The Darcy-Weisbach Jacobian and avoiding zero flow failures in the global gradient algorithm for the water network equations

This paper considers two issues related to iteratively solving the non-linear equations governing the flows and heads in a water distribution system network. The first concerns the use of the correct Jacobian for the Global Gradient Algorithm (GGA) when the Darcy-Weisbach head loss model is used. The second relates to dealing with zero flows in the iterative solution process. A regularization procedure for the GGA with the Hazen{Williams model is demonstrated on an example network which has zero flows but for which the (full) Jacobian is invertible.Sylvan Elhay and Angus R. Simpso

Pumps as turbines (PATs) in water distribution networks affected by intermittent service

A hydraulic model was developed in order to evaluate the potential energy recovery from the use of centrifugal pumps as turbines (PATs) in a water distribution network characterized by the presence of private tanks. The model integrates the Global Gradient Algorithm (GGA), with a pressure-driven model that permits a more realistic representation of the influence on the network behaviour of the private tanks filling and emptying. The model was applied to a real case study: a District Metered Area in Palermo (Italy). Three different scenarios were analysed and compared with a baseline scenario (Scenario 0 - no PAT installed) to identify the system configuration with added PATs that permits the maximal energy recovery without penalizing the hydraulic network performance. In scenarios involving PAT on service connections, the specification of PAT operational parameters was also evaluated by means of Monte Carlo Analysis. The centralized solution with a PAT installed downstream of the inlet node of the analysed district, combined with local PATs on the larger service connections, proves to be the most energy-efficient scenario

Extending the global gradient algorithm to unsteady flow extended period simulations of water distribution systems

This paper introduces an extension of the Global Gradient Algorithm (GGA) to directly solve unsteady flow problems arising from the presence of variable head water storage devices, such as tanks, in Extended Period Simulations (EPS) of looped water distribution networks (WDN). Such a modification of the original algorithm was motivated by the need to overcome oscillations and instabilities reported by several users of EPANET, a worldwide available package, which uses the GGA to solve the looped WDN equations. The set of partial differential equations describing the time and space behaviour of a water distribution system is here presented. It is shown how an unsteady flow GGA can be derived by simple modifications of the original steady-state GGA. The performances of the new algorithm, referred to as EPS-GGA, are compared with the results provided by EPANET on an extremely simplified example, the solution of which is qualitatively known. As opposed to EPANET which shows significant instabilities, the EPS-GGA is stable under a wide variety of increasing integration time intervals

Testing linear solvers for global gradient algorithm

Steady-state Water Distribution Network models compute pipe flows and nodal heads for assumed nodal demands, pipe hydraulic resistances, etc. The nonlinear mathematical problem is based on energy and mass conservation laws which is solved by using global linearization techniques, such as global gradient algorithm (GGA). The matrix of coefficients of the linear system inside GGA belongs to the class of sparse, symmetric and positive definite. Therefore a fast solver for the linear system is important in order to achieve the computational efficiency, especially when multiple runs are required. This work aims at testing three main strategies for the solution of linear systems inside GGA. The tests are performed on eight real networks by sampling nodal demands, considering the pressure-driven and demand-driven modelling to evaluate the robustness of solvers. The results show that there exists a robust specialized direct method which is superior to all the other alternatives. Furthermore, it is found that the number of times the linear system is solved inside the GGA does not depend on the specific solver, if a small regularization to the linear problem is applied, and that pressure-driven modelling requires a greater number which depends on the size and topology of the network and not only on the level of pressure deficiency

Accounting for Local Water Storages in Assessing WDN Supply Capacity

AbstractIn many real WDNs, as in the Mediterranean area, customers are traditionally supplied by local water storages (i.e. roof or basement tanks) fed from the top by service pipes of the urban WDN through volume-controlled orifices. The present contribution shows that the prediction of WDN water supply capacity achieved by a model accounting for the filling/emptying of local tanks, is different from both classical demand-driven analysis and the pressure-driven analysis based on Wagner's demand-pressure relationship at each node. The WDNetXL system (www.hydroinformatics.it) is used to perform multiple simulation runs to assess WDN capacity under increasing demand scenarios

Investigation into the pressure-driven extension of the EPANET hydraulic simulation model for water distribution systems

Several hydraulic modelling approaches have been proposed previously to simulate pressure deficient operating conditions in water distribution networks more realistically. EPANET-PDX is an extension of EPANET 2 that has an embedded logistic nodal head-flow function. The EPANET-PDX algorithm was investigated to address the weaknesses uncovered under conditions of extremely low pressure. It was observed that, under certain circumstances, the norm of the system of equations increased from one iteration to the next. A criterion that detects false convergence was included. In general, in the examples considered, the formulation proposed had more consistent computational properties, required fewer iterations of the global gradient algorithm, and application of the line minimization procedure was frequent. The formulation proposed is significantly faster in conditions of extremely low pressure. The hydraulic and water quality modelling functionality of EPANET 2 was preserved. For the operating conditions with satisfactory pressure, where direct comparisons with EPANET 2 were possible, EPANET 2 was consistently faster

