CHANAPAI Anat - Workspace - Imperial College London

Modeling of Crystallization Fouling in 

Shell-and-Tube Heat Exchangers 

Anat Chanapai 

September 2010 

Supervised by: 

Professor Sandro Macchietto 

Dr. Francesco Coletti 

A thesis submitted to Imperial College London in partial fulfilment of the requirements for the 

degree of Master of Science in Advanced Chemical Engineering with Process Systems 

Engineering and for the Diploma of Imperial College 

Department of Chemical Engineering and Chemical Technology 

Imperial College London 

London SW7 2AZ, UK

Abstract 

Heat exchanger fouling is still regarded as a chronic problem in many industries even though 

prediction and mitigation methods have been continuously developed. An estimation of total 

cost of heat exchanger fouling in the UK is about 1.6 billions GBP (Müller-Steinhagen, 1995). 

Various fouling mechanisms of several fluids such as crude oil, milk, and salt solutions, have 

been studied by modeling approach. However, there are many other fluids for which the 

fouling behavior has not been explored. This project aimed to develop a mathematical model 

that can effectively capture the fouling behavior of a pre-heater unit in an industrial plant. 

This fouling problem caused the plant to be shut-down every year for cleaning heat 

exchangers in this unit and sometimes generated emergency interruptions during the normal 

operation period. All of these resulted in an increase of energy consumption, maintenance 

cost and a reduction of the plant’s production capacity. 

Firstly, the fouling mechanism of the chemical considered (referred to as chemical A to 

protect proprietary information) was identified by analyzing temperatures and flowrates from 

industrial data of several heat exchangers. Crystallization/precipitation was found to be the 

dominant deposition mechanism. 

A mathematical model (Coletti and Macchietto, 2010) previously developed for chemical 

reaction fouling was then adapted to the particular system studied here. The existing model 

could capture the crude oil fouling behavior with considerations of fouling deposit local 

variation, temperature-dependent fluid properties, and moving boundary characteristics. 

Changes to the existing model involved modifying the shell-side model to accommodate a 

condensing fluid and substituting the chemical reaction fouling model with a crystallization 

fouling one. To this end, eight models were proposed, incorporated, and tested against plant 

data. The parameter estimation and validation procedures proposed by Coletti and 

Macchietto (2010) were used here. The model that yielded the best results represented the 

fouling rate as functions of a degree of supersaturation and temperature. 

Simulation results showed that an accuracy of the fouling model developed was within 

±0.5 ºC for over 75% of total plant measurements. Moreover, by the use of the model, it was 

possible to detect changes in the fouling behavior of chemical A due to the variation in 

plant’s operating conditions resulted from plant emergency shut-downs. Several 

recommendations were made for the plant to mitigate the problem, with further investigation 

plans proposed. 

i

Acknowledgement 

I would like to express my gratitude to my supervisors; Professor Sandro Macchietto and Dr. 

Francesco Coletti, for their dedicated support, valuable guidance and excellent supervision 

throughout this research. 

I am thankful to my employer, SCG Chemicals, for sponsoring my study at Imperial College 

London. I also gratefully acknowledge to my colleagues at SCG for their attentiveness, 

encouragement, and useful advice with regards to providing the plant data used in this 

project. 

Finally, I would like to take this opportunity to express my express my deep gratefulness and 

love to my beloved family for their understanding, moral support, and endless love. 

ii

List of Contents 

Abstract ................................................................................................................................ i 

Acknowledgement .............................................................................................................. ii 

List of Figures .................................................................................................................... vi 

List of Tables ....................................................................................................................... x 

Nomenclature ..................................................................................................................... xi 

Chapter1: Introduction ....................................................................................................... 1 

1.1 Background............................................................................................................. 1 

1.2 Problem Identification ............................................................................................. 1 

1.3 Research Objectives ............................................................................................... 3 

Chapter2: Literature Review ............................................................................................... 4 

2.1 Review of Fouling Mechanisms ............................................................................... 4 

2.2 Particulate Deposition .................................................................................................. 4 

2.1.1 Transport Mechanism ...................................................................................... 4 

2.1.2 Particle Adhesion ............................................................................................. 5 

2.2 Crystallization Deposition ........................................................................................ 5 

2.2.1 Precipitation Fouling ........................................................................................ 5 

2.2.2 Liquid Solidification .......................................................................................... 7 

2.3 Chemical Reaction Fouling ..................................................................................... 7 

2.4 Corrosion Fouling ................................................................................................... 8 

2.5 Biological Fouling .................................................................................................... 9 

2.6 Fouling Resistance ................................................................................................. 9 

2.7 Review of Models Relevant to Chemical A Fouling ............................................... 10 

2.8.1 Precipitation or Crystallization Fouling Models .................................................. 10 

2.8.2 Crude Oil Heat Exchanger Models .................................................................... 14 

2.8.2.1 Thermal Fouling Models .............................................................................. 14 

2.8.2.2 Shell-and-Tube Heat Exchanger Models ..................................................... 17 

2.8.3 Dynamic, Distributed Shell-and-Tube Exchanger & fouling model .................... 18 

2.8.3.1 System Definition ......................................................................................... 18 

iii

2.8.3.2 Distributed Model with moving Boundaries for Each Domain ....................... 19 

2.9 Conclusion ............................................................................................................... 22 

Chapter3: Research Methodology ................................................................................... 23 

3.1 Analyze and Categorize the Fouling Data ............................................................. 23 

3.1.1 Data Availability ............................................................................................. 24 

3.1.2 Fouling Categorization ................................................................................... 27 

3.2 Develop the Model for Chemical A ........................................................................ 30 

3.2.1 Study the Coletti and Macchietto (2010) Model .............................................. 31 

3.2.2 Distinguish the Model Differences .................................................................. 32 

3.2.2.1 Distributed Thermal Model ...................................................................... 33 

3.2.2.2 Fouling Resistance Model ....................................................................... 35 

3.2.2.3 Ageing Model .......................................................................................... 37 

3.2.3 Develop the Coletti and Macchietto (2010) Model for Chemical A .................. 38 

3.3 Validate Chemical A Model ................................................................................... 41 

3.3.1 Process Running Test ....................................................................................... 42 

3.3.2 Fluid Properties Estimation on Clean Period ..................................................... 42 

3.3.2.1 Data Filtering .............................................................................................. 43 

3.3.2.2 Experimental/Parameter Data Entering ....................................................... 44 

3.3.3 Fouling Parameters Estimation on Fouling Period ............................................. 47 

3.3.4 Model Prediction ............................................................................................... 47 

3.4 Provide Mitigating Options ......................................................................................... 48 

Chapter4: Result and Discussion .................................................................................... 49 

4.1 Fluid Properties Estimation ........................................................................................ 49 

4.2 Fouling Parameters Estimation .................................................................................. 52 

4.2.1 Finding of Appropriate Fouling Parameter Initial Guesses .................................. 52 

4.2.2 Estimation Result of ‘Supersaturation’ Models ................................................... 56 

4.2.2.1 Model 1: ....................................................................................................... 56 

4.2.2.2 Model 2: ....................................................................................................... 58 

4.2.2.3 Model 3: ....................................................................................................... 59 

iv

4.2.2.4 Model 4: ....................................................................................................... 60 

4.2.3 Estimation result of ‘Mass diffusion’ models ....................................................... 62 

4.2.3.1 Model 5: ....................................................................................................... 63 

4.2.3.2 Model 6: ....................................................................................................... 65 

4.2.3.3 Model 7: ....................................................................................................... 65 

4.2.3.4 Model 8: ....................................................................................................... 66 

4.3 Model Prediction ....................................................................................................... 68 

4.3.1 Prediction Result of ‘Supersaturation’ Models .................................................... 68 

4.3.2 Prediction Result of ‘Mass diffusion’ Models ....................................................... 70 

4.3.3 Fouling Parameters Estimation by Using One Year Data Period ........................ 71 

4.3.4 Comparison of 2.5 Months and One Year Estimation Data Period ..................... 75 

4.3.5 Prediction of Model 3 ......................................................................................... 77 

4.4 Provide Mitigating Options ......................................................................................... 81 

Chapter5: Conclusion and Future Work .......................................................................... 86 

5.1 Conclusion ................................................................................................................. 86 

5.2 Future Work ............................................................................................................... 87 

References ........................................................................................................................ 88 

Appendix A: ....................................................................................................................... 94 

Appendix B: ....................................................................................................................... 99 

Appendix C: ..................................................................................................................... 102 

Appendix D: ..................................................................................................................... 109 

v

List of Figures 

Figure 1 Diagram of the pre-heater unit................................................................................. 2 

Figure 2 Particle transport regime (Bott, 1995) ...................................................................... 4 

Figure 3 Normal and inverse solubility curves (Khan et al. 1996) .......................................... 6 

Figure 4 Bubble growth and scale formation (Bott, 1995) ...................................................... 7 

Figure 5 Gum formation (Bott, 1995) ..................................................................................... 8 

Figure 6 Concentration and temperature profile around fouling layer (Bohnet, 2005) .......... 12 

Figure 7 Model domains (Coletti and Macchietto, 2010) ...................................................... 18 

Figure 8 Research methodology flow chart ......................................................................... 23 

Figure 9 Sketch drawing of E-1 heat exchanger .................................................................. 24 

Figure 10 Pressure - Temperature correlation for saturated steam ..................................... 26 

Figure 11 Fouling deposit of E-1 exchanger ........................................................................ 28 

Figure 12 Inspection result of E-1 (deposit was in 'Red' color) ............................................ 28 

Figure 13 fouling inspection of E-2 and E-5 (deposit was in 'Red' color).............................. 29 

Figure 14 Proposed chemical A fouling processes .............................................................. 30 

Figure 15 Model development methodology ........................................................................ 30 

Figure 16 Four major advantages of the Coletti and Macchieto model ................................ 31 

Figure 17 Conceptual difference of the Coletti model and others ........................................ 32 

Figure 18 Three sub-models of the Coletti model ................................................................ 33 

Figure 19 Three domains of chemical A model ................................................................... 34 

Figure 20 Example of the deposit collected from the E-1 tube side ..................................... 38 

Figure 21 The shell input interface ...................................................................................... 39 

Figure 22 The tube side interface ........................................................................................ 39 

Figure 23 An example of the deposit properties setting ....................................................... 40 

Figure 24 An example of modified fouling model for Model 1 .............................................. 41 

Figure 25 Fouling and ageing parameters ........................................................................... 41 

Figure 26 Model validation methodology ............................................................................. 42 

Figure 27 An example of control variables .......................................................................... 45 

Figure 28 An example of measured variable ....................................................................... 45 

Figure 29 An example of variance model setting ................................................................. 46 

Figure 30 An example of parameters to be estimated ......................................................... 46 

Figure 31 Estimated values of three trial tests of clean period estimation............................ 49 

Figure 32 Measurement plot result of clean period properties estimations .......................... 50 

Figure 33 Parity plot of the first estimation .......................................................................... 51 

Figure 34 The fit test result of the second trial test of properties estimation ........................ 51 

Figure 35 The fit test result of the third trial test of properties estimation ............................. 51 

vi

Figure 36 Comparison between no fouling prediction and actual 1Y data of E-1 ................. 53 

Figure 37 Difference of no fouling and the actual tube side outlet temperature data ........... 53 

Figure 38 Example of proper initial guesses and temperature reduction rate ...................... 54 

Figure 39 Example of improper bounds (too large) of fouling parameters ........................... 55 

Figure 40 Example of estimation error resulted from bad setting of the bounds .................. 55 

Figure 41 Estimated result of fouling parameters of Model 1 ............................................... 56 

Figure 42 Fit test result of Model 1 ...................................................................................... 57 

Figure 43 Measurement plots result of Model 1 (variance constant 0.1 ) ......................... 57 

Figure 44 parity plot result of Model 1 ................................................................................. 58 





Figure 49 Estimated parameters result of Model 4 .............................................................. 60 


Figure 51 Measurements plot result of Model 4 (variance constant 0.1 ) .......................... 61 

Figure 52 Parity plot result of Model 4 ................................................................................. 61 

Figure 53 Estimated parameter result of Model 5 ................................................................ 63 


Figure 55 Measurement plot result of Model 5 .................................................................... 64 





Figure 60 Fit test result of model 7 ...................................................................................... 66 



Figure 63 Prediction result of Model 1 ................................................................................. 69 

Figure 64 Absolute error of predicted and measured data of Model 1 ................................. 70 



Figure 67 1Y-period estimation measurements plot of Model 3 (variance 0.2 ) ............... 73 

Figure 68 1Y-period estimation parity plot of Model 3 (variance 0.2 ) .............................. 73 

Figure 69 1Y-period estimation parity plot with 0.1 constant variance of Model 3 ............ 75 

Figure 70 Comparison of 2.5M, 1Y estimation and the actual data of Model 3 .................... 76 

Figure 71 2.5M and 1Y errors compared to the actual data of Model 3 ............................... 76 

Figure 72 Prediction result of Model 3 compared to another 1Y actual data ........................ 78 

vii

Figure 73 Absolute errors of predicted and measured data ................................................. 79 

Figure 74 Average fouling resistance ( ) ........................................................................ 79 

Figure 75 Deposit thickness at Inlet of E-1 ( ) ................................................................... 80 

Figure 76 Deposit thickness at E-1 tube side outlet ( ) ..................................................... 80 

Figure 77 1Y daily data of calculated U-value ..................................................................... 82 

Figure 78 Overlay plots of U-value and 2.5M error .............................................................. 83 

Figure 79 Assumption of rapid fouling rate .......................................................................... 84 

Figure 80 Measurements plot result of Model 2 ................................................................... 94 


Figure 82 Measurement plots result of Model 3................................................................... 95 


Figure 84 Measurements plot result of Model 6 ................................................................... 96 


Figure 86 Measurement plot result of model 7 .................................................................... 97 


Figure 88 Measurement plots result of model 8................................................................... 98 

Figure 89 Parity plot result of model 8 ................................................................................. 98 



Figure 92 Prediction result of Model 7 ............................................................................... 100 

Figure 93 Absolute error of predicted and measured data of Model 7 ............................... 100 

Figure 94 Prediction result of Model 8 ............................................................................... 101 

Figure 95 Absolute error of predicted and measured data of Model 8 ............................... 101 

Figure 96 1Y-period estimation measurements plot of Model 1 (variance 0.2 ) ............. 102 

Figure 97 1Y-period estimation parity plot of Model 1 (variance 0.2 ) ............................ 102 

Figure 98 1Y-period measurements plots of Model 2 (variance 0.2 ) ............................ 103 

Figure 99 1Y-period parity plot result of Model 2 (variance 0.2 ) ................................... 103 

Figure 100 1Y-period measurements plot of Model 4 (variance 0.2 ) ............................. 104 

Figure 101 1Y-period parity plot of Model 4 (variance 0.2) ................................................ 104 

Figure 102 1Y-period measurements plot of Mode 5 (variance 0.2 ) ............................... 105 

Figure 103 1Y-period parity plot of Model 5 (variance 0.2 ) ............................................. 105 


Figure 105 1Y-period parity plot of Model 6 (variance 0.2 ) ............................................ 106 


Figure 107 1Y-period parity plot of Model 7 (variance 0.2 ) ............................................ 107 


viii

Figure 109 1Y-period parity plot of Model 8 (variance 0.2 ) ............................................. 108 

Figure 110 1Y-period parity result of Model 7 (variance 0.1 ) .......................................... 109 

Figure 111 1Y-period parity result of Model 9 (variance 0.1 ) ........................................ 109 

Figure 112 1Y-period parity plot of Model 10 (variance 0.1 ) ........................................... 110 

ix

List of Tables 

Table 1 A brief summary of crystallization fouling models ................................................... 10 

Table 2 Models of chemical reaction fouling (Crittenden, 1988) .......................................... 14 

Table 3 Summary of data availability ................................................................................... 24 

Table 4 Summary of assumptions for the lack of data ......................................................... 27 

Table 5 Summary of changed items in the distributed model .............................................. 35 

Table 6 Summary of fouling models to be tested in this research ........................................ 36 

Table 7 Summary of data filtering criterion .......................................................................... 44 

Table 8 Final estimated fluid properties ............................................................................... 52 

Table 9 Comparison of estimation results for 'Supersaturation' models ............................... 62 

Table 10 Comparison of estimation results for 'Mass diffusion' models ............................... 67 

Table 11 Summary of models to be used in the prediction step .......................................... 68 

Table 12 Comparison of 1Y-period fouling parameters estimation result ............................. 72 

Table 13 Models remain to be tested .................................................................................. 74 

Table 14 1Y-period estimation with 0.1 constant variance .............................................. 74 

Table 15 Items to be suggested to the chemical A plant ..................................................... 85 

x

Nomenclature 

frequency factor of the ageing model 

cross-sectional area for flow 

crystal nucleation and growth area 

fluid saturated concentration at bulk 

frictional factor dimensionless 

specific heat at constant pressure 

saturated concentration at surface 

saturated concentration at film 

supersaturate concentration at bulk 

diameter 

direction of flow 

activation energy for ageing model 

heat transfer coefficient 

length 

mass flowrate 

deposit mass 

number of tube pass per shell 

pressure wetted perimeter 

fouling probability 

sticking probability 

Prandtl number dimensionless 

heat duty 

xi

heat flux 

heat flux 

universal gas constant 

radial coordinate 

dimensionless radial coordinate dimensionless 

radius 

Reynolds number dimensionless 

fouling thermal resistance 

flow radius 


temperature 

film temperature 

wall temperature at time zero 

time 

Subscripts 

mean fluid velocity in the tube 

overall heat transfer coefficient 

youth variable 

deposit thickness 

axial coordinate 

fouling, film 

inner 

xii

inlet 

fouling layer 

pass number 

outer 

outlet 

shell-side 

tube-side 

wall 

Superscript 

Greek letters 

Initial state of deposit 

Final state of deposit 

deposition parameter 

removal parameter 


foulant thickness 

thermal conductivity 

dynamic viscosity 

kinematic viscosity 

density 

shear stress 

heat balance closure parameter 

xiii

model domain 

scale strength factor 

mass transfer coefficient 

water quality factor 

xiv

Chapter1: Introduction 

1.1 Background 

Fouling of heat exchangers is one of major operating problems which results in significant 

losses. This phenomenon increases the heat transfer resistance and therefore decreases 

the efficiency of heat exchangers. The fouling deposition also affects an increase of pressure 

drop, energy consumption, maintenance cost and the throughput reduction. Giving a specific 

example, some chemical industrial plants have to be shut down frequently to clean their heat 

exchangers which result in greatly reduction in plant throughput and increase in 

maintenance cost. 

