Modeling and comparative study of heat exchangers fouling in phosphoric acid concentration plant using experimental data


Fouling still remains one of the most difficult problems for the use of heat exchangers. A methodological process of advanced analysis of experimental data on heat exchangers fouling allowing building predictive models is necessary to determine the fouling degree. Here, three different methods were used to predict the fouling resistance from some easily measurable variables of the system which are: Kern and Seaton, Partial Least Squares (PLS) and Artificial Neural Networks (ANN). Indeed, the fouling resistance was estimated according to the inlet and outlet temperature of the cold fluid, the temperature of the hot fluid, the density and the volume flow rate of the cold fluid and time for three types of heat exchangers, i.e. tubular stainless-steel and graphite blocks (Supplier (A) and Supplier (B)).The best modeling was determined by maximizing certain statistical accuracy indices. Results show that modeling by the use of Artificial Neural Networks is very performing compared with modeling by Partial Least Squares regression and Kern and Seaton. One of the key features of ANN model is their small levels of error in comparison with other models.

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Absolute average relative deviation


Mean square error


Root mean square error

R2 :

Determination coefficient

r2 :

Correlation coefficient

C1 :

Coefficient in Eq. (15), Pa−1.s−1

Cb :

Bulk concentration of particles, kg.m−3


Specific heat capacity, J.Kg−1.K−1

Cw :

Concentration of particles at the wall, kg.m−3


Correction Factor (=1 for a steam condenser)


Gravity acceleration (=9.81 m.s−2)


Total manometric head, m

kp :

Mass transfer coefficient, m.s−1

mp :

Mass of deposited particles per surface area, kg.m−2


Mass flow rate, kg.s−1


Observation number


Pressure, bar


Thermal power,W


Fouling resistance, m2.K.W−1


Area, m2


Temperature, K


Time, h


Global exchange coefficient, W.m−2.K−1

\( \dot{v} \) :

Volume flow rate, m3.h−1

ρ :

Density, kg.m−3

Φd :

Particle deposition rate, kg.m−2.s−1

Φr :

Particle removal rate, kg.m−2.s−1

τ :

Shear stress, Pa

ϴ :

Time required to reach 63.2% of Rf*, h


Difference of greatness between two points
















Logarithmic mean
















Asymptotic value


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Correspondence to Rania Jradi.

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Jradi, R., Marvillet, C. & Jeday, M.R. Modeling and comparative study of heat exchangers fouling in phosphoric acid concentration plant using experimental data. Heat Mass Transfer (2020).

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  • Heat exchanger
  • Fouling
  • Artificial neural networks
  • Kern and Seaton model
  • Partial least squares regression
  • Experimental data