Chemical reactors, basic studies and practical

MAGNETIC FIELD ASSISTED FLUIDIZATION A UNIFIED APPROACH Part 7. Mass Transfer: Chemical reactors, basic studies and practical implementations thereof

Jordan Hristov Department of Chemical Engineering University of Chemical Technology and Metallurgy Sofia 1756, 8 "Kliment Ohridsky", blvd., BULGARIA, e-mail: Jordan, hristovßlmail. bg: website: http://hristov. com/Jordan CONTENTS SUMMARY PREFACE 1. INTRODUCTION 1.1. Brief commentss on the topics analyzed and review outlines 1.2. Review outcomes 2. FLOW PATTERNS IN REACTORS WITH MAGNETICALLY ASSISTED FLUIDIZED BEDS 2.1. Reactor design and modelling - introductory notes relevant to magnetically assisted bed applications 2.7.7. Plug flow reactor - basic definitions 2.1.2. Residence time distribution of fluid in a vessel 2.1.3. Models for non-ideal flow 2.1.4. Fitting the dispersion model to the real reactor 2.2. Fluid mixing modelling of non-ideal plug flow reactors practical approach 2.2.1. Axial dispersed plug flow model applied to packed bed 2.2.2. Parallel cascade of mixers (4-parameter model) - PCM-4 2.2.3. Radial mixing - Dispersed plug flow model 2.3. Gas-Solid Beds: Axial Dispersion Coefficients: Experimental results with Batch Solids mode 2.3.7. Fitting with axial dispersion plug flow model 2.3.2. Fitting the 4-parameter (parallel cascades of mixers) flow

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model 2.4. Gas-Solid Beds: Radial Dispersion Coefficients: Experimental results with Batch Solids mode 2.5. Gas-Solid Beds: Discussion on field effects on axial and radial fluid dispersions 2.5.1. Geuzens' analysis with additional comments 2.5.2. Siegell analysis with approximate scaling and additional comments 2.6. Gas-Solid Beds: Solids mixing in moving beds 2.6.1. Phosphorescence technique of Geuzens (1985) 2.6.2. Modelling of solids mixing 2.6.3. Solids mixing - experimental results 2.6.4. Solids mixing - comments of the results 2.7. Liquid-Solid Beds: Axial Dispersion Coefficients: Experimental results with Batch Solids mode 2.8. Liquid-Solid Beds: Axial Dispersion Coefficients: Experimental results with Moving beds (countercurrent flow) 2.9. Gas-Liquid-Solid Beds: Axial Dispersion Coefficients: Experimental results 3. TWO-PHASE (Gas-Solid) REACTORS BASED ON MAF - Mass Transfer studies 3.1. Introductory thoughts 3.2. Adsorption and G-S catalytic processes 3.2.1. Adsorption in admixture beds 3.2.2. Water vapour adsorption in admixture beds 3.2.3. SO2 adsorption in admixture beds 3.3. Magnetic adsorbents for specific uses - case studies and comments 3.3.1. Magnetizable zeolites for adsorption of hydrocarbons 3.3.2. Magnetizable particles with metal oxide shell 3.3.3. Magnetizable particles through calcinations and pelleting 3.3.4. Porous cobalt sphere for high temperature magnetically assisted beds 3.3.5. Ferrimagnetic ceramic adsorbent for cleanup of H2S from exhaust gases 3.4. Adsorption processes in bed entirely created by functionalized magnetic particles

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3.4.1. Some initial thoughts 3.4.2. Selective acetylene hydrogenation 3.4.3. Pressure-swing adsorption 3.4.4. Magnetically assisted bed chromatography 3.4.5. Some new trends in mass transfer performance of magnetically assisted flu idized beds 3.5. Ammonia synthesis and auxiliary processes 3.5.7. Basics of ammonia synthesis over iron-based catalyst 3.5.2. The Bulgarian trials in ammonia synthesis 3.5.3. Carbon oxide conversion by water vapour: Bulgarian trials 3.5.4. Other ideas for ammonia synthesis in magnetically assisted beds: The Exxon approach 3.5.5. Dry flue gas Desulphurization 4. TWO-PHASE (Liquid-Solid) REACTORS BASED ON MAF - Mass Transfer Studies 4.1. Introduction 4.2. Liquid-phase mass transfer of magnetic ion exchangers 4.2.1. Experimental approach 4.2.2. Model equations 4.2.3. Mass transfer data and analysis 4.2.4. Comments on the mass transfer coefficients ofFranzreb et al. 4.3 Dechlorination of Chlorophenol and sludge remediation 4.3.1. Chemistry of the process 4.3.2 Kinetic studies with freely suspended catalyst 4.3.3. Kinetic studies with alginate beads with entrapped Pd/Fe catalyst 4.3.4. Particle mass transfer model 4.3.5. Mass transfer tests in magnetically assisted bed 4.3.6. Modelling the magnetically assisted dechlorination of pchlorophenol 4.4. Copper cementation in magnetically controlled fluidized beds 4.4.1. Cementation process - initial note on process mechanism 4.4.2. Copper cementation in magnetically assisted liquid-solid fluidized beds 4.4.3. Comments on copper cementation in magnetically assisted liquid-solid fluidized beds 5. THREE-PHASE (G-L-S) REACTORS BASED ON MAF - Mass

