Fouling in Industrial Heat Exchangers: Formation, Detection and Mitigation

Abstract

Heating or cooling of a fluid by another is made in a heat exchanger with heat dissipation from surfaces of the equipment. Over time, the abundant quantity of impurities promotes fouling in a heat exchanger. This equipment has extensive domestic and industrial applications. The concepts of design, operation, and maintenance of heat exchanger are available in the form of complete technical literature, but this literature is extensively distributed throughout the industrial bulletins, industrial design codes and standard, technical journals, etc. Thus, the aim of this book chapter is to reveal the concepts design, operation, cleaning, and maintenance of heat exchanger closely related to the industrial practices.

1. Introduction

Heat exchanger has an important role in an industrial application whose aim is to heat and cool of large-scale industrial process fluids [1]. Due to their dynamic design, heat exchangers can be personalized to adapt to any industrial process depending on many thermodynamic properties, such as the temperature, pressure, type of fluid, phase flow, density, chemical composition, and viscosity [2, 3]. Efficient heat recovery or heat dissipation becomes a vital challenge for scientists and engineers because of the global energy crisis [2]. The optimization of the surface area of the wall between two fluids in order to maximize the efficiency while minimizing resistance to fluid flow across the exchangers within the limits of material cost is the main reason for the design of heat exchangers. The enhancement of heat exchanging surfaces performance could be done by the addition of corrugations or fins in the heat exchanger, which increase surface area and may channel fluid flow or induce turbulence [4]. Online monitoring of the industrial heat exchanger’s efficiency is made by following up the overall heat transfer coefficient based on its temperatures, which tend to decline over time due to fouling [1].

Scale formation can cause potential damage to equipment. This deposit can be very costly if processed water is not treated correctly. In the industry, chemical products are commonly used to treat the water. It is estimated that a total of 7.3 billion dollar worth of chemical products per year in the U.S. is rejected into the air, dumped in streams, and buried in landfills every year. Industry purchased 40% of these chemical products, which represents more than 2 billion dollar of toxic waste which contribute to trillion of gallon contaminated water disposed annually into the earth, for control of scale in the cooling tower, boiler, and other heat transfer equipment. Several methods can be used to clean fouled tubular heat exchangers such as acid cleaning, sandblasting, high-pressure water jet, and bullet cleaning or drill rods [5]. Water treatment as purification, catalytic approach, addition of chemicals, etc., are used to minimize fouling of the heat exchanging equipment in large scale cooling water systems for heat exchangers [2] and other processes are also used in steam systems for power plants to minimize fouling of the heat exchanger and other equipment. For fouling mitigation, most of the chemicals and additives used are dangerous to the environment [6]. For that reason, it is necessary to apply chemical products that have a mild approach to the environment [1, 6].

2. Heat exchanger in industry

Heat exchanger in the industry is heat transfer equipment that uses a thermal energy exchange process between two or more medium available at a different temperature [7]. This equipment is applied in various industrial processes [8], for example in power plant generation, in petroleum oil and gas industry, chemical processing plants, transportation, alternate fuels, cryogenic, air conditioning, refrigeration, heat recovery [9], and in other industries and this device is always closely related to our daily life, such as evaporators, air preheaters, automobile radiators, condensers, and oil coolers. In general, a heat transfer surface separates the fluid for most heat exchangers. This surface incorporates a wide range of different flow configurations to achieve the desired performance in different applications [9, 10]. Heat exchangers can be classified in many different ways. For industrial heat exchangers, the classification is generally based on the construction, transfer processes, degrees of surface compactness, flow arrangements; pass arrangements, phase of the process fluids, and heat transfer mechanisms as is shown in Figure 1 [9].

Figure 1.

Classification of industrial heat exchanger [9].

3. Design concepts for heat exchanger

Normal process requirements specified through service conditions for combinations of un-corroded and corroded conditions and the clean and fouled conditions must be taken into consideration in the design concepts of the heat exchanger. The most important of the critical criteria is the design of a heat exchanger for the facility of maintenance, which means parts cleaning or replacing (tubes, fittings, etc.) damaged by aging, vibration, corrosion, or erosion throughout the service period. Therefore, the design of the heat exchanger should be as simple as possible especially if significant fouling is expected. By minimizing temperature in conjunction with the choice of fluid velocity and by reducing the concentration of foulant precursors, this incidence of potential fouling can be reduced. Furthermore, the highest flowing velocity should be allowed under the constraints of pressure drop and erosion from the flow. In addition, material selection within a limited cost delays the accumulation of deposits and allows shorter residence time, which should also be compatible in terms of pH, corrosion, and not only just heat exchanger, but also in terms of heat equipment and transfer lines of the heat exchanger.

4. Fouling

4.1 Definition

The deposition and the accumulation of undesirable materials or substances on heat exchanger surfaces formed the fouling of thermal equipment [11]. This deposit, which forms on one or both sides of the heat exchanger surface has a lower thermal conductivity than that of the metal constituting the exchange surface, which creates a significant increase in overall resistance to heat transfer and therefore, a decrease in the performance of the heat exchanger. It also impacts the cross-section of the fluids, which causes an increase in the pressure drop.

It should be noted that the larger size of the heat exchanger, the greater the duration of the production shutdown.

By way of illustration, Figure 2 [12] shows a bundle of heat exchanger tubes in a dirty (Figure 2a) and clean state (Figure 2b).

Figure 2.

Fouled and clean heat exchanger tubes bundles [12].

Other than its repercussions on energy performance, fouling in heat exchangers poses problems in terms of their exploitation and inevitably induces notable additional costs on the investment during the design of the devices but especially during their exploitation. These additional costs are mainly due to the growth of energy consumption, production losses, and maintenance and cleaning costs associated with the capping and clogging of pipes [13].

4.2 Different types of fouling

It is possible to classify fouling according to the mechanism which controls the deposition rate, according to the conditions of use of the exchanger, or according to the dominant mechanism, even if it does not control the deposition velocity. In our work, we have adopted, like most authors [14], the classification which distinguishes four different types of fouling:

• Fouling

• Corrosion

• Scaling

• Mixed types

4.2.1 Fouling

Fouling appears following to the accumulation of finely divided solids suspended in the treatment fluid on the heat transfer surface. Three different forms of fouling can be distinguished [14]:

• Particulate fouling;

• Chemical reaction fouling;

• Biological fouling.

4.2.1.1 Particulate fouling

This type of fouling arises when the solid particles suspended in the process stream accumulate onto the heat transfer surface [13, 15]. The process is seen as “sedimentation” fouling if the settling occurs due to gravity as well as other deposition mechanisms. This also involves deposition of corrosion products dispersed in fluids as clay and mineral particles in river water, suspended solids in cooling water, soot particles of incomplete combustion, magnetic particles in economizers, deposition of salts in desalination systems, deposition of dust particles in air coolers, particulates partially present in fire-side (gas-side) fouling of boilers, etc.

The concentration of suspended particles, fluid flow velocity, temperature conditions on the fouled surface (heated or non-heated), and heat flux at the heat transfer surface are some factors that may influence the particulate fouling. Figure 3 [16] shows a photograph of the particulate fouling.

Figure 3.

Accumulation of solid particles in the plate of a tubular heat exchanger [16].

4.2.1.2 Chemical reaction fouling

Result of the formation of deposits due to one or more chemical reactions between reactants contained in the flowing fluid in which the surface material itself is not a reagent or participant [13, 15]. In this case, the heat transfer surface may act as a catalyst as in cracking, coking, polymerization, and autoxidation. Thermal instabilities of chemical species can also induce fouling precursors, as asphaltenes and proteins. The occurrence of his types of fouling is for over a wide temperature range from ambient to over 1000°C but is more pronounced at higher temperatures. An unwanted chemical reaction occurring during the heat transfer process is the consequence of the mechanism of this fouling. Several applications in process industry promoted the formation of chemical reaction fouling, such as petrochemical industries, oil refining, vapor-phase pyrolysis, cooling of gas and oils, polymerization of process monomers, etc. In addition, fouling of heat transfer surface by biological fluids may involve complex heterogeneous chemical reactions and physicochemical processes. In the case of the formation of the protective oxide layer is inhibited, the deposits from chemical reaction fouling may promote corrosion at the surface. This type of fouling is often extremely tenacious that requires a special measure to clean off the deposits from heat exchanger surfaces to provide them with satisfactory operation life [6]. Figure 4 [16] shows a photograph of the chemical reaction fouling.

