Articulo Phenomena Transport.doc

8/13/2019 Articulo Phenomena Transport.doc

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SCALE UP OF CHEMICAL REACTORS

1. Scale up and process Innovation

Even if often no distinction is made between invention and innovation,the difference is definitely not a subtle one.

As a matter of fact, it is not always possible to turn a good idea intoan innovation and put it into practice: an invention can sometimes layunused for ages without paying back in terms of industrial realizationand of profitable business.

This review will not go into discussion on issue related to the market,nor will deal with the attitude of companies and management to promoteinnovation. We shall focus instead on the technical knowledge and on thetools that are necessary to change an invention into a true innovation.

The chemical business being mature, the attention should be paid more tothe innovation of processes than to the invention of new products.

From this point of view, the study and the development of new reactors,thai are able lo convert raw material into products with high conversionand selectivity, play an important role in the innovation of the chemicalbusiness.

1.1. Main problems in the scaling up of reactors

Scaling up of reactors is a major task for chemical engineers and is thefundamental step in the realitation and optimiiation of industrialplants.

The scale up activity represents the synthesis of the know howaccumulated in the various phases of process development from the design

of laboratory experiments and the derivation of kinetic correlations, tofluid dynamic experiments, mathematical modeling, design and operation ofpilot and industrial plants.

The term scale up has been usually explained us how to design a pilotor industrial reactor able to replicate through a standard methodologythe results obtained in the laborat ory.

This is a limiting definition, since experience has shown that it doesnot really exist a standard way through process innovation: actualproduction processes are the result of successful decisions, andsometimes of many mistakes.

Crucial factors in the scale up are not only the technicalunderstanding but also the ability of assuming the risk of the business.

As a matter of fact, in the past, decisions have not always beensufficiently supported by adequate experimental evidences and, eventoday, industrial plant operation is mamly based on experience.

From the above remarks, it can he drawn a broa der definition of scale -up, a s a mixture of know how, innovative ideas, standard methodologiesand basic criteria with a glimmer of entrepreneurship.


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With reference to chemical reactors, as the core of a process, there isno general rule and no straightforward procedure to achieve theseobjectives.

The reasons are many:

-kinetic data are peculiar to the reactive system. Often kinetics aremasked by transport phenomena and fluid dynamics to the point thatsometimes they have no relevance for the process.

-industrial scale technologies are seldom related to laboratory equipmenteven if industry is full of enlarged laboratory equipment.

-completely different apparatuses are possible for the same reaction andreactions can be carried out in different phases: solution, suspension,fixed beds, trickle beds, fluidized beds, distillation and extractioncolumns.

-other issues, often ignored in the development work, such as impurities,aging of catalysts, corrosion, fouling, safety and environmental aspects

can represent a major risk for the success.

1.2. Scale up and process development

Though not an easy task, we will try to outline some basic criteriasimple and general enough to act as a guide in facing the chemicalreactors scale up problem. These criteria are reported in the literaturebut are often hidden underneath heavy mathematical approaches.

A discussion of some examples resulting from experience in thedevelopment of several processes will help in illustrating how scale upis indeed a compromise between general rules and more complex approaches.

1.2.1. Luboratory experiments

The laboratory reactor should not necessarily be similar to the idea wehave of the industrial one but has to be designed in order to give thebest information. In particular fluid dynamics and transport propertiesare to be accurately checked.

Experiments in the laboratory could follow some structural design such asthe factorial or centralized ones. It is imperative, however, toinvestigate in a proper way the experimental space of industrialinterest. Extrapolation of data and models is a risky procedure thatshould always be avoided.

Experiments should be carried out, if possible, in a sequential way andshould be followed by a sound statistical and mathematical modelinganalysis in order to improve their quality and to provide the first toolsfor scaling up.

Process analysis and economic evaluation, even in the first steps ofresearch, is a sound procedure, which could even change the experimentaldomain of interest, improve a lot the quality of the work and help inmoving last toward the final goal


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1.2.2. Pilot scale experiments

The pilot plant is usually a costly apparatus and therefore the decisionof building it is always a hard one.

A pilot plant is no intended only to prove that an existing laboratoryunit yields thc same results on a larger scale.

Its main purpose is to test the technologies that will be used on anindustrial scale, which need not to be the same ones employed in thelaboratory, in order to point out those phenomena not present on thelaboratory -scale.

A pilot plant is also important to evaluate product specifications andset up automation and control systems that will be ready for theindustrial plant.

However some information on technologies do not need a real pilot, lesscostly and more practical mock-up experiments made on pilot and even onlarger scale cold models can help in evaluating stirring efficiencies,

heat exchange, flow patterns and flow distribution, residence times,diffusion effects, etc.

The use of mock-ups followed by a clear mathematical interpretation ispushed by many factors:the incomplete knowledge available to chemical engineers on complextransport phenomena and on their scale up rules, the impossibility andthe cost of building too large pilots, the difficulty of making specificmeasurements directly on the pilot with the real fluids and operatingconditions.

Sometimes the pilot may not be strictly necessary, as for example in thecase where there is an already operating industrial plant. We wanthowever to emphasize the fact that the scope of the pilot is to beclearly stated in terms of results and quality of results expected.

In addition, following the objective, the pilot could be similar to anindustrial plant or only to a part of it that needs additionalinvestigation and demonstration.

1.2.3. Industrial unit

The operation of industrial plants has been discussed previously. Thereason why plants are not so well known lays in the development anddesign phases and in the lack of a continuous updating of technologywhich is the only way to maintain competitiveness.

One formidable tool that is now available is represented by computers andautomation that allow to collect data in real time, the on-line use ofmathematical models and, as a consequence, a better understanding,control and optimization of plant operation.

In order to take advantage of this opportunity, all the development/scaleup tests have to be performed in a more knowledge oriented and rigorousway.


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The future is going to change the professional background of chemists andchemical engineers in this direction and the present requires technicianswith a wide range of expertise and an open minded attitude.

Investment in new plants will probably decline in the developedcountries, with increasing export of known technologies to the newlyindustrialized regions. There is however a lot to do on existingtechnology to maintain competitiveness and to stay in the chemicalbusiness.

1.2.4, Reactor technologies

This topic will he better shown in the examples. We want only to pointout the key issues that are relevant in process development and are to beconsidered in modeling reactors.

As for catalytic gas phase reactors, critical factors that affect theselection, the modeling and design are heat exchange, effectivenessfactor and aging of catalyst, flow pattern and pressure drop.

Heat exchange can be obtained with multitubular reactors, adiabaticintercooled layers or fluidized beds.

Diffusion in catalyst pores is related lo rale of reaction and pelletsize and is always a factor to be taken into account.

Flow pattern affects directly the yield and is managed through priperreactor design and operating conditions as a trade-off with pressuredrop.

Aging or poisoning of the catalyst affects life and economy of changesand sometimes makes the process unfeasible.

Scale up of fixed bed reactors is a relatively easy task.

The fluidized bed reactor is an elegant answer to many of the problems offixed bed and sometimes the only possible choice. The scale up is not sowecll known and the application has been in the past limited to thosecases that had no alternative, where the advantages were relevantcompared to the risk to be taken.

For homogeneous catalytic reactors the only recommendation is related toflow pattern and mixing.

Flow pattern may affect yield, selectivity and product quality and can beimposed by the reactor technology such as multitubular, vessel or

cascades of stirred autoclaves.Macro and micro mixing is important when reaction rate is competitivewith these phenomena Gas-liquid reactors, with homogeneous orheterogeneous catalysis, in spite of the complexity of phenomenainvolved, have almost only one scale up variable: the interphase area perunit volume.

