Volume 11, numéro 2, 1998

FR :

Ces 10 dernières années, certains épisodes pluvieux marquants ont entraîné une prise de conscience du risque encouru par les agglomérations modernes face à des phénomènes hydrologiques particuliers. La gestion du risque pluvial passe par une amélioration de la connaissance de l'aléa pluvieux. Dans cet article, on développe une approche stochastique exploitant le potentiel d'informations contenu dans un échantillon d'épisodes pluvieux extrêmes ayant ou ayant pu engendrer des crues dévastatrices. Une approche spatiale est utilisée pour caractériser l'aléa pluvieux. A partir d'un jeu d'épisodes extrêmes sélectionnés sur une région méditerranéenne entre 1958 et 1993, on estime l'aire des surfaces où les précipitations dépassent un seuil de pluviométrie fixé. L'estimation des aires des surfaces pluvieuses nécessite le recours à un modèle d'interpolation spatiale des hauteurs de pluie. La justification du krigeage climatologique est présentée ainsi que l'estimation des paramètres du modèle retenu. Les distributions des aires des isohyètes, à différents seuils de pluviométrie, sont ensuite analysées. Il apparaît que quelle que soit l'isohyète considérée, une loi gamma peut être ajustée sur l'échantillon de surface. Une relation entre les paramètres des lois permet une généralisation du modèle probabiliste à n'importe quel seuil de pluie compris entre 50 et 300 mm.

EN :

In the last 10 years many cities in southern Europe have been affected by heavy rainfall events leading to severe runoffs. The assessment of rainfall risk requires a better knowledge of the climate hazards and particularly rainfall hazards. The most usual rainfall risk assessment is based on a stochastic approach and point rainfall frequency analysis remains the most-used method. However, in the Mediterranean region great variations of rainfall depth frequencies can be observed according to the point considered, and according to the period of observation. Moreover the recent hydrological catastrophes which have affected the south of France have been studied on an individual basis and studies based on a global approach, using the whole information contained in a sample of several observations, remain unusual.

A rainfall risk assessment has been proposed in the Languedoc-Roussillon, a 28,000 km² region along the Mediterranean sea. This study has been based on a sample of 93 daily extreme rainfall events, which have occurred in the region. They have been extracted from the Météo-France database for the 1958-1993 period of observation, if a rainfall depth greater or equal to 190 mm in 24 hours or 48 hours (because of the sampling constraints) has been observed at one rain gauge in the region at least. The spatial extension of the rainy surfaces defined at different rainfall thresholds, varying from 50 to 250 mm/24 hours and 50 to 300 mm/48 hours, have been investigated. For a given threshold, the area of the rainy surface corresponding to a given frequency has been estimated.

The estimation of the rainy surfaces area has required the choice of a spatial interpolation method: the climatological kriging method has been used. This method is based on the assumption that all the rainfall events came from the same meteorological situation, but some studies have shown that there may be different meteorological situations (TOURASSE, 1981; RIVERAIN, 1997). Thus the sensitivity of the interpolation model according to this assumption has been tested. A different interpolation model has been estimated for each season because the information about the meteorological situations which have generated the selected events is not available. Only the variogram over June to August differs significantly from the "annual" variogram. The differences between the rainy surfaces area estimated with the "seasonal" variogram and the "annual" one did not exceed 10% in proportion of the areas estimated with the "annual" variogram. The rainy surface areas are less sensitive to the climatological assumption.

For each time step and each rainfall threshold considered, it has been observed that the two parameter Gamma law could best fit the frequencies of the rainy surface areas. The relation between each of the Gamma law parameters and the rain threshold has been estimated (relations R1 and R2). The quantiles of the rainy surface areas have been estimated with two methods :

- directly from the fitting of a Gamma function to the sample of rainy surface areas;

- using the previous relation to estimate the Gamma function parameters.

It has been observed that the quantiles estimated with the second method were close to those estimated with the first method, even if the fitting errors of the R1 and R2 relations were considered. Such a result allows one to estimate the regional frequency of a rainy surface areas defined at each threshold between 50 and 300 mm/48 hours or 50 and 250 mm/24 hours. However extrapolations beyond the studied threshold intervals should not be done because the R1 and R2 relations are empirical.

The isohyets area quantiles have been defined: they represent the isohyet area corresponding to a given rainfall threshold and a given return period. The isohyet area quantiles may be very large; for example at the 200 mm / 48 hours threshold the isohyets area represents 15% of the region (4500 km²). This can be explained by the time step dt. The isohyets area represents the dynamics of the convective cells integrated over dt, which remains unknown but is greater than 48 hours. Moreover for a given rainfall threshold and a given event, several separate isohyets could be observed. However in this study only the all areas corresponding to the different isohyets have been estimated. Thus it could give a very large area when the event affects the all region.

The ratio between the isohyet area quantiles at the 48-hour and 24-hour time steps evolved from 1.3 to 20: it increased with the rainfall threshold for a given return period. This can be explained by the strong dynamics of the convective cells which generate the highest rainfall depths, compared to the rain cells at a larger spatial scale, which generate lower rainfall depths. Thus the isohyet areas defined at a high rainfall threshold are sensitive to the time steps than isohyet areas defined at a smaller rainfall threshold.

The frequencies estimated in this study have been regional frequencies, but it appears that the isohyet areas are not independent of the event's location. However, at this stage the sample is too small to allow a study of conditional frequencies. In order to perform this study the sample has already been enlarged by considering all the French Mediterranean region which have been affected by heavy rainfall depths. It has been based on all the information included in the Météo-France data base over this region (since 1870). The rainfall threshold used to select the rainfall events has been diminished to 90 mm/ 24 hours to include the high intensity events over short time steps which could generated severe floods, especially over small catchments.

Combined with the information about the meteorological situations, the development of this work should allow improved studies of the relations between the rainy surfaces and the meteorological situations at the origin of the rainfall events.

