Vapor Phase Pressure Drop Methods

7/30/2019 Vapor Phase Pressure Drop Methods

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9 Theoretical Basis 157

9 Theoretical Basis

Pressure Drop

Pipe Pressure Drop Method

Vapor Phase Pressure Drop Methods

Pressure drop can be calculated either from the theoretically derived equationfor isothermal flow of a compressible fluid in a horizontal pipe2:

02

2In

22

1

2

2

2

1

2

a

GLf

RT

PPM

P

P

a

Gf

I

9.1

weightMolecularM

eTemperaturT

lengthEquivalentL

diameterInternal

factorfrictionFanningf

constantgasUniversalR

pressureDownstreamP

pressureUpstreamP

pipeofareasectionalCrossa

flowMassGwhere

f

I

2

1

:


2/32

158 9 Theoretical Basis

Or from the theoretically derived equation for adiabatic flow of a compressible

fluid in a horizontal pipe2:

-

-

1

2

2

2

1

2

1

1 In

1

V

V

V

V

G

a

V

PLAff

I

9.2

heatsspecificofRatio

lengthEquivalentL

diameterInternal

factorfrictionFanningfvolumespecificDownstreamV

volumespecificUpstreamV

constantgasUniversalR

pressureUpstreamP

pipeofareasectionalCrossa

flowMassG

where

f

:

2

1

1

I

The friction factor is calculated using an equation appropriate for the flowregime. These equations correlate the friction factor to the pipe diameter,Reynolds number and roughness of the pipe4:

Turbulent Flow (Re > 4000)

The friction factor may be calculated from either the Round equation:

-

5.6135.0log61.3

1e

fRe

Re

f I

9.3

roughnesspipeAbsolutee

diameterInternal

numberReynoldsRe


where

f

I

:

Or from the Chen21 equation:

-

8981.01098.1149.7

8257.2

/log

0452.5

7065.3

/log4

1

Re

e

Re

e

ff

II


3/32


9.4


diameterInternal

numberReynoldsRe


where

f

I

:

Transition Flow (2100 d Re d 4000)

-

Re

e

Re

e

Re

e

ff

0.13

7.3log

02.5

7.3log

02.5

7.3log0.4

1

III

9.5


diameterInternal

numberReynoldsRe


where

f

I

:

Laminar Flow (Re < 2100)

Reff

16

9.6

numberReynoldsRe


where

f

:

The Moody friction factor is related to the Fanning friction factor by:

fm ff x 4

9.7

factorfrictionMoodyf

factorfrictionFanningfwhere

m

f

:


4/32


2-Phase Pressure Drop

Although the Beggs and Brill method was not intended for use with verticalpipes, it is nevertheless commonly used for this purpose, and is therefore

included as an option for vertical pressure drop methods.

Beggs and Brill

The Beggs and Brill9 method is based on work done with an air-water mixtureat many different conditions, and is applicable for inclined flow. In the Beggs

and Brill correlation, the flow regime is determined using the Froude numberand inlet liquid content. The flow map used is based on horizontal flow and

has four regimes: segregated, intermittent, distributed and transition. Once

the flow regime has been determined, the liquid hold-up for a horizontal pipeis calculated, using the correlation applicable to that regime. A factor is

applied to this hold-up to account for pipe inclination. From the hold-up, atwo-phase friction factor is calculated and the pressure gradient determined.

Fig 9.1

The boundaries between regions are defined in terms of two constants and

the Froude number10:

32

10207.0481.0757.362.4exp xxxL

9.8

5322 000625.00179.0609.1602.4061.1exp xxxxL


5/32


9.9

flowratevolumetricsituInq

qqqcontentliquidInput

Inx

where

gasliquidliquid

:

According to Beggs and Brill:

1 If the Froude number is less than L1, the flow pattern is segregated.

2 If the Froude number is greater than both L1 and L2, the flow pattern isdistributed.

3 If the Froude number is greater than L1 and smaller than L2 the flowpattern is intermittent.

Dukler Method

The Dukler10 method breaks the pressure drop into three components -

Friction, Elevation and Acceleration. The total pressure drop is the sum of thepressure drop due to these components:

AEFTotal PPPP ''''

9.10

onacceleratitoduepressureinChangeP

elevationtoduepressureinChangeP

frictiontoduepressureinChangeP

pressureinchangeTotalP

where

A

E

F

Total

'

'

'

'

:

The pressure drop due to friction is:

Dg

VLfP

c

mmTPF

144

2

'

9.11

)(

)/2.32(g

)/(

)(

)(

:

2

3

ftpipeofdiameterInsideD

slbfftlbmconstantnalGravitatio

ftlbmixturephasetwoofDensity

sftvelocity

equalassumingpipelineinmixturephasetwotheofVelocityV

ftpipelinetheoflengthEquivalentL

yempiricalldeterminedfactorfrictionphaseTwof

where

c

m

m

TP


6/32


The pressure drop due to elevation is as follows:

144

'

HEP

Lh

E

9.12

changeselevationofSumH

densityLiquid

yempiricalldeterminedfactorheadLiquidE

where

L

h

)(

:

The pressure drop due to acceleration is usually very small in oil/gasdistribution systems, but becomes significant in flare systems:

' FRV

1

1

144

1 2222

2

USL

LPLL

L

GPLg

DSL

LPLL

L

GPLg

c

AR

Q

R

Q

R

Q

R

Q

AgP

9.13

bendpipetheofAngle

capacitypipelineofpercentageaaspipelineinholdupLiquidR

hrftpressureandetemperaturpipelineatflowingliquidofVolumeQ

hrftpressureandetemperaturpipelineatflowinggasofVolumeQ

densityGas

areasectionalCrossA

where

L

LPL

GPL

g

)/(

)/(

:

3

3

Orkiszewski Method

The Orkiszewski11,12 method assumes there are four different flow regimes

existing in vertical two-phase flow - bubble, slug, annular-slug transition and

annular-mist.

The bubble flow regime consists mainly of liquid with a small amount of afree-gas phase. The gas phase consists of small, randomly distributed gas

bubbles with varying diameters. The gas phase has little effect on thepressure gradient (with the exception of its density).

In the slug flow regime, the gas phase is most pronounced. The gas bubblescoalesce and form stable bubbles of approximately the same size and shape.The gas bubbles are separated by slugs of a continuous liquid phase. There isa film of liquid around the gas bubbles. The gas bubbles move faster than the

liquid phase. At high flow velocities, the liquid can become entrained in the

gas bubbles. The gas and liquid phases may have significant effects on thepressure gradient.

Transition flow is the regime where the change from a continuous liquid phase

to a continuous gas phase occurs. In this regime, the gas phase becomes


7/32


more dominant, with a significant amount of liquid becoming entrained in the

gas phase. The liquid slug between the gas bubbles virtually disappears in the

transition regime.

In the annular-mist regime, the gas phase is continuous and is the controlling

phase. The bulk of the liquid is entrained and carried in the gas phase.

Orkiszewski defined bubble flow, slug flow, mist flow and gas velocitynumbers which are used to determine the appropriate flow regime.

If the ratio of superficial gas velocity to the non-slip velocity is less than thebubble flow number, then bubble flow exists, for which the pressure drop is:

Dg

R

V

fPc

L

sL

Ltp2

2

'

9.14

)(

)/2.32(

)/(

)/(

:

2

3

2

ftdiameterHydraulicD

slbfftlbmconstantnalGravitatiog

velocityslipnonondependentfactoressDimensionlR

sftvelocityliquidlSuperficiaV

ftlbdensityLiquid

factorfrictionphaseTwof

lengthoffootperftlbdropPressureP

where

c

L

sL

L

tp

'

If the ratio of superficial gas velocity to the non-slip velocity is greater thanthe bubble flow number, and the gas velocity number is smaller than the slug

flow number, then slug flow exists. The pressure drop in this case is:

*

'

rns

rsL

c

nsLtp

VV

VV

Dg

VfP

2

2

9.15

ConstantvelocityriseBubbleV

velocityslipNonV

where

r

ns

*

:

The pressure drop calculation for mist flow is as follows:

Dg

VfP

c

sg

gtp2

2

'


8/32


9.16

)/(

:

3ftlbdensityGas

sftvelocitygaslSuperficiaV

where

g

sg

The pressure drop for transition flow is:

ms PxPP ''' 1

9.17

numbersvelocitygasandflowslugflowmistondependentfactorWeightingx

flowmixedfordropPressurePm

flowslugfordropPressurePs

where

,,,

:

'

'

The pressure drop calculated by the previous equations, are for a one-footlength of pipe. These are converted to total pressure drop by:

''

246371144

p

ftotal

total

PA

GQ

PLP

9.18

)(

)(

)(

)(

)/(

)/(/

:

2

3

3

ftsegmentlineofLengthL

abovecalculatedasdroppressureUnitP

psiasegmentinpressureAveragep

ftpipeofareasectionalCrossA

sftrateflowGasG

slbgasliquidcombinedofrateMassQ

ftlbregimeflowingtheofDensity

where

p

f

total

'


9/32


Fittings Pressure Change MethodsThe correlations used for the calculation of the pressure change across a

fitting are expressed using either the change in static pressure or the change

in total pressure. Static pressure and total pressure are related by therelationship:

2

2vPP st

9.19

In this equation and all subsequent equations, the subscript t refers to totalpressure and the subscript s refers to the static pressure.

Enlargers/Contractions

The pressure change across an enlargement or contraction may be calculatedusing either incompressible or compressible methods. For two phase systems

a correction factor that takes into account the effect of slip between thephases may be applied.

Figure A.2 and A.3 define the configurations for enlargements andcontractions. In these figures the subscript 1 always refers to the fitting inlet

and subscript 2 always refers to the fitting outlet.

Fig 9.2

Fig 9.3


10/32


Fitting Friction Loss Coefficient

The friction loss coefficients for Enlargements & Contractions are given by:

Sudden and Gradual Enlargement

For an enlarger, both Crane & HTFS methods use the same the fittings losscoefficients which are defined by Crane26. These methods are based on the

UDWLRRIVPDOOHUGLDPHWHUWRODUJHUGLDPHWHU

IfT < 45q

221 2

sin6.2

K

9.20

Otherwise

22

1 K

9.21

2

1

GLDPHWHUODUJHURGLDPHWHUWVPDOOHURIUDWLRWKHLVZKHUH

d

d

Sudden and Gradual Contraction

For a contraction the fittings loss coefficient in Crane & HTFS methods arecalculated differently for abrupt sudden contractions. Otherwise the

coefficients are same for Crane & HTFS methods. These calculation methodsare as described below:

Crane

The fitting loss coefficient is calculated as per HTFS27. These methods are

EDVHGRQWKHUDWLRRIVPDOOHUGLDPHWHUWRODUJHUGLDPHWHU

21

ctCKK

9.22

57806.00.39543

0.5

1.52.52

tK

9.23

2

1

2

d

d

where:


11/32


The contraction coefficient, is defined by

25.079028.4 leCc

9.24

o

:

where

HTFS

The fittings loss coefficients are defined by HTFS27. These methods are same

as the previous Crane method (Equations A.22 A.24) except for sudden

contractions where the contraction coefficient is calculated differently.

If = 180 q (Abrupt contraction)

1

cC

9.25

Incompressible Single Phase Flow

The total pressure change across the fitting is given by:

2

2111

vKPt '

9.26

Velocityv

densityMass

tcoefficienlossFittingsK

changepressureTotalp

where

'

:

1

Incompressible Two Phase Flow


The static pressure change across the fitting is given by HTFS27

2

2

121

11

LO

l

s

mK

P I

'

9.27

g

g

g

l

g

g

LO

xx

1

22

2

I


12/32


9.28


fractionmassPhasexfractionvoidPhase

densitymassPhase

fluxMassm

where

1

:



2222

LO

l

ts

mKP I

'

