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MATHEMATICAL MODELLING OF WAX DEPOSITION INCRUDE OIL PIPELINES (COMPARATIVE STUDY)M.V. Kok

a& R.O. Saracoglu

a

aDepartment of Petroleum and Natural Gas Engineering , Middle East Technical University

Ankara, 06531, Turkey

Published online: 27 Apr 2007.

To cite this article:M.V. Kok & R.O. Saracoglu (2000) MATHEMATICAL MODELLING OF WAX DEPOSITION IN CRUDE OIL PIPELIN(COMPARATIVE STUDY), Petroleum Science and Technology, 18:9-10, 1121-1145, DOI: 10.1080/10916460008949895

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PETROLEUM SCIENCE AND TECHNOLOGY, 18 9 10), 1121-1145 2000)

M THEM TI L MODELLING OF WAX DEPOSITION IN CRUDE

OIL

PIPELINES OMPARATIVE STUDY)

M.V.Kok and R.O.Saracogiu

Department

Petroleum and Natural Gas Engineering Middle East Technical

University 653

Ankara Turkey

ABSTRACT

In this research, wax deposit ion in different crude oil pipel ine systems was studied.

In oil pipel ines, the main mechanism for wax appearance is the temperature change

along the pipeline. A computer program was developed to simulate the wax

precipitation phenomena. Temperature profile along the pipeline was determined and

sol id l iquid equil ibrium constant, wax mole fraction and wax th ickness along the

pipel ine were calculated. This computer program was applied to different crude oil

pipeline systems in Iraq Baiji-Daura, Rumaila-Zubair-Fao and Haditha-Rumailia).

In Haditha-Rumaila crude oil pipel ine system, it

was observed that wax thickness

after a year is approximately 0.1 mm and temperature declined from 303 K to around

300.5 K. The wax mole fraction after a year is approximately 0.2. The solid- liqu id

equil ibrium constant for the first component around 0.228 and around 165 for the

second component af te r a year. Similar results were obse rved in other c rude oil

pipeline systems studied.

Keywords: crude oil pipel ine , wax thickness, temperature prof ile , sol id-l iqu id

equilibrium constant, wax mole fraction

INTRODUCTION

Many crude oils throughout the world contain significant quantit ies of wax

which will readily crystallise during the production, transportation and storage of the

1121

opyrightce2 by Marcel Dekker Inc

www.dekker.com

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1122

KOK AND S R OGLU

oil. This results in an increase in viscosity by several orders

of

magnitude, oil

gelation the formation of a yield stress and deposition on pipeline walls

Ward/wI/gil

and

Boger 1991 . Depos it ion of wax on the wall of p ipel ines is often

regarded as a problem since the tube diameter is reduced. Consequently, more power

is needed to force the same amount

of

oil through the system

Svendsen

1993 . The

wax precipitated from oil mixtures primarily consists of CIS to C

l 6

paraffin waxes

or C

l O

to C

60

microcrystall ine waxes , both made up of aligned paraffinic and

naphthenic molecules, paraffin waxes are also called microcrystalline

amoudaand

Davidsen 1995 . Waxes are multitude of higher-molecular-weight paraffinic

components Ihat are minutely soluble in the liquid phase of black oils and

condensates. As the fluid cools,

each

wax component becomes less soluble until the

higher-molecular- weight components solidify. This onset of crystallisation is known

as the cloud-point , or wax-appearance, temperature. As the fluid continues to cool,

lower-molecular-weight species also sol idi fy, adding to the solid fraction. Wax

crystallisation is controlled by temperature but is also dependent on fluid

compos ition , especia lly the light ends. To avoid waxing, thermal techniques are

applied by keeping the flowing-fluid temperature higher than the wax-appearance

temperature. Provided the pipeline is not totally blocked, hot fluids to melt the

deposit arc widely used. Waxes are multitude of higher-molecular-weight paraffinic

components that are minutely soluble in the liquid phase of black oils and

condensates. As the fluid cools , each wax component becomes less soluble until the

higher-molecular- weight components solidify. This onset of crystallization is known

as the cloud-point , or wax-appearance, temperature. As the fluid continues to cool,

