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Chemical Engineering and Processing 49 (2010) 74–83

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

journa l homepage: www.e lsev ier .com/ locate /cep

ase-based selection of a model of a reverse flow reactor

laudiu C. Botar-Jida, Yuri Avramenkob, Andrzej Kraslawskib,∗, Paul-Serban Agachia

Babes-Bolyai University, Department of Chemical Engineering and Oxides Material Science, 11 Arany Janos, RO-400028, Cluj-Napoca, RomaniaLappeenranta University of Technology, Department of Chemical Technology, P.O. Box 20, FIN-53851, Lappeenranta, Finland

r t i c l e i n f o

rticle history:eceived 1 June 2009eceived in revised form6 November 2009ccepted 22 November 2009vailable online 4 December 2009

eywords:ecision support systemeverse flow reactorsase-based reasoningesign model selection

a b s t r a c t

Key steps in configuration of a reverse flow reactor for industrial application include finding the mostsuitable operation model and identifying reactor behaviour. The design of a configured reactor requiresknowledge about the influence of operating conditions on overall process performance and precise eval-uation of operating parameters range for which a sustained dynamic behaviour can be obtained. In caseof a reverse flow reactor and in general in case of a complex reactor the design requires knowledge aboutreactor behaviour, process operation, important system parameters and their optimum values, the wayof mathematical formulation and phenomena description, solving methods, control specific aspects, etc.One possible way for finding such information is studying one by one all the articles related to the reverseflow reactors which is often a time consuming and moreover a tedious task. Despite of the relatively largebody of the literature no detail procedure exists for the design of the reverse flow reactors in order tocover all possible applications. Moreover, the design is carried out by a trial and error approach coupledwith extensive and detailed numerical simulations. Therefore, in this paper a much faster and simplerprocedure to optimize the way of knowledge gathering and information gaining for design purposes isdiscussed. This procedure uses the capabilities of a computational tool which provides specific infor-mation that may be used inside a reasoning process to find new solutions for new problems based onpast experience. The paper is dealing with the implementation and testing of a computer tool capable toprovide design information for reverse flow reactors. The computer tool relies on a decision supportingmethod which involves a case-based reasoning (CBR) algorithm. The tool querying procedure was vali-dated and once the reliability of the tool was proofed finding solutions for new problems based on past

experience becomes less time consuming and much more efficient than a classical literature survey. Inthis paper, the reverse flow reactor model selection for design purposes has been identified using a case-based reasoning tool capable of interactive querying and abstraction procedure. The results of queryingprocedure have been adapted in order to fit to new needs. The case study in this paper has been theselective catalytic reduction of NOx with ammonia in a reverse flow auto-thermal reactor. The solution

r too

provided by the computesimulation.

. Introduction

Complex mathematical modelling which includes descriptionsf transport phenomena and reactions that take place in multi-hase systems must be used in the investigation of a reverse flowrocess. The detailed mathematical models of such systems needo account for inter- and intra-phase gradients as well as exchanger interaction between phases. They are very complex and may be

xpressed in the form of several partial differential equations in twor three spatial coordinates and in time. In addition, these detailedodels contain a large number of physical–chemical parameters.

here are regions in the domain of the parameters values in which

∗ Corresponding author. Tel.: +358 5 62 111; fax: +358 5 621 2350.E-mail address: andrzej.kraslawski@lut.fi (A. Kraslawski).

255-2701/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2009.11.010

l has been adapted to the new problem and validated through external

© 2009 Elsevier B.V. All rights reserved.

the rates of some of the reaction or transport processes are muchslower or faster compared to other parts of the same domain. Dueto a big complexity of the phenomena that take place inside thereactors the models become very often inadequate for analysis orcomputation. The mathematical procedures used to solve reverseflow systems employ highly efficient numerical methods that sim-plify mathematical models to one dimension and fix the boundaryvalues in time at the beginning and end of the half cycle to avoid theneed to solve over long transient periods before the establishmentof stationary conditions.

Despite the relatively large body of the literature in this

field [11–15] no detailed procedure exists for the design ofreverse flow reactors in order to cover all possible applications;usually the design is carried out by trial and error approachcoupled with extensive and tedious detailed numerical simula-tions.