If the reaction rate is sufficiently high. as always is for cases ofindustrial interest, it occurs in a very thin layer around bubbles.


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Technologies that provide high interphase area are favorite and should beselected for scale up and for industrial application.

Techniques for the evaluation of bubble surface at various scales areavailable and are the basic tools for scaling up.

When a reaction is strongly influenced by thermodynamic equilibrium andthe need of a high conversion is a valuable competitive advantage, onecan combine separation technologies with reaction, which could allow toremove the products and shift equilibrium.

Example are distillation columns with reaction, reactive liquid-liquidextraction, membrane reactors,

These observations are introductory ones and need to be quantified.Before proceeding any further we need however some insight inmathematical modeling of phenomena.

2. Scale up and modeling

Scale up is the ability of finding out the quantitative rules thatdescribe the operation of a chemical reactor at different scales,operating conditions and with different reaction technologies.

Therefore it does not only imply the capability of designing andoperating large plants hut also the skill of developing new and moreefficient reaction technologies in order to become cost and productquality competitive and to nwet environmental aspects.

Fig. 1 represents the key elements to be considered in performing thisjob. Not all the tools are in principle to be always taken into accountand often the selection is forced by the availability of information andsystems.

The procedure does not always stan from laboratory to industrial but mayfollow an opposite path, from industrial to laboratory or it is possibleto operate in parallel depending on the specific problema and theobjective.

There are however three elements that should always be kept in mind andthat are sometimes forgotten in industrial practice: ideas, mathematicalmodeling and fluid dynamic studies.

Innovative ideas are the key to the success of an industrial venture andthe guideline for every R &D project.

The mathematical model is the synthesis of ideas and experimental dataand is the main tool to be used for scaling up or improving theperformance of an industrial unit.

The mathematical model may be a simple or a complex one within availabledata, knowledge, ideas and objectives.

One can choose within transport phenomena models, population balancemodels, empirical models or combinations of them.


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Examples of transport phenomena models are mass, momentum and energybalances. Population balances are based on residence time distributions.Polynomials used to fit empirical tLita are examples of empirical models.

We suggest to rely as much as possible on phenomenological balanceequations, writing them down with the necessary complexity of descriptionand solving them by straightforward procedures as shown by Donati; suchmodels can usually be extrapolated at a certain extent beyond theexperimental range of operating variables studied, while an empiricalmodel can never be extrapolated.

Moreover, it must be always remembered the fact that, if a model gives agood description of reality, it does not necessarily mean that theassumptions upon which it is based are true.

Significant limitations are however to be recognized and formidableobstacles hinder the engineering progress.

Shortage and inaccuracy of data and the effort to estimate modelparameters on the basis of experimental data is almost always the major

and time consuming task.One area of considerable importance to reaction engineenng is kineticsand this is the area of greatest uncertainty. We do not need to know thetruc kinetics but we must know for sure the relation between what isderived from laboratory experiments and what is used to design anindustrial reactor, side effects included. We must be able to recognizethe competitive effects of kinetics and fluid dynamics: inter and intraphases transport phenomena, mixing, dead spaces and bypasses that canalter completely the performance of a reactor when compared to theideal represe ntation.

These phenomena can sometime be taken into account by a theoreticalapproach but often require mock up experiments to be quantitativelydefined. On the other hand the presence of these defects in theoperation of real reactors offers an impor tant key for scaling up andfor improving the performance of industrial plants.

It is also important to understand if a further complication of the modelis useful to obtain more accurate results, or if it cannot add newknowledge to scale-up.

These remarks give an hint of the difficulty in dic actual use ofmathematical models when applied to scale up and analysis of a commercialplant and of the challenge that the skilled chemical engineer faces whencomparing these problems.

Another possible difficulty is the availability of tools for themathematical manipulation of equations.

This is no more a difficulty today, given the long list of computerprograms available in the literature and on the market that fulfillalmost every computation requirement. The real problem is theavailability of skilled engineers able to use these tools for their dailyactivity.


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We have shown in an old paper how even complex problems can be reduced tothe solution of mass and energy balances and how equations can be writtenand solved with a general computerized methodology.

Other papers show how expenmenis can be designed, kinetic data analyzedand used for the calculation of reactors.

Our effort now is focused on the topic of demonstrating how simple thingscan be when guided by sound ideas and by the knowledge a what can bedonc and of what represents a trap or a mere speculation withoutindustrial interest.

The general cases related to different reaction technologies are intendedto evidence, with a non conventional approach, the complexities and topoint out a way o overcome difficulties. The applications to problems ofindustrial interest will show the practical way used and the resultsobtained.

2.1. Mathematical modeling

The application of computers to the analysis of chemical processes hasbeen accepted as a basic tool for scaling up. Despite of this fact thediscussion on this topic is still up in the air among academic people andoften misunderstood in industry. During the plenary discussion in ISCRE12 (International Symposium on Chemical Reaction Engineering, Tocino, 22June I July 1992)the topic raised a lot of criticism.

We want to state that, apart from the different professional attitudesand tasks, a common basis of all chemical engineers is the computationand the application of matter and energy conservation principles, whichis the framework of mathematical modeling.

In the already mentioned paper on this topic (Donati) we have shown howeven complex reactors and flowsheets can be tackled in a very simple andstraightforward way.

Examples of balances are the following:

2.1.1 Ideal plug flow reactors

2.1.2 Continuos stirres tanks

2.1.3 Cascades of CSTR

2.1.4 Reactors witch complex fluid dynamics (isothermal)

Where X is a concentration (mol/m1), R is the reaction rate (m ourn s),and T is the residence time (s) as the ratio of volume V to volumetricflowrate Q.

T, p, c, H, U and S are temperature, density, specific heat, reactionheal heat exchange coefficient and heat exchange surface per unit volume.

The simpler differential equations can be solved numencally byapplication of the Euler or Runge Kulta integration procedures. Morecomplex is the case of non isothermal reactors with counter current heat


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exchange or in the presence of important longitudinal dispersionphenomena.

Simple and complex models can however be transformed in a series ofelements or unit cells and solved with the use of algorithms andcomputer programs for the solution of sparse systems of non-linearequations.

The approach is general and independent ut the complexdy, number ofequations and boundary conditions.

It can be applied to modeling of local transport phenomena, to thecalculation of unit operations and reactors and to the solution of massand energy balance equation in a chemical process. The solution ofequations, no matter their number nor their complexity, is up incomputers, whereas the task of the engineer is essentially that ofanalyzing the specific problem of identifying the key issues and offormulating the balance equatuns at lhe desired level of detail.

This leads on one side to the banlization of the modeling activity and on

the other side to a tremendous increase in engineering productivity, asthe time wasted in trying to find out a solution can be more profitablydedicated to the creative aspects of analyzing phenomena and thinking tothe relevant problems encountered in the scale up and process developmentactivity. We again refer to the mentioned paper for the details of thealgorithms and procedures. The application of these simple ideas will beclear in the examples.

2.2. Fluid dynamic models

From the previous paragraph it may appear that with good idea,experience, some knowledge of chemical engineering and a computer one cansolve every problem of scaling up reactors and unit operations.

We regret to say that this is not always true. It is an habit oftheoreticians to complicate the simple things and to oversimplify thecomplex ones.

There are topics in chemical engineering that are not completely known interms of sound theory and where a more practical approach can easily givethe desired results avoiding complex and sometimes useless mathematicalcomputations.

Let us have for example a tank with a stirrer and baffles and assume thatmacro and micro mixing is important for the reaction under study.