FR :

Les paramètres chimiques jouent un rôle important dans l'équilibre des écosystèmes aquatiques. De nombreuses études ont déjà démontré que les caractéristiques chimiques d'un cours d'eau peuvent changer avec les saisons. Cette étude a pour but de revoir les relations débit- concentration sur un petit cours d'eau, dans le contexte des variations entre deux périodes climatiques. Pour ce faire, une analyse de régression entre le débit et six paramètres de qualité de d'eau (sodium, magnésium, conductivité, pH, azote total et le carbone organique dissous) provenant d'un petit bassin versant forestier (ruisseau Catamaran, N.-B., Canada) a été réalisée afin de déterminer la différence entre la saison sans glace et la saison avec glace. Des échantillons mensuels d'eau ont été récoltés sur le ruisseau Catamaran depuis 1990. Les analyses chimiques faites sur ses échantillons ont permis de déterminer les concentrations des paramètre étudiés. La plupart des variables de qualité ont démontré une relation significative avec le débit, sauf l'azote total. Les coefficients de détermination variaient entre 0.752 et 0.898, exception faite du carbone organique dissous dont le r2 était de 0.294. La conductivité était le paramètre dont le débit expliquait le plus la variance. Une étude des rapports des sommes des carrés des résidus a permis de déterminer que seul le pH requiert un modèle différent pour la période sans glace et la saison avec glace.

Les variations saisonnières de la relation débit-pH revêt une importance significative pour les ruisseaux comme celui de Catamaran, qui incluent de nombreux habitats pour le saumon de l'Atlantique. Les résultats des analyses de régressions indiquent que lorsque la géochimie est plus complexe, comme c'est le cas pour le pH, il faut diviser les séries temporelles en sous-composantes saisonnières avant de tenter d'établir une relation débit-concentration.

EN :

The chemical composition of water is of great importance to ecosystem functioning and in habitat management. Many studies have already shown that the chemical characteristics of a stream change with seasons. These variations have a strong impact on the ecosystem, especially on fish populations. The objective of this study is to quantify the relationship between the logarithm of discharge and six water quality parameters (sodium, magnesium, conductivity, pH, dissolved organic carbon and total nitrogen) for a small forested catchment (Catamaran Brook, N.B., Canada) and to verify the importance of seasonality.

Monthly water samples have been gathered at Catamaran Brook since 1990. Detailed water chemistry performed on these samples provided a data base for this project. Various linear regression models were tested to verify if regressions were required for the winter season. The criterion used was the ratio of the squared sum of residuals for each data set, which follows a Fisher distribution. Of the six water quality parameters, all except total nitrogen showed a significant relationship with discharge. On an annual basis, the coefficient of determination (r²) varied between 0.752 and 0.898, except for dissolved organic carbon which showed a r² of 0.294. Of the studied parameters, conductivity was the parameter for which discharge explained the most variance. Ratios of the squared sum of residuals were analyzed to verify the need for different regression models for the ice-covered and ice-free seasons. Only streamwater pH required 2 different models. This is of specific importance and interest because of an important salmon population in Catamaran Brook. Other researchers have shown that salmonids can be negatively impacted by pH depressions during snowmelt events.

These results show that most dissolved ions which follow simple geochemical reactions can be modelled year-round with only one linear regression. When the geochemistry is more complex, such as in the case of pH, linear regression models can sometimes be used, provided that the annual time-series is divided into seasons with relatively homogenous hydrological and geochemical functions.

FR :

Les outils mathématiques sont de plus en plus utilisés pour simuler la contamination d'origine agricole des eaux souterraines. Le modèle AgriFlux permet, à l'aide du module PestiFlux, de simuler les processus responsables du devenir des pesticides dans le sol: ruissellement, volatilisation, adsorption/désorption rapide, adsorption/désorption lente, complexation par la matière organique dissoute, biodégradation en sous-produits, hydrolyse, drainage et lessivage. AgriFlux est utilisé pour simuler le devenir de l'atrazine et du dééthylatrazine sur une parcelle expérimentale de la région de Québec (Québec, Canada) cultivée en maïs sucré (Zea mays, L.) traité à l'atrazine. Des prélèvements d'eau interstitielle ont été réalisés (1986-1990) à l'aide de lysimètres avec succion (0,5 et 1,0 m de profondeur) et analysés pour leur contenu en atrazine et dééthylatrazine. De manière générale, AgriFlux reproduit bien l'évolution des concentrations mesurées, dans le temps et dans le profil de sol (r=0,76). Certains pics de concentrations observés sur le terrain ne sont toutefois pas représentés ou sont décalés dans le temps, ce qui pourrait être attribué à une sous-estimation de la variabilité spatiale des paramètres. Le rapport dééthylatrazine/atrazine est relativement bien simulé en 1988 à 0,5 m, mais est moins représentatif pour les autres données, ce qui pourrait être dû à une certaine imprécision dans la simulation de la biodégradation. Une analyse de sensibilité du modèle aux variations de différents paramètres a montré que le paramètre le plus influent dans les conditions testées est la constante de biodégradation. Les résultats obtenus montrent la pertinence d'AgriFlux (PestiFlux) dans la simulation du devenir des pesticides dans le sol et donc des risques de contamination des eaux souterraines en région agricole.

