Iraqi Journal of Chemical and Petroleum Engineering 

 Vol.14 No.1 (March 2013) 47- 53 

ISSN: 1997-4884 

 

 

 

 

Theoretical Study on Heat Transfer in the Presence of Fouling  

 
Waqar Abdulwahid Abdulnabi Al-Hallaf

 

Chemical Engineering Department, Nahrain University, Baghdad, Iraq 

 
Abstract 

   The fouling depositions of crude oil stream were studied theoretically in a shell and 

tube heat exchanger to investigate the effect of depositions on the heat transfer 

process. The employed heat exchanger was with steam flowing in the inner tubes and 

crude oil in the shell at different velocities and bulk temperatures. It is assumed that 

fouling occurs only on the heated stream side (crude oil). The analysis was carried out 

for turbulent flow heat transfer conditions with wide range of Reynolds number, bulk 

temperature and time. Many previously proposed models for fouling resistance were 

employed to estimate a new model for fouling rate. It is found that the fouling rate 

and consequently the heat transfer coefficient were affected by Reynolds number, 

Prandtls number, film temperature, activation energy, and time.  

   The results obtained showed that fouling resistance decreased with the increasing of 

Reynolds number and Prandtls number, and increased with the increasing of film 

temperature and time. The analyses of results were compared with some experimental 

work and a reasonable agreement is attained. 
 

Keywords 

Heat exchanger, Shell and tube, Fouling rate, Crude oil 

 

Introduction 

   The term fouling is defined as the 

deposition of unwanted material on 

heat transfer equipment, which results 

in an increase in thermal resistance to 

heat transfer and subsequent loss of 

equipment thermal efficiency [1].  

   Fouling leads to reduce heat transfer, 

increase pressure drop, block process 

pipes, and these effects are costly. The 

cost factors include higher heat 

exchanger requirements, increase fuel 

consumption, reduce throughput and 

increase maintenance. In addition to 

the operation losses, fouling forces 

significant capital expenditure, these 

fouling factors are taken into 

consideration. 

 

 

Reported causes of fouling from crude 

oils include [2]: 

i) Impurities such as water, rust and 
other particulates. 

ii)  Gum or polymeric species formed 
through oxidation of reactive 

species in the oils. 

iii) Insoluble asphaltenes from self-
incompatible oils or from blending. 

iv) Iron sulphide formation. 
v) Coke formation due to reactions of 

polar fractions. 

These factors (i) to (v) become 

progressively more important as the oil 

temperature is raised, i.e., factor (i) can 

predominate at lower temperatures in 

the preheat train, whereas factors (iv) 

Iraqi Journal of Chemical and 

Petroleum Engineering 

 

University of Baghdad 

College of Engineering 



Theoretical Study on Heat Transfer in the Presence of Fouling 

 

 

48                                        IJCPE Vol.14 No.1 (March 2013)            -Available online at: www.iasj.net 
 

and (v) become more important near 

the furnace inlet temperature. 

Scaling of the heat exchanger surfaces 

has been of most concern because of 

the breakage of the fragile impregnated 

graphite tubes. Figure 1 shows a fouled 

heat exchanger.  

 

 
Fig.1, Graphite shell and tube heat exchange. 

 

   As scaling becomes more serious, 

maintenance costs and downtime 

increase, while the production rate 

decreases. After some time of 

operation, the internal surfaces of 

equipment in contact with crude oil are 

covered with scale, which is removed 

by washing at high velocity. This 

descaling action is partly by 

dissolution and partly by abrasion. The 

main equipments which require regular 

washing are: flash chamber, heat 

exchangers, and acid pipework [3]. 

 

Parameters Affecting the Fouling 

   The fouling characteristic of a fluid 

in contact with a heat transfer surface 

depends on the following main 

parameters [4]: 

1. Flow velocity of the fluid. 
2. Surface temperature. 
3. Fluid bulk temperature. 
4. Material and geometry of the heat 

transfer surface. 

5. Characteristics of the fouling fluid. 
 

Fouling Characteristics 

   Many types of fouling can occur on 

the heat transfer surfaces. Based on the 

different physical and chemical 

processes involved, it is convenient to 

classify the fouling main types as       

[4, 5]: 

 

Precipitation Fouling: Crystallization 

of dissolved salts due to solubility 

changes with temperature, and 

subsequent precipitation onto the heat 

transfer surface. 

 

Particulate Fouling: Deposition of 

suspended particles in the process 

stream onto the heat transfer surfaces. 