C.C. Botar-Jid et al. / Chemical Engineerin

aiiar

yselpmp

itvfipssuattipb

Cna[mp

pirrrIfiC

ing general changes of a certain property such as temperature,

Fig. 1. Illustration of the CBR.

In view of the complexity of reverse flow systems emphasizedbove and without diminishing the importance of classical query-ng for information in the scientific literature and problem solving,t seems that a more effective way of finding design informationnd solutions in a fast and easy way is by applying the case-basedeasoning (CBR) approach.

CBR is a paradigm of artificial intelligence and in recentears it has received increased interest induced by the idea thatimilar problems may present similar solving algorithms andven similar solutions. The approach of solving a new prob-em by taking into consideration experience accumulated fromast similar problems has often proved to be much easier andore efficient than generating a new solution from basic princi-

les.The CBR process can be described as a cyclic procedure, as shown

n Fig. 1. The current problem is defined by a set of features withheir values, e.g. compound names, physical properties, operationalues such as feed temperature and space velocity. During therst step, retrieval, a new problem is matched against problems ofrevious cases by calculating the similarity function, and the mostimilar problem and its stored solution are found. If the proposedolution does not meet the necessary requirements of the situationnder consideration, the next step, adaptation, occurs in order to fitdifference to the new needs and a new solution is created. Then,

he solution is evaluated by a set of criteria validated by a humanhrough mathematical modelling and simulation to check that its suitable for the actual problem. A received solution and a newroblem together form a new case that is incorporated in the caseased during the learning step.

Many domains of activity would benefit from the principles ofBR in solving different tasks. Some fields related to chemical engi-eering in which CBR has found applicability are product design [1]nd quality control [2], process synthesis [3] and flow-sheet design4], abstract models generation for process alternatives [5], equip-

ent selection [6] and equipment design [7], process control andlant supervision [8].

The case-based approach enables engineers to handle evenoorly structured domains, as it is well-known that decision mak-

ng is more an art than a science and it is very difficult to completelyepresent knowledge of such domain using rules [9]. A case-basedeasoning approach can handle incomplete data: it is robust with

espect to unknown values because it does not generalize the data.n addition, complex systems require tedious querying work tond reliable information and solutions. Consequently, the use ofBR for decision making process would appear to be both valid

g and Processing 49 (2010) 74–83 75

and effective when finding solution in complicated domain such asdesign.

2. Problem statement

Chemical engineering problems, especially design and mod-elling tasks, are often difficult to be represented as a structured listof features of one or two data types. The representation of designdata comprised in cases requires great attention because designcontent involves various chemical and physical properties, geo-metric aspects and relations between them [10]. Many problemsin chemical engineering are very complex and their description isoften incomplete and uncertain. Structuring such problems (cases)by features must be precise in order to avoid the loss of essentialcharacteristics and information that could influence the retrieval ofsimilarity and appropriate solution suggestion. The input informa-tion in case of unsteady state reactor operation analysis consists ofnumerical value representation of the technical characteristics andsome textual aspects related to the description of the problem.

The reverse flow reactors problem is defined by a complexstructure, which contains features of various data representation(number, logic, sets and symbols). Expert opinion was used to setup the most important features for the correct identification ofthe reverse flow system statement. Design experience of existingreverse flow reactors is stored in the case base. The case represen-tation is systematized further, depending on specific information,as presented in Table 1. The information is represented decom-posed in the case structure into a problem part (left two columnsin Table 1) and a solution part (right two columns in Table 1).

Each case is organised by features grouped in specific sets thatcorrespond to the reverse flow operation process. There are fourmain sets in which the features can be grouped and that may haverelevance in the retrieval process, namely, the:

(1) boundary conditions on the feeds and product streams anddesign species for the reaction system;

(2) reactor characteristics,(3) assumptions and simplifications used in the phenomena

description;(4) supplementary data or sets of comments.

The features corresponding to each set are quantified in numer-ical values and/or symbolic representation. The features are takendirectly from existing cases and the classes are generated auto-matically through the application of the abstraction procedure.All cases have a specific number of common characteristics suchas reactor characteristics (reactor type, catalytic support type,inert length, catalytic length, and reactor elements with interstagecooling/heating), the process variables, reaction characteristics(species, yield), generic functional specifications for design (reac-tion to extinction or yield based, dynamic stability, physicalresources that are being considered in the modelling for the design)species, mass, energy, momentum, power, and relevant time scales,controllability issues and the abstraction level.