Figure 4.

Residue of hydrocarbon in the tubes of a heat exchanger [16].

4.2.1.3 Biological fouling

Biological fouling is due by the attachment and growth of macroorganisms and/or microorganisms and their products on the heat transfer surface, called usually “Biofouling”, and it is generally a problem in water streams [13, 15]. Biological fouling generally can be divided into two main subtypes of fouling: microbial and macrobial. Microbial fouling can be defined as the accumulation of microorganisms such as algae, fungi, yeasts, bacteria, and molds, while macrobial fouling is the accumulation of macroorganisms, for example, clams, barnacles, mussels, and vegetation as found in seawater or estuarine cooling water. Generally, microbial fouling precedes macrobial deposition so it may be considered of primary interest. Biological fouling generally has the shape of a biofilm or a slime layer on the surface that is uneven, filamentous, and deformable but difficult to remove. Biological fouling is generally associated with open recirculation or once-through systems with cooling water despite it can occur in suitable liquid streams. Biological fouling may promote corrosion fouling under the slime layer. One of the common problems [16] in heat exchanger operation is the growth of attached organisms. Several processes may suffer biofouling such as food processing industries, power plant condensers using seawater, etc. A photograph illustrating biological fouling is given in Figure 5 [16].

Figure 5.

Presence of biofouling in tubular bundle of a heat exchanger [16].

4.2.2 Corrosion

Corrosion involves a chemical or electrochemical reaction between the heat transfer surface itself and the fluid stream to produce corrosion products which, in turn, change the surface’s thermal characteristics and foul it. This type of fouling is both a reactant and consumed. The reaction between the surface and the fluid allows creating a corroded surface [13, 15]. Corrosion fouling may be caused in two ways. Firstly, the accumulation and adhesion of corrosion products perform on the surface providing resistance to heat transfer, such as, the presence of sulfur in fuel can cause corrosion in gas and oil-fired boilers. Secondly, corrosion products may be transported from the corrosion site as particulate materials and be deposited on the heat transfer surface in another site of the system as particulate fouling, such as corrosion products originating in the condenser or feedtrain may cause fouling on the waterside of boilers. Corrosion is widespread in many applications where chemical reaction fouling takes place and the protective oxide layer is not formed on the surface that is of significant importance in the design of the boiler and condenser of fossil fuel-fired power plant. Figure 6 [16] shows a corroded tube bundle.

Figure 6.

Corroded tube of a heat exchanger [16].

4.2.3 Scaling

Scaling is defined as the formation of hard incrustations, adhering to heat exchange surfaces and thermally insulating [13, 15]. These incrustations are known as “scale” associated mainly with the production of crystalline solid from liquid solution. The type of scaling depends on the nature of the heated solution, the heating process used, and its operating conditions. This phenomenon reduces the efficiency of heat transfer and increases the effort deployed to clean the scaled surfaces. Scaling may occur in heat exchangers, in water-cooled exchangers, in seawater or brackish water desalination units, in boilers, etc. Crystal growth during precipitation, which requires the formation of a primary nucleus is the most important phenomenon involved in this type of fouling. Nucleation is the mechanism that controls the process, as a rule, heterogeneous in the presence of impurities and on the heat transfer surface. An example of scaling cases on an exchange surface is presented in Figure 7 [16].

Figure 7.

Precipitated salts in the tubes of a heat exchanger [16].

4.2.4 Mixed types

Various mechanisms of fouling have been briefly described, in the practical case; it is rare that heat exchanger fouling is the result of a single mechanism. Two or probably more mechanisms are involved in most process streams where fouling occurs [15]. From a practical standpoint, one mechanism may be dominant, and the other mechanisms present can be ignored when remedial action is being considered. For instance, the circulating water in cooling water systems may contain dissolved solids, suspended particulate matter, and, perhaps, also aggressive chemicals in addition to microorganisms. Microorganisms, particles, scale, and products of corrosion maybe contained in the accumulated deposit on the equipment surfaces. The fouling on heat exchangers may be due to particle deposition, chemical reactions, and corrosion in fouling associated with combustion. From these two examples, it will be clear that the process of fouling may be extremely complex necessitating, a rather empirical approach to its understanding and investigation.

5. Fouling process

Generally, two simultaneous sub-processes formed the overall fouling process which is a deposition process and a removal process as illustrated in Figure 8 [2]. It is important to note that, some of these sub-processes are not applicable in some fouling instances such as corrosion.

Figure 8.

Fouling process [2].

Three basic steps may be visualized concerning the deposition on surfaces from a moving fluid, which are:

1. The diffusional transport of the foulant or its precursors across the boundary layers adjacent to the solid surface within the flowing fluid.

2. The adhesion of the deposit to the surface and to itself.

3. The transport of material away from the surface.

The sums of these three basic components correspond to the growth of the deposit on the surface. Mathematically, the rate of deposit growth (fouling resistance or fouling factor, Rf) is regarded as the difference between the deposition and removal rates [11]:

$$\mathit{Rf}={\dot{m}}_d-{\dot{m}}_r$$E1

Where (${\dot{m}}_d$) represents the deposition rate and (${\dot{m}}_r$) represents the removal rate that can be expressed in the units of thermal resistance as m² K/W or in the units of the rate of thickness change as m/s or in the units of mass change as kg/m² s.

Five main stages are made successively to form the fouling and can be summarized as initiation of fouling, transport to the surface, attachment to the surface, removal from the surface, and aging at the surface [17], which can be summarized briefly as follows:

1. Initiation of fouling or formation of foulant materials in the bulk of the fluid is the first stage in the fouling process. This event is preceded by an induction period or a delay period, (t_d) as shown in Figure 9 [11]. During this period, the basic mechanism involved is heterogeneous nucleation, and (t_d) is shorter with a higher nucleation rate. Several factors can affect (t_d), such as temperature, fluid velocity, composition of the fouling stream, and nature and condition of the heat exchanger surface. In the case of low-energy surfaces (unwettable), the induction periods are longer in comparison with those of high-energy surfaces (wettable). t_d appears to be decreased in crystallization fouling by the increasing degree of supersaturation, however, it tends to be decreased in chemical reaction fouling by increasing surface temperature. Due to available suitable sites for nucleation, adsorption, and adhesion, (t_d) decreases when the surface roughness increases in all fouling mechanisms.

2. Transport of species to the surface is the second stage in the fouling process. This event means the transfer of the fouling species itself from the bulk of the fluid to the heat transfer surface. It is the best understood of all sequential events. Normally, this is done through the action of one or more of the following mechanisms:

   • Diffusion: it involves the mass transfer of the fouling constituents from the circulating fluid toward the heat transfer surface by reason of the concentration difference between the bulk of the fluid and the fluid adjacent to the surface.

   • Electrophoresis: fouling particles carrying an electric charge may move closer together or further from a charged surface according to the polarity of the surface and the particles due to the action of electric forces. Due to electrophoresis, deposition increases by decreasing the electrical conductivity of the fluid, by increasing fluid temperature, and by increasing fluid velocity and it also depends on the pH of the solution. London-van der Waals and electric double layer interaction forces are some of the surface forces, which are usually responsible for electrophoretic effects.

   • Thermophoresis: it is about moving fine particles from a hot zone to a cold zone thanks to a “thermal force” in the direction of the negative temperature gradient. Near a hot wall, a high-temperature gradient will prevent particles from settling, while near a cold wall; the same absolute value of the gradient will promote particle deposition. The thermophoretic effect is more important for gases than liquids.

