Fouling Models for Heat Ex Changers

235

9 Fouling Models for Heat Exchangers

Sundar Balsubramanian, Virendra M. Puri, and Soojin Jun

CONTENTS

9.1 Introduction ................................................................................................... 235

9.2 Fouling Mechanism ...................................................................................... 238

9.2.1 Hydrodynamic and Thermodynamic Models ................................... 239

9.2.1.1 One-Dimensional Models ................................................... 239

9.2.1.2 Two-Dimensional Models ................................................... 243

9.2.1.3 Three-Dimensional Models ................................................245

9.2.2 Dynamic Fouling Model Incorporating

Physio-Chemical Changes ................................................................. 247

9.2.2.1 One Phase Approach ........................................................... 247

9.2.2.2 Two Phase Approach ...........................................................248

9.2.2.3 Three and Four Phase Approaches .....................................250

9.2.3 Cleaning and Economic Models .......................................................254

9.3 Concluding Remarks ..................................................................................... 257

References .............................................................................................................. 258

9.1 INTRODUCTION

One of the most critical and widely used unit operations in the food processing

of heat utilization through heat recycling and better heat transfer. During heat treat-

ment the food products undergo structural and chemical changes. Owing to changes

occurring in the food product some of the constituents like proteins and minerals

ment surface. These deposits are generally referred to as foulants and this phenom-

enon of deposition of food constituents on the equipment surface is termed fouling.

It has been documented in the literature that deposition of fouling layers on the

surface of the food processing equipment results in:

1. Increase in electrical and thermal energy usages due to the decrease in heat

2. Increase in pressure drop across the heat exchanger unit thereby lowering

the overall system performance.

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industry is thermal treatment. Heat exchangers offer an effective and efficient means

precipitate resulting in film-like deposits which adhere to the food processing equip-

transfer coefficient.

© 2009 by Taylor & Francis Group, LLC

236 Food Processing Operations Modeling: Design and Analysis

3. Additional increase in the use of electrical and thermal energies and water

usage due to the increase in the frequency and duration of cleaning opera-

tions to remove foulants.

Economically, fouling is a burden to the food industry. In the USA, the total costs

of fouling have been estimated to be $7 billion [1]. This includes the costs incurred

due to cleaning of the equipment, loss of production, additional energy consump-

tion, and over-sizing of the heat exchanger unit. The impact of fouling is so severe

that it is estimated that the total fouling costs equates to about 0.25% of the gross

national product of a developed country such as the USA [2]. In the dairy industry

alone fouling accounts for about 80% of the total operating costs involved [3]. Spe-

or redundant equipment, additional downtime for maintenance and repair, loss of

production, cleaning equipment and waste of energy [4,5]. With such a high impact

on the total operating costs, there is a need to minimize or delay the process of foul-

ing of the equipment surface thus prolonging the operation of the equipment and

conserve energy. In dairy industries it is a common practice to shut down the plate

heat exchanger (PHE) operation at least once a day in order to clean the equipment

[6]. The frequent interruptions during processing due to fouling causes extended

plant operation while lowering the desired output. Cleaning the foulants is also a

time consuming and energy intensive process that consumes a substantial amount

of water and chemicals. A typical dairy processing plant handling 75,000 gallons of

milk per day could use up to 110 million gallons of water per year [7]. Rebello et al.

[8] estimates that water (23.9%) and cleaning agents (7.5%) were the top contributors

towards the cleaning costs incurred during removal of foulants. Once the cleaning

ner further adds to the cost of production. Hence, prolonging the operation of the

equipment down-time, thus translating into increased production.

The exact mechanisms and underlying chemical reactions that result in fouling

is still not well understood. However, it has been widely believed that the denatura-

tion of the protein β-lactoglobulin plays a critical role in the fouling process during

dairy processing. The temperature and pH of the product aid in the unfolding of

the protein chain. Once the protein chains unfold, they form aggregates and get

adsorbed on the walls of the contact surface. Subsequently, calcium and phosphate

ions precipitate and add to the layers of adsorbed protein aggregates. This results

in a solid layer spread over the food equipment surface resulting in fouling. The

food processing equipment surface also plays an important role in fouling. Visser

and Jeurnink [9] have listed some of the factors pertaining to the food processing

following conditions that relate to fouling in stainless steel surfaces:

1. Presence of an additional covering layer like chromium oxide that inhibits

corrosion and oxidation of the stainless steel.

during manufacture dictate the nature of the surface charge.

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cifically, the costs incurred due to fouling includes increased cost due to oversized

heat exchanger unit by reducing the rate of fouling could be beneficial in reducing

2. Surface charge; the cleaning process and the industrial finishing conditions

process is completed, disposal of the effluents in an environmentally friendly man-

equipment surface that have an influence on the fouling process. They observed the


Fouling Models for Heat Exchangers 237

3. Surface energy or in other words, the degree of hydrophobicity.

4. Micro structure of the surface like surface roughness.

5. Presence of residual proteins, microbes, and other contaminants which

were left behind during the earlier processing operations.

6. Type of steel used.

position, location of fouling, operating condition of the heat exchanger and the type

and characteristics of the heat exchanger. While processing milk, factors such as

pH, age of the milk, protein composition, calcium ions present, pre-chilling of milk

24 hours prior to thermal processing, whether the milk is reconstituted or not, and

fouling observed [3].

Two types of fouling deposits have been documented depending on the process

temperatures during dairy processing. At lower processing temperatures (between

75°C and 105°C) the foulants are predominantly proteins [9]. These deposits, i.e.

type A, are soft and bulky [10] containing about 50–60% protein (mostly β-lac-

toglobulin in milk), 30–50% minerals (like calcium and phosphate), and about 4–8%

fat [9]. The type B fouling occurs at temperatures above 100°C and has a hard,

granular structure. These deposits comprise mostly of minerals (about 70–80%),

followed by proteins (15–20%) and fat (4–8%). Table 9.1 summarizes the fouling

deposit characteristics obtained during type A and B fouling [11]. Thus, essentially

during fouling two processes take place: calcium phosphate deposition (mineral

fouling or crystallization fouling) and protein fouling (or chemical reaction fouling).

Both these processes follow different kinetics. Fouling deposits from a range of food

products, including milk [12,13], orange juice [14] and tomato juice [15], have been

studied. In particular, fouling during milk processing has been extensively studied

TABLE 9.1Characteristics of Type A and Type B Fouling Deposit Formed During Heating of MilkDeposit Content Type A Type B

Mineral content (%) 30–40 70–80

Protein content (%) 50–70 10–20

Fat content (%) 4–8 4–8

Temperature of occurrence (°C) 75–110 > 110

Color of deposit White/cream Grey/brown

Characteristics of the deposit Soft, curd like and voluminous Hard, brittle and granular

Type of protein and minerals present β-LG, calcium, phosphate β-casein, α-S1 casein, calcium,

phosphate

Source: From Prakash, S., Datta, N., and Deeth, H.C. Methods of detecting fouling caused by heating of

milk. Food Reviews International 21, 267–93, 2005. With permission.

