**8. Results and discussion**

#### **8.1 Temporal evolution of the fouling resistance**

The evolution of the fouling resistance in the phosphoric acid concentration process heat exchanger was followed for a study period quoted previously. This heat exchanger is already in service for 100 days before the be-ginning of the present study. However, it has carried out a stop that lasted 12 hours then its return to service. This stop is for the heat exchangers cleaning.

All the results from the fouling resistance are presented on **Figure 5**.

According to the values of these resistances, which are the majority higher than zero, this experimental data presents a fouling state. This is evident since, as mentioned before, this exchanger is in service for more than 3 months. The curves presented show that the temporal evolution of the fouling resistance, seems to follow an asymptotic evolution, which conforms to the model of Kern and Seaton [17], with the absence of the induction period. That can be explained to the rapid evolution of this phenomenon associated in particular with the characteristics of the *Tubular Heat Exchanger Fouling in Phosphoric Acid Concentration Process DOI: http://dx.doi.org/10.5772/intechopen.88936*

#### **Figure 5.**

*Us* <sup>¼</sup> *U t*ðÞ¼ <sup>m</sup>\_ ac,cir <sup>∗</sup>*Cpac* <sup>∗</sup> ð Þ *Tout*,*ac* � *Tin*,*ac*

This relation is taken by the evaluation of energy on the heat exchanger by supposing the isolated system and the physical properties of the two fluids, as well

In the phosphoric acid concentration unit, the operating conditions at the limits of the heat exchanger unstable, it is necessary to disclose the heat exchange coefficients in the proper conditions *Up* corresponding to the new operating conditions. Assuming that the cleaning between operational runs is perfect and that the heat exchangers are totally free of fouling at the beginning of a new run. The initial value of the overall heat transfer coefficient at the beginning of every cycle is considered

The evolution of the fouling resistance in the phosphoric acid concentration process heat exchanger was followed for a study period quoted previously. This heat exchanger is already in service for 100 days before the be-ginning of the present study. However, it has carried out a stop that lasted 12 hours then its return to

According to the values of these resistances, which are the majority higher than zero, this experimental data presents a fouling state. This is evident since, as mentioned before, this exchanger is in service for more than 3 months. The curves presented show that the temporal evolution of the fouling resistance, seems to follow an asymptotic evolution, which conforms to the model of Kern and Seaton [17], with the absence of the induction period. That can be explained to the rapid evolution of this phenomenon associated in particular with the characteristics of the

All the results from the fouling resistance are presented on **Figure 5**.

as, the heat transfer coefficients stay constant along the exchanger.

*The measurement method at the boundaries of the heat exchanger.*

*Inverse Heat Conduction and Heat Exchangers*

as the value of the overall heat transfer coefficient in the clean state.

*Up* ¼ *U t*ð Þ¼ ¼ 0

**8.1 Temporal evolution of the fouling resistance**

service. This stop is for the heat exchangers cleaning.

**7.2 Calculation of** *Up*

**Figure 4.**

**8. Results and discussion**

**56**

*A* ∗ *F* ∗ *ΔTml*

m\_ ac,cir ∗*Cpac* ∗ ð Þ *Tout*,*ac* � *Tin*,*ac A* ∗ *F* ∗ *ΔTml*

(12)

(13)

*Variation of the fouling resistance as a function of time for the stainless-steel-tubular heat exchanger.*

treated phosphoric acid. As it appears clearly as the fouling resistance increases with the time until reaching a maximum value varied from 1.38 \* 10<sup>4</sup> to 1.61 \* 10<sup>4</sup> m<sup>2</sup> .K.W<sup>1</sup> .

The series functioned for more than 5 days, a sufficient period so that the resistance asymptotic value is reached. The fluctuation observed on these curves are due to the variation of flow, which, acting on the shear stress to the wall, causes re-entrain deposit particles or their deposition according to the sent flow value.

#### **8.2 Temporal evolution of the overall heat transfer coefficient**

From Eq. (11), we notice that the overall heat transfer coefficient is inversely proportional to the fouling resistance.

#### **Figure 6.**

*Variation of the overall heat transfer coefficient as a function of time for the stainless-steel-tubular heat exchanger.*

**9. Conclusion**

coefficient.

after the last stop.

**Nomenclature**

A area, m2

P pressure, bar Q thermal power, W Rf fouling resistance, m<sup>2</sup>

T temperature, K

ml logarithmic mean

\* asymptotic value

t time, h

ac acid cir circulation ex exchange in input

0 clean out output p clean state s dirty state st steam

Greek letters

Subscripts

**59**

Cp specific heat capacity, J.Kg<sup>1</sup>

ṁ mass flow rate, kg.s<sup>1</sup>

F correction factor (=1 for a steam condenser)

U overall heat transfer coefficient, W.m<sup>2</sup>

Δ difference of greatness between two points τ time required to reach 63.2% of Rf\*

The monitoring of heat exchangers provides the sound knowledge of the fouling evolution in the specific conditions of the process. Deposit formation is a thermal

The aim of this work was the study of the heat exchanger fouling phenomenon

The results achieved revealed an asymptotic evolution of the fouling resistance, compliant with the model of Kern and Seaton with the lack of the induction period, which is explained by the consequence of an improper cleaning, or a deviation between the present study and the beginning of the heat exchangers functioning

.K<sup>1</sup>

.K<sup>1</sup>

, h

.K.W<sup>1</sup>

in the concentration phosphoric acid process. Secondly, the study concerned the temporal evolution of the fouling resistance and the overall heat transfer

resistance which leads important economic penalties.

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

*Tubular Heat Exchanger Fouling in Phosphoric Acid Concentration Process*

**Figure 7.** *Kinetics of fouling of the stainless-steel-tubular heat exchanger.*

The fouling resistance increases over time, which leads to a decrease in the flow of heat exchanged between the phosphoric acid and the steam, and subsequently the decrease in the overall heat transfer coefficient. As it appears clearly on **Figures 5** and **6**, when the fouling resistance increases with the time, the overall heat transfer coefficient decreases until reaching a minimum value varied from 1821 to 2078 W.m�<sup>2</sup> .K�<sup>1</sup> .

#### **8.3 Temporal evolution of the fouling resistance obtained from both measurement and the Kern and Seaton model**

One of the earliest correlative models for the characterization of the asymptotic kinetics of fouling, we distinguish Kern and Seaton [17], whose general expression is as follows:

$$Rf(t) = Rf \stackrel{\*}{\
u} \* \left[\mathbf{1} - \exp\left(-\frac{t}{\tau}\right)\right] \tag{14}$$

This model gives rather satisfactory results, provided that the asymptotic value of the thermal resistance *Rf*\* as well as the time constant τ are evaluated, which strongly conditions the accuracy of the model.

The analysis of the experimental data which makes it possible to carry out the plots of **Figure 7** gives us the results of the two greatness *Rf*\* and *τ* for the stainless steel tubular heat exchanger. The asymptotic model is fairly faithful to the experimental data with determination coefficient *R*<sup>2</sup> close to 1 (**Table 1**).


**Table 1.**

*Values of the asymptotic fouling resistance, the time constant and the determination coefficient for the stainless-steel tubular heat exchanger.*

*Tubular Heat Exchanger Fouling in Phosphoric Acid Concentration Process DOI: http://dx.doi.org/10.5772/intechopen.88936*