EN :

Groundwater and surface water contamination by agricultural practices has become an increasingly preoccupying problem. Mathematical models are valuable tools to help prevent this type of pollution from non-point sources. AgriFlux is a mechanistic, stochastic model simulating the fate of agricultural contaminants in the unsaturated zone at the scale of the agricultural field. AgriFlux, through the PestiFlux module, now simulates pesticide transformations in the soil from their application to the field until their leaching with percolating water. The processes represented include volatilization, complexation by the soluble organic matter, instantaneous adsorption and desorption, slow adsorption and desorption to less available sites, biodegradation to by-products and hydrolysis to non-toxic compounds. The pesticide freely dissolved in solution or complexed with soluble organic matter can be mobilized with runoff, drainage and leaching water

An application of PestiFlux to an experimental field near Quebec City (Quebec, Canada) is presented. The soil is a well-drained loamy sand cropped from 1986 to 1990 with sweet corn (Zea Mays, L.) receiving atrazine treatments (1.6 to 1.8 kg.ha-¹ of active ingredient). Interstitial water was sampled using 12 suction lysimeters located at both the 0.5 and 1.0 m depths in the soil. All stations were sampled monthly in 1986 and 1987 and the collected water was analyzed for atrazine alone. In 1988, the sampling (every two weeks) was limited to the lysimeters which had previously shown the highest pesticide concentrations (two lysimeters at 0.5 m and one lysimeter at 1.0 m). The interstitial water was analyzed for atrazine and deethylatrazine. There was no sampling in 1989. In 1990, all stations were sampled on a weekly basis and a composite water sample obtained for each depth was analyzed for both compounds. Most of the pesticide-related parameters required to run PestiFlux were deduced from the literature, with the exception of the biodegradation rate coefficient which was estimated from field monitoring of atrazine. The parameters required to simulate water fluxes and plant uptake were the same as those used in a previous application of AgriFlux to the same experimental field for the simulation of nitrate fluxes (LAROCQUE and BANTON, 1995).

Results show that PestiFlux generally represents well the measured atrazine and deethylatrazine concentrations in the interstitial water at 0.5 and 1.0 m. A linear regression using all measured and simulated concentrations indiscriminately gives a correlation coefficient of 0.76 when using the logarithm of concentrations. The temporal evolution of the pesticide concentrations is relatively well simulated, especially on the long term with an adequate representation of the increase in pesticide concentrations in the soil profile at 1.0 m. This increase is probably due to the fallow existing in 1985 which would have favored leaching of adsorbed pesticide below the soil profile, leaving only low residual pesticide concentrations. Over one growing season, the transport of atrazine and deethylatrazine is well represented by the model, although some peak concentrations are delayed or attenuated. This result could be due to an underestimation of the spatial variability of the different parameters. It is possible that the coefficient of variation of 10% adopted may not represent adequately the spatial variation of some parameters. Nevertheless, most measured concentrations of both compounds are within the mean simulated concentrations and included between two standard deviations. For 1988, most of the measured concentrations are located near the upper limit of the envelope curve which is consistent with the fact that the sampled lysimeters were those yielding the highest concentrations. The simulated concentrations show a generally good representation of the relative atrazine and deethylatrazine concentrations. The ratio of the mean deethylatrazine to atrazine concentrations provides a closer look at the adequacy between the simulated concentrations of both compounds. A comparison between the measured and the simulated ratios shows a good adequacy at 0.5 m in 1988 and both over- and under-estimation of the ratio for the other available data. This is probably due to an imprecision in the simulation of biodegradation rates during some periods. All the parameters used in the simulation have an important uncertainty, due to the significant spatial variation of the parameters in the field and to the imprecise knowledge of some pesticide characteristics. In order to identify the parameters which have the most important influence on the results, an analysis of the sensitivity of the cumulated leaching mass of both compounds at 1.0 m to variations of the different input parameters was performed. The results show that the biodegradation rate has the greatest influence on the results. This is probably due to the importance of this process in the simulated situation. This result confirms the importance of an adequate quantification of this parameter and of its spatial variation.

PestiFlux offers a comprehensive representation of pesticide transformations in the soil and is easy to use. As a module of AgriFlux, it has the advantage of being integrated into a well-tested and reliable modeling environment. The presented simulation results show that, apart from some limits due to the quantification of some of the parameters, PestiFlux is a useful and comprehensive tool for estimating potential groundwater pollution by pesticides.

FR :

Les affluents et sous affluents congolais du fleuve Congo se partagent en deux systèmes hydrologiques, qui, tout en étant proches dans l'espace, sont sensiblement différents dans leur fonctionnement. Cette distinction repose sur la différenciation manifeste entre les deux régions naturelles que sont les "Plateaux Tékés" d'une part et la "Cuvette congolaise" d'autre part, nettement contrastées du point de vue du couvert végétal et lithologique et subsidiairement du climat

La classification hydrologique que nous présentons est basée sur l'étude des coefficients d'écoulement interannuel (rapport de la lame d'eau écoulée sur la lame d'eau précipitée, exprimé en pourcentage) et sur le coefficient d'irrégularité saisonnière moyen des débits qui est le rapport moyen sur les chroniques disponibles, entre débits mensuels maximum et débits mensuels minimum par année hydrologique. Pour les rivières Tékés, le premier paramètre présente des valeurs comprises entre 45% et 60% contre 20% à 30% pour la "Cuvette Congolaise", alors que le deuxième paramètre varie respectivement pour ces deux régions de 1,1 à 1,5 et de 2,5 à 5,5.

Cette classification présente l'avantage d'être à la fois adaptée à ces deux contextes régionaux voisins mais aussi de mettre en évidence le rôle prépondérant des formations géologiques et des couvertures végétales sur les écoulements des cours d'eau concernés, ainsi que sur la qualité des eaux.

En effet, après son passage au travers d'un important aquifère gréseux, les eaux des Plateaux Tékés à couverture de savane font partie des "eaux claires", à très faible minéralisation, marquée essentiellement par la présence de silice dissoute. En revanche, les " eaux noires " couleur de thé qui drainent la Cuvette Congolaise, couverte de forêts, sont très riches en matière organique et très acides

EN :

The Congolese tributaries and sub-tributaries of the Congo river come from two adjacent regions that have similar annual rainfall volumes (1,700 and 1,900 mm.year-¹) but very different physiographic characteristics. These latter characteristics are the main reasons accounting for the differences in their hydrological behavior. The purpose of this work is to introduce a regional hydrological classification - adapted to the particularities of the regions that are crossed by these tributaries - that points out the major influence of the geological formations and the vegetative cover on the runoff of the rivers, as well as on their water qualities.