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Other factors that have an influence on the fouling process are the product com-

seasonal variations are some of the factors that have an influence on the extent of



owing to the importance of thermal processing in the dairy industry. There are vari-

ous factors that contribute to the fouling process during processing; similar to these

mentioned previously for milk. These include, the product composition, tempera-

ture, pH, surface geometry of the processing equipment, presence of air bubbles,

plate corrugation are some of the known critical factors that impact the fouling rate.

To develop fouling models in order to simulate and predict the fouling mechanism

useful in building reliable models that can shed light on the fouling occurring in

surface can be taken into account thus developing models that could closely analyze

model that can closely predict the fouling behaviour under various operating con-

processing conditions. Operating under the best processing conditions will ensure a

balance between safely processed foods and prolonged equipment operation (due to

less fouling). Therefore, this chapter reviews the work to date by various researchers

to develop an optimum fouling model for the fouling mechanisms that occur in heat

exchangers with particular emphasis on plate heat exchangers.

9.2 FOULING MECHANISM

ing mechanism that leads to the fouling formation on the equipment surface. There

are two main schools of thought regarding the fouling process. One thought is that

the fouling process is a bulk-controlled homogenous reaction process independent

of mass transfer or a surface reaction process [9]. The other line of thought is that

thermal boundary layer. The aggregated proteins formed then adhere to the equip-

ment surface and the deposition of the protein is proportional to the concentration

of the aggregated protein in the thermal boundary layer. Fouling models have been

derived based on these assumptions. Once the fouling takes place, the deposit layer

removal of the deposits [3].

There has been extensive research conducted on the fouling in milk process-

ing equipment. However, the exact mechanism of fouling is not fully understood.

It has been agreed upon that when milk is heated, the native protein β-Lg (β-Lac-

toglobulin) chain denatures and exposes the protein molecules containing reactive

sulphhydryl (-SH) groups. These reactive groups from the unfolded (or denatured)

protein react with similar or other milk proteins like casein and α-La (α-lactal-

bumin) to form aggregates. It is here that the fouling mechanism becomes debat-

layer and others believe that it is the aggregated proteins that are involved in form-

ing the fouling layer. Hence, researchers modeling the fouling mechanism follow

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different food equipment surfaces. With the advent of improvements in the field of

In order to model the fouling process it is imperative to first understand the underly-

able by researchers. Some believe that the denatured proteins form the first fouling

and the mixing intensity which is dependent on both the fluid flow rate and the

accurately is a challenge owing to the various factors that influence the process.

However, a thorough understanding of the chemistry and fluid mechanics are very

computational fluid dynamics (CFD) the detailed geometry of the heat exchanger

the interactions between processing surface geometry and fluid flow. An optimum

ditions like temperature, residence time, and flow rate will help in optimizing the

mass transfer takes place between the bulk fluid containing the proteins and the

is subjected to hydrodynamic forces from the moving fluids resulting in possible



different assumptions. There is literature dealing with modeling assuming that only

the aggregated proteins resulted in fouling [16] and others based on the assumption

that the aggregated proteins are not involved in the fouling process [17]. Yet another

group of researchers believe that the fouling process is due to both the denatured

and aggregated proteins [18,19]. Hence, there are various fouling models proposed

in literature pertaining to different starting assumptions. This results in the ambi-

guity of the actual fouling mechanism during thermal processing of food products.

There also have been attempts made to model the protein adsorption onto stainless

steel surfaces in conjunction with Langmuir-type adsorption isotherms. However,

this approach is disputed by some researchers who believe that the Langmuir-type

9.2.1 HYDRODYNAMIC AND THERMODYNAMIC MODELS

To completely understand the problem of fouling that occurs in heat exchangers, it is

essential to understand the relationship between fouling and the hydrodynamic and

are hence very keen in developing fouling models that can predict the performance

of heat exchangers. It has to be mentioned that most of the research activities related

to heat exchangers have been performed by engineers in auto, aerospace and chemi-

cal industries. Comparatively, fewer studies have been found in the food-processing

area. Hence, we have included some key studies in the non-food industry areas with

our current study on fouling modeling.

9.2.1.1 One-Dimensional Models

exchangers was experimentally and theoretically discussed by Rene et al. [21]. An

experimental model was developed by them that could predict the temperature pro-

This is of particular importance owing to the change in rheological and physical

properties of foods due to changes in temperature. Most studies have been limited

to numerical analysis or analytical formulation of the steady state behaviour in heat

exchangers including multi-stream or multi-channel heat exchangers. However, in

real life conditions heat exchanger systems always undergo transients resulting from

external load variations and regulations. Including the effect of transients in the pro-

The transient response of a multi-pass PHE was studied and a model based on

from shell-and-tube heat exchangers because of the phase lag at the entry and the

studies have been extended to include the phase lag effect in multi pass PHE units.

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adsorption isotherms will not be an ideal fit for biopolymers [20].

files inside each channel of the PHE. The developed model defined the calorific fac-

posed models is expected to lead to significant enhancements in the food industry.

thermodynamic flow patterns occurring within the heat exchanger. Food engineers

The thermal processing of non-Newtonian food fluids in continuous plate heat

tor which was used to estimate the calorific temperatures of the cold and hot fluids.

the axial heat dispersion in the fluid was developed [22]. This model took into con-

sideration the deviation from ideal plug flow. The fluid flows in PHEs are different

successive channels. The phase lag increases with increase in number of flow chan-

nels because of decrease in fluid velocity in the port. In multi-pass PHE this delay

further increases due to fluid mixing. Studies have analyzed single-pass PHEs with

axial dispersion in fluid taking care of the phase lag effect at the port [23]. The



passes.

Certain assumptions need to be made prior to developing a one-dimensional

model for fouling in PHEs. The following assumptions have been made during the

developments of a one dimensional fouling model [22,24,25].

plate width.

ii. Heat transfer only takes place between channels and not between channels

and ports or through the seals and gaskets.

sure and temperature.

v. The loss of heat to the environment is negligible. Negligible radiation heat

losses are encountered.

of solid plate Figure 9.1, the energy balance over these control volumes taking into

tions related to the channel and plate [26]:

g CpTt

vTx

U Ti i ii

ii

i iρ ∂∂

∂∂c c

c cp+

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟= −( ( 11 2) )+ −T Ti ip c (9.1)

Channel

i–1

Channel

iChannel

i+1

vi

Tci

Plate

iPlate

i–1T

pi

Fluid control

volume

x

Δx

FIGURE 9.1

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The developed algorithms also took into consideration the mixing of fluids between

i. The flow rate and temperature profiles are uniform across the channel and

iii. The thermal and physical properties of the fluids are not dependent on pres-

iv. Each fluid is split equally between all related channels. In other words, the

same volume of fluid flows across each channel meant for that particular

fluid type.

vi. The flow cross-sectional area of each channel is the same.

vii. There is uniform flow distribution within each channel giving a ‘plug flow’

of fluid inside each channel.