9.29

222 1 gLLO xII

9.30

2

2 11XX

CL I

9.31

5.0

l

g

g

g

x

x

X

9.32

5.05.0

l

g

g

lC

9.33


fractionmassPhasex

fractionvoidPhase

densitymassPhase

fluxMassm

where

1

:


13/32


Compressible Single Phase Flow



'

1

2

1

1

2

1m

Ps

9.34

densitymassPhase

fluxMassm

where

:


The static pressure change across the fitting is calculated using the two-phase

method given in Compressible Two Phase Flow below. The single-phase

properties are used in place of the two-phase properties.

Compressible Two Phase Flow



'

12

2

1

E

Es v

vmP

9.35

bygivenvolumespecificEquivalentv

where

E

:

-

1

11

11

5.0

2

l

g

R

R

g

glgRggE

v

v

u

u

xxvxuvxv

9.36

5.0

l

HR

v

vu

9.37

lgggH vxvxv 1


14/32


9.38

fractionmassPhasex

densitymassPhase

fluxMassm

where

:


The pressure loss comprises two components. These are the contraction ofthe fluid as is passed from the inlet to the vena contracta plus the expansion

of the fluid as it passes from the vena contracta to the outlet. In the followingequations the subscript t refers to the condition at the vena contracta.

For the flow from the inlet to the vena conracta, the pressure change ismodeled in accordance with HTFS27 by:

-

2

2

11

1

2

1

11

11

2

cE

EtE

E

E

Cv

v

P

vmd

v

v

9.39

1

P

P

9.40

For the flow from the vena contracta to the outlet the pressure change is

modeled used the methods for Sudden and Gradual Expansion given above.

Tees

Tees can be modeled either by using a flow independent loss coefficient foreach flow path or by using variable loss coefficients that are a function of the

volumetric flow and area for each flow path as well as the branch angle. Thefollowing numbering scheme is used to reference the flow paths.

Fig 9.4

Constant Loss Coefficients

The following static pressure loss coefficients values are suggested by the

API23:


15/32


13K 23K 12K 31K 32K 21K


16/32


9.42

2

2

2

2

23

3

2

332

2

22

23v

Pv

Pv

K

9.43

Dividing Flow

2

2

2

2

23

1

2

113

2

33

31v

Pv

Pv

K

9.44

2

2

2

2

23

2

2

223

2

33

32v

Pv

Pv

K

9.45

Miller Method

A typical Miller chart for 23K in combining flow is shown.

Fig 9.5

Gardel Method


17/32


These coefficients can also be calculated analytically from the Gardel28

Equations given below:

x Combining flow:

rr

rr

qq

qqK

12

cos1

118.01

cos2.1192.0

2

2

2

13

MM

TM

MM

GU

rr

rr

qq

qqK

12

138.01cos

62.11103.022

23

M

MM

TU

9.46

x Dividing Flow

rr

rr

qq

qqK

12

tan1

14.0

9.011.04.03.02

tan3.1195.02

2

2

31

TM

MU

MMT

rrrr qqqqK 12.035.0103.0 2232

9.47

Where,

qr = Ratio of volumetric flow rate in branch to total volumetric flow rate

$UHDUDWLRRISLSHFRQQHFWHGZLWKWKHEUDQFKWRWKHSLSHFDUU\LQJWKH

total flow

5DWLRRIWKHILOOHWUDGLXVRIWKHEUDQFKWRWKHUDGLXVRIWKHSLSHFRQQHFWHGwith the branch

$QJOHEHWZHHQEUDQFKDQGPDLQIORZDVVKRZQLQ)LJ

Orifice Plates

Orifice plates can be modeled either as a sudden contraction from the inletpipe size to the orifice diameter followed by a sudden expansion from the

orifice diameter to the outlet pipe size or by using the HTFS equation for athin orifice plate.

1

2

12

4

2.825 0.08956 mPs

'

9.48

See Incompressible Single Phase Flow on Page 263 for a definition of the

symbols.


