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Chemical Engineering Journal xxx (2012) xxx–xxx

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Chemical Engineering Journal

journal homepage: www.elsevier .com/locate /cej

A new model for the design and analysis of trickle bed reactors

S. Schwidder ⇑, K. SchnitzleinBrandenburg University of Technology Cottbus, Department of Chemical Reaction Engineering, Burger Chaussee 2, 03044 Cottbus, Germany

h i g h l i g h t s

" A new model for the design and analysis of catalytic trickle bed reactors was developed." Local liquid distribution is obtained as a function of operating conditions and physical properties of all three phases." Impact of local incomplete wetting on conversion is taken into account." Modeling of the kinetics and mass transport on a particle as well as on a reactor scale." Performance is demonstrated by comparison of model predictions to experimental data.

a r t i c l e i n f o

Article history:Available online xxxx

Keywords:ModelingTrickle bedMultiscale analysisMultiphase reactor

1385-8947/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.cej.2012.07.054

⇑ Corresponding author. Tel.: +49 (0)355 69 1111;E-mail addresses: [email protected] (S.

tu-cottbus.de (K. Schnitzlein).

Please cite this article in press as: S. Schwidder,dx.doi.org/10.1016/j.cej.2012.07.054

a b s t r a c t

A new discrete model was developed for the design and analysis of catalytic trickle bed reactors operatingin the low interaction regime based on the local structure of packed beds. By detailed comparisons ofmodel predictions to experimental data the performance of the new model is demonstrated.

By means of this model the steady-state behavior of trickle bed reactors can be studied in terms ofoperating conditions, physical properties of all three phases, transport parameters and isothermal reac-tion kinetics on a particle as well as on a reactor scale.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Catalytic trickle bed reactors are multiphase systems consistingof a fixed bed of catalytic particles with in most cases cocurrentdownflow of liquid and gas. The behavior of trickle bed reactorsis very complex and depends on mass and heat transfer as wellas on hydrodynamics [1]. At low liquid flow rates, as encounteredin the low interaction regime, maldistribution of liquid flow isfound to occur. Such maldistribution may arise from a large num-ber of potential reasons, e.g. improper initial distribution of feed,varying local structural properties of the packing, wall effects, wet-ting characteristics of the catalyst, liquid properties as well asoperating conditions. It can result in incomplete wetting, existenceof hot spots and catalyst deactivation. Therefore, detailed informa-tion about the liquid flow distribution inside the packing is essen-tial for a proper design of trickle bed reactors [2,3].

For a quantitative prediction of the reactor performance math-ematical models are needed which are able to represent the localinteractions between liquid and solid on a reactor as well as on aparticle scale [4]. In the past several models have been proposed

ll rights reserved.

fax: +49 (0)355 69 1110.Schwidder), k.schnitzlein@rt.

K. Schnitzlein, A new model for

in the literature which can be classified according to their basicassumptions with respect to the representation of liquid flow.

� Pseudohomogenous models represent the liquid flow as contin-uous functions of local position [5–9] thus totally ignoring thediscrete structure of liquid flow in the trickling regime. It hasbeen shown that these models are able to satisfactorily predicttrickle bed performance provided that all model parameters andtheir dependencies are known, the liquid is distributed uni-formly and all particles are completely wetted [10]. Howeverthis is not a realistic description of the low interaction trickleflow regime in packed bed reactors [11,12].Partial wetting conditions may be taken into account by use of aglobal wetting parameter as done by Iliuta et al. [13,14].� Discrete models represent liquid flow as a result of single dis-

crete transport processes occurring at the particle scale. There-fore, they are ideally suited for representing the discretestructures of liquid flow in the trickling regime. Furthermore,experimental investigations have shown that the liquid–solidinteractions in the low interaction regime are locally randombut stable with time.Basically these models rely on a representation of the pore spaceas a combination of recurring basic elements, i.e. cells, compris-ing one or more particles or even only a part of a particle itself[15–17]. Liquid flow distribution is obtained by balancing the

the design and analysis of trickle bed reactors, Chem. Eng. J. (2012), http://

http://dx.doi.org/10.1016/j.cej.2012.07.054

mailto:[email protected]

mailto:k.schnitzlein@rt. tu-cottbus.de

mailto:k.schnitzlein@rt. tu-cottbus.de


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Nomenclature

as specific area of particle per unit volume (m2/m3)c concentration (mol/m3)c(1) concentration inside dynamic volume (mol/m3)c(2) concentration inside exchange volume (mol/m3)Dax axial dispersion coefficient (m2/s)d diameter (m)E(t) mean residence time distributionMf maldistribution factor [26]p partial pressure (Pa)q volumetric flow rate (ml/min)q1 volumetric flow rate between dynamic and exchange

volume (ml/min)r reaction rate (mol/m2s)t time (s)u superficial velocity (m/s)V volume (m3)V(1) dynamic volume (m3)X conversionz length (m)

