Algorithmic Optimal Management of a Potable Water Distribution System: Application to the Primary Network of Bonaberi (douala, Cameroon)

The optimal management of a potable water distribution system requires the control of the reference (standard) data, the control points, control of the drainage parameters (pressure, flow, etc.) and maintenance parameters. The control of the mentioned data defines the network learning process [1]. Besides classic IT functions of acquisition, storage and data processing, a geographical information system (GIS) can be used as the basis for an alarm system, allowing one to identify and to localize the presence of water leaks in the network [2]. In this article we propose an algorithm coupling the various drainage parameters for the management of the network. The algorithm leads to an optimal management of leaks. An application is in progress on the primary network in the region of Bonaberi in Douala, the largest city of Cameroon.


Introduction
Drinking water is a precious raw material [3].It is also an economic and strategic stake in the world [4], that is increasingly reaching crisis status as we are consuming more fresh water than the planet procduces.To meet our needs, we are emptying the many years-old ground water reservoirs, we divert the course of major rivers [5] and contaminate sources of drinkable water.If a man can be days without electricity and without food, it is on the other hand impossible to be more than a day without drinking [2,6].
In view of the amounts spent on obtaining, treating and transporting water, the economic stakes [7], and the quoted social and cultural facts, it is important to minimize the volume of water lost to leaks.This suggests the usage of an algorithm, as an indispensable tool for the optimal management of a potable water distribution system.
After the presentation of the structure of the network in the Section 2, we present in Section 3 the network management parameters.Section 4 is dedicated to the optimization algorithm and Section 5 describes the application on the network of Bonaberi in Douala, Cameroon.

Presentation of the site
The water of the city of Douala comes from two 800 mm diameter pipes which carry the fluid from the Japoma treatment station.One of the pipes supplies the lower part of the city (low network), while the other one supplies the high part of the city (the high network).
Bonaberi is a low region of Douala.The water network which supplies it comes from the low network (Figures 1 and 2) via a pipe 400 mm in diameter.At the entry of the bridge the pipe diameter is 350 mm until Bonassama.At the exit of the on pressure side of Bonassama the diameter of the pipe is 800 mm up to the castle (Figure 1).

Elements of the network
The different parts of the Bonaberi network are similar to those of classic urban networks [8].We find cast iron or PVC pipe constituted of (Figures 1 and 2

Problems
The drinkable water distribution system in sub-Sahelian Africa is dilapidated [3,6,7].The main problems are generally:  difficulty of real-time detection of the leaks  impossibility to minimize the volumes of water lost during the leaks  impossibility to predetermine the degradation of the network  absence of the appropriate sizing of the network  degradation of the environment due to the leaks.
Hence the necessity to set up an algorithm which minimizes the volume of lost water, optimizing the access to the drinking water and widely contributing to the environmental protection.

Network Data Management
The learning phase of the drinking water network (Figure 3) was realized during a suitable period, and allows knowing the behaviour of the network and the range of its functional data (pressure, geographical flow, coordinates, etc.) [9,10]. in a logical database Eb(i,j).When Eb(i,j) = 1 the database of activation, maintenance and control points on the map contribute to diagnose any dysfunction of the network.At the same time, an efficient maintenance plan is generated, closing motorized gates to limit any losses during a leak.

Algorithm
The proposed algorithm is summarized in the scheme shown in Figure 4. where: Et (i,j) matrix standard of line i and of column j (the hour of a day), varies from 1 to 24 and i corresponds to the sensors on the network; Et(i,j) or δ(i,j) defines the tolerance of variation of every element of Et(I,j); Er(i,j) matrix of the data real-time statement.Lines i and column j.The parameter j varies from 1 to 24 and i corresponds to sensors of the network; Eb(i.j) matrix defines from Et(i,j) and Er(i,j).It contains Boolean values; Bm(i,j) is the base of datum of the maintenance; Rh(i,j) is the base of geographical reference of the control point i at the precise hour j.For i constant, R (i j) keep the same value.m = number of sensor settled on the network; Vect(i,j) Is the matrix for activation of the motorized gates.
At the beginning of the program, the user must declare the number of control points in the network.This number is indicated by m.The function of the real data of Eb(i,j) are introduced for the progress of the algorithm.The state of the Boolean data Eb(i,j) informs about the state of functioning of the network and indicates the action to be undertaken.

Yield of the network
The yield on the network is obtained by calculating the ratio between the volume of water consumed and the volume produced in a month.The sum of the daily volumes read on the meter placed in the entrance of the zone allows us to obtain the monthly volume.These volumes are directly obtained in the service of operation of the network.The invoicing of the monthly volumes consumed by subscribers is assured by the sales department of the national drinking water distribution company.The sum of the volumes charged by zone gives the monthly charged volume monthly volume: Monthly yield = Charged volume per month/ volume produced per month = R i Table1.Volume of water distributed in Bonaberi.

Month
Volume produced (m The average of yield on production is 61 %.
After three months of survey on the network of Bonaberi before the application of this technique, we noticed that the average return was 61%.This represents a loss of about 40% a month for a zone in lack of water.These losses are enormous and explain the preoccupation of the agents for developing a method for limiting the leaks.

Network system management
The maintenance of the distribution network is essentially curative, the idea being to reduce the losses by an automatic detection or a semi-automatic detection of the leaks.It implies the practice of conditional or systematic maintenance.For this fact, four sensors are placed on the network.For the first time, we checked the primary channelling.The data collected during three years allowed us to elaborate the control matrix Et(i,j).Similar searches suggest that the optimal time of elaboration of Et(i,j) should be 9 years, so, Et(i,j) has to be improved.Et(1,j) is represented on the corresponding curve in Figure 5 by three values (maximal, average and minimal).The databases Bm(i,j) and Rh(i,j) are created according to the profile of the maintenance technicians, the tools indispensable for the maintenance and according to the characteristics of every water conduit (diameter, materials, nature of the ground, the volume of the pipe, breakdown history), the real-time or recorded location, matrices Er(i,j) are entered into in the algorithm and it is allowed to activate every hour.In case of noticed disfunction, the algorithm isolates the breakdown with motorized gates and generates an action plan of maintenance or it defines the:  place of the incident  chaining of the maintenance actions in the form of a Gantt schedule  profiles of the recommended technicians  materials and the equipment indispensable for the maintenance  location of the motorized gates to be activated at the end of repair. of this method is to allow an optimal reduction of the volume of water lost during the break-downs.All this is very expensive.
A recorded treatment allows an investment reduced to the work of conception and to the collection and processing of data.No supplementary component is added to the network except some recorders judged useful and placed in the points of collection of the drainage parameter.For the special case of Bonaberi in Douala, Cameroun, where losses are situated about 40% of the production, such an application is free of charge.It is the one which is at present adopted and has allowed to reduce the losses to (or by) 10%.In every case, the network learning, the low collections of data, GIS (geographical information of the system) and cartography is imperative for an algorithm to optimize the management of water leaks.In view of the importance of the water for men, animals and the plants it is important to encourage this set-up in the urban networks where pipes, typically buried for over half a century, lose their waterproofnesses and present numerous leaks.

Figure 1 .
Figure 1.Overview diagram of the Bonabri-primary network.Extracted from the CDE archives.

Figure 5 .
Figure 5. Curve of the pressures before the bridge.

Figure 6 .
Figure 6.Algorithmic treatment of a leak.From 6 a.m. to 9 p.m.The BREAKDOWN curve is the evolution of Er(i,j) data during the leaks, compared to Et(i,j) data.