedule 1. pipe is used) the actual velocity is found by connecting the Inde; ith ,&in*

schedule 1. to get V : ?)3.. ftBmin*

Note If a different fluid is involved) the value of the density 'or specific volume( needed to make the

calculation can be obtained from @ection 9 of this book) under KDensity and specific volume of gasesand vapors*K

Source

"lo# of "luids $hrouh Val%es& "ittins& and Pi!es) %echnical Paper No* ,0.) /&03) Crane Company)

Chicago) Illinois '098?(*

omogra!h for calculating velocity of liquids in !i!es



Derivation of Basic $ltrasonic 'lo( )quations

%he actual measurements performed by ultrasonic flometers are of flo velocity) ith all other

variable effects due to temperature) pressure) density) viscosity) etc*) being canceled via a differentialsensing technique*

>ultiplication by the cross&sectional pipe area readily enables the output to be conditioned to read involumetric flo rate scaled to engineering units* 5efinement of the technique enables density andother physical properties to be measured as ell) so that mass flo rates and other parameters

pertaining to various process variables can be determined

%o cancel the effects of variations in the velocity of sound c in the medium itself) the circuitry isarranged to compute the reciprocal of each flight time and to subtract one from the other* %his

difference of the flight time reciprocals leads to the relationship

@olving for v



%he circuitry hich performs the reciprocal time computation procedures an output frequency since

@ubstituting in #quation 3 e have the basic velocity equation

or

is the flo velocity scaling factor) and is usually e;pressed in ft per second or ft per minute* Note thatit is a function of the square of the distance beteen the transducers* %his is an important

consideration hen providing for re&6eroing of the meter calibration each time the transducers are

removed and re&inserted*



+or volumetric flo) the velocity must be multiplied by the cross&sectional area of the pipe) and the

folloing considerations are involved

Volumetric flo

%herefore) volumetric flo

%he relationship

is the volumetric flo scaling factor) and is usually e;pressed in cubic ft per minute*

+urther information on the physical properties of the floing medium is also acquired in the process

of the basic measurement* @pecifically) the velocity of sound in the medium itself can be measuredindependent of the velocity of its motion*

#quation / computed the difference of the reciprocals of the upstream and donstream flight times*

In the instrument this is performed in the delta computer channel* @upposing an addition of the

reciprocals of the respective separate computing channel) called the sigma channel* %he folloingrelationships ensue

be the sound velocity scaling factor



%he speed of sound c in a medium is a function of its bulk modulus and its density) and is e;pressed by the folloing equation

here

: bulk modulus of elasticity

! : density

+rom this) the equation for density may be derived thus

@ubstituting the value of c from #quation -. into -/ gives

+or a given gas) is essentially constant*

is a fair representation*

An interesting relationship may be derived at this point) namely) an equation for mass flo* @ince



or) letting k 0k , : k 8

+urther) the density of a gas is related by the equation

here

P : pressure

% : temperature '27(

%herefore) if the pressure is knon) the temperature may be e;tracted from the sigma channel thusly

Let us go back to #quation -,* If the chemical properties of the gas or the ratio of the mi;ture

beteen to or more gases changes) then is not a constant* If separate transducers are used tomeasure density) say via the pressureBtemperature relationship) then the variation of can also be

measured*

%he above relationship holds for liquids or gases*

In the case of a gas) e may further say



"o( 'ast Does *il &ove in a Pi!e Line+

Divide the throughput) in barrels per day) by the square of the nominal diameter) in in*M divide this

result by 0..M and subtract 0 from the anser* %he anser is the speed of the oil column in miles perhour*

Example. A 0-&in* line has a throughput of ?.)... bpd ?.)... B 0,, : ,13

,13 B 0.. : ,*13

,*13 & 0*.. : /*13

%he oil moves about , miles per hour*

%his rule is rough) but seldom is an e;act anser needed for this problem* <reater accuracy can behad by using the true inside diameter of the line in the folloing formula

V : .*..10 ; 'J B d-(

here

V : speed) mphJ : throughput) bpd

d : inside diameter of pipe) in*

%ake the above e;ample If the all thickness of the pipe is /B1 in*

V : '.*..10( ; '?.)... B 0,,(

V : /*9,

or about , miles per hour*

Example. A -.&in* pipe line has a throughput of -..)... barrels per day* !o fast does the oil move

inside the pipe line"

y the first method

-..)... B ,.. : 8..

'8.. B 0..( & 0 : , miles per hour

y the second method



Example. @i;&in* schedule ,. pipeM inside diameter is 3*.38 in*

3*.38 ; 3*.83 ; 8*0/ : 011*? barrels per mile

If the correct inside diameter is used) the rule gives the correct linefill in standard ,-&gallon barrels

per mile of pipe*

)stimate Leakage Amount -hrough %mall "oles in a Pi!e Line

%he amount of fluid lost through a small hole in a pipeline can be estimated using the folloingequation

hereJ : flo in cu ftBsecond

A : cross sectional area) sq ft

g : gravitational constant) ftBsecBsec

h : head) feet

Example# Assume the folloing conditions

!ole diameter : .*0-8 inches

Pressure : /. psig

@p* gr* of fluid : .*18

A : .*....18- sq fth : 10*8 feet

g : /-*-

J : .*../?38 cu ftBsec

-a#le Gives Velocity "eads for Various Pi!e Diameters and Different.ates of Discharge

Liquids-general (Chapter 12)

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