Greek lettersa model parameter for the CSTR with Exchange Volume

b model parameter for the CSTR with Exchange Volume� liquid holdupm stoichiometric coefficients space time (s)�s mean residence time inside the reactor (s)

Subscripts and superscripts0 inlet conditions1 species 1, gas2 species 2, liquidb bulkdyn dynamicG gasL liquidp particles solidstat statict tube⁄ saturation� global parameter

2 S. Schwidder, K. Schnitzlein / Chemical Engineering Journal xxx (2012) xxx–xxx

inflow and outflow of all interconnected cells. Similarly, percola-tion models represent the pore space as a body-centered cubiclattice consisting of sites and bonds. Liquid flow through thelattice is modeled as a percolation process based on statistic cal-culations (Monte Carlo method) [12].Based on a detailed knowledge of the geometry of the porespace, the liquid flow can also be simulated using a Lagrangianapproach, i.e. interpreting the entire trickling liquid flow as thesum of distinctive motions of individual liquid elements [18].According to the authors a liquid element can encounter variousactions (e.g. roll, split or coalescence) while traveling throughthe packed bed. At every geometric location of the packing therespective action is randomly chosen out of a set of possibleactions.

In view of the discrete structure of the liquid flow in trickle bedreactors operating in the low interaction regime, Lagrangian meth-ods are regarded to be the most promising methods for simulatingthe liquid flow on a particle scale. It is the objective of this contribu-tion to demonstrate that by using a Lagrangian method the three-dimensional liquid distribution inside the packing can be obtainedin terms of physical properties of the liquid–solid system used.Moreover, it will be shown that the impact of partial wetting on con-version can be reliably predicted provided the kinetics and the masstransport of the reaction system under consideration is known.

Fig. 1. Computer generated sphere packing with catalytic (bright color) and non-catalytic (dark color) particles.

2. Model development

2.1. Packing generation

Maldistribution of liquid flow arises from a large number of po-tential reasons, among others the varying local structural proper-ties of the packing are found to be dominant. Therefore, in orderto account for maldistribution effects, the model is based on adetailed knowledge of the local structure of the packed bed. Unfor-tunately, these geometrical data can only be obtained with largeexperimental effort.

As was shown by Schnitzlein [19], computer generated spherepackings closely resemble real packings, i.e. predicted radial

Please cite this article in press as: S. Schwidder, K. Schnitzlein, A new model fordx.doi.org/10.1016/j.cej.2012.07.054

voidage distributions are in good agreement with reported litera-ture data. Recently, the packing generation procedure has been ex-tended to account for other particle geometries, e.g. cylindricalextrudates, too. Therefore, as a remedy all the necessary informa-tion about the local structural properties of the packed bed are re-trieved from such simulated packings. By specifying type (e.g.sphere, cylinder), size and catalytic activity for every particle apolydispersed packing inside a cylindrical container can be gener-ated. It is noted that the hydrodynamic model shown below is con-fined to spherical particles. A small section of a simulated packedbed with catalytic (bright color) and non-catalytic (dark color) par-ticles is shown in Fig. 1. It is possible to generate realistic packingswith several thousands of particles.




0 0.01 0.02 0.03 0.04 0.05

measured ε stat [ - ]

0

0.01

0.02

0.03

0.04

0.05

calc

ulat

edε st

at [

- ]

Fig. 3. Comparison between calculated and measured static liquid holdup fordifferent liquid–solid systems and geometrical properties (20% variance) [20].

