Hydraulic Network Analysis Research Articles

Modernization of Todini Global Gradient Algorithm for hydraulic analysis of networks with choked flow

The modification of well-known Global Gradient Algorithm for hydraulic network flow distribution problem is proposed. This modification is based on problem equations rewritten in “upstream” form and on modified form of linearization, and can be effectively used for piping networks with gas and multiphase gas-liquid flow with multiple choked flow.

Urban Drainage Network Rehabilitation Considering Storm Tank Installation and Pipe Substitution

The drainage networks of our cities are currently experiencing a growing increase in runoff flows, caused mainly by the waterproofing of the soil and the effects of climate change. Consequently, networks originally designed correctly must endure floods with frequencies much higher than those considered in the design phase. The solution of such a problem is to improve the network. There are several ways to rehabilitate a network: conduit substitution as a former method or current methods such as storm tank installation or combined use of conduit substitution and storm tank installation. To find an optimal solution, deterministic or heuristic optimization methods are used. In this paper, a methodology for the rehabilitation of these drainage networks based on the combined use of the installation of storm tanks and the substitution of some conduits of the system is presented. For this, a cost-optimization method and a pseudo-genetic heuristic algorithm, whose efficiency has been validated in other fields, are applied. The Storm Water Management Model (SWMM) model for hydraulic analysis of drainage and sanitation networks is used. The methodology has been applied to a sector of the drainage network of the city of Bogota in Colombia, showing how the combined use of storm tanks and conduits leads to lower cost rehabilitation solutions.

Development and Applications of K-NRisk for Pressure Dependent Demand Analysis in Water Distribution Networks

Hydraulic analysis of water distribution networks is important not only for the assessment current status, but also for the near and far future prediction with uncertainties. Hydraulic analysis models can be classified into demand driven analysis (DDA) and pressure driven analysis (PDA) depending on nodal outflow assumption. However, the EPANET2, which is globally used model, does not include PDA module, and therefore hydraulic analysis under abnormal conditions is impossible. In this study, a new multi-scenario based hydraulic analysis model for abnormal conditions, K-NRisk is developed by combining PDA technique. The K-NRisk is compared with the existing commercial softwares, and verified by multi-scenario based modeling for typical abnormal conditions. The results show that, the K-NRisk developed in this study can visualize pressure deficient area under abnormal conditions, and also can quantify the water shortage reasonably. Therefore, the K-NRisk can be used as a decision support tool to improve the efficiency of water distribution network operation, to enhance the revenue water ratio at pressure deficient area. Keywords: Water Distribution Networks, Pressure Driven Analysis, K-NRisk, Abnormal Condition Analysis

Automated Framework for Water Looped Network Equilibrium

In this paper, a novel algorithm is proposed for balancing water looped network in steady state through a fully automated general framework of hydraulic networks regardless of their topological complexity. The model is developed by combining the following two steps, firstly a set of independent loops are identified based on a graph theoretical analysis in a looped network. Further the second step is devoted to the equilibrium process by determining the flow rate distribution within the network ducts and the pressure in the delivery nodes. The above such equilibrium process gives rise to a system of non linear algebraic equations which are solved numerically using both Hardy Cross (HC) and Newton Raphson (NR) methods. In HC method, the flow correction term is modified and a generalized expression is given to consider various possibilities of independent loops selection. Some real networks topologies that were commonly used as benchmarks, for testing various independent loops selection algorithms, are taken as case studies to apply the general automatic framework for hydraulic network analysis. Such network analysis enhances proving the applicability as well as the effectiveness of the proposed approach. Also, during the equilibrium procedure, it is proved that NR method is capable of producing accurate results and it converges more rapidly comparing to the widely used HC method. Moreover, it is demonstrated that NR’s iterative process, contrary to HC’s one, converges to reliable results even with a choice of random initial flow rates which makes a NR algorithm quite simple to implement without affecting the accuracy of the results.

Constraint-Preconditioned Inexact Newton Method for Hydraulic Simulation of Large-Scale Water Distribution Networks