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Transfer Studies 5.1. Bubble Columns with chemically inert coarse particles 5.2. Slurry Bubble Columns (SBC) 5.2.7. Slurry Bubble Columns with chemically inert flne particles 5.2.2. Slurry Bubble Columns with fine suspended catalyst particles: laboratory studies 5.2.3. Slurry Bubble Columns with fine suspended catalyst particles: process oriented examples 5.4. Trickle beds (Counter-current flow) 5.4.1. General comments 5.4.2. Flue gas desulphurization - Approach ofGui et al. 5.4.3. Flue gas desulphurization by enhanced iron corrosion in a magnetic field 5.4.4. L-S mass transfer with SRNA-4 catalyst in magnetically assisted trickle bed 5.4.5. Comments and suggestion about the mass transfer dimensionless correlations. 5.4.6. Final comments on magnetically assisted trickle beds 5.5. Magnetically assisted airlifts - mass transfer issues 6. INDUSTRIAL IMPLEMENTATIONS - Trials and errors 6.1. Preamble 6.2. Early attempts: Bulgarian pilot-plant experiments 6.2.7. Results 6.2.2. Principle drawbacks 6.3 The EXXON Era 6.4. The Chinese Wave 6.5. Critical Overview and Lessons 7. CLOSING COMMENTS ACKNOWLEDGMENTS LIST OF SYMBOLS REFERENCES

SUMMARY Part 7 of the series Magnetic Field Assisted Fluidization (MFAF)-A Unified Approach is devoted to chemical reactor design utilizing

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magnetically assisted fluidized beds. Basic reactor principles wellimplemented in the chemical engineering science are used to analyze the existing situation of those special types of mass transfer devices. The hydrodynamics of all systems reviewed in the previous parts of the series (GS, L-S and G-L-S) serves as a foundation assuring proper understanding of their mass transfer performances. Thorough analysis of MFAF mass transfer studies in both laboratory and pilot scales is performed. Special attention is paid to the attempts to do industrial implementations of MFAF based chemical reactors: trial-error steps, pitfalls and recent achievements. Part 7 refers only to reactor designs and chemical reaction performances whilst magnetically assisted bioreactors are at issue in a separate part of the review series. All these issues make Part 7 a comprehensive review thoroughly investigating one undeveloped, but with a great potential and directly applicable to practice, branch of magnetic field assisted fluidization.

PREFACE Dear readers, Part 7 of the series Magnetic Field Assisted Fluidization (MFAF) finally arrived to the point where contacting devices based on this fluidization technique and their mass transfer performances have to be analyzed. As it was mentioned continuously in the previous reviews, the hydrodynamics and the proper knowledge of the regimes enable to understand and control the mass and heat transfer operations in a correct way. Now, with knowledge accumulated systematically in the preceding 6 issues, we approach mass transfer operations performed by various groups of investigators over 45 years and provoked by different reasons and starting assumptions. With the standpoint of the unified approach created in this series we perform analyses directly related to the bed hydrodynamics. In many cases, some points of this review merge sections of Part 5 (Hristov, 2006) and Part 6 (Hristov, 2007) but from a mass transfer point of view they are completely new. This special approach enables straightforward parallelism without repetition of bed hydrodynamics. Obviously, whenever this is necessary to explain the results under discussion, we briefly repeat the important hydrodynamic issues and refer to sources with more information. The mass transfer based on magnetically assisted fluidized beds takes place in chemical and biochemical (bioreactors) contacting devices. A

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principle point developed in this review refers to axial and radial fluid dispersions and solids mixing enabling to create reactor models close to those already established for non-magnetic chemical reactors (Levenspiel, 1962). Magnetically assisted bioreactors are especially excluded from the present review since, in fact, they differ either in purposes (operating modes such upstream and down-stream) or particles (bio-supports) used; even though the principle of design and operating modes (fluid-particle regimes) are the same as those of the chemical reactors. The bioreactors are of special interest in many MFAF applications but before the appearance of the next Part 8 of the series we refer to the only published review on this subject (Hristov and Ivanova, 1999). Essential part of the review addresses mass transfer operations in two and three-phase systems as outcome of browsing and analyzing astonishing plethora of articles on practical (technological) applications of MFAF, predominately in the early 60 and 70s of the last century, and performed from standpoints that really make upset readers with normal chemical (or mechanical) engineering education. We will especially explain these strong words in the section devoted to the early attempts of practical implementations. As a continuation of the saga of MFAF a special section devoted to the Exxon's era of systematic research providing many articles and patents is developed. The new China wave of successful industrial applications of MFAF is especially commented drawing trends in the development of processes and units. At the end of these initial notes I would like to mention an event forcing me in the process of review writing, especially Part 7 of this series. In the 2006, when Part 5 was in press, I have met in Belgrade (Serbia) Prof. Octave Levenspiel. This meeting was surprising to me, since I never imagined talking to him in person. In a splendid September morning (Belgrade is fantastic in September with its smells, colours and friendly people) I have presented to Prof. Levenspiel the published issues of the series. His reaction was so friendly and encouraging to me and was briefly formulated in a couple of words: Jordan, start to write a book with examples and problems! Obviously, the final result of this systematic work on the review series will be a book. However, I think that preliminary thoroughly performed studies of specific topics of MFAF will facilitate both the state-of-the art analyses and a consequent collation of a book. Hence, highly motivated by the words of Prof. Levenspiel, and the help of many colleagues and friends worldwide

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stimulating me permanently with materials and new (some time in press) articles I forced the work on the series. To this end, the current issue matches to some extent ideas of two guiding examples in my work: Chemical Reaction Engineering by O. Levenspiel (1962) and Fluidization Engineering by D. Kunii and O. Levenspiel (1991). Part 7 devoted to mass transfer problems is an amalgam of knowledge merging classical chemical engineering approach to reactor modelling, magnetism, tailored particle design, material science and fluidization problems. The "glue" enabling to collate all these issues in a slenderer analysis was provided by the author's enthusiasm and faithful work over 25 years of his scientific life devoted to MFAF.