Attempts to model and predict deposition behaviors have been carried out for decades. 

Several experiments and/or simulations have been conducted to help improve the accuracy 

and reliability of such mathematical models. However, many fouling problems in industrial 

applications are still not well-predicted and their mitigations are sometimes inefficient. 

This project is aimed to develop the model which can effectively predict the fouling behavior 

of shell-and-tube heat exchangers in an industrial chemical plant (the fluid flowing through 

such heat exchangers will be called ‘chemical A’ to protect confidential information).The 

methodology used is to adapt the model developed by Coletti and Macchietto (2010). Their 

model is a dynamic, distributed model of shell-and-tube heat exchanger capable of 

predicting the behavior of crude oil fouling in the tube-side. The model was reported to have 

good predictive capabilities showing accuracy within 2% error when compared with refinery 

measurements (Coletti and Macchietto, 2010). Although, the mechanisms occurring in crude 

oil fouling are most likely different from those occurring in deposition from chemical A, the 

author is convinced that the novel model by Coletti and Macchietto (2010), can be adapted 

to take into account the different underlying phenomena. Moreover, this can be utilized to 

find mitigation methods for such fouling problem. 

1.2 Problem Identification 

Heat exchangers at pre-heater units of this chemical plant have been seriously fouled by the 

particles suspended in chemical A for decades. These problems have been unsolved for 

long time and occasionally caused severe problems resulted in the plant emergency 

shut-down; Figure 1 shows a brief diagram of the pre-heater unit. Typically, the plants have 

to be shut-down in every year for cleaning, by high pressure water jetting, of these 

exchangers. This has been a risky and expensive task. 

1

H-6 

H-4 

H-3 

H-2 

H-1 

E-6 

E-5 

E-4 

E-3 

E-2 

E-1 

2 

Reactor 

Figure 1 Diagram of the pre-heater unit 

Discussion with plant experts highlighted that, the exchanger E-1, E-2 and E-3, at the cold 

end of the train, faced severe fouling while E-4, E-5 and E-6, located in the hot end, were 

less subject to fouling. Chemical A flowing through those exchangers was in a slurry fluid, an 

aqueous solution containing solid particle in relatively high concentration. Moreover, the 

solubility of chemical A increased with an increase of temperature. Therefore, such solubility 

at the cold end exchangers was obviously less than that of the hot end ones. This indicated 

that the fouling of chemical A was inversely proportionate to temperature and solubility. This 

behavior was believed to be explained by crystallization/precipitation fouling mechanism 

which was later discussed in Chapter 2 and 3. However, further analysis of such actual 

fouling data from the plant was required to get better understanding of the fouling behavior 

and to be able to develop the model to predict the deposition.

1.3 Research Objectives 

Obtain necessary geometric data of one heat exchanger, E-1, thermal and physical 

properties of chemical at pre-heater unit from the chemical A plant. 

Analyze the data and identify the fouling mechanism. 

Adapt the dynamic, distributed model of Coletti and Macchietto (2010) to be able to 

explain tube-side fouling behavior of chemical A 

Estimate to obtain the estimated fluid physical properties and fouling model parameters. 

Validate the model prediction against plant measurements. 

Provide operating recommendations to mitigate fouling. 

3

Chapter2: Literature Review 

2.1 Review of Fouling Mechanisms 

There are five major types of fouling (Epstein, 1983); particulate, crystallization, chemical 

reaction, corrosion and biological deposition. Combinations of these types can often occur. 

2.2 Particulate Deposition 

Particulate fouling is used to explain the mass transport phenomena of unwanted particles 

from bulk liquids or gases through boundary layers and eventually deposit on the wall or 

heat transfer surface. Those particles can be generated by any mechanisms such as 

crystals formulated by nucleation process in crystallization fouling or products of chemical 

reaction which occurs in bulk liquid that far from the surface. Moreover, this fouling type is 

considered to play a role in the other deposition mechanisms 

Considering a flowing fluid in heat exchanger, there are two important mechanisms involved 

that generate particulate deposition, transport of the particles to the surface and particle 

adhesion (Bott, 1995). 

2.1.1 Transport Mechanism 

The basic driving force of mass transport is concentration gradient. However, other 

phenomena are involved in particle transport still. Studies of the transport of particles based 

on isothermal conditions help develop the theory to explain this complex mechanism. 

Epstein (1988) reviewed a simple particle freely falls to a surface under gravity and then 

found the correlation between relaxation time and transport coefficient. He suggested three 

particle transport regimes, a diffusion, inertia and impaction as Figure 2. 

Figure 2 Particle transport regime (Bott, 1995) 

In the diffusion regime, the ‘Brownian motion’, the force which is generated by the random 

motion of molecules within the fluid result from the concentration gradient, plays a role in 

4

transporting particles across boundary layers if the flowing characteristic of fluid is laminar. If 

the flowing is turbulent, combination of the ‘Eddy diffusion’, the force of chaotic movement of 

particles caused by turbulent condition, and the ‘Brownian motion’ are involved. In the inertia 

regime, the relatively large particles will receive additional energy from the fluid to force them 

pass through the viscous sub-layer. So, the transport coefficient is high while it remains 

virtually constant in the impaction regime since particles have already reached to the surface 

(Bott, 1995). 

Considering further in non-isothermal conditions, thermophoresis caused by temperature 

gradient may be an augmentation to increase deposition from the driving forces described 

above. 

2.1.2 Particle Adhesion 

The mechanism which makes a particle sticks with the surface is briefly described as the 

interaction between two competing forces, the attractive van der Waals force and the 

repulsive electrostatic double layer force. Van der Waals force is occurred majorly by the 

electric polarization of two solid materials stayed close to each other results in the attractive 

force of the opposite charged surfaces (Bowling, 1988). Electrostatic double layer force, in 

contrast, is caused by the same charged surface of such two solids in aqueous fluid which 

triggers the repulsive force. 

It is believed that adhesion will take place if the thermal energy of the particle is more than 

the total interaction energy between van der Waals and double layer forces. Moreover, a 

roughness of surface area will enhance such adhesion forces due to an increase of the 

contact area (Bott, 1995). 

2.2 Crystallization Deposition 

This type of fouling is common for any substances in particular conditions, e.g. aqueous or 

non-aqueous solutions, which trigger precipitation and deposition on heat transfer surface. 

Those substances can be cooling water, geothermal water, organic or inorganic solutions. 

Moreover, this also includes solidification fouling, a deposition of dissolved components on 

sub-cooled surface (Epstein, 1983). 

2.2.1 Precipitation Fouling 

Three sequential mechanisms are involved in crystallization process, supersaturation, crystal 

nucleation and crystal growth. 

5

Supersaturation is regarded as the pre-condition for substances in a solution to be 

crystallized. This can be occurred by continuously cooling the ‘normal solubility’ solutions, 

solubility enhanced by an increase of temperature, or heating the ‘inverse solubility’ 

solutions, vice versa. Many studies were focused on salt precipitation in aqueous solutions. 

Figure 3 shows the cooling of a normal solubility salt solution and the heating of an inverse 

solubility salt solution. It is believed that crystallization occurs between point C and D in 

supersaturation zone (Khan et al., 1996). 

Figure 3 Normal and inverse solubility curves (Khan et al. 1996) 

Apart from heating or cooling a solution, the supersaturation can be reached by several 

phenomena such as an evaporation of water in solution which increases concentration of 

dissolved substances, a mixing of different solutions or the same solution in saturated 

regime with different temperatures may result in supersaturation as well (Bott, 1995). 

Crystal nucleation is the stage that nuclei start to be created, or can be said the first 

appearance of crystals which can be induced by particles in solution or purely formulated by 

a solution itself. The former is likely to influence crystallization fouling than the latter. 

Crystal growth is considered to be the final step of crystallization which consists of several 

complex mechanisms. Combinations of at least three fundamentals are involved, surface 

energy effect, adsorption layer and diffusion (Mullin, 1972). 

Bott(1995) stated that crystals growth rate is equal to the different of supersaturated and 

equilibrium saturated concentration; 

Where is the mass of solid deposited in unit time; , is the bulk concentration in the 

bulk (supersaturated) and equilibrium saturation concentration at the face of growing 

crystals; is the mass transfer coefficient. 

6 

(1)

Considering other type of crystallization fouling than general salt precipitation, scaling under 

boiling conditions is common for steam boilers, evaporators. Such equipments are usually 

operated in high temperature which may lead to bubbles of vapor generation. These bubbles 

at the rough heat transfer surface possibly provide supersaturation zone for nuclei to take 

place and also contact areas for particles to precipitate. Figure 4 shows scale formation 

underneath bubble (Bott, 1995). 

2.2.2 Liquid Solidification 

Figure 4 Bubble growth and scale formation (Bott, 1995) 

This type of deposition is typically formulated by a fluid flowing under its freezing point which 

liquid solidification is possible to be occurred at the surface. Since the deposition is already 

existed at the wall, diffusion or other mass transport mechanisms are not involved (Bott, 

1995). 

Crystallization fouling due to organic materials is also considered as one of solidification. 

This is often occurred in transferring pipelines of liquid hydrocarbons or crude oils. Bott 

(1988) observed wax deposition from kerosene that crystals could be firstly nucleated if the 

sub-cooled surface temperature was lower than ‘cloud point’ of such hydrocarbon wax. 

2.3 Chemical Reaction Fouling 

Chemical reaction fouling is usually considered as a major fouling type of organic 

substances. The heat exchanger deposition occurred at crude oil preheat trains in refinery 

plants is a common example. Such problem is often severe at the hot end of the unit due to 

high temperature condition. This regime possibly increases chemical reaction of crude oil 

components which generates unwanted materials to be deposited at the surface. The 

mechanisms of this fouling type are also complex and probably consist of several 

phenomena. Watkinson et al. (1997) mentioned three main categories of reactions, 

7

autoxidation, polymerization and thermal decomposition. Hence, many other factors are also 

involved. 

Autoxidation is concerned majorly in fuel storage stability and jet fuel fouling (Watkinson et 

al., 1997). It is believed to generate gum formation in jet fuel pipelines. Taylor (1967, 1968) 

suggested simple mechanisms which involve oxidation processes to form an insoluble 

polymer or so-called gum as Figure 5. 

Figure 5 Gum formation (Bott, 1995) 

A reaction of excess oxygen and free organic radicals results in many soluble and insoluble 

products which may or may not be the precursor of deposition such as hydroperoxides, 

polyperoxides and carbonyls. 

In an absence of oxygen, chemical reaction fouling could also be occurred by polymerization 

or thermal decomposition processes. Polymerization is probably dominated thermal 

decomposition in the moderate temperature regime where the latter requires higher 

temperature gradient. A vinyl-type polymerization is an obvious example for this mechanism 

(Watkinson et al., 1997). 

Thermal decomposition or so-called thermolysis, pyrolysis and cracking is obviously 

presented in the high temperature conditions. It is likely to be the deposition mechanism of 

gas phase substances. 

2.4 Corrosion Fouling 

Corrosion fouling may be expressed by an agglomeration of materials lost from heat transfer 

surface by forms of chemical attack (Bott, 1995). This could be considered as a chemical 

reaction between fluids, or particles in fluid, and the surface which causes corrosion. A 

common example to explain present of corrosion is brown rust, ferric hydroxide, deposition 

on an iron surface. Metal surfaces usually has metal oxide films to protect corrosion of their 

underneath material. In case of damage of the film by means of physical or chemical attack, 

the underlying metal could be severely corroded. Several mechanisms of corrosion can be 

founded by the book of Bott (1995). 

8

2.5 Biological Fouling 

Biological fouling is the deposition of living substances, so-called bio-films, which has two 

significant types based on their size, micro-organisms such as bacteria, algae and fungi and 

macro-organisms such as mussels, barnacles and vegetation. This fouling is typically 

occurred in the temperature regime which suitable for biological activities, cooling water for 

instance. It is believed that bio-fouling facilitates the other deposition mechanism. For 

example, sticky products of micro-organism type may help increase adhesion forces to hold 

particles to be deposited at the surface (Bott, 1995). 

2.6 Fouling Resistance 

In order to better understand the dynamic fouling behavior of heat exchangers, fouling 

resistance is probably the most important parameter which almost all researchers try to 

predict correctly. It plays a vital role in changing, often reducing, overall heat transfer 

coefficient that may trigger several consequential losses. Fouling resistance could be 

expressed by a simple equation proposed by Epstein (1983); 

Where, is the fouling resistance; are the overall heat transfer coefficient at time zero 

and at current time respectively; are wall temperature at time zero and at current 

time respectively; is heat flux. 

Above equation easily explain relations between fouling resistance (or thermal fouling 

resistance) and the wall temperature at time zero, under clean conditions, and at current 

time, any times after operating particular exchanger. However, it is nearly impossible to 

obtain such wall temperature in future to calculate the unknown fouling resistance. 

Therefore, Kern and Seaton (1959) suggested the general mathematical model of fouling 

phenomena in term of deposit layer thickness by times as 

Where, are constants; is mass flow rate; is deposit concentration; is deposit 

thickness at current time; is shear stress. 

It can be seen that the competing two terms, rate of deposition and removal terms, were 

presented which then lead to developments of the model by many scientists. 

9 

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(3)

A review of fouling mechanism and fouling resistance is provided. The next section will 

observe mathematical models which are related to the work of this project. 

2.7 Review of Models Relevant to Chemical A Fouling 

The review of precipitation fouling model is taken into account since the information from 

experts at the plant, and a study of deposition mechanisms stated earlier, the fouling of 

chemical A is probably dominated by form of precipitation phenomena. 

2.8.1 Precipitation or Crystallization Fouling Models 

Since this type of fouling is often considered as a common for various substances mentioned 

previously, the mathematical model of crystallization fouling has long been studied and 

developed as well. However, as the processes of material adhesion to crystal lattice are 

considerably complex, crystallization fouling is, instead, usually estimated to be similar 

mechanism with the chemical reaction one (Bott, 1995). The work of Kern and Seaton 

(1959) is also considered as a based-model of precipitation fouling for further development. 

Table 1 shows brief historical works on modeling this type of deposition. 

Table 1 A brief summary of crystallization fouling models 

Authors Models or related works Remarks 

Kern and 

Seaton 

(1959) 

Taborek et 

al. (1972) 

Asymptotic fouling model stated in section 3.1. 

which includes deposition and detachment 

terms. 

(4) 

Where, are constant; is the deposit 

thickness ; is a fouling probability ; water 

quality factor; is the surface temperature; is 

the shear stress; and is a scale strength 

factor 

10 

Regarded as the pioneer work of both 

chemical reaction and crystallization 

fouling. 

It is critiqued to have too many 

unknown parameters ( , and 

complex combination of particulate 

and precipitation fouling mechanisms 

(Valiambas et al., 1993).