Considering a small control volume of fluid inside the channel and a control volume

account the above mentioned assumptions gives rise to the following fluid flow equa-

One dimensional view of control volume of fluid inside the PHE channel.



δ ρ ∂∂p p p

pc c pi i i

ii i iCp

T

tU T T T

⎡

⎣⎢⎢

⎤

⎦⎥⎥= + −+( ( )1 2 ii ) (9.2)

cith channel formed

between plate i and i + 1; Tpi = temperature of ithci

th channel; Cppi

in ithci

thpi

th plate; gi = gap

between plates i and i + 1; δpi = thickness of ith plate; Ui = overall heat transfer coef-th

The above Equations (9.1) and (9.2) were derived based on the fundamental

energy conservation law and describe the energy transfer between a channel and its

Neighboring plates.

less numbers such as Nusselt number (Nu), Reynolds number (Re) and the Prandtl

number (Pr). The Re and Pr numbers are related to the Nu number by the following

Equation [27,28];

Nu 0.214 (Re 3.2)Pr0.662 0.4= − (9.3)

where the Re and Pr numbers can be derived from the following relationships;

Re , ,= = =ρ

μvD p

kgi

eePr

CD

μ2 (9.4)

e

lated using the relation,

Nue=

hDk

(9.5)

T

1 1 1

U h h k= + +

hot cold

p

p

δ (9.6)

where hhot cold = con-

p

vity of the plate.

Another dimensionless quantity of major importance during fouling modeling

is the Biot number. Due to the deposition of foulants on the heat exchanger surface,

the heat transfer rate changes. The rate of deposition of the foulants is related to the

concentration of the aggregated proteins present in the thermal boundary layer (CA* ).

The Biot number is used to express the rate of change of heat transfer due to fouling

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plate; Cp = specific heat at con-

ficient in the i

The overall heat transfer coefficient (U) can be calculated using the dimension-

From the Nu number, the convective heat transfer coefficient (h) can be calcu-

he overall heat transfer coefficient (U) can now be calculated by;

where t = time; x = axial position; T = temperature of fluid in i

stant pressure of fluid in i = specific heat at constant pressure of fluid

plate; ρ = fluid density in i channel; ρ = fluid density in i

channel; v = average fluid velocity which can be positive or negative

depending upon the direction of flow.

where k = thermal conductivity of the fluid; h = convective heat transfer coefficient;

μ = viscosity of the fluid; and D = equivalent diameter.

= convective heat transfer coefficient of the hot fluid stream; hvective heat transfer coefficient of the cold fluid stream; and k = thermal conducti-



and is related to the rate of deposition of the aggregated proteins by the following

expression [26]:

∂∂

β ∗Bim A

tk C= (9.7)

e m A∗

centration of aggregated protein in the thermal boundary layer.

under fouling condition, Uf, are related by the Equation

UU

fBi

=+

0

1 (9.8)

e 0

are considered to be important in the design of heat exchangers by engineers. A foul-

ing model which is able to predict the fouling thickness, Biot number and bulk milk

temperature in relation to time and position within a triple tube heat exchanger has

been proposed and demonstrated to be effective [29]. This model could be extended

for other heat exchangers.

and to the terminal block. Thus, the equations for these two channels for a PHE

having N plates can be written as follows [30]:

g CpTt

vTx

U T T1 1 11 1

1 1 1ρ ∂∂

∂∂c

c cp c+

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟= −( )) ( )+ −∞ ∞U T Tc1 (9.9)

g CpTt

vTx

U TN N cNN N

N Nρ ∂∂

∂∂

c cp+

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟= −( ( )1 −− + −∞ ∞T U T TN Nc c) ( ) (9.10)

1 1 1

U h h k∞= + +

hot cold

b

b

δ (9.11)

where kb = thermal conductivity of the front and back terminal blocks of the PHE;

δb = thickness of the front and back terminal blocks of the PHE; and T∞ = ambient

temperature.

One of the useful measurements used for modeling of fouling which helps to

drop. The drawback of using one-dimensional hydrodynamic model for modeling

the performance of PHE during fouling is that this model cannot be used to estimate

vide an estimate of the milk temperature along the plate height. The estimated tem-

perature distributions of the product at various locations along the height of the plate

provided curvatures in the isotherms. The results obtained from this model fueled

interest in the development of two-dimensional and three-dimensional models for

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wh re Bi = Biot number; β = constant; k = mass transfer coefficient; and C = con-

It can be shown that the Biot number and the overall heat transfer coefficient

wh re, U is the heat transfer coefficient under no fouling conditions. Biot numbers

characterize the geometrical changes in the corrugated plate profiles is the pressure

A quadratic temperature profile model has been developed [31] that could pro-

The first and last channel in a PHE transfers heat to one adjacent fluid channel

the pressure drop varying across the PHE because of over simplified flow streams.



studying the hydrodynamic performance of heat exchangers. Models have also been

developed to estimate the temperature in each channel in the PHE [28]. These empir-

ical models were based on the steady state simulation of PHEs. Simulation results

from these models show an average deviation of about 4.9% from actual experimen-

tal results when the outlet temperatures were compared.

9.2.1.2 Two-Dimensional Models

The equations obtained for one-dimensional models can be expanded to form

directions. In order to compute the two-dimensional models incorporating the veloc-

be solved. The assumptions made in the case of two-dimensional modeling are that

by Kays [32] include the continuity and momentum equations as given below:

Continuity equation: ∂∂

∂∂

ux

vy

+ = 0 (9.12)

x-momentum: ∂∂

∂∂

∂∂ ρ

∂∂

ϑ ∂∂

∂∂

ut

uux

vuy

Px

ux

uy

+ + = − + +⎡

⎣⎢⎢

1 2

2

2

2

⎤⎤

⎦⎥⎥ (9.13)

y-momentum: ∂∂

∂∂

∂∂ ρ

∂∂

ϑ ∂∂

∂∂

vt

uvx

vvy

Py

vx

vy

+ + = − + +⎡

⎣⎢⎢

1 2

2

2

2

⎤⎤

⎦⎥⎥ (9.14)

where ϑ = kinematic viscosity; ρ = density; P = pressure; t = time; u = velocity

component in the x direction; and v = velocity component in the y direction.

noted by Ozisik [33] which is essentially an extension of Equation 9.1 and Equation

9.2 are given as follows:

g CpTt

uTx

vTy

i i ii

ii

iiρ ∂

∂∂∂

∂∂c c

c c c+ +⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟= + −−U T T Ti i i i( )( )p p c1 2 (9.15)

δ ρ ∂∂p p p

pc c pi i i

ii i iCp

T

tU T T T

⎡

⎣⎢⎢

⎤

⎦⎥⎥= + −+( ( )1 2 ii ) (9.16)

involved than solving one-dimensional model equations. To simplify the proc-

the momentum equations. A vorticity-stream function approach applicable to

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and plate, respectively, and have been defined previously.

two-dimensional models by considering the velocity vectors of the flow in x and y

ity and pressure distribution of the flow, the Navier–Stokes (N–S) equations have to

the plate surface is flat and smooth. The two-dimensional N–S flow equation given

The transient energy equation for a two dimensional incompressible flow as

where subscripts i, i + 1, i − 1, c and p refer to the plate i, plate i + 1, plate i − 1, fluid

The solving of the flow equations for the two-dimensional model is much more

ess of solving two-dimensional model flow equations, it is essential to transform

the flow equations into a simpler form by eliminating the pressure terms between



ity vector and streamline functions for a two-dimensional Cartesian coordinate

simpler form.