S. Schwidder, K. Schnitzlein / Chemical Engineering Journal xxx (2012) xxx–xxx 3

2.2. Hydrodynamics

Following the approach of Spedding and Spencer [18] the liquidflow distribution is simulated by considering a large number of dis-crete liquid elements of finite size introduced at the top of thepacking. On its way through the packed bed a liquid element (dy-namic liquid holdup) can appear either as rivulet, film or singledrop (see Fig. 2b–d). Moreover, the liquid can be trapped at contactpoints between two or more particles thus contributing to the sta-tic liquid holdup (see Fig. 2a) [13].

Based on the information about the local position of every sin-gle particle inside the packed bed the stagnant liquid bonds be-tween two particles and between a particle and the wall can bepredicted in terms of the liquid–solid properties. Therefore, thesurface tension, the contact and the half filling angle as well asthe critical separation distance have to be experimentally deter-mined for each liquid–solid system under consideration. The goodagreement between predictions and experimental data is noted(see Fig. 3). Details of the calculation are given elsewhere [20].

While traveling through the packed bed each discretized liquidelement evolves through local interactions with other elementsand its environment as well as with external forces. In contrastto the original approach of Spedding and Spencer [18], the variousactions a liquid element can encounter are mainly governed by thephysical properties of the liquid–solid system [21,22] and only to asmall extent by random processes. In order to identify the relevantactions and to quantify their impact, a large number of experi-ments have been carried out varying the physical properties ofthe liquid, the material of the spherical particles, the wettability

(a)

(c)Fig. 2. Different appearanc


and the properties of the packed bed as well [23]. The respectiveexperimental conditions are summarized in Table 1.

Experimentally, the liquid distribution inside the reactor can beobtained by varying the reactor height and measuring the liquiddistribution at the outlet via the mixing-cup technique, provided

(b)

(d)es of a liquid element.




Table 1Varied parameters for the liquid distribution measurements.

Parameter Range of variation

Particle material Glass, polyoxymethylene,Vitrified clay

Surface tension 0.032–0.079 N/mLiquid density 991–1181 kg/m3

Liquid viscosity 1–2.5 and 100 mPasContact angle 0 –75�Particle diameter 0.004–0.014 mCylinder diameter 0.05 and 0.10 mPacking height 0.004–0.70 mLiquid load 0.6–6 kg/(m2s)Liquid distribution Single central,

Uniform distribution

Fig. 4. Collector – schematic (le

Fig. 5. Simulated liquid distribution (left, dark colored spheres are in con



that the packing structure is not disturbed by the collector device.This was achieved by using a new collector type consisting ofhemispherical caps arranged in a structure similar to an orderedpacking of spheres as shown in Fig. 4 [24].

The liquid leaving the reactor in every interstice comprised bycontacting particles is collected into compartments, which are inturn connected to separate liquid reservoirs. The content of eachreservoir is obtained gravimetrically. It is noted that by applyingdifferent combinations of compartments the liquid flow distribu-tion can be obtained with a high local resolution. Prior to eachexperiment the packing was prewetted according to Levec et al.[25]. Moreover, in order to measure the dynamic liquid holdupduring the experiments the reactor was suspended on a tensionS-type load cell.

Fig. 5 exemplarily shows a simulated liquid distribution as wellas a radial flow distribution for a sphere packing with a reactor-to-

ft) and photography (right).

tact with liquid) and radial flow distribution over the height (right).





particle-diameter ratio of dt/dp = 10 for different horizontal cutsthrough the reactor at distinct heights.

Despite the fact that the simulated packings closely resembleexperimental packings the actual positions of individual spheresmay be different. Therefore, one cannot expect an exact localagreement of the simulated liquid flow distribution with experi-mental data. In order to provide a reasonable means for compari-son, the maldistribution coefficient as proposed by Marcandelliet al. [26] was used. Fig. 6 shows a comparison of the maldistribu-tion coefficients as obtained for simulated and experimentally ob-tained liquid flow distributions. Despite the fact that liquid flow inpacked beds is to a certain extent governed by random processes,the model is able to predict the maldistribution in packed bedsin good agreement with experimental data for all liquid–solid sys-tems under consideration.

Knowing the liquid flow distribution inside the packed bed thedynamic holdup is calculated by summing over all discrete liquidelements inside the packing. A comparison between experimentaland simulated dynamic liquid holdup is shown in Fig. 7. Moreover,

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1measured M

f [ - ]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

calc

ulat

ed M

f [

- ]

Fig. 6. Measured and simulated maldistribution factor [26] (0.2 deviation).