 

Biological Fouling "bio-fouling": 
This type occurs in raw water due to 

the attachment and growth of macro 

organisms on the heat transfer surfaces. 

 

Chemical Reaction Fouling: Is a 

result of chemical reactions between 

reactants in the flowing fluid in which 

the surface material itself is not a 

reactant. 

 

Corrosion Fouling: Due to chemical 

or electrochemical reaction between 

the heat transfer surface itself and the 

fluid stream to produce corrosion 

products. 

 

Solidification Fouling: Due to 

freezing of a pure liquid or a higher 

melting point components of a multi-

component solution onto a cooler 

surface. 

   This paper covers the impact of shell 

side fouling on the thermal 

performance and economics of shell 

and tube heat exchangers employed in 

the refinery and petrochemical plant 

processes. 

 

Fouling Curves 

   The fouling process is indicated by 

the fouling resistance, Rf which is 

measured either by a test section or 

from the decreased capacity of an 

operating heat exchanger [4].  

The results are presented by Rf versus 

time curve. The delay time, td indicates 



Waqar Abdulwahid Abdulnabi Al-Hallaf 

 

-Available online at: www.iasj.net                   IJCPE Vol.14 No.1 (March 2013)                                 49 
 

an initial period of time that can elapse 

where no fouling occurs. The most 

important fouling curves (Fig. 2) are: 

 

i) The linear fouling curve: In this 
mode, the mass of deposition rate, 

md increases linearly with time and 

there is no deposition removal, mr, 

or md - mr = constant. The fouling 

curve in this case takes the form of:

  

Rf= a (t-td)                                   … (1) 

 

Where "a" is the slope of the line as 

shown in Fig. 2 

 

 
Fig.2, Fouling curves [4] 

 

ii) The asymptotic fouling curve: In 
this mode, the rate of fouling 

gradually increases against time, 

until a steady state is reached when 

there is an asymptotic fouling 

resistance, R
*
f is obtained. In 

practical industrial situations, the 

asymptote may be reached in a 

matter of hours, weeks or months 

depending on the operation 

conditions. The general equation 

describing this behavior takes the 

form 

 

R
*
f = (1-e

- β t
)                              … (2) 

 

This mode is the most widely existed 

in the industrial applications 

 

iii) The falling rate fouling curve: In 
this mode, the mass of deposit 

increases with time nonlinearly and 

without reaching a steady state of 

asymptotic value, i.e., md - mr= f (t) 

and takes the form  

 

Rf = f (t)                                        … (3) 

 

Crude Oil Fouling Models 

   A large number of models for crude 

oil fouling have been presented. Ebert 

and Panchal (1995) have presented a 

fouling model that is expressed as the 

average (linear) fouling rate under 

given conditions as a result of two 

competing terms, namely, a deposition 

term and a removal term [5, 6, 7, 8, 9]. 

 
Fouling Rate = (deposition term) - (removal 

term) 

 

w

f

f

TR

E

dt

dR

















 
 expRe

…(4) 

 

Where α, β, γ and E are constants to be 

determined from experimental data. 

And w


 is the tube wall shear stress 

and can be given by. 
 

                                  …(5) 
 

The friction factor can be calculated 

from the Blasius equation [9]: 

 
25.0

Re0791.0


f
                       … (6) 

 

The relationship in Eq. (4) points to the 

possibility of identifying combinations 

of temperature and velocity below 

which the fouling rates will be 

negligible. Ebert and Panchal present 

this as the “threshold condition”. This 

model suggests that the heat exchanger 

geometry which affects the surface and 

film temperatures, velocities and shear 

stresses can be effectively applied to 

maintain the conditions below the 

“threshold conditions” in a given heat 

exchanger. 



Theoretical Study on Heat Transfer in the Presence of Fouling 

 

 

50                                        IJCPE Vol.14 No.1 (March 2013)            -Available online at: www.iasj.net 
 

   Ebert and Panchal model assumes all 

the chemical reactions to be included 

by the Arrhenius term in Eq. (4). In 

addition, it ignores the effects of crude 

oil thermal conductivity and specific 

heat and only considers the impacts of 

crude oil density and viscosity as 

presented by Reynolds number. To 

modify this correlation, Prandtl 

number was also incorporated into the 

model by Polley etal. (2002) as shown 

by Eq. (7). 

 

8.033.0
ReexpPrRe 












 




w

f

TR

E

dt

dR

                                                     … (7) 

 

The model differs primarily in the use 

of wall temperature, Tw, in the 

deposition term and Reynolds number 

rather than wall shear stress in the 

removal term. 

