Algorithme Génétique (AG) pour le choix optimal des stations d’appoint de chlore sur les réseaux d’eau potable Genetic Algorithm (GA) for optimal choice of chlorine booster stations in drinking water networks

Résumé

La chloration sur les réseaux de distribution d’eau potable constitue une tâche délicate. Elle assure la protection contre la reviviscence microbienne et contre la contamination du réseau. Les réactions du chlore avec la matière organique du système entraînent la formation des sous‑produits chlorés, indésirables pour la santé humaine. Ainsi, le maintien du taux de chlore libre à des valeurs admissibles, sur tout le réseau et à tout moment, constitue un objectif principal des gestionnaires des réseaux.

Lors de la chloration à partir des sources d’eau, les processus de réaction-transport créent sur les réseaux, caractérisés par des temps de séjours importants, de mauvaises distributions des taux de chlore libre. Les stations d’appoints sur les réseaux constituent une alternative efficace. La détermination de leur nombre et le choix des emplacements optimums constituent les deux difficultés auxquelles sont confrontés les gestionnaires. Le présent travail utilise un algorithme génétique (AG) pour la détermination du nombre et des emplacements optimums des stations d’appoint de chlore sur les réseaux. Deux objectifs ont été fixés : (1) l’amélioration de l’homogénéité spatio-temporelle de la chloration et (2) la minimisation du nombre de stations d’appoint. L’application du modèle développé sur un réseau test a permis d’identifier les emplacements des deux stations d’appoint de chlore. La solution optimale a considérablement amélioré l’homogénéité et a assuré, pour 98 % des noeuds, des taux de chlore libre dans l’intervalle admissible (0,1-0,5)  mg/L.

Mots clés:

• optimisation,
• algorithmes génétiques,
• homogénéité,
• chloration,
• réseau d’eau potable

Summary

The chlorination of drinking water networks represents a delicate task. It ensures protection against microbial regrowth and network contamination. However, chlorine also reacts with organic matter in the system and leads to the formation of chlorinated by-products, which are undesirable for the human health. Thus, one of the main objectives of the water network manager is to maintain acceptable levels of free residual chlorine, at all network nodes and at all times. When water sources are chlorinated, reaction-transport processes create an unbalanced distribution of free chlorine concentrations, especially in networks characterized by long water residence times. Booster stations in networks constitute an efficient alternative to improve the spatial and temporal chlorine distribution. Their number and their optimum locations are two challenges facing network managers. In this respect, this paper suggests the use of a genetic algorithm (GA) to determine the number and the optimum locations of chlorine booster stations in networks. The two main objectives of this study were: (1) the improvement of the spatio-temporal homogeneity of chlorination and (2) the reduction of the number of booster stations.

A solution to this optimisation problem is an arrangement of n_s booster stations in n consumption nodes of the water network. To resolve this problem, we linked the toolkit of the hydrodynamic computer program EPANET, which uses a one-dimensional reaction-transport model, to the proposed genetic algorithm (GA). In this application, we assume that free chlorine reactions through distribution networks are first-order. First, the EPANET computer program simulates temporal and spatial chlorine spreading in the network for each solution. Next, the GA calculates the sum square deviation E(NN, T), for the average chlorine concentration required for adequate sanitation (0.1‑0.5) mg/L, which corresponds to an optimal free chlorine concentration of 0.3 mg/L in the network. The number of booster stations is also defined for each solution studied. The optimal solution must minimize the sum square deviation and the number of booster stations used. Therefore, solution j can be evaluated by its fitness representing the weighted sum of the homogeneity function F_h(j) and the function of booster stations number F_smin(j). According to the fitness of the solution, genetic operators (tournament selection, two points crossover and mutation) associated with an elitist evolution strategy (ES), combine individuals and create new populations. This iterative process explores the solution space and improves the maximum population fitness until stagnation, to achieve the optimal individual.

The test network configuration maintained for modelling is formed by a tank and 20 km of pipes. The stretched-out shape of the network imposed long water residence times and usually created an unbalanced distribution of free chlorine concentrations at consumption nodes. In order to evaluate chlorination, three control nodes were chosen: N145 (first consumption node), N168 (middle of the network) and N206 (extremity of the network). For this network example, the best initial chlorination homogeneity was reached with a constant free chlorine concentration equal to 0.5 mg/L, usually imposed by the manager at the exit of the water tank. This initial management approach created in the network a sum square deviation of 65.9 mg²/L², as well as an unbalanced spatial chlorination distribution with 27% of the consumption nodes having free chlorine concentrations less than the minimum required value for adequate sanitation (0.1 mg/L). The simulation of higher free chlorine concentrations at the exit of the water tank (0.8 mg/L) led to concentrations above the maximum value required for adequate human health protection (0.5 mg/L) at 26% of the consumption nodes. Also, 10% of the nodes had concentrations lower than the minimum concentration required for human health. For all constant chlorination scheduling studied (0.4; 0.5; 0.6; 0.7 and 0.8 mg/L), an important fraction of consumption nodes remained with free chlorine concentrations outside the desired concentration range. Therefore, this management approach is not suitable for networks with long residence times.

Before its application, the GA required the definition of the crossover and the mutation probability (respectively 0.9 and 0.05), the size of the population (100) and the maximum number of generations (300). In addition, in the present application, chlorination homogeneity and the reduction of the booster stations number (p1 = p2 = 0.5) were given the same importance. According to boundary conditions, we imposed a free chlorine concentration of 0.5 mg/L at both the exit of the water tank and at the booster stations. The application of the GA, developed in this study, ensures the evolution of the initial population until stagnation of its maximum fitness. The resulting optimal solution involved the creation of two booster stations at nodes N179 and N196. The simulation of this chlorination management improves the spatio-temporal homogeneity of free chlorine concentrations in consumption nodes. It reduced the sum square deviation from 65.9 to 38.8 mg²/L². Finally, 98% of the consumption nodes had free chlorine concentrations (0.1-0.5 mg/L) that were required in the context of human health.

This model represents a first step in the optimization of chlorination homogeneity in networks characterized by long water residence times. The use of this tool requires network hydraulic modelling, the simulation of the free chlorine behaviour, the definition of the chlorine reaction coefficients and the GA parameters. The optimization of the chlorine concentration scheduling (in water sources and in booster stations) represents an additional step in the present work.

Keywords:

• optimization,
• genetic algorithms,
• homogeneity,
• chlorination,
• drinking water network