We want to evaluate velocity patterns, how these patterns change from the

small scale to the large one and possibly how to change shapes and sue ofstirrer and baffles, rotating speed and, maybe, to introduce other typesof internals lo improve reaction efficiency of the system.

We have various alternatives in how to face this problem.

The most simple models give some correlations in terms of non-dimensionalnumbers.


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To keep the interpretation as simple as possible the flow is consideredto be perfectly ordered with uniform velocity.

This requires sufficiently high velocity and a ratio of tube to particlediameter of at least ten to avoid ioo much circuiling along the wall.

Small particle diameter also helps in reducing diffusion effects in thecatalyst pellets.

Although computers have enabled to handle non-isothermal situations,isothermal conditions are preferred and these are approximated by heatexchange at the wall and, for highly ezothermic reactions, by dilution ofthe catalyst bed.

3.1.1.2 Analysis of experiments. If the reactor is designed and operatedin an integral and isothermal way, that is with relatively highconversions, the balance equations are very simple:

A series of experiments have been carried out in order to cover theexperimental space of industrial interest as far as independent

variables, inlet concentrations X1, temperature T, pressure P anddependent variables, outlet concentrations X, are concerned.

Experiments could be planned following patterns such as factorial,fractional factorial or centralized composite designs and could also bearranged sequentially (Fig. 8).

The reaction rate R can be of the Hougen Watson type and can be derivedby the Langmuir Hinshetwood approach or can be built by automaticselection procedures based on the best fitting of data.

For example br the simple reaction

A+B=C+D

a typical expression is a fractional form of the type

The numerical integration of Equation and the fitting of Computedresponses X to experimental values X, by non-lincar least squares(OPTREG), easily determines kinetic parameters K and E.

3.1.1.3. Modeling the industrial reactor. The availability of a kineticmodel is the starting point for scaling up from laboratory to industrialreactors. The way to the industrial one may be however very long.

Several points have to be taken into account:-first of all the selection of the technology: multitubular, adiabaticmultilayer, moving or fluidized bed;

-if inter and intra particle diffusion phenomena are relevant, theyshould be included in the calculation; the flow pattern in the porous bedshould be carefully investigated;


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-catalyst aging and system stability are to be cxumincd in vicw of theopeiation of the plant.

All this problems are treated in the literature and well known inengineering practice. However the method offered in scientific papers isoften too cumbersome to be of use in practice and rules derived fromexperience are often too rough for our scope.

We will leave some of these problems to the examples and focus here theattention on the important phenomenon of diffusion and effectivenessfactor in catalyst pellets to demonstrate the level of complexity neededfor practical purposes.

3.1.1.4. Diffuson in a porous catalyst. When reaction occurs on the porewalls of a catalyst pellet diffusion and reaction are linked together.Comprehensive discussions are available in Satterfield and Aris.

Aris also shows for first order reactions the influence of particle shapeand Dente proposed and accomplished new shapes in order to improve theefficiency of some reactions.

Froment and Bishoff show how simple particle geometry can be unified withthe concept of asymptotic coincidence (Fig. 9).

The assumptions we propose for the computation of grain efficiency arethe following:

grains are spherical with u niform diameter;

grains are isothermal:

the diffusion is a multicomponent one,

The mass balance into the grain is:

where R is the reaction rate and N, the molar flux

where X is the molar fraction and C the total concentration.

The effective diffusivity is related to molecular diffusivity D,mthrough the void fraction D and pore tortuosity T.

The computation of the molecular diffusivity can be oNaincd with the aidof Stefan Maxwell equation together with stoichiometry.

The linear diffusion coefficients can bc computed with the Fullerequations


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The balance equation can be transformed in:

No analytical solution is available being the reaction rate expressionnon linear. Eq. (3.8) is a second order differential equation withboundary conditions and could in principle be numerically integued duringthe numerical integration, step by step, of the material balance Eq.(3.5)for the reactor.

This requires a relative long computing time and sometimes impliesnumerical problems for convergence.

We suggest from a practical point of view the analogy with a first orderreaction that has analytical solution through the definition of a Thickmodulus and the calculation of an efficiency factor to correct kinetics.

For an equilibnum reaction rate of the type 13.21 we delinc the Thielecriterion as:

and a non dimensional variable

Eq. (3.8) can be written in non-dimensional form

and the efficiency can be computed as:

For a first order reaction efficiency can be computed analytically:

The same expression may be used defining a modificd Thiele criterionWith a procedure similar to the onc used for different pellets geometry(see Fig. 10) and thanks to the modified Thiele criterion, the twoasymplotes for 0 . () and 0 arc exactly computed. In intermediatesalues error is normally less than 10%.

This is sufficiently acceptable in practical engineering calculationswhere errors caused by other factors as gas mixture and particleproperties are normally larger.

With this example we hope o have shown how there must always he acompromise between calculation, rigorous but still affected by errors anda practical engineering approach in the modeling of reactors.

3.2. Dehvdrogenation of ethyl benzene to styrene (An example of scale upfrom laboratory to industrial reactors)

It may happen that a company is operating industrial plants, built withthe support of a licenser of technology, and decides to build largerplants using in-house and consultants skills and experience.


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In the casc of the styrene synthesis the objectives of the developmentactivity were:

the obtainment of kinetic equations for different commercial catalystswith the aim of selecting the best one to design the commercial unit.

evaluating scale up factors and the aging of the catalyst throughextensive pilot plant campaigns.

building a complete mathematical model to compare calculations withexisting industrial plant data and use the model to design new reactors.

3.2.1. The synthesis of styrene

The catalytic dehydrogenation of ethylbenzene to styrene is anequilibrium endothermic reaction carried out in gas phase at hightemperature (550 600C). The reaction tocan is diluted by importantquantities of steam (90 95%) with the scope of shifting thermodynamicequilibrium, reducing the partial pressure of reactants, thus hinderingcracking and side reactions, regenerating the catalyst and supplying the

heat necessary to the reaction.The industrial catalysts are mixtures of iron oxidcs, chrome, potassiumand calcium (SHELL, CCI.GIRDLER).

The main and sidc reactions are the following:

Catalytic dehydrogenation to styrene

H,-C2H5 CH -CHCH2+H2

Homogeneous and catalytic dealkylation to benzene

ChH5.CZH3 - C,H6 + CH2 CH2

Catalytic hvdrodealkylation to toluene

Cf,ll-C,H% + F12 C6Il5 -CH + Cil4

The aging of the catalyst, due to poisoning, loss of active components,coking, tweaking, is opposed by an increase in temperature which favorsside reactions and accelerates aging.

Experiments and analysis have been organized as reponed in Fig. 11.

3.2.2. Micro kinetics

The main effort was first dedicated to the identification of the kineticequation of styrene formation. A series of preliminary 32 experimentalruns, obtained on an isothermal tubular reactor filled with smallparticles of catalyst (0.6


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Among the several expressions investigated, the following one betterfitted experimental data:

The reactor has been computed by the balance equation:

and parameters were found by the minimization of the sum of squares

The optimization was realized using the OPTREG non-linear regressionanalysis computer program and followed by a statistical analysis ofresults.

The analysis shows:

the parameters correlation matrix;

the variance analysis which gives the error variance computed with themodel to be compared to experimental variance from repeated experiments,the determination index that gives the risk to discard the proposedmodel, the F ratio between the square mean due to regression and thesquare mean duc to error calculated with the model and parametersconfidence limits:

experimental and computed responses and mean and percent errors.