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WAXDEPOSITION INCRUDE OIL PIPELINES

3

lower-molecula r-weight species also solidify, adding to the sol id fraction . Wax

crystallisation is controlled by temperature but is also dependent on fluid

composi tion , especially the light ends. Solid waxes , when present in sufficient

quantities, can significantly affect oil viscosity. hey especially act as dispersion,

causing non-Newtonian, shear-thinning behaviour. If sufficient waxes are present in

the solid phase in static or very-low-flow conditions, they can interact to form a

matrix that entraps the liquid phase and effectively gels the fluid. The temperature at

which this occurs is known as the pour point.

Wardaug and oger

1991 defined waxy rude a rheologically complex

material whose flow proper ties are determined by the shear and thermal history

imparted to the oil. They concluded that the equil ibrium flow proper ties depend

s trongly on the shear history with very low shear his tories resulting in the highest

shear stresses. This results in a minimum operating condition below which flow in a

pipel ine would cease. This is of particular concern in the operation of declining oil

fields and poin ts to the need to design a waxy crude oil pipeline, not only for the

maximum flow but also for the minimum anticipated flow. In the rheological sense,

flow improver additives act to reduce the effect of the shear history and to reduce the

minimum operating condition to lower shear stresses pressure drops and shear rates

flow rates .

Svendsen

1993 developed a mathematical model for prediction

of

wax

deposition in both open and closed pipeline systems by using a combination

of

analytical and numerical models. The model includes several scientific disciplines

such as phase equilibr ium, phase transition and fluid dynamics. In any case the

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4

KOK AND SARACOGLU

model predicts that wax deposition can be cons ide rably reduced when the wall

temperature is below wax appearance point, provided the liquid/solid phase transition

expressed by the change in moles of liquid with temperature. If, in addition, the

coefficient of thermal expansion is sufficiently large, some components may separate

and move in opposite radial directions at temperatures below WAP.

Hamouda and Davidsen 1995 performed experiments, which was designed

to simula te the now characteris tics at pipel ine .pressure. They developed three-

dimensional model for paraffin deposition rates at various flow regimes. They

concluded that the paraffin deposit ion by molecular d if fusion mechanism is the

dominant one and also the paraffin concentration gradient is the driving force of the

molecular diffusion mechanism but on the other hand shear dispersion mechanism

becomes more pronounced as the temperature gradients decreases. They also

observed wax depos ition rate with the flow rate might be explained by the increase

of the temperature gradient until the point where the sh r stress on the wall becomes

large enough to affect the adhesion of the wax crystal onto the pipe wall.

urger Perkins and Striegler

1981 studied to investigate mechanisms of

wax deposition and to determine the expected nature and thickness of deposits in the

Trans Alaska Pipeline System TAPS as a function of time and distance. Deposition

is bel ieved to occur as a resul t of lateral t ransport by diffusion, shear dispersion and

Brownian diffusion. They identified three mechanism accounting for lateral transport

molecular diffusion, sh r dispersion and Brownian diffusion. Molecular diffusion

dominates at the higher temperature and heat flux conditions, whereas shea r

dispersion is the dominant mechanism

at

the lower temperatures and low heat fluxes.

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WAX DEPOSITION

RU E OIL PIPELINES 1125

The contribution of Brownian diffusion is small compared with the other

mechanisms. The size distribution of the precipi tated waxy particles increases

linearly with decreasing temperature. Gravity settling of particles as a mechanism

for wax deposition is negligible under flow conditions due probably to the

redispersal of the particles by shear dispersion.