   Saleh et al. (2003) proposed a model 

that can only be able to predict fouling 

without considering the effect of fluid 

velocity on the removal term as 

follows: 

 













 


f

f

TR

E
uP

dt

dR
exp




         … (8) 

 

The latest threshold fouling model (Eq. 

(9)) has been developed by Nasr and 

Givi (2006) Which, is independent of 

Prandtl number. 

 

 
                                                      …(9) 

 

Nasr has estimated the constant 

parameters of Eq. (9) using the 

experimental data, measured by Saleh 

et al. 

   It should be mentioned that to extend 

the model for the other type of crude 

oil the constant values have to be 

recalculated correspondingly.  

 

The Proposed Model 

   To propose a new model the 
experimental results reported by 

Polley, Nasr, and Ebert were used. The 

new model can be expressed by the 

following equation: 

 













 


f

f

TR

E

dt

dR
expPrRe


    … (10) 

 
Film temperature can be obtained by 

the following equation: 

 

wbf
TTT  68.032.0           … (11) 

 

The activation energy was obtained by 

drawing ln(dRf/dt) versus 1/Tf. The 

following constants were used in the 

proposed model: 

 

α =36.71 (m2 K/ kW hr) 

β = -0.085 

γ = -1.14 

E = 22.618 (kJ/ mol) 

The correlation coefficient was 0.943. 

 

Results and Discussion 

   The study was carried out to examine 

the effect of operating conditions on 

fouling of crude oil. The following 

ranges of conditions were covered: 

velocity of 0.25 to 0.4 m/s, surface 

temperature of 177 to 245
o
C, bulk 

temperature of 79 to 120
o
C. 

 

Effect of Reynolds Number 

   Velocity effects provide a key to 

understanding the fouling mechanism. 

If fouling rates increased with velocity, 

transport of fouling species is likely 

important. If fouling rate decreases 

with increasing velocity the dominant 

step is likely to be adhesion of foulants 

at the surface or chemical reaction. 

   As Reynolds number was raised 

from 4051 to 6233, the fouling rate 



Waqar Abdulwahid Abdulnabi Al-Hallaf 

 

-Available online at: www.iasj.net                   IJCPE Vol.14 No.1 (March 2013)                                 51 
 

decreased from 0.002543m
2
.K/kW. hr 

to 0.002443 m
2
.K/kW. hr for bulk  

temperature of 79°C and surface 

temperature of 245°C. Figure 3 shows 

the relationship between fouling rate 

and time at different values of 

Reynolds number. 

 

 
Fig.3, Effect of Reynolds number on fouling 

resistance at Tb= 79°C, Tw = 245
o
C 

 

Effect of Film Temperature 

i) Effect of Wall Temperature  
   As shown in Figure 4 fouling rates 

were most intensive at highest wall 

temperature. Fouling rates ranged from 

0.005435 m
2 

K/kW. hr at wall 

temperature of 177
o
C to 0.01037 m

2 

K/kW. hr at wall temperature of 245
o
C 

for bulk temperature of 79
o
C and 

Reynolds number of 3895. 

 

 
Fig.4, Effect of wall temperature on fouling 

resistance at Tb= 79°C, Re = 3895 

 

ii) Effect of Bulk Temperature 
   Figure 5 shows fouling resistance 

versus time for three bulk temperatures 

of 77, 79 and 120
o
C, with fixed wall 

temperature of 177
o
C and Reynolds 

number of 5924.  

   By increasing the bulk temperature 

from 77 to 120
o
C, and hence the film 

temperature from 145 to 158.8
o
C, the 

fouling rate was increased from 

0.001204 to 0.00222 m
2 
K/kW. hr. 

 

 
Fig.5, Effect of bulk temperature on fouling 

resistance at Tw= 177°C, Re = 5924 

 

Effect of Prandtls Number 

   Figure 6 shows that as Prandtls 

increased from 10.46 to 14.92 the 

fouling resistance decreased from 

0.003449m
2
K/kW. hr to 0.002301 

m
2
K/kW. hr for the same values of 

film temperature and Reynolds 

number. 

   

 
Fig.6, Effect of Prandtls number on fouling 

resistance at Tf= 191.24°C,Re = 5924 

 

Comparison of the Results with 

Proposed Models 

   The results of the proposed model 

were compared with other proposed 

models carried out at the same 

conditions for Tb= 77°C, Tw= 242°C 

and Re= 5924, see Fig.7. 