The organization of cases in the library is performed accordingto the type of function accomplished by certain features or classesof feature:

- General function: a function that can be achieved by several itemsof the case specific domain. These functions may deal with thetransformation of mass or energy. For example, functions denot-

concentration, etc.- Specific function: an abstract function as known in the case specific

domain of the process. These functions relate process variables tospecific physical–chemical properties.

76 C.C. Botar-Jid et al. / Chemical Engineering and Processing 49 (2010) 74–83

Table 1Structure of the case of model of a reverse flow reactor.

Process characteristics Reactor characteristics Mathematic model Simplifications

Substances involved Type of reactors Type of mathematic models used Type of gasesSpace velocity Reactor shape Dimension of the model Spatial mass transportFeed temperature Type of catalysts and its geometric

characteristicsNumber of phases considered Reaction media (homogeneous/heterogeneous)

Pollutant concentration Type of the inert zones and their Solving method Types of energy transport

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geometric characteristicsReactant concentration Type of the active zones and their

geometric characteristicsRe

Switching time Co

. Case-based model selection procedure

The procedure of finding the solution of the reverse flow pro-esses involves engineering analysis of existing data, composing theathematical model for the current situation and numerical sim-

lation of the constructed and simplified model. The CBR approachs used for selection of an appropriate type of the mathematical

odel and simplifications.Several stages in the problem-solving procedure can be identi-

ed:

1) Problem identification using engineering analysis of the processdata.

2) Case retrieval based on similarity assessments of previous prob-lems.

3) Simulation of the proposed models with initial data and sug-gested simplifications.

4) Evaluation of the obtained solutions.5) Learning the system by storing the studied problem with the

approved solution.

.1. Problem definition

The type and properties of physical objects create the engineer-ng problem description. The properties are grouped into the classesccording to structure of the case representation.

The case is represented by a set of features, with their corre-ponding values. The features can be quantified in numerical andierarchical values and symbolic representation. The solution in aase is defined by the mathematical model representation which isependent on certain characteristics and specifications related tohe case which can affect the model structure.

.2. Case retrieval

The new problem statement is organized according to the struc-ure of all cases stored in the case base. The new case problem isompared against all the cases in the case base. In this step the levelf abstraction is decided and the classes of features from which thelternatives have to be generated are defined. The retrieval processakes into account the possibility of weighting the importance ofhe case features according to the desired information that needso be found.

The quality of the results of the retrieval process mainly dependsn the similarity measure that is used to retrieve the similar casess the retrieved cases constitute the starting point for finding theolution of the actual problem. During the retrieval procedure, theurrent problem is matched against the problems stored in the case

ase. Matching is the process of comparing two cases to each othernd determining their degree of similarity.

For two cases A and B of one type, characterized by a set of fea-ures with their values VA = (a1, a2, . . ., an) and VB = (b1, b2, . . ., bn),here corresponding indices represent corresponding features of

t characteristics Catalyst specifications

nts Inert species

the cases, the similarity is defined as

sim(A, B) = 1n

n∑i=1

identi where identi ={

1, ai = bi

0, ai /= bi(3.2.1)

If the cases have a weighted structure the similarity is calculatedconsidering also the weights value wi:

sim (A, B) =∑n

i identiwi∑iiwi

(3.2.2)

In case of conditionally similar cases the conditional degree ofsimilarity is calculated with the following equation:

sim(A, B|C) =∑n

i �iwi∑iiwi

,

where

�i ={

1, ai, bi ∈ Ck

0, ai ∈ Ck, bi ∈ C ′k

, Ck, C ′k − some classes (3.2.3)

where C represents the condition, a is the classification law; � isthe affiliation value of a and b features to a class. If the value ofthe affiliation to a class is difficult to be calculated or if it couldpresent a degree of uncertainty than the parameter � takes valuesin the domain [0, 1]. If bi is a member of a class, the function �(ai,bi) represents the value of similarity between ai and bi.

Taking into consideration the hierarchical representation of acase the global similarities as presented before and the local or par-tial similarities between singularly features can be calculated. It ispossible in this way to talk about the determination of the distancebetween two features.

Between two features a and b the local similarity l can be calcu-lated by the following equation:

l(a, b) = 1 − d(a, b) (3.2.4)

where d(a, b) is the distance function. The distance d takes valuesin the interval [0, 1]. The distance is inverse proportional with thesimilarity level. Therefore the value 1 attributed to the distancecorresponds to the total dissimilarity between features.