The vorticity vector is given by:

ω ∂∂

∂∂

= −vx

uy

(9.17)

and the streamline function (ψ) for the velocity vectors, u and v is given by:

∂ψ∂

∂ψ∂y

ux

v= = −, (9.18)

From Equation 9.17 and Equation 9.18, the vorticity vector can be transformed into

the following relationship

∂ ψ∂

∂ ψ∂

ω2

2

2

2x y+ = − (9.19)

From t

to the continuity equation (Equation 9.12). Transformation of the dependent vari-

ables from ‘u, v’ to ‘ω, ψ’ is applied to Equation 9.13 and Equation 9.14 to obtain a

relationship for the vorticity (ω) upon elimination of the pressure term. This trans-

formation leads to the following relationship:

∂ω∂

∂ω∂

∂ω∂

ϑ ∂ ω∂

∂ ω∂t

ux

vy x y

+ + = +⎡

⎣⎢⎢

⎤

⎦⎥⎥

2

2

2

2 (9.20)

One can obtain a differential equation for the pressure term from the momentum

equations. The pressure term can be shown to be a function of the velocity vectors

and the density by the following relation:

∂∂

∂∂

ρ ∂∂

∂∂

∂∂

∂∂

2

2

2

22

Px

Py

ux

vy

uy

vx

+ = −⎡

⎣⎢⎢

⎤

⎦⎥⎥ (9.21)

Reducing this equation by including the streamline function (ψ) the differential

equation for the pressure term can be given by:

∂∂

∂∂

ρ ∂∂

∂∂

2

2

2

2

2

2

2

22

Px

Py x y

+ =⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎛

⎝⎜ψ ψ⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟−

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

∂∂ ∂

2 2

ψx y

(9.22)

s

mined if the stream line function is known. Jun et al. [30] have noted that by using

the one-dimensional model for predicting the temperatures at various zones on the

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two-dimensional modeling is usually used [33]. This approach defines the vortic-

he streamline function definition it is obvious that the relationship is identical

U ing finite-difference approximation and Gauss-Seidel iterative solver, the pres-

system and use these terms to transform the two-dimensional flow equations to a

sure distribution at various locations on a grid for the entire flow field can be deter-



plate large prediction errors (up to 43.2%) were observed. With the use of the two-

dimensional model they observed good agreement of the predicted temperatures

with the experimental temperatures. The average percentage deviation between the

predicted and measured temperature values observed by them was about 6.2%. Since

etry the error observed during prediction could be due to the fact that the actual plate

two-dimensional model was superior in predicting the temperatures across the plate

surface when compared to the one-dimensional model, an interesting fact observed

by the authors [30] was that both the models performed identical while estimat-

tures at various locations on the plate surface fairly accurately the two-dimensional

model could be used as an effective tool to gain information on possible milk fouling

sites. The one dimensional model lacks this potential when compared with the two-

dimensional model. Hence, the two-dimensional model is better suited for studies on

fouling behavior and control than the one-dimensional model.

Regarding the pressure drop, there are various components which contribute

toward the drop in pressure observed in a heat exchanger. Drop in pressure due

are the major contributing components for the pressure drop observed in a heat

exchanger [34]. Out of these factors the pressure drop due to friction is the largest

contributor. This term can be calculated using the relation:

ΔPfm L

D=

4

2

2

ρ h

(9.23)

area; L = plate length; and Dh = hydraulic diameter, which is usually twice the plate

spacing.

The value for the friction factor for a Chevron plate which is the common type

of plate design used in plate heat exchangers in the food processing area can be

obtained from the correlations given by Shah and Focke [35]:

f x y= −Re (9.24)

The values for x and y can be obtained from the published literature [35].

9.2.1.3 Three-Dimensional Models

The use of three-dimensional models to study the fouling behavior in PHE was aided

with the advent of advanced computer software packages. Numerical simulations of

Patankar [37] called the Semi-Implicit Method for Pressure-Linked Equation Revised

(SIMPLER) algorithm was used to numerically solve the governing equations for

continuity, momentum and energy iteratively. The results of the study showed the

55534_C009.indd 24555534_C009.indd 245 10/22/08 10:14:05 AM10/22/08 10:14:05 AM

Chevron plates was first reported in the late 1990s [36]. An algorithm proposed by

the two-dimensional model was based on the assumption of a flat plate surface geom-

geometry was not flat and had a corrugated surface geometry. The plate corrugations

guide the fluid flow to distribute evenly across the whole plate area. Though the

ing the average energy balance of mass flow. By being able to predict the tempera-

to friction, changes in velocity, changes in direction of flow and changes in height

where ΔP = pressure drop; f = friction factor; m = mass flow rate per cross sectional

the turbulent, three-dimensional fluid and heat transfer flow between two parallel



only one channel to study the fouling behaviour will not give a true picture of the

actual fouling process that occurs in multi-channel and multi-pass PHE systems.

of milk between two corrugated plates was studied by Grijspeerdt et al. [38] using

CFD (Computational Fluid Dynamics). The three-dimensional calculations showed

culations. This clearly showed the limitations of two-dimensional calculations for

temperature regions. These regions of elevated temperatures are potential fouling

locations on the plate surface. Eliminating such occurrence is essential to minimiz-

models have immense potential in optimizing the design of plates for heat exchang-

ers. So far the CFD based studies on fouling behavior have been concentrated towards

cal and chemical aspects into three-dimensional model studies of fouling behavior

for various food products will go a long way in better understanding the process of

fouling, and thus, help in better design of control strategies to minimize fouling. For

this, the denaturation of β-LG and its relation to wall adhesion needs to be critically

examined and incorporated in the three-dimensional model. This is in fact not an

easy task and adds to the complexity of three-dimensional model calculations.

the continuity and momentum equations by extending the two-dimensional model

which was described in detail earlier.