   • Diffusiophoresis: it involves condensation of the gas stream onto a surface.

   • Sedimentation: the particulate matter settles on the surface under gravity action as rust particles, clay, and dust. To occur sedimentation, the downward gravitational force must be greater than the upward drag force. Sedimentation is important for both large particles and low fluid velocities. In processes where rust and dust particles may act as catalysts and/or enter complex reactions as cooling tower waters processes, sedimentation is frequently observed.

   • Inertial impaction: for not following fluid streamlines and as a result, depositing on the surface, the “coarse” particles should have sufficient inertia.

   • Turbulent downsweeps: the fluid is being transported toward the surface by turbulent downsweeps if the viscous sublayer in a turbulent boundary layer is not truly steady, which can be thought of as suction areas of measurable strength distributed randomly all over the surface.

3. Attachment of the fouling species to the surface is the third stage of the fouling process and implies both physical and chemical processes. In this stage, three interlinked factors play crucial roles which are surface conditions, surface forces, and sticking probability. The combined and simultaneous actions of these factors are largely accounts responsible for the attachment event.

   • Surface properties: the most important properties of surface conditions for attachment events are the surface free energy, wettability (contact angle, spreadability), and heat of immersion. The difference between the surface free energy of the wall and the adjacent fluid layer increases by increasing wettability and heat of immersion. The induction period is longer for unwettable or low-energy surfaces which suffer less from deposition (such as polymer and ceramic coatings) in comparison with wettable or high-energy surfaces. The increase of the effective contact area of a surface and the provision of appropriate sites for nucleation and the promotion of the fouling initiation are the causes of surface roughness. This increases the wettability of wettable surfaces and decreases the unwettability of the unwettable ones.

   • Surface forces: among the most important surface forces is the London-van der Waals force. This force describes the intermolecular attraction between nonpolar molecules and it is always attractive, while the electric double layer interaction force can be attractive or repulsive. Whereas, viscous hydrodynamic force influences the attachment of a particle moving to the wall, which increases as it moves normal to the plain surface.

   • Sticking probability: the fraction of particles that reach the wall and stay there before any reentrainment occurs. A useful statistical concept conceived to analyze and explain the complicated event of attachment.

4. Removal of the fouling deposits from the surface: correspond to the fourth stage in the fouling process. This step may or may not occur simultaneously with deposition under the single or simultaneous action of the following mechanisms; shear forces, turbulent bursts, re-solution, and erosion.

   • Shear forces: the actions of the shear stress exerted by the circulating fluid on the depositing layer is the result of shear forces. The accumulation of deposit causes the cross-sectional area for flow decreases, thus increase in the average velocity of the fluid for a constant mass flow rate and increasing the shear stress. If the deposit bond resistance is greater than the prevailing shear forces at the solid-fluid interface, new deposits will form.

   • Miniature tornadoes use to raise deposited material from the surface by periodic turbulent bursts randomly distributed (about less than 0.5% at any instant of time) and by continuity, these fluid bursts are offsetted by softer fluid return scans, which promote deposition.

   • Re-solution: the solubility of the material deposited is related to the removal of the deposits by re-solution. The dissolution will occur only if there is a change in the properties of the deposit and in the circulating fluid, or in one of them, because of local changes of certain operational variables such as temperature, velocity, alkalinity, and this by considering that the fouling deposit is presumably insoluble at the time of its formation. For instance, sufficiently high or low temperatures could kill a biological deposit, thus weakening its attachment to a surface and causing sloughing or re-solution. The removal of corrosion deposits is done by re-solution at low alkalinity in power-generating systems and the resolution is associated with the removal of material in ionic or molecular form.

   • Erosion: this process and the overall removal process are closely related. It is heavily dependent on the shear strength of the foulant and on the steepness and length of the sloping heat exchanger surfaces, where appropriate and it is associated with the removal of material in particulate form. If the fouling layer is composed of well-crystallized pure material (strong formations), the removal mechanism becomes largely ineffective; in contrast, if the fouling layer is composed of a wide variety of salts each having different crystal properties, the removal mechanism is highly effective.

5. Transport from the deposit-fluid interface to the bulk of the fluid: the destruction of deposits may or may not causes the transport from the deposit-fluid interface to the bulk of the fluid and this depends only on the mass and volume of the sloughed piece and on the hydrodynamic forces of the flowing fluid. In the case of the sloughed piece is sufficiently broad, it may move on the surface and settled on another site on the system as certain corrosion products. Because of the erosion effect, all deposits that are removed will be transported to the bulk of the fluid. Without this action, the removal process is not complete. The aging of deposits is the most important parameter, which affects deposit sloughing. It may strengthen or weaken the fouling deposits.

Figure 9.

Fouling curves [11].

6. Fouling curves

Figure 9 [11] illustrates the initiation period or time delay in heat exchanger fouling. This period is considered the time when there is no deposition for some time during the commissioning of a clean heat exchanger [18, 19]. Due to changing flow characteristics near the wall, the initial growth of the deposit can cause an increase in heat transfer coefficient rather than a decrease, resulting in fouling resistance. By changing flow characteristics near the wall, the resulting turbulence increases the film heat transfer coefficient at the solid/liquid interface and this increase may overcome the thermal resistance offered by the deposits but the net heat transfer coefficient may increase.

The negative values of fouling resistance have been reported by several authors [20].

This process continues until the additional heat transfer resistance overcomes the advantage of increased turbulence. The time period from the beginning of the fouling process until the fouling resistance again becomes zero represents the roughness delay time [21]. The time period from the beginning of the induction period when the formation of stable crystalline nuclei and their concretion to a compact fouling layer takes place and ends up with the increase of fouling resistance above zero level represents the roughness delay time.

For particulate fouling, the initiation period and the roughness delay time are very small in comparison with scaling fouling where the delay time is fairly long [6].

According to the fouling mechanism and conditions and after the roughness delay time, the fouling curves can be classified into four categories: linear (A), falling (B), accelerating, asymptotic (C), or saw-tooth (D) as the case may be as illustrated in Figure 9 [11].

Normally, the rate of fouling is defined as the average deposit surface loading per unit of surface area in a unit of time. Utilization of deposit thickness (μm) and porosity (%) are also frequently necessary for the description of the amount of fouling.

1. Linear fouling (curve A): it may be the most common type of fouling. The fouling rate can be steady with time with increasing fouling resistance and deposit thickness for this type of fouling. It occurs generally when the temperature of the deposit in contact with the flowing fluid remains constant.

   The fouling model developed by Ebert and Panchal has been reported in [11]. The average (linear) fouling rate under given conditions are expressed in the form of two competing terms. Mathematically, it is equal to the subtraction of the anti-deposition term from the deposition term.

   $$\frac{\mathit{dRf}}{\mathit{dt}}=\alpha {Re}^{\beta }{Pr}^{\delta }exp\left(\frac{-E}{{\mathit{RT}}_{\mathit{\text{film}}}}\right)-{\mathit{\gamma \tau }}_w$$E2

   α, β, γ, and δ represent the parameters determined by regression, τ_w represents the shear stress at the tube wall and T_film represents the fluid film temperature (average of the local bulk fluid and local wall temperatures). Depending on the relationship in Eq. (2), it is possible to identify a combination between the temperature and the velocity below which the fouling rates will be negligible. This is presented as the “threshold condition” by Ebert and Panchal. The developed model in Eq. (2) suggests that the heat exchanger geometry can be effectively applied to maintain the conditions below the “threshold conditions” in a given heat exchanger because it affects the surface and film temperatures, velocities, and shear stresses.

2. Falling fouling (curve B): the decreasing of the fouling rate with time, and the not mitigation of a constant value of the deposit thickness, despite the fouling rate never drops below a certain minimum value are the characteristics of the falling fouling. This type of fouling is generally due to an increase in removal rate with time.