When organizing the cases by independent features the simi-larity assessment has to cover all attributes of these features. Ingeneral, the degree of importance of a specific feature is repre-sented by its attribute and the corresponding weight. Two featuresof different cases are considered correspondent if they accomplishthe same function in relation to other features in their own case.Similarity between two cases is attributed when all or just someof the features have the same values; when no feature can bematched with another one from a different case complete dissimi-

larity is attributed. In this way a complete or partial similarity canbe computed. The value expressing how much two cases are similardefines the degree of similarity. In general, the degree of similarityis normalized in the range of 0–1. The value 1 is attributed to 100%similarity and the value 0 to total absence of similarity. The total

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C.C. Botar-Jid et al. / Chemical Engi

egree of similarity is computed from the weighted sum of eacheature similarity.

The similarity retrieval process works with real (symbolic) ornteger values. Determination of numerical distance is applied

hen comparing values of variables such as temperature, velocity,iameter, and concentration. The symbolic measure works withets of features describing attributes in the case functions, i.e.t searches for similar features between two different data sets.he hierarchical measure finds the distance between tree nodesecause classes contain trees composed of merged classes and/oreatures. Thus, the hierarchical measure determines the distanceetween two classes and/or features according to their tree repre-entation.

A more detailed description of the similarity measurements uti-ized in the developed tool can be found in [1].

.3. Simulation and evaluation of the solution

In addition to similarity, each retrieved case is computed to sug-est the most suitable succession of features and, as a consequence,he solution. In the adaptation phase the differences between thearget case and the solution case and the relationships betweeneatures and their influence on the overall process are identified.n this way, through evaluation of the solution (verification), alleatures affected downstream or upstream are taken into accountn the process solution validation. The validation of the solution iserformed by numerical simulation.

The mathematical approach to heat and mass transfer pro-esses in fixed bed reactors has two general models types: (a) onehase models in which both phases are approximated by a quasi-omogeneous medium and (b) two phase models in which bothhases exchange mass and/or heat, the processes being accountedeparately.

Recommendations obtained from the CBR search are used toeet minimal accuracy requirements to describe satisfactorily the

ynamic behaviour of each reactor type. Simplifications of theelected model are applied in order to reduce the computationalffort needed to find the system solution. In this way the approx-mation of the internal reactor state is realized in a shorter timehan when using a detailed model, giving the control system theossibility to take more efficient and prompt control actions.

Neither adaptation nor verification, as specified before, can beerformed automatically on the CBR tool because the suggestedolution corresponds to real items and real complex processes. Inddition, the modifications made by users to some sections dur-ng the CBR tool exploitation may affect the global performance ofhe process and implicitly the reliability of the retrieved solutions.daptation is highly domain dependent and requires verificationf the solution performance based on top level specific knowledge.nly rigorous mathematical modelling and numerical simulationan predict if the retrieved solution could be acceptable or not. Asconsequence, the adaptation and verification steps suppose an

terative and interactive cycle where the human designer checkshe performance of the proposed solutions. The iterative processnds when the alternative solution satisfies the new requirements.

.4. Learning

The new found solution with its corresponding problem state-ent is organized as a new case and stored in the library of cases

or future use. The alternative process is not retained as a whole,

nly the new classes and their corresponding features obtained orerived from the case base are stored. This avoids redundancy of

nformation in the library. It is important to maintain the consis-ency of the adapted case (classes and features) with respect to theverall process such as general and specific functions and informa-

g and Processing 49 (2010) 74–83 77

tion about the goal. For this reason, the overall alternative processmust be modelled again to identify the adapted characteristics andthe different sections to be retained in the library of cases.

The scope of the system increases during learning and itbecomes a better problem solver.

4. Model selection tool

The developed CBR tool performs two of the four typical CBRstages: the similarity assessment within retrieval stage and thestorage stage. Its performance is integrated in an interactive cycle inwhich the human designer plays a critical role. The tool processesa problem description of a new reverse flow process matching itagainst all the cases in the case base. The most similar cases areretrieved and the best one is selected. The selection process followstwo steps: the first one—tool based corresponding to the usual CBRretrieval and the second one—expert based taking into considera-tion the specific supplementary information or comments relatedto features in order to improve the reliability of a possible newsolution.