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100 120

Time (hr)

F
o

u
l
i
n

g
 
R

a
t
e
 
(
m

2
.
 
K

/
 
k
W

)

Re=4051

Re=5454

Re=6233

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

Time (hr)

F
o

u
l
i
n

g
 
R

e
s
i
s
t
a
n

c
e
 
(
m

2
.
 
K

/
 
k
W

)

Tw=177ºC

Tw=220ºC

Tw=245ºC

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100 120

Time (hr)

F
o

u
l
i
n

g
 
R

e
s
i
s
t
a
n

c
e
 
(
m

2
.
 
K

/
 
k
W

)

Tb=77ºC

Tb=79ºC

Tb=120ºC

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 20 40 60 80 100 120

Time (hr)

F
o

u
l
in

g
 R

e
s
is

ta
n

c
e
 
(m

2
. 

K
/ 

k
W

)

Pr=10.46

Pr=14.2

Pr=14.92



Theoretical Study on Heat Transfer in the Presence of Fouling 

 

 

52                                        IJCPE Vol.14 No.1 (March 2013)            -Available online at: www.iasj.net 
 

 
Fig.7, Comparison of the fouling resistance 

versus time for the proposed model with other 

models at Tb= 77°C, Tw= 242°C and Re = 

5924 

 

Conclusion 

   A study of fouling at bulk liquid 

temperatures of 77-120°C, surface 

temperatures in the range 177-245°C 

and Reynolds number in the range of 

3895-6233 has shown that: 

1. Fouling rates increase strongly with 
both the surface and the bulk 

temperature. 

2. Surface temperature has a major 
impact on fouling rates. Fouling rate 

is correlated using a modified film 

temperature, which gives more 

weight to the surface temperature 

than to the bulk temperature. 

3. Fouling rate decreases as Reynolds 
number increases to the power -

0.085. 

4. There is a linear dependence of the 
fouling resistance on time. 

5. Bulk temperature effect can not be 
separated from the flow effects, 

since as the bulk temperature 

increases, the Reynolds number 

goes up slightly at fixed velocity. 

6. Fouling rate decreases as Prandtls 
number increases to the power -

1.14. 

 

Nomenclature 

E activation energy, kJ/mol 

f friction factor, 

dimensionless 

P pressure, kPa 

Rf  fouling resistance, m
2
 

K/kW  

Re Reynolds number, 

dimensionless 

t time, h  

td delay time, h 

Tb bulk temperature, K or °C 

Tf film temperature, K or °C 

Tw wall temperature, K or °C 

u fluid velocity, m/s 

Greek symbols 

α constant parameter in Eqs. 

4, 7, 8, 9 and 10 

β constant parameter in Eqs. 

4, 7, 8, 9 and 10 

δ Constant parameter in Eq. 

10 

γ constant parameter in Eqs. 

4, 7, 8 and 9 

ρ density, kg/m
3
 

τw wall shear stress, N/m
2
 

 

Acknowledgment 

   The authors are thankful for the 

comments and advice given by Dr. 

Qasim J. M. Slaiman and Dr. Basim O. 

Hasan. They have substantially 

improved the content of this work and 

pointed out some research directions of 

particular interest. 

 

References 

1. A. S. KOVO, (2006), 
“Mathematical Modelling and 

Simulation of Fouling of Nigerian 

Crude Oil Equipment Installations”, 

Leonardo Journal of Sciences, 9 

,111-124. 

2. M.Srinivasan and A.P.Watkinson, 
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oils”, in “Heat Exchanger Fouling 

and Cleaning: Fundamentals and 

Applications”, ECI conference, 

Santa Fe, 2003. 

3. R. M. Behbahani, H. Müller-
Steinhagen, M. Jamialahmadi, 

“Heat exchanger fouling in 

phosphoric acid evaporators 

evaluation of data”., conference 

proceedings ECI on Heat Exchanger 

Fouling, Santa Fe, 2003. 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 20 40 60 80 100 120

Time (hour)

F
o

u
li
n

g
 R

e
s
is

t
a
n

c
e
 
(
m

2
.K

/k
W

)

Polley model

Nasr model

Ebert model 

Proposed model



Waqar Abdulwahid Abdulnabi Al-Hallaf 

 

-Available online at: www.iasj.net                   IJCPE Vol.14 No.1 (March 2013)                                 53 
 

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8. Z. Saleh, R. Sheikholeslami, A.P. 
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