3. Asymptotic fouling (curve C): this type of evolution is observed when the fouling rate decreases with time until it becomes negligible after a period of time when the deposition rate becomes equal to the deposit removal rate and the deposit thickness remains constant. The asymptotic fouling occurs generally where the tube surface temperature remains constant while the temperature of the flowing fluid drops as a result of increased resistance of fouling material to heat transfer. It may also be the result of soft or poorly adherent suspended solid deposits upon heat transfer surfaces in areas of fast flow where they do not adhere strongly to the surface with the result that the thicker the deposit becomes, the more likely it is to wash off in patches and thus attain some average asymptotic value over a period of time.

   By increasing particle concentration and by decreasing fluid bulk temperature, flow velocity, and particle diameter, the asymptotic fouling resistance increases. The first correlation describing the asymptotic fouling model was developed by Kern and Seaton. Note that no further increase in fouling occurs in this model beyond asymptotic fouling resistance. Based upon the asymptotic values, fouling factors for several fluids are suggested by the Tubular Heat Exchanger Manufacturers Association (TEMA). However, this approach does not address all fouling phenomena. For example, it does not address fouling at the “hot” end of a crude oil preheat train because fouling there does not exhibit asymptotic behavior.

4. Saw-tooth fouling (curve D): this type of fouling occurs when part of the deposit is detached after a critical residence time or once a critical deposit thickness has been reached. In that case, the fouling layer then builds up and breaks off again. Pressure pulses, spalling, trapping of air inside the surface deposits during shutdowns, or other reasons could cause the periodic variation which often corresponds to the moments of system shutdowns, startups, or other transients in operation.

7. Conditions affecting fouling

The most important conditions, which influence fouling is: operating parameters, heat exchanger parameters, and fluid properties [19, 22].

7.1 Operating parameters

Velocity, surface temperature, and bulk temperature are among the main important events of operating parameters that affect fouling at a significant level.

Velocity has a significant effect on fouling. The increase of fluid velocity in diffusion-controlled process causes more fouling. For high fluid velocities, the fouling decreases in most cases. By increasing flow velocity, the fluid shear stress increases, which causes more removal. This leads to lower fouling rates that causes lower fouling resistance. In the case of particulate fouling, for weak deposits, the increase of the flow velocity may completely eliminate fouling. In contrast, for stronger deposits, the increase of the flow velocity beyond a particular point may not decrease fouling significantly and for very strong deposits, the increase of the flow velocity may not have any effect at all.

Diverse behaviors, among which the increase of surface temperature may increase, decrease, or has no effect on the fouling rates [7]. The increase in temperature causes the increase in both the rates of the chemical reaction and inverse solubility crystallization. Because of higher concentration gradients and higher reaction rate constants, higher surface temperature increases fouling for inverse solubility salts. Cooling results in more fouling in the case of normal solubility salts.

The bulk temperature affected also the increase in the fouling rate. The increase of the temperature increases the rate of crystal formation and thus deposition and this is when precipitation happens in the fluid bulk in inverse crystallization. Thus, the bulk temperature has effects on chemical reaction rate and polymerization rate.

7.2 Heat exchanger parameters

Among the significant heat exchanger parameters that affect fouling are: surface material, surface structure (roughness), heat exchanger type, and geometry. Due to the potential to react and form corrosion products, the surface material is considered seriously for corrosion fouling. Various materials have different catalytic actions and may promote or reduce fouling for different processes. The surface roughness affects significantly on the initial fouling rate and scale formation. Theoretically, the free energy change associated with crystal nuclei formation is much less on a rough surface than on a smooth surface [6]. Because of protected zones in the cavities or pits where flow velocities are very low, rough surfaces result in the higher deposition.

The surface roughness strongly depends on the nuclei attachment and not on the rate of nucleation, according to Rankin and Adamson and Chandler [6]. Generally, for all types of fouling, the rough surface causes more fouling and that reduces the delay time. Surface roughness increases turbulence near the surface, which in turn increases the removal rate of fouling on the surface. The best performance corresponds to the increase of surface roughness with deposit formation [6]. The mirror-finished surfaces in heat exchangers are used to reduce fouling in practice which is reiterated by Marriott [6].

7.3 Fluid properties

Among the most known properties that affect fouling processes are the nature of the fluid and the species dissolved or entrained in the fluid. In cooling systems, for example, the quality of water has a significant impact on fouling mechanisms, which cause in crystallization of reverse solubility salts, particle deposition, corrosion, and biofouling [16].

The intrusion of small amounts of impurities into fluids can trigger or significantly increase fouling which can either deposit as a fouling layer or act as a catalyst for fouling processes. For instance, fouling by chemical reaction or the polymerization of hydrocarbons in refineries is due to the presence of oxygen and/or trace elements such as vanadium and molybdenum.

The presence of fine particles of impurities triggers the seeding deposition process in the case of crystallization fouling. The properties of impurities are the basis for the manufacture of many anti-fouling chemicals. These impurities as sand or other particles suspended in cooling water can sometimes have a deposit reduction or removal action [15].

Suspended solids promote the sedimentation of particles by gravity on the heat transfer surfaces. In this case, prevention is achieved by avoiding stagnant areas. Indeed, high water velocities (greater than 1 m/s) of the water help prevent the clogging of particles. It is often economical to install upstream filtration.

8. Fouling models

Various models have been proposed for different types of fouling but the analysis and the improvement of the model are still progressing because of the complex nature of deposit formation and the lack of reproducible measurement of fouling resistance. Several assumptions were assumed in order to simplify various models [23, 24], such as:

• Generally, only one type of fouling is considered.

• Homogeneity of the fouling layer.

• The form of deposits, such as crystals and particles, is ignored.

• In most cases, the changes in the physical properties of the fluids are neglected.

• In general, the changes in flow velocity with changing cross-sectional area because of fouling are overlooked.

• Surface roughness is neglected.

• Change in surface roughness with deposit formation is also neglected.

A few attempts have been made to model the initiation or roughness delay period and almost all the models predict fouling after the delay period. The majority of models usually take into account the main parameters related to fouling such as flow velocity, concentration, wall and bulk temperature, and time. In contrast, other some notable parameters that are effect of simultaneous action of different fouling mechanisms, equipment design, surface parameters such as surface material and surface roughness, increase in surface area with deposition, properties of foulant stream, nature of the process, and the fluctuations in operation are neglected in modeling [24].

Accumulation is usually considered to be the net result of two simultaneous processes: a deposition process and a removal process. Mathematically, the net rate of accumulation can be expressed as the difference between the deposition and removal rates which represent the equation of material balances. It should be noted that the semi-empirical modeling was developed on the basis of this equation whose general expression is:

$$\text{Rate of accumulation}=\text{Rate of deposition}–\text{Rate of removal}$$

$$\frac{{\mathit{dm}}_f}{\mathit{dt}}={\dot{m}}_f={\dot{m}}_d-{\dot{m}}_r$$E3

The deposition rate depends on the type and mechanism of fouling, while the removal rate depends on both the hardness and the adhesion strength of the deposit and the shear stress which results from the flow velocity.

Help the designer or indeed the operator of heat exchangers; to assess the impact of fouling on heat exchanger performance in certain operating conditions is the purpose of any fouling model. Providing a fouling model is based on its mathematical interpretation but the inclusion of an extensive set of conditions for such a model would be difficult and even impossible. Concerning the production of a mathematical model for the fouling process, the general material balance given in Eq. (3) is the basis of the modeling, which is centered on evaluating the functions ${\dot{m}}_d$ and ${\dot{m}}_r$ for specific fouling situations, some of these models are:

8.1 McCabe-Robinson model

This model developed in 1924 concerns the fouling of the surfaces of heat exchangers used as evaporators. The correlation proposed to evaluate the solid mass deposited is [24]:

$${\dot{m}}_d=a\dot{q}$$E4

Note that no information has been specified concerning the physical meaning of the coefficient “a” and the deposit elimination mechanism.

