Paul F. Boulos

A graph-theoretic approach to explicit nonlinear pipe network optimization

Abstract An explicit algorithm for nonlinear constrained pipe network optimization is developed. The explicit approach can be effectively used for directly determining a variety of pipe network characteristics to exactly satisfy defined values of quasi-linear boundary equality constraints. The constraint set represents stated supply pressure and volumetric flow requirements at designated critical nodes and pipes throughout the pipeline system for a range of operating conditions. The solution of the problem is based on an analytical reformulation of the quasi-linear steady-state network equilibrium equation set and the corresponding boundary specifications in terms of selected pipe system parameters. Owing to the presence of nonlinearity in these equations, the incremental Newton-Raphson method is utilized as the basic solution procedure. The solution, which is defined in a continuous variable space, is optimal in the sense that the decision parameters are calculated to meet the specified pressure and flow constraints. Every type of pipe conveying system can be optimized with this method. The solution space is secured through a well-arranged interaction between network topology, boundary constraints, and decision parameters. In order to illustrate the developed algorithm an example application is presented.

An event-driven method for modelling contaminant propagation in water networks

Abstract An efficient computer-oriented methodology is presented for use in analyzing water quality variations in drinking-water distribution systems. The proposed method can be effectively used for modelling chemical, biological, and hydraulic changes that result from distribution system activities and to predict the transient distribution of contaminants throughout the pipe system. It is predicated on the material mass balance accounting for transport and kinetic reaction processes. Perfect advective one-dimensional displacement with complete mixing of material at the network nodes is assumed. The method is event-driven and determines the optimal pipe segmentation scheme with the smallest number of segments necessary to carry out the simulation process. The resulting approach allows for dynamic water quality modelling that is less sensitive to the structure of the network and to the length of the simulation than previously proposed methods. In addition, numerical dispersion of concentration profile resolution is eliminated. The applicability of the method is illustrated using an example water distribution network. Enhancement of distribution system water quality management is a principal benefit of the methodology.

Explicit network calibration for multiple loading conditions

Abstract A semi-analytical methodology has been developed for use in calibrating hydraulic network models under multiple demand loading conditions. The resulting algorithm is able to correlate the observed and predicted pressures through the use of global headloss adjustment factors. The proposed algorithm is shown to be computationally efficient and guaranteed to yield a converged solution in an expeditious manner.

Optimizing distribution storage water quality: A hydrodynamic approach

Abstract A rigorous three-dimensional hydrodynamic model of distribution reservoir water quality is developed for use in simulating chemical mixing and internal patterns of flow exhibited within distribution storage reservoirs. The model is predicated on the principles of computational fluid dynamics and considers the basic forces and energy of the mixing fluid. In this approach, the three-dimensional time-averaged Navier-Stokes fluid flow equations with a k-e turbulence model are discretized and are solved over a finite-difference grid across the reservoir geometry. The motion of fluid particles throughout the reservoir can then be determined as a function of space and time. The resulting model is both accurate and robust, and it can be applied readily to all types of storage reservoir configurations, characteristics, and hydraulic conditions. The proposed numerical model was tested for a number of locations in the United States by comparing the results with both bench-top and full-scale test data. The applicability of the model is demonstrated herein by application to a water plant clearwell. The effects of baffling on residence time distribution for disinfection effectiveness were also investigated, and conclusions are stated. The effective use of the proposed model can lead to improved designs, retrofitting plans for existing facilities, or modified operational policies for new or existing reservoirs, and to aid in optimizing distribution water quality and securing regulatory compliance and consumer satisfaction.

An explicit algorithm for calculating operating parameters for water networks

Abstract An explicit methodology has been developed for use in comprehensive modelling of water distribution networks. The resulting algorithm is able to calculate directly the distribution system operating variables required to exactly meet specified operating conditions. Operating variables include pump speed, control valve settings, pressure regulating valve settings, and settings for flow limiting (pressure sustaining) devices. Specified operating conditions represent stated minimum pressure and volumetric flow requirements at designated locations throughout the distribution system. The proposed algorithm is shown to be robust and efficient, and guaranteed to converge in an expeditious manner. The wide range of capabilities and flexibility of the proposed approach are demonstrated using an example network. Enhancement of real-time modelling is a principal benefit of the methodology.

Convergence of Newton method in nonlinear network analysis

The convergence of Newton method in nonlinear network analysis is discussed. It is shown that formulating the nonlinear edge flow resistances in terms of edge flow rates (Flow method) or corrected loop flow rates (Loop method) gives better convergence than the nodal head or pressure formulation (Node method). This evaluation is based on the estimation of the magnitude of the radius of attraction for the Newton method. Our result applies to both water and low pressure gas networks.

EXPLICIT CALCULATION OF WATER QUALITY PARAMETERS IN PIPE DISTRIBUTION SYSTEMS

Abstract Explicit algorithms have been developed for use in water quality studies and management of distribution networks with sources of dissimilar quality. The proposed algorithms can be effectively used for directly determining a variety of blended water quality parameters for a given set of network loading and operational conditions. The parameters include the spatial distribution of constituent concentrations, the flow influence characteristics of supply sources, and the water age distribution throughout the system. The developed algorithms are formulated analytically from mass balance relationships as contingent linear boundary value problems in conjunction with a topological sorting methodology. The resulting formulations yield coefficient matrices, of order equal to the number of junction nodes, that are triangular and positive definite. The parameter solutions sought are, thus, derived through a direct application of a one step substitution process. The proposed algorithms are both robust and eff...

On the solvability of water distribution networks with unknown pipe characteristics

Necessary and sufficient conditions for the solvability of water distribution networks with unknown pipe characteristics are developed. They are predicated on the interdependence between the unknown pipe characteristics and the network hydraulic performance. These characteristics are determined to exactly satisfy defined values of nonlinear boundary equality constraints. The constraint set consists of the stated supply pressure or energy grade requirements to be maintained at critical locations throughout the distribution network. The determination of such conditions is important for a comprehensive and effective modelling and optimization of water networks.

Using Genetic Algorithms for Water Distribution System Optimization

Computer optimization models are vital for the evaluation and management of hydraulic infrastructure systems. While many water distribution optimization algorithms have been developed few are currently in practical use by water utilities mainly due to the lack of suitable packaging, maintenance, and support. This paper describes the development of a comprehensive decision support system for use in the effective management of water distribution piping systems. The developed software integrates geographical information system for spatial database management and analysis with optimization theory in a built-in AutoCAD interface to provide a computer aided decision-support tool for water engineers. The interactive graphical interface offers an informative structured framework for spatial data collection and management, network optimization, and results presentation. The optimization model uses an efficient variation of the genetic algorithm for solving network model calibration, field sampling design, pump scheduling, and network design and rehabilitation problems in an optimal fashion. The integrated software system will greatly assist water utilities in planning, designing, and operating sound systems and in optimizing their capital improvement programs.

An explicit approach for modelling closed pipes in water networks

Abstract An explicit approach has been developed for use in modelling closed pipes in water distribution networks. The explicit approach is able to directly incorporate the zero-flow effect of closed pipes into the overall network modelling process. The resulting method is based on an analytical reformulation of the quasilinear set of flow continuity and energy equations governing the network hydraulics in terms of energy displacement for the individual closed pipes that exactly meet the corresponding zero-flow boundary constraint imposed. The proposed algorithm is shown to be robust and efficient, and is guaranteed to converge in an expeditious manner. The method compares favorably with others by eliminating numerical diffusion and computational instability or repetitive network topology alterations suffered by the previous procedures. An example application is presented. Enhancement of mathematical modelling of water distribution networks is a principal benefit of this methodology.