Hsu and rubaker 1995 developed a wax deposit ion scale-up model

including the molecular diffusion effect and shear effect to scale-up laboratory wax

deposition results for waxy crude production lines. The wax deposition model allows

users to predict wax deposition profile along a cold pipeline and predict potential

wax problems and pigging frequency. They concluded that the flow turbulence effect

has significant impact on wax deposition and can not be neglected in wax deposition

modelling. Also shear rate, shear stress, and Reynolds number can not be used as a

scaler. Critical wax tension is verified as a reasonable scaler. They also concluded

that many wax deposition models only apply a molecular diffusion mechanism in

modelling and neglect shear effect. However, the flow turbulence effect has

significant impact on wax deposition and can not be neglected in wax deposi tion

modelling.

Hsu Santamaria and rubaker

1994 developed a new method to measure

wax deposi tion of waxy live crude oils under turbulent flow conditions without

knowing oil properties or disassembling the system for wax deposition measurement.

Under turbulent flow conditions the pseudo-plastic non-Newtonian behaviour of cold

waxy crude significant ly affects wax deposition rate. They concluded that wax

deposition from waxy crude could be reduced significantly under turbulent flow

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1126

KOKANDSARACOGLU

conditions.

he

flow turbulence depresses the temperature at which maximum wax

deposit ion rate occurs. Also the s loughing effect generated under turbulent flow

conditions has significant impact on wax deposit ion rate and can not be neglected in

wax deposition modelling. As another observation, oil composition is factor affecting

wax deposit ion. Usually, wax deposit ion rate decreases with increasing oil bubble

point pressure under turbulent flow conditions. However, at specific flow conditions

for waxy live oil with a specific oil bubble point p ressure may have the same wax

deposit ion rate as its stock tank oil. They also concluded that the wax hardness and

carbon number of the wax deposited on the pipe wall increase with retention time.

Wardallgh and oger 1991 concluded that the yielding behaviour of waxy

crude oil is accomplished by three distinct characteristics as elast ic response, slow

deformation, leading to a breakdown of structure fracture-like and fracture-like

behaviour resembling the fracture solids.

Weingarten and uchner 1986 developed experiments to measure wax

crystallisation conditions and deposition rates. They concluded that, wax solubility

can be expressed in accordance with ideal-so lu tion theory for paraffinic waxes in

paraffin-based oils. Also, sloughing of deposits occurs when the

she r

rate is high

enough that the shear stress at the wall exceeds the strength of the wax deposit. he

onset of sloughing is not related to a transition from laminar to turbulent flow.

Mendell and Jessen 1972 used chemica l addit ives to present paraffin

deposit ion exhibited varying degrees of effectiveness, depending on the crude oil

being treated. he degree of crystal modificat ion caused by an addit ive is reflected

by the cold flow test. A change in the cold flow curve was accompanied by a change

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WAX DEPOSITION RU E OIL PIPELINES

1127

in the paraffin deposition curve. The extent to which each fractional part of the

paraffin content of the crude oil is affected by the changes observed in the molecular

weight distribution compared with that of the saturated fraction of the crude oil.

Pan Firoozabadi and FOlland 1997 studied the effects of pressure and

composition on wax precipitation. They observed the cloud point temperatures at

live-oil conditions and the amount of precipitated wax at stock-tank-oil conditions.

The model showed that, normal paraffins readily precipitated, followed by

naphthenes and iso-paraffins, while aromatics stayed in the liquid phase. The cloud

point tempera ture was strongly influenced by heavy normal paraffins while the

amount of the precipitated wax depends on the concentration

of

n-paraffins as well as

isoparaffins and naphthenes.

According to Hamouda

n

Viken 1996 , wax deposit ion occurred by

molecular diffusion, shear dispersion and gravi tational set tl ing, but molecular

diffusion seemed to be dominant mechanism. They observed the wax appearance

point, and found a linear relationship between wax component and temperature.

Lira Galeana Firoozabadi and Prausnitz.

973 developed a

thermodynamic framework for calculating wax precipitation in petroleum mixtures

over a wide temperature range. The framework used the experimentally supported

assumption that precipitated wax consisted of several phases; each solid phase was

described as a pure component or pseudo-component that did not mix with o ther

solid phases.