Due to the complexity of reverse flow processes, the inclusion ofadaptation and evaluation of the application stages within the CBRtool would have implied the integration of a complex knowledge-based system and a chemical process simulator. The objective of thepresent CBR tool is to support the user in the generation of processalternatives and not to carry out such generation autonomously

The overall system for model selection consists of a library ofcases (the case base) and the CBR tool. The library of cases con-tains files of special format describing the processes (problems)and models (solutions). The main functions of the CBR tool are tonavigate over all past cases, to facilitate the introduction of prob-lem description, and to generate the list of similar cases ranked bydegree of similarity to introduced problem.

4.1. The library of cases

Each case in the library of cases is represented by featuresgrouped in specific classes that correspond to reverse flow oper-ation processes. The features are taken directly from existingprocesses and appropriate classes of features are generated throughapplication of the abstraction procedure. The cases have a specificnumber of common characteristics such as the process variables,the type of reactor and its characteristics, and the abstraction level.

The solution description contains the type and dimension ofmathematical model, the type of transport phenomena consid-ered, and supplementary information, as shown in Fig. 2. Dataabout the model also include the method of the solving approach,such as type of finite difference method approximations, as wellas references to the solution source. One of the important charac-teristics of the model is the list of simplifications applied to themodel. The way the model simplifications are represented is givenin Fig. 3.

The library also includes additional reference materials. It con-tains a description of finite differences method approximations inorder to support the simulation process. Several cases include cor-responding articles in Portable Documents Formats as additionalreferences. The classification tree of reaction processes consideredin the tool and the type of the reactors is attached. This infor-mation may guide the process of data preparation from a newproblem.

4.2. Input of a new problem

After grouping problem data into the classes (see Section 2),such as determination of reaction type (decomposition, reduction,oxidation or synthesis) and class of compounds, new problem is

78 C.C. Botar-Jid et al. / Chemical Engineering and Processing 49 (2010) 74–83

Fig. 2. Example of solution description in the case representation.

description in the case representation.

iTf

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r

4

fo

Fig. 3. Example of simplifications

ntroduced into the CBR module using New Case Form (see Fig. 4).he case form appears when the user starts the search of solutionor the current problem.

The retrieval process can be adjusted according to problem spec-fications. The rule for selection of most similar cases might behosen (acceptance of all cases with similarity higher than a certainalue or collect only a specific number of similar cases) and a setf weights of importance for each features could be assigned. Theatalyst type can be chosen only from the pre-defined list; how-ver, it is possible to add a new type of catalyst by adding a newatalyst description directly to special system file. A new catalystype must be presented at least in one problem in the library fororrect similarity assessments.

Once the new problem has been introduced into the system theetrieval procedure may start.

.3. Retrieval of similar problems

After introduction of the new problem data, the tool searchesor analogous classes and features that satisfy the specific aspectsf the target case. Similarity measures, as presented previously, are

Fig. 4. Introduction of a new problem and adjustment of the parameters of retrievalprocedure.

C.C. Botar-Jid et al. / Chemical Engineering and Processing 49 (2010) 74–83 79

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Following the procedure given earlier, the most similar case thathas been found in the case base, during the querying process, hada degree of similarity of 0.9481. Its characteristics are presented in03—Case 1.

Table 2Problem description of the target case.

Parameter Value

Reaction type ReductionPollutant name Nitrogen oxides (NOx)Pollutant concentration Lean (order of ppm)Reactor shape TubularCatalyst support MonolithicReactor length (dimension) 0.45 mCatalyst type Pt/Al O

Fig. 5. Main window of t

sed. Only classes and features with the same specific functionalroup are considered for retrieval.

Computation of similarity is performed by a measure of similar-ty obtained from the abstract description of the target case. If theBR system returns no solutions with reasonable similarity withinomain of similarity acceptance then the retrieval procedure maye repeated, with changed input information, until a desired levelf similarity is achieved. The selection set may also be refined whendvanced search option are used. The search then takes into accountodel simplifications based on the user’s preferences.The results received from the search could be browsed and

nvestigated. The main window of the tool showing retrievedesults is given in Fig. 5. The solution for the new problem is nothinglse then the most similar case or cases stored in the case based.he information stored in the case or the cases found during theetrieval process represent the knowledge that is going to be usedn solving a new problem.