We do not want here to go deeper inside he algorithms used for fittingexperimental data and the use of statistics to validate a kinetic modeland reter to books and papers for more details on this topic.

The importance of efficient regression algorithms and of a soundstatistical analysis is never to be forgotten because it gives thenecessary confidence in scaling up.

The examined case evidenced correlation between parameters that could bereduced and it suggested, with a procedure similar to that reponed in, aseries of new experiments for a better determination of the parameters.

In order to improve the microkinetics the model has been used to:

build the kinetic models for seco ndary homogeneous and heterogeneousreactions:

. validate the assumption of plug flow and absence of important diffusivephenomena.

This was obtained by mathematical analysis followed by additionalexperiments with diluted catalyst and without catalyst.

The experimental runs at high conversion, necessary to cover theexperimental domain and requested by statistical analysis, beingimpracticable on the laboratory equipment, were simulated by feeding


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styrene into the reactor.

Thc scale up from small grains to industrial sur catalyst pellets wasobtained trough isothermal experiment and the application of theeffectiveness model previously shown.

Table 1 shows a comparison of two computed profiles with small particks(d 0.08 cm) and large ones (d - 0.7 cm). One can see that for Thickmodulus equal 0.4 the effectiveness factor (ETA) is nearly 1, while forvalues of Thick from 4.2 to 3.3 it vanes from 0.5 to 0.6 that is areduction in the reaction rate (REFF) of 40 50%.

Heat exchange and diffusion between the bulk of fluid and the particlessurface have also been evaluated and computed but their importance wasminimal compared with intraparticle effects.

3.2.3. Pilot scale experiments

The pilot plant used for experiments was a two catalyst layers adiabaticI in I.D. reactor with steam injection between layers as in the

industrial case. The reactor has been tilled with industrial sizecatalyst pellets between alumina layers, equipped with thermocouples andsampling devices along the bed and controlled for adiabatic conditionswith hedi barriers and heating devices to reduce both the exchangecoefficient and delta T.

The operation was a continuous one and control, data logging and samplingwas realized by a process computer.

The model of the reactor combines three mass balance differentialequations and one enthalpy balance.

where y is the molar ratio referred to ethylbenzene feed.

Fig. 12, Fig. 13 and Fig. 14 show a comparison between computed andmeasured results for a typical sampling in the first 200 400 h ofcatalyst life (fresh catalyst).

Catalyst aging was investigated over a period of 5000 hours that is lessthan half lhe catalyst life (13000 h).

The proposed model included the definition of an aging factor F as afunction of temperatura, concentration and their history.

This factor corrects the catalytic reaction rates and aging parametersare fitted to experimental data.

The fitting is very good but it is our opinion that such a complexphenomenon should he treated with some caution and the model developedshould be continuously revised during the operation of the industrialplant.


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The aging phenomenon and model are, in fact, strongly related to thehistory of industrial plant operation and can be used only if amonitoring of the plant. abnormal conditions included, is available.

3.2.4. industrial reactor

The application of the model to industrial data had to face a series ofproblems:

the availability of complete industrial records was poor and only twocampaigns were practically available the first data were available in aperiod between 500 and 9600 hours of operation and no information hadbeen recorded before and alter this period except for an emergency changeof 40% of catalyst on the second bed ai 7500 h:

the set of data has been recorded from the start up but operation wasstopped at 3500 h for problems on the second reactor.

The fitting of thcsc data with the model, aging factor included, was madepossible by the introduction of additional assumptions.

It was however clear to everybody that something was wrong on the secondreactor and needed funher investigation.

In particular a selection of the initial data of the second campaignrevealed some surprising discrepancies between experimental and computedconversions.

The calculation of styrene production was almost exact on the firstreactor and in excess of 10 15% on the second one.

Simulated and experimental benzene conversion showed good agreement onboth reactors while toluene production, which is mainly catalytic, wascomputed in excess of 30 40%.

This observations remained qualitatively true for higher time-on-streamexperiments.

It is in fact known that catalytic beds having large diameters comparedto height may exhibit undesired channeling and flow irregularities if aproperly designed distributor is not provided.

A glance to the shape of the two industrial reactors increased thissuspect.

In order to take into account these phenomena in che calculations,process engineers use an empirical corre ction called catalystutiliiation factor that is a percent of the catalyst really used for thereaction.

To match experimental data on the second reactor an utilization factor50% was necessary, that is 50% of the catalyst bed was not used in theproduction process.


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The excessively large figure together with the anomalies encountered inthe industrial operations forced us to investigate this phenomenon.

The application of the fundamental equations of motion in porous media,that is of continuity equation combined to Darcy law, resulted in theintegration of the following differential equations:

The obtained stream pattern is responsible for flow non uniformity, andtue computed dead space was of the same order of magnitude necessary tojustify the loss of conversion.

A basis was then available to design new reactors for higher yields andgood operation.

3.3. The ammonia synthesis reactor (An existing plant with the need ofoptimization of operation)

The history of ammonia synthesis dates back to the very beginning of

chemical engineering when Haber in Germany and Fauser in Italy made thefirst experiments to demonstrate the possibility to use atmosphericnitrogen for fertilizers and other applications including dyes andexplosives.

The gun barrel where first Fauser performed the reaction departsconsiderably from the concept of the Fauser Montecatini multilayeradiabatic reactor with intcrmcdiatc heat exchange, and from the simplerdesign of Topsoc having interlayer cold reagent injections.

The idea is very simple and provides a formidable example of scaling upand innovation. The success of thc developed reactor technology resultedin applications to other processes. Let us show the basics of this ideawith a graphic representation.

The ammonia synthesis reaction is an equilibrium one and the equilibriumline in the conversion temperature space moves right with increasingpressure.

At a given pressure lhe operation of the reactor is limited betwccn theactivation temperature of the catalyst and the equilibrium line.

Three basic reactor designs can be used for conversions sufficiently highto be industrially practiced:

ve ry high pressure (1000 bar) adiabatic reactor

high pressure (300 bar) isothermal multitubular reactor; high pressure (3(X) bar) saged rcactor with intermediate cooling.

The first solution implies high capital and operating costs, the secondrequires elevated capital costs and the third is lhe right compromiseFauscr found with the limited knowledge of the process available in thosedays. Topsoe and successively Nielsen refined this concept, simplifiedthe reactor design and improved catalyst performance to come to what isknown to be the most popular reactor technology for ammonia synthesis


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(Fig. 15). The technology is nowadays a very mature one and few thingsremain on the frontier of innovation:

new and more active low tempera ture catalysts

. new materials and reactor Concepts.

This breakthrough being tar to be achieved, the only possibility is theoptimization of today technology design and operation.

A mathematical model approach is presented for the simulation of theindustrial unit, stability analysis and optimization.

3.3.1. Mathematical model of she reactor

A lot of work has been done mainly by Nielsen on catalysis and manyreaction rate expressions are reported in the literature. As a suitableexpression, we have considered the equation of Temkin and Pyzhev, in theform proposed by Dyson and Simon and by Buzti Ferrans and Donati.

The values of the kinetic constarns and equilibrium expression are thosereponed in the reference

The computation of grain efficiency was performed with the alreadypresented simplified approach

The examined reactor consists of two adiabatic layers with intermediatesupply of cold feed and a heat recuperator as shown in Figs. 16 and 17.

Mass and energy balance were written for the adiabatic layers, therecuperator and cold injection.

The adiabatic layer model was represented by a differential equation forthermal balance and an algebraic equation for mass balance. In case ofadiabatic reactors the correlation between temperature and conversion isstraightforward.