Calibration in Water Distribution Networks with Pressure-Driven Analysis

Water distribution networks (WDN) connect consumers to the water sources, and its goal is to fulfil water demand. However, it is a well-known fact that WDN have losses and an important part of them occur at pipe level. Despite all the research efforts focused on this subject, the identification of leaky pipes is still a major challenge. EPANET is frequently used to simulate WDN’ models, using a link-node formulation, similar to a graph, where the water demands are assigned to the nodes. A linearized system of equations (mass and energy conservation laws) is iteratively solved by a Newton-Raphson algorithm. The EPANET is demand-driven, since it assumes the water pressure is always enough to satisfy the demands. However, on real WDN, states of insufficient pressure also occur. Besides that, the demand-driven approach is not suitable for pipe leakage simulation, which depends on the pressure. WaterNetGen — an EPANET extension— allows both demand and pressure driven simulations, including pipes’ leakage modelling. However, the leakage parameters (bursts and background leakage coefficients and exponents) must be set manually by an expert — manual calibration — for the whole network or for each pipe. This work proposes a calibration methodology to estimate the pipe background leakage parameters. The approach is tested on a set of synthetic models, generated by WaterNetGen, and then applied to a real WDN to assess its performance on real world conditions.info:eu-repo/semantics/publishedVersio

Improving the efficiency of the loop method for the simulation of water distribution networks

Efficiency of hydraulic solvers for the simulation of flows and pressures in water distribution systems (WDSs) is very important, especially in the context of optimization and risk analysis problems, where the hydraulic simulation has to be repeated many times. Among the methods used for hydraulic solvers, the most prominent nowadays is the global gradient algorithm (GGA), based on a hybrid node-loop formulation. Previously, another method based just on loop flow equations was proposed, which presents the advantage that it leads to a system matrix that is in most cases much smaller than in the GGA method, but has also some disadvantages, mainly a less sparse system matrix and the fact that introducing some types of valves requires the redefinition of the set of network loops initially defined. The contribution of this paper is to present solutions for overcoming the mentioned disadvantages of the method based on loop flow equations. In particular, efficient procedures are shown for selecting the network loops so as to achieve a highly sparse matrix and methods are presented to incorporate check valves and automatic control valves while avoiding the need to redefine the loops initially selected. (C) 2015 American Society of Civil Engineers.This work has been partially supported by "Ministerio de Economia y Competitividad" from Spain, under the project TEC2012-38142-C04-01 and by PROMETEO FASE II 2014/003 project of Generalitat Valenciana.Alvarruiz Bermejo, F.; Martínez Alzamora, F.; Vidal Maciá, AM. (2015). Improving the efficiency of the loop method for the simulation of water distribution networks. Journal of Water Resources Planning and Management. 141(10):1-10. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000539S1101411

Application of «Gradient» Algorithm to Modeling Thermal Pipeline Networks with Pumping Stations

The paper deals with the analysis of flow distribution in regulated pipeline systems. Proposed inclusion of nodal elevations and piezometric heads into «global gradient» system of equations allows estimation of hydraulic regimes of thermal networks with pump stations, flow- and pressure-control valves during the process of iterative approach. Application of proposed modification of the Todini’s GGA method to calculation of flow distribution is shown on example of a small thermal network with pumps.В статье рассмотрены вопросы анализа потокораспределения в регулируемых трубопроводных системах. Предложено в систему уравнений метода «глобального градиента» ввести отметки рельефа местности и пьезометрические напоры, что позволяет в процессе итеративного приближения оценивать гидравлические режимы тепловых сетей с насосными подстанциями, регуляторами расхода и давления. На примере небольшой тепловой сети показана схема применения предлагаемой модификации метода Тодини к расчету потокораспределения

Efficient Modeling of Active Control Valves in Water Distribution Systems Using the Loop Method

[EN] This paper presents a novel approach to model pressure- and flow-regulating devices in the context of the Newton-Raphson loop method for water distribution network simulation. The proposed approach uses a symmetric matrix for the underlying linear systems, which enables simpler implementation and faster solution, while producing iterations very close to the global gradient algorithm of EPANET. The structure of the matrix is kept unchanged regardless of the operational status of the valves. The paper presents results that validate its formulation, accuracy, and speed in various case studies.Alvarruiz Bermejo, F.; Martínez Alzamora, F.; Vidal Maciá, AM. (2018). Efficient Modeling of Active Control Valves in Water Distribution Systems Using the Loop Method. Journal of Water Resources Planning and Management. 144(10):1-9. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000982S191441