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2measured ε

dyn[ - ]

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

calc

ulat

ed ε

dyn [

- ]

Fig. 7. Comparison between experimental and simulated dynamic liquid holdup(0.05 deviation).


local degree of wetting can be calculated for each single particle byadditionally considering the local static holdup.

2.3. Network model

In order to account for the mixing characteristics of liquid flowinside the packing the obtained liquid distribution is transformedinto a three-dimensional directed graph structure [27], the verticesand the edges of which are represented by contact points and ele-ments of liquid flow (see above), respectively. Small basic reactortypes (e.g. Plug Flow Reactor PFR, Continuous Stirred Tank ReactorCSTR, Dispersed PFR) of different size are attributed to the verticesand edges as shown in Fig. 8.

By choosing an appropriate reactor type with an exchange vol-ume the interaction between static and dynamic liquid elements[28] is accounted for, as well. The characteristic parameters foreach basic reactor (e.g. type, size) are retrieved from tracer exper-iments. These experiments have been carried out by injecting anelectrolyte sample at the top of the bed and monitoring its spreadat the outlet with respect of time (axial dispersion) and radial po-sition (radial dispersion).

Since the radial tracer distribution is mainly governed by thestructural properties of the packing, only axial tracer distributionsare used to obtain values for the model parameters for the individ-ual basic reactor types (e.g. D�ax;a� and b�). The axial dispersioncoefficient is obtained by fitting the axial tracer distribution as ob-tained by means of a one-dimensional dispersion model to exper-imental data. Subsequently, the remaining parameters areiteratively adjusted until a good agreement is achieved (see Fig. 9).

The instationary mass balance equations for each basic reactorare formulated in terms of concentrations in both phases takinginto account the respective catalytic surface or catalyst mass (seeEqs. (1)–(7)).

Continuous Stirred Tank Reactor:

@c@t¼ qL0

Vðc0 � cÞ þ masrðcÞ ð1Þ

Plug Flow Reactor:

@c@t¼ �u

@c@zþ mas rðcÞ ð2Þ

Dispersed Plug Flow Reactor:

@c@t¼ �u

@c@zþ D�ax

@2c@z2 þ mas rðcÞ ð3Þ

Continuous Stirred Tank Reactor with Exchange Volume:

Fig. 8. Simulated liquid flow (left) and representation by a three-dimensionalnetwork of minireactors (right).




0 10 20 30 40 50 60 70 80 90

t [s]

0

0.01

0.02

0.03

0.04

0.05

E(t

) [

- ]

simulationexperiment

τR

Fig. 9. Comparison between experimental and simulated mean residence timedistribution.


� Dynamic Volume (1):

p1

g

Fig. 10.phase r

Pleasedx.doi

@cð1Þ@t¼ qL0

a�Vðc0 � cð1ÞÞ þ b�qL0

a�Vðcð2Þ � cð1ÞÞ þ masrðcð1ÞÞ ð4Þ

with

a� ¼ Vð1ÞV

ð5Þ

b� ¼ qL1

qL0ð6Þ

� Exchange Volume (2):

@cð2Þ@t¼ b� qL0

ð1� a�Þ Vðcð1Þ � cð2ÞÞ þ m as rðcð2ÞÞ ð7Þ

REACTION

GAS / LIQUID LIQUID / SOLID

GAS / SOLID

c1b

c2b

c*1

p*1

b

particle

gas film unwetted

c

c

2s

1s

p1s

wetted

liquid film

gas

liquid

interface

gas film liquid film

interface

as

catalystporous

Mass transfer steps (top) and concentration profiles (bottom) for a three-eaction with a partially wetted porous catalyst particle (1 – gas, 2 – liquid).

cite this article in press as: S. Schwidder, K. Schnitzlein, A new model for.org/10.1016/j.cej.2012.07.054

The entire arrangement yields a mathematical model consistingof a very large number of (partial) differential equations which arelocally discretized via a finite volume approach [29]. The resultingset of differential equations is integrated following the approach ofCochlovius and Schnitzlein [30].

2.4. Kinetics

Knowing the local degree of wetting, the amount of the localcatalytic surface attributed to each graph element can be obtainedfor every basic reactor. Thus, for a given reaction system the per-formance of each basic reactor can be calculated provided theparameters for the kinetics and the mass transport processes areknown. A schematic representation of the relevant intraphase masstransfer steps is shown in Fig. 10.