The differential cquation of thermal balance that relates temperature Tto the ammonia molar ratio x and to inlet composition x

the algebraic equation for the ammonia molar ratio x

the equations of mass balance that stoichiometrically relate thecomponents of the mixture


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We could alternatively write a differential equation for mass and analgebraic equation for enthalpy.

The model of the recuperator is a very simple one. As may he seen in Fig.17 the warm stream passing through the heat recuperator consists of thewhole fluid, whereas he cold stream is only a fraction of it. In fact apart (A Wc)) is directly sent to the second layer and another fractionL, (1 X )W1, bypasses the heat recuperator providing a mean to controlthe first layer inlet temperature.

The model is constituted by the following equation:

The intermediate cold injection model was also written in terms of massand enthalpy balances:

Thermodynamic functions were derived from Flougen. Watson and Ragals withnon ideality correction provided by Niaron and Turnhull.

3.3.2. Stability analysis of the auto thermal system

If we consider the reactor (Fig. 17) alone and look al it as a systemthat we have to control and to optirnite, the variables identifying thefeed (flow rate, composition, temperature and pressure) are independentand non controlling. In fact the only free variables (Fig. 18) are theheat recuperator bypass fraction A1, and the fraction A to the secondcatalytic layer. These two variables are at theoperator s disposal bothfor reactor optimization, and for the stationary state control. Themathematical model of the ditfereni sub-systems of the reactor must beable to compute every internal and output conditions for eachdetermination of the input variables and bypass fractions A, and A. As iswell known after Van Heerden, this result canno be reached in one step,because the termal feedback duc mo feed preheaung by the effluent gas,gives rise to an intrinsically boundary value problem.

The non linearity of the model makes it impossible to solve the problemby a marching method and lhe use of an iterative method is required. Wehave thought that it was better lo change, from both logical andoperational point of view, the variable heat recuperator bypass fractionA1, with the variable feed temperature to the first layer T,1. In thisway it is possible to open the internal reactor loop and to compute thelayers, the injection and finally the amount of heat generated andexchanged; those two last ternis appear in Eq. (3.24) of thermal balance

on the rccuperator. For a given value A, the study of the intersectionsof the two quantities mentioned before as a function o temperature T,constitutes the basis for the system stability analysis according to theVan Heerden stationary criterion (see Fig. 19 in which both generatedarid exchanged heats are plotted in terms of tcmperature differencesagainst temperature T).

By this change in the operational variables, it is possible to find astationary state point, if it exists, without iterating the computationof the adiabatic layers. This iteration in fact would require a certain


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amount of computing time. On the other hand it is enough to iterate therecuperator equation that requires shorter computing time. In our opinionthis is important; actually, if we look for the optimal operatingconditions, the model must be computed several times in order to reachthe optimum by a direct method. In this case, the developed computingprocedure, using as optimization sanables A and 7 instead of A and A,avoids a double iteration cycle.

In this way, we have tackled both the reactor partial optimizationproblem (with the use of the two decision system variables) and theanalysis of stability at the operating point found.

Before examining the optimization algorithm, let us make someobservations on the stability analysis. The need of controlling and ofoptimizing the reactor during its operduons arises from the existence ofdisturbances on the independent input system variables (feed), Theconsequence of these disturbances is that the reactor leaves the optimalcondiions previously attained and it is necessary to adjust it to a ncwoptimal point. During optimization, we must control the danger to reachblow-out points. The optimal operation point and the extinction

(unstable) point, as other AA. already remarked (48,451, are fairly closeone to the other.

We have adopted two oiles that, during optimization, can be used, eitherseparately or together.

The first consists in the comparison between the derivative of thegenerated arid exchanged heat functions lo temperature 7 computed at theoperating point (see Fig. 19). It can be numerically done with only anadditional reactor computation.

The second rule consists in the approximate evaluation of the extinctionpoint and the computation of its distance (in terms of temperature 1, andbypass traction A,) from the operating poirn found by us. These twodifferences T and A must he sytematically compared with the values thatsimulation and sensitivity off-line studies, information on theinstrumentation degree of confidence and overall control experience, haveproved to be reasonable. It may be convenient to make funher observationsabout the strategy used, which was experimented only for simulaied cases.Under normal operating conditions, the optimization program looks for theopimal point without taking into account the reactor stability. For thisresearch a certain number of iterations are used (objective functionevaluations). Afterwards the main program computes the distance betweenthe actual point and the blow-out point (second rule). This requiresthree or four reactor mathematical model computations. If the comparisonwith the reference values is positive we accept the point; in theopposite case the optimization program starts a new calculation cycle

using an objective function that is penalized by the degree of proximityat the unstable point measured by the first rule. Other options are atthe operators disposal if he wants lo intervenc directly.

3.3.3. Optimization program used

The program of process optimization exhibits some peculiarities thatrequire the study of a special optimization algorithm. The reasonsconditioning the optimized structure are, for a large number of on-line


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optimization problems, essentially the following: (1) process computershave small dimensions and (2) a large number of computations cannot bedevoted to the search of optimal conditions.

Small computers are generally used in an industrial unit and theyaccomplish several services, such as the solution of mass balanceequations, the regulator control etc.: these tasks cover a great part ofthe available computing time. The introduction of on-line optimizers isreasonable, if by taking into account the aforementioned functions, thereis enough time and memory space, and the intervention time is consistentwith the frequency of the disturbances. No matter how synthetic andingenious the mathematical model is, a considerable amount of computertime and memory is employed during optimization.

We understand the necessity to have a particularly compact optimizationprogram. Due to the above reasons and in order to obtain the mostconvenient on-line optimize intervention, it is not possible to devote agreat number of computations to the objective function. Then a verycomplex program is not required (as it may be a general optimizationprogram), but it is necessary to improve the objective function as fast

as possible for the given number of function evaluations. If, on theother hand, we consider the fact that the program works again and againon the process and that the optimal conditions change duringoptimization, we can reasonably say that the attailuncnt of themathematical optimum may have only a relative interest. Theseobservations led us to the building of a program for on-line optimizationof industrial units.

Among the various efficient criteria reported in literatura, which do notrequire a great memory occupation, we have chosen those proposed by Hookeand, Jeeves and by Spandley (Simplex) in the version modified by Nelderand Mead. The proposed algorithm results by the proper union of the twocriteria with the purpose to profit by the advantages of both. Inparticular. In the first phase of the search, we use the Hooke and Jeevesmethod since it is possible to know reasonable values for the independentvariables modifications. The first guess values for the search steps canbe in tact estimated on the basis of the experience acquired during theprevious optimization cycles. The Simplex method, on the other hand, hasproved lo be useful since it very rapidly modifies the search patternwhen the initial step guess values were not proper.

The constraints of the independent variables were handled by penalizingthe objective function with weights depending on the local values of thefunction and of the constraints.

3.3.4. Simulation experience

With the aid of the mathematical model and of the optimization algorithm,a certain number of simulation trials have been performed. Theseexperiments are similar to those that should be done by the processoptimizer during the operation of the industrial unit to make it workunder optimal and stable conditions.

The results reported concern the reactor alone (its characteristics arerepresented in Table 2). Table 3 shows the results obtained for thesimulations of the disturbances on the unit input variables:


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the levels of the input variables, the initial and final value (after50 optimization program iterations) of the objectivc function F (tons ofNH,. per day);. the number of iterations required in order to increase the objectivefunction to 80% and 95%:

the optimal values of the first layer feed temperature T,1 and thevalues of the bypass fr4sctions k

All operating points are stable according to the static criterion;nevertheless some of them are very close lo the extinction conditions.