1. INTRODUCTION Part 7 of the ongoing MFAF series collates and analyzes results on mass transfer performance of chemical reactors based on magnetically assisted fluidized beds. This is actually the first step toward a systematic analysis of the topic starting from basic chemical reactor principles and addressing either laboratory scale experiments or industrial implementations. A common feature of articles dealing with mass transfer operation with fluidized magnetic solids is unbalanced information between the hydrodynamic background and the mass transfer performance. Most of them deal with simple technological operations and the goals are in very narrow areas: to perform a particular mass transfer operation holding particles in the working volume by help of external magnetic field. This impedes the formation of a common source of knowledge since in many cases basic hydrodynamic information (the background of any mass transfer operation) is basically missing. The present review tries to encompass both the hydrodynamic behaviour and its effects on the mass transfer processes. Hereafter, previous parts of the review series (Hristov, 2002, 2003a, b, 2004, 2006, 2007a) will be referred as Part 1, Part 2, Part 3, Part 4, Part 5 and Part 6 respectively for the sake of simplicity.

1.1. Brief remarks on the topics analyzed and review outlines The original works usually motivate the studies with the need to operate

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either at high working velocities impossible in fixed bed regime or to retain fine magnetic catalyst particles in the working volume under such high velocity conditions. This is true, but the main idea from a chemical engineering standpoint is quite simple: to achieve high particle-fluid slip velocity, that is, to decrease mass transfer diffusion resistance in the continuous phase (liquid or gas); that finally yields enhanced mass transfer operations. This is an essential formulation of the main idea how to apply external magnetic fields to fluidized magnetic solids, either on preliminary fluidized particle or on fixed bed, enabling creation of a "stabilized bed" regime. The present analysis begins with Chapter 2 devoted to fluid dispersion problems commonly harvesting either axial or radial dispersion coefficients (Levenspiel, 1962). The idea to create a common basis of terms, formulations and analytical solutions based on the Levenspiel's book was quite successful since, as it can be seen, most of the authors used this theoretical basis for data analysis. Even though most of the studies reviewed used similar experimental techniques and data post-processing procedures to find fluid dispersion coefficients, such a collection of data and relevant analysis do allow to see the current status of this important topic in chemical reactor characterization. Section 3, 4 and 5 are devoted to particular process involving MFAF in G-S, L-S and G-LS reactors, respectively. In contrast to the previous reviews in the series, the approach developed here does not compare directly such as column design, magnetic fields, etc. although tables collecting such data are available for comprehensive presentation of the information. Actually, this was done in Part 1, Part 5 and Part 6, respectively. Now, the hydrodynamic background is directly used for granted and the review focuses only on mass transfer characteristic with adequate links to bed behaviour. Particles used in MFAF specifically depend on the process performed; the topic addresses material science issues beyond the subject of this review. Albeit this statement, a special section in Chapter 3 is devoted to magnetizable particles for G-S processes, thus creating a basis for further systematic analysis. The problems discussed for each process in particular address its chemistry, particle synthesis, mass transfer data and modelling issues. Even though not all studies refer to these topics, the review strictly follows the scheme thus enabling to figure the existing situation in the MFAF-based chemical reactors. It is possible that some readers will not accept such detailed approach but the information about the mass transfer performance of reactors

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based on MFAF is quite dispersed in literature sources, incompletely presented and re-published many times as well, thus such a detailed review is to a certain extent necessary as a first attempt screening and arranging the available results. Chapter 6 is dedicated to industrial implementation of MFAF and gives a special flavour to the review (together with Chapter 2) since a discussion concerning attempts and pitfalls at industrial levels was never performed before. This subject is hard to be analyzed due to many obstacles in recovering information: nobody reports the pitfalls, but everybody speaks a lot about the success. The information about industrial implementations was collected step-by step from many sources, sometimes with incomplete and incorrect information. However, it might suggest this chapter is a serious step toward a complete picture of the problems of MFAF.

1.2. Review outcomes Each reader will obviously form his specific standpoint after reading the review. However, the main idea of collating and analyzing the information reviewed can be briefly formulated in several points, among them: • Systematic analysis of axial and radial fluid dispersion studies in reactors with MFAF in order to provide compressive information enabling further studies pertinent to reactor design - a problem not discussed yet. • Reviews of specific mass transfer issues with MFAF via a unified approach with respect to bed hydrodynamics, mass transfer data, models and process efficiency. • To draw a picture representing adequately industrial implementations of MFAF with their trials, errors and successes. This hard task, accomplished to some extent, demonstrates that MFAF is not only "a toy" for master and doctor students but a technique which really works in practice. • The outcome of the enormous work on this review, from educational standpoint, is that the entire available information is arranged as a textbook with relevant commentaries and analyses. This comprehensive source of information gives to scholars (experienced or beginners) a basis for further research and avoids unproductive browsing of publications with unsystematic and many time re-published

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After these introductory thoughts explaining the review target and idea, let us start with the systematic analysis of problems at issue through this first attempt to write a magnetic textbook similar to Levenspiel's famous Chemical Reaction Engineering taken as example.

2. FLOW PATTERNS IN REACTORS WITH MAGNETICALLY ASSISTED FLUIDIZED BEDS

2.1. Reactor design and modelling - introductory notes relevant to magnetically assisted bed applications Magnetically assisted fluidization is generally performed in tubular (columnar) vessels and the following briefs address only their basic features allowing further correct descriptions of results at issue. First we refer to the plug flow reactor as ideal model visually similar to magnetically assisted fluidized devices and commonly used in their analyses. Some basic characteristics will be briefly reviewed in order to facilitate the further explanations, model build-ups and experimental data analyses and correlations. 2.7.7. Plug flow reactor-basic definitions The plug flow reactor is characterized by ordered fluid flow and no diffusion along the reactor axis and velocity differences are considered. Such ideal assumption allows lateral fluid mixing but the longitudinally motions of any fluid elements along the flow paths are not allowed (Levenspiel, 1962; Carberry, 1975). "To some extent, in the present study we will refer to the constant flow stirred tank reactor (CFSTR) where the total flow backmixing is allowed and the fluid flow content is well stirred and uniform over the entire volume and throughput. Referring to reactor volume Vreact in the analyses to follow it means that it is the volume of the reactor occupied by reacting fluid. In the specific case of magnetically assisted fluidized bed reactors, the reactor volume has to be understood as the space occupied by magnetizable solids. In this case the reactor volume should take into account the bed voidage; the reactor volume is Vreact = ^£^4 where we distinguish the real reactor volume Vreact and the gross volume of the reactor Vr. The time required to get a given conversion for any component Λ in a reactor (Levenspiel, 1962).