The two natural regions concerned are the Téké plateaus and the Congolese basin. The first region, centered on Congo but also spread into Gabon in its western part and into Congo on its eastern side, consists of sand-gritty formations of the Tertiary going from 200 to 400 m in thickness, covered with savanna. The second region builds up a continuation of the wide Congo depression that occupies the whole center of the Congo river basin. It comprises Quaternary alluvial deposits, covered with swamps and dense equatorial rain forests.

The hydrological characterization we present here is based on two hydrological coefficients that do not have physical linkages but illustrate the differences in the regimes of their respective flows. These are the interannual runoff coefficient (KE) and the average seasonal variability of the discharges (CIS) observed over a period of forty years. Concerning the Téké rivers, the first parameter (KE) has values ranging between 45 % and 60 % versus 20 % o 30 % for the Congolese basin. The second parameter (CIS) has values ranging from 1.1 to 1.5 for the Téké rivers, versus 2.5 to 5.5 for the Congolese basin. The specific discharges of the first region vary from 25 to 35 l.s-¹.km-² versus 10 and 15 l.s-¹.km-² for the second region.

Concerning the Téké plateaus, the weak average seasonal variations of the discharges can only be explained by a great capacity for storage, and consequently for flow regulation, of the sand-gritty aquifer. Infiltration of the rainfall waters is important and they are mostly replaced by this important aquifer which attenuates the floods and helps minimize the droughts. This is also the reason why it is in this region that some of the most regular rivers of the planet are encountered.

Concerning the Congolese basin, the lower permeability of the soils, the interception of rain waters, the evapotranspiration of the forest cover, and the direct evaporation on the floodable areas as well as the swamps, lead to an important water deficit. As there is no aquifer, at least none as important and regulating as in the Téké plateaus, the hydrological regime is more similar to the regional rainfall rhythm. The Téké hydrological regimes are for their part practically independent of the regional rainfall regime.

From a qualitative point of view, these waters are also very distinct. Indeed, after crossing the important gritty aquifer, the waters of the Téké plateau - which is covered with savanna - consist of highly diluted clear waters, relatively rich in dissolved silica. These waters, with dissolved inorganic matter ranging from 1 to 3 mg.l-¹ (not taking into account the dissolved silica), are similar in composition to rainfall waters. These are among the most dilute surface waters of the world, the soluble ions of the mentioned formations having been almost totally leached.

On the other hand, waters draining the Congolese basin originate from a long residence time under the forest cover. They are very rich in organic matter (up to 44 % of particulate organic carbon) and very acid (pH can be lower than 4). They are truly qualified as "black rivers". Their mineralization, although low (11 to 30 mg.l-¹, without dissolved silica), can be considered high when compared to the plateaus' waters, and also of a greater diversity. For both regions, the content in dissolved silica is identical to the world wide average, varying between 8 and 10 mg.l-¹.

If the specific export rates in dissolved matter are low, they are nevertheless identical in the two geographical domains despite the important differences in concentrations. For matter of mineral and organic origins, we calculate respectively 10 t.km-².year-¹ in the basin versus 9.7 t.km-2.year-1 on the plateaus, and 19.3 t.km-².year-¹ in the forest versus 13.5 t.km-².year-¹ in the savanna. This apparent similitude is obviously linked to the compensation by the specific discharges of the Plateau rivers, more than twice as much as in the basin.

FR :

Ce travail propose un nouveau procédé d'élimination du Cu2+ par adsorption sur des résines échangeuses d'ions poreuses, mises en œuvre dans un réacteur à membrane à lit mobile de particules. Ce procédé a été étudié sur le plan cinétique pour des solutions synthétiques de Cu(II) dans de l'eau. L'application visée à moyen terme est l'intégration de cette opération unitaire dans une filière de traitement complète des effluents industriels liquides.

L'étude cinétique a été réalisée avec une résine cationique forte Mono C-350H en réacteur agité fermé et thermostaté. Les isothermes d'adsorption ont été établies à 21°C et les paramètres de Langmuir et de Freundlich ont été calculés. Une étude de l'influence de la vitesse d'agitation et de la température sur la vitesse réactionnelle apparente a permis de déterminer la zone opératoire correspondant à un régime cinétique. Ce régime est obtenu pour un Reynolds d'agitation supérieur à 4700 et une température inférieure à 60°C. Dans ces conditions, l'ordre de la réaction par rapport au Cu²⁺ est de un et la constante cinétique exprimée par unité de masse de particules est k_wapp=0,03721 lg_rés^-1min^-1 à 21°C. L'énergie d'activation de la réaction a également été déterminée.

Par ailleurs, en s'appuyant sur les résultats de l'étude cinétique, les premiers éléments de comparaison d'un réacteur classique à lit fixe et d'un réacteur original à membranes à lit de particules sont présentés. Pour le même débit à traiter, en fixant dans les deux cas un taux de conversion objectif de 95 %, le nouveau procédé permettant d'utiliser des particules de plus faible diamètre conduit à une réduction du volume de particules réactives d'un facteur 4, de la puissance énergétique à fournir au système d'un facteur 3 à 5. Les performances prometteuses de ce procédé restent à valider lors d'une étude pilote.

EN :

Legislation in France and in Europe is becoming more rigorous for industrial fluid wastes, which is encouraging many industries to find a proper solution to their effluent problems and to include a complete wastewater treatment plant in their process. This paper focuses on effluents containing metallic compounds, which can be toxic. For Cu(II) the maximal allowed concentration is 1 mg/l. Many unit operations can be used to remove metal compounds from industrial waste waters, but the most widely used are scaling followed by settling and/or filtration, adsorption, solvent extraction and incineration. The main drawbacks encountered with these processes are:

1. a low yield,

2. high operating and investment costs,

3. sludge production.