T ORY

Deposition of solid material on pipe walls is frequently observed in fluid flow

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8

KOK AND SARACOGLU

systems.

It

is very important to estimate the wax deposition criteria during

production and transportation. he main mechanisms by which the wax deposition

occur in pipelines are molecular diffusion, shear dispersion and rownian diffusion.

he gravity se ttli ng mechan ism has a ls o been identif ied; however. molecular

diffusion is the predominant mechanism. Certain conditions must be fulfilled if wax

deposition shall occur. he best known is:

-Measurable wax deposition will occur only if the wall temperature is bel ow the

prccipitation temperature of the particular oil WAP .

-A negat ive radial temperature gradient must be present in the flow. A zero gradient

implies that approximately no deposition will occur.

-Wall friction must be so large that wax crystals can stick to the wall.

Molecular Diffusion

For all flow condi tions, oil will be in laminar flow either throughout the pipe

or at least in a thin laminar sub-layer adjacent to the pipe wall. When the oil is being

cooled, there will be a temperature gradient across the laminar sub-layer. If

temperatures are below that level where solid waxy crystals can be precipitated, then

the flowing elements

of

oil will contain precipitated solid particles and the l iquid

phase will be in equil ibrium with the sol id phase, ie., the l iquid will be saturated with

dissolved particles as the temperature decreases . he temperature profi le near the

wall, t herefo re, will lead to a concent ra tion gradien t

of

d is so lved wax, and this

dissolved material will be transported toward the wall by molecular diffusion. When

this diffusing material reaches the solid/liquid interface, it will be precipitated out of

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WAX DEPOSITION IN CRUDE OIL PIPELINES

9

sol ution. T he mass flux of dissolved wax mol ec ul es c ont rol le d by mo le cul ar

diffusion only is defined as Svendsen, 1993);

dW

d

_

D de dT

t

w

m dT dr

From the above equation, the wax deposition rate reaches its m axim um value just

below the cloud point

Hammouda and Davidsen,

1995

Brownian Diffusion Mechanism

Small, solid waxy crystals, when suspended in oil, will be bombarded

continually by thermally agitated oil molecules. These collisions will lead small

random Brownian movements of the suspended particles. If there is a concentration

gradient of these particles, Brownian motion will lead to a net transport, which,

nature and mathematical description, is similar

to

diffusion. The Brownian diffusion

coefficient for spherical, non-interacting particles is given by

Burger et al,

1981 ;

and a dispersing of particles. Wax deposition by shear dispersion can be described by

Burger et ai, 1981; Weillgarlell

nd

Euchner, 1986);

d

s

=

k yA

dt

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1130

Gravity SeWing Mechanism

KOK AND SARACOGLU

Precipi ta ted waxy crystals are denser than the surrounding liquid oil phase.

Hence, if panicles were non-interacting, they would settle in a gravity field and could

be deposited on the bol tom of pipes or tanks. For an initially uni form mixture in a

vessel, there would be an initial rate of se tt ling followed by a diminishing rate of

deposition, which asymptotically would approach zero at complete settling.

Overall Deposition Mechanism

Total deposition in pipelines can be described by combin ing molecular

diffusion and shear dispersion by

urger

et al

1981 ;

IV = AD dCdT k C i4

I P dT

dr

...

p

=

a

T

-

T

)+

P

a

where;

a.;

P a

a

... and P a must be determined exper imental ly for each oil, and

where T is a reference temperature.

Freezing Temperature and Heat of Fusion

V 1986 used a correlation between freezing temperature

of

component i

i and molecular weight of the component i M as;

TJi

= 74 5 + O 02617M

i

_

~

I

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1132

II

=

L O

i

=

L

aj-E, = a-E

=

i l

Determination of Wax Weight Fraction as Function of z

KOK N SARACOGLU

The weight fraction 11 ;asIuuction of d is ta nc e from inlet, z can be d et ermi ne d

from a mass b ala nce on a pipe s eg me nt b et wee n z and z+Llz, whe re z is an a rb it ra ry

position in the pipe. The mass now rate of each component i in the p os it io n z at time

r is

P,(z,l)q

where

q

is the

volumetric

oil now rate, a ss um ed to be a pp ro xi ma te ly

constant. The mass balance for component i over Llz is Svendsen, 1993 ;