18/32


Vertical Separators

The Pressure change across the separator comprises the following

components:

Expansion of the multiphase inlet from the inlet diameter, d1, to the bodydiameter dbody.

Contraction of vapor phase outlet from the body diameter, d body, to the outletdiameter, d2

Friction losses are ignored.

Fig 9.6

Horizontal Separators

The Pressure change across the separator comprises the following

components calculated using the methods described in Incompressible SinglePhase Flow on Page 263:

Expansion of the multiphase inlet from the inlet diameter, d1, to the vapor

space characterized by equivalent diameter of the vapor area.

Contraction of vapor phase outlet from the vapor space characterized by the

equivalent diameter of the vapor area, to the outlet diameter, d2

Friction losses are ignored.

Fig 9.7


19/32


Vapor-Liquid Equilibrium

Compressible GasThe PVT relationship is expressed as:

ZRTPV

9.49

eTemperaturTconstantGasR

factorilityCompressibZ

VolumeV

PressureP

where

:

The compressibility factor Z is a function of reduced temperature and

pressure. The overall critical temperature and pressure are determined usingapplicable mixing rules.

Vapor PressureThe following equations are used for estimating the vapor pressure, given the

component critical properties3:

1

*0

** ,Q,Q,Q rrr ppp

9.50

60* 169347.0In28862.109648.692714.5In rrr

r TTT

p


20/32


9.51

61* 43577.0In4721.136875.162518.15In rrr

r TTT

p

9.52

)(

)(

)/(

)(

)(

)/(

:

*

**

RetemperaturCriticalT

ReTemperaturT

TTetemperaturReducedT

factorAcentric

abspsipressureCriticalp

abspsipressureVapourp

pppressurevapourReducedp

where

o

c

o

cr

c

cr

This equation is restricted to reduced temperatures greater than 0.30, and

should not be used below the freezing point. Its use was intended forhydrocarbons, but it generally works well with water.

Soave Redlich KwongIt was noted by Wilson (1965, 1966) that the main drawback of the Redlich-

Kwong equation of state was its inability of accurately reproducing the vaporpressures of pure component constituents of a given mixture. He proposed a

modification to the RK equation of state using the acentricity as a correlating

parameter, but this approach was widely ignored until 1972, when Soave(1972) proposed a modification of the SRK equation of this form:

bVVTTa

bV

RTP c

9.53

The a term was fitted in such a way as to reproduce the vapor pressure ofhydrocarbons using the acentric factor as a correlating parameter. This led to

the following development:

bVV

a

bV

RTP c

9.54

RK22

assametheP

TRa a

c

cac ::


21/32


9.55

5.0 rTS

9.56

2 S

9.57

The reduced form is:

2599.0

2559.0

3

rrr

rr

VVV

TP

9.58

The SRK equation of state can represent with good accuracy the behavior of

hydrocarbon systems for separation operations, and since it is readilyconverted into computer code, its usage has been extensive in the last twenty

years. Other derived thermodynamic properties, like enthalpies and entropies,are reasonably accurate for engineering work, and the SRK equation enjoys

wide acceptance in the engineering community today.

Peng RobinsonPeng and Robinson (1976) noted that although the SRK was an improvementover the RK equation for VLE calculations, the densities for the liquid phasewere still in considerable disagreement with experimental values due to a

universal critical compressibility factor of 0.3333, which was still too high.

They proposed a modification to the RK equation which reduced the criticalcompressibility to about 0.307, and which would also represent the VLE of

natural gas systems accurately. This improved equation is represented by:

bVbbVVa

bV

RTP c

9.59

c

cc

P

TRa

22

45724.0

9.60

c

c

P

RTb 07780.0

9.61

They used the same functional dependency for the Dterm as Soave:


22/32


5.0 rTS

9.62

2 S

9.63

0642.05068.0

2534.0

2573.32

rrr

rr

VVV

TP

9.64

The accuracy of the SRK and PR equations of state are roughly the same

(except for density calculations).

