Chemical Engineering Science 56 (2001) 5727–5738www.elsevier.com/locate/ces

Computer aided synthesis of RTD models to simulate the air (owdistribution in ventilated rooms

C. Laquerbea, J. C. Labordeb, S. Soaresb, L. Ricciardib, P. Floqueta ;∗, L. Pibouleaua,S. Domenecha

aLaboratoire de G�enie Chimique, UMR CNRS 5503, INP-ENSIGC-18, Chemin de la Loge, F 31078 Toulouse Cedex 4, FrancebInstitut de Protection et de Suret�e Nucl�eaire, D�epartement de Protection et d’Etude des Accidents, Service d’Etudes et de Recherches en

A�erocontamination et en Con0nement, CEA Saclay-Bat. 389, F 91191 Gif-Sur-Yvette Cedex, France

Received 24 July 2000; received in revised form 27 April 2001; accepted 3 July 2001

Abstract

In order to achieve a satisfactory level of hygiene and comfort in ventilated premises and to assess the pollutant transfers, it isnecessary to control the air (ow distribution. An intermediate approach between predictive numerical simulations and experimentaldeterminations of aerodynamic parameters characterizing air distribution in rooms, is constituted by the systemic approach. Thisarticle presents the main principles of this approach, which is based on the residence time distribution (RTD) theory, commonlyused in chemical engineering, and gives an illustration of its potential extension to ventilation problems. The aim of the IDTS codedeveloped is to build a model from a combination of elementary systems representing basic ideal (ow patterns (perfect mixed(ow, plug (ow,: : :). The adjustment of the model lies in the comparison of the response to a stimulus injected into the model withan experimental tracer emission performed in a ventilated room inlet.The general solving strategy adopted, consisting in a two-level dissociated treatment of parametric identi8cation and structural

identi8cation of models, is 8rst presented. Then, two problems tackled during the quali8cation step of the IDTS code are presentedto illustrate the applications of this computer-aided design tool for the description and the quanti8cation of air (ow patterns and theassociated pollutant transfers observed in ventilated indoor spaces, and particularly in nuclear ventilation networks. The comparisonbetween experimental residence time distribution curves recorded in two ventilated laboratory enclosures and the simulated onesshows good agreement. For the last illustrative problem, a comparison with results obtained from a computational (uid dynamicstool has been performed. ? 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Air (ow description; Industrial ventilation; Pollutant transfers; Residence time distribution; Structural and parametric identi8cation

1. Introduction

The control of the airborne contamination transferslinked to the operators’ protection and to the facilities’safety is an essential feature in the nuclear industry, par-ticularly to prevent radiological risk. So, it is necessaryto have tools in order to assess airborne contaminationtransfers inside a ventilated enclosure, since the ventila-tion constitutes a system of contamination containment.In this way, the systemic approach concept aims at

interpreting residence time distribution (RTD) in a room.

∗ Corresponding author. Tel.: +33-5-62-25-72-18; fax: +33-5-62-25-23-18.E-mail address: pascal.(oquet@ensigct.fr (P. Floquet).

Residence time distribution theory (Danckwerts, 1953)is commonly used to describe the (ow patterns in a widevariety of applications. This approach constitutes an inter-mediate way between numerical simulations using com-putational (uid dynamics (CFD) codes and experimentaldeterminations of characteristic parameters. It appears tobe of great interest when the predictive method based onCFD codes cannot be used, particularly in the case oflarge and cluttered systems which correspond to the scopeof the present study. Furthermore, this approach leads tomore integrated results, giving a physical signi8cance tothe (ow model within reasonable CPU times.The proposed method lies 8rst in the experimental de-

termination of the residence time distribution curve, ob-tained generally through the response of the system to a

0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved.PII: S 0009-2509(01)00292-5