For heterogenous reactions partial wetting of porous catalystparticles may result in an increased global reaction rate [31].Therefore, gas–solid as well as liquid–solid mass transfer stepshave to be taken into account.

The kinetic as well as the mass transport parameters are deter-mined by preliminary experiments using a laboratory-scale cocur-rent trickle bed reactor as well as a liquid-full recycle reactor [23].

3. Validation

In order to validate the reactor model, experiments were carriedout using a laboratory-scale trickle bed reactor (reactor diameter3 cm and reactor heigth 21 cm) using a porous 0.3 wt.% eggshellPd/Al2O3-catalyst (Süd-Chemie, particle diameter 2–4 mm, BETsurface area 61.54 m2/g). The hydrogenation of alpha-methylsty-rene to cumene was chosen as model reaction [23,32–35]. Due tothe large excess of the liquid reactant the reaction can be regardedto be first order with respect to hydrogen. The kinetic parametersare determined using the experimental strategy as proposed byMorita and Smith [35]. Due to the small catalytic layer (thicknessof the active layer 200 lm) internal diffusion effects are neglectedthroughout.

In order to demonstrate the impact of partial wetting on reactorperformance exclusively, the conversion should be concentrationindependent. This was achieved, by operating the trickle bed

S2

GAS

LIQUID

S1

TBR

SP

G P

A

T

T

T

PI

PI

Fig. 11. Experimental setup schematic (A – absorber, G – gassing stirrer, P – pump,PI – pressure indicator, S1/S2 – sampling for gas chromatograph, SP – sonic probe, T– temperature, TBR – trickle bed reactor).





reactor as differential recycle reactor (see Fig. 11). The differentialoperating conditions have been verified experimentally.

All experiments have been carried out at 1 bar and liquid flowrates within the trickle flow regime. The conversion was obtainedby measuring the concentration of the liquid reactant by means ofa sonic probe featuring an excellent time resolution [36]. Prior toeach run, the bed was flooded with alpha-methylstyrene (99% pur-ity). The liquid as well as the pure hydrogen were injected at thetop of the packed bed. The reactor was kept isothermal at a tem-perature of 40.6 �C by a double jacket.

Fig. 12 shows the obtained conversion as a function of liquidflow rate. The good agreement between model predictions andexperimental data is noted. The nonlinear decrease of conversionis an indication, that in this case incomplete wetting governs theoverall reaction rate.

This is further exemplified in Fig. 13, where conversion is plot-ted as a function of space time. Again, the model is able to predictthe experimental data with good agreement. Moreover, predicted

0 200 400 600 800 1000

qL [ml/min]

0

0.005

0.01

0.015

0.02

X [

-]

experimentsimulation

Fig. 12. Predicted and experimental conversion in dependence of the liquid flowrate.

0 10 20 30 40 50 60 70

τ [s]

0

0.003

0.006

0.009

0.012

0.015

0.018

0.021

X [

-]

experimentalPDE ModelPDE Model with wettingnew model

Fig. 13. Measured and simulated conversion in dependence of the space time.


conversions are shown which are calculated by means of thewell-established PDE model [32,33,37] with and without consider-ing incomplete wetting by means of a global wetting efficiency[38]. The large deviations between these model predictions andthe experimental data indicate, that incomplete wetting is a localphenomenon which cannot be adequately accounted for by usinga global wetting parameter. The superiority of the new modelwhich accounts for the relevant processes at a particle scale isevident.

4. Conclusions

It is well known that in trickle bed reactors operating in the lowinteraction regime the impact of local incomplete wetting on con-version is dominant. The reliable prediction of the phenomenondemands a reactor model which is able to account for the localproperties of liquid flow in packed beds at a particle scale. Sincethe new reactor model meets these conditions, it is able to reliablypredict the performance of catalytic trickle bed reactors.

Due to the flexible structure and the modular setup the hydro-dynamic model can be easily extended to incorporate other parti-cle geometries, provided all the model parameters characterizingthe liquid–solid interactions are known. Since the network modelis based on the liquid distribution it can be applied in this casewithout any modifications.