∂∂

∂∂

∂∂

ux

vy

wz

+ + = 0 (9.25)

The equations for the momentum in the x, y and z directions are now described by

the following Equations:

x-momentum: ∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

ut

uux

vuy

wuz

Px

ux

u+ + + = − + +

1 2

2

2

ρϑ

yyu

z2

2

2+

⎡

⎣⎢⎢

⎤

⎦⎥⎥

∂∂

(9.26)

y-momentum: ∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

vt

uvx

vvy

wvz

Py

vx

v+ + + = − + +

1 2

2

2

ρϑ

yyv

z2

2

2+

⎡

⎣⎢⎢

⎤

⎦⎥⎥

∂∂

(9.27)

z-momentum: ∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

wt

uwx

vwy

wwz

Pz

wx

w+ + + = − + +

1 2

2

2

ρϑ

yyw

z2

2

2+

⎡

⎣⎢⎢

⎤

⎦⎥⎥

∂∂

(9.28)

wh

55534_C009.indd 24655534_C009.indd 246 10/22/08 10:14:06 AM10/22/08 10:14:06 AM

potential of using finite element analysis to have a better understanding of the foul-

designing new plate configurations that could reduce fouling. The three-dimensional

ing fouling and that could be done by better plate configuration design. Thus CFD

The continuity equation in this case is defined by

ing phenomenon occurring between a flow channel. However, the results from using

A detailed two-dimensional and three-dimensional study on the flow pattern

the virtual flow velocity fields which were not possible using two-dimensional cal-

calculations help to identify regions of turbulent backflows that could cause elevated

the thermodynamic and hydrodynamic aspects of fluid flow. Incorporating the physi-

The flow equations describing the three-dimensional model can be derived from

ere w is the velocity component of the flow in the z direction.



be written as [39]:

∂∂

∂∂

∂∂

∂∂ ρ

∂∂

∂∂

∂Tt

uTx

vTy

wTz

kC

Tx

Ty

+ + + = + +p

2

2

2

2

2TTz∂ 2

⎡

⎣⎢⎢

⎤

⎦⎥⎥ (9.29)

stituting the thermal diffusivity term α = k/ρCp. The thermal diffusivity is the ratio

of the thermal conductivity to the volumetric heat capacity of a substance. Hence, the

Equation can now be written as

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

Tt

uTx

vTy

wTz

Tx

Ty

Tz

+ + + = + +α2

2

2

2

2

22

⎡

⎣⎢⎢

⎤

⎦⎥⎥ (9.30)

Using the above three-dimensional model and coupling it with a CFD software

package FLUENT (Fluent Inc., NH, USA), Jun and Puri [39] studied the fouling

behavior in a PHE system. The three-dimensional model incorporated the surface

This gives the three-dimensional model an advantage over the two-dimensional

model in which a detailed study of the fouling behavior on the PHE surface can be

carried out. Results from the three-dimensional study can be utilized for designing

with a two-dimensional model.

9.2.2 DYNAMIC FOULING MODEL INCORPORATING PHYSIO-CHEMICAL CHANGES

The dynamic fouling model was developed based on the fact that fouling is essen-

tially a transient process. In the beginning the heat exchanger starts clean and slowly

with change in time the foulants build-up in the equipment. With this in mind the

dynamic fouling model was approached under various phases of fouling. Some of

the models just took into account the protein denaturation occurring, while others

took into account the induction period also.

9.2.2.1 One Phase Approach

As discussed earlier, to obtain a comprehensive model that includes the hydrody-

namic and thermodynamic factors of fouling with the physical and chemical con-

tributing factors of fouling it is imperative to understand the protein denaturation

process. The dynamic fouling models study the denaturation of β-LG and its rela-

tionship to the fouling observed.

of 13 plates. They developed a model that can predict the amount of native β-LG at

the outlet of the PHE. The model was tested by simulating the amount of denatured

proteins which was determined based on the steady state conditions and the numeri-

denatured β-LG was then compared with the actual amount obtained from experi-

ments through measurements using immunodiffusion methods. From the developed

55534_C009.indd 24755534_C009.indd 247 10/22/08 10:14:07 AM10/22/08 10:14:07 AM

configuration of the PHE which was not possible with the two-dimensional model.

new surface configurations that can help in minimizing fouling. This is not possible

cal determination of temperature profile for each channel. The simulated quantity of

For a three-dimensional incompressible flow the transient energy equation can

where T is the temperature of the fluid. The above Equation can be simplified by sub-

Delplace et al. [40] studied the complex flow arrangements in a PHE consisting



model they could predict the native β-LG at the outlet of the PHE with an experi-

mental error of less than 10%.

The model for predicting the β-LG was given by

C tCkC t

( ) =+

0

01 (9.31)

For T ≤ 363.15 K, log k = 37.95 – 14.51 (103/T).

For T ≥ 363.15 K, log k = 5.98 – 2.86 (103/T).

where C is the β-LG concentration, C0 is the initial β-LG concentration, k is the sec-

ond order rate constant, t is the time, and T is the temperature. Similar models have

been developed to predict the amount of dry mass deposited based on the steady

of β-LG protein [6,40]. Some of these models were found to be suitable for online

applications.

9.2.2.2 Two Phase Approach

The two phase approach was based on the observation that there may be an induction

phase prior to the actual fouling phase. During the induction period the conditions

the fouling period begins resulting in increased pressure drop and decreased heat

ing period consists of a deposition and removal process. The difference between the

rates of deposition and removal of deposits constitutes a simple model that explains

the rate of build up of deposit on a surface.

d

dD R

mt

= −θ θ (9.32)

e D R

area for the deposition and removal periods. This simple model forms the basis of the

local fouling factor model. Fryer and Slater [41] have suggested a generalized equa-

tion for the fouling deposition process based on the above Equation 9.32:

dBi

de Bid r

fi

tk k

E

R T= −−⎡

⎣⎢⎢

⎤

⎦⎥⎥

1

(9.33)

where kd and kr are, respectively, the rate constants for the deposition and removal

expressed in s − 1. Tfi is the temperature (oC) at the interface of the fouling deposit and

priately to include various factors relevant to fouling such as chemical reaction,

relation result in linear (constant rate), falling rate or asymptotic fouling growth

55534_C009.indd 24855534_C009.indd 248 10/22/08 10:14:08 AM10/22/08 10:14:08 AM

state conditions, predicted temperature profiles and the amount of heat denaturation

of pressure and temperature do not change significantly. These later change when

transfer coefficients. Most models developed deal with the fouling period. The foul-

The general equation described above (Equation 9.32) can be modified appro-

wh re m is the mass deposited, θ and θ are the mass flow rates per unit surface

the process fluid.

mass transfer, fluid shear, and bond resistance. The models developed using this



models (Figure 9.2). The falling rate and constant rate fouling phenomenon is mostly

observed in food processing applications [42]. Constant rate fouling leads to rapid

of calcium sulfate scale deposition on heat transfer surfaces a falling rate of fouling

locations of the heated surface which was determined numerically, the CaSO4 scale

formation rate was not uniform. The assumption made in this study was that there

was no removal of scaling occurring. However, models for CaSO4 fouling including

the removal term have been developed earlier [46]. This model took into account

the rate of particulate fouling, rate of crystallization and the rate of removal of the

deposits. The rates of crystallization and particulate fouling together constitute the

rate of deposition of CaSO4 on the heated surface. The particulate fouling term was

determined taking into account the physical mechanism for particle transport and

adherence. The crystallization term was estimated based upon the ionic diffusion

deposit properties. This model also took into account both linear and asymptotic

fouling conditions.́

In general, two phenomena occur during fouling; heterogeneous nucleation and

crystal growth. Heterogeneous nucleation refers to the nuclei formation on any for-

eign body, just as in the case of heat exchanger surface. The heterogeneous nuclea-

tion can be calculated using the term [44]:

H BNV

R T SN = −

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟

’exp(ln )

16

3

2 3

3 3 2

π σm

i

(9.34)

where B′ is the pre-exponential factor, N is the Avagadro’s number, Vm is the molar

i

solid–liquid interface temperature, and S is the supersaturation. A low energy sur-

face (having high contact angle) will require higher supersaturation for nucleation to

cation techniques like those that use coatings to alter the surface roughness can help

Induction

period

Fouling

period

Linear fouling

Falling rate fouling

Asymptotic fouling

Time

Fouling

resistance

FIGURE 9.2 Fouling curves.

