Hydraulic And Water Quality Simulation And Uncertainty Analysis Of Water Distribution System Models

The construction and application of water distribution model (WDM) are essentialmeasure and approaches for realizing the modernization management of waterdistribution system (WDS), which can get hydraulic and quality conditions of WDSandprovide support for optimal operation and scientific management. Because the nodaldemand, pipe roughness, bulk decay coefficient and wall decay coefficient can’t bemeasured directly, the WDM constructed needs to be calibrated based on themeasurements of nodal pressure, pipe flow and water quality. How to calibrate theWDM with insufficient measurements and to improve the calibration efficiency are thehot and difficult subjects in the research filed of WDS.The weighted least squares (WLS) has been proposed for on hydraulic modelcalibration, it employs gradient of state variables as the search vector, has the advantageof rapid convergence and high computation efficiency. The calculation of Jacobianmatrix is the key to usethe Gradient-based algorithm for parametercalibration, this paperproposes the matrix analysis method todeduce the analytical solutionof Jacobian matrixof hydraulic state variables. Analytic solution can be obtainedafter a hydraulic modelcalculation, avoiding the process of repeated hydraulic model calculation when theJacobian matrix is calculated byperturbation method. The calculation of analyticalsolution is described in detail with small network, and analytical solution is comparedwith perturbation method.Jacobian matrix also include the information of parametersensitivity,it can facilitate the parameter sensitivity analysis.When the Jacobian matrix is obtained through matrix calculation, the WLS canrealize real-time node demand calibration. The WLS is used for small network nodedemand calibration, even under the condition of monitoring data contain error, the nodedemand calibrationisclose to the real value, the check result is good. The same methodisused to calibratereal-time node demandof T town water distribution system, the dailychange curve of node demand is obtained.The node pressure and pipe flow calculatedby model is compared with SCADA observed data at monitoring node and pipe,theabsolute average of node pressure is0.39m andpipe flow is3.56m3/h, it satisfies thestandard of hydraulic model calibration, the hydraulic simulation results can betterresponse real-time hydraulic condition of T town water distribution system.The water age characteristics of T town water distribution system are studiedbasedon calibrated hydraulic model. The node age of T town water supply networkis less than 1d, water quality update fast, and water quality is good.The starts of node age curveisstraight line whoseslope is1, the form of node age curve is similar for near node. Thewater quality monitoring stations should contain nodes with differentnode age curve.Jacobian matrix of water quality is related with time, which shouldbe obtained byperturbation method,the calculated Jacobian matrix based on perturbation(0.001)satisfies theprecision requirement of water quality calibration. The residualchlorinedecay coefficientcalibration of example water supply network is based onWLS,when there is a small error between water quality calculated by initial waterquality model and observed at monitoring nodes, the target solution of residual chlorinedecay coefficient can be obtained quickly, it’s the advantage of WLS in water qualitymodel calibration. The preliminary residual chlorine model is used to simulate residualchlorine concentration of T town water distribution system, the quality simulationresults show that residual chlorine concentration in pipe network satisfies water qualitystandard. The water quality simulation results are overall smaller than measured values,residual chlorine model of T town water distribution system need to improve in thefuture.In order to analyze the influence of water distribution system hydraulic and qualitycharacteristics by the uncertainty ofinput parameters, and search for the early warningcriterion of water supply networkaccident,Monte Carlo Simulation (MCS) has beenused to calculate the uncertainty distribution of node pressure and water quality. Theresults show that, the largest uncertainties of node pressure and water quality occurwhen all input parameters are uncertain, node demand has more effect on node pressureuncertainty than pipe roughness for the single parameter, and it is applicableon waterquality; residual chlorine reaction coefficient has the most effect on node water qualityuncertainty. It’s suggested that the lower limit of largest uncertainties of node pressureand water quality at monitoring nodes should be set as early warning criticalvalue ofhydraulic and quality accidentseparately.