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Reliable prediction of heat transfer coefficient in three-phase bubble column reactor via adaptive neuro-fuzzy inference system and regularization network

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Abstract

In the present article, generalization performances of regularization network (RN) and optimize adaptive neuro-fuzzy inference system (ANFIS) are compared with a conventional software for prediction of heat transfer coefficient (HTC) as a function of superficial gas velocity (5–25 cm/s) and solid fraction (0–40 wt%) at different axial and radial locations. The networks were trained by resorting several sets of experimental data collected from a specific system of air/hydrocarbon liquid phase/silica particle in a slurry bubble column reactor (SBCR). A special convection HTC measurement probe was manufactured and positioned in an axial distance of 40 and 130 cm above the sparger at center and near the wall of SBCR. The simulation results show that both in-house RN and optimized ANFIS due to powerful noise filtering capabilities provide superior performances compared to the conventional software of MATLAB ANFIS and ANN toolbox. For the case of 40 and 130 cm axial distance from center of sparger, at constant superficial gas velocity of 25 cm/s, adding 40 wt% silica particles to liquid phase leads to about 66% and 69% increasing in HTC respectively. The HTC in the column center for all the cases studied are about 9–14% larger than those near the wall region.

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Abbreviations

e:

Unit vector

G:

Green’s matrix

H:

Smoother matrix

I :

Identity matrix

N:

Number of neurons

\( \underline{w} \) :

Synaptic weight vector

\( \underline{x} \) :

Input vector

\( \underline{y} \) :

Real response values

μ :

Membership function

X:

Input variable

a, b, c:

Premise parameters

p, q, r:

Consequent parameters

O:

Membership grade

w:

Firing strengths

A, B:

Linguistic label

T S :

Surface temperature

T ∞ :

Bulk fluid temperature

h :

Heat transfer coefficient

λ :

Regularization parameter

\( {\underline{w}}_{\lambda } \) :

Linear synaptic weight

σ:

Isotropic spread

ANFIS:

Neuro-fuzzy inference system

HTC:

Heat transfer coefficient

RN:

Regularization network

SBCR:

Slurry bubble column reactor

ANN:

Artificial neural network

RMSE:

Root-mean-square error

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Acknowledgements

The authors wish to acknowledge the financial support granted by Ferdowsi University of Mashhad.

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Authors and Affiliations

  1. Chemical Engineering Department, Faculty of Engineering, University of Bojnord, Bojnord, Iran

    A. Garmroodi Asil

  2. Chemistry Department, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran

    A. Nakhaei Pour

  3. Chemical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Sh. Mirzaei

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  1. A. Garmroodi Asil
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Correspondence to A. Garmroodi Asil.

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Garmroodi Asil, A., Nakhaei Pour, A. & Mirzaei, S. Reliable prediction of heat transfer coefficient in three-phase bubble column reactor via adaptive neuro-fuzzy inference system and regularization network. Heat Mass Transfer 54, 2975–2986 (2018). https://doi.org/10.1007/s00231-018-2332-4

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