For the present case all the adaptive factors that take into account theslow drifts of the unit (aging and poisoning of the catalyst etc.) werefixed al their nominal values.

3.3.5. fluidized bed reactors (a tentative scale up)

Even though the rational design of (luidized beds is not completely

established at the present time, some aspects have been studiedextensively and are summarized in the bixks of Leva Zenz, and Othmer,Davidson and Harrison and Kunii and Lcvcnspicl, one of the majorcomplications in developing a mathematical model of a fluidized bed isthat experimental observations seem to indicate that, in a wide range ofgas velocities. two distinct regions exists in lhe bed:

a dense region with a large f raction of particles:

a dilute or bubble phase

With reference to Fig. 20 bubbles are formed at the distributor, moveupward and in chis motion they lift a certain quantity of solids (cloudand wake) generating a mixing and a powder recirculation in the bed.

Gas permeates the dense phase or emulsion and is transferred from bubblesto cloud and to the emulsion phase.

A simple single-dispersion to represent gas and solid mixing has not beensuccessfully correlated in a general fashion to the extent that adequatepredictions can be extracted. It is therefore a risk to use them forscaling up.

A number of models all having dense and bubble phases have been proposed.

The two phase models consider bubbles and emulsion and differentcombinations of flow patterns, plug, completely mixed.

Even if they do not justify the real motion of solids and the downwardmotion of gas together with solids at sufficiently high gas superficialvelocity, they are simple to compute and closer tan dispersion models toreality and can be used to provide an idea of the reactor performance insome situations.

Too many assumptions are however used to define model parameters to beconfident in their reliability


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The models used by Davidson and by Kunii Levenspiel are based on aphysical picture closely related to the hydrodynamics of the bubblemotion, but nevertheless bubblc diameter cannot be accurately predicted.

In addition real fluidized bed hase different distributors, may heprovided with baffles and internals that break bubbles and modify theflow pattern and usually operate in the fast fluidization regime that ishardly represented by the Davidson picwre Given these difficulties thatcan be solvcd only by experiments on mock-ups and by experiencedacceptance of the scale up risk, we will show how easily can be built themost complex three phase model and how can be used for sensitivityanalysis.

3.3.6. The three phase model

The three phases model (Fig. 20), as developed by Kunii and Levenspieland by Freyer and Potter, takes into account in a phenomenological waythe back mixing of solids and gas in fluidized beds.

The solids lifted by hubbies are in fact released at the top of the bed

and fall back in the emulsion phase. 1f this movement is sufficientlyhigh, for fluidization velocities greater than a critical value (u> ut,),the gas changes direction in the emulsion phase and crosses the solidsdownwards.

With reference to cell model in Figs. 21 24 and assuming u constant themass balance for a cell height dh can he written in terms ofconcentrations C1:

With the boundary conditions:

The mass transport coefficients are computed using the equations thatDavidson and Hamson have derived from Higbie penetration theory:

The bubble velocity has been computed by:

The minimum fluidization velocity IJ has been evaluated with theempirical correlation derired from experiments:

The bubble diameter was assigned or evaiuated with the expressionavailable for the maximum bubble diameter.

Cloud to bubble fraction f and bubble fraction b in the bed were computedas velocity ratios:

where u is the superficial bubble velocity.

The solution of the resulting system of non linear equation was obtainedby the SISPAR program mentioned in.

3.3.7. A possible application

Let us suppose we wish to evaluate the possibility of application of thefluidized bed technology to a well known reaction as the formaldehyde


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The emulsion polymerization of a gaseous monomer to yield a valuablecommercial product is a complex problem from many points of view.

If one wants to go deep into all the involved elementary phenomena, oneis faced by a combination of problems in fluid mechanics, turbulentdiffusion, chemical kinetics, particle growth, interphase and intraphaseheat and mass transfer, and so on.

Extensive experimental and theoretical work is necessary, which oftencontrasts with pressing production. In this situation the need for anengineering approach is obvious.

In many cases the analysis of the system, made in cooperation with theexperts in the field, can lead to thc selection of the most importantphenomena and finally to a strategy of solution in terms of a few basicideas, which can be developed by means of relatively low cost experiments

This work shows how it is possible to characterize an emulsionpolymerization reactor completely and to obtain results of industrialrelevance through a series of fluid dynamic experiments performed on

reactor models at various scales and using both the industrial emulsionand very simple reacting systems.

4.1.1. Statement of the Problem

The emulsion polymerization is carried out in stirred unbaffled reactors.

The industrial facilities include a pilot 50 I autoclave, the aim ofwhich is testing various polymerization rcipes, experimenting differentprocess conditions and developing new products.

Gaseous monomer is sent into the ceiling of the reactor. The polymergrows under stirring as a particulate dispersion in water originating anemulsion, the concentration of which increases with time.

The polymerization reaction is exothermic and temperature is controlledby cold water in the jacket. Pressure can be varied to control reactionrale.

At the start-up of production a lot of problems became evident regardingmonomer purity, catalyst addition policy, lhe type and quantity ofchemicals to be used, temperature and pressure level. Some of theseproblems were solved by research chemists and plant operators.

The productivity and emulsion concentration achieved in the pilot plantwere however not reproduced in the industrial autoclave which exhibitedlower performances.

In the industrial reactor, in order lo have an acceptable polymenzalionrate, intense agitation was needed, bccuusc an increase in the stirrerspeed causes an increase in the overall rate. However intense agitationhas a negative effect on the stability of the emulsion.

On the basis of these simple observations the study was focused on thefluid dynamic effects on emultion stability and reactor productivity.


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Namely a stirring device had o be studied having a low shear on theemulsion for stability and suitable to be easily scaled up from the pilotto the industrial autoclave for productivity.

4.1.1.1. Basic concepts. Since a scale-up at constant productivity has tobe made, the polymerization overall rate must be examined.

Generally speaking, for a gas liquid reaction the overall reaction rale(macro kinetics) is due to two combined processes:

diffusion of the gase ous reactant within thc liquid phase (masstransfer):

. reaction in liquid phase (micro kinetcs)

The first step is strongly influenced by fluid dynamics while the microkinetics depend only on the local state variables.

Following Calderbank three regimes may be considered:

very slow kineti cs where the chemical reaction rate is ratedetennining;

fast reaction rate where diffusion controls the overall rate

. very fast reaction in which material transfer is increased duc to thechemical reaction in the diffusion zone.

In the last case if the reaction is of first order and irreversible theoverall rate depends on fluid dynamics only through the interphasecontact area but is independent of the mass transfer coefficient.

Since the polymerization studied is a very fast reaction, with theassumption of first order with respect to monomer concentration, it maybe inferred thai the interphase area per unit volume of the reactor mustbe scaled up if the same productisity has to be obtained.

The total interphase contact area in the unbaffled reactor consists inlhe surface of the vortex and, if the speed of the stirrer is highenough, in the surface of bubbles generated by the cavitation of theblades.

It s apparent that the interphase area per unit solume is stronglyinfluenced by the reactor scale and by the impeller type and speed.

In order to determine this influence a series of experiments wasperformed at the laboratory and pilot scale with different types of

stirrers and rotational speeds.The vortex dimension can be measured and computed following Nagata, thetotal interphase area can be determined by the absorption of oxygen incatalyzed sodium sulfitc solutions following Westerterp.

For the agitation conditions examined, emulsion stability can heevaluated by degradation tests on the industrial product.


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4.1.2. Fluid dynamic model

4.1.2.1. Vortex dimension. In a stirred unbaffled reactor the liquidsurface is not plane but it assumes the shape of a cone vortex.