This paper deals with a new unit operation to be included in a complete treatment line in place of adsorption, for removing metallic compounds. This new operation consists of a membrane moving bed reactor, which uses very fine dispersed adsorbent particles, so as to increase the particles' specific area. The particles are circulated with the water and separated from the treated water by an ultrafiltration hollow fibre or tubular membrane. The potential advantages of the process are the following: use of high specific area particles, production of a permeate without particles or suspended matter, no bed fouling (in comparison with fixed bed adsorption), continuous separation of metallic compounds and particles by the membrane. Moreover, we have chosen porous ion exchange resins as adsorbent particles, thus allowing a further continuous regeneration and recycling of the particles.

The aim of this first paper on this new reactor is to introduce a comparison between the performances of a conventional fixed bed reactor and those of the moving bed membrane reactor, for the removal of Cu(II) from pure water. The first step for this study consists of a characterization of the particles/metallic compounds interactions in terms of kinetic rates and adsorption isotherms. Ion exchange is here considered with a chemical engineering approach, as a heterogeneous liquid/solid reaction.

Experiments have been carried out in a thermostatted 1 litre stirred batch reactor. The solutions are prepared with CuSO₄ . 5H₂0 in demineralised water. Cu(II) concentrations are measured by spectro-colorimetry using the regulation T90022 from AFNOR. Particles are cationic ion exchange resins referenced as Mono C-350H. Their mean diameter (315 mm) is higher than the membrane pore diameter (0.01 mm). No membrane internal fouling will then occur during particle filtration. Moreover the particle diameter is lower than the inner diameter of the fibres to prevent plugging of the hollow fibre.

The adsorption isotherms have been determined at 21°C and the relevant Langmuir and Freundlich parameters are given in Table 2. The influence of stirring velocity and temperature in the reactor on the reaction rate has been studied. For stirring velocities above 100 rpm, the apparent reaction rate is independent of the stirring velocity. That means that the kinetic regime is obtained for stirring Reynolds numbers higher than 4700. The plot of Lnkwapp against T-¹, at a constant and high enough stirring velocity to prevent external diffusion limitations, shows two linear areas :

- under 60°C, the kinetic regime is obtained, thus allowing the determination of the reaction activation energy (given in Table 3);

- above 60°C, the internal diffusion is limiting.

In the kinetic controlled area, the reaction was found to be first-order and the rate constant expressed by mass of particles is k_wapp=0.03721 lg_rés^-1 min^-1 at 21 °C.

Using the kinetic data, it is possible to design and to compare the characteristics of a fixed bed reactor and a moving bed reactor, which would have the same conversion rate (95 %), for the same effluent flow rate to treat (5 m³/h). As a first approximation, we consider operating conditions inducing a kinetic regime. We also consider that the reaction mostly takes place at the particle surface. This assumption allows one to obtain the reaction rate expressed by particle's area for any particle size. At 21 °C, the previously defined reaction rate is k_s=4.43x10^-5 m³/s.m². The expression of the conversion rate as a function of ks, the reaction volume and the particle diameter is obtained for each reactor from the mass balance written in terms of Cu(II). The pressure drop expression is also given for the reactors. In the case of the moving bed reactor the increase of dynamic viscosity induced by the presence of particles has been taken into account. For each reactor, a solid retention, particle diameter and fluid velocity corresponding to values widely used industrially have been chosen (see Table 4). For the membrane reactor, we consider hollow fibres with 0.93 mm inner diameter, 1.2 m length and a total filtration area of 50 m² per module. Calculations have been done for two limit values of the permeation flux: 50 and 100 l/h.m².

A comparison of the two reactors is given in Table 5, which demonstrates the interest of the moving-bed reactor, as it allows one to reduce the volume of adsorbent particles by a factor 4. This result is linked to the high specific surface of the fine dispersed particles. The membrane reactor also induces a high reduction of the pressure drop (by a factor 40) and of the energy consumption (from 4.7 for a one- module plant to 2.6 for a two-module plant).

These promising results are encouraging to continue the research on this process with the aim to optimize it. Further studies will include:

- comparison of different adsorbent particles and choice of the best available;

- validation of this preliminary simulation by experiments on a pilot plant, with synthetic and then industrial waters;

- integration of this unit operation in a complete treatment plant.

FR :

Les outils informatiques développés dans le cadre de la conception des réseaux d'assainissement permettent de concevoir plusieurs solutions de réseaux pour un même problème. Il revient ensuite au décideur de choisir quelle solution retenir. Le problème qui se pose alors est la comparaison des propositions selon des critères économiques, écologiques, de fonctionnement, de maintenance, .... La difficulté vient du fait que certains de ces critères sont difficiles à évaluer. Nous présentons dans cet article une méthode permettant d'évaluer l'un de ces critères : le fonctionnement global d'un réseau d'assainissement suite à l'extension de ce dernier. Cette méthode est basée sur des simulations hydrauliques. Or ces simulations donnent des informations en chaque noeud du réseau (histogrammes de vitesses, débits ou hauteurs de charge) et non une indication sur la qualité de fonctionnement du réseau dans son ensemble. Il nous a donc fallu élaborer une technique d'agrégation permettant de passer de l'élément isolé (le tronçon) à l'ensemble organisé (le réseau). Cette technique d'agrégation utilise les notions de "période d'insuffisance" d'un tronçon qui est la période de retour d'une pluie pour laquelle ce tronçon dépasse un certain seuil de dysfonctionnement (dans notre cas, le débordement) et de sensibilité du tissu urbain à un dysfonctionnement hydraulique du réseau. Cette dernière notion est nécessaire car certains tronçons peuvent très bien déborder sans induire de désordres apparents s'ils ont, par exemple, une capacité d'écoulement faible et/ou s'ils se trouvent dans une zone non bâtie. Les informations nécessaires à l'utilisation de cette méthode étant souvent de qualité inégale en termes de précision, nous avons pris le parti de raisonner non sur des valeurs déterminées ais sur des classes d'appartenance modélisées sous forme de sous-ensembles flous.