5728 C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738

tracer release. Then, a model is built and consists in acombination of elementary ideal (ow systems: plug (ow(PFR), perfect mixing (CSTR), by-pass and recycling(Levenspiel, 1972). Each elementary system is charac-terized by speci8c parameters such as mean residencetime or volume. The adjustment of the model is derivedfrom the comparison between the simulated response ofthe model to a stimulus, and the experimental responserecorded in the room outlet to a tracer emission realizedin the inlet duct. The parameters of the various candidatestructures (volumes and (owrates) are optimized in orderto 8t the experimental curve.In previous works, only softwares performing the iden-

ti8cation of a small number of parameters for modelswhose structures are provided by the user were available(Thereska, 1998; Leclerc, Detrez, Bernard, & Schweich,1995; Berne & Blet, 1998). For example, Leclerc et al.(1995) identify some parameters (volumes, (owrates) fora structure model 8xed after several trials. No softwareallowing a complete computer aided design (CAD) ofthe structures has been developed. The purpose of thisstudy is to try to 8ll this gap and to show the potentialitiesbrought by this approach to ventilation problems.The paper 8rst provides an overview of the global

methodology adopted for the development of a compu-tational package allowing the synthesis of RTD modelstructures. The main aspect of the procedure is constitutedby a master problem performing the structural identi8ca-tion of the models. The problem of discrimination of thevarious schemes is solved by two stochastic proceduresbased on the one hand on simulated annealing (SA) algo-rithm and on the other hand on genetic algorithms (GAs).The implementation of these two algorithms is not de-tailed here, having been presented previously (Laquerbe,Laborde, Floquet, Pibouleau, & Domenech, 1998; Laque-rbe et al., 2000). Finally, two industrial applications areproposed for the quali8cation step of the IDTS code andfor the description of the air (ow patterns and the mon-itoring of the associated pollutant transfers observed inventilated indoor spaces. The comparison between exper-imental residence time distributions on the two ventilatedlaboratory enclosures and the simulated ones shows goodagreement, as well as the comparison performed with re-sults from a CFD tool for the last example.

2. Problem statement

The establishment of an RTD model lies in the com-parison of a simulated response of a proposed model to astimulus, with an experimental response obtained gener-ally through the response of the system to a tracer release(classically helium in ventilation premises).The problem can be formulated as a two level identi-

8cation problem: a structural identi8cation problem anda parametric identi8cation one.

3. General structure of the code

The IDTS code (Laquerbe, 1999) presented here aimsat solving this problem in a large general framework andas a consequence, the modelling strategy is split into twoalgorithmic loops as shown in Fig. 1: an inner loop per-forming the evolution and the choice of the continuousparameters of each model, and an outer loop performingthe evolution of its structure.This original strategy allows to tackle the highly com-

binatorial aspect of the problem. Furthermore, this choiceprovides an easy selection of eEcient solving proceduresfor each identi8cation level. As a result, an outer loop isdedicated to the structural identi8cation (always initial-ized by a unique CSTR reactor whose volume is equal tothe total enclosure volume), i.e., the master problem ofchoosing the model structures (number and nature of ele-mentary ideal (ows, connections: : :). This loop proposesthe structure of the models for the inner level in order toidentify their parameters, i.e. solving the slave problemrelated to parametric identi8cation (volumes, (ow rates)for a 8xed structure.The solving strategy implemented in the computational

package implies three modules: a simulation module, aparametric estimator module and a structural evolutionmodule. A concise description of these three modules isgiven below.

3.1. Simulation module

This module is implemented for calculating the simu-lated response ym of a model M (p), model correspond-ing to the structure M (:) associated with the set of pa-rameters p, for a given stimulus u. The problem can beformulated as a classical system of diFerential and alge-braic equations. The various types of equations solvedare given below.

• Ordinary diFerential equations (ODE) are solved todescribe CSTR models:

dCout

dt=

Qin

VCSTR× (Cin − Cout):

• Algebraic equations (AE) are solved to describe PFRmodels:

C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738 5729

Fig. 1. Structure of the general identi8cation strategy.

Cout(t)=Cin

(t − VPFR

Qin

):

• AE are also solved to describe the mixing nodes in-volved in the scheme:

Cout =∑

i (Qiin ;C

iin)∑

i (Qiin):

3.2. Parametric identi0cation module

This section describes the inner loop performing theidenti8cation of the set of parameters p for a 8xed modelstructure M (:), in order to 8t the experimental signalwith the simulated response. The adjustment of these twocurves consists in a constrained nonlinear least squareminimization problem solved by a general successivequadratic procedure (Schittkowski, 1980). The objectivefunction j(p) is then given by

Minp

[j(p)=

1N

N∑i=1

[y(ti)− ym(ti; p)]2];

where N is the number of experimental sampling points,y the experimental response, ym the model response, tthe time and p the set of parameters to be identi8ed in astructure composed with:

• the volumes of the CSTRs;• the volumes of the PFRs;

• the (ow rates in the various streams present in theoriented graph describing the (ow model.

