Elsevier

Chemical Engineering Science

Volume 59, Issue 24, December 2004, Pages 5787-5794
Chemical Engineering Science

Prediction of pulsation frequency of pulsing flow in trickle-bed reactors using artificial neural network

https://doi.org/10.1016/j.ces.2004.06.030Get rights and content

Abstract

Based on an extensive experimental database (946 measurements) set up from the literature published over past 30 years, a new correlation relying on artificial neural network (ANN) was proposed to predict the basic pulsation frequency of pulsing flow in the trickle-bed reactors. Seven dimensionless groups employed in the proposed correlation were liquid and gas Reynolds (ReL,ReG), liquid Weber (WeL), gas Froude (FrG), gas Stokes (StG) and liquid Eötvös (Eo¨L) numbers and a bed correction factor (Sb). The performance comparisons of literature and present correlations showed that ANN correlation is significantly an improvement in predicting pulsation frequency with an AARE of 10% and a standard deviation less than 18%. The effects of the variables including the properties of fluid and bed, and flow rate of liquid and gas on pulsing frequency were investigated by ANN parametric simulations and the trends were compared with exiting experimental results that confirmed the coherence of the proposed method with the previous experiments.

Introduction

Trickle bed reactor (TBR), which is a packed bed of catalysts with cocurrent downflow of gas and liquid, is used extensively for hydrotreating and hydrodesulfurization application in the refinery industry, and for hydrogenation, oxidation, and hydrodenitrogenation applications in the petrochemical and biochemical, and water treatment industries (Al-Dahhan et al., 1997, Dudukovic et al., 1999, Dudukovic et al., 2002).

TBR can experience several flow regimes depending on the flow rates and properties of the two-phase fluids, and the geometry and size of the packing. In general, TBR is operated under trickle flow regimes. Pulsing flow can be observed in TBR under relatively high gas and liquid flow rate. This regime is characterized by the alternating passage of liquid-rich and gas-rich pulses down the column with higher mass and heat transfer rates (Rao and Drinkenburg, 1985, Boelhouwer et al., 2001). This intensive interaction between the phases is beneficial for many chemical and physical processes. Catalyst utilization is increased due to the increased wetting of catalyst pellets, and axial dispersion is significantly reduced due to the “washing” action of liquid-rich pulses (Tsochatzidis et al., 1995; Iliuta et al., 1999b). For the fast exothermic reactions local hot spots are eliminated, which prevents the catalyst deactivation and runaway of reactors. In addition, in some case significant changes in both yield and selectivity could occur with the change of the pulsation frequency (Wu et al., 1995, Huang et al., 2003). Because of the relative short residence time of liquid phase during pulsing flow, pulsing flow is suitable for very fast reactions. To fully benefit the advantages of pulsing flow while keeping relative long residence times, liquid-induced pulsing flow is proposed and considered as a promising operation mode (Boelhouwer et al., 2001, Boelhouwer et al., 2002a, Wilhite et al., 2003). For modeling and developing rules for design and scale-up of commercial units operated in the pulsing flow regime or under the liquid-induced pulsing flow mode, it is necessary to know its basic characteristics involving the frequency of pulsations, velocity and structure of pulse.

Some early researchers have reported some data on pulsing flow characteristics determinated by measurement of pressure fluctuations, optical and conductometric techniques (Weekman and Myers, 1964, Beimesch and Kessler, 1971, Sato et al., 1973). Later, systematical investigations of Blok and Drinkenburg (1982) and Rao and Drinkenburg (1983) using conductance techniques examined the influences of liquid and gas superficial velocities, packing type and size, and column size on pulsation frequency of pulsing flow; moreover, they developed the first set correlations. In more recent studies, Tsochatzidis and Karabelas (1995) and Tsochatzidis et al. (1998) examined the influences of two phase flow rates and viscosity of liquid phase on the pulsation frequency determined by measurement of pressure fluctuations and conductance techniques and provided two sets of new correlations. Burghardt et al. (1999) investigated the effects of physicochemical properties of liquid phases and packing size on the frequencies of pulses traveling along the bed using the optical method and conductometry and correlated the results with a novel empirical relationship. Szlemp et al. (2001) evaluated the effect of foaming power for foaming systems on pulsation frequency based on the conductometry. Burghardt et al. (2002) observed that an increase in the pressure at constant velocities of the two phases leads to a marked increase in the frequency of pulsations for air–water under 0.1–0.9 MPa. Boelhouwer et al. (2002b) performed experiments with conductance techniques and a cylindrical hot film anemometer to provide the qualitative information concerning the gas–liquid distribution during pulsing flow in columns of 110 and 50 mm on diameter, packed with 3 and 6 mm glass spheres and 6.5 mm Raschig rings using air–water system. Burghardt et al. (2003) studied the pulsing flow properties with argon, nitrogen, and helium as gas phase and a specific class of systems forming foams of various stability (including water solutions of methanol, ethanol and isopropanol) as liquid phases. They concluded that a higher density of gas generates a higher pulsing frequency. Furthermore, new correlations for systems forming weak and strong foams have been elaborated separately.

