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The following paper presents a method to optimise a discontinuous permeable adsorptive barrier (PAB-D). This method is based on the comparison of different PAB-D configurations obtained by changing some of the main PAB-D design parameters. In particular, the well diameters, the distance between two consecutive passive wells and the distance between two consecutive well lines were varied, and a cost analysis for each configuration was carried out in order to define the best performing and most cost-effective PAB-D configuration. As a case study, a benzene-contaminated aquifer located in an urban area in the north of Naples (Italy) was considered. The PAB-D configuration with a well diameter of 0.8 m resulted the best optimised layout in terms of performance and cost-effectiveness. Moreover, in order to identify the best configuration for the remediation of the aquifer studied, a comparison with a continuous permeable adsorptive barrier (PAB-C) was added. In particular, this showed a 40% reduction of the total remediation costs by using the optimised PAB-D.

Robustness of water distribution networks is related to their connectivity and topological structure, which also affect their reliability. Flow entropy, based on Shannon's informational entropy, has been proposed as a measure of network redundancy and adopted as a proxy of reliability in optimal network design procedures. In this paper, the scaling properties of flow entropy of water distribution networks with their size and other topological metrics are studied. To such aim, flow entropy, maximum flow entropy, link density and average path length have been evaluated for a set of 22 networks, both real and synthetic, with different size and topology. The obtained results led to identify suitable scaling laws of flow entropy and maximum flow entropy with water distribution network size, in the form of power-laws. The obtained relationships allow comparing the flow entropy of water distribution networks with different size, and provide an easy tool to define the maximum achievable entropy of a specific water distribution network. An example of application of the obtained relationships to the design of a water distribution network is provided, showing how, with a constrained multi-objective optimization procedure, a tradeoff between network cost and robustness is easily identified., Competing Interests: The authors declare no conflict of interest.

In order to improve the management and to better locate water losses, Water Distribution Networks can be physically divided into District Meter Areas (DMAs), inserting hydraulic devices on proper pipes and thus simplifying the control of water budget and pressure regime. Traditionally, the water network division is based on empirical suggestions and on 'trial and error' approaches, checking results step by step through hydraulic simulation, and so making it very difficult to apply such approaches to large networks. Recently, some heuristic procedures, based on graph and network theory, have shown that it is possible to automatically identify optimal solutions in terms of number, shape and dimension of DMAs. In this paper, weighted spectral clustering methods have been used to define the optimal layout of districts in a real water distribution system, taking into account both geometric and hydraulic features, through weighted adjacency matrices. The obtained results confirm the feasibility of the use of spectral clustering to address the arduous problem of water supply network partitioning with an elegant mathematical approach compared to other heuristic procedures proposed in the literature. A comparison between different spectral clustering solutions has been carried out through topological and energy performance indices, in order to identify the optimal water network partitioning procedure.