Authors Models or related works Remarks 

Hasson 

(1981); 

Hasson et 

al. (1975, 

1968) 

Müller- 

Steinhagen 

et al. 

(1988) 

(5) 

Where, is a deposit mass; is constant; 

is a crystal nucleation and growth area; water 

quality factor; is sticking probability 

Hasson’s ionic diffusion model 

(6) 

Where, is scaling mass flux; is the 

molar solubility product and the reaction rate 

constant respectively; are the 

calcium and carbonate ion concentrations at 

the liquid/solid interface. 

Where, is mass transfer coefficient; 

can be found in their papers. 

11 

(7) 

The detachment process is not 

considered and also contains several 

unknown parameters. 

Having worked on scaling in 

pipes, they established the classic 

diffusion model which explains the 

dynamic of scaling mass flux. 

Developed from Hasson’s diffusion 

model but using the diffusion of ionic 

species from the bulk to the surface 

instead of ion concentrations at the 

liquid/solid interface. 

Müller-Steinhagen and Branch (1988) also stated the fouling resistance calculation as; 

Where, is scaling mass flux; is scaling density and thermal conductivity, 

respectively. 

Moreover, the result of experiment, which was also aimed to study fouling behavior, 

conducted by Watkinson (1983) mentioned that was about 5,000 . 

However, the detachment term has not been taken into account since the Hasson et al. 

(1975) model because, perhaps, its mechanism was complex and difficult to capture. 

Bohnet (2005) concluded that crystallization fouling could be majorly influenced by two 

mechanism; mass diffusion or surface reaction as models shown below 

(8)

Mass diffusion controlling 

Surface reaction controlling 

Where is bulk concentration; is concentration in the vicinity of fouling layer; is 

saturation concentration. Figure 6 showed locations of the three concentrations. 

Figure 6 Concentration and temperature profile around fouling layer (Bohnet, 2005) 

It can be seen that the model development is majorly subjected to salt precipitation, 

especially which is a common scaling in cooling water. Many following works were 

still focused on the same type of salt solutions and also utilized models from Table 1 to 

predict fouling behavior. Al-Ahmad et al. (1994) used a simple Kern and Seaton (1959) 

asymptotic fouling model to predict the fouling in one of desalination plants in Saudi Arabia 

and compared the result with the actual fouling data. The result showed the correlation 

coefficient between the two data was more than 90%. Mwaba et al. (2006) performed an 

experiment to study scaling and proposed the model which they called semi-empirical 

correlation. The originality of their model was very similar to the Kern and Seaton (1959) 

one. 

Interestingly, Isogai et al. (2003) suggested the model to predict the organic crystallization 

fouling in crystallizer unit in an aromatic compound plant which is not salt solutions. Then, for 

the same problem, Inokuchi et al. (2007) proposed the fouling model which is originally 

consists of the Reitzer model (Reitzer, 1964) as the formation term and the Kern and Seaton 

(1959) model as removal term, yields; 

12 

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(10)

11) 

Where, is the fouling resistance; are constant; is heat flux and heat transfer 

coefficient, respectively; is shear stress and is deposit thickness (noted that this model 

is based on the assumption that characteristic of temperature dependence of solubility is 

linear and order of the Reitzer (1964) model is one). 

The fluid considered in the study by Isogai et al. (2003) and Inokuchi et al. (2007) is form of 

organic slurry, similar to that of the chemical A plant. Therefore, analogies with the model 

formulation of Isogai et al. (2003) and Inokuchi et al. (2007) are useful for this project. 

However, new models which are different from ones in Table 1 were also presented. 

Behbahani et al. (2003) proposed a lumped, one-dimensional heat exchanger model 

incorporated with precipitation fouling mechanism by evaluating the evaporator fouling data 

of the phosphoric acid plant. The result of the predicted data was virtually fitted with actual 

fouling. However, the variation of fouling resistance along the length of the tube was 

neglected. Khan et al. (1996) built the experiment to observe fouling of . They 

reported the scaling resistance as a function of a tube surface temperature, tube diameter 

and Reynolds number. This was further developed by taking concentrations into 

account and considering the dynamic of fouling behavior along the length of heat 

exchanger’s tube (Khan et al., 2001). The result showed an increase of the fouling 

resistance along the tube’s length due to an increase of fluid temperature while being flowed 

pass through the tube. However, this empirical dynamic model may be suitable only for 

particular salt precipitation with controlled conditions, as well as the work of Becker et al. 

(1995) which obtained the precipitation fouling resistance of one industrial solution as a 

function of Reynolds number. 

Numerical methods are also utilized to build the crystallization fouling model. Kostoglou et al. 

(1998) developed numerical model based on population balance method to explain several 

mechanism involved in precipitation fouling such as crystal nucleation, growth, coagulation 

and particulate deposition. However, their model required extensive parameters which are 

sometimes difficult to measure and their application was focused in fouling of turbulent pipe 

flow, not in a heat exchanger. Brahim et al. (2003) also worked on simulating of the heat 

exchanger fouling numerically by using CFD. This extensive computational capability allows 

the simulation to be able to express local variations of precipitation fouling along the fouling 

layer and deposit accumulation periods. The fouling simulation was compared and reported 

to have a good agreement with experimental result of scaling at heat exchanger. 

13

However, the model may be applicable for specific scaling and yet to be validated with other 

various crystallization fouling problems of real applications. 

Precipitation fouling models have been reviewed. The following section will provide a review 

of crude oil fouling model which Coletti and Macchietto (2010) used in their model. 

2.8.2 Crude Oil Heat Exchanger Models 

Economic impact of crude oil fouling in US refinery pre-heat trains was estimated 

approximately at US$1.2 billion per annum (ESDU, 2000). This explains huge numbers of 

research in this area. In order to find effective mitigation methods, the need to understand 

and accurately predict such fouling behavior is extensively required. Therefore, many 

researchers attempted to develop it for a better prediction capability. Some conducted 

experiments as pilot systems with fouling conditions to observe and propose the deposition 

models, others analyzed the data obtained from industrial plant measurements and 

sometimes suggested different models with different accuracy as well. Moreover, many 

papers included fouling consideration to improve heat exchanger network design and also 

proposed retrofit options. The review of these works is in following sections. 

2.8.2.1 Thermal Fouling Models 

Crude oil fouling is majorly explained by asphaltene deposition which is the product of 

chemical reaction of crude oil components. Therefore, crude oil fouling models is usually 

based on chemical reaction mechanism. Crittenden (1988) reviewed the development 

chemical reaction fouling models as Table 2. 

Table 2 Models of chemical reaction fouling (Crittenden, 1988) 

Authors Application Deposition term Removal term Remarks 

Nelson (1934) Oil refining Rate is directly dependent 

upon thickness of thermal 

boundary layer 

Atkins (1962) Fired 

heater in oil 

industry 

Constant monthly increase in 

coke resistance for various 

refinery streams 

14 

Not considered Fouling rate can be 

reduced by increasing 

fluid velocity 

Not considered two layer concept – 

porous coke adjacent 

to fluid and hard coke 

adjacent to wall

Authors Application Deposition term Removal term Remarks 

Watkinson 

and 

Epstein (1970) 

Crittenden 

and 

Kolaczkowski 

(1979) 

Liquid 

phase 

fouling from 

gas oils 

Hydrocarbons 

in 

general 

Mass transfer and adhesion 

of suspended particles; 

-Sticking probability 

proportional to 

-Sticking probability inversely 

proportional to 

hydrodynamics forces on 

particle as it reaches wall 

Kinetics and/or mass transfer 

control with first order 

reaction (later with other 

orders) 

15 

First order Kern 

and Seaton 

(1959) shear 

removal term 

-Diffusion of 

foulant back into 

fluid bulk 

- First order 

Kern and 

Seaton (1959) 

shear removal 

term 

-Correct prediction of 

initial rate dependence 

on velocity 

-Incorrect prediction of 

asymptotic resistance 

dependence on 

velocity 

-Complex-many 

parameters 

-Limited testing with 

oils 

-Tested with styrene 

polymerization 

-Extended to two layer 

concept proposed by 

Atkins (1962) 

As above table, deposition and removal terms were both considered by the last two models, 

Watkinson et al. (1970) and Crittenden et al.(1979) Moreover, their removal terms presented 

by the classical fouling model proposed by Kern and Seaton (1959) mentioned earlier. 

However, such removal rate was complicated by the multiplication of deposition thickness 

and shear stress which required further developments. Nevertheless, Crittenden et al.’s work 

was also utilized the two layer concept suggested by Atkins (1962) which considered the 

changing of coke deposition properties in aging periods. 

Models were continually developed by several scientists. Crittenden et al. (1987a) 

progressed their works by majorly focusing on experimental-based analysis. They reported a 

fouling model that fitted well with the fouling behavior of model fluids used in their 

experiments. However, various types of crude oil feedstocks, which their clear properties are 

often unavailable, are used in real refinery applications. So, the fouling models from 

controllable experiments could not be directly utilized for predicting the real deposition 

phenomena occurred in refinery plants (Yeap et al., 2004). 

Another interesting model was proposed by Epstein (1994). This is probably the only recent 

model that combines deposition and removal into a single term. He suggested that the 

fouling rate in a low velocity regime increases as the velocity increases. This probably due to 

the dominance of mass transfer mechanism that enables particles from bulk fluid crossing 

boundary layers and deposit at the surface. In contrast, in a high velocity regime, the fouling

ate is decreased by increasing the velocity due to an influence of chemical attachment 

directly at the surface. Furthermore, this paper also reported an effect of temperature on the 

fouling rate, the higher value of temperature, the higher rate of deposition. However, this 

model is complex and consists of many parameters, which usually could not be obtained by 

plants measurements. In order to use this, an estimation of several parameters have to be 

conducted which may deteriorate an accuracy of the model. 

Ebert and Panchal (1995) proposed a threshold model as follows; 

Where, are deposition and removal constant respectively; is constant; is Reynolds 

number; is activation energy; is gas constant; is film temperature; is shear stress. 

This was claimed to deviate from Kern and Seaton (1959) work that Ebert and Panchal 

(1995) model is attempted to anticipate the film temperature which firstly triggers the 

deposition process, the removal term is presented without fouling thickness involved while 

Kern and Seaton (1959) one is intended to predict a fouling resistance at steady state 

conditions, and its removal term is influenced by such deposition thickness. The useful 

model of Ebert and Panchal (1995) is widely studied and later developed by many 

researchers. Panchal et al. (1999) improved such threshold model and added , Prandtl 

number in the deposition term to be able to use with wider range of data sets. The threshold 

concept was actually observed by the fouling experiment done by Knudsen et al. (1999). 

They varied velocities and temperatures and reported the tube surface temperature values 

which likely to initiate deposition of a particular crude oil used in the experiment. Polley et al. 

(2002) further compared between Panchal et al. (1999) model and the result of Knudsen et 

al.’s experiment and claimed to find an inaccuracy of such model. They then modified 

Panchal et al. (1999) model by replacing the film temperature with the wall temperature in 

the Arrhenius term and changing an expression of the removal term from shear stress 

influence to be in form of mass transfer mechanism. Nasr et al. (2006) continued to improve 

Polley et al.(2002) model by comparing with the result of Australian light crude oil experiment 

performed by Saleh et al. (2003).Their new proposed model is also similar to Polley et al. 

(2002) one but removing and changing the wall temperature back to the film temperature. 

They then calculated new threshold temperature for thus light crude oil data. 

It can be seen that the development of crude oil fouling model is majorly based on the 

threshold concept originally proposed by Ebert and Panchal (1995), an exception would be 

noticed by the work of Yeap et al. (2004) that they improved Epstein (1994) model and 

16 

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claimed the better prediction result than the other two models, Panchal et al. (1999) model 

which developed from Ebert and Panchal (1995), and Polley et al. (2002) one. However, 

those improved models were adjusted to fit with particular crude oil. So, one general model 

with fixed parameters could not be perfectly predicted the fouling resistance of all various 

crude oil feedstocks mentioned earlier in this section. A dynamic, distributed model 

suggested by Coletti and Macchietto (2010) incorporated Panchal et al. (1999) fouling model 

and focus more to the underlying model of the heat exchanger using moving boundary 

approach to express local fouling behavior along the tube side. This will be discussed in the 

following section. 

2.8.2.2 Shell-and-Tube Heat Exchanger Models 

Well understanding in heat transfer model of heat exchangers is essential to model dynamic 

conditions inside those equipments. In fact, a good dynamic model of heat exchanger 

together with an appropriate fouling model may result in better accuracy in predicting fouling 

behavior. Also, some papers are intended to construct the model that represents the 

behavior of heat exchanger. However, they are often utilized the lumped model, which 

usually neglects a different of local conditions throughout heat exchangers, to explain the 

fouling phenomena. This may lead to poor predictions of the model. 

In the work of Yeap et al. (2004), mentioned in the previous section. It is assumed the same 

fouling thickness over times along the tube side, or so-called ‘thin slap’ assumption. By 

assuming this, they could easily estimate the total thermal fouling resistance. However, in 

real problems, the fouling layer accumulated at the wall may be far more than a thin plate 

and the layer thickness is often different along the tube side. This assumption may under- 

estimate the severity of fouling. 

Xuan and Roetzel (1993) proposed the thermal dynamic model of shell-and-tube heat 

exchangers. Numerical algorithms are used to inverse complex differential equations, which 

are constructed by energy balance concept, to obtain transient behavior. Having compared 

the model with the result of experiment, by varying temperature and inlet flowrate, their 

predicted graphs were virtually fitted well with the experimental data. However, fouling issue 

was not taken into consideration. Yin et al. (2003) and Luo et al. (2003) further studied and 

developed the similar kind of dynamic models as Xuan and Roetzel (1993) without an 

involvement of fouling as well. Radhakrishnan et al. (2007) and Aminian et al. (2009) applied 

statistical and neutral network methods to predict deposition behavior by entering many 

historical data of particular heat exchanger, such as operational and maintenance data 

17

including fluid properties. However, these models need to be re-trained by huge data 

regularly and their prediction capabilities are seemed to be less than previous techniques. 

Coletti and Macchietto (2010) proposed dynamic, distributed model of shell-and-tube heat 

exchanger to predict the fouling phenomena. Their model utilized the fouling model of 

Panchal et al.(1999), pressure drop equations and additional ageing model developed by 

Ishiyama et al. (2010). As described earlier., this project will further improve the model based 

on Coletti and Macchietto (2010). The following section gives brief equations of their model. 

2.8.3 Dynamic, Distributed Shell-and-Tube Exchanger & fouling model 

All equations in this section were introduced by Coletti and Macchietto (2010) unless 

otherwise stated. 

2.8.3.1 System Definition 

The refinery’s heat exchanger in the work of Coletti and Macchietto (2010) is multi-pass 

tubular TEMA type AET (Noted that the type of the exchanger will be adapted to match with 

the chemical plant’s one, six-pass tubular TEMA type BEM, which requires some changes in 

definition). Four divided domains are defined as Figure 7. 

Figure 7 Model domains (Coletti and Macchietto, 2010) 

: Shell-side domain (the shell volume outside the tubes) 

: Wall domain (between the tube’s inner radius, and the outer one, ) 

: Fouling layer domain (between the fouling layer interface, and ) 

: Tube-side domain (between the center of a tube ) 

18

These domains are applied along a tube’s length (from = 0 to = ). The model 

assumptions are; 

1. The same Temperature along radial axis at the shell-side. 

2. The same relative temperature gradient to the shell of all tubes. 

3. The same driving-force for each tube in the same pass. 

4. The same behaviors of all tubes in each pass (only single tube per pass can be 

represented for all other tubes). 

5. Perfect mixing at all entrances and exits. 

The physical properties used in all equations such as density, , viscosities, and , heat 

capacity, , and thermal conductivity, , will be changed from crude oil to chemical A. 

2.8.3.2 Distributed Model with moving Boundaries for Each Domain 

Details of model equation can be found in Coletti and Macchietto (2010), only the main 

equations will be briefly mentioned here. They used fundamental concept of energy balance 

(Bejan, 1984) to formulate equations for each domain as 

Where 

[1] = Rate of energy accumulation in control volume 

[2] = Net energy transfer by fluid flow 

[3] = Net energy transfer by conduction 

[4] = Rate of internal heat generation 

[5] = Net work transfer to environment 

2.8.3.2.1 Shell-side (Domain ) 

The summarized heat balance of the shell-side domain ( ) is 

Where, if the first tube pass is in co-current flow, otherwise. 