Pi z+ t:lz,t)q

-

Pi (z,t}/

=-2nR iit:lz

whe re , Rw and ji are both fun ct io ns of z and t. After d iv is io n with

LIz

and taking the

limit Llz approaches to zero Svendsen, /993 ;

dP

i

=

-2nR ,J;

dZ

q

The weight fraction of wax in position

z+Llz

then yields

Svendsen, 1993 ;

)

2nR ,J; .z

)

Pi Z,I -

p. z+ .Z,t

lV.(Z+ .Zt)= = q

,

m (z+ .z,t) 27fR

w

j

p

.z

Z,I -

LJ

p q

The overall weight fraction

of

wax in p os it io n z at time I is Svendsen, 1993 ;

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WAX DEPOSITION N CRUDE OIL PIPELINES

w, z,r)=

t

W i Z,t)=

t

Wi

Z,t)V i z.t)

i j l

Temperature Distribution

1133

The oil flow temperature distribution T r,Z) depends on the velocity profile I , r).

In the fol lowing it is assumed that the sys tem is operat ing

at

approximately steady-

state thermal conditions.

Solut ion for Small Values of z

A practical solut ion for T r,z when z is small. The solut ion is valid if the

Graetz

number

GZ=Pmaqc kL

is large, that is, if heat convection is much larger than

heal conduction and yields Svendsen, 1993 ;

T

T r , z =T

0 Jexp -I J II

o

r 4 /3)

R r

I

_

_ _

V9{3z

= a

o

u m l ~

The temperature gradient in position r.z) is then:

T

To

J

-r -(4-/- -3) V9 { zexp -I ,

z

0

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1134

KOK AND SARACOGLU

Mole Fraction Determination

Accoun ting for the total composition effect on mole fractions, McCain

1973 proposed a model for liquid and gas mixtures, converted for solid and liquid

mixtures.

Xi

=

=

I

1 ll

s

i

I

i

=

- - - - - - - : - - -

=

1

L

-

1

I

II

- I

i

,

RESULTS AND DISCUSSION

Paraffin deposit ion mostly results from cooling and precipi ta tion high

molecular weight hydrocarbons during the movement

particles. Precipitation is an

example fluid/solid phase equilibrium. In pipeline systems, because

precipitated

particles, pipeline diameter reduces, and more power is needed to transport the same

amount of oil through the system. When oil cools below the cloud point/wax

appearance point WAP , a concentration gradient leads to transport by molecular

diffusion with subsequent precipitation and deposition occurs at the wall. The aim

this study is to determine the expected nature and thickness of deposits in the

pipeline as a function time and distance in oil pipelines. Wax deposition is usually

a slow process, and total blockages are rare. However, small reductions in diameter

and, more significantly, an increase in the pipe-wall roughness have a dramatic effect

on flow-line.

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WAX DEPOSITION IN CRUDE OIL PIPELINES

Table-I

Input Data for Computer Simulation

A Pa.s)

1.056.10 /

To

K)

303

B K)

3429,5

T, K)

278

am

kg/nr . K) -0.65

T, K)

293

Pm kg/m )

855

k W/m.K)

0.134

a

w

k g/m .K) -0.5 p J/kg.K) 1920

pw, kg/nr )

885 Tn K)

272

M, kg/kmol)

215

TrdK)

341

M

2

kg/kmol) 530

L .Hn

kJ/mol)

34.9

w, paraffin wax) 0.85

I

kJ/mol)

107.8

W2 microcrystalline wax) 0.15

1135

In the course of this research, Baiji-Daura, Rumaila-Zubair-Fao and Haditha-

Rumailia crude oil pipeline systems have been simulated on

computer

with constant

wall temperature as a boundary condition for the temperature distribution Table-t).

