“Computational Civil Engineering - "Intersections" International Journal

“Computational Civil Engineering 2005”, International Symposium 2895 0.30 0.22 0.22 0.23 0.23 0.29 0.22 0.306 0.22 0.22 0.23 0.23 0.29 0.22 0.30 0.297 0.25 0.20 0.21 0.20 0.20 0.24 0.22 0.258 0.34 0.38 0.20 0.20 0.20 0.44 0.24 0.239 0.27 0.20 0.20 0.21 0.21 0.27 0.20 0.2710 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.2011 0.20 0.28 0.26 0.26 0.25 0.20 0.27 0.2012 0.23 0.20 0.43 0.32 0.21 0.31 0.20 0.21Table 5. Nodes for chlorine injection and injected quantities, in mg/L, corresponding to thewater flow rates transported in 24 hoursNODE/H 1 2 3 4 5 6 7 81 23.86 23.90 23.61 23.45 24.71 24.61 18.86 16.742 0.08 0.11 0.15 0.15 0.16 0.15 0.15 0.104 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.008 0.00 8.38 0.00 0.00 0.00 0.00 0.10 0.0012 1.67 3.20 0.00 0.00 11.78 13.77 15.89 58.29NODE/H 9 10 11 12 13 14 15 161 17.09 15.74 14.37 17.54 20.01 25.20 25.67 18.912 0.04 0.20 0.20 0.20 0.19 0.18 0.12 0.124 0.46 0.56 0.52 0.53 0.68 0.15 0.00 0.008 1.68 1.47 1.33 1.29 0.00 0.00 1.35 0.4612 0.00 15.26 39.81 0.00 42.67 0.00 0.00 15.67NODE/H 17 18 19 20 21 22 23 241 18.87 19.78 19.72 24.78 18.48 25.55 25.11 22.752 0.04 0.05 0.20 0.20 0.17 0.16 0.02 0.204 0.00 0.30 0.33 0.21 0.32 0.04 1.52 4.988 2.55 3.75 0.62 0.61 0.59 2.58 1.05 0.0012 0.00 3.63 20.54 2.08 0.00 1.70 0.00 0.003.3. Comparison between the cases :network without failures and the networkwiththe failure on (1-2) pipelineFor the situation from fig. 1, witout failures on pipelines, the unknowns in simplexproblem are the chlorine concentrations at nodes and the chlorine quantitiesintroduced in injection points with the condition as 0.2 mg/L ≤ concentration atnode ≤ 0.5 mg/L, but the optimum is obtained by minimization the sum of chlorinequantities introduced in injecting nodes. In fig. 2, 3, 4, 5, blue line presents theevolution of chlorine concentrations at nodes established in specified conditionsabove, for 2 and 5 nodes in 24 hours. In fig. 2 and 3 black line presents theconcentration calculated at 2 and 5 nodes by elimenation of pipeline (1-2), withthe same total chlorine quantities injected in network, the unknown being only thechlorine concentrations at nodes. In fig.3 and 4, black line shows the evolution ofchlorine in 24 hours for nodes 2 and 5 when the pipeline (1-2) is eliminated and asuplementary injection is introduced in node 2 to have an optimal solution.