8.2 Kern and Seaton model

In 1958, Kern and Seaton from some experimental fouling results managed to say that the rate of deposition mass, ${\dot{m}}_d$, remained constant with time t but the rate of removal mass, ${\dot{m}}_r$, is proportional to the accumulated mass, $m_f$, and therefore increased with time to approach ${\dot{m}}_d$ asymptotically.

The particle wall transport phase controls the deposition process whereas the shear stress controls the removal phase. Considering that (${\dot{m}}_d$) is proportional to the deposited mass of particles, the expressions of (${\dot{m}}_d$) and (${\dot{m}}_r$) are the following [11]:

$${\dot{m}}_d=k_p\times \left(C_b-C_w\right)$$E5

$${\dot{m}}_r=C_1\times {\tau }_w\times m_f$$E6

(k_p) represents the transport coefficient, (C_b) represents the particle concentration in the fluid, (C_w) represents the particle concentration at the wall, (C₁) represents a dimensional constant, and (τ_w) represents the shear stress exerted by the fluid on the deposit.

So, Eq. (3) becomes:

$$\frac{{\mathit{dm}}_f}{\mathit{dt}}=k_p\times \left(C_b-C_w\right)-C_1\times {\tau }_w\times m_f$$E7

The integration of Eq. (7) from the initial condition (m_f = 0) at (t = 0) gives:

$$m_f=\frac{k_p\times \left(C_b-C_w\right)}{C_1\times {\tau }_w}\times \left[1-{\mathrm{e}}^{\left(-C_1\times {\tau }_w\times t\right)}\right]$$E8

Acknowledging that: $\tau =\frac{1}{C_1\times {\tau }_w}$ and ${m_f}^{\ast }=\frac{k_p\times \left(C_b-C_w\right)}{C_1\times {\tau }_w}$.

Eq. (8) is expressed as follows:

$$m_f={m_f}^{\ast }\times \left(1-e^{-\theta \times t}\right)$$E9

where (m_f^*) is the asymptotic value of m_f and $\theta =\frac{1}{t_c}$ . (t_c) is the time constant which represents the average residence time for an element of fouling material at the heat transfer surface.

Assuming that the initial fouling flow is equal to the deposition flow and that the thermophysical properties of the deposit (conductivity and density) are constant, Eq. (9) can be written in the form of a thermal fouling resistance:

$$\mathit{Rf}\left(t\right)={\mathit{Rf}}^{\ast }\times \left[1-exp\left(-\frac{t}{\tau }\right)\right]$$E10

(Rf (t)) represents the evolution of the fouling resistance as a function of time (expressed in (m² K W⁻¹)), (Rf*) represents the asymptotic value of the fouling resistance (expressed in (m² K W⁻¹)) (this value characterizes the situation where the deposition rate and the breakout speed are equals), (𝑡) represents the time (expressed in (s)) and (τ) represents the characteristic time (expressed in (s)) and generally its value is attributed to the time required for the fouling resistance to reach its asymptotic value in case the evolution of this kinetics was linear.

The real solution would be to find expressions for (Rf^*) and (t_c) as a function of variables affecting the fouling process.

8.3 Taborek et al. model

Helalizadeh reported in [24] the water characterization factor introduced by Taborek et al in 1972 to the deposition term which is used to account for the effect of water quality. Diffusion of the potential depositing substance to the surface (1) and bonding at the surface (2) are the two processes of the deposition term. This deposition rate is expressed in an Arrhenius type equation as the following:

$${\dot{m}}_d=k_1{P}_d{\Omega }^{n}exp\left(\frac{-\mathit{Ea}}{R_g{T}_s}\right)$$E11

(K₁) represents the deposition constant, (P_d) represents the deposition probability factor related to velocity and “Stickiness” or adhesion characteristics of the deposit, (n) represents an exponent, (Ω) represents the water characterization factor, $\left(\frac{-\mathit{Ea}}{R_g{T}_s}\right)$ represents the Arrhenius reaction rate function, (Ea) is the activation energy, (R_g) is the universal gas constant and (T_s) is the absolute surface temperature.

In the proposed model, the removal rate was assumed that is a function of shear stress, deposit thickness, and bonding strength of the deposit. The removal function was given as follows:

$${\dot{m}}_r=k_2\left(\frac{\tau }{\psi }\right)x_f$$E12

(k₂) represents the removal constant, (τ) represents the fluid shear stress exerted on the deposit surface, (Ψ) represents the strength or toughness of the deposited layer. In material balance (Eq. (1)), by replacing the deposition rate (Eq. (11)) and removal rate (Eq. (12)), the resulting equation is as follows;

$$\mathit{Rf}=\frac{x_f}{{\lambda }_f}=\frac{k_1{P}_d{\mathrm{\Omega }}^n{e}^{-\mathit{Ea}/R_g\times T_s}\left(1-e{-}^{-k_2{\lambda }_f\mathit{\tau t}/\mathrm{\Psi }}\right)}{\frac{k_2{\mathit{\tau \lambda }}_f}{\mathrm{\Psi }}}$$E13

And ${\mathit{Rf}}^{\ast }=\frac{k_1{P}_d{\mathrm{\Omega }}^n{e}^{-\mathit{Ea}/R_g\times T_s}}{\frac{k_2{\mathit{\tau \lambda }}_f}{\mathrm{\Psi }}}$, $\theta =\frac{k_2{\mathit{\tau \lambda }}_f}{\mathrm{\Psi }}=\frac{1}{t_c}$

8.4 Watkinson et de Martinez model

Watkinson and Martinez proposed in 1975 a model based on the models developed by Kern and Seaton (1958) and Reitzer (1964) taking into account the phase of elimination of the deposit. The general expression for this model is [24]:

$$\mathit{Rf}={\mathit{Rf}}^{\ast }\times \left(1-e^{-\mathit{Bt}}\right)$$E14

The parameter (B) is determined from the experimental data.

For crystallization fouling, the fouling resistance (Rf^*) is given by the following equation:

$${\left({\mathit{Rf}}^{\ast }\right)}^3+\frac{2}{{\alpha }_i}{\left({\mathit{Rf}}^{\ast }\right)}^2+\frac{{\mathit{Rf}}^{\ast }}{{{\alpha }_i}^2}-\frac{0.0002751T-0.08489}{{\left({\alpha }_{i}v\right)}^2}=0$$E15

Where (α_i) is the inside heat transfer coefficient and (v) is the flow velocity.

8.5 Watkinson model

Based on the model developed by Watkinson and Martinez, Watkinson reported the effect of fluid velocity on the asymptotic fouling resistance in three cases as [15];

1. Calcium carbonate scaling (with constant surface temperature and constant composition)

   $${\mathit{Rf}}^{\ast }=\frac{0.101}{v^{1.33}\times D^{0.23}}$$E16

2. Gas oil fouling (with constant heat flux)

   $${\mathit{Rf}}^{\ast }=\frac{0.55}{v^2}$$E17

3. Sand deposition from water (with constant heat flux)

$${\mathit{Rf}}^{\ast }=\frac{0.015}{v^{1.2}}$$E18

Where (Rf^∗) is the asymptotic fouling resistance, (v) is the fluid velocity and (D) is the tube diameter.

8.6 Hasson et al. model

In 1981, Hasson et al. expressed the degree of fouling by crystallization due to calcium carbonate (CaCO₃) per interface unit by the following relation [24]:

$${\dot{m}}_d=K_r\left({\left[{\mathrm{Ca}}^{2+}\right]}_i{\left[{{\mathrm{CO}}_3}^{2-}\right]}_i-K_{\mathit{sp}}\right)$$E19

Where [Ca^{2 +}] is the concentration of calcium ion and [CO₃²⁻] is the concentration of carbonate ion.