Many sequential mathematical optimization methods and simulation-based heuristics for optimal control and design of water distribution networks rely on a large number of hydraulic simulations. In this paper, we propose an efficient inexact subspace Newton method for hydraulic analysis of water distribution networks. By using sparse and well-conditioned fundamental null space bases, we solve the nonlinear system of hydraulic equations in a lower-dimensional kernel space of the network incidence matrix. In the inexact framework, the Newton steps are determined by solving the Newton equations only approximately using an iterative linear solver. Since large water network models are inherently badly scaled, Jacobian regularization is employed to improve the condition number of these linear systems and guarantee positive definiteness. After presenting a convergence analysis of the regularized inexact Newton method, we use the conjugate-gradient (CG) method to solve the sparse reduced Newton linear systems. Since CG is not effective without good preconditioners, we propose tailored constraint preconditioners that are computationally cheap because they are based only on invariant properties of the null-space linear systems and do not change with flows and pressures. The preconditioners are shown to improve the distribution of eigenvalues of the linear systems and so enable a more efficient use of the CG solver. Since contiguous Newton iterates can have similar solutions, each CG call is warm-started with the solution for a previous Newton iterate to accelerate its convergence rate. Operational network models are used to show the efficacy of the proposed preconditioners and the warm-starting strategy in reducing computational effort.

An MS Excel tool for water distribution network design in environmental engineering education

AbstractAn MS Excel tool for teaching hydraulic analysis of water distribution networks (WDNs) was developed. The tool is able to perform both steady‐state and extended period simulations of a WDN. The tool does not require installation and offers a portable solution to WDN design problem in undergraduate environmental engineering studies.

Extending EPANET Capabilities with Add-In Tools

EPANET is probably the most widespread model for water distribution network (WDN). More than twenty years after its appearance, it has become a global reference both for hydraulic and quality analysis of water networks. In 2000, EPANET 2 appears, which includes as most important computational feature a new Toolkit. This toolkit was a library of functions allowing the modification of network data and reading results without access to the appropriate files. Over time, the use of this library has been the communication protocol for every application developers who use the method propose by Todini and Pilati to analyze the behavior of WDN. This library also provides interface tools that allow the execution of a simulation from an external application, as long as the network characteristics had been previously defined.This paper presents a change in the original EPANET model, including a new menu in the graphical user interface (GUI). This menu allows users to set up a personal collection of Add-In tools, which use both project data and simulation results. These tools can be customized and allows to extend the analysis capability of EPANET. All of them can access EPANET functions through the Toolkit and were developed by the authors during the Spanish translation of EPANET, taking into account the homologous Add-in tools developed for SWMM model. As an example of the operation and capabilities of this new menu, several applications integrated as EPANET add-in tools are presented. These tools perform tasks such as importing data network from both CAD and GIS systems, the design of WDNs using genetic algorithms, automatic assignment of initial water quality to network nodes; the skeletonization of a network or optimization of pumping schedule in the network in order to achieve a minimum energy cost.

Hydraulic Analysis of Urban Water-Supply Networks in Marivan

Hydraulic Analysis of Urban Water-Supply Networks in Marivan

Comparison of solution methods for analyzing water distribution networks under pressure-deficient conditions

Demand-driven analysis method is used in most current existing models for hydraulic evaluation of water supply networks. This method is based on the assumption of constant use, regardless of the available pressure in nodes. Demand-driven analysis method does not have sufficient efficiency in hydraulic analysis of networks under pressure-deficient conditions. In this study, the combination of pressure-deficient network algorithm (PDNA), modified pressure-deficient network algorithm (MPDNA), and complementary reservoir solution (CRS) methods with hydraulic model have been used to analyze series networks, looped networks, and a full-scale distribution network (part of the water network in Ilam city, Iran) in critical operating conditions. The critical condition in networks is created by breakage in a pipe network and fire-fighting demands on one node. Results showed that the required flow in networks has not been quite satisfied. The supplied outflow in the series, looped networks, and zone-6 network which used the three aforementioned methods are calculated as 76.40%, 90.25%, and 98.56% of total network demand, respectively. The results also showed that the number of required iterations to achieve the solutions in the PDNA method is more than in the MPDNA and CRS methods.

Uncertainty quantification of pressure-driven analysis for water distribution network modeling

The hydraulic analysis of water distribution networks (WDNs) is divided into two approaches: namely, a demand-driven analysis (DDA) and a pressure-driven analysis (PDA). In the DDA, the basic assumption is that the nodal demand is fully supplied irrespective of the nodal pressure, which is mainly suitable for normal operating conditions. However, in abnormal conditions, such as pipe failures or unexpected increase in demand, the DDA approach may cause unrealistic results, such as negative pressure. To address the shortcomings of DDA, PDA has been considered in a number of studies. For PDA, however, the head-outflow relation (HOR) should be given, which is known to contain a high degree of uncertainty. Here, the DDA-based simulator, EPANET2 was modified to develop a PDA model simulating pressure deficient conditions and a Monte Carlo simulation (MCS) was performed to consider the quantitative uncertainty in HOR. The developed PDA model was applied to two networks (a well-known benchmark system and a real-life WDN) and the results showed that the proposed model is superior to other reported models when dealing with negative pressure under abnormal conditions. In addition, the MCS-based sensitivity analysis presents the ranges of pressure and available discharge, quantifying service reliability of water networks.