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*A

ί=

(2. la) react

This general relationship gives the conversion time for either isothermal or non-isothermal operations and in many cases may be simplified for a number of circumstances Constant mixture volume l = CAO f—— =

J -r.» 0 A

f —A J -rA CM

/·» iu\

The mixture volume varies proportionally to the conversion X

A

IT

dxA

Space time and Space velocity are defined through relations between the feed rate FAO and the reactor volume Vreact in a flow system, namely (Levenspiel, 1962) 'time required to process one reactor volume of Space time = τ = — = = time feed measured at specified conditions 'volumetric rate of entering ^ feed at specified conditions Space velocity = VS = — = = time~l void volume of reactor τ

(2.2a)

(2.2V)

The space velocity is frequently used in this review mainly in cases where only the volumetric flow rates of the streams are of interest and the reactor hydrodynamics is neglected such as ammonia synthesis, three-phase reactors with suspended catalyst , etc. To this end, Vs = 7A"1 i.e. the so-called Hourly-based Space Velocity (HSV) means that seven reactor volumes of feed at specified conditions are being fed into the reactor per hour (Levenspiel, 1962).

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Reactor holding time (mean residence time) and space time When the density of the fluid stream is the same at all points of the reactor volume, then

(2.3)

The relationship shows that the mean residence time for fluid in the reactor (or reactor holdup time) and space time (reciprocal space velocity) can be used interchangeably. The residence time in a plug flow reactor does not have physical meaning (Levenspiel, 1962-p.l 14) since each fluid element resides in the reactor for that period of time, but the composition of fluid changes from point to point within the reactor. Hence, velocity of the fluid varies, because the density varies too, as the fluid passes through the reactor. If the reactor is assumed to be an ideal one, the residence time is presented by (2.1.a), whilst with varying reaction volume (2.1c) is a valid relationship. Obviously, these basic notes, available in every textbook on chemical reactors, refer to the ideal case but dealing with real packed or fluidized particle bed reactors the situations will be quite different and the definitions have to be modified. In reality the flow of fluids is never ideal. We briefly review some basic characteristics and techniques pertinent to non-ideal plug flow reactor (in the same sense we can use the term "tubular reactor") which are extensively used in this review for description of the mass transfer performance of magnetically assisted fluidized bed reactors. 2.7.2. Residence time distribution of fluid in a vessel Following Levenspiel (1962), the approach is to find out how long individual molecules stay in the vessel. This information could be obtained by experimentation. Recalling all times defined above, we may define a dimensionless variable measure time in units of mean residence time or holding time, and it's called reduced time defined as / (volumetric flow rate) χ time Qr t Θ = - = ^----- = ^— = reducedtime(2.4) τ reactor volume ^ react

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Fraction of ν···*Ι content* ' younger than (».,

Ag· distribution of fluid In * » i t stream; total area under the curve la unity

, Iniarn·! aga dlatrlbutlon; •lop· I· never ρο·ΚΙν·; total area undar curve 1· unity

Fraction of exit stream older than 82

Θ2

Θ)

Step tracer Input «Ign·!

Pul·· tracer Input » Ι 0 η · ΐ Output •tonal

Output ilgnal

C) D· It·-function or put·· Μ tracer Input algnal

Step function tracer Input «Ignal

Tracer output •Ignal or C curve

.Tracer Input algnal or F curve

Flat velocity profile

Fluctuation·

Tracer Input •Ignal Plug flow

Dl«per**d plug flow H)

Tracer output elgnal

JL

1-2) 1 r a c e r Input algnal

Tracer output » I g n a l

Tracer Input algnal

Tracer output algnal

Fig. 2.1: Fluid mixing model of the reactor-basic definitions. After Levenspiel (1962) and many other textbooks on Chemical Reactors . a) I (internal) age distribution curve-schematically, b) E (exit) age function of residence time of fluid in the vesselschematically c) Stimulus-response technique with a step-change as input signal d) Stimulus-response technique with a delta function as input signal e) Typical downstream signal (F curve) as a response of step-change input signal f) Typical downstream signal (C curve) as a response of delta-function input signal g) Plug flow dispersion model schematically- left: ideal flow; right: disturbed flow h) Determination of dispersion in an open vessel

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i) Determination of dispersion in closed-open (left) and open-closed (right) vessel. The age of an element of fluid is measured since the moment of its entrance in the reactor (see Fig. 2. la) and I is a measure of the distribution of ages of the fluid, so that product I d® represents the fraction of materials with age between Θ and Θ + d®. Since the sum of all the fractions in the oo

vessel is unity, we have

lid® = 1. The fraction of the vessel content 0

e,

Θ,

younger than ΘΙ is

I Id®, whilst that older than 0j is 1- I Id®. Since 0 0 the measurements inside the reactor volumes are not straightforward tasks, an alternative measure which easily can be estimated is the exit age distribution Junction Ε (see Fig.2.1b) of fluid leaving the reactor. This measure is called also RTD (residence time distribution) and we will use this term further in oo

this review. By analogy we have

\Ed® = 1. Hence, for the exit stream 0

Θ2 younger than ©2 we have Γ Ed®, whilst for the fraction older than Θ 2 , 0 oo

&2

we have $Ed® = \- \Ed®. &2

0

Experimentally, the non-ideal flow in the reactor estimation by the internal I and the external Ε age distributions need techniques which may be termed as stimulus-response techniques (Levenspiel, 1962). Stimulus means a tracer input signal to the vessel and the response is the recording tracer leaving the vessel. The analysis of the response provides the desired information about the system. When no tracer is injected into the vessel, at the moment / = 0, a step change (jump) tracer signal of concentration Cf_s is imposed to the stream entering the reactor. Then, recording the outlet tracer concentration in time the so-called F = CjCf_s curve (see Fig.2.1c,e) can be obtained with a time-scale expressed through the reduced time Θ ; obviously F rises from 0 to 1. Otherwise, if the tracer impulse is an almost Dirac delta