Physical Properties

Vapor DensityVapor density is calculated using the compressibility factor calculated fromthe Berthalot equation5. This equation correlates the compressibility factor to

the pseudo reduced pressure and pseudo reduced temperature.

-

2

0.60.10703.00.1

rr

r

TT

PZ

9.65

ZRT

PM

9.66

Liquid Density

Saturated liquid volumes are obtained using a corresponding states equation

developed by R. W. Hankinson and G. H. Thompson14

which explicitly relatesthe liquid volume of a pure component to its reduced temperature and asecond parameter termed the characteristic volume. This method has been

adopted as an API standard. The pure compound parameters needed in thecorresponding states liquid density (COSTALD) calculations are taken fromthe original tables published by Hankinson and Thompson, and the API data

book for components contained in Aspen Flare System Analyzer's library. The

parameters for hypothetical components are based on the API gravity and thegeneralized Lu equation. Although the COSTALD method was developed forsaturated liquid densities, it can be applied to sub-cooled liquid densities, i.e.,


23/32


at pressures greater than the vapor pressure, using the Chueh and Prausnitz

correction factor for compressed fluids. The COSTALD model was modified to

improve its accuracy to predict the density for all systems whose pseudo-reduced temperature is below 1.0. Above this temperature, the equation ofstate compressibility factor is used to calculate the liquid density.

Vapor ViscosityVapor viscosity is calculated from the Golubev3 method. These equations

correlate the vapor viscosity to molecular weight, temperature and thepseudo critical properties.

Tr > 1.0

167.0

)/29.071.0(667.05.0

0.10000

5.3

c

T

rc

T

TPM r

9.67

7U

167.0

)965.0(667.05.0

0.10000

5.3

c

rc

T

TPM

9.68

Liquid ViscosityAspen Flare System Analyzer will automatically select the model best suited

for predicting the phase viscosities of the system under study. The modelselected will be from one of the three available in Aspen Flare System

Analyzer: a modification of the NBS method (Ely and Hanley), Twu's model,and a modification of the Letsou-Stiel correlation. Aspen Flare SystemAnalyzer will select the appropriate model using the following criteria:

Chemical System Liquid Phase Methodology

Lt Hydrocarbons (NBP < 155 F) Mod Ely & Hanley

Hvy Hydrocarbons (NBP > 155 F) Twu

Non-Ideal Chemicals Mod Letsou-Stiel

All the models are based on corresponding states principles and have beenmodified for more reliable application. These models were selected since theywere found from internal validation to yield the most reliable results for the

chemical systems shown. Viscosity predictions for light hydrocarbon liquidphases and vapor phases were found to be handled more reliably by an in-house modification of the original Ely and Hanley model, heavier hydrocarbon

liquids were more effectively handled by Twu's model, and chemical systems

were more accurately handled by an in-house modification of the originalLetsou-Stiel model.


24/32


A complete description of the original corresponding states (NBS) model used

for viscosity predictions is presented by Ely and Hanley in their NBS

publication16. The original model has been modified to eliminate the iterativeprocedure for calculating the system shape factors. The generalized Leech-Leland shape factor models have been replaced by component specific

models. Aspen Flare System Analyzer constructs a PVT map for each

component and regresses the shape factor constants such that the PVT mapcan be reproduced using the reference fluid.

Note: The PVT map is constructed using the COSTALD for the liquid region.The shape factor constants for all the library components have already been

regressed and are stored with the pure component properties.

Pseudo component shape factor constants are regressed when the physicalproperties are supplied. Kinematic or dynamic viscosity versus temperature

curves may be supplied to replace Aspen Flare System Analyzer's internalpure component viscosity correlations. Aspen Flare System Analyzer uses theviscosity curves, whether supplied or internally calculated, with the physicalproperties to generate a PVT map and regress the shape factor constants.

Pure component data is not required, but if it is available it will increase theaccuracy of the calculation.

The general model employs methane as a reference fluid and is applicable to

the entire range of non-polar fluid mixtures in the hydrocarbon industry.Accuracy for highly aromatic or naphthenic oil will be increased by supplyingviscosity curves when available, since the pure component property

generators were developed for average crude oils. The model also handles

water and acid gases as well as quantum gases.