Sparse Null Space Algorithms for Hydraulic Analysis of Large-Scale Water Supply Networks

AbstractIn this article, a comprehensive review of existing methods is presented and computationally efficient sparse null space algorithms are proposed for the hydraulic analysis of water distribution networks. The linear systems at each iteration of the Newton method for nonlinear equations are solved using a null space algorithm. The sparsity structure of these linear equations, which arises from the sparse network connectivity, is exploited to reduce computations. A significant fraction of the total flops in the Newton method are spent in computing pipe head losses and matrix-matrix multiplications involving flows. Because most flows converge after a few iterations, a novel partial update of head losses and matrix products is used to further reduce computational complexity. Convergence analyses are also presented for the partial-update formulas. A new heuristic for reducing the number of pressure head computations of a null space method is proposed. These savings enable fast near-real-time control of ...

A Graph Portioning Approach for Hydraulic Analysis-Design of Looped Pipe Networks

This study introduces a new formulation for hydraulic analysis and design of looped pipe networks. The network is partitioned into two sub-graphs so-called the base and the remainders graphs. The base graph is a spanning tree of the network and, the remainders graph includes pipes hypothetically removed from the network to open the loops. The network governing equations of mass and energy conservation are manipulated so that, pipe flows in the remainders and head losses in the base graph are considered as independent variables to calculate pipe diameters directly. The method is applied to two example networks and the results are discussed. The new approach is found to be computationally efficient and useful for design and optimization of pipe networks.

Hydraulic Analysis of Water Supply Networks Using a Modified Hardy Cross Method

There are different methods for the hydraulic analysis of water supply networks. In the solution process of most of these methods, a large system of linear equations is solved in each iteration. This usually requires a high computational effort. Hardy Cross method is one of the approaches that do not need such a process and may converge to the solution through scalar divisions. However, this method has two shortcomings: first, initial discharges should satisfy continuity equation at each node; second a large number of iterations are required to converge to solution. In this article an algorithm is suggested for initial discharges that are close to the final results while the continuity equations are automatically established. This algorithm may be directly implemented in the Hardy Cross method. To reduce the number of iterations the Hardy Cross method is combined with third-order and sixteenth-order methods. The results of some numerical examples demonstrate that the use of the combined approach with the suggested initial guess reduces the number of iterations and hydraulic analysis time and the solutions converge with a high accuracy.

Uncertainty analysis of water supply networks using the fuzzy set theory and NSGA-II

This work introduces an approach for taking into account the uncertainty of pipe friction coefficients and nodal demands in the hydraulic analysis of water supply networks. For this purpose, uncertainties are represented by fuzzy numbers and incorporated into the network׳s governing equations. Input uncertainties are spread out on the network and influence its hydraulic responses, including pipe velocities and nodal pressures. To estimate the responses׳ uncertainty, input fuzzy numbers are discretized in some levels of membership function. Then, a multiobjective optimization problem is developed for each level to find the extreme values of the node pressures and pipe velocities. The raised problem is solved using the method of Non Dominated Sorting Genetic Algorithm (NSGA-II) coupled to the network hydraulic simulation model. The proposed approach is applied to an example and a real pipe network. It is found that small uncertainties in input variables can significantly influence the network׳s responses as well as its performance reliability. It is also concluded that NSGA-II has a great role in solving the problem systematically, and improves the computational efficiency of the whole process of network fuzzy analysis.

Water networks of Roman gold mines of Northwestern Iberian Peninsula

This paper presents a synthesis of the work done by the research group Social Structure and Territory—Landscape Archaeology (Institute of History, CSIC) in North Western Spain, for which the study and analysis of hydraulic networks related to Roman mining exploitation has been a fundamental part. The gold-bearing areas of the Iberian Peninsula’s North West had a great importance for the Roman Empire, which integrates their exploitation in the overall control of the territory from the very beginning of the 1st century AD. To ensure the essential supply of water for the whole of the mining process was one of the main axes of the reorganization of the provincial territories. The aim of this paper is to present both the historical context of these water networks and the methodology and approach of our work, in which the fieldwork and network analysis is an important research aim. We will do this by using the example of the Roman gold mines of the Sierra de Francia region where an extensive and very well preserved hydraulic system has been recorded and analysed. Our team has gathered archaeological evidence for the study of water networks and mining exploitation and their incidence on the revaluation of natural resources in the region.