The constraints include equality constraints related tomass balances at each node of the (ow diagram and tovolume conservation of the real global volume of the en-closure, and also inequality constraints corresponding toidenti8ability conditions given by the structural identi8-cation loop.

3.3. Structural identi0cation module

This module constitutes the highest level implementedin the computational package. Stochastic procedures havebeen chosen here to tackle the combinatorial aspect ofthe problem. This choice of evolutionary procedures isalso motivated to avoid an explicit de8nition of the searchspace.The problem considered here is the following:

MinM [j(M)= j(M; p) + � dim(p)].The least square criterion given by the parametric

identi8cation module at optimal parameters (j(M; p))is added here to a penalty term (� dim(p)) proportionalto the leading dimension of the parameter set of thestructure tested. This dimension is then directly relatedto the complexity of the model. On the one hand, forhigh values of �, the term � dim(p) is preponderant inthe criterion j(M) and leads to simple structures. Onthe other hand, a small value of � may signi8cantly andunnecessarily increase the number of structure elements(reactors, recycles, by-pass,: : :).The objective function considered allows the procedure

to propose a simplest possible model although well rep-resenting all the observed (ow patterns. From an initialstructure composed of unique CSTR, the procedure with

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a 8xed value of �, increases the complexity of the struc-ture step by step if the criterion j(M) decreases. Further-more, with a known structure complexity (same valuesof dim(p)), the elementary systems may change: for ex-ample, a CSTR may be changed in a PFR (or vice-versa)or replaced by a by-pass.Two stochastic procedures have been implemented:

• a simulated annealing (SA) procedure (Kirkpatrick,Gellat, & Vecci, 1983);

• a GA (Goldberg, 1989), which proposes many alter-natives at the end of the procedure.

The implementation and a comparison of these twoprocedures on theoretical examples used in the vali-dation step of the code are given in Laquerbe et al.(1998) and Laquerbe et al. (2000). The results showthat the GA procedure appears more eEcient and robustbut needs more computational capabilities than the SAprocedure.

3.4. Encoding strategy

Both procedures, SA algorithm or GA, work on a spe-ci8c encoding of the candidate solutions.The models are 8rst represented through a (ow sys-

tem made up of ideal components (plug (ow, continuousstirred tank) connected by (ow mixers, (ow splitters andrecycling loop. Leaks, in8ltrations or short-circuits canalso be introduced.The encoding, proposed by Laquerbe et al. (1998),

is based on an original decomposition strategy of eachstructure that ensures distinguishability of the variouscandidate models with a unique decomposition for struc-tures which are structurally equivalent according tomodel linearity. This decomposition is carried out ina unique and hierarchical way based on four complexbuilding blocks, represented in Table 1: linear cascade,recycling loop, parallel distribution and intermediatedistribution.This encoding allows to generate the most common

possible schemes and thus to explore a large solutionspace. An example of decomposition and encoding isgiven in Fig. 2.

3.5. Integration of physical considerations in thestructural identi0cation step

With the encoding strategy adopted, it is easy to imag-ine that a model with some branches in parallel, or with acascade of complex blocks, can be proposed by the code.In these kind of structures, some regions exist withoutconnection with others, prohibiting a mass transfer be-tween these zones. This corresponds classically to a realindustrial ventilation network leading to several rooms,but cannot characterize the air (ow in a single room. To

Table 1Inventory of building blocks used for the encoding

Building block Representation

Ideal component CSTR, PFR, Short-circuit: : :

Cascade

Recycling loops

Paralleldistribution

Intermediatedistribution

keep a large general framework of applications for thecode to distinguish these two diFerent cases, an additionaloption has been implemented in the computational pack-age. The stochastic nature of the structural identi8cationprocedure is not able to take into account, in any case,this absolute constraint in ventilation problems: all theidenti8ed zones must exchange air between each other.A (ag can then be activated when the problem con-

sidered corresponds to a single room; in this case, all theelementary regions proposed by the procedure must ex-change a fraction of air with each other. When this (agis activated, the previous objective function consideredin the structural identi8cation module (j(M)= j(M; p)+� dim(p)) is replaced by the following one:

j(M) = [j(M; p) + � dim(p)]

(1 + �× Nbr Violations);where Nbr Violations correspond to the total number ofimpossible exchanges between every couple of regionsof the structure and � is a penalty factor, whose value hasbeen arbitrarily 8xed at 10%.