EN :

Software packages developed for the design of urban storm drainage networks allow several solutions to be proposed for the same problem. It then falls to the designer to choose which solution to use, the main problem being the evaluation of the efficiency (quality) of each solution. A multi-criteria approach represents one theoretical solution to the problem. This necessitates the determination of which criteria to use and how to evaluate them. In this paper, we present a method of evaluation of the criteria related directly to the functioning of an urban storm drainage network after its extension. This method is developed on the basis of hydraulic simulations of the network. These simulations produce results (histograms of discharge, water levels, rates of filling, hydraulic head, ...) for each pipe. Given these results, the designer must be able to assess whether the proposed solution is satisfactory, and then compare it with other solutions. The problem is therefore to be able to evaluate a complete network, whereas the results of conventional simulations present a fragmented and partial view of its functioning (pipe by pipe). A solution to this problem is proposed in the form of a tool, able to calculate a single combined value from the simulation results. The following calculation steps are proposed:

1. First we model the effectiveness of each pipe. To do that, we determine the "return period of failure" of a pipe which is the return period of a rainfall for which the pipe passes a certain level of failure (in this paper, we take the level of failure as the state of overflow). The rainfall model used is the same one used for the design of the network. Then we attribute a numerical value (S) for the operation of a pipe according to its return period of failure by way of a satisfaction function.

2. Secondly we model the weighting given to each pipe. This weighting is constructed from the discharge capacity of the pipe and the sensitivity of the urban fabric (in proximity to the pipe) to system failure. The discharge capacity is calculated using Manning's formula on the basis of diameter, slope and internal roughness. The value of the coefficient (R), which indicates the sensitivity, necessitates a good knowledge of the urban fabric. Among the important variables related to this factor, we can identify the population density, the traffic density and the density of land use -DLU- (this variable is identified by the density of residential land use, the density of commercial land use, ...). We can then write R=f(density of population, density of traffic, DLU,...). Considering the difficulty of the identification of (f), we preferred to explore an expert approach. The rules have been identified from a bibliographical analysis and limited expertise. An example of theses rules is presented here : IF density of population is high and density of commercial land use is average THEN the degree of sensibility is average. The examination of the identified rules shows the use of words like low, average and high. To model this linguistic qualifying information, we have chosen fuzzy sets. Also the inferences of fuzzy information are treated by using operations of fuzzy logic.

3. Finally, we aggregate the results with the following equation:

    n

C=∑Q_aixR_ix∆S_i

  i=1

where DS_i=S_i - S_i' represents a measure of the effect of network modification upon the operation of the pipe i (S_i and S_i' are the effectiveness of the pipe respectively before and after the proposed modification), Q_ai is the discharge capacity of the pipe i, R_i is the coefficient of sensitivity of the area to failure associated with pipe i and C is a factor which quantifies the effect on the general operation of the network.

With the coefficient C, the designer is now able to classify the different solutions of extension of an existing urban drainage network according to their impacts on its functioning and to introduce this classification order in a multi-criteria method.

FR :

La notion d'appartenance partielle d'une station hydrométrique à une région hydrologique est modélisée par une fonction d'appartenance obtenue en appliquant les concepts de l'analyse floue. Les stations hydrométriques sont représentées dans des plans dont les axes sont des attributs hydrologiques et/ou physiographiques. Les régions hydrologiques sont considérées comme des sous-ensembles flous. Une méthode d'agrégation par cohérence (Iphigénie) permet d'établir des classes d'équivalence pour la relation floue "il n'y a pas d'incohérence entre les éléments d'une même classe": ce sont des classes d'équivalence qui représentent les régions floues. La fonction d'appartenance dans ce cas est stricte. Par opposition, la seconde méthode de type centres mobiles flous (ISODATA) permet d'attribuer un degré d'appartenance d'une station à une région floue dans l'intervalle [0,1]. Celle-ci reflète le degré d'appartenance de la station à un groupe donné (le nombre de groupes étant préalablement choisi de façon heuristique). Pour le cas traité (réseau hydrométrique tunisien, débits maximums annuels de crue), il s'avère cependant que le caractère flou des stations n'est pas très prononcé. Sur la base des agrégats obtenus par la méthode Iphigénie et des régions floues obtenues par ISODATA, est effectuée une estimation régionale des débits maximums de crue de période de retour 100 ans. Celle-ci est ensuite comparée à l'estimation régionale obtenue par la méthode de la région d'influence ainsi qu'à l'estimation utilisant les seules données du site, sous l'hypothèse que les populations parentes sont des lois Gamma à deux paramètres et Pareto à trois paramètres.

EN :

The concept of partial membership of a hydrometric station in a hydrologic region is modeled using fuzzy sets theory. Hydrometric stations are represented in spaces of hydrologic (coefficient of variation: CV, coefficient of skewness: CS, and their counterparts based on L- moments: L-CV and L-CS) and/or physiographic attributes (surface of watershed: S, specific flow: Q_s=Qmoyen/S, and a shape index: I_c). Two fuzzy clustering methods are considered.

First a clustering method by coherence (Iphigénie) is considered. It is based on the principle of transitivity: if two pairs of stations (A,B) and (B,C) are known to be "close" to one another, then it is incoherent to state that A is "far" from C. Using a Euclidean distance, all pairs of stations are sorted from the closest pairs to the farthest. Then, the pairs of stations starting and ending this list are removed and classified respectively as "close" and "far". The process is then continued until an incoherence is detected. Clusters of stations are then determined from the graph of "close" stations. A disadvantage of Iphigénie is that crisp (non fuzzy) membership functions are obtained.