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function C/_D, the exit curve C = C/Cf=f(&)

(see Fig.2.1d,f) is called

C curve, and similarly we read GO

OO

= 1, Cf_D = \Cd0 = i \Cdt, ·* f ·* 0

where 7 = Vreact/Qf

κ me

(2.5a,b)

0

reactor holding time.

Treatment of the information obtained through F, C, I and Ε provides information about the reactor internal life and can be found elsewhere (Levenspiel, 1962; Carberry, 1975) and every book on chemical reaction engineering), so detailed presentation is beyond the scope of the present review. However, when this is necessary to comment particular measurements of RTD and relevant information pertinent to a specific type of a reactor with a magnetically assisted fluidized bed, we will stress the attention to the technique and mathematics used for signal processing. 2.7.3. Models for non-ideal flow Now, refer to the plug flow reactor chosen as basic flow model of magnetically assisted fluidized bed reactors, we address models for the nonideal flow descriptions. Such types of models are relevant to description of the reactor mass transfer performance, rather than to the true fluid dynamics in the reactor volume. Models (mathematical structures, descriptions) can greatly vary depending on the complexity of our imagination and the goals to describe the reactor behaviour with simplicity or through sophisticated mathematical structures. The simplest model used in the plug flow reactors is the so-called dispersion model which adequately represents packed beds or tubular reactors. This is the most employed model in the studies of magnetically assisted reactors, so briefly we will present its structure even though it will be again presented in detail further in this work. The main idea of the dispersion plug flow model is to present the fluid flow through the reactors as a mechanistic sum (see Fig.2.1g) of: • Convection transport of species with the fluid superficial velocity U, i.e. a section propagating as a piston from the inlet towards the reactor exit ^V*

point, U—,and cbc • Diffusion transport represented commonly by the Pick's form as a

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pseudo-diffusion mass flow but with an effective diffusion coefficient /V*

called dispersion coefficient: — = Oeff_ _ axiai

The pseudo-diffusion flow corrects the assumption of plug flow conditions and avoids the need to use the information about the real fluid dynamics inside the reactor. Hence, the dispersion plug flow model is

Λ ot

" ~

Λ ox

ν(2 6) /

: D eff—axiol „ , *\ 2

οχ

This form of the dispersion plug flow model is one dimensional and longitudinal dispersion is that represented by the effective diffusion coefficient Α^-αχ,α/ and the common term is axial dispersion coefficient denoted in this work as DL (i.e. longitudinal dispersion). Because the nonuniformities may occur in the lateral (radial) direction too, similar flow model for the radial flow is developed too; it will be discussed further in this work. Skipping classic chemical reaction information available elsewhere (Levenspiel, 1962, for example) we refer to methods relating the stimulusresponse information obtained experimentally to get the real value of the axial dispersion coefficients since it cannot be predicted theoretically. 2.1.4. Fitting the dispersion model to the real reactor The scaling (2.6) provides the dimensionless group PeL = Di/UL^j , where L^j denotes the length of the actual reactor volume. In fact, for small deviations from plug flow, i.e. small DL /ULbed, the solution to (2.6) is

c= C _

f D

(ι-ογ

} ± — D'L 4

(2.7)

which is a Gaussian distribution. Cf_D is the concentration of the Dirac feed. Therefore, in a general dimensionless form the solution (2.7) can be expressed as

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(2.8)

UL

bed

where the time evolution C = C(0) is controlled by the parameter PeL . Note: The definition of the Peclet number PeL = Di/UL^j in (2.8) differs from the common expression Pe = UL/D , but we will follow Geuzens (1985) since in the solutions (see 2.7 for example) the group DL/ULi,ej naturally occurs as well as in some practically developed relationships commented next. Hence, the general solution (2.7) results in a family of C or F curves, but we really need only those of them which most closely fit the experimentally obtained C and F curves. For flow with small deviations from plug flow (small DL/ULbed ) the mean and the variance of (2.7) are (Levenspiel, 1962p.266)

(2.9)

UL

bed

In general, the solution depends on the boundary conditions of the reactor vessel at the tracer inlet or tracer outlet (see Fig.2.1-i): in former case (closedopen system) the dispersion occurs at the tracer injection, whilst in the latter (open-closed system) the dispersion is due to conditions at the tracer recording point. As to the solution (2.7), when PeL 0

V ν

=σί

variance

(2.19a, b)

Φ ')

The application of (2.19a) and (2.19b) to equation (2.15a) by Geuzens (1985) resulte in dimensionless residence time (valid for both cases) ΘΙ = 1 (sic!) even though result ΘΙ = 1 is valid for closed boundary conditions (see Levenspiel, 1962-p.265). In fact Geuzens (1985) solved (2.15a) with openvessel boundary conditions (2.19a and 2.19b). For the variance (dimensionless) of the RTD (Residence Time Distribution) curve, against Θ we have

σ =


_

V

(

(2.25)

4xDR)

Mtracer is the mass rate of tracer injection. Employing (2.25) DR can be obtained from a plot in natural logarithmic co-ordinates, since the slope In C (*,/·)- In/·2 is - [(Ur2 )/(4xDR )] .