C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738 5731

Fig. 2. Example of decomposition.

In this way, the penalization of the structures not re-specting the physical considerations speci8c to the venti-lation of a single room constitutes a gradation and allowsto generate intermediate nonsatisfactory structures whichcan be useful in the evolutionary process to generate 8-nally acceptable structures.

4. Validation on theoretical examples

A systematic scheme of validation for the whole identi-8cation process presented has been performed on elemen-

tary examples. Reference models have been used to gen-erate a theoretical experimental RTD curve. This curve isthen used and proposed to the code to generate a candi-date structure which is then compared to the original one.A statistical analysis is carried out to evaluate the robust-ness of the procedure according to the parameterizationof the algorithms and according to their stochastic aspect.The results of the validation scheme can be found in

Laquerbe (1999), Laquerbe et al. (1998), Laquerbe et al.(2000). These results clearly show the potentialities ofthe structural identi8cation procedures.

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Many remarks can be formulated. First, it is very im-portant to notice that for both identi8cation procedures,the nature of the stimulus (Dirac or impulse, step-upor purge) or the presence of measurement uncertaintieshave no in(uence on the robustness of the procedures. Infact, the probability to recover the optimal structure, cor-responding to the original model, is the same with andwithout the presence of a noise on the experimental data;this noise is simulated by adding to the signal a randomGaussian variable characterized by its standard deviation�. Furthermore, the GA structural identi8cation proce-dure appears to be more robust and eEcient than the SAone, the original solution being attained more frequently.Undoubtedly, the implicit parallelism notion of GAs ex-plains these better results. We can notice the eEciencyof the procedure which generates the optimal solutionwith a low number of discernable structures synthesized(¡ 200).For a nonexperienced user, automatic initialization

procedures are available in the IDTS code for speci8cparameters of the algorithms, for example, for the ini-tialization of the penalty factor (�) or for the initial SAtemperature. These automatic procedures of initializa-tion have also been validated, giving similar results thanmanual initializations.

5. Quali�cation on experimental data

In this part, the quali8cation of the code is illus-trated in two diFerent ventilated test benches avail-able at IPSN=DPEA=SERAC: the small scale facilitiesSIMEVENT and MELANIE.

5.1. Application to a ventilation network:SIMEVENT facility

This test bench constitutes a small scale model of ageneral industrial ventilation network where it is possi-ble to obtain diFerent air (ow patterns by con8guringthe ventilation system in various ways (Raboin, Perdriau,Laborde, & Mulcey, 1991). The con8guration retainedhere corresponds to Fig. 3 and includes two tanks in paral-lel with a short-cut. Helium tracer method correspondingto a continuous release followed by a purge in the blow-ing duct is used to characterize the ventilation system.This con8guration has been used to test the capability

of the software to recover a known real (ow structureproviding the experimental RTD curve recorded in theexhaust duct only to the IDTS code.To analyse the results given by the IDTS code, it is

8rst necessary to perfectly characterize the real (ow pat-tern present in the network, that is to say, to determine ifthe tanks A and B can constitute perfectly mixed zones.If it is not the case, we have to propose a model whichcan correctly represent the air (ow inside each tank. The

Fig. 3. Ventilation con8guration studied for SIMEVENT facility.

whole model obtained in this way for the total networkcould constitute a “reference model” and could be com-pared to the structures given by the IDTS code.To obtain this model, additional data are necessary:

the local tracer responses in the exhaust ducts of tank Aand B, and the global response recorded in the generalexhaust duct. So while recording the general RTD curve,the partial residence time distributions directly obtainedfrom tanks A and B have also been recorded. In thisway, the (ow pattern in each tank can be characterizedseparately.For tank B, a log-diminution of the tracer concentration

can be observed after a purge. As a consequence, tank Bcan be considered as a perfectly mixed zone, with an airchange of 26 h−1.This is not the case for tank A, as illustrated in Fig. 4. In