A second method of clustering is considered (ISODATA), which consists of minimizing fuzziness of clusters as measured by an objective function, and which can assign any degree of membership between 0 to 1 to a station to reflect its partial membership in a hydrologic region. It is a generalization of the classical method of mobile centers, in which crisp clusters minimizing entropy are obtained. When using Iphigénie, the number of clusters is determined automatically by the method, but for ISODATA it must be determined beforehand.

An application of both methods of clustering to the Tunisian hydrometric network (which consists of 39 stations, see Figure 1) is considered, with the objective of obtaining regional estimates of the flood frequency curves. Four planes are considered: P1: (Q_s,CV), P2: (CS,CV), P3: (L-CS,L-CV), and P4: (S,I_c), based on a correlation study of the available variables (Table 1).

Figures 2, 3a, 4 and 5 show the clusters obtained using Iphigénie for planes P1 through P4. Estimates of skewness (CS) being quite biased and variable for small sample sizes, it was decided to determine the influence of sample size in the clusters obtained for P2. Figure 3b shows the clusters obtained when the network is restricted to the 20 stations of the network for which at least 20 observations of maximum annual flood are available. Fewer clusters are obtained than in Figure 3, but it can be observed that the structure is the same: additional clusters appearing in Figure 3 may be obtained by breaking up certain large clusters of Figure 3b. In Figure 3c, the sample size of each of the 39 stations of the network is plotted in the plane (CS,CV), to see if extreme estimated values of CS and CV were caused by small samples. This does not seem to be the case, since many of the most extreme points correspond to long series.

ISODATA was also applied to the network. Based on entropy criteria (Table 2, Figures 6a and 6b), the number of clusters for ISODATA was set to 4. It turns out that the groups obtained using ISODATA are not very fuzzy. The fuzzy groups determined by ISODATA are generally conditioned by only one variable, as shown by Figures 7a-7d, which respectively show the fuzzy clusters obtained for planes P1-P4. Only lines of iso-membership of level 0.9 were plotted to facilitate the analysis. For hydrologic spaces (P2 and P3), it is skewness (CS and L-CS) and for physiographic spaces (P1 and P4) it is surface (Q_s and S).

Regionalization of the 100-year return period flood is performed based on the homogeneous groups obtained (using an index-flood method), and compared to the well-known region of influence (ROI) approach, both under the hypothesis of a 2-parameter Gamma distribution and a 3-parameter Pareto distribution. For the ROI approach, the threshold corresponding to the size of the ROI of a station is taken to be the distance at which an incoherence first appeared when applying Iphigénie. Correlation of the regional estimate with a local estimation for space P1 is 0.91 for Iphigénie and 0.85 both for ISODATA and the ROI approach. Relative bias of regional estimates of the 100-year flood based on P1 is plotted on Figures 9 (Gamma distribution) and Figure 10 (Pareto distribution). The three methods considered give similar results for a Gamma distribution, but Iphigénie estimates are less biased when a Pareto distribution is used. Thus Iphigénie appears superior, in this case, to ISODATA and ROI. Values of bias and standard error for all four planes are given for Iphigénie in Table 3.

Application of an index-flood regionalization approach at ungauged sites requires the estimation of mean flow (also called the flood index) from physiographic attributes. A regression study shows that the best explanatory variables are watershed surface S, the shape index I_c and the average slope of the river. In Figure 8, the observed flood index is plotted against the flood index obtained by regression. The correlation coefficient is 0.93.

Iphigénie and ISODATA could also be used in conjunction with other regionalization methods. For example, when using the ROI approach, it is necessary to, quite arbitrarily, determine the ROI threshold. It has been shown that this is a byproduct of the use of Iphigénie. ISODATA is most useful for pattern identification when the data is very fuzzy, unlike the example considered in this paper. But even in the case of the Tunisian network, its application gives indications as to which variables (skewness and surface) are most useful for clustering.

FR :

Le processus de nitrification joue un rôle essentiel dans le cycle de l'azote dans les milieux aquatiques naturels. La mesure de l'activité nitrifiante est une étape obligée pour bien comprendre et quantifier les flux d'azote dans ces milieux. Ce travail présente une réévaluation de la méthode de mesure de l'activité nitrifiante autotrophe par la méthode d'incorporation de bicarbonate marqué au 14C et son application pour estimer des biomasses de bactéries nitrifiantes. La validité générale de la méthode a été démontrée par des tests menés sur des inhibiteurs de nitrification qui ont montré que l'utilisation combinée de N-serve (5 ppm) et de chlorate (10 mM) inhibait de manière complète et spécifique l'oxydation d'azote et l'incorporation de carbone des deux groupes de bactéries nitrifiantes. Un facteur de rendement (carbone incorporé par azote oxydé) de 0,1 mole C/mole N a également été déterminé sur des cultures pures de bactéries nitrosantes et nitratantes. Pour l'activité potentielle, en particulier, les conditions optimales pour la mesure d'activité nitrifiante ont également été établis: un pH entre 7 et 8, une température entre 20 et 30°C, une concentration en ammonium d'au moins 1 mmol/l et en oxygène d'au moins 6 mg/l. Une relation entre les mesures d'activité nitrifiante potentielle et la biomasse des bactéries nitrifiantes a été établie sur culture pure. Elle montre que dans les conditions de mesures de l'activité potentielle, 1 µg C de bactéries nitrifiantes oxyde 0,04 µmol N/h

EN :