However, all the experimental results and correlations are obtained under limited conditions and it is very difficult to extrapolate the correlations to a wide range of operating conditions, fluid physical properties and reactor structures. Hence, it is important to develop a general correlation for prediction of pulsing flow characteristics in TBR under a wide range of conditions. Meanwhile, the method surrounding the application of artificial neural network (ANN) has been successfully used in estimating and computing the trickle-to-pulse transition, pressure drop, liquid holdup, mass transfer, heat transfer and other properties in TBR (Larachi et al., 1999, Larachi et al., 2001, Larachi et al., 2003; Iliuta et al., 1999a, Iliuta et al., 1999b). Up to now little information has been reported on the application of ANN to predict the pulsation frequency of pulsing flow.

The objective of this research is to extend the application of ANN and to provide an effective tool for predicting the pulsation frequency of pulsing flow in TBR.

Section snippets

Pulsing flow properties database

In the present study, a comprehensive database has been built for the first time by bringing together literatures published over 30 years in view of its broad coverage of the literature. The database contains more than 940 experimental data for frequency of pulsations available in the literatures between 1970 and 2003. The frequencies of pulsing flow were mostly measured through optical, conductometric techniques and pressure fluctuations. A wide range of fluid physical properties, gas and

Development of ANN correlations

In order to derive the desired correlations, three-layer feed-forward backpropagation (BP) models of ANN were designed. The topological structure of the network is presented in Fig. 1.

The raw variables, such as fluid properties, operating conditions, particle and bed geometrical properties, are first combined into several dimensionless groups. Following the criteria and strategy suggested by Larachi et al. (2001) and Larachi et al. (2003), seven dimensionless groups including liquid and gas

Results of ANN correlation

Table 3 lists the fitted weights of ANN correlation. Fig. 2 depicts parity plot of the predicted versus experimental pulsation frequency on the training and test file. From Figs. 2a and b, more than 94% of the measured data in the training file are predicted within the envelopes of ±20%(±2AARE), while more than 97% of the measured data in the test file are predicted to fall within the ±2 AARE envelopes, i.e., ±15% error. For the whole database, the developed correlation yields an AARE of 10%

Conclusions

Based on the largest pulsation frequency database containing more than 940 experimental data from the literatures published during past 30 years, a new correlation for the prediction of pulsation frequency of pulsing flow in TBR was developed with the combined approaches relying on feed-forward neural network and dimensionless analysis. Seven dimensionless groups employed in the proposed correlation were liquid and gas Reynolds (ReL,ReG), liquid Weber (WeL), gas Froude (FrG), gas Stokes (StG)

Notations

aspacking specific surface area,
m-1(=6(1-ε)/(Φsdp)+4/dc)
AAREaverage absolute relative error
(=1Ni=1Nyexp(i)-ypred(i)yexp(i))
dccolumn diameter, m
dhKrischer-Kast hydraulic diameter,
m(=dp16ɛ3/9π(1-ɛ)23)
dpequivalent diameter of sphere having same volume
as the particle, m
Eo¨LEötvös number (=ρLgdp2Φs2/σL(1-ε)2)
fpfrequency of pulsation, s-1
FrGgas Froude number (=uG2/dpg)
Hhidden layer of ANN
I,inumber of nodes in the input layer
J,jnumber of nodes in the hidden layer
ppressure, MPa
ReαReynolds number (=uαdp

Acknowledgements

Financial support from the State Key Development Program for Basic Research of China granted by G2000048005 and SINOPEC granted by X503023 are gratefully acknowledged. We are also indebted to Professors A.J. Karabelas, A. Burghardt, G. Bartelmus, and D. Janecki who provided us with their original experimental data or papers. Special thanks are given to Miss A. Zhang for her help in verification and debugging of Pulsing Flow Properties Database, and Dr. Y. Ren, Prof. L. Wang for helpful

References (28)

  • F. Larachi et al.

    Prediction of liquid wetting efficiency in trickle flow reactors

    International Communications in Heat and Mass Transfer

    (2001)
  • A. Szlemp et al.

    Hydrodynamics of a co-current three-phase solid-bed reactor for foaming systems

    Chemical Engineering Science

    (2001)
  • M.H. Al-Dahhan et al.

    High-pressure trickle-bed reactorsa review

    Industrial Engineering Chemical Research

    (1997)
  • W.E. Beimesch et al.

    Liquid-has distribution measurement in the pulsing regime of two-phase concurrent flow packed beds

    A.I.Ch.E. Journal

    (1971)
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