Although the modified NBS model handles these systems very well, the Twu

method was found to do a better job of predicting the viscosities of heavierhydrocarbon liquids. The Twu model18 is also based on corresponding states

principles, but has implemented a viscosity correlation for n-alkanes as its

reference fluid instead of methane. A complete description of this model isgiven in the paper18 titled "Internally Consistent Correlation for Predicting

Liquid Viscosities of Petroleum Fractions".

For chemical systems the modified NBS model of Ely and Hanley is used forpredicting vapor phase viscosities, whereas a modified form of the Letsou-Stiel model15 is used for predicting the liquid viscosities. This method is also

based on corresponding states principles and was found to perform

satisfactorily for the components tested.

The parameters supplied for all Aspen Flare System Analyzer pure library

components have been fit to match existing viscosity data over a broad

operating range. Although this will yield good viscosity predictions as an

average over the entire range, improved accuracy over a more narrowoperating range can be achieved by supplying viscosity curves for any given

component. This may be achieved either by modifying an existing librarycomponent through Aspen Flare System Analyzer's component librarian or byentering the desired component as a hypothetical and supplying its viscosity

curve.


25/32


Liquid Phase Mixing Rules for ViscosityThe estimates of the apparent liquid phase viscosity of immiscibleHydrocarbon Liquid - Aqueous mixtures are calculated using the following

"mixing rules":

If the volume fraction of the hydrocarbon phase is greater than or equal to

0.33, the following equation is used19:

oilvoileff e

16.3

9.69

phasenHydrocarbofractionVolumev

phasenHydrocarboofViscosity

viscosityApparent

where

oil

oil

eff

:

If the volume fraction of the hydrocarbon phase is less than 0.33, thefollowing equation is used20:

OH

OHoil

OHoil

oileff v 22

2

9.70

phasenHydrocarbofractionVolumev

phaseAqueousofViscosityphasenHydrocarboofViscosity

viscosityApparent

where

oil

OH

oil

eff

2

:

The remaining properties of the pseudo phase are calculated as follows:

)( weightmolecularmwxmw iieff

9.71

densitymixturepx iieff

9.72

)( heatspecificmistureCpxCp iieff


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9.73

Thermal ConductivityAs in viscosity predictions, a number of different models and component

specific correlations are implemented for prediction of liquid and vapor phasethermal conductivities. The text by Reid, Prausnitz and Polings 15 was used asa general guideline in determining which model was best suited for each class

of components. For hydrocarbon systems the corresponding states method

proposed by Ely and Hanley16 is generally used. The method requiresmolecular weight, acentric factor and ideal heat capacity for each component.

These parameters are tabulated for all library components and may either be

input or calculated for hypothetical components. It is recommended that all ofthese parameters be supplied for non-hydrocarbon hypotheticals to ensurereliable thermal conductivity coefficients and enthalpy departures.

The modifications to the method are identical to those for the viscositycalculations. Shape factors calculated in the viscosity routines are used

directly in the thermal conductivity equations. The accuracy of the methodwill depend on the consistency of the original PVT map.

The Sato-Reidel method15 is used for liquid phase thermal conductivitypredictions of glycols and acids, the Latini et al. Method15 is used for esters,

alcohols and light hydrocarbons in the range of C3 - C7, and the Missenard

and Reidel method15 is used for the remaining components.

For vapor phase thermal conductivity predictions, the Misic and Thodos, and

Chung et al. 15 methods are used. The effect of higher pressure on thermalconductivities is taken into account by the Chung et al. method.

As in viscosity, the thermal conductivity for two liquid phases is approximated

by using empirical mixing rules for generating a single pseudo liquid phaseproperty.