The dimensions of the vortex depend on the geometry of the vessel andagitator and on the speed of the stirrer.

The voiles may be stable (Fig. 25a) or unstable duc to the fact that itreaches the top of the autoclave (Fig, 25h) or cavitation of the agitatormay be present (Fig. 25c) with a spreading of bubbles in the liquid. Asimple fluid dynamic model that explains vortex formation and thedependence of the shape on thc speed of the stifler, under stableconditions, is given by Nagata.

The model assumes for the tangential velocity itic following expressions:

where w is the angular velocity of the stirrer, r is a characteristicradius and r, is the radius of the vessel.

The shape of the vortex is obtained from applying the condition that thefree surface is isobaric.

With the symbols of Fig. 26 the following equations are obtained:

The conservation of the liquid volume gives an equation for the vortexdepth L:

From experimental data for L (or L1) it is possibk to compute theparameter r, which for high Reynolds numbers (>40000) is fairly aconstant for a given stirrer.

In the case of a stable vortex the interphase area can be easily computedby the following expression:

When cavitation occurs the area of the bubbles generated by agitator isto be added to the area of the vortex given by expression (4.5).

In this case, the global area can be obtained by a series of experimentsas the ones described in the following section,

4.1.2.2. Overall interphase contact area. Given a substance S that

diffuses from a phase into a second one, where it is consumed by a firstorder irreversible reaction, the reaction rate is given by film theoryas:

where V is the reactor volume. K is a kinetic constant. K, the masstransfer coefficient and D, the diffusivity in the liquid phase.


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If the Hatta number sp ( KD,) /K, is greater than 2. Eq. (4.6)simplifies to:

This condition is verified for the absorption of oxygen in catalyzedsodium sulfite solutions, so that this method can be used to evaluate gasliquid intertacial area.

Moreover, if an independent measurement uf lhe interfacial area is known,as that of non cavitating vortex, an estimate of the constant KD can bemade.

4.1.2.3. Emulsion stability. The emulsion stability can be measured bydegradation experiments in a vessel equipped with different stirrers atdifferent velocities under sariw standard conditions.

The efficiency of a stirrer in terms of low mechanical stress on theemulsion may be characterized by observing the degradation phenomenon atconstant stirrer speed.

By this method it is possible to obtain an empirical classification of

the behavior of the various types of stirrers with respect to thiscomplex phenomenon.

4.1.3. Impeller selection: laboratory experiments

A series of experiments was planned in the laboratory in order to performa screening among some stirring devices that appeared promising on thebasis of previous experience.

The experimental apparatus is a 3,1 unbaffled jacketed glass vessel asthe one shown in Fig. 6. stirred by an agitator drawn by a variable speedelectric motor and with interchangeahle impellers.

Three different types of impellers were examined:

axial propeller;

radial curved blade impeller:

special radial impeller with modified bladcs.

In principle all these stirrers could produce the desired effect of highinterfacial area without excessive emulsion stress.

The determination of the vortex depth yielded the results plotted in Fig.27 as a function of revolutions per minute N and impeller type.

It is apparent from this graph that for a given stirrer speed the specialradial impeller shows the highest interphase contact area in the absenceof impeller cavitation.

When cavitation of the impeller is present thc interphase area is the sumof the vortex area and bubble area generated in the mass of fluid.

The total area can be measured by the sulfite oxidation method using Eq.(4.7] if the parameter KD is known and the reaction rate is determined.


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Conversely the parameter KD can be computed by a series of experiments ofsulfite oxidation with non cavitacing impeller and therefore withindependently known area.

Great care must be taken when using the sulfite method.

As a matter of fact a strict control of the operating conditions such asimpurities, quantity of catalyst, temperature, pressure and sulfiteconcentration is necessary in order w obtain valuable experimental data.

The best results were obtained using distilled water, avoiding anycontacts of the solution with metallic surfaces and operating the kinetic

expenments at 35C and 1 bar oxygen pressure with 160 mg/l copper catalystand 40 mg/1 sulfite concentration.

Under these conditions the reaction is independent of sulfite concentraltion and consequently the kinetic curves are straight lines (Fig. 28).

As shown in these figures, for every agitator, the slope of the lines andconsequently the reaction rate and the interphase surface increases withstirrer speed.

This effect is better seen in Fig. 29 where for the three stirrers used,the interphase area is plotted vs. the stirrer speed. The graph shows thehuge increase in surface when cavitation occurs and clearly indicates thespecial radial impeller as the one producing the higher interphasecontact area.

Other experiments were made in order to find out the optimum impellerposition but they gave less significant results.

Degradation experiments with emulsions produced in the pilot reactor wereperformed to obtain data on the behavior of the examined impellers, Thesedata and those obtained by oxidation experiments were used for impellerselection.

The special radial impeller was chosen.

4.1.4. Scale-up procedures: experiments at the pilot scale

A rule has to be defined for the conservation of the specific interphasearea in the scale-up from the laboratory to lhe pilot and finally lo theindustrial reactor. For an impeller speed N less than a critical value N,that is under non cavitating conditions, this area is given by Eq. (5),so that the scale-up rute is straightforward.


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When cavitation occurs (N> 1) the interphase area per unit volume of thereactor is given by:

where a = area of the vortex/volume of the reactor, a= area ofbubbles/volume of the reactor, so that Eq. (4.5) does not hold anylonger.

Experiments were performed, both in the laboratory 31 reactor and in a 501 glass vessel, full scale with lhe pilot reactor, in order to determinehow the vortex shape is modified by cavitation. Visual observation showedthat while the lower part of the vortex, which interacts with theimpeller, is no more detectable, the upper part of it still maintains ashape similar lo that under non cavitating conditions (Fig. 30).

Moreover it was experimentally found that the height L, of the vortex atthe vessel wall for N> N,. still obeys Eq. (4.4), as when cavitation isabsent (Fig. 32).

This suggests that the vortex shape, under cavitating conditions, can

still be represerued by Eq. (4.2) for r> I. if (Fig. 30) is the radiuswhere lhe vortex comes in contact with the impeller.

So the vortex area, that determines a in Eq. (4.8), can be computed by anequation similar to (4.5). Actually il does not make a great differenceif one assumes that a is given by Eq. (4.5) evaluated at N = Nc, sincethis is a good approximation for N not much greater than Nc, while, forhigher speeds, ac becomes negligible compared to ab, and therefore itsexact value is not essential for scale-up purposes.

Thus, in order to scale-up ac, only a rule for scaling lhe parameter rc/ris needed, Nagata has shown that this parameter is a fof the Reynoldsnumber:

The experimental data for L (Fig. 31) can be used to determine theconstants and for the selected impeller, using Eq. (4.4) to correlatethem.

Once che scale-up rule for rC/rR is known, the critical stirrer speed Nalso can be computed for different reactor scales, using Eq. (4.3) andsetting L, equal to the depth of Lhe impeller. Using these computedvalues for rC/rft and Nc, the evaluation of ac, from Eq. (4.5) isstraightforward. In order to evaluate ab, one can write:

where E is the gas hold-up and d2 is the Sauter mean diameter of bubbles.

According to Hinze d2 can be related lo the Weber number:

where -y is a constant dependent on reactor shape and on impeller type ofdiameter d, and:

The gas hold-up E is by definition the ratio between the volume of gasand the volume of the liquid.


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The volume of gas, under cavitation conditions, may be assumed equal tothe dotted volume in Fig.30. As a matter of fact, since it was assumedthe upper pan of the vortex has the same profile il has when there is nocavitation, some gas volume must be entrained in the liquid, when thelower part of the vortex disappears, in order to maintain the same law(Eq. 4.4) for the liquid height L1.