55534_C009.indd 24955534_C009.indd 249 10/22/08 10:14:09 AM10/22/08 10:14:09 AM

decrease in the heat transfer coefficient. This leads to rapid increase in pressure

volume, σ is the specific interfacial energy, R is the universal gas constant, T is the

occur than for a surface with high energy (having low contact angle). Surface modifi-

drop and blockage of the passage of fluid flow due to the foulants [43]. In the study

growth model was observed [44,45]. Owing to the non-uniform heat flux at various

and the removal term was estimated based upon the hydrodynamics of flow and



in delaying the nucleation occurrence by altering the surface energy [47]. The super-

saturation can be expressed as the ratio of the bulk concentration (cb) to the saturation

concentration (cs). The cs value is calculated from the solubility curve for the particular

the Ti value.

Once the nucleation occurs, the crystallization begins and the fouling layers

begin to form. There are various models that explain crystal growth. For example in

the absence of any removal term, the rate of deposit growth on a heat transfer surface

due to crystallization can be expressed as [48]:

d

d r

b s

r

mt k

c ck

=⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟⎟+ − −

⎛

⎝⎜⎜⎜

⎞

⎠β β β1

2

1

4( ) ⎟⎟⎟⎟⎟ +

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟⎟ −

⎧⎨⎪⎪

⎩⎪⎪

⎫⎬⎪⎪

⎭⎪⎪

⎡ 2βk

c cr

b s( )

⎣⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥ (9.35)

T r

from the Sherwood number,

Sh Sch= +

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟0 023 1

60 8 0 33. Re . . dx

(9.36)

where Sc is the Schmidt number and dh is the hydraulic diameter at position x. The

Sherwood number is given by:

Shh=

βαd

where α is the thermal diffusivity of the ions.

9.2.2.3 Three and Four Phase Approaches

The above discussed models deal with bulk-controlled homogeneous reaction proc-

esses. In contrast, the three and four phase model deals with surface reaction proc-

ess. This model deals with the varying protein characteristics during denaturation;

native, unfolded, aggregated, and deposited [9]. Usually the three and four phase

approaches go hand-in-hand, because once the protein aggregates are formed, the

fourth phase, i.e. the attachment of the aggregated protein to the contact surface

occurs. A mathematical fouling model where both the surface and bulk reactions

are considered has been proposed in the 1990s [49]. The foundation of this model

was the consideration of the denaturation of β-LG protein as a series of consecutive

reaction kinetics involving unfolding and aggregation. The model can be stated as

follows:

N ↔ U → A (9.37)

The terms N, U and A stand for the native, unfolded and aggregated β-LG protein,

respectively. It can be seen that from the model there is some unfolded protein being

converted back into the native state.

55534_C009.indd 25055534_C009.indd 250 10/22/08 10:14:10 AM10/22/08 10:14:10 AM

salt followed by curve-fitting techniques to obtain a standard equation in relation to

he term k is the rate constant, and the mass transfer coefficient β can be obtained



The rate of disappearance and formation of these protein phases are given by the

relation [18,19]:

− = −d

d

NU N

aN U

bCt

k C k C (9.38)

d

d

UU N

aN U

bA U

cCt

k C k C k C= − − (9.39)

d

d

AA U

cCt

k C= (9.40)

e

reaction. The orders of the reaction vary according to the assumptions made and

the process condition like temperature of denaturation, and also the product being

processed [19,50]. Hence, the values of the orders of the reaction (a, b, c) are not

always the same. For example; Chen et al. [19] considered the orders of the reaction

values of a, b, and c to be respectively, 1, 0, and 2.

If the β-LG protein denaturation process is modeled considering the entire proc-

ess to be irreversible, i.e. no unfolded protein is converted back into its native state,

then Equation 9.36 can be written as:

N → U → A (9.41)

This approach means that all of the native proteins get unfolded and immediately

get converted to its aggregated state. The rate of disappearance and formation of the

different protein states can then be written as:

− =d

d

NU N

aCt

k C (9.42)

d

d

UU N

aA U

cCt

k C k C= − (9.43)

d

d

AA U

cCt

k C= (9.44)

The main mechanism in the fouling process of skim milk is a reaction-controlled

adsorption of the unfolded β-LG protein [39]:

F k CR D U= 1 2. (9.45)

where FR is the fouling rate and D is the deposited β-LG protein. The rate constants

are denoted by kU, kN, kA and kD, and are dependent on the temperature, T as given

by the Arrhenius law:

k An n

E

RTn

=−

e (9.46)

55534_C009.indd 25155534_C009.indd 251 10/22/08 10:14:11 AM10/22/08 10:14:11 AM

wh re C is the protein concentration. The suffix a, b, c, pertain to the orders of the

to be a = 1, b = 1, and c = 2. Jun and Puri [39] have described a simplified model with



where An is the Arrhenius constant, and E is the activation energy for n = U, N, A,

and D and R is the universal gas constant.

Attempts have been made to use the developed models for protein denatur-

ation in conjunction with a process model and cost predictive model to optimize

the process of PHE operation in relation to the desired product quality and safety

[51,52]. It is interesting to note that Grijspeerdt et al. [53] mention that the aggregated

reacted with the milk constituents (M) to form aggregated milk constituents (D).

These aggregated milk constituents were later adsorbed to the heat exchanger wall

(D*) causing fouling. Their reaction scheme was as follows:

N → U (9.47)

2U → A (9.48)

U D DM+⎯→⎯ → ∗ (9.49)

It should be mentioned that the models studied by de Jong [10,51,52] mainly dealt

with the fouling caused by β-LG. Fouling can also be caused by the precipitation

of minerals. The mechanics and nature of mineral fouling is different from that of

protein fouling. The underlying mechanism of mineral fouling is more complex than

protein fouling and this could be the reason of why this phenomenon has been least

studied in detail. Other probable reasons for this phenomenon of fouling getting

lesser attention than protein fouling is that the mineral foulants being less volumi-

nous in occurrence than protein fouling could have a lesser impact on the pressure

layer is known to be proteinaceous in nature. In milk calcium phosphate is the major

mineral component which constitutes the mineral deposits in the fouling process.

