**6. Fouling models**

A number of models have been proposed for different types of fouling. Analysis and model improvement is still progressing as there are difficulties due to the complex nature of deposit formation and lack of reproducible measurement of fouling resistance. Most of the models have been simplified with many assumptions [40] as stated below:


According to Rankin and Adamson [29], it is not the rate of nucleation but the nuclei attachment which is strongly dependent on the surface roughness. Chandler [30] also observed similar results. In general the rough surface causes more fouling which reduces the delay time for all types of fouling. Surface roughness increases turbulence near the surface, which in turn increases the removal rate of fouling on the surface. Better performance occurred due to the increase in surface roughness with deposit formation and has been reported by some authors [1, 2]. Marriott [31] reiterated that mirror finished surfaces in heat

**5. Heat exchanger type, geometry and process fluid influencing fouling** 

Shell and tube heat exchangers are used most commonly but they are not particularly suitable for fouling conditions. Fouling can be reduced with special baffle and tube design. Several studies [32-35] have shown that finned tubes foul less than plain tubes. Non-uniform thermal expansion leads to lower deposit strength and hence less deposition. Freeman et al. [36] found that tubes with longitudinal grooves on the outside had less particulate fouling

Fluidised-bed heat exchangers are used in several applications to reduce or even eliminate fouling completely. Fluidised particles remove deposits from the heat transfer surface. They also enhance the heat transfer efficiency as they interrupt the viscous sub-layer. These heat exchangers have been used successfully to reduce fouling by hard, adhering silica deposits [37]. Graphite heat exchangers are also reported to have less fouling. Direct contact heat transfer may be another alternative to reduce fouling [38]. Properties of the process fluid such as the nature and concentration of the dissolved constituents or suspended particles,

Excessively high over-concentration of solids in the evaporating liquid may lead to carryover in the steam and cause fouling in process heat transfer equipment. Corrosion is very important on the steam side of process equipment. Water pH, over-concentration of treatment chemicals in evaporating liquids and dissolved gases (mainly oxygen and carbon dioxide) are very important contributors to corrosion fouling [39]. The presence of living organisms causes biological fouling and makes biofilms. This can sometimes enhance other fouling mechanisms too, as microbial deposits may trap suspended particles. They may also

A number of models have been proposed for different types of fouling. Analysis and model improvement is still progressing as there are difficulties due to the complex nature of deposit formation and lack of reproducible measurement of fouling resistance. Most of the

presence of any living organisms, solution pH etc. affect fouling significantly.

change the chemistry of water and can cause scaling or corrosion [39].

models have been simplified with many assumptions [40] as stated below:

Change in surface roughness with deposit formation is also neglected.

Changes in physical properties of the fluids are neglected in most of the cases.

exchangers are used to reduce fouling in practice.

(by alumina particles) than the plain tubes.

**6. Fouling models** 

Surface roughness is neglected.

Only one type of fouling is usually considered.

The fouling layer is assumed to be homogeneous.


It is also observed that few attempts have been made to model the initiation or roughness delay period. Almost all the models predict fouling (scaling) after the delay period. Some other notable parameters are neglected in modelling such as: (a) effect of simultaneous action of different fouling mechanisms, (b) equipment design, (c) surface parameters e.g. surface material and surface roughness, (d) increase in surface area with deposition, (e) properties of foulant stream, (f) nature of process, and the (g) fluctuations in operation.

Modelling is usually done taking into consideration only (a) flow velocity, (b) concentration, (c) wall and bulk temperature, and (d) time.

Watkinson and Martinez [11] developed a model, based on the fundamental material balance equation (2.1). For the deposition rate the following expression is adopted:

The deposition rate is expressed as shown in equation (6.1).

$$\frac{d\mathbf{x}\_f}{dt} = \frac{\mathbf{K}\_R}{\rho\_f} (\mathbf{c}\_F - \mathbf{c}\_{Sa})^n \tag{6.1}$$

For sparingly soluble salts with inverse solubility (e.g. CaCO3), the deposition rate is controlled by the slow reaction rate and the constant of reaction rate *KR* that obeys the Arrhenius equation:

$$K\_R = A\_0 e^{\left(\frac{-E}{R\_g T\_f}\right)}\tag{6.2}$$

with T as the interface temperature.

Kern and Seaton [43] recommend for the removal rate the equation:

$$\stackrel{\bullet}{m}\_r = a\_8 \tau\_f \propto\_f \tag{6.3}$$

Where is the shear stress exerted by the liquid flow on the fouling film. Even though CaCO3 deposits are much stronger than the particulate deposits considered by Kern and Seaton [43] the removal rate was assumed to be directly proportional to deposit thickness, which may not be correct for all the cases.

Kern and Seaton [41] proposed a model for particulate fouling which takes into account removal or re-entrainment of deposits. The mathematical model is based on a general material balance equation (2.1). Deposition and removal rates act separately and combine into a net deposition rate. The rate of deposition is expressed as:

$$
\stackrel{\bullet}{w}\_d = a\_\Theta \mathcal{E}' w \tag{6.4}
$$

Where, *c* is dirt concentration and w is constant weight flow of fluid. The removal rate is roughly proportional to the total depth of dirt deposited on the heat transfer surface as stated below.

