A growth model for water distribution networks with loops

Abstract

Water distribution networks (WDNs) expand their service areas over time. These growth dynamics are poorly understood. One facet of WDNs is that they have loops in general, and closing loops may be a functionally important process for enhancing their robustness and efficiency. We propose a growth model for WDNs that generates networks with loops and is applicable to networks with multiple water sources. We apply the proposed model to four empirical WDNs to show that it produces networks whose structure is similar to that of the empirical WDNs. The comparison between the empirical and modelled WDNs suggests that the empirical WDNs may realize a reasonable balance between cost, efficiency and robustness in terms of the network structure. We also study the design of pipe diameters based on a biological positive feedback mechanism. Specifically, we apply a model inspired by Physarum polycephalum to find moderate positive correlations between the empirical and modelled pipe diameters. The difference between the empirical and modelled pipe diameters suggests that we may be able to improve the performance of WDNs by following organizing principles of biological flow networks.

Python Routine for an Easy Visualization of the Influence of Supply Network Characteristics on the Hydraulic Behavior of a Small Closed Loop

“…A conceptual framework for the water distribution scheme is proposed [14], which builds looped networks and is suitable for systems with numerous water sources. The proposed methodology is used to four actual networks to demonstrate that it generates networks with comparable architecture to the actual ones.…”

Online Edge Flow Prediction Over Expanding Simplicial Complexes

“…simplicial complex expands over time [15,16,17]. This arises in numerous applications, for instance, predicting the water flow in a new pipe between hydraulic components of a water network [18], providing a global ranking where new alternatives are coming over time in statistical ranking, or predicting the exchange rates in a financial market where a new trade between two commodities establishes over time [6,10]. Nevertheless, existing methods [19,13,20] only process simplicial signals on static settings and do not capture the expanding nature of the topology.…”

Two Iterative Methods for Sizing Pipe Diameters in Gas Distribution Networks with Loops

“…Explanation of the first improvements to the Hardy Cross method [28,29,33,34,38] (useful are also [30][31][32])-accelerated Hardy Cross and versions of loop-versus nodeoriented approach; • Flow pattern in already existing pipe network with loops [36]; • Very illustrative but simple example of application of Hardy Cross and node-loop methods for water distribution [37]; • Approach involving virtual loop that connects two nodes with the same pressure in order to ensure a linear independent matrix needed for calculation (also application of the methods to ventilation systems of underground mines) [39]; • Various versions of methods for ventilation [39,[49][50][51][52][53], oil [54] (compare also similarities with [2]), water distribution [40][41][42][43][44][45][46][47][48] and district heating systems [57][58][59];…”