Enthalpy

Ideal Gas

The ideal gas enthalpy is calculated from the following equation:

432 TETDTCTBAH iiiiiideal

9.74

termscapacityheatgasIdealEDCBA

eTemperaturT

enthalpyIdealH

where

,,,,

:


27/32


Lee-Kesler

The Lee-Kesler enthalpy method corrects the ideal gas enthalpy fortemperature and pressure.

depideal HHH

9.75

-

s

c

depr

c

dep

r

s

c

dep

c

dep

RT

H

RT

H

RT

H

RT

H

9.76

-

E

VT

d

VT

T

cc

VT

T

b

T

bb

ZT

RT

H

rr

k

rr

r

kk

rr

t

k

r

kk

k

r

k

c

dep

3

52

332

0.15

2

2

2

322

432

9.77

-

2

23

4

r

k

V

r

kkk

k

r

k

eVT

cE

9.78

enthalpydeparturegasIdealH

termsKeslerLeedcb

enthalpyIdealH

fluidSimples

fluidReferencer

factorAcentric

enthalpySpecificH

etemperaturCriticalTwhere

dep

ideal

c

:

Equations of State

The Enthalpy and Entropy calculations are performed rigorously using the

following exact thermodynamic relations:

dVPT

PT

RTZ

RT

HHV

V

ID

f

w

w

11


28/32


9.79

dVVT

P

RP

PZ

R

SSV

V

o

ID

o f

w

w

11InIn

9.80For the Peng Robinson Equation of State, we have:

bV

bV

dt

daTa

bRTZ

RT

HH ID

12

12In

2

11

5.0

5.0

5.1

9.81

BZ

BZ

adT

Tda

B

A

P

PBZ

R

SSo

ID

o

12

12In

2InIn

5.0

5.0

5.1

9.82

ijjiN

i

N

j

ji kaaxxa

where

1

:

5.0

1 1

9.83

For the SRK Equation of State:

V

b

dt

da

TabRTZRT

HH ID

1In

1

1

9.84

Z

B

adT

Tda

B

A

P

PBZ

R

SSo

ID

o 1InInIn

9.85

A and B term definitions are provided below:

Term Peng-Robinson Soave-Redlich-Kwong

ib

ci

ci

P

RT077796.0

ci

ci

P

RT08664.0

ia icia icia


29/32


Term Peng-Robinson Soave-Redlich-Kwong

cia

ci

ci

P

RT2

457235.0

ci

ci

P

RT2

42748.0

i 5.011

riiTm

5.011

riiTm

im2 ii

2 ii

ijjiN

i

N

j

ji kaaxxa

where

1

:

5.0

1 1

9.86

N

i

iibxb

and

1

9.87

EntropyS

EnthalpyH

constantgasIdealR

stateReference

gasIdealID

o


30/32


NoiseThe sound pressure level at a given distance from the pipe is calculated from

the following equations. In these equations the noise producing mechanism isassumed to be solely due to the pressure drop due to friction.

'

4

36.1

2I

L

PWm v

9.88

tr

LWSPL mr

2

13

log10

9.89

velocityfluidAveragev

lossontransmissiwallPipet

pressureinChangeP

efficiencyAcoustic

diameterInternal

pipefromDistancer

levelpressureSoundSPL

lengthEquivalentL

where

'

:

I


31/32


Fig 9.8

The transmission loss due to the pipe wall is calculated from:

0.365.0

0.17

I

mvt

9.90

velocityfluidAveragev

diameterInternal

areaunitpermasswallPipem

where

I

:

The acoustical efficiency is calculated from the equation below.

5388.9ln*9986.4exp MPrK

9.91

where

Pr = Ratio of higher absolute Pr over lower absolute Pr between two ends ofthe pipe (i.e. if upstream pr.> downstream pr., Pr = upstream

pr./downstream pr. Else if upstream pr.< downstream pr., Pr = downstream

pr./upstream pr.)

M = Mach No.

0 .0 0.2 0 .4 0 .6 0. 8 1.0

Mach Num ber

10- 11

10- 10

10- 9

10- 8

10- 7

10- 6

1 0-5

10- 4

10- 3

AcousticalEfficiency

pt = 1 0.0

p t = 1.0

p t = 0. 1


32/32

Documents

Vapor Phase Pressure Drop Methods