Under this assumption, the gas volume Vg can be computed using Eq. 14.21as:

that is for N not too much larger than N. Using Eq. (4.10) to (4.13) onecan write:

If geometrical similarity is maintained and the same fluids (gas andliquid) are used, and asuming that ac is negligible compared to ab and

that rc/rR is approxrniately constant, the scale-up rule based onconstani interfacial area per unit volume simplifies to:

Assuming Ne/N does not vary mo much in the scale-up. Eq. (4,16) can befurther simplified to:

Actually Eq. 4,17 can be used to obtain a first guess for N. and Eq.(4.16) employed to refine the estimate. A final check can he made usingthe more rigorous Eq. 4.81 when necessary.

The interfacial arca per unit reactor volume was experimentallydetermined by sulfite oxidation, both in the 3 I and in the 50 1 reactor.

Results are plotted in Fig. 32. where continuous lines were drawncomputing ab and ac as described in this section.

4.1.5. Studies in pilot polymeritation reactors

As already stated, for a fast first order reaction the overall racedepends on the interphase contact area.

If this is still true for a very complex reaction set such as the radicalpolymerzation under study, the monomer demand per unit time and unitvolume must have the saine dependence on the stirrer speed, as the oxygenabsorption (per unit time and unit volume) in sulfite oxidation. In orderto verify this assumption, parallel experiments were performed in thepolymerization pilot 50 1, autoclave and in the 50 1, sulfite oxidation

reactor. The stirring device was the one currently used in the pilot,that is the axial propeller.

The experimental results are shown in Fig. 33 where the monomer demandand die interphase contact area vs. stirrer revolutions per minute areplotted.

As it can be seen, choosing a proper scale for the monomer demand and theinterphase contact area, the experimental points lie on the same curve.This shows that the interphase contact area is an important parameter to


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be used in scak-up procedures. Obviously the emulsion stability must beconserved in the scale-up.

The impeller selected on the basis of cold model experiments was tried ondifferent scales. The reaction rales agreed with those predicted by thescale-up procedure. The emulsion stability was as expected: in fact atotal absence of clots in the emulsion was observed and the surfaces ofthe reactors at the end of the polymerization were very clean and freefrom any coagulated material.

4.1.6. Industrial application

The scale up rules developed have been used for the design of thestirring system of the industrial 500 1, unit and for defining optimaloperating conditions.

The first result obtained was a 30% increase in productivity and 30%increase in latex concentration that is producing 30% more polymer in thesame batch time.

The experience gained on mock-up and the scale up procedure developedsuggested the possibility to investigate alternative productiontechnologies.

Latex stability studies and interphase area measurement have been made onbaffled reactors.

The result was an increase of 300% of productivity and lateconcentration. An additional result was the design and realization of a 3m3 reactor that alone is able to almost double the capacity of the wholeindustrial plant.

5. Reaction and separation technologies

5.1.1.1. Distillation with chemical reaction. Distillation with reactionis an industrail practice when reactions must be promoted by thecontemporary steady-slate separation of one or more products. In order toenhance productivity.Rigorous modeling of reaction plus separation continuous systems isrecognized to be a quite more complicated problem than ordinarydistillation calculations.

Recent literature is mainly related to the reaction of acetic acid withethanol to yield ethyl acetate and water. Some papers deal with thepropylene oxide synthesis from chiorohydrins and others, mostly devotedto the reaction technique rather than to the chemical problem, refer to abimolecular reversible reaction.

The most popular application of this technology is the MTBE synthesisfrom isobutylene and methanol.

In the sequel, an industrial example will be reported for atransesterification reaction.

5.2. Reaction thermodynamics and physicochemical properties


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This is a very particular example where vapor liquid equilibrium are usedin order to promote reaction conversion to an economical extent.

The reaction A + B - C + D, taking place in the liquid phase, is slightlyendothcrmic and dramatically influenced by the thermodynamic equilibrium:the value of the equilibrium constant is of the order of 10 at themaximum allowable system temperature T as shown in Fig. 34.

The reaction is activated by a homogeneous, non volatile catalyst dilutedin a 5 10% of an inert solvent (I).

The behavior of the kinetic constant with temperatura, for a definiteliquid phase concentration of catalyst, is shown in Fig. 34.

The volatility values of all the components (relative to B) are plottedin Fig. 35 as a function of temperature.

A is considered the light reactant, B the heavy one, C the light product

and D the heavy one.Vapor liquid equilibrium correlation were obtained from laboratorymeasurements, reaction kinetics and equilibrium from liquid phase batchreaction investigations at the laboratory scale.

5.3. The reaction system

The aim of using a distillation column is to influence the equilibrium byreaching very low level of light product C, thus increasing product Dconcentration.

This can be achieved by stripping product C with light reactant A in thebottom of the column.

Reaction trays hase a much higher hold-up than traditional separationcolumns, to accomplish the desired liquid residence lime for reactionkinetcs.

The investigated industrial system is depicted in Fig. 36.

The chemical reaction takes place only on the trays below the feed ofreagents A and B, that contains the non-volatile catalyst.

The upper portion of the distillation column is iniended for recovering

the heavy reagem B, leaving in the distillate a mixture of only A and C,that are separated in another column to recover product C and A forrecycle.

5.4. Mathemancal modeling and optimization

Mathematical modeling of distillation with reactions is based on lhesolution of the overall system of algebraic equations for all columntrays.


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The set of equation for tray i is a follows:

Material balance on component (j=I..NC)

Enthalpy Balance

Phase cquilibrium (j I..NC)

Kx ()

Chemical equilibrium (r I..NR)

fl,X PL _ o

or Chemical kinetics (r 1.. NR)

Ea ,. vc Ea.,

A, kflxi p . 1 flxp .

j I K,, j IFor non reactive trays, the trivial equation A=0 is used.

The total number of equations is (2 NC + I +NR) NP and equals the numberof variables I,, v,,. i, r.i that is all the other parameters of thesystem, such as tray pressures, tray feeds compositions and temperatures,and tray mass arid heat withdrawals not included tray No 1 (condenser)and No NP (reboiler) must be assigned.

Usually the condenser and reboiler heat balance equations are substitutedby two compatible constraint equations to be chosen among totaldistillate flow rate, reflux rate or ratio, and reboiler or condensertemperature.

In the case of total condenser, the NC equations of vapor liquidequilibrium on tray No. 1 are replaced by NC 1 equations of equality ofconcentrations in the distillate and in the reflux, and one equation forassigning condenser temperature.

Comparison of model results with industrial runs, in terms of theconversion of component B, evidence the influence of mass-transferresistance due to the very low level of C concentration reached in thebottom of the column.

This rate mechanism was accounted for and calibrated in the model,leading to the development of a very useful tool for process performances

evaluation and optimization.With reference to Table 4:

Model A accounts only for chemical equilibrium (nor kinetics, nor masstransfer are included).

giving therefore the maximum achievable conversion for a given set ofoperating conditions.


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Model R accounts for equilibrium influenced chemical kinetics, allowingthe study of residence time effects (liquid hold-up):

Model C takes into account both kinetics and light product masstransfer resistance, giving conversion values close to the experimentalone.

Tables 5 and 6 summarize the results of a parametric analysis on thereaction/distillation performances of the number of reaction trays(global liquid hold-up) and the vapoi to liquid feed ratio (strippingeffect). It can be seen that, with respect to usual industrialconditions, (lo trays. VIr 3) there is room for further Optimization.

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