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2.3. Gas-Solids Bed: Axial Dispersion Coefficients: Experimental results with Batch Solids mode 2.3.1. Fitting with axial dispersion plug flow model Geuzens (1985) performed a unique systematic study on both axial and radial dispersion of gas (see Fig. 2.3) as well as of solid mixing issues. The three problems will be discussed separately.

j— air -hydrogen top cover

Analyser

hydrogen •^

air hydrogen Gaussmeter

Gaussmeter Solenoid

Solenoid

A) ethylene

ethylene

Fig. 2.3: Experimental set-up of Geusens (1985) for both axial and radial mixing measurements a) Axial gas mixing experiments b) Radial gas mixing experiments Details : Fluidization column , 15.24cm,ID; 45 cm ID magnetic coil (solenoid) ; Tracer gas : ethylene detected by flame ionization detector , an collected at measuring points by 0.2 mm capillary tube. •

Axial mixing : RTD and D,

Geuzens (1985) simply determined the residence time from the first moment of the measured RTD curve. For both sets of boundary conditions, the main residence time holds that the system bed + CSTR equal the

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volumetric one. By simply adding the volumetric residence times of the bed and CSTR one supposes a closed boundary at the bed top surface that yielded reace . calc = --- + ---

T

QG

QG

(-

-„ (2-26)

The prediction of (2.26) matched quite well the experimental results (Geuzens (1985), thus confirming the adequacy of the chosen sets of boundary conditions i.e. closed boundary at the bed surface. In this context, Geuzens (1985) points out that the calculated dimensionless residence time is greater than 1 for moderate and low gas velocities. Hence, a backmixing of the gas occurs through the bed top surface in contrast to the case of high gas velocities. Note: To be precise in the comments with respect to (2.26) and in further analyses we have to mention that in the experiments of Geuzens (1985) a propeller and a turbine are located beyond the bed before the gas exit from the column. The creation of such CSTR cell (with a volume YCSTR ) above the bed was due to gas removal from the vessel only through one central point (see the figure). The mixing characteristics of the CSTR established in separate experiments with short gas impulses and In C ~ t plot resulted in almost a straight line providing the volumetric residence time VcSTR/Qgas · Geuzens (1985) determined the axial dispersion coefficient by 4 different methods according to Eqs. (2.16), (2.17) and (2.20a, b). Results are shown in Fig. 2.4a,b. Geuzens (1985) states that DL calculated through W\ (s), Wi (j),a12,a"J -\ v'*/ ~

1,

dz

lum '-"r, "g" (r. n\" V~lum-0)

\

Π "?1a M ^Z.Jja, D;

—^ = 0

(2.33c,d)

dz

Figure 2.12b shows calculated steady light profiles (Geuzens, 1985) with "lum = 3 -

• RTD of solids in a bed with continuous solids throughput. In this case the residence time distribution of the solids requires experimental measurements of the light intensity at certain height above the distributor as a function of time. A delta function of light emitting particles can be created at the bed top by a flash light or via lighting the bed source for a certain period of time. The mass balance of the excited light emitting particles is

^%-Pe, ^--b, (Ys)"""» =^r (Geuzens, 1985) dz dz dq

40

(2.34a)

Jordan Hristav

Reviews in Chemical Engineering Magnetic distributor downcomer

UV tube lightings

nl

Ε

^^τ^ξί*

ΔΡ

Λ°

0.5

photo-electric· to th* recorder

A) =

B)

0.25

It'll

tI

0.5 's «s

U, A,

0.20

» υ

' U = 26.58 cm / s -

• OA/m » 4125 A / m

• 6600 A / m

Qs

i

η

0.15

* 0

U mf = 1 3 c m / s

1.5

I

C)

2.5

5

7.5

10

. Lateral position

D)

H ( kA / m )

Fig. 2.12: Experiments of Geuzens (1985) on solids mixing in axial field assisted beds. a) Experimental set-up b) Calculated light profile with nlun = 3 and as (see equation 2.32b) as parameter c) Superficial solids flow velocity as function of the intensity of the field applied. d) Lateral solids flow pattern: U = 26.58 cm/s (with =13 cm/ s for the material used).

p

_ *~

S

nlum φ n,um ' °

A

um

p

f "*~

(2.34b,c,d)

41

Vol. 25, Nos. 1-2-3. 2009

Magnetic Field Assisted Fluidi:ation A Unified Approach-Part 7

where L/um is the distance between the bed surface and the photoelectric cell (measurement point) Equation (2.34a) has no straightforward solution and Geuzens (1985) did a simplification based on the fact that the most significant section of decay curve ( 35s :'·.-

0.10 0 01

x < v'i·

Tracer Injection ι i£Check valv

10

100

10t

dn u

0

Distributor

100 A Magnetization FIRST

•U_

= Wa ter

A

1.0

Reynolds number

B)

Electrodes

0.10

>

fr

• Magnetization LAST 10

I ' u

α a.

M

1

^"«v^

A · "~A

0.01

C)

Reynolds number

dn u

Fig. 2.14: Experiments of Siegell (1982) on axial dispersion in liquid-solid magnetically assisted bed. a) Experimental set up: schematically b) Himmelblau-Bisschoff diagram with the results of Siegell (1982) with particle diameter as a length scale in the definition of the Peclet number Pe^ - Dijudp . c) Inverse Peclet number l/Pe^ =udpJDi based on the particle diameter as a length scale and the fluid interstitial velocity u.