19 

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2.8.3.2.2 Tube Wall (Domain ) 

Assuming the heat capacity, the thermal conductivity, and the density are 

constant and neglecting variations of the direction and no heat sources. The heat balance; 

And the heat flux, for each pass, 

2.8.3.2.3 Fouling Deposit Layer (Domain ) 

is and ) 

Assuming the deposit layer density, and the heat capacity, are constant and no heat 

sources but the local layer temperature, and the thermal conductivity are a function 

of coordinates .The heat balance is and ) 

Where, is the dimensionless radial coordinate= and the heat flux is 

2.8.3.2.4 Tube-side (Domain ) 

Similarly to the shell-side, the heat balance is 

Where for odd pass, for even pass. 

2.8.3.2.5 Pressure Drop calculation 

As an increase of the fouling layer at the inner-wall of the tube side, its velocity, is 

increased due to a reduction of the flow area, . This results in an increase of the 

pressure drop as below equation 

Where is the Fanning friction factor for rough tubes (Wilkes, 2005) : 

20 

(15) 

(16) 

(17) 

(18) 

(19) 

(20)

(21) 

2.8.3.2.6 Fouling Model 

Coletti and Macchietto (2010) selected Panchal et al (1999) fouling model and implement 

distributed functions at direction to obtain local fouling resistance, : 

Where the parameters, and activation energy are changeable. The film temperature, 

is obtained by: 

However, as mentioned earlier., the fouling mechanism of chemical A is tended to be a 

precipitation fouling and the severity of fouling is in low temperature regime. This fouling 

model has to be modified to match with the fouling phenomena of chemical A. 

2.8.3.2.7 Ageing Model 

Ageing phenomenon is described as a change, which may result from chemical reaction, in 

physical structure of deposition, which is accumulated over long periods, from a soft 

substance to a harder one, so-called a coke. This leads to a different of thermal conductivity 

of fouling layer, between the coke deposition that usually stays close to the wall and the 

soft one that stays close to fouling layer surface. In case of ageing mechanism is involved, 

the fouling behavior is seemed to be inaccurately predicted if the thermal conductivity of 

deposit layer is assumed to be constant. 

Coletti and Macchietto (2010) utilized a kinetic model of ageing in chemical reaction fouling 

which is developed by Ishiyama et al. (2010). Only main equation will be mentioned here. 

Defining as a maximum value of the thermal conductivity of a completely coked 

deposition and as a minimum thermal conductivity of newly arrived and soft fouling 

substance yields : 

Where is a ‘youth’ variable. if the deposition layer is firstly occurred. Assuming 

the dynamic of fouling is linear, can be calculated as 

21 

(22) 

(23) 

(24)

Where are pre-exponential constant characteristics and activation energy of the 

ageing process, respectively. is the universal gas constant. 

Again, ageing mechanism of chemical A may be different from crude oils. Further 

development is required before actually apply to predict the fouling of chemical A. 

2.9 Conclusion 

From above literature survey, the previous works are seemed to focus on improving the 

fouling model for better accuracy but paying less attention to incorporate with heat 

exchanger and ageing models. This could be used to estimate a fouling resistance of any 

particular fluid but may not be used to accurately predict behavior of other important 

parameters which significantly affect plant operation and efficiency such as outlet 

temperatures or pressure drops. Moreover, assuming that heat exchanger fouling 

phenomena as lumped models may results in poor prediction. 

The dynamic, distributed model for crude oil recently proposed by Coletti and Macchietto 

(2010) could explain the fouling behavior well. The objective of this project is to improve their 

model to be able to predict the heat exchanger fouling of the chemical A plant. Since the 

fouling of chemical A could be majorly generated by crystallization/precipitation mechanism, 

Panchal et al.(1999) fouling model that used in Coletti and Macchietto (2010) work may have 

to be adapted with some of precipitation models described earlier. Also, the Coletti and 

Macchietto (2010) shell-and-tube heat exchanger model will be modified to match with the 

exchanger in the chemical A plant and ageing model will be considered whether it is 

necessary for this fouling. After all, this obviously has as least two advantages; the reliability 

of the Coletti and Macchietto (2010) model could be strengthened and also confidently 

utilized to other applications and the major problem of that the chemical A plant could be 

predicted or even found out mitigation methods based on such accurate prediction results. 

22 

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Chapter3: Research Methodology 

The research methodology consisted of four major steps; analyze/categorize the fouling 

data, develop a model for fouling of chemical A, validate the model and provide retrofit 

options. Figure 8 showed the work flow chart. 

Analyze and categorize the 

fouling data 

Develop the model for fouling 

of chemical A 

Validate the 

Model 

Provide mitigating options 

Figure 8 Research methodology flow chart 

3.1 Analyze and Categorize the Fouling Data 

As mentioned earlier in chapter 1 about pre-heater unit of the chemical A plant, only the 

study of E-1, the first cold end exchanger, fouling was the scope of this project. So, the data 

used throughout the project was for E-1. Figure 9 showed the sketch drawing of heat 

exchanger E-1. However, regarding to the secrecy agreement with the plant, the actual 

geometry and process data of the exchanger were not shown in this thesis. 

23

3.1.1 Data Availability 

Figure 9 Sketch drawing of E-1 heat exchanger 

The data required for this fouling study of E-1 was classified into three groups which are heat 

exchanger geometry, fluid/deposit properties and exchanger input/output process data. The 

geometry such as tube inside/outside diameter, total number of tubes were used to 

calculate, for example, fluid flow cross sectional area, fluid velocity which were important for 

the model. Fluid and deposit properties such as density, heat capacity, thermal conductivity 

were crucial for almost all thermal balance equations used in the model as well as the 

input/output process data which were inlet/outlet temperature, flowrate of both shell and tube 

side of the exchanger. These were summarized as Table 3. Noted that all information given 

by the plant were in daily with one year interval (one operating cycle of E-1). 

Table 3 Summary of data availability 

Exchanger geometry Data availability 

1. Tube side 

- Tube inner/outer diameter available 

- Tube length available 

- Number of tubes available 

- Number of tube passes available 

- Heat transfer surface area available 

2. Shell side 

- Shell inner diameter available 

- Number of shells available 

- Number of baffles available 

- Baffles details e.g. baffle cut available 

24

Fluid properties (tube&shell) Data availability 

Density 

Heat capacity 

Viscosity 

Thermal conductivity 

Fouling deposit properties 

Density 

Heat capacity 


1. Tube side 

Process data 

25 

available 

available 

available 

N/A 

N/A 

N/A 

N/A 

- Inlet temperature available 

- Outlet temperature available 

- Volumetric flowrate available 

2. Shell side 

- Inlet temperature N/A 

- Outlet temperature N/A 

- Volumetric flowrate N/A 

- Pressure available 

There could be seen as above Table 3, summary table of data received from the plant, that 

the shell side inlet/outlet temperature and flowrate (three sets of data) were not available. 

So, it was necessary to make certain assumptions in order to omit those unavailable data 

from chemical A model. 

Regarding to sketch drawing of E-1 in Figure 9, there mentioned that the shell side inlet is 

recovery steam which comes from the plant’s crystallizer unit and the shell side outlet is 

condensation. Having discussed with the plant’s expert, the condition in the shell side could 

be assumed that all inlet steam (gas phase) is completely condensed to become water 

(liquid phase) at the outlet. Moreover, all of heat exchanged between the shell side fluid and 

tube wall was assumed to be the energy taken out from the change of the shell side fluid 

phase from steam (gas) to condensate (liquid). Therefore, the fluid temperature was then 

assumed to be constant throughout the shell side. However, by the fact that there was no 

any temperature sensor at the shell side, the value of such constant temperature could not 

be known directly.

Nevertheless, as above Table 3, there was the shell pressure measurement available. So, 

the shell side temperature could be obtained by converting fluid pressure to temperature 

from their correlation given by the plant in Figure 10. In fact, by assuming that the shell side 

inlet recovery fluid was purely steam, neglecting other small amount of fine particles 

generated from crystallizer unit within the steam, the pressure-temperature correlation could 

be said to be very similar to that of the general saturated steam table. 

Temperature (C) 

190.00 

180.00 

170.00 

160.00 

150.00 

140.00 

130.00 

120.00 

110.00 

Figure 10 Pressure - Temperature correlation for saturated steam 

Moreover, there were unavailable properties which were thermal conductivity of chemical A 

slurry and three properties of the deposit; its density, heat capacity and also thermal 

conductivity. Nevertheless, these properties could be estimated by gPROMS (PSE), the 

program that was used throughout the project (by setting initial guess values of those 

unknown properties to be similar to the crude oil ones which were known from Coletti and 

Macchietto’s work (2010). The summary of assumptions to be made for the lack of data was 

shown in Table 4. 

1.0 1.3 1.5 1.8 2.0 2.5 3.0 3.6 4.1 5.1 6.1 7.1 8.1 

Pressure (kg/cm2-G) 

26

Table 4 Summary of assumptions for the lack of data 

Unavailable data Alternative data Assumptions 

Shell side 

Inlet temperature 

Outlet temperature 

Flowrate 

Fluid properties 


Fouling deposit 

Density 

Heat capacity 


Shell pressure 

Crude oil data 

Chemical A data 

Chemical A data 

Crude oil data 

1. Neglected the fine particles which were mixed with 

recovery steam at shell inlet (pure steam). 

2. Such steam was fully condensed and then quickly 

dropped to shell outlet. 

3. Shell temperature was converted by its pressure via 

saturated steam table. 

4. Assumed no temp. variation along inlet &outlet of the 

shell, only a phase changed from vapour(steam) to 

liquid(condensate) occurred. 

Similar to the crude oil value. 

Similar to the up-stream particle’s value. 

Similar to the up-stream particle’s value. 

Similar to the estimated value of chemical A. 

Having made those assumptions, the plant data could then be analyzed to find the proper 

fouling mechanism. This will be explained in the following section. 

3.1.2 Fouling Categorization 

As mentioned in Chapter 1 that the plant expert believed that chemical A fouling was 

possibly categorized as crystallization/precipitation type. This section discussed in details 

about that assumption. E-1 exchanger has been frequently taken out to perform inspection 

and cleaning task every one year, this fixed period was set based on fouling records and 

experience of the plant’s operators. Figure 11 showed an example of fouling problem of E-1. 

27

Figure 11 Fouling deposit of E-1 exchanger 

According to the plant maintenance team, the fouling was found majorly at the tube side 

(fouling at shell side was rare) and, obviously, the problem was more severe at its inlet than 

the outlet as shown in Figure 12. The same pattern of this problem also occurred at other 

cold end exchangers, E-2 and E-3 as well. However, as discussed in Chapter 1, this fouling 

trouble was rarely found at the hot end exchangers, E-4, E-5 and E-6. Figure 13 showed 

inspection result of E-2, the low temperature regime exchanger, and E-5, the high 

temperature regime one, which both had the same operating period about one year but E-2 

had much deposit (‘Red’ color dots in Figure 13) than E-5. 

Outlet (higher temp.) 

Inlet (lower temp.) 

Figure 12 Inspection result of E-1 (deposit was in 'Red' color) 

28

E-2 fouling inspection (1Y operating period) E-5 fouling inspection (1Y operating period) 

Cold end unit 

Figure 13 fouling inspection of E-2 and E-5 (deposit was in 'Red' color) 

Turning to consider the crystallization theory reviewed in Chapter 2, it mentioned that 

supersaturation is a major factor for particles to be crystallized which can be achieved by 

cooling ‘normal solubility’ or heating ‘inverse solubility’ solutions. An example of both normal 

and inverse solubility curves was shown as Figure 3. In this particular case, information 

given by the plant suggested that chemical A slurry is a ‘normal solubility’ solution; solubility 

is increased by an increase of temperature. Since the operating temperature at the cold end 

exchangers is lower than that of the hot end ones, solubility of chemical A being passed 

through E-1, E-2, and E-3 is certainly lower than when it is flowed through E-4, E-5, and E-6. 

Moreover, Bott (1995) stated that the crystallization growth rate depends on degree of 

supersaturation, which is the different between bulk and saturated concentration of a fluid. 

Therefore, in chemical A case, the lower solubility of chemical A slurry at the cold ends could 

lead to the lower saturated concentration and finally generated the higher degree of 

supersaturation and crystallization rate than the slurry at the hot end exchangers. This 

analysis supported above inspection results which reported that the severe fouling problem 

has been occurred at the cold end heat exchangers rather than the hot end ones. 

Having focused on the exchanger E-1 which was the scope of this research and has been 

operated the lowest operating, it could be seen that, at the E-1 tube side inlet, the slurry with 

relatively low temperature had a high degree of supersaturation (or low solubility). This may 

cause a high fouling deposition rate. In contrast, when the slurry was at the outlet of its tube 

side, it had the higher temperature which led to the lower degree of supersaturation (or high 

solubility) and also resulted in the lower deposition rate. This could be used to explain the 

inspection result of E-1 shown in Figure 12 and suggest that its fouling rate is inversely 

29 

Hot end unit

proportionate to temperature. Figure 14 depicted flow chart of the fouling mechanism at the 

tube side inlet and outlet of E-1. 

Outlet 

Inlet 

Figure 14 Proposed chemical A fouling processes 

Finally, from above analysis, it suggested that the crystallization/precipitation fouling 

mechanism could be used to reasonably describe the heat exchanger fouling behavior which 

has been occurred at the chemical A plant. Therefore, the modification of fouling model, 

which was the next step of the research, was fundamentally based on crystallization fouling 

theories. 

3.2 Develop the Model for Chemical A 

As stated at the objective in Chapter 1 that this study would modify Coletti and Macchietto 

model (2010) to be able to correctly describe the fouling of chemical A. The model 

development consisted of three steps; study the Coletti and Macchietto (2010) model, 

distinguish the different Coletti and Macchietto (2010) and chemical A fouling and finally 

modify it to be used for chemical A application. Figure 15 showed the work methodology of 

this task. 

High temp. Low solubility Low deposition rate 

Fouling rate is inversely proportionate with temperature 

Low temp. High solubility High deposition rate 

Study the model developed by Coletti 

and Macchietto (crude oil fouling ) 

Distinguish the model differences 

Develop the Coletti model to use for 

the chemical A 

Figure 15 Model development methodology 

30

3.2.1 Study the Coletti and Macchietto (2010) Model 

The model was already introduced in literature review, Chapter 2, the full model can be 

found in Coletti and Macchietto work (2010) but would not be repeatedly mentioned here. 

This section was to state the model’s four major advantages which consisted of the 

consideration of local variation of fouling/fluid properties/process data along the tube side, 

exchanger thermal model involvement, the use of simplified fouling resistance (Panchal et al. 

model, 1999) and the addition of deposit ageing model. Figure 16 summarized these 

advantages. 

Consider local 

variation of fouling 

along tube side 

Account for 

exchanger thermal 

model 

Figure 16 Four major advantages of the Coletti and Macchieto (2010) model 

The model considered a changing of several process data such as fluid temperature, 

velocity, density along the tube side so that the fouling resistance calculated from those 

variables was not steady along the tube side as well. This feature was useful for chemical A 

case because, as stated earlier, the amount of deposit was also not constant, it was severely 

accumulated at the tube side inlet but very little fouling substances found at the outlet as the 

inspection result of E-1 shown in Figure 12. 

A dynamic, 

distributed 

model of shelland-tube 

heat 

exchanger 

The Coletti and Macchietto (2010) model also accounted for exchanger thermal model which 

included a lot of the thermal balance equations from boundary layers briefly mentioned in 

Chapter 2. In fact, the model attempted to predict the temperature outlet of both shell and 

tube side by inputting their temperature inlets and flowrates. This differed from other 

previous works that they tried to predict only fouling resistance. Figure 17 showed the 

conceptual difference of the Coletti and Macchietto (2010) model and others. This advantage 

31 

Use simplified 

fouling resistance 

model 

Include the 

deposit ageing 

model

was also applicable for chemical A because the tube side temperature inlet/outlet and 

flowrate have been measured online but the fouling resistance had to be calculated from the 

U-value which might involve a large error that led to inaccurate data. 

Coletti and Macchietto (2010) model Other models 

Input 

Exchanger thermal 

model (geometries, 

fluid properties, 

fouling and ageing 

model) 

Output 

Input Fouling 

resistance model 

Output 

Input : Inlet temperatures, flowrate 

Output : Outlet temperature 

32 

Input : Inlet/outlet temperature, flowrate 

Output : Fouling resistance ( 

Figure 17 Conceptual difference of the Coletti and Macchietto (2010) model and others 

The simplified fouling model was used as well as involvement of ageing model. These 

features were already explained in Chapter 2, however, they had to be modified in order to 

be applied to chemical A case which was mentioned in the following section. 

In summary, even though the Coletti and Macchietto (2010) model was used to study crude 

oil fouling problem which was believed to be occurred by chemical reaction fouling, not 

crystallization as chemical A, the model still had lot of advantages from above explanations 

which could be developed to effectively apply to this particular case. The following section 

discussed the difference between Coletti and Macchietto (2010) model and chemical A that 

needed to be modified. 