Calcium phosphate fouling predominantly occurs at higher temperatures (tempera-

tures greater than 100oC) than protein fouling and the reason of this occurrence

is because calcium phosphate is less soluble at higher temperatures resulting in its

precipitation. The fouling caused by calcium phosphate involves the competition

between different types of reactions involving calcium phosphate, the contact sur-

actual mechanism of calcium phosphate fouling is complex to understand and has

not been fully understood, Visser and Jeurnink [9] have postulated a possible path-

way for the fouling mechanism. According to them, as a pre-cursor to the fouling

phate complex. This complex is transformed to amorphous calcium phosphate (ACP)

and is subsequently converted to hydroxyapatite (HAP) after going through another

phase change, which involves the formation of octa-calcium phosphate (OCP). The

phosphate fouling and is accompanied by an increase in solution turbidity, indicating

that this process might be taking place in the bulk liquid. Due to the formation of

insoluble calcium phosphate this process is generally accompanied by a decrease in

pH [56]. This explains the complex nature of the mineral fouling mechanism.

55534_C009.indd 25255534_C009.indd 252 10/22/08 10:14:12 AM10/22/08 10:14:12 AM

β-LG played a less significant role in the fouling process, while the unfolded β-LG

drop and thermal resistance encountered during the fouling process. Also, the first

phenomenon, the calcium and phosphate ions first form a colloidal calcium phos-

final product formed, namely HAP is the thermodynamically stable form of calcium

face, the solvent and any other solute present in the fluid system [54,55]. Though the



The model proposed by Petermeier et al. [57] follows a slightly different pathway

than the model proposed by de Jong (Equations 9.46 through 9.48) [51,52]. Accord-

ing to their model the pathway for β-LG denaturation is given by:

− =d

d

NU N

Ct

k C (9.50)

d

d

UU N A U D U

Ct

k C k C k C= − −2 (9.51)

d

d

AA U

Ct

k C= 2 (9.52)

d

d

DD U

Ct

k C= (9.53)

The above pathway for protein denaturation and deposit formation indicates that

some of the unfolded β-LG protein gets lost due to the deposition process (Equa-

tion 9.50).

A more comprehensive model has been developed that takes into account the

assumption that for each protein present, mass transfer takes place between the bulk

and thermal boundary layer [58]. But it is the aggregated proteins that can adhere to

the wall in such a way that the amount of deposit is proportional to the concentra-

tion of aggregated protein in the thermal boundary layer. Figure 9.3 and Figure 9.4

this model is an extension of the models proposed by de Jong et al. [51]. The key

assumptions followed while developing this model are as follows:

are then transformed by a second order reaction to form aggregated proteins.

ii. For each protein present whether it is N, U, or A, mass transfer takes place

between the bulk and thermal boundary layer.

iii. Only the aggregated protein is deposited on the wall.

iv. The thickness of the deposit dictates the magnitude of the fouling resis-

tance to heat transfer.

A major difference between the models proposed by de Jong [51] and Toyoda and

Fryer [58] is that in the former case the main mechanism of fouling was believed to

be due to the reaction-controlled adsorption of unfolded β-LG; while in the latter

case the fouling deposit on the walls was assumed to be only due to the aggregated

proteins. Most of the models proposed have been validated with experimental data.

tions and relationships between minerals and denaturation of milk proteins. Such

a model will be more suitable for real world conditions. However, to date due to

the complexity of forming a model that can relate to all the fundamental reactions

55534_C009.indd 25355534_C009.indd 253 10/22/08 10:14:13 AM10/22/08 10:14:13 AM

Unfolded proteins are formed by a first order reaction from native proteins and

It would be beneficial to have a comprehensive model that can encompass the reac-

schematically represent the flow and reaction model dynamics proposed. Basically

i. Proteins react in both the bulk and thermal boundary layer in fluid milk.



that give rise to fouling, it is not possible to point out which fouling model is more

suitable for real world conditions from the impressive array of proposed models.

Also, it is imperative to channel the collective knowledge and wealth of information

available from past research experiences to dwell upon a threshold value of mineral

amount that will accelerate the fouling process and how controlling the bulk tem-

perature can control this mineral precipitation.

9.2.3 CLEANING AND ECONOMIC MODELS

Cleaning of the fouled deposits has been a major concern for food processors as

Channel i

Plate

i–1

Plate

i

y

Δx

Height

Width

y

x

FIGURE 9.3

N* U*

UN A

A*

Reaction

Mass transfer

Adhesion

Thermal

boundary

layer

Wall

FIGURE 9.4 Protein reaction scheme for milk fouling. (From Georgiadis, M.C., and

Macchietto, S. Dynamic modelling and simulation of plate heat exchangers under milk

fouling. Chemical Engineering Science 55, 1605–19, 2000. With permission.)

55534_C009.indd 25455534_C009.indd 254 10/22/08 10:14:14 AM10/22/08 10:14:14 AM

Two-dimensional view of control volume of fluid inside the PHE channel.

Bulk fluid

it dictates the amount of resources and time spent, not to mention the influence



on product quality and safety. Hence, it is natural that the cleaning process has

been studied in detail and various models been proposed. During fouling both

organic and mineral deposits are formed. The deposits formed depend on the prod-

uct processed and the processing conditions. Altering the composition of the liquid

observed. The aim of an appropriate cleaning model developed is to optimize the

cleaning agent and the other cleaning parameters. An important parameter that

needs to be studied to develop a cleaning model is the strength of adhesion of

the foulants with the food processing surface or in other terms the force required

to dislodge the foulants from the food processing surface. This parameter is not

known directly and needs to be determined by other methods. For instance it has

been shown that altering the surface energy of a surface alters the adhesive force

between the foulants and the surface. This is one of the key components in the

design of frictionless coating materials to reduce fouling. Some researchers have

focussed on the sticking probability [64,65] to ascertain the force required to

remove the deposits. Though the sticking probability helps in providing informa-

tion about the probability of a surface being fouled, it can also provide information

regarding the amount of force required to dislodge a particle from the surface. A

study conducted on the adhesive strength while baking tomato paste in an oven at

100oC and the baking time [15]. The study revealed that the adhesive strength of

the tomato starches increased with baking time, but the increase became less sig-

hydration time. It was found that the adhesive strength of tomato starch decreased

by a factor of three initially, and then became constant. The results of the study

show that a larger amount of the tomato foulants can be removed at the initial

chemical concentration. Similar studies on the removal of milk proteins revealed

that the deposits could not be removed completely with water alone. Chemical

proteins decreased with time. Also, the order of use of the acid and base chemicals

ies clearly show that the cleaning models need to be developed keeping in mind

the type of food product processed and the other cleaning parameters involved.

The foulants adhering to the food processing surface are attached by cohesive and

adhesive forces. Studies on the adhesive and cohesive forces will reveal the appro-

priate cleaning model or cleaning protocol to be developed. Various studies have

been conducted on the adhesive and cohesive forces encountered during fouling

to develop appropriate cleaning models [67,68]. The adhesive forces are related to

the foulant and surface interaction and the cohesive strength relate to the particle

and particle interaction. Deposits of tomato paste, bread dough and egg albumin

have less adhesive strengths than cohesive strengths causing them to be removed

in larger chunks from the attached surface. On the other hand, deposits like milk

proteins have more adhesive strengths than cohesive, resulting in their removal in

smaller chunks [67].