Further extensions will include amongst others a detailed rep-resentation of the fluid dynamics of the gas phase, thus extendingthe applicability of the model beyond the limits of the low interac-tion regime.

Acknowledgment

The German Research Foundation (DFG) is kindly acknowl-edged for their financial support.

References

[1] M.P. Dudukovic, F. Larachi, P.L. Mills, Multiphase reactors – revisited, Chem.Eng. Sci. 54 (1999) 1975–1995.

[2] M.H. Al-Dahhan, F. Larachi, M.P. Dudukovic, A. Laurent, High-pressure trickle-bed reactors: a review, Ind. Eng. Chem. Res. 36 (1997) 3292–3314.

[3] V.V. Ranade, R.V. Chaudhari, P.R. Gunjal, Trickle bed reactors – reactorengineering & applications, Elsevier, 2011.

[4] Y. Jiang, J. Guo, M.H. Al-Dahhan, Multiphase flow packed-bed reactormodeling: combining CFD and cell network model, Ind. Eng. Chem. Res. 44(2005) 4940–4948.

[5] R.J.G. Lopes, V.S.L. de Sousa, R.M. Quinta-Ferreira, CFD and experimentalstudies of reactive pulsing flow in environmentally-based trickle-bed reactors,Chem. Eng. Sci. 66 (2011) 3280–3290.

[6] M. Nijemeisland, A.G. Dixon, CFD study of fluid flow and wall heat transfer in afixed bed of spheres, AIChE J. 50 (5) (2004) 906–921.

[7] X. Gao, Y.-P. Zhu, Z.-H. Luo, CFD modeling of gas flow in porous medium andcatalytic coupling reaction from carbon monoxide to diethyl oxalate in fixed-bed reactors, Chem. Eng. Sci. 66 (2011) 6028–6038.

[8] A.G. Dixon, M. Nijemeisland, CFD as a design tool for fixed-bed reactors, Ind.Eng. Chem. Res. 40 (2001) 5246–5254.

[9] S. Mitra, Computational Fluid Dynamics Modeling of Trickle Bed Reactor, VDMVerlag Dr. Müller, Saarbrücken, Germany, 2011.

[10] V. Stanek, Fixed Bed Operations: Flow Distribution and Efficiency, 1. ed., EllisHorwood, 1994.

[11] P.J. Hoek, J.A. Wesselingh, F.J. Zuiderweg, Small scale and large scale liquidmaldistribution in packed columns, Chem. Eng. Res. Des. 64 (1986) 431–449.

[12] Th. Krauss, H. Hofmann, Some experiences with the application of thepercolation concept for modelling trickle-bed fluid dynamics, Chem. Eng.Process. 33 (1994) 67–72.

[13] I. Iliuta, F. Larachi, M.H. Al-Dahhan, Double-slit model for partially wettedtrickle flow hydrodynamics, AIChE J. 46 (3) (2000) 597–609.

[14] I. Iliuta, F. Larachi, Hydrodynamics of power-law fluids in trickle-flow reactors:mechanistic model, experimental verification and simulations, Chem. Eng. Sci.57 (2002) 1931–1942.

[15] Y. Jiang, M.R. Khadilkar, M.H. Al-Dahhan, M.P. Dudukovic, Single phase flowmodeling in packed beds: discret cell approach revisited, Chem. Eng. Sci. 55(2000) 1829–1844.





[16] A.K. Saroha, K.D.P. Nigam, A.K. Saxena, V.K. Kapoor, Liquid distribution intrickle-bed reactors, AIChE J. 44 (9) (1998) 2044–2052.

[17] X. Wen, Y. Shu, K. Nandakumar, K.T. Chuang, Predicting liquid flow profile inrandomly packed beds from computer simulation, AIChE J. 47 (8) (2001)1770–1779.

[18] P.L. Spedding, R.M. Spencer, Simulation of packing density and liquid flow infixed beds, Comput. Chem. Eng. 19 (1) (1995) 43–73.

[19] K. Schnitzlein, Modelling radial dispersion in terms of the local structure ofpacked beds, Chem. Eng. Sci. 56 (2001) 579–585.

[20] S. Schwidder, K. Schnitzlein, Predicting the static liquid holdup for cylindricalpackings of spheres in terms of the local structure of the packed bed, Chem.Eng. Sci. 65 (23) (2010) 6181–6189.