3.2.2 Distinguish the Model Differences 

In order to clearly explain what to be changed in the Coletti and Macchietto (2010) model, it 

was then divided into three groups which were distributed thermal model, fouling model and 

ageing model. These groups were considered separately. Figure 18 depicted the division of 

these three groups.

Ageing 

model 

Figure 18 Three sub-models of the Coletti and Macchietto (2010) model 

3.2.2.1 Distributed Thermal Model 

As briefly explained in Chapter 2, the thermal model of Coletti and Macchietto (2010) 

consisted of four domains which were shown in Figure 7; shell side, tube wall, fouling layer 

and tube side. Each of these domains was divided to ten small sections in axial direction 

along the tube length which allowed fluid data such as temperature, velocity, density to be 

varied from one section to others. This characteristic was also called the distributed model 

(some of the data had local variation in both axial and radial directions such as fluid 

temperature). However, according to assumptions summarized in Table 4, the shell side 

temperature was assumed to be constant throughout the exchanger and the shell side 

flowrate was not available. The lack of input data and unchanged temperature suggested 

that the whole shell side domain of the model was no longer considered. The geometry, fluid 

properties and flowrate of the shell side were then neglected. Therefore, the modified model 

would be reduced to three domains which were tube wall (with constant temperature along 

the tube length at the wall surface which attached to the shell side), fouling layer and tube 

side. Figure 19 showed those three domains. 

Distributed 

thermal 

model 

Full model of 

Coletti and 

Macchietto 

33 

Fouling 

model

Single tube sketch drawing 

There could also be stated that the model was aimed to describe the fouling behavior of a 

single tube. By assuming that every tube in a heat exchanger would have identical 

conditions, the Coletti and Macchietto (2010) model could then be used to explain the overall 

fouling problem of any exchanger. 

Moreover, from Coletti and Macchietto work, it was mentioned that there were significant 

variation of crude oil properties such as density, , heat capacity, , viscosity, , and 

thermal conductivity, , they used to study which highly depended on the oil temperature, 

specific gravity, , mean average boiling point, ,and kinematic viscosity at 100 , 

, Since their dependence on such temperature, crude oil properties were obviously 

distributed in both axial and radial directions as well. Nevertheless, in the case of chemical 

A, that correlation between fluid properties and temperature was not known from the plant. 

So, for simplicity, chemical A properties were assumed to be independent from temperature 

so that they were constant throughout the tube side. 

The other difference had to be mentioned was that chemical A slurry actually consisted of 

two phases fluid, liquid solution and solid particles. It was different from the crude oil which 

was considered as single liquid phase. Therefore, one assumption to be made that chemical 

A slurry was then assumed as single liquid phase with using the weight average properties 

between those solution and particles. Other parameters to be modified to match with 

chemical A case were given by the plant such as exchanger geometry, fluid properties and 

input/output process data. Table 5 summarized the items to be changed in the distributed 

thermal model. 

Figure 19 Three domains of chemical A model 

34 

r 

z 

Shell side 

Constant temp. 

Wall 

Fouling layer 

Tube side

Table 5 Summary of changed items in the distributed model 

Items to be changed Reasons or assumptions 

1.Model domains were reduced from four to 

three by eliminating the shell side domain 

2. Three properties; , , 

were deleted 

3. Four properties; , , , were 

independent from the change of temperature 

4. Weight average values of the properties 

were used 

5.Tube side geometry, fluid properties, 

process data input/output were change 

3.2.2.2 Fouling Resistance Model 

35 

Assumed that there was no variation of 

temperature at the shell side which led to 

constant temperature at the tube wall. The 

shell side geometry, fluid properties, flowrate 

were also neglected. 

Those were unnecessary for chemical A 

case, the other four basic properties; , , 

, were directly estimated and used in the 

model instead 

Unknown correlation between those four 

properties and temperature given by the 

plant. 

Chemical A slurry which consisted of water 

(liquid) and upstream particles (solid) was 

considered as a single liquid phase. 

Used all chemical A data instead of the 

crude oil one. 

As stated earlier that Panchal et al. (1999) fouling resistance model was used in the Coletti 

and Macchietto (2010) model. Panchal et al. (1999) model was applicable for the fouling 

which was dominated by chemical reaction mechanism such as crude oil. However, from 

chemical A data analysis, its fouling type was crystallization/precipitation fouling. Therefore, 

this part had to be modified to be able to correctly describe the fouling behavior. 

According to the literature review, there were lots of crystallization model proposed by many 

researchers. Moreover, scaling in salt solutions was prone to become the main study of this 

area of research, very few scientists have worked on crystallization fouling in aromatic slurry 

which its fouling rate increased when temperature decreased that was similar to the fluid in 

the chemical A plant. Therefore, several models which were primarily based on an influence 

of degree of supersaturation towards crystallization rate were taken into account in this 

project in order to find the best one which its result could fit well with chemical A fouling data. 

Table 6 summarized the fouling resistance models to be used in this research.

Model 1 

Table 6 Summary of fouling models to be tested in this research 

Fouling models to be tested Remarks 

Where , are supersaturated and 

saturated concentration of the fluid respectively; 

is shear stress; is fouling resistance; , 

are deposition and removal constant, 

respectively. 

Model 2 

Model 3 

Model 4 

Model 5 

Where , is saturated concentration at 

bulk and surface, respectively. 

Model 6 

Model 7 

Model 8 

36 

-The deposition term was similar to the 

crystals growth rate in Equation (1) which the 

driving force of crystallization fouling was the 

degree of supersaturation. 

-The removal term was similar to that of Kern 

and Seaton (1959) model. 

Similar to Model 1 but removed from the 

removal term which was identical to that of 

Ebert and Panchal (1995) model in Equation 

(12) 

Removed the removal term of Model 1 and 

used only the deposition term. 

Added a second order of reaction (n=2) at 

the deposition term to accelerate the fouling 

rate 

-The deposition term was similar to Equation 

(9) mass transfer control, except the minus 

sign added due to negative difference of 

and . 

- The removal term is identical to Model 1 

Similar to Model 5 but removed from the 

removal term which was identical to that of 

Ebert and Panchal (1995) model in Equation 

(12) 

Removed the removal term of Model 5 and 

used only the deposition term. 

Added a second order of reaction (n=2) at 

the deposition term which was similar to 

Equation (10) surface reaction control. There 

is no minus sign at the deposition term due 

to absolute positive value of

It could be seen from Table 6 that there were generally two different sets of driving force in 

the deposition term to be tested; , and . The first driving force considered 

that the fouling rate could majorly depend on a degree of supersaturation which was the 

basic fundamental of crystals growth. The second one, however, considered the mass 

diffusion which came from a difference of fluid solubility (or saturated concentration) at the 

bulk and surface (deposit/fluid surface). Nevertheless, for chemical A case, as the 

temperature at the fluid bulk was lower than at the surface, solubility at the bulk was clearly 

lower which made value negative. Therefore, the minus sign added to invert it to be 

a positive value. The second order of reaction (n=2) to accelerate fouling rate was also 

tested on both of them. For simplicity, the first group of fouling models which involved 

were called ‘Supersaturation’ models and the second one with were 

‘Mass diffusion’ models throughout this thesis. 

Turning to consider the removal term, since the influence of the shear stress, , on chemical 

A deposit was still unknown, three different sets of this term were also tested; combination of 

shear stress and fouling resistance, , only shear stress, , and no removal term. The 

procedure to test and compare the result of all models in Table 6 was explained in the model 

validation section. 

3.2.2.3 Ageing Model 

Ageing model was described in Chapter 2 that it accounted for variation of the deposit’s 

thermal conductivity by times. In the case of crude oil, the gel-like deposit found at the 

beginning of operating period had lower thermal conductivity than the coke-like deposit 

occurred by physical transformation of such new-born deposit when the time passed by. In 

order to know if the deposit of chemical A had been physically or chemically changed over 

times, the plant collected a sample of such deposit and sent to the laboratory to analyze its 

properties and compare with the upstream particles ones. Figure 20 showed chemical A’s 

deposit collected from the tube side of exchanger E-1. 

37

Figure 20 Example of the deposit collected from the E-1 tube side 

However, the plant’s laboratory could not analyze the deposit’s thermal conductivity or heat 

capacity. The laboratory, instead, did visually check its physical appearance, analyze its 

chemical components and compare to those of the upstream particles (input material of this 

unit). The results were reported that there were not significant differences between the 

deposit and the upstream particles in both chemical and physical aspects. Moreover, there 

was no trace of gel-like and coke-like found in such sampled deposit. Therefore, it could be 

assumed that the deposit ageing behavior was not likely to occur in this particular case. 

Then, the ageing model was not used in chemical A model. 

Having gone through the preparation steps before the model development, the following 

section showed examples of modified parts of the Coletti and Macchietto (2010) model to be 

readily used for chemical A application. 

3.2.3 Develop the Coletti and Macchietto (2010) Model for Chemical A 

The modification of the Coletti and Macchietto (2010) model was performed by following all 

preparations and assumptions previously described. This section illustrated examples of the 

work actually performed. However, some modifications were not shown due to the un- 

disclosure agreement between the Coletti and Macchietto (2010) model developer and the 

author. 

The shell side domain was deleted by the developer so that the shell side geometry was not 

required. However, the input interface (which is used to allow user to input variables such as 

fluid properties, temperature and flowrate) of the shell side variables was still available. In 

order to successfully run the model, user had to enter any arbitrary values of fluid properties, 

flowrate, pressure of the shell side inlet but those values were not used in any model 

equations. The shell side temperature was the only one variable still used by the model. 

38

Figure 21 showed the shell input interface. According to secrecy agreement with the plant, 

all confidential values stated in any figure were omitted or not the actual values. 

Figure 21 The shell input interface 

Nevertheless, the tube side data was still used. The fluid properties were also changed by 

the developer, three crude oil properties ( , , ) were deleted and four 

chemical A ones ( , , , ) were directly introduced as input variables instead. Figure 22 

showed the tube side input interface. As mentioned earlier that those four properties were 

assumed to be constant, the fluid properties correlations previously used for crude oil case 

were also deleted. The other data such as the tube side geometry, temperature and flowrate 

were adapted for chemical A application as well. 

Figure 22 The tube side interface 

The values of the deposit’s thermal conductivity, and , density, , and heat 

capacity, , were also changed from crude oil to chemical A ones. By using an analyst 

39

esult from the plant’s laboratory mentioned earlier that the deposit and the upstream 

particles had similar characteristics, the three values of the deposit were set to be equal to 

those of the upstream particles given by the plant. Figure 23 showed the setting of those 

three properties in the model. It could be seen that thermal conductivity of gel-like and coke- 

like, and , were set at the same values due to an assumption that there was no 

variation of the thermal conductivity over times. 

Figure 23 An example of the deposit properties setting 

All fouling resistance models in Table 6 were modified and tested one by one. Figure 24 

showed an example of modified fouling model from Model 1. It could be seen that two 

variable were newly introduced; supersaturated concentration, , and saturated 

concentration, , of chemical A slurry. From the data given by the plant, the daily 

calculated value of was available and the correlation between and fluid temperature 

or so called solubility curve was also known (both of them are confidential so that their true 

data were not shown in this thesis). Moreover, the fouling coefficients of this model were 

only two values; the deposition constant, , and the removal one, . The activation energy 

constant, , used in the Panchal et al. (1999 )model was not existed in the crystallization 

ones. 

40

Figure 24 An example of modified fouling model for Model 1 

The ageing model was no longer used which implied that the thermal conductivity of the 

deposit of chemical A was not changed over times. In order to omit the ageing behavior, two 

coefficient of the ageing model; activation energy and pre-exponential constants were set to 

zero. Figure 25 illustrated example of fouling and ageing parameters. 

3.3 Validate Chemical A Model 

Figure 25 Fouling and ageing parameters 

There were four steps to validate chemical A model; process running test, fluid properties 

estimation on clean period, fouling parameters estimation on fouling period, and model 

prediction. These followed the procedure of Coletti and Macchietto (2010) work. Moreover, 

as stated earlier, all of proposed crystallization fouling models were planned to test one by 

one. Their results were then compared to find the best model for chemical A. Figure 26 

showed the work flow chart. 

41

3.3.1 Process Running Test 

Process running test 

Fluid properties estimation 

on clean period 

Fouling parameters 

estimation on fouling period 

Model prediction 

Compare results of all 

fouling models 

Figure 26 Model validation methodology 

This first step was to run the process of the model after all of model modifications had been 

done to ensure that the model could be run without any problem. All of input variables such 

as fluid inlet temperature, flowrate were fixed at their nominal values (the values given when 

the plant was operated in normal/stable operating conditions). The initial guesses of the fluid 

properties of the tube side were set to be the same values as the calculated weight average 

properties and the fouling parameters were set arbitrarily. If the running test was failed, such 

fouling parameters, and , were the first values to be adjusted until the test was passed. 

3.3.2 Fluid Properties Estimation on Clean Period 

It was mentioned earlier that thermal conductivity, , of chemical A was not available. 

Moreover, even though the other three fluid properties; density, , heat capacity, , and 

viscosity, , were known but, with multiphase (liquid solution and solid particles) condition, 

they had to be calculated to find the weight average values which might be inaccurate. 

42

Therefore, this step was to correctly estimate those four fluid properties which were 

important for the model accuracy since they were involved in almost all thermal balance 

equations in the model. The clean period data, which was about two weeks after E-1 was 

cleaned, was used to minimize an affect of fouling on the properties estimation. The input 

and output process data of that clean period were used as experimental data which allowed 

the parameter estimation in gPROMs (PSE) to try to fit the output (outlet temperature) of 

chemical A model with that of the experiment by adjusting the fluid properties (the 

parameters to be estimated). By doing that, the corrected values of those four properties 

would be finally obtained. There were two preparation steps to be performed before 

conducting the parameter estimation; data filtering and experimental/parameter data 

entering. 

3.3.2.1 Data Filtering 

In order to obtain a good fit result, certain range of data which were highly fluctuated or 

seemed to be un-realistic would be filtered out. In the Coletti and Macchietto (2010) work, 

heat check, which was the difference between amounts of heat duty calculated by the tube 

and shell side, was used as the data filtering criteria. Theoretically, with constant heat loss 

involved, the difference of those two should be steady. However, with a measurement error 

in the practical exchanger, the heat check value is sometimes widely varied. Therefore, one 

could set criteria of such heat check, for example, the filter data must have a heat check less 

than 10%, so the ‘bad’ data which had more than 10% heat check would be filtered out. 

Then, only filtered data were put as a performed experiment in gPROMS and the parameter 

estimation could be run effectively. 

However, for chemical A case, the heat check value could not be obtained due to lack of 

shell side data so that the heat check method was not applied. So, the data filtering method 

used in this project was performed by only visual check at the fouling data. The data to be 

considered for ‘Supersaturation’ models were the calculated U-value that the plant operators 

usually monitor, the tube side inlet/outlet temperature, the tube side flowrate, the shell side 

temperature and supersaturated concentration of the tube side fluid. However, for the ‘Mass 

diffusion’ models, there was no need to enter a concentration data since both and 

were calculated values by the known correlation with the fluid’s bulk and surface 

temperature. Table 7 summarized certain filtering criterion to filter out the improper data. 

43

Table 7 Summary of data filtering criterion 

Data filtering criterion (‘Bad’ data) Remarks 

Rate of change of the U-value daily data 

more than 100 kcal/m2.hr.deg.C per day 

Rate of change of the tube side flowrate daily 

data more than 20 m3/hr per day 

Rate of change of the tube side inlet and 

outlet temperature daily data more than 1 

per day 

Rate of change of the shell side temperature 

daily data more than 1 per day 

Rate of change of the fluid supersaturated 

concentration of the tube side data more 

than 5 g/100gH2O per day 

44 

Filtered out the data period which was highly 

fluctuated 


fluctuated or in the shutdown occasions 


fluctuated or un-realistic 


fluctuated or un-realistic 

-Filtered out the data period which was 

highly fluctuated or in the load-down 

occasions. 

-Only considered for ‘Supersaturation’ fouling 

models 

The following section discussed the method to utilize the filtered data obtained from above 

criterion for the parameter estimation on clean period. 

3.3.2.2 Experimental/Parameter Data Entering 

The filtered data was entered as performed experimental variables. In this clean period 

estimation, only the first two weeks data after cleaning were considered. Such range of data 

was divided into two groups; control and measured variables. The control variables for the 

‘Supersaturation’ models were the tube side inlet temperature, tube side flowrate, shell side 

temperature, and the tube side fluid supersaturated concentration whilst only the first three 

involved in the ‘Mass diffusion’ models. The only one measured variable was the tube side 

outlet temperature for both of them. Figure 27 and Figure 28 showed an example of control 

and measured variables of fouling model in Model 1.

