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Licensed Unlicensed Requires Authentication Published by De Gruyter September 4, 2018

Robust Prediction of Filtrate Flux for Separation of Catalyst Particles from Wax Effluent of Fischer-Tropsch Bubble Column Reactor via Regularization Network

A. Garmroodi Asil, A. Nakhaei Pour and Sh. Mirzaei


The effectiveness of an internal filtration system intended for separation of wax-catalyst from Fischer–Tropsch synthesis products is investigated in the present study. The generalization performances of in-house Regularization Network (RN) equipped with efficient training algorithm is recruited for prediction of filtrate flux. The network was trained by resorting several sets of experimental data obtained from a specific system of air/paraffin liquid phase/alumina oxide particle conducted in a slurry bubble column reactor. The RN is employed to explore the relationship between the slurry phase temperature (10–60 °C), pressure difference (0.3, 0.6 and 0.9 bar) and time (0–120 min) on the rate of outcome filtrate from various size of filter element (4, 8 and 12 microns). The superior recall and validation performances with different exemplars data points show that the optimally trained RN which has solid roots in multivariate regularization theory, is a reliable tool for prediction of filtrate flux. Faithful generalization performance of RN revels that around 66 % reduction in filtrate flux is observed by decreasing temperature from 60C to10C for filter pore size of 4 microns. Decreasing of slurry viscosity is the main reason of such behavior. Increasing pressure driving force has a significant effect on elevating filtrate flux. Due to cake formation, filtrate flux is decreased from 2 to 1.4 (ml/min.cm2) at constant temperature of 60C for filter pore size of 8 microns. Furthermore, the backwashing process is more effective for smaller pore size filter and temperature variation does not have any considerable effect on filter recovery.


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



Unit Vector


Green’s matrix


Smoother matrix


Identity matrix


Number of neurons


Synaptic weight vector


Input vector


Real response values


Temperature (°C)


Time (min)


Pressure difference (bar)

Greek letters

Regularization parameter


Optimal regularization parameter


Isotropic spread


Optimal isotropic spread



Regularization network


slurry bubble column reactor




Slurry bubble column reactor


Artificial neural network


Gas to liquid


Leave one out cross validation


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Received: 2018-04-28
Revised: 2018-08-07
Accepted: 2018-08-08
Published Online: 2018-09-04

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