By regenerating oxidised forms of nitrogen (nitrate), the nitrification process plays an important role in the nitrogen cycle of aquatic environments. The measurement of the activity and biomass of nitrifying bacteria is thus essential to understand and quantify the general nitrogen fluxes in those environments. Different methods of measuring the nitrifying activity exist. The first methods developed were based on the use of specific nitrification inhibitors: N-serve, allyl thio-urea, acetylene, methylfluoride and dimethyl ether, as most used. They consist in measuring differences of ammonium, nitrite and nitrate dynamics in an inhibited and control sample during time. These methods can be applied as long as the inhibitors are specific for nitrifying bacteria, and activities are high enough to allow the measurement of concentration variations during incubation times which are not too long. At the present time, the most used methods are dealing with isotopic tracers: 14C or 15N. 15N methods allow the direct measurement of the nitrifying activity, while 14C methods represent the measurement of a biomass production which can be converted into a substrate oxidation rate by the use of a yield factor. This factor is considered to be constant in the standard incubation conditions. The most frequently used enumeration methods of nitrifying bacteria are not very satisfactory. Classical culture techniques (most probable number) and immunofluorescence techniques are known to greatly underestimate the numbers of active organisms. Recently developed gene-probes techniques work well for the identification of particular strains, but are not yet useful for the numeration. A good alternative to these methods consists in the measurement of potential nitrifying activity which is correlated to the nitrifying biomass.

This work presents a reassessment of the autotrophic nitrifying activity measurement by the 14C-bicarbonate incorporation method and its use to estimate the biomass of nitrifying bacteria. Several methods were used for our study: Continuous enrichment cultures of nitrifying bacteria were obtained from an inoculum coming from the Seine estuary (freshwater section). Pure cultures of Nitrosomonas europaea and Nitrobacter winogradskyi were obtained from the National Collection of Industrial and Marine Bacteria (Aberdeen, Scotland) and a continuous enrichment culture of mixed heterotrophic bacteria, without nitrifying organisms, was obtained with a freshwater inoculum by imposing a residence time of 2 hours (less than the generation time of nitrifying bacteria). Nitrifying cell numbers and size in the pure cultures were determined by epifluorescence with a microscope, after DAPI staining. Biovolumes were estimated according to cell size and converted in biomasses according to a conversion factor determined experimentally with a carbon analyser. Ammonium was measured with the indophenol blue method, nitrate was reduced in nitrite on a cadmium bed and nitrite was measured with the sulfanilamide method. Bicarbonate was measured by acid titration in natural water samples, and with the evolution method for culture samples. C incorporation rates are measured by the incubation of samples with 14C-bicarbonate, the samples being filtered on 0.2 µm membranes, acidified and counted for radioactivity by liquid scintillation.

The general validity of the method was demonstrated by experiments on nitrification inhibitors in enrichment cultures. These experiments consisted in measuring the effect of different combinations of N-serve, ethanol (the organic solvent of N-serve) and chlorate, on N-oxidation rates and C incorporation rates on samples of the two nitrifying enrichment cultures (ammonium- and nitrite-oxidising bacteria). The inhibitors effects were also determined on the C incorporation rates of heterotrophic bacteria. The results showed that the use of a combination of N-serve (5 mg/l, final concentration) and chlorate (10 mmol/l, final concentration) gave the best inhibition of ammonium- and nitrite-oxidation. However, the ethanolic solution of N-serve had an unwanted result on C incorporation. The organic solvent enhanced heterotrophic incorporation of C which totally masked out the autotrophic contribution of nitrifying bacteria. For this reason N-serve was added in the empty flask before the sample to allow the evaporation of the solvent. By acting this way, inhibition of autotrophic C incorporation by nitrifying bacteria was also complete, while heterotrophic incorporation was unaffected.

To measure potential nitrifying activities, the optimal growth conditions of nitrifying bacteria were determined on enrichment cultures: a pH between 7 and 8, a temperature between 20 and 30 °C, an ammonium concentration over 1 mmol/l, and an oxygen concentration over 6 mg/l. An experience consisting in following N oxidation, C incorporation and cell growth in a pure culture of Nitrosomonas europaea and Nitrobacter winogradskyi in optimal conditions allowed us to determine a yield factor (incorporated C/oxidised N) of 0.09 and 0.02 molC/molN for the ammonia- and nitrite-oxidising bacteria respectively. The determined optimal growth rate was 0.05 h-1 for the two nitrifying species. The specific activity of nitrifying bacteria, which correspond to the maximum N-oxidation rate of 1 µg C of nitrifying bacteria, is given by the ratio between the growth yield and the growth rate of those organisms. This factors allowed us to establish a relationship between potential nitrifying activity measurements and nitrifying biomass: in optimal growth conditions, 1 µgC of ammonium-oxidising bacteria oxidised 0.05 µmolN/h and 1 µgC of nitrite-oxidising bacteria oxidised 0.21 µmolN/h.

Our conclusion is that the results presented in this paper allow the validation of the 14C-bicarbonate incorporation method with and without inhibitors to measure the nitrifying activity. The main differences of our protocol to the original ones is that we propose the use of a combination of 2 inhibitors, N-serve and chlorate, and the elimination by evaporation of the organic solvent of N-serve (ethanol) to avoid any interference with the heterotrophic populations. The method can be used in in situ conditions, to allow real nitrifying activities measurements in samples. In this case, carbon incorporation rates can be converted in ammonium oxidation rates with the use of the conversion factor 0.11 µmoles incorporated C by µmoles oxidised N (0.09 molC/molN for ammonium oxidation and 0.02 for nitrite-oxidation). The method can also be used by placing the sample in optimal temperature, pH, oxygen and ammonium conditions for nitrifying bacteria, to allow potential nitrifying activity measurements. This potential activity can be used to estimate the nitrifying biomass by considering a conversion factor of 0.04 µmolN/h/µgC (0.05 µmolN/h/µgC for ammonium-oxidation and 0.21 µmolN/h/µgC for nitrite-oxidation). The rapidity of the method, itís sensitivity and the fact that no special equipment is needed, except the one for 14C detection, makes it a very useful method in aquatic ecology.