**3. Rate of fouling**

compromises energy recovery in these process. Progress is hampered by the lack of quantitative knowledge of the dynamic effects of fouling on heat transfer exchanger [6]. Generally, phosphoric acid, which is the cold fluid, flows through the tube side while steam, which is the hot stream, flow through the shell side in heat exchangers [7]. The solution of concentrated phosphoric acid is supersaturated with calcium sulfate, resulting in the deposition on the contact material [8]. Given that the thermal conductivity of these scales is low, even a thin layer of scale can drastically reduce the overall heat transfer coefficient [9]. Furthermore, fluorosilicate and fluoroaluminate deposits on the acid ducts of clarifier tanks and evaporators can be imbedded in gypsum scale, which reduces pipe diameter and flow rate. In spite of considerable research efforts at the phosphoric acid type scale, no viable commercial solution has been found [10–12]. Behbahani et al. [13] have done a high number of fouling experiments in a side-stream of a phosphoric acid plant for various flow velocities, surface temperatures and concentrations in order to determine the mechanisms which control the deposition process. After identifying the effects of operational parameters on the deposition process, a fouling kinetic model by crystallization has been developed in Behbahani et al. [8]. A mathematical model has been elaborated to predict the fouling resistance in concentrating phosphoric acid [14]. The predicted fouling resistances were compared with the experimental data. Majority engineering calculations on heat transfer use the experimental heat trans-

In this survey, we will examine the fouling phenomenon of the heat exchanger tubes for the preheat circuit of the phosphoric acid. The heat exchanger used for heating phosphoric acid is exposed to the fouling problem at the tube side of heat exchangers. In this context an experimental determination of the thermal fouling resistance by measuring the inlet and outlet temperatures of phosphoric acid, the temperature of steam, suction and discharge pressure of the pump and acid density measurement, the overall heat transfer coefficient has been determined. The determination of the overall heat transfer coefficient for the heat exchanger with clean

Fouling can be divided into a number of distinct mechanisms. In general, many of these fouling mechanisms occur at the same time and each requires a different prevention technique. Among these different mechanisms, some represent different stages of the fouling process. The main mechanisms or stages of fouling include:

accumulation. This accumulation of relatively small deposits can even improve heat transfer over a clean surface and give the appearance of a "negative"

4. Separation and deposition phase involving nucleation or initiation of fouling

1.Period of initiation or delay. This is the clean surface period before dirt

fouling rate and a total negative fouling amount.

sites and attachment leading to deposit formation.

auto-retardation, erosion and elimination.

2.Particle fouling and formation, aggregation and flocculation.

3.Mass transport and migration of fouling agents to fouling sites.

5.Growth, aging and hardening and increase of deposit resistance or

and fouled surfaces makes it possible to calculate the fouling resistance.

fer coefficients [15].

*Inverse Heat Conduction and Heat Exchangers*

**2. Fouling mechanisms**

**48**

Fouling is defined as a phenomenon that occurs with or without a temperature gradient in many natural, domestic and industrial processes. A surface is "dirty" when unwanted material accumulates there.

The fouling rate is normally defined as the average deposit surface loading per unit of surface area in a unit of time. Depending on the fouling mechanism and conditions, the fouling rate may be linear, falling, asymptotic or saw-tooth, as the case may be. **Figures 1** and **2** shows the different types of fouling rate.

1.Linear fouling is the type of fouling where the rate of fouling can be stable over time with the increase of fouling resistance and deposit thickness. It usually occurs when the temperature of the deposition in contact with the flowing fluid remains constant.

Ebert and Panchal [16] presented a fouling model expressing the average (linear) fouling rate under given conditions following two competing terms, namely a deposit term and an attenuated term.

Fouling rate ¼ ðdeposit termÞ � ð Þ anti � deposit term

$$\frac{d\text{Rf}}{dt} = \alpha \text{ } \text{Re}\,\, ^\beta \text{Pr}\,\, ^\delta \exp\left(\frac{-E}{RT\_{film}}\right) - \gamma \tau\_w \tag{1}$$

**Figure 1.** *Fouling curves.*

**Figure 2.** *Practical fouling curve.*

where *α*, *β*, *γ* and *δ* are parameters determined by regression, *τ<sup>w</sup>* is the shear stress at the tube wall and *T*film is the temperature of the fluid film (average of local bulk and local wall fluid temperatures). The relationship in Eq. (1) indicates the possibility of identifying combinations of temperature and velocity below where fouling rates will be negligible. Ebert and Panchal [16] present this as the "threshold condition." The model in Eq. (1) suggests that the geometry of the heat exchanger which affects the surface and film temperatures, velocities and shear stresses can be effectively applied to maintain the conditions below "threshold conditions" in a given heat exchanger.

2.Thickness measurement: in many examples of fouling the thickness of the deposit is relatively small, perhaps less than 50 μm, so that a direct

measurement is not easy to obtain. A relatively simple technique provided there is reasonable access to the deposit, consists in measuring the thickness. By using a removable coupon or plate, the thickness of a hard deposit such as a scale, can be obtained using a micrometer or traveling microscope. For a deformable deposit containing a large proportion of water, e.g., a biofilm it is

3.Heat transfer measurements: in this method, the fouling resistance can be determined according to the changes in heat transfer during the deposition process. The equation for the following operations will be Eq. (11). The data can be reported in terms of changes in overall heat transfer coefficient. A major hypothesis of this method is that the presence of the deposit does not affect the hydrodynamics of the flowing fluid. However, during the first stages of deposition, the surface of the deposit is generally rougher than the metal surface so that the turbulence in the fluid is greater than when it is flowing on a smooth surface. As a result the fouling resistance calculated from the data will be lower than if the increased turbulence level had been taken into account. It is possible that the increased turbulence offsets the thermal resistance of the deposit and negative values of thermal resistance will be

4.Pressure drop: as an alternative to direct heat transfer measurements it is possible to use changes in pressure drop caused by the presence of the deposit. The pressure drop is increased for a given flow rate due to the reduced flow area in the fouled condition and the roughness of the deposit. The shape of the curve relating pressure drop with time will generally, follow an asymptotic shape so that the time to achieve asymptotic fouling resistance can be determined. The method is often associated with the direct measurement of thickness of the deposit layer. Friction factor changes can also be used to

5.Other techniques for assessing fouling: with regard to their effect on heat exchanger performance the measurement of heat transfer reduction or increase in pressure drop provide a direct indication. The simple methods of measuring deposit thickness described above are useful, but in general they require that the experiment be completed in order to allow access to the test sections. Ideally non-intrusive techniques would allow further deposition while maintaining experimental conditions without disturbance. Such techniques include the use of radioactive tracers and optical methods. Laser techniques can be used to study the accumulation and removal of deposits. In addition, infra-red systems are used to study the development and removal of biofilms from tubular test sections. Microscopic examination of deposits may provide further evidence of the mechanisms of fouling, but this is usually a

As noted above, fouling has the effect of forming on the heat transfer surface a substantially solid deposit of low thermal conductivity, through which heat is to be

"backup" system rather than providing quantitative data.

possible to use an electrical conductivity technique.

*Tubular Heat Exchanger Fouling in Phosphoric Acid Concentration Process*

*DOI: http://dx.doi.org/10.5772/intechopen.88936*

calculated.

indicate fouling of a flow channel.

**5. Prediction of fouling factor**

**51**