Figure 27 An example of control variables 

Figure 28 An example of measured variable 

45

After finished creating the performed experiment for clean period, the parameter estimation 

had to be configured. The variance model, which used to mention the overall accuracy 

of those measurements in the experimental data, was set as constant, 0.2, at first. Initial 

guesses of four parameters to be estimated; density, , heat capacity, , thermal 

conductivity, , and viscosity, , of the tube side’s chemical A slurry, were set as the 

calculated weight average values stated earlier. Figure 29 and Figure 30 showed an 

example of the variance model setting and parameters to be estimated 

Figure 29 An example of variance model setting 

Figure 30 An example of parameters to be estimated 

46

The parameter estimation on clean period would be performed after all configurations had 

been set. Those four estimated properties would be continually adjusted until the tube side 

outlet temperature of chemical A model (the predicted value) fitted well with its measured 

temperature (the measured value) from the experiment. 

3.3.3 Fouling Parameters Estimation on Fouling Period 

After obtaining the proper values of the four properties, the longer period of data was then 

used to estimate the fouling parameters that fitted well with the fouling data of chemical A. 

There were two parameters; , and , for the models in Table 6 which had both deposition 

and removal terms but only for the ones which had only deposition term. The data filtering 

criterion were identical to the previous section so that they were not repeatedly explained. 

For the experimental/parameter data entering, the first 2.5 months data period after cleaning 

was considered. 

Having estimated all fluid properties and fouling parameters, they were used to predict a 

whole one year of E-1 and compare the result with its actual fouling data which were 

explained in the following section. 

3.3.4 Model Prediction 

All of estimated fluid properties and fouling parameters obtained from the previous sections 

were then used for prediction. As mentioned in Figure 17 that an input of the Coletti and 

Macchietto (2010) model was an inlet temperature, flowrate and its output was an outlet 

temperature. Therefore, in order to perform the prediction of chemical A case, one year E-1 

data of the tube side inlet temperature, flowrate, the shell side temperature and the fluid 

supersaturated concentration were used as inputs for ‘Supersaturation’ fouling model tests 

whilst only the first three data used for ‘Mass diffusion’ tests. The fluid properties and fouling 

parameters were fixed at their estimated values given by the previous two estimation steps. 

The prediction results of all tests were the tube side outlet temperature. They were then 

used to compare with that of the real E-1 data to find the best fouling model which was fitted 

with this particular case. 

47

3.4 Provide Mitigating Options 

Having gone through all steps to develop the model which could explain the fouling behavior 

of chemical A, the mitigating options would be suggested. In general, there have been 

several methods proposed to mitigate the heat exchanger problem fouling problem such as 

exchanger chemical cleaning, addition of special chemicals which could resist an 

agglomeration of fouling substances in any other particular cases, modification of tube 

size/material to increase fluid velocity or prolong an induction period of fouling, or heat 

exchanger network re-arrangement which may reduce the severity of fouling in the long 

operating period. However, this research focused on an improvement of operating conditions 

which was believed to play a major for the fouling problem of E-1 exchanger. This was then 

discussed in the result and discussion section. 

48

Chapter4: Result and Discussion 

This section reported the result of all the estimation and prediction works explained in the 

previous section which were fluid properties estimation on clean period, fouling parameters 

estimation on fouling period, model prediction, and model result comparison. 

4.1 Fluid Properties Estimation 

As stated earlier that, in this clean period, the fouling resistance was assumed to be zero. 

So, the fouling parameters; , and in every fouling models in Table 6 were set be zero. 

Therefore, the results of all tests were identical. However, since there were four parameters 

to be estimated ( , , , ), this could led to several combinations of the values obtained 

from the parameter estimation. Figure 31 showed the estimated values of three trial tests of 

this clean period estimation. 

Figure 31 Estimated values of three trial tests of clean period estimation 

49

Noted that initial guesses of all properties were set to their weighted average values. It could 

be seen that the final estimated values of above three trial tests were different. Moreover, 

there was no calculated t-value for the first test due to an error in calculating of co-variance 

matrix which suggested that the estimation might be over-parameterized. This error was not 

occurred at the second and third tests because they both fixed one parameter, and , 

respectively, and estimated only three properties. However, they both did not pass the t-test 

(the individual 95% t-value was smaller than the reference t-value) which indicated that the 

available of fouling data entered might not be sufficient to estimate parameters accurately. 

Nevertheless, these patterns of error were expected for this estimation step because only 

two weeks daily data (totally 15 data points) period were used to estimate four fluid 

properties. The t-test could be generally improved by entering longer period of data (more 

numbers of available data points). However, the longer period of data should not be used in 

this particular case since it may be significantly influenced by the fouling behavior occurred 

continuously at the tube side of E-1. Therefore, the period of data was still fixed at only 15 

data points in order to minimize fouling effect to the properties estimation. 

Even though all above three estimations did not pass the t-test, their predicted tube side 

outlet temperature values were fitted well with that of measured data (the actual tube side 

outlet temperature of E-1 data). Figure 32 and Figure 33 showed measurements and parity 

plots of those three estimations (as the plot results of the three trial tests were almost 

identical, only one set of plots was shown). The variance of measured data was set to be 

constant at 0.2 . 

Temperature (deg.C) 

131.4 

131.2 

131 

130.8 

130.6 

130.4 

130.2 

130 

129.8 

129.6 

129.4 

129.2 

0 2 4 6 8 10 12 14 16 

Days 

Figure 32 Measurement plot result of clean period properties estimations 

50 

Predicted value 

Measured value

Figure 33 Parity plot of the first estimation 

Moreover, the fit test results of the second and third trial tests were passed (there was no fit 

tested available for the first test due to the over-parameterized error) with constant variance 

0.2 . These suggested that the estimated values of such properties could possibly be used 

to explain the actual conditions of E-1 at clean period. Figure 34 and Figure 35 showed the 

fit test results of the second and third tests, respectively. 

Figure 34 The fit test result of the second trial test of properties estimation 

Figure 35 The fit test result of the third trial test of properties estimation 

51

It could be seen from above fit test results that the weight residuals of the two tests were 

nearly the same values and both of them were less than value which indicated a good fit 

between their predicted and measured data. So, either the estimated values from the second 

or the third test could be used for the next estimation step. However, having compared with 

initial properties data given by the plant, the values from the third test were closer than the 

second ones (i.e. the estimated heat capacity, , of the second test seemed too high). 

Therefore, the final estimated values of the third test would be used throughout this 

research. Table 8 showed summary of estimated fluid properties obtained this step. 

Heat capacity, 

Table 8 Final estimated fluid properties 

Fluid properties Final estimated values 

52 

3465.5 J/kg.deg.C 

Thermal conductivity, 0.061119 W/m.deg.C 

Viscosity, 

Density, 

4.2 Fouling Parameters Estimation 

0.0003 Pa.s 

1120.2 kg/m3 

The fluid properties which gave the good fit result of the predicted and actual tube side outlet 

temperature of E-1 was obtained from the clean period estimation step, this section used 

those properties to estimate two fouling parameters; , and with around 2.5 months data 

period. All fouling models in Table 6 were tested to estimate their fouling parameters. 

However, the initial guesses of the parameters to be estimated; , and , had to be stated 

before performing the estimation step. The estimation might be uncompleted or take too long 

time to finish the task if the initial guesses were improper. Since those two values of this 

particular chemical were unavailable from other literatures, they were carried out by trial and 

error method. 

4.2.1 Finding of Appropriate Fouling Parameter Initial Guesses 

The estimated fluid properties from clean period (the first two weeks data) will be used to 

predict the tube side outlet temperature for one year operating period without any fouling 

occurred. Its prediction inputs (tube side inlet temperature, flowrate, shell side temperature 

and supersaturated concentration of the tube side fluid) were used the same as the actual 

one year fouling data because the prediction output temperature from the model would be

compared with that of E-1 data. Figure 36 showed comparison graph between predicted and 

actual tube side output temperature. 


Figure 36 Comparison between no fouling prediction and actual 1Y data of E-1 

It could be clearly seen that the difference of the two data was continuously increased by 

times. Figure 37 showed their temperature different values. 

Absolute error (deg.C) 

133 

132 

131 

130 

129 

128 

127 

3.000 

2.500 

2.000 

1.500 

1.000 

0.500 

0.000 

-0.500 

1 

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281 

291 

Figure 37 Difference of no fouling and the actual tube side outlet temperature data 

53 

Days 

Predicted_no fouling data 

Actual fouling data 

1 

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291 

Days

From Figure 37, It could be noticed that, at the first three months (90 days), the difference 

values were gradually increased to around 0.4 . So, the initial guess values of the two 

fouling parameters should generate the gradual fouling rate which reduced the outlet 

temperature from clean period at around 0.3-0.7 / 3 months. This trial and error task can 

be performed easily by fixing all inputs of the model at their nominal values (i.e. the values 

when the chemical A plant is in stable operating conditions) and simulate the model to obtain 

the outlet temperature. By manually changing the fouling parameters; , and , the 

reduction rate of the outlet temperature at above approximated criteria would be achieved at 

and such values of the fouling parameters would be used as initial guesses for the 

estimation step. Figure 38 showed an example of the proper initial guesses and reduction 

rate of outlet temperature from the Model 1 fouling model. 


130.9 

130.8 

130.7 

130.6 

130.5 

130.4 

130.3 

130.2 

130.1 

1 

13 

25 

37 

49 

61 

73 

85 

97 

109 

121 

133 

145 

157 

169 

181 

193 

205 

217 

229 

241 

253 

265 

277 

289 

301 

313 

325 

337 

349 

361 

Figure 38 Example of proper initial guesses and temperature reduction rate 

It could be seen that, at the first three months (90 days), the temperature reduction rate was 

around 0.3 / 3 months which was in the criteria mention above. So, this set of parameters; 

= 1E-14 and = 1E-8 could be used as initial guesses of the fouling parameters estimation 

which was a good starting point for this task. This trial and error procedure was applied to 

find initial guesses for every fouling model to be tested. 

54 

Days 

= 1E-14 

= 1E-8

The other important figures were the lower and upper bounds of those two parameters. As 

above example of , and initial guesses that were very small values (1E-14 and 1E-8, 

respectively), their lower and upper bounds had to be entered to allow certain feasible 

regions for the estimation to be performed. It was significant that those bounds were tight 

enough to avoid the program to reach an infeasible region during performing the parameter 

estimation task. Figure 39 illustrated an improper setting of the bounds of the two 

parameters which resulted in repeatedly error and uncompleted estimation in Figure 40. 

Figure 39 Example of improper bounds (too large) of fouling parameters 

Figure 40 Example of estimation error resulted from bad setting of the bounds 

55

From above example, it could be seen that the lower and upper bounds of , and , were 

too large (0 and 1, respectively) compared to their initial guesses (1E-14 and 1E-8, 

respectively). This led to the estimation failure because the program often found infeasible 

region when it was trying to optimize the parameter values. The estimation result then could 

not be obtained. This problem could be corrected by tightening the bounds (i.e. reduced the 

lower and upper bounds from 0, and 1 to 1E-6, and 1E-15, respectively). 

The following section provided the fouling parameters estimation results. They were shown 

by separating into two group of models; ‘Supersaturation’ and ‘Mass diffusion’ models. 

4.2.2 Estimation Result of ‘Supersaturation’ Models 

Form Table 6, there were four fouling models, Model 1-4, considered as ‘Supersaturation’ 

fouling models. All of those had the same driving force of deposition rate which was 

. Their differences were majorly at the deposition term. The results were reported in 

order from Model 1 to Model 4. 

4.2.2.1 Model 1: ( 

After finding a proper initial guesses of the fouling parameters; , , and tightening their 

lower and upper bounds, the estimation could be performed by using 2.5 months data period 

after E-1 exchanger cleaning. Figure 41 showed the estimated values of , and . 

Figure 41 Estimated result of fouling parameters of Model 1 

It could be noticed from above result that the four fluid properties previously estimated in the 

clean period were then fixed. There were only two fouling parameters to be estimated in this 

fouling period. Moreover, the final estimated value of passed the t-test whilst did not 

pass. This suggested that the estimated value of was certainly reliable but was still 

56 

)

obscure. The fit test of this result was not passed as shown in Figure 42. This, however, 

resulted from a very small variance constant, 0.1 , of the measured value set to force the 

estimation to find a better estimated value. Figure 43 and Figure 44 showed measurements 

and parity plots of this estimation result, respectively. 


132 

131.5 

131 

130.5 

130 

129.5 

129 

Figure 42 Fit test result of Model 1 

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 

Figure 43 Measurement plots result of Model 1 (variance constant 0.1 ) 

57 

Days 


Measured value

Figure 44 parity plot result of Model 1 

From above measurements and parity plots, it could be visually seen that the predicted 

value fitted well with its actual temperature data. So, this suggested that, with very small 

variance constant 0.1 , the fit test was acceptable. 

4.2.2.2 Model 2: ( 

This model removed from the removal term to be identical with that of Ebert and Panchal 

model (1995) in Equation (12) which assumed that the removal mechanism depended only 

on the shear stress, , exerted by the flowing fluid towards the deposit layer. The estimated 

values and fit test result were shown in Figure 45 and Figure 46, respectively. 


58 

)


It could be seen that the estimated value of had a higher t-value than that of Model 1 but 

the value reached to its lower bound. This suggested that the estimation tried to reduce an 

influence of the removal term by continually decreasing as small as possible. However, 

with the same variance constant, 0.1 , the fit test was still very similar to that of Model 1as 

well as the measurements and parity plots which were shown in Appendix A. 

4.2.2.3 Model 3: ( 

) 

The whole removal term was removed to test an influence of removal term to this particular 

case. So, there was only one fouling parameter to be estimated, , and the model depended 

purely on degree of supersaturation. Figure 47 and Figure 48 showed the estimated values 

and fit test result, respectively. 



This could be seen that the final value of passed the t-test with higher value than that of 

Model 1 and Model 2 due to it was only one parameter to be estimated. However, the weight 

residual were almost identical to the previous two models. The measurements and parity 

plots result of this estimation was nearly identical to that of the previous models, they were 

shown in Appendix A. 

59

4.2.2.4 Model 4: ( 

This model accelerated the fouling rate by changing the degree of supersaturation to the 

power of two. This could be said that the deposition rate was more sensitive to a small 

changing of both supersaturated and saturated concentrations of the tube side fluid. 

Moreover, since such saturated concentration was proportionate to the film temperature, the 

fouling rate would be sensitive to that temperature as well. Figure 49 and Figure 50 showed 

the estimated values and fit test result, respectively. 

Figure 49 Estimated parameters result of Model 4 


It could be noticed that both of , and final values did not pass the t-test and the value of 

was also significantly reduced from its initial guess to lower bound (almost limited by the 

lower bound). Moreover, the final value of was less than that of the previous three models 

for one magnitude. This might result from the second order of reaction added at the 

deposition term exaggerated the fouling rate so that the estimation tried to further decrease 

the parameter of deposition term; to compensate such second order effect. Furthermore, 

the weighted residual from the fit test result was more than those previous models which 

indicated that this model could not fit with the actual fouling data as well as the first order of 

reaction models in Model 1-3. The measurements and parity plot of this estimation were 

slightly worse than the previous models as shown in Figure 51 and Figure 52, respectively. 

60 

)


132 

131.5 

131 

130.5 

130 

129.5 

129 

0 10 20 30 40 50 60 70 80 90 

Figure 51 Measurements plot result of Model 4 (variance constant 0.1 ) 

Figure 52 Parity plot result of Model 4 

61 

Days 


Measured value

Having reported the fouling parameters estimation result of all of the ‘Supersaturation’ 

fouling models to be tested, their results could be compared before showing the result of 

‘Mass diffusion’ models. Table 9 summarized important results of the four ‘Supersaturation’ 

models from this estimation step. 

Table 9 Comparison of estimation results for 'Supersaturation' models 

Models lower bound T-test Fit test 

Model 1 6.60E-15 1E-13 1E-13 : passed 

62 

: not passed 


: reached bound 

Weighted residue : 

118.58 

( = 99.617) 


118.75 

( = 100.75) 

Model 3 6.68E-15 - - : passed Weighted residue : 

Model 4 1.15E-16 1E-15 1E-15 : not passed 

: not passed 

118.62 

( = 100.75) 


132.97 

( = 99.617) 

From above table, it could be noticed that the estimated values of for all three models were 

the same as their lower bound. This suggested that the estimation always tried to minimize 

the removal term effect to fit the models with the actual fouling data. Moreover, the final 

values of of Model 1-3 were very close which indicated that the effect from their deposition 

terms were nearly identical. All of these strengthen the conclusion that the whole removal 

term might be unnecessary for this chemical A case. Furthermore, the fit test of Model 4 was 

worse than the others and it also did not pass the t-test. This is implied that the second order 

of reaction added at the deposition term could not accurately explain the fouling of this 

particular case. 