By performing mathematical manipulations on the previous relationships, the fouling rate is obtained by the following relationship:

$$K_1\left(\frac{{\dot{m}}_d}{K_r}+K_{\mathit{sp}}\right)(\frac{{\dot{m}}_d}{\beta }+\left[{\mathrm{CO}}_2\right]=4K_2{\left[{\mathrm{Ca}}^{2+}\right]}^2\left(1-\frac{{\dot{m}}_d}{\beta \left[{\mathrm{Ca}}^{2+}\right]}\right){\left(\frac{\left[{{\mathrm{HCO}}_3}^{-}\right]}{2}-\frac{{\dot{m}}_d}{\beta }\right)}^2$$E20

Where (K₁) and (K₂) are the first and second dissociation constant, (K_sp) is the molar solubility product, and (k_r) is the reaction rate constant.

The expressions allowing having these constants are:

$$log{K}_1=\frac{-17052}{T}-215.21logT+0.12675T+545.56$$E21

$$log{K}_2=\frac{-2902.39}{T}-0.02379T+6.498$$E22

$$log{K}_{\mathit{sp}}=-0.01183\left(T-273.2\right)-8.03$$E23

$$K_r=exp\left(41.04-\frac{10417.7}{T}\right)$$E24

By doing mathematical operations, the expression of the Eq. (20) reduces to:

$${\dot{m}}_d=\frac{0.5\mathit{\beta b}\left[{\mathrm{Ca}}^{2+}\right]\left({\left(1+\frac{4\mathit{ac}}{b^2}\right)}^{0.5}-1\right)}{a}$$E25

Where:

$$a=1-\frac{4K_2{K}_r\left[{\mathrm{Ca}}^{2+}\right]}{K_1\beta }$$E26

$$b=\frac{\left[{\mathrm{CO}}_2\right]}{\left[{\mathrm{Ca}}^{2+}\right]}+\frac{4K_2{K}_r\left[{{\mathrm{HCO}}_3}^{-}\right]}{K_1\beta }+\frac{K_{\mathit{sp}}{K}_r\left[{\mathrm{CO}}_2\right]}{\beta \left[{\mathrm{Ca}}^{2+}\right]}$$E27

$$c=\frac{K_2{K}_r{\left[{{\mathrm{HCO}}_3}^{‐}\right]}^2}{K_1\beta \left[{\mathrm{Ca}}^{2+}\right]}-\frac{K_{\mathit{sp}}{K}_r\left[{\mathrm{CO}}_2\right]}{\beta {\left[{\mathrm{Ca}}^{2+}\right]}^2}$$E28

(β) is the mass transfer coefficient, calculated using the following relation, proposed by Hasson et al. and reported in [24]:

$$\beta =0.023{Re}^{0.85}{\mathit{Sc}}^{0.33}\frac{D}{d_{\mathit{eq}}}$$E29

8.7 Ritter model

In 1983, Ritter examined all possible parameters to correlate both the induction period and the fouling rate associated with calcium sulfate. He showed that the induction period and the fouling rate depend on the supersaturation of the solution and that the secondary correlation parameter is the mass transfer coefficient. The expressions proposed by Ritter are [24]:

For the induction period:

$$\theta =\frac{2.1\times {10}^{-4}\rho }{\beta {\left(\frac{C_b-C^{\ast }}{C^{\ast }}\right)}^2}$$E30

For the fouling rate:

$$\frac{\mathit{dRf}}{\mathit{dt}}=\frac{1.9\times {10}^{-9}\beta }{\rho }{\left(\frac{C_b-C^{\ast }}{C^{\ast }}\right)}^2$$E31

Where (ϴ) is the induction period and $\frac{\mathit{dRf}}{\mathit{dt}}$ is the fouling rate.

Note that for these results, Ritter did not specify the operating conditions.

8.8 Knudsen analysis

The fouling process is complicated and dynamic. Generally, the fouling resistance is not measured directly but must be determined from the degradation of the overall heat transfer coefficient [25], and the fouling factor, Rf, could be expressed as [15];

$$\mathit{Rf}=\frac{1}{U_f}-\frac{1}{U_c}$$E32

On the basis of the change in the overall heat transfer coefficient of the fouling test section experimental fouling data have been analyzed as in Eq. (34). It is assumed that the thermal-hydraulic condition in the test section remains reasonably constant for the duration of the fouling test. Through the use of the model of Taborek et al., the two parameters (Rf^∗) and (t_c) can be determined for each fouling situation. The (Rf^∗) represents the asymptotic fouling resistance contains all the factors that influence fouling and (t_c) represents the time constant of the fouling resistance exponential curve i.e. the time required for the fouling resistance to reach 63% of its asymptotic value (i.e. (t_c) ≈ 0.63 × (t^∗)). This parameter (time constant) depends on the shear stress, the deposit strength factor, and the deposit thermal conductivity;

$$t_c=\frac{\psi }{\tau k_2{\lambda }_f}$$E33

From the deposition-removal model, which was first presented by Kern and Seaton and reported in [15] (Eq. (10)) and from Eq. (32), the overall heat transfer coefficient of the fouled surface. U_f, may be given as;

$$U_f=\frac{U_c}{1+U_c\times \mathit{Rf}}$$E34

Then

$$U_f=\frac{1}{\frac{1}{U_c}+{\mathit{Rf}}^{\ast }\times \left(1-e^{\left({}^{\frac{-t}{t_c}}\right)}\right)}$$E35

In Eq. (35), if the two coefficients (Rf^*) and (t_c) can be obtained accurately either empirically or analytically, they will be useful for predicting the fouling factor which can be used in practical heat exchanger design.

9. Prediction of fouling factor

Fouling is generally defined as the formation of an essentially solid deposit of low thermal conductivity upon the heat transfer surface, through which heat must be transferred by conduction. But, the thermal conductivity of the fouling layer and its thickness is generally unknown, that’s why the possible solution to the heat transfer problem is to introduce a fouling factor in order to take into account the additional resistance to heat transfer and make possible the calculation of the overall heat transfer coefficient [7]. The opposite value of the fouling factor represents the fouling coefficient.

It is necessary to be careful in selecting fouling factors in calculating heat transfer, particularly where fouling resistances completely dominate the thermal design. Generally, the uncertainties in design parameters such as fluid properties, flow rates, and temperatures have less effect than that of the uncertainty inherent in fouling factors [11, 26]. A significant fouling factor is considered as a safety margin to cover uncertainties in fluid properties and even in process knowledge, but the use of an excessively significant fouling factor will result in an oversized heat exchanger with two or three times more area than is really necessary.

Several experience-based tables available provide typical fouling factors such as TEMA Table RGP-T-2.4 [27]. For each particular application, an acceptable evaluation of the effects of fouling needs to be judged and evaluated. However, these tables are being considered as a guide in the absence of more specific information.

To predict the rate of fouling in heat exchangers or to estimate fouling factors to use in heat transfer calculations, several semi-empirical models have been developed over the years and some of them are presented in the previous section. Recent research work has recourse to the use of digital computers which are able to provide rapid means to perform calculations. The ANN method has been applied in many disciplines of engineering and has produced promising results. The ANN method becoming a powerful tool and progressing at an impressive rate due to its feature which is the ability to learn and generalize the relationships in a data set and to provide quick and satisfactory predictions. This technique became attractive for many different applications [28, 29].

The ANN method is an efficient and powerful non-linear computational structure derived from a biological neural system and composed of very simple and highly interconnected elementary units called neurons [30, 31, 32]. The neurons are organized according to architecture and the connection to each other is made by weighted links over which signals can pass. Each neuron treats the weighting factor, which is attached to the input (wX) and which is added to the bias coefficient (θ) with a suitable activation or transfer function (f). Thus, the output (Y) can be mathematically expressed as [30]:

$$Y=f\left(\sum \mathit{wX}+\theta \right)$$E36

Several used transfer functions, such as the hyberbolic tangent, the linear transfer function and the Gaussian function, and the tangent sigmoid function [33].

In engineering applications, the back propagation (BP) learning algorithm has become the most popular and exciting kinds of ANNs [34]. It is designed to solve the problem of determining weight values for a multi-layer ANN with feedforward connections from the input layer to the output layer through the hidden layer. The application of the ANN approach can be used to develop the best configuration in the training period.