order to con8rm the fact that tank A cannot be consideredhomogeneous, samples have been performed directly in-side the tank (Fig. 5). It can be noticed that the shapeof the concentration response after an impulse stimuluschanges with the position of the internal sampling pointthough, validating this hypothesis. The presence of peakscharacterizes internal recirculation, and tank A cannot bemodelled as a CSTR. So, an empirical two-zone model,classically used in industrial ventilation, has been pro-posed. This model which allows to correctly representthe RTD curve in the exhaust of tank A, can be consid-ered as having a good representation of the (ow patternin this tank with this model. With such information, amodel like the one shown in Fig. 6 can be elaboratedwith engineering rules to represent the general ventilationnetwork. The software package has recently been usedfor volume identi8cation, realized on the structure estab-lished above “by hand”. For this case, the criterion valueis 0.016 (with arbitrary units).When only the global response, recorded in the general

exhaust duct of the network, has been proposed to theIDTS code, the best model obtained is reported in Fig. 7,with a criterion value of 0.064 (with the same arbitraryunits). It can be noticed that all the main characteristics

C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738 5733

Fig. 4. Purge response in tank A.

Fig. 5. Internal response in tank A.

of the air (ow have been identi8ed: three branches inparallel, volume of tank A (error of 15% from the realvolume), tank B (33%) and (owrates of upper and in-ner branches (10%) and by-pass (owrate (19%). Some

deviations appear on the values of the parameters proba-bly because of the nonideal behaviour of tank A. In fact,if another identi8cation without constraint on the globalvolume is made, the model proposed is close to Fig. 6,

5734 C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738

Fig. 6. First model proposed, elaborated “by hand”.

Fig. 7. Model obtained with the IDTS code.

Fig. 8. Model obtained with the IDTS code and without constrainton the global volume.

but with a loss of 0:5 m3 of global volume. This model ispresented in Fig. 8. The result con8rms that the presenceof a dead zone misleads the interpretation of the code.The model presented in Fig. 6 is nevertheless satisfactoryfor representing the general air (ows and the associatedtransfers present in the equipment. This model is simplerthan the one obtained “by hand”, but it is very importantto notice that it has been obtained with a lower experi-mental eFort, only one curve compared to the three abso-

lutely necessary to build a model “by hand”, and withoutany assumption of the 8nal structure of the model. Thecode can be used to satisfactorily identify the structureand all the parameters of the model.This example clearly illustrates the potentialities of this

software as a CAD tool to generate RTD model for ven-tilation applications.

5.2. Application to a ventilated laboratory enclosure:MELANIE facility

A real ventilation room (100 m3), the laboratory en-closure called MELANIE and represented in Fig. 9, hasthen been used to illustrate an application of the IDTScomputational package in a single ventilated room. In-side this room, it is possible to obtain various air (owsand residence time distributions by either changing theposition of blowing and exhaust openings (near the (ooror near the ceiling), or modifying the exhaust (ow rate(Espi, 2000).The con8guration studied here corresponds to an ex-

haust (ow rate equal to 1100 m3=h at 20◦C, and to theclassical location of blowing and exhaust opening foundin nuclear ventilation applications (blowing in the upperpart of the room and exhaust in the lower part). For thiscon8guration, identi8cations have been performed by theIDTS code using the experimental response of this sys-tem from an impulse release of helium used as tracer gas.A 8rst attempt at identi8cation has been made with-

out activating in the code the (ag to integrate in theresults physical considerations on mass exchanges. Thebest model obtained in these conditions is given in Fig.10 (total volume adjustment: 99.97%). Although theadjustment of the experimental curve by the simulatedresponse of the model is quite good, this structure is notacceptable physically, comporting two main branches inparallel, prohibiting any exchange of air between thosebranches. Let us recall that, in a ventilation enclosure,there is always mass exchange between each identi-8ed zone included in the global volume with the otherones.Other identi8cations have been realized with the ac-

tivation of the (ag to integrate physical considerations.Among the structures proposed by the code, the bestobtained and physically probable is represented in Fig.11 (total volume adjustment: 100%). The comparison be-tween the experimental curve and the simulated one isquite satisfactory. The value of the criterion correspond-ing to Fig. 11 is better than the one corresponding toFig. 10 (approximately a rate of two between the formerand the latter). This structure answering to the physicalconsiderations enounced before is retained to representthe (ow pattern in the ventilated enclosure for the cor-responding operating conditions. The importance of acti-vating the (ag orientating the code to generate structures

C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738 5735

Fig. 9. MELANIE laboratory facility.

Fig. 10. Best structure obtained by the code without physical considerations.