4.2.3 Estimation result of ‘Mass diffusion’ models 

There were four equations, Model 5-8, considered as ‘Mass diffusion’ fouling models. All of 

those had the same driving force of deposition rate which was which were widely 

used in other literatures. Those researchers majorly applied this deposition term with 

‘inverse’ solubility solutions. However, as mentioned earlier that chemical A slurry is ‘normal’ 

solubility solution, the value from become negative. Therefore, the minus sign was

added to invert the value to be positive. Moreover, this research intended to test the models 

which were in the first (n=1) and second (n=2) order of reaction as similar as the equations 

shown in Mass diffusion controlling and Surface reaction controlling 

4.2.3.1 Model 5: ( 

The deposition term of this model is in first order of reaction (n=1). This was similar to 

Equation (9)Mass diffusion controlling which stated that the fouling rate was dominated by 

mass diffusion behavior rather than surface reaction. This was because The 2.5 months 

period data was also applied as an input of this model. However, the supersaturated 

concentration was no longer used because both and were known by their correlation 

entered in the model. Figure 53 and Figure 54 showed the estimated values and fit test 

result, respectively. 

Figure 53 Estimated parameter result of Model 5 


It could be notice that the estimate values of passed t-test but reached its lower bound. 

This behavior was very similar to the ‘Supersaturation’ models as well as the weighted 

residual in fit test result. Figure 55 and Figure 56 showed measurements and parity plots, 

respectively. 

63 

)


132 

131.5 

131 

130.5 

130 

129.5 

129 

0 10 20 30 40 50 60 70 80 90 

Figure 55 Measurement plot result of Model 5 


64 

Days 


Measured value

4.2.3.2 Model 6: ( 

This model was similar to Model 5 but was removed from the removal term. Such 

removal term was then become equal to that of Model 2. The final estimated value and fit 

test result were shown in Figure 57 and Figure 58. 



Both of and values did not pass the t-test but, interestingly, the value did not reach it 

lower bound which was different with other previous models. However, the fit test result was 

similar to those models in the same variance constant, 0.1 which indicated that, with the 

final values of and , the Model 6 could fit with the actual fouling data as well as the 

previous ones. The measurements and parity plots result of this estimation was nearly 

identical to that of Model 5, so, they were shown in Appendix A. 

4.2.3.3 Model 7: ( 

) 

This model intended to test only the deposition effect. So, the parameter to be estimated 

was then reduced to only one which was . The final estimated value and fit test result were 

shown in Figure 59 and Figure 60, respectively. 

) 

65


Figure 60 Fit test result of model 7 

It could be seen that the value of was fixed to be zero which gave to same result as 

elimination of the removal term. The value of passed the t-test and fit test result was very 

close to Model 5-6 as well as the measurements and parity plots result which were shown in 

Appendix A. 

4.2.3.4 Model 8: ( 

This model also accelerated the fouling rate by addition of second order of reaction. The 

deposition term of this model was then similar to Equation (10)Surface reaction controlling 

which suggested that the fouling rate was influenced by surface reaction rather than mass 

diffusion as the first order fouling models. Figure 61 and Figure 62 showed the estimated 

parameter values and fit test result, respectively. 


66 

)


The estimated values of Model 8 were also similar to the Model 5 that the value of was 

minimized to reach its lower bounds and the value of passed t-test. The measurements 

and parity plots results were also very close to those of Model 5, they were shown in 

Appendix A. 

Having reported the fouling parameters estimation result of all of the ‘Mass diffusion’ fouling 

models to be tested, their results were compared as shown in Table 10. 

Table 10 Comparison of estimation results for 'Mass diffusion' models 



67 


Model 6 1.36E-12 5.58E-17 1E-20 : not passed 

: not passed 


118.37 

( = 100.75) 


118.35 

( = 99.617) 




118.36 

( = 100.75) 


117.95 

( = 100.75) 

From above table, there could be seen that the values of is equal to their lower bounds 

except for Model 6 that it did not reach to the lower bound but its value was still very small. 

So, this strengthened the previous conclusion on ‘Supersaturation’ models that the removal 

term might be insignificant. However, the second order fouling model in Model 8 obtained a 

good fit result which was contrast to that of Model 4. 

Having gone through all results from fluid properties and fouling parameters estimations, 

certain fouling models could be filtered out because the conclusion that the removal term 

might be unnecessary for chemical A fouling model. Therefore, the fouling models to be 

used in the next step were reduced from eight to five models as shown in Table 11.

Table 11 Summary of models to be used in the prediction step 

Models to be used for prediction step Remarks 

Model 1: 

Model 3: 

Model 6: 

Model 7: 

Model 8: 

68 

‘Supersaturation’ model 


‘Mass diffusion’ model 



There could be seen that Model 1, 6, and 8 which had removal terms were still chosen. 

These were because they would be used to compare the prediction result with Model 3 and 

7 which had only deposition terms. The following section reported the prediction result from 

those five fouling models. 

4.3 Model Prediction 

All fluid properties and fouling parameters estimated from the previous sections were used to 

predict the tube side out let temperature for one year. Then, the predicted data was 

compared with the actual one year temperature for chemical A to find the accuracy of all five 

models stated in Table 11. The results were reported separately into two groups which were 

‘Supersaturation’ and ‘Mass diffusion’. 

4.3.1 Prediction Result of ‘Supersaturation’ Models 

As the chosen models in Table 11, there were two models categorized as ‘Supersaturation’ 

which were Model 1 and 3. Figure 63 showed the prediction result of Model 1.


133 

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Figure 63 Prediction result of Model 1 

It could be clearly seen that the predicted temperatures of Model 1 could fit well with the 

actual data only first half of a year (the first 170 days of filtered daily data in Figure 63) but 

had a significant error at the second half. Figure 64 showed the absolute error of the 

predicted and measured value. The error was suddenly increased at the beginning period of 

the second half of the year and gradually increased after that. It was finally reached around 

1.2-1.5 at the end of the operating period. This indicated that Model 1 still could not 

explain the fouling behavior for the whole one year operating period of chemical A. 

Turning to consider the Model 3, it interestingly had a nearly identical prediction result with 

Model 1. This was because they had very close values of ; 6.6052E-15 and 6.6846E-15 for 

Model 1 and Model 3, respectively. Moreover, the value of in Model 1 was small enough to 

nearly eliminate an influence of its removal term and Model 1 then became almost the same 

as Model 3 which had no removal term. Therefore, Model 3 result could not fit with chemical 

69 

Days 


Measured data

A fouling data for a whole one year period. The prediction and error plots of Model 3 shown 

in Appendix B were almost the same as Model 1. 

Figure 64 Absolute error of predicted and measured data of Model 1 

4.3.2 Prediction Result of ‘Mass diffusion’ Models 

Three ‘Mass diffusion’ models which were Model 6, 7, and 8 were used for prediction. Figure 

65 showed the prediction result of Model 6. 


Absolute Error (deg.C) 

133 

132 

131 

130 

129 

128 

127 

2.000 

1.500 

1.000 

0.500 

0.000 

-0.500 

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70 

Days 

Days 


Measured data

It can be seen that the prediction result of Model 6 was almost the same as the result from 

‘Supersaturation’ Model 1 and 3. Only first 6 months that the predicted values could fit well 

with the measured ones and a large error occurred after that. Figure 66 showed an absolute 

error between the predicted and measured value of Model 6. This suggested that conclusion 

which was the same as Model 1 and 3 that the Model 6 could not describe this particular 

fouling data for whole one year period. This also was the same conclusion for Model 7 and 8 

since they had almost identical prediction results, which were shown in Appendix B, as those 

of Model 6. 


2.000 

1.500 

1.000 

0.500 

0.000 

-0.500 

1 

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291 


Having reported all results of model prediction from five proposed models, all of them could 

not explain the actual fouling in one year period correctly. Moreover, those five models had 

the nearly same behavior and almost identical error. These suggested that the estimated 

values of the fouling parameters obtained from 2.5 months data period could not be used to 

fit the whole one year fouling data. Therefore, this research was further progressed to use 

one year data to estimate such fouling parameters. 

4.3.3 Fouling Parameters Estimation by Using One Year Data Period 

Since the exchanger E-1 was taken out to perform cleaning every one year, so, the data 

used to estimate fouling parameters in this step was considered as one cycle of chemical A 

fouling behavior. All the proposed models (Model 1-8) were used for this task and compare 

71 

Days

the result again. Table 12 showed the summary of 1Y-period estimation results for all fouling 

models. 

Table 12 Comparison of 1Y-period fouling parameters estimation result 



72 



: not passed 


895.46 

( = 330.72) 


878.43 

( = 329.65) 



: not passed 



Model 6 5.63E-12 2.56E-16 1E-16 : not passed 

: not passed 

874.33 

( = 330.72) 


895.45 

( = 329.65) 


896.01 

( = 330.72) 


894.83 

( = 329.05) 




893.92 

( = 330.72) 


896.56 

( = 330.72) 

From above Table 12, it could be seen that all models had similar weight residues from the 

fit test result which suggested that they had nearly identical behavior again. Moreover, 

estimated values of for all models was increased (i.e. increase from 6.68E-15 to 1.26E-14 

for Model 3) which suggested that the models captured the fouling rate at the second half of 

the year which was changed dramatically. As Model 3 had the smallest weight residue, its 

measurement and parity plots were shown in Figure 67 and Figure 68, respectively, whilst

plots of the other models were shown in Appendix C. Noted that the variance constant of all 

models in Table 12 were 0.2 . 

Temperature (deg. C) 

132.5 

131.5 

130.5 

129.5 

128.5 

127.5 

126.5 

0 50 100 150 200 250 300 350 

Figure 67 1Y-period estimation measurements plot of Model 3 (variance 0.2 ) 

Figure 68 1Y-period estimation parity plot of Model 3 (variance 0.2 ) 

73 

Days 


Measured value

It could be seen from the above plots of Model 3 that the predicted data fitted quite well with 

the measured one even though it did not pass the fit test (weighted residue, 874.33, was 

more than value, 330.72).Moreover, from Table 12, almost all values of were equal to 

its lower bounds which were the same behavior as 2.5 months estimation period. So, this 

strengthen the previous conclusion again that the removal term was believed to be 

unnecessary for chemical A fouling and the models which have removal term could be 

filtered out from the fouling models to be tested. The proposed models were then remaining 

only four models as shown in Table 13. 

Model 3: 

Model 9: 

Model 7: 

Model 10: 

Table 13 Models remain to be tested 

Models remain to be tested Remarks 

74 


Modified from Model 4 by removing its 

removal term. 


Modified from Model 8 by removing its 

removal term. 

As stated earlier that the 1Y-estimation results all models had a visually good fit with 0.2 

constant variance although the fit test was failed, it could be possible to tighten the variance 

to be only 0.1 in order to further compare those four models and reduce number of the 

proposed models. Table 14 showed 1Y-estimation result of the four fouling models with 

0.1 constant variance. 

Table 14 1Y-period estimation with 0.1 constant variance 

Models T-test Fit test 

Model 3 1.271E-14 : passed 

Model 9 3.1854E-16 : passed 

Weighted residue : 3497.2 

( = 330.72) 

Weighted residue : 3715 

( = 330.72) 

Model 7 5.5945E-12 : passed Weighted residue : 3575.7 

( = 330.72)

Models T-test Fit test 

Model 10 1.243E-11 : passed Weighted residue : 4023.3 

75 

( = 330.72) 

From the fit test result in Table 14, the fit test results of all four models were failed. However, 

Model 3, which previously had the best (smallest) weight residue of 1Y-estimation with 0.2 

constant variance, also had the smallest value of the weight residue (3497.2). This 

suggested that, from all of models tested in this research, Model 3 could be the best to fit the 

actual one year fouling data by using one year fouling parameters estimation period. Figure 

69 showed the parity plot of Model 3 with constant variance 0.1 whilst the plots of the 

other models were shown in Appendix D. However, there was no any model that could 

reasonably fit the whole data with 2.5 months estimation period. 

The following section was to compare the result of 2.5 months and one year period 

estimation of Model 3. 

Figure 69 1Y-period estimation parity plot with 0.1 constant variance of Model 3 

4.3.4 Comparison of 2.5 Months and One Year Estimation Data Period 

According to previous observation that Model 3 could fit with whole one year data with one 

year rather than 2.5 months estimation periods, this section illustrated the results of the two 

and compare with the actual data. This might give some reasons to explain the difference of

those two periods. Figure 70 showed comparison plot of 2.5 months, 1Y, estimation period 

and the actual data of Model 3 and Figure 71 showed their errors. 



133 

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131 

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127 

1 

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291 

Figure 70 Comparison of 2.5M, 1Y estimation and the actual data of Model 3 

2.000 

1.500 

1.000 

0.500 

0.000 

-0.500 

-1.000 

Figure 71 2.5M and 1Y errors compared to the actual data of Model 3 

76 

Days 

2.5M_Predicted value 

Measured data 

1Y_Predicted value 

1 

11 

21 

31 

41 

51 

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81 

91 

101 

111 

121 

131 

141 

151 

161 

171 

181 

191 

201 

211 

221 

231 

241 

251 

261 

271 

281 

291 

Days 

2.5M_Error 

1Y_Error

From above graphs, it could be seen that, at the first half of the year, the error of 2.5 months 

data estimation was very small with an average around ±0.2 . However, such error was 

suddenly increased at the beginning of the second half of the year and finally reached 

around 1.3 . This was because the dramatic increase of error was beyond the first 2.5 

months data period that the estimation could not capture so that it tried to fit only the period 

which was probably in stable operating conditions of the chemical A plant. 

Moreover, in case of one year estimation, the whole fouling data which included slow, 

sudden, and gradual change of fouling rate were entered and the estimation tried to balance 

the error throughout one year period. So, at around the first six months, the error was 

continually decreased to about -0.7 which indicated that the predicted values were lower 

than the actual data. In contrast, the error was abruptly increased to become positive at 

around half of the year (day 182 in the graphs) and then gradually increased until reaching at 

about 0.4 the end of the operating cycle. The result of 1Y-estimation suggested that the 

normal procedure, which stated in the Coletti and Macchietto (2010) work, to use about the 

first 2-3 months of fouling data to estimate fouling parameters could not be applied for this 

particular case due to a sudden change of fouling rate during the operation of E-1 

exchanger. Moreover, such abrupt increase of error also indicated that some activities or 

operating conditions might be significantly changed at the half of the year. The details of this 

analysis were shown in the section of providing mitigating options. 

The next section reported the predictability of Model 3. 

4.3.5 Prediction of Model 3 

This section provided an example of the predictability of Model 3 which used the fouling 

parameter values from 1Y-estimation period even though it did not pass the fit test and still 

had some errors from the fouling parameter estimation step. The fouling data used to 

validate the Model 3 was obtained from another operating cycle of E-1 (i.e. last year data). 

Figure 72 showed the prediction result of Model 3 compared to another 1Y actual data and 

Figure 73 illustrated the absolute error of predicted and measured result. 

It could be seen that there was a large error, about 1.3 , at the beginning of operating 

period which might come from a fluctuation of the operating conditions during plant loading- 

up to a steady conditions. One or two weeks of unstable conditions after start-up were 

common for the chemical A plant. After about two weeks, the error was gradually decreased 

and had small changes within ±0.5 for around four months. Then, it was started 

fluctuating for about one month and then gradually increased in the last three months until 

77

the end of operating cycle. The overall prediction result suggested that the Model 3 could 

capture the behavior of fouling but the errors were quite high in some occasions. Regarding 

to the plant expert’s point of view, it was quite difficult to compare the temperature of the 

Model 3 with this one year actual data due to fluctuation of plant conditions (i.e. the plant 

throughout was continuously changed along this one year data due to market situations) and 

there was no other operating cycle data available to allow the Model 3 to perform another 

prediction task. However, with this current data, there were 75% of total number of data that 

the error were within ±0.5 . Those errors might not be satisfied numerically but could be 

accepted by the plant side. 