45

Vol. 25, Nos. 1-2-3, 2009

Magnetic Field Assisted Fluidization A Unified Approach-Part 7

in the fluidizing liquid (de-ionized water). The method was the δ pulse technique generating C = C/Cy curve (see Eq. 2.5). Siegell (1982) did not provide a theoretical basis but referred to Levenspiel and Smith (1957) relationship (2-37)

uLe with axial Peclet number PeeL = DL/uLg

defined through the fluid

interstitial velocity and the distance between the electrodes Le as length scale. This differs from the measurements with G-S beds where the entire bed depth is considered to contribute to PeeL. The superscript e means "electrodes". • Unstauilized Ί • Stabilized Flmdized bed

Ifπ

flar 0.3

A)

0.2

0.1

0.0

0.1

0.2

0.3

D)

Radial position

Fluldlzed bed

«

2 ° 0.1 B)

0.25

0.15

0.05

0.05

0.15

Re p ( Μ

0.25

Radial position

Fluldlzed bed

tiff 55

0.25 ...

0.15

0.05

0.05

0.15

0.25

Rjdiil petition

Fig. 2.15:Results from the dispersion experiments of Burns and Graves (1988) a,b.c) Radial concentrations profiles at different interstitial fluid velocity d) The ratio DR/D as a function of the particle Reynolds number e) l/PeR as a function of the particle Reynolds number f) The dimensionless dispersion group DRpLlr\L as a function of the particle Reynolds number

46

Jordan Hristov

Reviews in Chemical Engineering

Note: Figures d, e and f are graphical presentations of data summarized in Table 1 of Burns and Graves(1988) The experiments performed by Siegel! (1987) revealed that the axial dispersion in the liquid phase with MSB regime was nearly the same as that for packed beds; in fact, this confirms the results obtained with G-S systems. These results with steel sphere beds (88-122//) and C/m/o = 0.21 cm/s, led to DI expressed through Peud \ = D^/udp ) in packed and MSB regimes which are in good agreement with the prediction of the Himmelblau and Bisschoff (1968) diagram (Fig. 2.14b). The roll-cell regime (this is the chainlike regime) results in excessive axial mixing of the tracer and difficult to detect (practically flat) measured outputs. Siegell (1982) suggested these results as a flow pattern approaching almost perfect mixing conditions. The approach used to magnetize the bed was especially tested to detect its effect on DL (and ftwrf \ = DL/udp ) -see Fig,2.14c . Burns and Graves (1988) performed also experiments on both axial and radial dispersions in a bed stabilized by either axial or transverse magnetic field. These authors used a Helmholtz pair to create either axial or transverse fields by rotating the coils with respect to the vertical column axial. Some comments in the text of this article make clear that Burns and Graves (1988) preferred to work in axial fields; what they really did of course; rather than in a transverse field as was stated in the text. This article is not coherent enough in either result presentations or analysis and many explanations are quite obscure, as well. They reported dispersion values in magnetically assisted beds which are roughly 2 to 3 times those commonly reported for packed beds under the same flow throughputs. The results relevant to axial measurements were unsatisfactory and Burns and Graves reported data to only radial fluid dispersions. In this context, the approximate Andersons' solution (2.2S) was used for fitting to experiential data and getting values about DR. In this context, the bed retention times of magnetically assisted beds were higher than those in normal fluidized beds, a fact attributed to the less channeling environment-see Fig. 2.15a-d. This seems strange with respect to all other performed studies on the fluid dispersions in such beds and the comments of Siegell (1987), for example (see 2.5.2). Burns and Graves (1991) used three dimensionless presentations of the radial dispersion coefficients: 1) dimensionless ratio DR/Dt , where Dt is

47

Vol. 25, Nos. 1-2-3, 2009

Magnetic Field Assisted Fluidization A Unified Approach-Part 7

the diffusion coefficient of the tracer in water as fluidization agent; 2) dispersion group DRpLfai and 3) l/Pe^ =Udp/D based on the particle diameter as length scale. All these ratios as functions of the particle Reynolds number are shown in Fig.2.15d, e, f. In general, the magnetized bed exhibits lower radial dispersions with increasing field intensity in contrast to the gassolid counterparts. In fact, this study does not give sufficient information about the fluid dispersion and it is hard to get some substantial results about the bed performance as reactor. In this context, we have to mention that the work of Burns and Graves (1991) is an example of a poorly written scientific report with confliction in data and statements. To this end, even though the above dimensionless ratios are defined through DR, in the original graphs (d, f, and e) they are expressed through DL irrespective of the fact that the authors reported unsuccessful axial dispersion experiments. The fluidization (magnetization) mode used is also unclear. However, this is one of the first attempts to study the structure of MSB either as particle arrangements by means of either conductivity measurements (see Part 5) or tracer injection. Nishio et al. (1991) performed a detailed study on axial liquid dispersion in beds iron spheres (average diameter of 720/ym) magnetized by a Helmholtz pair (see Fig.2.16a) with Magnetization-LAST mode. The solution to Eq. (2.6) through Fourier series (Wakao and Funazkri, 1978) is

ca ('.

A f·

'«Jtf

V,

*fc

C)

5 10 15 20 25 30 35 Volume passed ( m l )

Fig. 2.18: Acetone pulse experiments of Nixon et al. (1991) Pulse profiles for fluidized bed (FB) and MSB-axial field for magnetite/agarose particles (212-355μ/η). U = 1.16cm/min. FB expanded bed volume, 8.5 ml. MSB expanded bed volume, 8.3 ml b) Pulse profiles for fluidized bed (FB) and MSB-axial field for magnetite/agarose particles (90 -212 μηΐ). U = l. 16 cm/min. FB expanded bed volume, 10.8/»/. MSB expanded bed volume, 9.6 ml c) Pulse profiles for MSB-axial field and MSB-transverse field stabilized beds. U = 1.16cm/min. Particles: magnetite/agarose particles (212-355 μ/»). MSB-axial expanded bed volume, 8.5 ml, MSB-transverse field expanded bed volume, 9.2 ml. a)