Crude Oil Pipeline Systems

Iraq decided in the 1970 s to build a pipeline between its northern and

s ou th ern oil fields, ess en ti al ly to enabl e oil p ro du ced in the north of the cou nt ry to be

exported from the Gulf. The pipeline was completed in 1975, the pipeline comprises

two s ecti on s, one 655 km. long l in ki ng H ad it ha to R um ai la and ano th er 105 km. long

connecting Rumaila to Fao. Storage facilities at Fao are linked by submarine

pip el ine s to the deep sea t er mi na ls of Mina a l- Ba kr and Kohr al- Arnaya , In 1988

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1136 KOK AND SARACOGLU

like the original pipeline, the second line

was

to be 42 inches i n di amete r and have a

capacity of 700,000 b d

Program Assumptions

The assumptions used for simplification of the program are listed below:

-Wax precipi ta tion occurs only when the pipeline fluid temperature is below wax

appearance temperature.

-Initially, solid concentration equals to zero.

-Pressure is assumed to be constant through the pipeline.

-When a solid par ticle occurs, it does not change into l iquid state . Also, sol id does

not have a reaction effect.

-The ratio of activity coefficient of liquid to solid is assumed to be equal unity.

-Inne r wall temperature is constant through the pipeline, which is less than wax

appearance

temper ture

Crude oil pipeline simulation results yearly wax deposition, bulk fluid

temperature, sol id-l iquid equil ibrium constant, wax mole fraction through the

pipeline and temperature effect in wax mole fraction is presented in figures 1-6 for

Haditha-Rurnailia crude oil pipeline . In figure-I yearly wax deposition thickness it

was observed that wax s tart s to depos it around 250 km. from inle t because of high

pumping rate and reaches about 0.10 mm after a year. In figure-2 bulk fluid

temperature it was seen that temperature starts to decline around 8 km. from inlet

and declines around 301 K. In figure-3 sol id l iquid equil ibrium constant for the first

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WAX DEPOSITION IN CRUDE OIL PIPELINES

1137

0 12

E

0 1

E

-:: 0 08

III

III

Q

0 06

:

:5 0 04

s:

0 02

a

..

/

/

/

a

100 200 300 400

500 600

700

Distance from Inlet, z km

Figure Yearly

Wax

Deposition

Thickness inHaditha- Rumaila

Crude Oil

Pipeline

303.5

303,0

-:: 302 5

::I

302,0

.

E 301,5

f

301,0

. ...

.

..

.

1.....

.

.

.

.

.

. .

.

.

.

.

.

.

.

.

300,5

o 100

200 300

400

500

600 700

Distance from Inlet, Z km

Figurc 2 Bulk Fluid Temperature in Hadilha Rumaila CrudeOil Pipeline

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8

0,235

0,230

0,225

e

o

0,220

0,215

0,210

KOK AND SARACOGLU

/

/

0,205

100

200

300 400 500

600

700

Distance from Inlet, z km)

Figure-S Solid

iquid Equilibria onstant

for

the first omponent

in

Hadllha

Rumaila

rude

il

Piperine

component} it was observed that K value starts to rise around 290 krn. from inlet

with a value

0,21 and reaches 0,23 at the end

the pipel ine, In figure-4 sol id

liquid equil ibrium constant for the second component it was observed that K value

starts to rise around 300 km. from inlet with value

120 and reaches 164 at the end

of the pipeline. In figure-S wax mole fraction it was observed that wax mole

fraction starts to rise around 350 km. from inlet with a value of 0.194 and reaches

0,20 at the end of the pipeline . In f igure-6 temperature effect in wax mole fraction

in an inverse proportional between wax mole fraction with tempera tu re was

observed which means that wax mole fraction increases as the temperature decreases,

Similar results were observed in other crude oil pipeline systems studied,

CONCLUSIONS

In this study, a mathematica l model for prediction wax deposi tion in

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WAX DEPOSITION IN

RU E

OIL PIPELINES

1139

I

..........