133.5 

133 

132.5 

132 

131.5 

131 

130.5 

130 

129.5 

129 

128.5 

1 

9 

17 

25 

33 

41 

49 

57 

65 

73 

81 

89 

97 

105 

113 

121 

129 

137 

145 

153 

161 

169 

177 

185 

193 

201 

209 

217 

225 

233 

241 

Figure 72 Prediction result of Model 3 compared to another 1Y actual data 

78 

Days 

Predict 

Measure

Temprature (deg.C) 

1.5 

1 

0.5 

0 

-0.5 

-1 

-1.5 

1 

9 

17 

25 

33 

41 

49 

57 

65 

73 

81 

89 

97 

105 

113 

121 

129 

137 

145 

153 

161 

169 

177 

185 

193 

201 

209 

217 

225 

233 

241 

Figure 73 Absolute errors of predicted and measured data 

Turning to consider the fouling resistance and fouling layer, these values could also be 

obtained from the Model 3. Figure 74 showed plots of average fouling resistance, . Figure 

75 and Figure 76 indicated the deposit thickness at inlet and outlet of E-1 tube side, 

respectively, for this prediction period. 

Rf (W.m2/K) 

4.50E-05 

4.00E-05 

3.50E-05 

3.00E-05 

2.50E-05 

2.00E-05 

1.50E-05 

1.00E-05 

5.00E-06 

0.00E+00 

Figure 74 Average fouling resistance ( ) 

79 

Days 

1 

12 

23 

34 

45 

56 

67 

78 

89 

100 

111 

122 

133 

144 

155 

166 

177 

188 

199 

210 

221 

232 

243 

254 

265 

276 

287 

298 

309 

320 

Days

Foulant Thickness (mm) 

Foulant Thickness (mm) 

0.003000 

0.002500 

0.002000 

0.001500 

0.001000 

0.000500 

0.000000 

0.003000 

0.002500 

0.002000 

0.001500 

0.001000 

0.000500 

0.000000 

1 

12 

23 

34 

45 

56 

67 

78 

89 

100 

111 

122 

133 

144 

155 

166 

177 

188 

199 

210 

221 

232 

243 

254 

265 

276 

287 

298 

309 

320 

Figure 75 Deposit thickness at Inlet of E-1 ( ) 

Figure 76 Deposit thickness at E-1 tube side outlet ( ) 

From the fouling resistance and deposit thickness plots, it could be seen that average 

was gradually increased from zero to around 4E-5 while both inlet and outlet 

deposit thickness also increased to around 0.0025 mm. According to the distributed 

temperature along the tube length, there were a different between deposit thickness at inlet 

and outlet but with a very small magnitude so that it could not be noticed from the graphs 

80 

Days 

1 

12 

23 

34 

45 

56 

67 

78 

89 

100 

111 

122 

133 

144 

155 

166 

177 

188 

199 

210 

221 

232 

243 

254 

265 

276 

287 

298 

309 

320 

Days

(i.e. 0.00249 and 0.00247 mm for inlet and outlet of E-1, respectively). However, this 

thickness obtained from the model might not reflect the real fouling layer actually deposited 

and accumulated inside the tube due to several assumptions made before start performing 

this research (i.e. constant temperature at shell side). Nevertheless, average was 

believed to be similar to the actual fouling resistance since its value allowed the model outlet 

temperature to fit with the actual temperature with an accuracy of ±0.5 for about 75% of 

total number of data. 

Having reported all results of estimation and prediction steps, the following section would 

suggest the mitigating options to the fouling problem. 

4.4 Provide Mitigating Options 

As stated earlier that there were several methods to reduce severity of fouling or prolong the 

problem which may range from chemical cleaning to re-design the exchanger geometry. 

However, this research was focused on operating conditions of the chemical A plant since, 

by checking the fouling data and the model result, it is believed that the severe fouling of this 

case could be occurred by improper conditions in the plant itself. This section provided the 

analysis of this problem. 

Apart from periodic cleaning schedule, the operators also regularly monitored two indicators 

in order to observe severity of the fouling problem occurred in the pre-heater unit. Firstly, 

they checked the discharge pressure indicator of the pump used to feed slurry of chemical A 

through exchangers in this unit. Value of that pressure measurement would be increased 

continuously whilst the fouling taken place. However, because there have been six 

exchangers using in series, they still could not specify which exchangers were the severely 

fouled ones. Then, secondly, the operator tried to find the trouble exchangers by calculating 

their overall heat transfer coefficient or U-value, and monitoring its tendency over the 

operating period. Figure 77 showed one year trend of the U-value of E-1 exchanger. It could 

be seen that its value was relatively stable at the first six months but continuously decreased 

at the second half of the operating period. This suggested that the fouling problem was 

possibly occurred at E-1. However, the U-value was strongly affected by variation of 

operating conditions such as changing of the plant production rate or plant emergency shut 

down. So, the main cause to make a change of U-value was sometimes obscure and could 

not be distinguished easily. 

81

U-value(kcal/m2.hr.K) 

2,850 

2,750 

2,650 

2,550 

2,450 

2,350 

2,250 

Figure 77 1Y daily data of calculated U-value 

Having checked above calculated U-value which was the same operating period of the 

fouling data used through out the parameter estimation steps, it could be noticed that several 

plant interruption had been occurred. First interruption, ‘A’, was happened in just two days 

which has been usually called ‘re-slurry’ period. Pressure and temperature in the pre-heater 

unit were still maintained as in normal period but chemical A slurry was then circulated (stop 

feeding reactants and generating products) and the plant operators would maintain the slurry 

concentration manually since the re-slurry period was usually an un-planned occurrence. 

The second one was, ‘B’, suspected to be the combinations of plant loading-down and 

measurements error. The third interruption, ‘C’, was planned shutdown, as mentioned earlier 

that the chemical A plant had to be shutdown every six months to fix other equipments but 

the E-1 exchanger was set to clean every year. So, every half of E-1 operating cycle (half of 

a year), the plant would be shutdown. The pre-heater unit was then de-pressurized and the 

temperature would drop to ambient temperature. The last interruption of this year, ‘D’, was 

the re-slurry again. 

A 

B 

C D 

1 

13 

25 

37 

49 

61 

73 

85 

97 

109 

121 

133 

145 

157 

169 

181 

193 

205 

217 

229 

241 

253 

265 

277 

289 

301 

313 

325 

337 

The U-value before and after those interruptions was not changed much except for after ‘D’. 

In fact, the value had been quite stable until the re-slurry ‘D’ interruption and then it was 

suddenly dropped few days later from the trouble. This suggested that there could be some 

specific activities occurred at thus re-slurry period which could accelerate the fouling rate. 

82 

Days

Moreover, the U-values of the others cold end exchangers in this unit; E-2, E-3, and E-4, had 

nearly the same behavior that their U-values were quickly decreased at the same day as E-1 

exchanger. This strengthened the previous assumption about the abnormal activities during 

‘D’ period. 

Continuing the analysis from previous section about comparison of 2.5 months and 1Y- 

estimation period, the error of the predicted and measured data suggest that there might be 

some changes of operating conditions at half of the year. So, in order to analyze this 

information the overlay plots between U-value and such error was shown in Figure 78. 

U-value (kcal/m2.hr.K) 

3,000 

2,900 

2,800 

2,700 

2,600 

2,500 

2,400 

2,300 

2,200 

U-value 

2.5M_Error 

Figure 78 Overlay plots of U-value and 2.5M error 

It could be clearly seen from the above graph that the error started to be suddenly increased 

right after an abruptly drop of the U-value. This suggested that if the re-slurry event ‘D’ had 

not been occurred, the error would have been stayed with in ±0.5 and the severe fouling 

would not have been happened. Therefore, detail investigation on event ‘D’ may help solve 

this fouling problem. Moreover, this phenomenon also indicated that, perhaps, the E-1 

exchanger already had a good design and arrangement since there was no any sign of 

severe problem before the re-slurry. 

A 

B 

C 

1 

14 

27 

40 

53 

66 

79 

92 

105 

118 

131 

144 

157 

170 

183 

196 

209 

222 

235 

248 

261 

274 

287 

300 

313 

326 

339 

Days 

83 

D 

2.000 

1.500 

1.000 

0.500 

0.000 

-0.500 

Absolute error (deg.C)

The fouling rate at the first six months was slow and could be fitted well with the 2.5 months 

period data which was the standard procedure to estimate fouling parameters in the Coletti 

and Macchietto (2010) work. 

This rapid fouling behavior was assumed that, in any activity performed during the re-slurry 

(called ‘trigger’) which rapidly built up the deposit layer in a short period until the layer was 

large enough to accelerate crystallization and agglomeration processes of the new chemical 

A particles attached to it. Then the fouling rate became much faster than the first six months 

period. An evidence to support this assumption was that the values of of all models were 

increased when using one year estimation period instead of 2.5 months (i.e. for Model 3, the 

estimated value of was increased from 6.68E-15 to 1.271E-14). Figure 79 showed 

mechanism of this assumption. 

'Trigger' ON 

during 'D' 

period 

Regarding to the Model 3; 

the deposit 

layer quickly 

built up 

Figure 79 Assumption of rapid fouling rate 

84 

, its equation was simple that there were 

two variables explicitly effect the fouling rate which were supersaturated concentration, , 

and saturated concentration, which totally depended on film temperature. Therefore, the 

implicit variable was the fluid inlet temperature (which would be calculated to find the film 

temperature). So, if , and the inlet temperature were unchanged or in normal variation, 

the fouling rate would not be suddenly changed. 

new 

particles 

easily 

attached and 

crystallized 

Fouling rate 

largely 

increased 

The other important variable was the fluid velocity. Even though the shear stress term which 

depended on fluid velocity (calculated by the flowrate) had been eliminated, the velocity was 

still considered to play a major role in generating the severe fouling. The plant operators 

have been regularly monitored the fluid velocity so as not to allow its value to be less than its 

criteria. So, it could be said that, in the normal operation period, value of the fluid velocity 

was always above its threshold so that the shear stress term was unnecessary for Model 3 

(i.e. the velocity was high enough that it had no longer effect the fouling rate). However, if 

the velocity was less than its criteria, it might cause significant effect to the fouling rate. 

Therefore, three variables should be considered which were supersaturated concentration, 

temperature of both shell and tube, and the flowrate. All of these were the model inputs.

Having checked all of the model inputs and compare with the model absolute error and U- 

value data, however, there was no any significant change in the re-slurry period or nearby 

(the overlay plots between the 2.5M error and other inputs were not shown due to 

confidential information agreement with the chemical A plant). Variations of those inputs 

were in normal range. Therefore, the main cause was still unclear. 

Nevertheless, some suggestions for further investigation could be useful to the plant side. 

This summarized as Table 15. 

Table 15 Items to be suggested to the chemical A plant 

Items to be suggested Remarks 

1.Detail investigate re-slurry ‘D’ period Focused on special activities or procedures which 

could cause significant change of , inlet 

temperature, and fluid velocity (or flow rate) that the 

measurement were not available at that period ( the 

changing of actual values could not be recorded by 

any reason) 

2.Compare the period ‘D’ with ‘A’ (or 

‘B’/’C’) 

3.Inspect E-1 exchanger at the half of 

the year, period ‘B’ (during planned 

shut down), this period could also be 

a trigger mechanism. 

4.Compare the operating condition 

before and after the period ‘D’ 

Period ‘A’ and ‘D’ had the same interruption type, 

re-slurry, but there was no any problem after the 

period ‘A’. Certain inappropriate actions (misprocedure) 

might be carried out during ‘D’ period 

due to unplanned problems. (could also compare 

with re-slurry period of another year) 

This task was to confirm the fouling condition after 

six months operation. Only little fouling should be 

found theoretically. If much of fouling were found, 

the shutdown procedure of that planned shutdown 

period should be checked in detail (may be too rush 

in decreasing temperature during shutdown which 

led to rapid fouling rate) 

This was to confirm all of operating conditions in 

general 

5.Monitor the U-value more often Several information could be obtained from the Uvalue 

(i.e. before and after period ‘D’ of this case) 

6.Pay attention in any unplanned 

shutdown occurred, especially after 

the six months shutdown period ‘B’. 

The period ‘B’ might play a role in changing of the 

fouling rate in the second half of the year. 

85

Chapter5: Conclusion and Future Work 

5.1 Conclusion 

Modeling of heat exchanger fouling is a considerably challenging field of study. Several 

mathematical models have been proposed by many researchers to be able to explain the 

fouling behavior of various fluids. This research focused on the fouling problem occurred in 

the pre-heater unit of the specific chemical plant called chemical A. Objectives of this 

research was to develop the model which could reasonably describe chemical A fouling 

behavior and provide mitigating options. The dynamic, distributed model for crude oil 

recently proposed by Coletti and Macchietto (2010) was used to develop the model for 

chemical A. There were four main steps to achieve the objective of this work as following; 

Analyze and categorize the fouling data: this step summarized availability of the 

data supplied by the plant and also provided assumptions made for the unavailable 

data. By analyzing the data and studying from literatures, it was believed that 

chemical A fouling behavior could be explained by crystallization/precipitation 

mechanism. 

Develop the model for chemical A: this step was to highlight the advantages of the 

Coletti and Macchietto (2010) model which was useful for this particular case, 

distinguish the difference between chemical A and crude oil fouling, which was the 

fluid that Coletti and Macchietto (2010) studied, such as the difference of fouling 

mechanism which resulted in using different fouling models. Eight fouling model 

were proposed and modified into the Coletti and Macchietto (2010) model. 

Validate the model: followed the procedure proposed by Coletti and Macchietto 

(2010) to validate the models which were performing fluid properties estimation on 

clean period, estimating fouling parameters on fouling period, and predicting the 

output temperature. The prediction results of all proposed fouling models were 

compared with the actual data given by the plant. The model in which fouling rate 

depended on a degree of supersaturation and temperature gave the best 

prediction result, within ±0.5ºC accuracy for over 75% of total plant measurements. 

Provide mitigating options: By analyzing the results from previous steps, changes 

of operating conditions due to the plant shut-downs were suspected to be a main 

cause of this fouling. Several mitigation plans were suggested for the chemical A 

plant to mitigate the problem. 

86

5.2 Future Work 

Approaching the exchanger fouling problem by modeling techniques is still an interesting 

field of study with a lot of improvement gaps. This research was intended to get better 

understanding of slurry fouling problems which generally categorized as crystallization/ 

precipitation fouling. However, most of modeling works in crystallization fouling area have 

been focused to salt solutions. Only few researchers are interested in study the deposition of 

slurry processes. So, an understanding of the behavior of slurry fouling is yet limited as well 

as the proposed models to describe its behavior. The works to be improved are summarized 

as follows; 

Study and propose crystallization fouling model for ‘Normal’ solubility solutions: 

Almost all works have been studied salt solutions which have ‘Inverse’ solubility 

characteristics which are opposite with several slurry processes in industrial plants. 

This project has been tried to apply the model which explain the ‘Inverse’ solubility 

solutions but its result still obscure. Therefore, further progressing in this area will be 

applicable for various industries, especially in petrochemical plants. 

Develop the exchanger model for two phase flows: this project assumed the slurry, 

which contains solid particles and liquid solutions, as a single phase fluid which may 

cause an inaccuracy of the model. 

Construct the heat exchanger network which considered the fouling behavior: this 

project focused only single heat exchanger. So, this can be further studied to 

construct the heat exchanger network which is essential for designing purposes. 

87

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Appendix A: 

Figure 80 and Figure 81 showed measurements and parity plots of Model 2, respectively. 

Figure 80 Measurements plot result of Model 2 


94


Figure 82 Measurement plots result of Model 3 


95


Figure 84 Measurements plot result of Model 6 


96

Figure 86 Figure 87 showed measurements and parity plots of Model 7, respectively. 

Figure 86 Measurement plot result of model 7 


97


Figure 88 Measurement plots result of model 8 

Figure 89 Parity plot result of model 8 

98

Appendix B: 

Figure 90 and Figure 91 showed the prediction and error result of Model 3, respectively. 



99




100




101

Appendix C: 

Figure 96 and Figure 97 showed 1Y-period measurements and parity plots of Model 1 

(variance 0.2 ), respectively. 

Figure 96 1Y-period estimation measurements plot of Model 1 (variance 0.2 ) 

Figure 97 1Y-period estimation parity plot of Model 1 (variance 0.2 ) 

102



Figure 98 1Y-period measurements plots of Model 2 (variance 0.2 ) 

Figure 99 1Y-period parity plot result of Model 2 (variance 0.2 ) 

103



Figure 100 1Y-period measurements plot of Model 4 (variance 0.2 ) 

Figure 101 1Y-period parity plot of Model 4 (variance 0.2) 

104



Figure 102 1Y-period measurements plot of Mode 5 (variance 0.2 ) 

Figure 103 1Y-period parity plot of Model 5 (variance 0.2 ) 

105





106





107

Figure 108 Figure 109 showed 1Y-period measurements and parity plots of Model 8 




108

Appendix D: 

Figure 110 showed 1Y-period measurements and parity plots of Model 7 (variance 0.1 ) 

Figure 110 1Y-period parity result of Model 7 (variance 0.1 ) 


Figure 111 1Y-period parity result of Model 9 (variance 0.1 ) 

109



110

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