Hydraulic Analysis of Water Distribution Network Using Shuffled Complex Evolution

Hydraulic analysis of water distribution networks is an important problem in civil engineering. A widely used approach in steady-state analysis of water distribution networks is the global gradient algorithm (GGA). However, when the GGA is applied to solve these networks, zero flows cause a computation failure. On the other hand, there are different mathematical formulations for hydraulic analysis under pressure-driven demand and leakage simulation. This paper introduces an optimization model for the hydraulic analysis of water distribution networks using a metaheuristic method called shuffled complex evolution (SCE) algorithm. In this method, applying if-then rules in the optimization model is a simple way in handling pressure-driven demand and leakage simulation, and there is no need for an initial solution vector which must be chosen carefully in many other procedures if numerical convergence is to be achieved. The overall results indicate that the proposed method has the capability of handling various pipe networks problems without changing in model or mathematical formulation. Application of SCE in optimization model can lead to accurate solutions in pipes with zero flows. Finally, it can be concluded that the proposed method is a suitable alternative optimizer challenging other methods especially in terms of accuracy.

Prevention of Discoloration Events in Water Distribution Systems

Mathematical modeling and simulation techniques represent powerful tools for optimizing the operation of drinking water supply networks. Water quality in the distribution systems is affected by the hydraulic regime in the network (Vreeburg, 2007). An incidental re-suspension of accumulated loose particles is the main cause of discoloration events in the network (Vreeburg, 2010). This article describes two technical tools that are being developed to help water utilities create and maintain programs for preventing the occurrence of discoloration events in their water distribution systems. The first of the two directly applicable tools is a portable measuring device that enables continuous measurement of hydraulic properties and water discoloration in the network. The other tool is a software application ADAM, which uses a non-data-hungry methodology based on a risk analysis approach and utilizes the author's previous experience with mathematical modeling of various water-supply networks. The probability of the presence of sediment accumulation in each pipe section in the network is estimated. Problems relating to uncertainty and poor input data quality are solved by the application of the FMEA/FMECA technique (Tuhovčák, Ručka, 2009). The analysis is performed using ADAM, the newly developed simulation software for hydraulic analysis of water supply networks. The tools presented in this paper have been developed under the framework of “Tools for prevention of water discoloration in water mains”, the current national research project of the Technology Agency of the Czech Republic (registration number TA02020604), a brief outline of which is also presented in this paper.

A Theoretical Model with Experimental Verification to Predict Hydrodynamics of Foams

An experimentally validated theoretical model, based on hydraulic resistance network and scale analysis at the pore level, is developed to predict the pressure drop for flow through foams. The complex microstructure of the foams is modeled as a matrix of interconnected solid ligaments forming simple cubic arrays of cylinders. New correlations for permeability and form drag (inertia) coefficient are presented as functions of the mean pore and ligament diameter as well as the foam porosity. The present model makes it possible to conduct parametric studies. Results obtained from the proposed model are successfully compared with our experimental data as well those found in the literature to observe good agreement.

Pressure-Driven Demand and Leakage Simulation for Pipe Networks Using Differential Evolution

Traditional techniques for hydraulic analysis of water distribution networks, which are referred to as demand-driven simulation method (DDSM), are normally analyzed under the assumption that nodal demands are known and satisfied. In many cases, such as pump outage or pipe burst, the demands at nodes affected by low pressures will decrease. Therefore, hydraulic analysis of pipe networks under deficient pressure conditions using conventional DDSM may cause large deviation from actual situations. In this paper, an optimization model is introduced for hydraulic analysis of water distribution networks using a meta-heuristic method called Differential Evolution (DE) algorithm. In this methodology, there is no need to solve linear systems of equations, there is a simple way to handle pressure-driven demand and leakage simulation, and it does not require an initial solution vector which is sometimes critical to the convergence. Also, the proposed model does not require any complicated mathematical expression and operation.

Virtual reality simulation system for water supply and distribution network

One of the challenges of Virtual Reality (VR) technology is implementing its effective integration with application models to provide feasible information in real time. This paper will investigate VR simulation systems in Water Distribution Networks (WDN). A framework of a VR simulation system for WDN was proposed and a prototype was developed to provide an intuitive user interface offering real-time simulation and interaction through multi-sensory channels. This enables data processing, visualisation, scene roaming, hydraulic and water quality calculation and network analysis. The hydraulic and water quality models are combined into the VR simulation system; dynamic hydraulic and water quality information is expressed visually and managed interactively in the three dimensional virtual environment. The proposed VR simulation framework and developed system were evaluated in a case study which demonstrated its effectiveness as a tool to enhance understanding and operational efficiency in the WDN.