Modélisation mathématique du taux de coagulant dans une station de traitement d'eau Mathematical modelling of optimal coagulant dose in water treatment plant

Résumé

Les auteurs, après une synthèse bibliographique sur la coagulation, présentent deux modèles mathématiques reliant la dose optimale d'un coagulant, le sulfate d'aluminium, à la qualité de l'eau brute.

Un premier modèle applicable aux eaux dont la turbidité est inférieure à 20 NTU tient compte de quatre variables caractéristiques de l'eau brute qui sont : la turbidité, la résistivité, la température, la teneur en matières organiques.

Le second modèle, utilisable pendant les périodes de crue, intègre un cinquième descripteur : la nature de la suspension minérale.

Des essais effectués sur l'usine de Clairfont, qui alimente la rive gauche de Toulouse, montrent que ces modèles sont parfaitement adaptés pour automatiser l'injection du coagulant.

Mots-clés:

• Coagulation,
• modélisation,
• sulfate d'aluminium,
• turbidité,
• résistivité,
• température,
• matières organiques,
• titration colloïdale

Abstract

When the source of supply of a water treatment plant has a streaming behaviour, it is sometimes difficult to adjust correctly the coagulant dose by jar-testing alone.

Following this remark, the municipal water utilities of Toulouse city (France) has decided to conduct a study on the modelisation of coagulant dose as a function of the quality of raw water.

This study started first by a bibliographic survey to find the main parameters which affect the flocculation mechanisms, followed by a hydrologic study of the upper Garonne river to characterize as well as possible its behavior.

This was following by a study of the influence of certain parameters on the efficiency of coagulation by aluminium sulfate on synthetic waters having characteristics close to those of the Garonne river (BAZER-BACHI, 1986). This work showed the rote of the turbidity, of the resistivity, of the temperature and of the nature of mineral suspension. It also indicated the non-linearity between the optimum coagulant dose and these parameters as well as the interactions between them.

These conclusions led us to use a second degree polynomial model, as :

              k            k             k

Y = b_o + ∑ b_i X_i + ∑ b_ii X²_i + ∑ b_ij X_i X_j

     i = 1, j = 2, i ≠ j

Data were collected from modified jar-test on water from the Garonne River, characterized by physico-chemical (turbidity, temperature, pH, resistivity, CEC, MES, colloid titralion, organic matters) and chemical analyses (mineralisation). As the hydrological study showed that the nature of colloid suspension changed only during storm events, the modelisation was divided in two sub-groups :- a « CALME » model, comprising four variables (turbidity, resistivity, temperature, organic matters), for low turbidity waters (below 20 NTU),- a « CRUES » a model, using a fifth parameter representative of the nature of suspension (the ratio between colloid titration and turbidity).

The « CALME » model, which fitted very well, showed the primordial influence of the temperature and organic matters, and then of the turbidity. Removal of resistivity was not advisable, as this parameter showed strong interactions with turbidity and organic matters (fig. 3, 4).

The « CRUES » model showed the primordial role of the turbidity followed by the temperature and then by organic matters. The two other parameters, less significant, should nevertheless be kept if a good quality of forecast is to be maintained with this model. It can be further improved once all the experimental domain has been investigated.

The very good results obtained in full-scale at the Clairfont plant, by adjusting the coagulant feed rate according to the forecast of our models, led us to implement a coagulation automate, in operation in 1989.

Keywords:

• Coagulation,
• modelisation,
• aluminium sulfate,
• turbidity,
• resistivity,
• organic matters,
• colloid titration