The ANN approach has been widely used in different applications, especially in the field of heat exchangers such as the design and control of heat exchangers [35, 36], and in the simulation of heat exchanger performance [35, 36, 37] and estimation of heat exchanger parameters [7, 35].

As an alternative and practical technique, the ANN approach has also been used to evaluate the rate of heat exchange and heat transfer coefficient for a different type of heat exchangers [36] and in other applications including in particular the prediction of the rate of fouling and fouling factor in a shell-and-tube heat exchanger [7, 38].

To predict the fouling rate and fouling factor in heat exchangers, an ANN model can be developed and the available data set used for training the network and verifying its generalization capability. The fouling factor are then calculated and the input-output pairs are presented to the network, and the weights are adjusted to minimize the error between the network output and the actual value. Once training is complete, predictions from a new set of data may be done using the already trained network.

A few works relating to the application of artificial neural networks to predict the fouling rate or fouling factor are: in [39], the input layer of the artificial neural network comprised five parameters, namely: the inlet and outlet temperatures of the cold fluid, the inlet temperature of the hot fluid, mass flow rate of cold and hot fluids is used for predicting the fouling factor. Aminian and Shahhoseini [40] predict the fouling rate of crude oil pre-heaters using a four layers feedforward neural network model. The velocity of crude oil, tube surface temperature, and tube diameter were employed as independent variables of the ANN model. Fouling threshold in crude oil pre-heaters was predicted as a function of surface temperature, Reynolds, and Prandtl numbers using a neuro-based model [41]. Shell and tube side input temperatures and tube side crude oil flow rate was considered as the independent variables of the proposed model, while the output variable was chosen to calculate the fouling factor [42]. Davoudi and Vaferi [7] employed the ANN for predicting the fouling factor from some easily measured variables of the system which are density, velocity, temperature of the fluid, oxygen content, hydraulic diameter of the fluid passage, surface temperature, and time. And more recently, Jradi et al. [30] estimated the fouling resistance according to the inlet and outlet temperatures of the cold fluid, the temperature of the hot fluid, the density and the volume flow rate of the cold fluid, and the time for three types of heat exchanger by using three different methods which are: Kern and Seaton, Partial Least Squares (PLS) and Artificial Neural Networks (ANN). Results have shown that modeling by the use of ANN is very performing compared with modeling by PLS and Kern and Seaton.

10. Fouling control

To avoid technical problems associated with fouling of heat exchangers (plugging and clogging of pipes, corrosion of materials, drop in energy performance, loss of production due to the shutdown of installations for maintenance and cleaning), there are currently several methods for detecting and/or monitoring the evolution of fouling [13]:

• Predictive maintenance,

• Direct measurements at the terminals of the exchanger,

• Measurements using probes.

10.1 Predictive maintenance

Several techniques for developing a predictive maintenance program are available either by thermography or by visual inspection.

• Thermography makes it possible to measure the intensity of emissions of infrared rays, that is to say, heat, in order to determine the operating conditions of the installations.

Three types of infrared devices can be used in predictive maintenance:

Infrared thermometers: these are designed to measure the actual surface temperature at a single, relatively small point in an installation. As the measurement is restricted to a single point, this method offers limited possibilities.

Linear scanners: they take a temperature reading along a particular line, and therefore in one dimension. Although this method opens up a somewhat wider field of vision, it is also limited.

Imagers: they analyze all the infrared emissions from the exchanger. Most often these are infrared cameras.

These methods, although effective and new, make it possible to locate the problem of fouling, but remain qualitative due to the numerous errors in temperature measurement by radiometry.

• Visual inspection

Regular visual inspection of industrial facilities is an integral part of a predictive maintenance program. The user, guided by his own experience, can detect, through visual inspection, the level of fouling of the exchangers in his installation. Thus, this routine operation provides subjective but necessary information for setting up the maintenance program.

The principle common to these techniques lies in the regular monitoring of the condition of the installation. They provide more or less information on the state of fouling of the exchangers, but very little on heat transfer.

10.2 Direct measurements at the exchanger terminals

In industrial practice, there are different methods for detecting and monitoring the progress of fouling. Generally, three methods are used based on [13]:

• Monitoring the variation of the heat transfer coefficient or the fouling resistance.

• Simultaneous observations of pressure drop and flow rate indicators.

• Temperature measurements at the inlet and outlet of the heat exchanger.

10.3 Measurements using a probe

In this case, the fouling is monitored using a probe. The devices are classified into four main categories according to their mode of operation:

• Devices using optical methods: these devices use optical methods such as lasers or pyrometers to determine the thickness of the deposit. However, these techniques are restricted to laboratory tests under very controlled conditions and are therefore difficult to extrapolate to industrial conditions.

• Devices using a deposit measurement: these probes are used to collect deposits qualitatively under controlled conditions. With such devices, the mass of the deposit on the exchanger tube cannot be determined. These probes are used to characterize the thermal properties of the deposit.

• Devices allowing the measurement of the mass increase: such a device allows the quantitative measurement of the deposit. This technique requires the control of many parameters such as the wall temperature or the gas temperature.

• Devices using flowmeters: measurement by flux meter makes it possible to follow the decrease in heat flow as a function of the clogging time. It thus makes it possible to follow the evolution of fouling resistances. On the other hand, these probes do not make it possible to obtain either the thickness or the profile of the deposit. So far, this type of probe has mainly been studied in settings where radiation is the primary mode of heat transfer.

11. Economic aspect of fouling

A very few works have been reported to accurate determine economic penalties caused by fouling in spite of the high cost in the heat exchanger, which is attribute to the cost of the difference aspect of the design and operation of this equipment. In order to evaluate the cost-efficiency of various mitigation strategies, reliable knowledge of fouling economics is desirable [2].

Fouling of heat transfer equipment in industries imposes additional operating costs which are not assessed precisely. Several concordant studies have been undertaken to determine the fouling-related costs in the industry. Generally, fouling costs can be divided into three major categories as shown in Figure 10 [43] which are: (1) cost related to the design of the heat exchanger, (2) cost related to the operation of heat exchanger, and (3) costs related to shutdown of operation.

Figure 10.

Cost imposed due to fouling [43].

The total fouling-related costs are as follows:

11.1 Costs related to the design of the heat exchanger

Generally, equipment manufacturers offer oversized heat exchangers, taking into account, among other things, an additional thermal resistance associated with the fouling phenomenon, the value of which is often of empirical origin. Thus, the additional surface area to the heat exchange surface required induces an additional cost of approximately 20% of the cost of acquisition of the heat exchanger.

11.2 Costs related to the operation of the heat exchanger

Operators resort to very often costly actions such as the treatment of fluids before introduction into the devices, online control of the operating parameters, in particular, the temperatures and the inlet and outlet pressures of the two fluids, and the supply of additional energy to limit the negative repercussions of fouling on the operation of heat exchangers. These often-costly actions generate additional costs high to the total cost of operating the facilities in the order of 62%.

11.3 Costs related to the shutdown of the installation

Whatever the actions used by the operators; the fouling phenomenon of heat exchangers is inevitable. The planned or unplanned shutdowns of installations to carry out cleaning and maintenance operations have repercussions in particular on the nominal production rate. These equally costly operations contribute to an increase of around 18% in the costs associated with operating the facilities.

12. Fouling mitigation

To reduce the negative effects of fouling on energy performance and the operation of heat exchangers, several methods are envisaged at different levels of the design-construction, and operation of this type of device.

Table 1 [15] regroups the main actions to be respected during the four stages of life of a heat exchanger.

Phase	Actions to respect
Design	Choice of heat exchanger type Choice of geometry and configuration Choice of operating conditions (temperature, flow, etc.).
Construction and assembly	Quality assurance on manufacturing Protection during transport and during storage Cleaning and passivation operation.
Operation	Maintaining operating conditions (temperatures, flow rates, etc.) Fluid pretreatment Use of additives (inhibitors, scale inhibitors, dispersants, acids).
Stop	Disassembly and manual cleaning Mechanical attacks on deposits (drilling, etc.) Hydraulic cleaning with a lance (steam, air).