Fouling and Fouling Mitigation on Heat Exchanger Surfaces 521

The heat transfer area of a heat exchanger is kept exaggerated to compensate retardation imposed by fouling. Oversized pumps and fans are selected to compensate design over-

In some occasions standby heat exchangers are kept in process design in order to ensure uninterrupted operation while a fouled heat exchanger is taken under cleaning maintenance. In-situ cleaning in some cases are recommended while chemical cleaning is preferred for others. All together, cost of cleaning, cleaning equipment, chemicals all are

Muller-Steinhagen [37] reported that total annual costs for highly industrialised countries such as the United States and the United Kingdom are about 0.25 percent of the countries gross national product (GNP). Even for a relatively less industrialised country like New Zealand, the total fouling costs are around 0.15 percent of its GNP. Muller-Steinhagen [37] has summarised the total fouling costs for various countries based on 1984 in Table 7.1.

Gilmour [42] reported that the degradation of heat transfer performance due to fouling in shell and tube heat exchangers occurs mainly due to poor shell-side design. In recent years numerous methods have been developed to control fouling. These methods can be classified as: (1) chemical methods, (2) mechanical methods and (3) changing the phase of the solution. By adding foreign chemicals in a solution, reduction of fouling is achieved by chemical methods of fouling mitigation. Chemical additives developed by many companies have been extensively used to mitigate fouling in the industrial sector. Various additives can be used to prevent scaling [43-44]. Bott [45] specified that the additives used act in different ways, such as (a) sequestering agents, (b) threshold agents, (c) crystal modifiers and (d) dispersants. Some of the common water additives are EDTA (sequestering agent), polyphosphates and polyphosphonates (threshold agents) and polycarboxylic acid and its derivatives (sequestering and threshold treatment). Sequestering agents such as EDTA complex strongly with the scaling cations such as Ca++, Mg++, and Cu++ in exchange with Na+, thus preventing scaling as well as removing any scale formed previously. They are used effectively as antiscalants in boiler feed water treatment. Troup and Richardson [46]

Polyphosphates and polyphosphonates as threshold agents are also used to reduce scaling in boilers and cooling water systems. Bott [45] said that they prevent the formation of nuclei thus preventing the crystallisation and mitigate fouling. Very small quantities of these

Crystal modifying agents (e.g. Polycarboxylic acid) distort the crystal habit and inhibit the formation of large crystals. The distorted crystals do not settle on the heat transfer surface, they remain suspended in the bulk solution. If their concentration increases beyond a certain limit, particulate fouling may take place. This is prevented either by using techniques to minimise particulate fouling or using dispersing agents along with crystal modifying

Though crystallisation fouling may not be prevented completely using additives, the resulting crystalline deposits are different from those formed in the absence of any

surfacing the enhanced pressure loss from reduction in the flow area.

claimed that their use is uneconomical when hardness levels are high.

agents are effective in reducing scaling from supersaturated salt solutions.

imposing extra to the capital cost of the plant.

**8. Fouling mitigation** 

agents.

$$\stackrel{\bullet}{m}\_{\mathbf{r}} = a\_{10} \boldsymbol{\pi}\_f \boldsymbol{\pi}\_f \tag{6.5}$$

Combining the equations for deposition and removal rates (6.4) and (6.5) with the material balance equation (2.1), the fouling resistance expression is obtained:

$$R\_f = \stackrel{\bullet}{R}\_f (1 - e^{-\theta t})\tag{6.6}$$

where is a time constant and *Rf* is the asymptotic value of the fouling resistance. For these also the following equations are obtained.

$$\stackrel{\ast}{R}\_{f} = \frac{a\_{9}c'w}{a\_{10}\lambda\_{f}\tau\_{f}}\tag{6.7}$$

$$
\theta = a\_{10}\tau\_f \tag{6.8}
$$

Here, is the thermal conductivity of the deposits, 9*a* and 10 *a* are proportionality constants. This model predicts asymptotic fouling behaviour with *Rf* being the fouling resistance after an infinite time of operation. According to this model, no matter what the conditions, i.e. type of fluid, heat exchanger surface, temperature driving force, an asymptotic fouling value will be obtained sooner or later with removal rates becoming equal to deposition rates.

#### **7. Cost imposed due to fouling**

An additional cost is imposed by fouling of heat transfer equipment in industries. Few studies have been undertaken to determine the fouling related costs in industry. Fouling costs can generally be divided into four major categories, such as (1) increased capital expenditure, (2) energy costs, (3) maintenance costs, (4) cost of production loss and (v) extra environmental management cost.


Table 7.1. Estimated fouling costs incurred in some countries.

The heat transfer area of a heat exchanger is kept exaggerated to compensate retardation imposed by fouling. Oversized pumps and fans are selected to compensate design oversurfacing the enhanced pressure loss from reduction in the flow area.

In some occasions standby heat exchangers are kept in process design in order to ensure uninterrupted operation while a fouled heat exchanger is taken under cleaning maintenance. In-situ cleaning in some cases are recommended while chemical cleaning is preferred for others. All together, cost of cleaning, cleaning equipment, chemicals all are imposing extra to the capital cost of the plant.

Muller-Steinhagen [37] reported that total annual costs for highly industrialised countries such as the United States and the United Kingdom are about 0.25 percent of the countries gross national product (GNP). Even for a relatively less industrialised country like New Zealand, the total fouling costs are around 0.15 percent of its GNP. Muller-Steinhagen [37] has summarised the total fouling costs for various countries based on 1984 in Table 7.1.