. Example

.1. The representation of the case study

In the present work, the target case has been represented bypecific features given in Table 2.

The maximum number of accepted cases to be retrieved wasxed at the three most similar ones. The number of cases stored

n the case base was 33; all related to reverse flow reactor oper-tion reactor operation. For each important feature used in theetrieval process a weight of importance was established, based onxpert opinion, according to the most critical information neededor design purposes and solution suggestion. The weights of impor-

l with retrieved results.

tance are used in order to optimize the similarity assessmentprocess (Table 4). An example of weights of importance associatedto the features used in the similarity assessment is presented in 0.

The CBR tool retrieved three cases based on the informationgiven and on the level of acceptance imposed. The problem state-ment of the retrieved cases is exemplified in Table 3.

Due to the fact that the case study in this paper is the NOx reduc-tion in reverse flow reactors, the weights of importance have beenestablish accordingly in order to retrieve information especiallyabout the NOx reduction process, reverse flow reactor geometryand operation and mathematical model implementation.

2 3

Length of the inert zone 0 mFeed temperature 298 KCatalyst temperature 630 KSwitching time 100 sSpace velocity 0.27 m/s

80 C.C. Botar-Jid et al. / Chemical Engineering and Processing 49 (2010) 74–83

Table 3Problem description of the retrieved cases.

Item Case 1 Case 2 Case 3

Similarity degree with the target case 0.9481 0.8742 0.8485

ParametersReaction type Reduction Combustion DecompositionPollutant name Nitrogen oxides Methane Diesel exhaustPollutant concentration Lean (order of ppm) Lean (order of ppm) Lean (order of ppm)Reactor shape Tubular Tubular TubularCatalyst support Monolithic Monolithic MonolithicReactor length (dimension) 0.3 m 0.5 m 0.58 mCatalyst type TiO2/V2O5/WO3 Al2O3/Pd TiO2/V2O5/WO3

Length of the inert zone 0 m 0 m 0 mFeed temperature 293 K 298 K 298 KCatalyst temperature 573 K 400 K 298 KSwitching time 15 s 1 s 50 sSpace velocity 0.1 m/s 0.1 m/s 0.1 m/sModel type 1-D, two phase model 1-D, two phase model 3-D, two phase modelTransport phenomena Convection diffusion Convection diffusion Convection diffusion

CommentsImproved bed conductivity No No NoHeat losses compensation No No NoGood agreement with analytical results Yes Yes YesGood estimation of the max asymptotic temperature Yes Yes YesNecessity of supplementary analysis of the system Not specified Not specified Not specifiedComplex dynamic behaviour Not specified Not specified Not specifiedCatalyst deactivation caused by temperature No No NoCatalyst deactivation caused by other causes Not specified Not specified Not specifiedCatalyst deactivation by water Not specified Not specified Not specifiedNormal feeding position No Yes YesSide feeding position Yes No No

SimplificationsIdeal gases Yes Yes Yes

tuiabuaststsv

TW

Uniform inlet mixing YesHeterogeneous reaction YesBulk temperature YesIsothermal system Yes

The CBR tool is designed to show all information characterizinghe case retrieved excepting the one corresponding to the featuressed in the retrieving process. The use of the CBR tool provides

nformation about the mathematical model description, degree ofssumption and phenomena that contribute to the overall processehaviour in the retrieved cases. The possible solutions obtainedsing the CBR tool were taken into consideration; the one accepted,fter expert opinion, was verified and adapted to fit new needs andtored as a new case in the case library. The solution provided by

he CBR has been adapted in the sense that different values of thewitching time were needed in the new case in order to obtain auto-hermal behaviour and high reaction yields. The values of the newwitching time and the new are provided in the case study modelalidation section.

able 4eights of importance corresponding to the target case features.

Parameter Weight

Reaction type 6Pollutant concentration 7Reactor shape 2Reactor length (dimension) 9Catalyst type 2Length of the inert zone 6Feed temperature 9Catalyst temperature 2Switching time 9Space velocity 8Substance class 9Mathematical model 8Phenomena described in the model 2Simplifications in the model 2Solving method 2

Yes YesNo YesYes YesNo (adiabatic) Yes

Information, in a simplified manner provided by the CBR tool,represents the solution (Case 1, Table 3), which suggests that:

- the catalyst used could be the one containing TiO2/V2O5/WO3,disposed on monolithic supports;

- the inert catalyst section used for the recuperation of the heatrelease during reaction could be absent;

- the feeding of the gas at normal ambient temperature does notaffect the process;

- the initial catalyst temperature could be 573 K;- the reaction could be considered heterogeneous;- the process could be described by a 1D two phase model without

affecting the reliability of the results.