52

Jordan Hristav

Reviews in Chemical Engineering

The transverse field orientation resulted in contacting characteristics of MSB better than those exhibited with axial fields. The acetone pulse experiments resulted in response profiles (see Fig.2.18c) which were sharper than those obtained with axial field. Nixon et al. (1991) suggested that this bed performance was due to larger fluid dispersions in axially stabilized beds. Additionally, the transverse field assisted beds expanded to greater extent than those in axial field with the same field intensity and fluid velocity (see for many examples in Parti), that finally yielded more pronounced tracer peaks in axial field. Further, the transverse field stabilization resulted in higher plate numbers (Fig. 2.19f) even though the stabilization was more difficult to attain (see Part 1). The general outcome of the Nixon's experiments (Fig. 2.19f) is that transverse field MSB performs nearly as well as conventional fluidized bed (FB) and better than the axial field MSB (see Fig.2.19d-f). Breakthrough experiments (graphical data are not shown here) performed by Nixon et al. (1991) with cytochrome-c revealed that the ordinary FB and the axial field MSB performed unsatisfactorily, but FB was more efficient. When a transverse field was applied the MSB performance was better than in axial field, but FB remained the most efficient mode. With respect to the field orientation effect, the low contacting performance in axial field was due to the vertical channeling (axial field). When a transverse field governs the internal particle arrangements, horizontal plates (separated by slits) result in better contacting characteristics of the bed. Referring briefly to the work of Nixon et al. (1991), we have to claim that this not frequently cited article provides much important information about the flow dispersion and field orientation effect that cannot be found in other extensively cited publications, such as those of Siegelt (1982) and Burns and Graves (1991). In this context, to be correct, the work of Goetz and Graves (1991) has to be commented. In fact, this work repeats the results of Nixon et al. (1991) with respect to: field orientation effect, field intensity effect and the number of theoretical plates. Goetz and Graves (1991) used eq. (2.37) to calculate DL. Graphs with results from this study are not presented here. Goto et al. (1995) drew attention to a situation exactly the opposite to that studied by Nixon et al. (1991). Precisely, they compared also fluidized and packed beds to the performance of a bed with the magnetization LAST mode. Axial magnetic field created by a Heimholte pair (see Fig. 2.20a) was used to control water-fluidized magnetite/chitosan composite beads

53

Magnetic Field Assisted Fluidization A Unified Approach-Part 7

Vol. 25, Nos. 1-2-3. 2009

(5%w/v Fe^O^) of 0.550mm average diameter. The hydrodynamic issues of this study were discussed in Part 5. Under the assumption of a linear adsorption isotherm ( Nad pulses were used) the moments of the impulse response curves were calculated as follows: Agarose composite particles ( 90 - 212 μη )

' Agarose composite particles ( 212 - 356 μιη ) MSB - axial field

25 20 H

- transverse field

ϊ 15 Ο

10

idized bed Packed bed

D)

1.0

1.2 1.4

1.6 1.8

2.0 2.2 2.4

2.6 2.8

3.0

U (cm / mln ) 15

Agarose composite particles (90-212 μιη )

Agarose composite particles ( 212 - 355 μηι)

MSB - transverse field

1.0

1.2 1.4

1.6 1.8

2.0 2.2 2.4

2.6 2.8

U (cm / min)

B)

1.0 1.2 1.4 1.6 1.8

3.8

Ε)

2.0 2.2 2.4 2.6 2.8

3.0

U ( cm / min)

100

Agarose composite particles (90-212 μιη}

I Agarose composite particle« ( 212 - 355 μΓη ) Packed bed

I

10

—,bed Fluidized

Fluidized bed

"^^*' -Y

MSB - transverse field MSB - axial field

C)

1.0

U ( cm / min)

F)

1.2 1.4

1.6 1.8 2.0 2.2 2.4 U (cm / mln)

2.6 2.8

3.0

Fig. 2.19: Graphical presentation of dispersion data obtained by Nixon et al. (1991). Present author extracted the data from Table la and Table Ib of the original work and did the graphs, a) Variance of eluted solute peaks as a function of the liquid superficial velocity. Magnetite/agarose particles (90-212μίΗ).

54

Jordan Hristov

Reviews in Chemical Engineering

b) Mean solute retention volume as a function of superficial velocity. Magnetite/agarose (90-212//OT). c) Number of theoretical plates as a function of superficial velocity. Magnetite/agarose (90 -212 μηί). d) Variance of eluted solute peaks as a function of superficial velocity. Magnetite/agarose (212-355 μηί). e) Mean solute retention volume as a function of superficial velocity. Magnetite/agarose (212-355 μηί) f) Number of theoretical plates as a function of superficial velocity. Magnetite/agarose (212 -355 μηί). L-bed [ τ . \-£bed

ι l-Zbed

Shed

2 R2 ( arf A>

A1C

3

the liquid particles the liquid particles the liquid particles the liquid particles

,- .... (2.41a)

eften

= - 1+ -

2Lbed u

the liquid particles

ι 1

\5Dp

1+-

^injection

12

(2.4 Ib)

Using the experimental response curves (see Fig. 2.20b), we have OO

CO

Jo*, μ-i =

μ= 0

(2.42a, b)

0

In general, the pulses of packed bed (PB) and magnetic bed are similar while that of fluidized bed (FB) is broader than them. Goto et al. (1995) concluded that axial dispersions in PB and the magnetized bed were almost the same. To clarify these results we refer to the phase diagram (not reported here but available in Part 5) indicating mat under H = 25 kAjm and

55

Vol. 25, Nos. 1-2-3, 2009

Magnetic Field Assisted Fhiidhation A Unified Approach-Part 7

U = 3.6x1O"4 m/s the bed is completely frozen. Hence, the initial isotropic PB and the anisotropic frozen bed exhibited similar response curves. The height equivalent to a theoretical plate HETP, the reduced HETP and the plate number Npiates were calculated through the moments, namely

HETP = L

b e d

HETP

, HETP_reduced =

> " plates ~

(2.43a,b,c) 5 4

Column

χ 3