-

I

20

a

a

180

160

C 140

il 120

E:

100

E

80

.:1

@

6

40

w

100

200 300

400

500 600

700

Distance from Inlet, z (km)

Figure 4

SOlid

Liquid Equilibria

Constant

for

the second

Component

in dith Rumaila Crude Oil Pipeline

I

1 -

1 --

r

-...... . I I

1

0,201

0,200

5

0,199

ii

0,198

e

u

0,197

0 0,196

:;;

) ( 0,195

0,194

0,193

0,192

a

100

200 300

400

500 600 700

Distance from Inlet z, (km)

Figurc 5

WaxMole Fraction in Haditha Rumaila Crude

Oil

Pipeline

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r

r

I

KOK AND SARACOGLU

140

0 12

0 10

c

0

0 08

l

lL

0 06

0

:;;

0 04

0 02

0 00

300 5

301

301 5

302

Temperature K

302 5 303

303 5

igllrc G Temperature effect inWaxMole raction inHaditha- Rumaila rude OilPipeline

different pipeline systems has been developed using a combination

or

analytical and

numerical models. The model includes several scienti fic discipl ines such as phase

equilibria phase transition and fluid dynamics.

It is also known that from published experiments that measurable wax

deposit ion will occur if the temperature

of

the bulk fluid is below the precipi tation

temperature of the particular oil and if simultaneously there is a nega tive radial

temperature gradient present in the flow.

The

amount of deposit ion also depends on the oil composi tion. The model is

consistent with experimental observations.

The

proposed combined phase t ransi tion and mass flux model is perhaps

quite generally valid and not restricted to oil and wax. Whether the derived

theoretical results hold well must be determined experimentally.

The

theory presented requires a lot of input data ranging from fluid

composition equilibrium data flow properties and thermal data.

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X DEPOSITION INCRUDEOILPIPELINES

As presented in figures as the temperature of the fluid declines along the

pipeline, the wax mole fraction, solid-liquid equilibrium constant and wax thickness

incre ses

At lower temperatures the possibility of wax appearance increases.

REFERENCES

Burger, E.D., Perkins, T.K and Striegler, J.H., 1981. Jour. of Petroleum Tech.l075.

Chung, T.H., 1992. SPE 24851, 61 Annual Technical Conference and xhibition-

Washington USA.

Erickon,D.D., Niesen,V.G and Brown, T.S., 1993. SPE 26604, 68 Annua Technical

Conference and Exhibition - Houston - Texas.USA.

Hamouda, A.A and Viken, B.K. 1993. SPE 25189,

International Symposium on

Oilfield Chemistry - New Orleans. USA.

Hamouda, A.A., Davidsen,S 1995. SPE 28996, lnternational Symposium on

Oilfield Chemistry. San Antonio. USA.

Hsu Ll.C. and Brubaker, J.P., 1995. SPE 29976, International Meeting on

Petroleum Engineering. Beijing. Chine. 241.

Hsu

i.r.c.

Santamaria, M.M. and Brubaker, J.P., 1994. SPE 28480, 69 Annular

Technical Conference and Exhibition - New Orleans USA 179.

Keating, J.F., Wattenbergen, R.A., 1994. SPE 27871, Westem Regional Meeting.

Long Beacti-Catifornia US

Lira-Galena.C. Firoozabadi, A.

and

J.M. 1996.,AlChE . 42, pp.235.

McCain, W.O., 1973. The Properties of Petroleum Fluids , Petroleum Publishing

Company, Chapter 5.

Mendell, J.L, and Jessen, F.W., 1972., Jour. ofCan. tro Techn. 60.

Pan H., Firozoodai, P and Folland, P. 1997. SPE Production

Facilities 250.

Svendsen, J 1993. AlChE 39, No.8, 1377.

Wardhaugh, L.T. and Boger, O.V., 1991. AlChE 37 No 6 871.

7/24/2019 Kok 2000

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1142

KOKAND SARACOGLU

Wardhaugh, L.T., and Boger, D.V. 1991. Jour Rheology 35 6), 1121.