Table 1.

Actions to be respected to reduce the impact of heat exchangers fouling [15].

Several works have been done to reduce fouling formation when heat exchangers are functioning. In the operation stage, numerous methods have been developed in recent years to control fouling [2, 6]. These methods can be classified as chemical means (inhibitor), mechanical means, changing the phases of the solution, electromagnetic fields, electrostatic fields, acoustic fields, ultraviolet light, radiation or catalytic treatment, surface treatment, green additives, fiber as a suspension, etc. In the past, chromate was a successful chemical agent for crystal growth control until it was banned. Then, chromate-based additives were been replaced with polyphosphate inhibitor which has a tendency to decompose the foulant in water containing high calcium hardness. Water fouling rich in calcium-containing phosphate fouling inhibitor has been studied by Knudsen et al. They demonstrated that acrylic acid/hydroxypropyl acrylate and acrylic acid/sulfonic acid were both very effective in inhibiting the deposition of calcium phosphate. Catalyst material composed of zinc and tourmaline was studied to mitigate fouling. To this end, Tijing et al. reported that this material potentially reduces calcium carbonate fouling formation. Teng et al. reported a similar finding but for calcium sulfate mitigation [44]. Furthermore, Tijing et al. further extended the research by using the same catalyst material to mitigate fouling on carbon steel piping. Most of the methods used in the past for fouling mitigation are dangerous to the environment. Thus, it is necessary to apply green technology methods and chemicals approaches benign to the environment [45].

One of safe and efficient nonchemical fouling mitigation method is physical water treatment (PWT) which is a good alternative. The PWT includes permanent magnets, solenoid coil devices, green additive and catalytic materials, and alloys [2]. Chemical additives are often used to mitigate scaling on heat transfer surfaces, but chemical products are expensive and pose a threat to the environment and health. Kazi [6] carried out the mitigation of calcium sulfate dehydrates scale formation on heat exchanger surfaces by using natural wood pulp fiber.

13. Cleaning of heat exchanger

It is often necessary to clean the heat exchangers to maintain or restore the efficiency of the heat exchanger. The cleaning operation of the heat exchanger may be classified into two groups: online and offline cleaning [46]. The cleaning can be done online during the phase of operation of the heat exchanger to maintain acceptable performance of the equipment without interruption of operation allowing thus to increase the service time between two maintenance shutdowns. In many other cases, it is necessary to proceed for complete cleaning of the equipment. The offline cleaning carries out during the stops phases of the installation.

13.1 Online cleaning

Generally, mechanical and/or chemical methods are used in online cleaning. These techniques of cleaning are designed for the tube side and do not require disassembly [13]. Among the main advantage of this type of cleaning is the continuity of service of the heat exchanger in the hope that no cleaning shutdown will occur. Abruptly stopping adds an extra cost of a new heat exchanger installation or a high cost of renovations and no guarantee that all the tubes would be cleaned sufficiently.

13.1.1 Online mechanical cleaning

1. Cleaning of the internal surface of tubes is made by means of circulation of sponge rubber balls [13], brushes, or a stretched spring. These techniques are able to prevent the accumulation of particulate matter, biofilm formation and scale, and corrosion product deposition. They are only applicable to flow through the inside of tubes.

2. Accoustic blow-molding [13]: this technique is based on the use of vibrations in the form of sound waves in high and low frequencies to relieve fouling problems on heat exchangers. It is a preventive technique and not curative. It has the advantage of not being aggressive for surfaces of exchange but it is much less effective in sticky and tenacious deposits that are generally associated with slagging.

3. Flow reversal: this technique allows for eliminating trapped particles in the entry collectors.

4. Overspeed: this technique allows finding operating conditions close to clean conditions. This type of cleaning removes the surface layer of the deposit, but leashes germs on the wall for deposit growth, which accelerates the deposit growth phase.

5. Thermal shock [13]: this technique is characterized by a quick change of temperature causing thus cracking of the foulant layer with the possibility of flaking.

6. Radiation [13]: the use of ultraviolet light and gamma rays has been considered for a long time for radiation sterilization of microbial-laden water.

13.1.2 Online chemical cleaning

1. Online chemical cleaning [13]: injection of chemical solutions into the process streams for cleaning purposes.

2. Scale inhibitors [13]

3. Chlorination used for combat bio-fouling [13]

13.1.3 Other online cleaning

It can be magnetic or electrical devices [13].

13.2 Offline cleaning

Offline cleaning is based on the stop operation and cleaning of the heat exchanger, which can be done by chemically or mechanical ways. This technique is used without needing to dismantle the heat exchangers, but generally, it is necessary to have access to the inside surfaces. It would be wise to consider the installation of a “standby” heat exchanger that provides the opportunity to clean the fouled heat exchanger while maintaining the production.

13.2.1 Offline mechanical cleaning

13.2.1.1 Pressurized water

This technique is proven and used in the most diverse industries. It is effective to remove deposits inside the tubes of the heat exchanger. However, there is a risk of surface erosion and especially of the destruction of the anti-corrosion protective film. The water flushing carries away the dislodged material and it is repeated until clean surfaces are obtained.

13.2.1.2 Using tools

This technique is used to remove even very hard deposits inside the tubes of heat exchangers. The removal devices are the pneumatic or electric motor, hole-punches, and hydraulic gun. The application of these devices may be to the rotating shaft including drills, cutting and buffing tools, and brushes that can be manufactured from different materials such as steels or nylon, brasses according to the tube material and the nature of the deposit.

13.2.2 Offline chemical cleaning

1. Acid solutions such as hydrofluoric, hydrochloric, citric, sulfuric, or complexing agents as EDTA are inhibitors for iron oxides, calcium/magnesium scales, etc. [13].

2. Chlorinated or aromatic solvents are inhibitors for heavy organic deposits such as tars and polymers [13].

3. Oxidant solutions of potassium permanganate [13] are inhibitors of carbon deposition.

14. Conclusion

Fouling is the main unresolved problem in heat exchanger operation and still remains a phenomenon misunderstood. Among the most serious concern of heat exchanger users is the problem of fouling deposition and its impact on the economy because there is a lack of awareness among relevant authorities. There are numerous and varied penalties for fouling and their effects on the effective, reliable, and safe functioning of equipment or structures are often very serious. Consequently, this present paper will encourage relevant organizations in different countries, seriousness of this problem, and application of possible mitigation approach. Fouling control and appropriate cleaning play an important role to reduce the production costs in the industry. Because of chemical usage, maintenance work and downtime loss, and water wastage, the production cost significantly increases. For that reason, the relevant authorities must understand the importance of control and cleaning of fouling and apply a specific standard of cleaning procedure in the industries.

Nomenclature

C	concentration (kg/m3)
D	diameter (m)
deq	equivalent diameter (m)
Ea	activation energy (J/mol)
f	transfer function
Ksp	solubility product
k1	first dissociation constant
k2	second dissociation constant
kr	reaction rate constant
ṁ	rate (kg/m2 s)
R	perfect gas constant (J/mol K)
Rf	fouling resistance (m2 K/W)
T	temperature (°C or K)
t	time (s)
U	global heat transfer coefficient (W/m2 K)
v	flow velocity (m/s)
α	heat transfer coefficient (W/m2 K)
β	mass transfer coefficient
δ	coefficient of linear expansion
ρ	density (kg/m3)
γ	concentration effect
σ	shear resistance of the fouling layer (N/m2)
τ	characteristic time or shear stress (s or N/m2)
ϴ	induction period (s)
Ψ	empirical structure parameter
Ω	water quality
d	relative to the deposit
f	fouling state
c	clean state
r	relative to removal
w	relative to the wall
*	relative to the asymptotic value
Pr	Prandtl number
Re	Reynolds number
Sc	Schmidt number