5.2. The case study model validation

Following the solution has been tested and validated throughsimulation. The mathematical model and the simulation results arepresented below for a reverse flow reactor as a type of reverse flowreactor.

Considering a heterogeneous mathematical model, anEley–Rideal mechanism describing the reaction between NOx

(as species A) in the gas phase and the ammonia (as a species B)adsorbed on the catalyst, the process structure is the followingone:

A + BS → C (5.1)

B + S → BS (5.2)

C.C. Botar-Jid et al. / Chemical Engineering and Processing 49 (2010) 74–83 81

on of t

r

r

wtato

r

ac

r

a

e

E

ttirtd

-

Fig. 6. The mean value outlet concentration of NOx and NH3 as a functi

The reduction reaction is considered to be of first order withespect to each reactant, hence:

red = −kredc∗A�B

˝, (5.3)

here �B is the ammonia surface coverage and c∗A is the concentra-

ion of reactant A at the gas–solid interface. If the adsorption rate ofmmonia on the catalyst surface is assumed to be proportional tohe ammonia concentration in the gas phase and to the free fractionf surface sites then:

ads = kadsc∗B(1 − �B)˝

, (5.4)

nd if the rate of desorption is assumed to be proportional to theoncentration of the adsorbed species then:

des = kdes�B · ˝, (5.5)

An Arrhenius type dependence of the kinetic constants k, kadsnd kdes from the temperature is assumed it results:

kred = k0,rede−Ea,red/RTS ,kads = k0,adse

−Ea,ads/RTS ,kdes = k0,dese

−Ea,des/RTS .(5.6)

A Temkin-type adsorption isotherm is assumed, the activationnergy for desorption is a function of the surface coverage:

a,des = E0a,des(1 − ˇ��

B ). (5.7)

In case of a monolith support catalyst considered for the selec-ive catalytic reaction (SCR) reaction: mass and energy dispersiveransport could not be taken into account due to the low conductiv-ty of the monolithic support and also the pressure loss inside theeactor can be neglected and if an adiabatic operation is assumed,he system of partial differential equation that describes the processynamic is the following:

gas phase mass balances:

∂cA

∂t= −v

∂cA

∂x+ hAav

(c∗

A − cA

), (5.8)

∂cB

∂t= −v

∂cB

∂x+ hBav

(c∗

B − cB

), (5.9)

Fig. 7. Axial profile of NOx, NH3 and NH3 adsorbed on the catalyst surface—non-i

ime in case of a RFR operated at a switching time of 900 s = “�” or “tsw”.

The values of c∗A and c∗

B, the gas concentration at the interfacecan be calculated from the mass balance at the interface assumingthat there is no accumulation:

−hAav(

c∗A − cA

)= rred, (5.10)

−hBav(

c∗B − cB

)= (rads − rdes) , (5.11)

- solid phase mass balance:

˝ · ∂�B

∂t= rads − rdes − rred, (5.12)

- gas phase energy balance:

∂TG

∂t= −v

∂TG

∂x+ hT av

�Gcp,G(TG − TS) , (5.13)

- solid phase energy balance:

�S · cp,S · ∂TS

∂t= −hT · av · (TS − TG) + rred · (−�Hred)

+ rads · (−�Hads) + rdes · (−�Hdes) (5.14)

The solution obtained from the querying process, represented bythe Case 1 in Table 3, which considered a catalyst length of 0.3 m,catalyst type TiO2/V2O5/WO3, inert zone length, 0 m, initial feedtemperature 293 K, catalyst temperature 573 K, switching time 15,gas velocity 0.1 m/s has been adapted for the new case in orderto obtain auto-thermal behaviour and high reactant conversion.The new found solution, for the target case Table 2, was to useswitching time of 900 s when isothermal conditions were imposedand a switching time 50 s for non-isothermal conditions.