5736 C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738

Fig. 11. Best structure obtained by the code with physical considerations.

that are physically acceptable is clearly put in evidencehere.To verify that this model can represent the reality of

the air (ow in the room, a complementary study has beencarried out. The model proposed by IDTS is analysed bycomparing the (ow patterns induced by this structure andthose calculated by 3D predictive numerical simulationsperformed by the FloventTM code. The helium transfersinside the ventilated enclosure have been simulated andare reported in Fig. 12 at various times. With this infor-mation, it is possible to localize the main parts constitut-ing the RTD model (Fig. 11).

• Fig. 12(a), obtained 20 s after the beginning of a con-tinuous release of helium inside the ventilated room,shows a small part of the blowing (ow rate passingquickly into the exhaust opening. This phenomenoncorresponds to the 8rst peak on the experimental RTDcurve, and can be generated by the branch n ◦ I of thestructure obtained by IDTS (Fig. 11).

• Fig. 12(b) illustrates a secondary recirculation near theexhaust opening, that appears on the RTD curve after40 s with a second peak. This can be related to therecycling branch n ◦ II in Fig. 11.

• After t=100 s, Fig. 12(c) illustrates a main recircula-tion loop from the exhaust opening to the blowing one.This phenomenon could be located in branch n ◦ III ofthe structure (Fig. 11).

• At least, around t=300 s and after (Fig. 12.d.), thetracer has 8lled the entire volume of the cell, and itschange involves the classical exponential decrease onthe RTD curve.

These results show as to how the two diFerent tools con-stituted by the IDTS code and a CFD code can be usedto analyse the air (ow distribution and the associatedcontaminant transfers in an industrial ventilated enclo-sure. Here, the use of these two kinds of computationalpackages has been possible owing to the geometrical sim-plicity of the room, 3D predictive simulations being eas-ily possible in those conditions.The structure of the model represented in Fig. 11 has

also been applied to various con8gurations of the ven-tilation system of the cell MELANIE: diFerent exhaust(ow rates (1100; 2200 and 3000 m3=h) and diFerent po-sitions of blowing and exhaust openings (four diFerentcon8gurations tested). For each ventilation con8gura-tion studied, only with an identi8cation of the operating

C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738 5737

Fig. 12. Visualization of the evolution of helium released inside MELANIE by using a CFD code.

parameters (volumes of CSTRs and PFRs, (ow rates) ofthe structure given in Fig. 11, it has been veri8ed thatthis model can represent quite satisfactorily the variouscorresponding RTD curves.Once an RTD model is proposed by the IDTS code,

it can be used as part of safety studies to simulate thecontaminant transfers after an accidental release in onedetermined region of the structure. Indeed, the con-tamination propagation can be simulated in all regionspresent in the model structure for a release in a givenregion.

6. Conclusion

The computational package presented in this paperconstitutes a useful and innovative tool to elaborate res-idence time distribution models in order to characterize(ow patterns and associated transfers. The computationalpackage includes various components: a simulation tool,a parameter identi8er for models with 8xed structures,but also a structure identi8er very useful in the concep-tion step in the modelling process.

A 8rst validation has been carried out. A 8rst quali-8cation has also been performed to study the operationof two ventilation systems and to predict the associatedairborne pollutant transfers, showing in this way the po-tentialities brought by the systemic approach to venti-lation problems. The complementarity between the sys-temic and the CFD approaches has also been illustrated.This CAD tool seems to have useful applications not

only in industrial ventilation but also in more classi-cal chemical engineering 8elds or other domains whichcommonly use the analysis of residence time distributioncurves, especially when the structure model represent-ing the real enclosure is diEcult to elaborate “by hand”.This point is particularly original compared with previ-ous works cited in Section 1.

Notation

C concentrationj(:) criterionM (:) structure of model MN Number of experimental points

5738 C. Laquerbe et al. / Chemical Engineering Science 56 (2001) 5727–5738

p set of parametersp optimal set of parametersQ (ow ratet timeu stimulusV volumey experimental responseym simulated response

Greek letters

� penalty factor� standard deviation of the noise

Indices

in inputout output

Abbreviations

AE algebraic equationCFD computational (uid dynamicsCSTR continuous stirred tank reactorGA genetic algorithmODE ordinary diFerential equationPFR plug (ow reactorRTD residence time distributionSA simulated annealing

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