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Predictive analysis of different models of the clean exchange coefficient in a heat exchanger from industrial
data
Rania Jradi, Ali Fguiri, Christophe Marvillet, Mohamed Razak Jeday
To cite this version:
Rania Jradi, Ali Fguiri, Christophe Marvillet, Mohamed Razak Jeday. Predictive analysis of different models of the clean exchange coefficient in a heat exchanger from industrial data. International Environment Security and Energy Congress, Feb 2018, Gabes, Tunisia. �hal-02388598�
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Predictive analysis of different models of the clean exchange coefficient in a heat exchanger from industrial data
Rania JRADIa, Ali FGUIRIa, Christophe MARVILLETb, Mohamed Razak JEDAYa
a University of Gabes , National Engineering School of Gabes ,Research unit « Energy & Environment » , Tunisia.
b French Institute of Refrigeration (IFFI),National Conservatory of Arts and Crafts(CNAM) ,Paris – France.
raniajradi@yahoo.fr, ali.fguiri@gmail.com, christophe.marvillet@cnam.fr, raz.jday@yahoo.fr ABSTRACT
Fouling in heat exchangers is a recurring problem in many industries. In this work, the heat exchange service parameter data from the phosphoric acid concentration loop allows the predictive models of the specific exchange coefficient to be analyzed at the beginning of each operating cycle for three types of heat exchangers. As such, several models obtained are compared.
Key words: Heat exchanger, fouling, modeling, clean exchange coefficient, fouling resistance.
1. INTRODUCTION
Fouling of heat transfer equipment is a predominant phenomenon in the reduction of the energy performance of these installations, it induces a certain number of undesirable effects having a significant economic cost, thus, the fouling can generate extra costs due to increased energy consumption, lost production, and maintenance and cleaning costs [1].
A developed procedure is based on the examination of the thermal exchange coefficient, on the simultaneous observation of the pressure drops and the mass flow rate, on the measurement of the temperature variation at the inlet and at the outlet of one of the two fluids. the use of a methodology to determine the fouling kinetics from experimental data. This method, which is the origin of this study, makes it possible to determine a model for predicting the clean exchange coefficient as a function of parameters of the installation. The calculation of the thermal resistance of fouling is made using the model obtained of the clean exchange coefficient and the global exchange coefficient. The determination of this resistance helps us to find a realistic kinetics of fouling and to allow to develop a suitable practice of maintenance with a view to a minimization of the energetic costs and the costs of intervention.
2. PRESENTATION OF THE INDUSTRIAL UNIT
The phosphoric acid concentration loop studied comprises 3 units operating in parallel. Its mission is to concentrate - by evaporation - the phosphoric acid from 28% P2O5 to 54%
P2O5 in a forced-circulation evaporator closed loop, operating under vacuum provided by a barometric condenser.
The concentration system used consists of a tubular heat exchanger made of stainless steel or graphite polyblocks, a centrifugal pump, a boiler or expansion chamber, a barometric condenser and a basket filter [2].
The addition of the dilute acid is carried out at the basket filter where it mixes with the circulating acid in order to ensure the protection of the pump from abrasion and to limit the fouling of the exchanger, which makes it possible to minimize the stopping frequency for washing. The circulation pump then sucks the mixture formed and sends it to the inlet of the exchanger at a temperature of the order of 70 ° C. The exchanger makes it possible to heat the phosphoric acid at a temperature of the order of 80 ° C. The steam undergoes condensation at a temperature of around 120 ° C. at the level of the exchanger. The condensate will be sent to a storage tank before being sent back to the utility center.
The superheated mixture of the acid leaving the exchanger then passes into the boiler where a quantity of water evaporates and the production of concentrated acid is done by overflow in a pipe inside the boiler and the rest will be recycled. The condenser also ensures the entrainment of incondensables coming out of the boiler by the effect of water tube created by a fall of the water. At the foot of the barometric guard, seawater is collected in a guard tank before being ejected towards the sea.
