Assignment #4

1) Article Reference
LEE, B. H. and DEININGER, R. A. (1992) “Optimal Locations of Monitoring Stations in Water Distribution Systems”, Journal of Environmental Engineering, 118(1) pp. 4-16

2) Summary
As a requirement of the Safe Drinking Water Act the water quality in water supply systems has to be monitored. Although the sampling frequency and the water quality parameters are prescribed by law, there are no specifications for representatively sampling within the pipe network. Placing a monitoring point in a demand point represents coverage for that specific demand. However this water might be coming from a series of upstream nodes and going to a series of downstream nodes. The water flow path within the network carries water quality information. The nodes upstream or downstream of a monitored node are likely to be known. The water flow in a pipe network is modeled today with a variety of hydraulic models.
The paper presents a small example to demonstrate its methodology. This network with seven nodes and seven demands is used to illustrate the principles of sampling and coverage nodes. “From this network is derived a matrix called the water fraction matrix. From this matrix several knowledge carrying matrices can be derived based on a decision on which fraction of water is acceptable to call a node covered”. A general form algorithm is presented for generating the coverage matrix. To apply this procedure a demand scenario, the flows and the flow directions for a given water distribution system must be knows. Basically one node is chosen arbitrary and all flows upstream are mapped and if the demand is greater than the threshold value its given value one otherwise zero.
An example of the formulation of an optimization model is provided considering the task of placing two monitoring point in a distribution system. The question is where to places this points to maximize the demand coverage. Two sets of variable are used. They are both 0 and 1 value and one represents the whether there is a sampling station or not and the other represents whether the demand is covered or not. A maximization function and constrains are derived for the simple case example.
A case study is presented at the distribution system for the city of Flint, Michigan. The system had 337 pipes, 211 nodes and 14 monitoring points covering 18% of the demands. An integer programming was formulated with 211 constrains, 422 variables and over 6.000 non zero entries in the tableau. The solution was developed using two different programs, the COVER and the COVTOIP. Respectively they are used to solve the hydraulic flows and determine the coverage matrix. An optimal solution if found with a coverage of 54%, considering only one scenario.
The multiple flow scenarios approach permits the inclusion and consideration of the patterns of variation of the demand, such as daily, monthly or seasonally differences. A general optimization equation is provided and a solution for the small example is also provided using LINDO programming.
A second example is provided, with a case study for the city of Cheshire, Connecticut. To model this system four scenarios were used, where each scenario represents a demand and flow pattern pre established. This problem had 245 variables and 197 constrains and was solved using LINDO integer programming code. There were 4 monitoring stations to be optimally placed. The results showed the best location for the monitoring station according with the number of station to be included.
As a conclusion the author demonstrated the importance of an optimal location of monitoring station within a water distribution system as its location can have a great affect in the coverage of the system.

3) Discussion
I really enjoyed reading this article as it is becoming clearer and easier to read this kind of approach. The authors used simple examples to clarify the methodology and presented two specific case studies to illustrate the point. The optimization functions, constrains and the set up of the matrixes were quite interesting. I think further research in this theme would be to verify different methods of optimization and to also implement water quality decays models between the nodes.