Weingarten, J.S., and Euchner , J.A., 1986, SPE 15654.

61 Allllual Technical

Conference and Exhibition New Orleans USA

Won. K.W., 1986.

Fluid Phase Equilibria 30.265.

NOMENCLATURE

am

Parameter

in oil density

model

kg/m

3 K

a Particle diameter rum)

a Parameter in wax densi ty model

(kg/m]K)

II First parameter in viscosity equation Pa.s)

Surface area of clean inncr pipe wall m

2

)

C Volume fraction concentration

of

wax in solut ion

C, Parameter in diffusion constant model N)

c

p

Specific heat capacity of the mixture J/kg.K)

c, Concentration of precipitated waxes at the wall

nnerdiameter of the tube m)

O

Diffusion constant m

2/s)

h Wax thickness m)

Gas/liquid equilibrium constant

Gz Graetz number

6H

r

Heat

of fusion Jzrnol)

j Mass flux

of

wax kg/s.m

2

)

k mpirical constant analogous to reaction alc constant

k Thermal conductivity

of

the mixture (W/m.K)

k

Thermal diffusion ratio

K Liquid/solid equilibrium constant

L Pipc length

in)

L, Number

of

moles in liquid phase per mole mixture

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WAX DEPOSITION IN CRUDE OIL PIPELINES

1143

y

L,

m

m.,

M

M

M

s

n

n

P

q

r

R

R

o

R,

Rw

s,

IS

T

Number

of

moles

of

gas

phase

per mole mixture

Number of

moles in solid

phase

per mole mixture

parameter

in power-law flow model

Wa x

deposition

pe r

> c lean wall at t ime

of measuring

(kg/m )

Molecular weight

of

component

i

(kg/krnol)

Mass of wax crystals which flow in the pipe of length at time of

measuring (kg)

Mass of wax crystals which flow outside th e pipe of length L at time of

measuring (kg)

Mass

of

wax crystals which flow in the whole closed at time of

measuring (kg)

Mass

of

wax depos it on the p ipe wall at time

of

measuring (kg)

Molecular

weight of component

Number

of components

Mole number

Pressure Nlm )

Volumetric flow rate (m)/s)

Heat source

(Jzs.nr )

Radial distance (m)

Ga s

constant=8.3143 (JlmoI.K)

Inner

radius of the clean pipe (01)

Reynolds number, R e = p v d l ~ l

Time

dependent

inner

radius of the pipe (rn)

Mole fract ion in sol id phase

Time

(s)

Residence

t ime in

closed

systems (s)

Length of simulation (s)

Temperature

(K)

Ambient temperature (K)

Freezing temperature of

component i K

Tube inlet temperature (K)

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u

v

v

v,

X;

j

z

w

WAP

WI

Subscripts

w

a

KOK AND SARACOGLU

Inner wall

steel )

temperature K

Precipitation temperature of wax temperature K

Reference temperature K

Heat-transfer coefficient

W/m .K)

Average axial velocity m/s

Maximum

axial velocity

m/s

Molar volume of mixture rrr )

Volume of the closed system reservoir rrr )

Mole fraction in liquid phase

Mole fraction in gas phase

Mole fraction in mixture

Mole fraction in mixture

Distance from pipe inlet m

Weight

fraction

Wax Appearance Point K

Total wax deposition kg

Component

Liquid phase

Solid Phase

Wax

nitial

Grcek Letters

B

y

Thermal Diffusivity

Coefficient

of

thermal expansion

Parameter

m )

Activity coefficient

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WAX DEPOSITION IN CRUDE OIL PIPELINES

1145

o

fl

n

J

Dimensionless weight function

Dimensionless length

l -L, fL,

ynamic

viscosity

N.sfnl

3.14159

Density of fluid mixture kgfm3

Density

of solid wax deposition kgfm3

Dimensionless weight function

Dimensionless weight function

Received: January 28, 2000

Accepted: March II 2000