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Figure 1: schematic diagram of the installation 3. THERMAL MODELING
A metrology is set up in the concentration loop in order to control the thermal and hydraulic performance of the exchanger through the usual parameters which are: the 3 temperature measurements mounted across the exchanger (acid inlet, acid outlet and steam), pump suction and discharge pressure measurements, and acid density measurement. The acquisition of this data is often done by a computer system present in the control room [3]. These measurements enable us to establish thermal and conservation balances in order to determine the thermal power (Q), the mass flow rate of the phosphoric acid which is the cold fluid (ṁac), the mass flow rate of the steam which is the fluid hot (ṁvap), the logarithmic temperature difference (ΔTml) and finally the global heat exchange coefficient (U (t)):
QmvapLv (1)
QmacCpac(Tout,acTin,ac) (2)
Q U (t) S
ex T
ml F
(3) F being a corrective factor of the log mean temperature difference between 0 and 1.To access the fouling resistance Rf, it is necessary to determine:
- At the start of the installation, the exchange coefficient under proper condition U (t = 0)
- Periodically, the global exchange coefficient in fouling conditions U (t)
This calculation is possible using equations (1), (2) and (3) and using the data from the instrumentation.
- The fouling resistance is given by:
1 1
( ) (t) ( 0)
R t
fU U t
(4) 4. RESULTATS ET DISCUSSIONSThe conditions at the terminals of the exchanger (flow rates, inlet and outlet temperatures) at the beginning of each cycle are not stationary, it is necessary to re-evaluate the overall exchange coefficient under the conditions corresponding to the new operating conditions. For this purpose, a model connecting the clean exchange coefficient must be determined according to the parameters of the installation.
From the own exchange coefficient obtained at the beginning of each cycle and by varying each time the parameters of the installation, several predictive models are developed. The results from these different models are analyzed in order to determine, for each of them, their precision with respect to the experimental data. We quantify the accuracy of the model from the following indicators: the mean relative error (ɛ) and the coefficient of determination (R2) (the square of the Pearson sampling correlation coefficient) according to the following definitions [4]:
0,mod 0,
0,
( re) *100
re
U U
U (5)2 2
2 2
( ) (y )
( ) (y )
x x y
R
x x y
(6)
Table 1: Results of the precision indicators (R2, ε) for the stainless steel tubular
Model R2 ε (%)
linear 0.9837 28.71
2FI 0.9907 27.2
Quadratic 0.9998 2.25
Cubic 1 0.67
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Table 2: Results of the precision indicators (R2, ε) for the graphite poly block exchanger (provider A)
Table 3: Results of precision indicators (R2, ε) for the graphite poly block exchanger (provider B)
The exploitation of the collected operational data allowed us to establish models linking the clean exchange coefficient (U (t = 0)) with the flow of phosphoric acid, the inlet and outlet temperatures of the acid and the vapor temperature, and this for the exchangers examined. The cubic model for the stainless steel and graphite poly block exchanger (provider A) is fairly faithful to industrial data with R2 coefficients of determination equal to 1 and relatively low relative error (Table 1 and 2). On the other hand, for the graphite poly block exchanger (provider B), the quadratic model is fairly faithful (Table 3).
From these models and values of the global exchange coefficient (U (t)), which are calculated from equation (3), we evaluate the fouling resistance for different types of heat exchangers. using equation (4).
5. REFERENCES
[1]:H.Demasles, P.Mercier, P.Tochon et B.Thonon, Guide de l’encrassement des échangeurs de chaleur, Editions GRETh, 2007.
[2] Becker, 1989 P.Becker, Phosphates and Phosphoric Acid:
raw materials, technology and economics of the wet process, second edition,1989.
[3] Tunisian chemical group manual, 2014.
[4] Weber C,Tremeac B ,Marvillet C,Castelain C. Analysis of different models of prediction of fouling in a heat exchanger from experimental data. In :Proc.Annual Conf of the French Thermal Society,Toulouse,France ;2016
6. NOMENCLATURE
Model R2 ε (%)
Linear 0.9929 2.64
2FI 0.9981 1.3
Quadratic 1 0.166
Cubic 1 0.057
Model R2 ε (%)
Linear 0.9967 1.97
2FI 0.9998 0.35
Quadratic 1 0.035
F Correction factor Greek symbols
ṁ Mass flow, kg.h-1 Δ Difference of a
magnitude between two points
Q Thermal power, kW ɛ Relative error,%
Rf Fouling resistance , m2.K.W-1 Indices and exhibitors
S Area, m2 ac acid
T Temperature , K ex Exchange
t Time, h in input
U Global exchange coefficient, W.m-2.K-1
ml logarithmic mean
x,y Sample data value mod Model
𝑥̅,𝑦̅ Arithmetic mean of x and y 0 Origin (own)
Cp Heat capacity of the acid , kcal.Kg-1.K-1
out output
Lv Latent heat of vaporization , cal.Kg-1
re real
vap vapor
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