The main parameters used in simulations are presented inTable 5:

The obtained results validate the solution suggested by the CBRtool as a good one when considering the conversion of reactantsand the authotermal behaviour obtained. Figs. 6 and 7 show the

RFR behaviour in terms of concentration profile as a function oftime and along the reactor length.

In Figs. 7 and 8 the concentration profiles are obtained whenoperating the reverse flow reactor was operated with a switchingtime (“tsw′′ or “�”) of 900 s in case of isothermal conditions, 50 s in

sothermal conditions in case of a RFR operated at a switching time of 900 s.

82 C.C. Botar-Jid et al. / Chemical Engineering and Processing 49 (2010) 74–83

Fig. 8. Axial profile of NOx, NH3 and NH3 adsorbed on the catalyst surface—non-

Table 5The main parameters.

cNOx 560 ppmV˝ 210 mol m−3

v 0.27 m s−1

�S 2500 kg m−3

ce

tt

pfa

wbbmp

6

erraaed

aem

cNH3 560 ppmVL 0.45 mtsw = � 30–1200 scp,S 0.9 kJ kg−1 K−1

ase of non-isothermal conditions and for a simulation time of longnough for the stationary state to be obtained.

The simulations results show that the choice of the model struc-ure and the parameters used represent an appropriate solution forhe new case.

As a consequence using the CBR based system as a decision sup-orting tool reduces considerable the time and the effort neededor solving complex problems related to reverse flow reactor oper-tion.

Nevertheless, the reliability of the suggested solution increasesith the number and with the diversity of cases stored in the case

ased. It is also true that the interactive querying procedure com-ines the experience gained using the CBR system associated withodel simulation and even experimental investigation of the pro-

osed new solution.

. Conclusions

Finding the optimum configuration for the reverse flow reactor,mploying the most suitable operation model and identifying theeactor behaviour are highly important steps to design a suitableeverse flow reactor for industrial applications. The design of andapted reactor requires knowledge about the influence of its oper-ting conditions on the overall process performance and a precisevaluation of the operating parameters range for which sustained

ynamic behaviour is obtained.

This paper describes a methodology for gaining informationbout reverse flow reactor design and operation in a fast andasy way including important process parameters and their values,athematical descriptions of the process, mathematical methods

isothermal conditions in case of a RFR operated at a switching time of 50 s.

of solving the system of partial differential equations, and otherspecific information.

The methodology considers implementation of a CBR system.The approach based on significant literature cases dealing with pro-cesses involving reverse flow reactor operation and giving the levelof abstraction it is possible to use feature like structures that canbe used to generate new solutions for new problems like the onerelated to the present issues.

The CBR tool is dedicated not only to expert users but also totrained engineers that could use it as a support in their under-standing of the reverse flow processes and to guide them throughreasoning and decision-making based on information that can besupplied by a case library.

Appendix A. Nomenclature

r reaction rate (mol m−3 s−1)av specific surface of the catalyst (m2 m−3)cp specific heat (J kg−1 K−1)c∗

A, c∗B gas concentration at the interface (mol m−3)

kred reaction rate constant (mol m−3 s−1)kads adsorption kinetic constant (m3 mol−1 s−1)kdes desorption kinetic constant (s−1)Ea activation energy (J mol−1)R ideal gas constant (J mol−1 K−1)T temperature (K)hA, hB mass transfer coefficients (m s−1)v gas velocity (m s−1)x axial coordinate (m)hT heat transfer coefficient (J m−2 s−1 K−1)k0,red pre-exponential factor of the reaction kinetic constant

(m3 mol−1 s−1)k0,ads pre-exponential factor of the adsorption kinetic constant

(m3 mol−1 s−1)

k0,des pre-exponential factor of the desorption kinetic constant

(s−1)t temporal coordinate (s)−H heat of reaction (J mol−1)tsw = � switching time (s)

neerin

Gˇ�ε�˝

SaABBradGS

R

[

[

[

[13] S.A. Velardi, A.A. Barresi, Chemical Engineering Science 57 (15) (2002)

C.C. Botar-Jid et al. / Chemical Engi

reek symbolsparameter for surface coverage dependencesurface coveragemonolith void fractiondensity (kg m−3)maximum catalyst capacity (mol m−3)

ubscripts and superscriptsds adsorption process

identifies NOXidentifies NH3

S identifies NH3 adsorbeded reduction processds adsorption processes desorption process

gas phasesolid phase

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