在配水管網中餘氯傳輸模式之研究

Abstract

在配水管網中，餘氯的殘留關係到飲用水的安全。二維非穩態氯傳輸方程式可以描述餘氯在管中傳輸行為，此方程式考慮氯在軸向的傳流及延散作用，徑向的擴散作用和發生在水體及管壁上的一階消耗反應。目前已有許多數值模式被發展來模擬管網中餘氯的濃度，然而，在這個領域中解析解的研究是相當的稀少。本論文首先利用拉式轉換和廣義傅立葉級數展開推倒出在紊流中二維非穩態氯傳輸方程式的解析解，並且結合忽略軸向延散作用的解析解，及一系列數學方法，發展出可模擬管網中餘氯濃度的解析模式。此模式以美國康乃狄克州部份供水區域 (South Central Connecticut Regional Water Authority) 進行實際模擬配水管網中的餘氯濃度，結果將與一維質量傳輸模式 (Rossman et al., 1994) 比較。此外，本論文亦發展在紊流中穩態氯傳輸方程式的近似解。相較於 Biswas et al. (1993) 提出的近似解，此近似解具有容易計算與精度高的優點，並且可結合模擬退火演算法，發展出可以預測管壁消耗參數的方法。兩個案例研究驗證此近似解和數學方法的應用性。第一個案例是利用近似解模擬 Rossman (2006) 的餘氯消耗實驗結果，而另一案例為美國康乃狄克州部份供水區域(South Central Connecticut Regional Water Authority)中管壁消耗反應常數的預估結果。

The residual chlorine concentration in a water distribution system concerns safety of drinking water. A mathematical model can be used to describe the transport behavior for chlorine in a pipe. This model is mainly make up of two dimension chlorine transport equation (CTE) considering the mechanisms of advection and dispersion in axial direction, the diffusion in radial direction, and the first-order decay reactions in the bulk liquid phase and at pipe wall. Many numerical techniques were utilized to solve the 1-D model and only few studies have been devoted to the development of analytical solution in this area. This study first derives the analytical solution of unsteady CTE in turbulent flow through utilization of Laplace transform and generalized Fourier series expansion, which is to simplify differential term in the radial direction. This solution is further simplified in absence of dispersion in axial direction and integrates with a series of methodology to establish an analytical model for simulating the chlorine residual at any location in a water network. This analytical model is used to predict the chlorine concentration distribution in the water network of the South Central Connecticut Regional Water Authority (SCCRWA). The simulated results are compared with those obtained from a mass-transfer-based model developed by Rossman et al. (1994). Moreover, an approximate solution of the 2-D steady-state chlorine transport equation under turbulent flow is also developed. This new approximate solution has advantages of easy evaluation and good accuracy when compared with Biswas et al.’s approximate solution (1993). This thesis also develops a methodology which combines simulated annealing (SA) with this new approximate solution to determine the wall decay parameter. Two cases are chosen to demonstrate the application of the present approximate solution and methodology. The first case is to use this new approximate solution in simulating chlorine decay in pipes with the experiment-observed data given by Rossman (2006) while the second case presents the determination of the wall consumption at the end of pipe in the water network of SCCRWA.