[21] K. Lappalainen, V. Alopaeus, M. Manninen, J. Aittamaa, Improvedhydrodynamic model for wetting efficiency, pressure drop and liquid holdupin trickle-bed reactors, Ind. Eng. Chem. Res. 47 (2008) 8436–8444.

[22] C. Julcour-Lebigue, F. Augier, H. Maffre, A.-M. Wilhelm, H. Delmas,Measurements and modeling of wetting efficiency in trickle-bed reactors:liquid viscosity and bed packing effects, Ind. Eng. Chem. Res. 48 (2009) 6811–6819.

[23] S. Schwidder, Reaktionstechnische Modellierung von Rieselbettreaktoren aufder Basis der lokalen Packungsstruktur. PhD thesis, BrandenburgischeTechnische Universität, 2012.

[24] S. Schwidder, K. Schnitzlein, Prediction of liquid flow distribution in trickle bedreactors in terms of liquid/solid properties, in: 19th International Congress ofChemical and Process Engineering CHISA 2010 & 7th European Congress ofChemical Engineering – ECCE-7, Prague, Tschechische Republik, 2010.

[25] J. Levec, A.E. Saez, R.G. Carbonell, The hydrodynamics of trickling flow inpacked beds, Part II: Experimental observations, AIChE J. 32 (3) (1986) 369–380.

[26] C. Marcandelli, A.S. Lamine, J.R. Bernard, G. Wild, Liquid distribution in trickle-bed reactor, Oil Gas Sci. Technol. – Rev. IFP 55 (4) (2000) 407–415.

[27] K. Schnitzlein, H. Hofmann, An alternative model for catalytic fixed bedreactors, Chem. Eng. Sci. 42 (11) (1987) 2569–2577.


[28] C. Mocciaro, O.M. Martinez, G.F. Barreto, Assessment of mass transfer in thestagnant liquid regions in trickle-bed reactors, Chem. Eng. J. 173 (3) (2011)813–827.

[29] K. Schnitzlein, A. Löwe, Anwendung einer konservativen finiten Volumen-Methode auf Probleme der chemischen Reaktionstechnik, Chem.-Ing.-Tech. 60(12) (1988) 1049–1051.

[30] E.G. Cochlovius, K. Schnitzlein, The system editor and simulator SES: applyinga digital simulator in chemical engineering education, Comput. Chem. Eng. 17(8) (1993) 785–798.

[31] A.K. Mogalicherla, G. Sharma, D. Kunzru, Estimation of wetting efficiency intrickle-bed reactors for nonlinear kinetics, Ind. Eng. Chem. Res. 48 (2009)1443–1450.

[32] R. Lange, M. Schubert, W. Dietrich, M. Grünewald, Unsteady-state operation oftrickle-bed reactors, Chem. Eng. Sci. 59 (2004) 5355–5361.

[33] A. Niksiar, M. Sohrabi, A. Rahimi. A note on the article titled: unsteady-stateoperation of trickle-bed reactors, in: R. Lange, M. Schubert, W. Dietrich,Grünewald, Published in Chemical Engineering Science, 59, 5355-5361 (2004).Chem. Eng. Sci., 66:115–116, 2011.

[34] A.T. Castellari, J.O. Cechini, L.J. Gabarain, P.M. Haure, Gas–phase reaction in atrickle-bed reactor operated at low liquid flow rates, AIChE J. 43 (7) (1997)1813–1818.

[35] S. Morita, J.M. Smith, Mass transfer and contacting efficiency in a trickle-bedreactor, Ind. Eng. Chem. Fundam. 17 (2) (1978) 113–120.

[36] S. Schwidder, S. Machefer, K. Schnitzlein, Konzentrationsmonitoring bei Gas/Flüssig-Reaktionen mittels einer modifizierten Schallgeschwindigkeits-Sonde,Chem.-Ing.-Tech. 80 (3) (2008) 389–392.

[37] F. Larachi, I. Iliuta, K. Belkacemi, Catalytic wet air oxidation with a deactivatingcatalyst analysis of fixed and sparged three-phase reactors, Catal. Today 64(2001) 309–320.

[38] P.L. Mills, M.P. Dudukovic, Evaluation of liquid–solid contacting in trickle-bedreactors by tracer methods, AIChE J. 27 (6) (1981) 893–904.




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