55534_C009.indd 25555534_C009.indd 255 10/22/08 10:14:15 AM10/22/08 10:14:15 AM

nificant after 3 h. The same study also focussed on the adhesive strength versus the

food material being processed has a significant influence in the fouling profiles

time involved with reference to the flow velocity, chemical concentration of the

stages of cleaning. This could be the time to decrease the flow rates and cleaning

concentration, flow rates of the cleaning solutions and temperature had a major

influence on the removal of the milk proteins. The force needed to remove the milk

during cleaning had an influence on the milk foulants removal [66]. These stud-



The minimum adhesive energy between the surface and the deposits can be

expressed in terms of the surface energy by the relationship [69]:

γ γ γsurfaceLW

foulantLW

fluidLW=

⎡

⎣⎢⎢

⎤

⎦⎥⎥

+⎡⎣⎢

1

2

⎤⎤⎦⎥ (9.54)

where γ γ γsurfaceLW

foulantLW

fluidLW, , are the Lifshitz van der Waals (LW) surface free energies

the surface free energy of the food contact surface can be reduced, this in turn will

reduce the adhesive forces between the surface and the foulant, thus making it easier

to remove the foulant attached to the surface.

A simple model for the removal of the calcium sulfhate deposits [46] is given by:

Wx

Sremovaldeposit

d

∝∇

(9.55)

where Wremoval = rate of removal of deposits; ∇ = shear stress in N/m2; Sd = strength

of deposit and xdeposit = deposit thickness (m).

The rate of removal of the deposit is time-dependent as the thickness of the

deposit formed and the strength of the deposit vary over time. This relationship does

not take into consideration the cleaning chemicals. A relationship has been proposed

for the adhesive strength per unit area, σadhesive and the deposit thickness [70]. This

relationship indicates that σadhesive increases with deposit thickness.

σ ω ψadhesive s v depositx= + (9.56)

where ωs = work needed to overcome surface bonds; and ψv = force required per unit

volume to overcome the deposit–deposit bonds.

This simple model however, is suited for low surface energies (about 28 mNm–1).

At higher surface energies this model is not as effective indicating that at higher sur-

face energies a different method of breakdown of the deposits could be possible.

A model incorporating the concentration of the chemicals for cleaning was pro-

posed as early as 1957 [71,72]. It is prudent to develop models incorporating the

concentration of the chemicals and the force required to remove the deposits. Such

models that involve the mechanical and chemical aspects of cleaning will be more

comprehensive in studying the cleaning process. The modeling of cleaning process

in heat exchangers is still in its infancy stage. But a lot of emphasis is laid upon the

CIP modeling in recent years. CIP is an energy intensive process. For example the

CIP process accounts for 9.5% of primary energy demand (energy consumption) in

the Dutch dairy industry and accounts for 0.14–0.30 MJ/cycle of thermal energy

requirement for milk pasteurization [73]. To add to this high energy requirement

the incidence of fouling causes an increase of about 8% in energy consumption and

about 21% increase in the total energy consumption related to the operation and

cleaning of milk pasteurization units [74].

With the advent of various food-grade frictionless coatings and emphasis on

energy conservation in the food industry models optimizing the cleaning process

is essential. Attempts have been made to model the optimum cleaning schedules for

55534_C009.indd 25655534_C009.indd 256 10/22/08 10:14:15 AM10/22/08 10:14:15 AM

of the surface, foulants, and the fluid, respectively. This relationship indicates that if



plate heat exchangers [75,76] and also the cost economies involved during cleaning

[77,78] in the petroleum industry. An accurate model predicting the correct direc-

tional change (CDC) values of more than 92% has been developed using neural net-

works for the petroleum industry [79]. CDC is a measure of the prediction capability

of a model to predict the correct direction of change in a variable. Using this model

it would be able to schedule optimum cleaning schedules. Using similar models in

the food industry it would be possible to develop cleaning strategies that will result

in optimum plate heat exchanger performance; saving costs and minimizing energy

usage. Attempts have been made to use neural networks to model the optimum clean-

ing schedule in heat exchangers for the dairy industry by monitoring the overall heat

transfer, deposit thickness and the critical time (time when cleaning is required). This

model worked irrespective of the type of milk (for either goat or cow milk) used since

network model updated the error continuously [80]. The results from the study show

that fouling was highest at low pH and high temperature. Using such models will

revolutionize the food industry and cut costs. A cost model has been proposed to

optimize the performance of a Stirling engine which encounters fouling in the heat

exchangers [81]. Taking into account the various costs encountered due to fouling the

proposed model for the total costs of fouling can be summarized as follows:

CT T

C C Cf

f c

p c u=+

+ +1

( ) (9.57)

where Cf = total costs due to fouling; Cp = costs due to changes in engine perform-

ance; Cc = costs due to cleaning; Cu = costs due to unavailability of the engine;

Tf = time for fouling to develop; and Tc = time required for cleaning.

The optimum time for fouling to develop was derived by the following rela-

tionship after taking into consideration the power requirements, and the engine

performance:

T TC C

a e b eTf c

u c

fu e

c= +++

−2 2( )

. . (9.58)

where efu = energy price for the fuel used as input for the Stirling engine; and

ee = average price of purchased and sold electricity. This value is weighted by the

change in purchased and sold energy due to fouling at the fouling period Tf.

Since, the value of ee depends on the fouling period, Tf, and Tf in turn depends

on the value ee , Equation 9.58 becomes an optimization problem where the values

of ee and Tf are determined by iteration. Georgiadis et al. [82] have modeled in detail

the cost economics involved during fouling in a dairy plant. Their comprehensive

model was derived after solving a set of integral, partial differential and algebraic

equations. The results of their model indicate that the cost factor due to interruption

of the dairy operation due to fouling (because of cleaning) is predominant, but the

sis of energy conservation and reports on the impact of fouling on energy loss any

modeling efforts in the future needs to address the issue of energy loss and their

resulting cost economics to optimize dairy operation.

55534_C009.indd 25755534_C009.indd 257 10/22/08 10:14:16 AM10/22/08 10:14:16 AM

increase in energy consumption due to fouling is not significant. With high empha-

it measured the heat flux directly from the plate heat exchanger unit and the neural



9.3 CONCLUDING REMARKS

The impact of fouling in the food processing industry is an issue of major concern.

With recent efforts towards energy conservation and energy utilization, controlling

savings. There has been a dearth in comprehensive models that can explain the foul-

ing mechanism in detail. This is because fouling occurs due to various processing

and physico-chemical changes. Development of a comprehensive model starts with

studying the existing models that have been attempted to integrate them. Under-

standing the fouling phenomena will help in optimizing the process conditions, and

timely scheduling of cleaning operations that will cut down costs, and increase per-

advent of frictionless coatings and new surfaces, the issue of controlling fouling has

gained momentum. Though the study of fouling in the food processing industry is

motive, aerospace, chemical, petroleum, and marine industries, where the issue of

fouling has been addressed for a long time.

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Fouling Models for Heat Ex Changers

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