Modeling Chlorine Decay in Pipes using Two State Random Walk Approach
Y. M. Mahrous1, Abdullah S. Al-Ghamdi2, A. M. M. Elfeki3
1Y. M. Mahrous,  Department of Civil Engineering, King Abdulaziz University, Jeddah, Saudi Arabia.
2Abdullah S. Al-Ghamdi,  Professor, Department of Civil Engineering, King Abdulaziz University, Jeddah, Saudi Arabia.
3A. M. M. Elfeki, Professor Department of Civil and Environmental Engineering, King Abdulaziz University, Jeddah, Saudi Arabia.
Manuscript received on January 06, 2015. | Revised Manuscript received on February 21, 2015. | Manuscript published on February 28, 2015. PP: 110-115  | Volume-4 Issue-3, February 2015. | Retrieval Number:  C3769024315/2013©BEIESP

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Abstract: As water moves through a distribution network, maintaining residual chlorine is essential to prevent the regrowth or recontamination of pathogens and inactivate harmful microorganisms that might be present. On the other hand, chlorine should be kept below a certain level because of concerns about formation of carcinogenic disinfection by-products within the distribution system. In this paper, a stochastic model is proposed as a tool to offer a cost-effective way to study the spatial and temporal variation of a number of water quality constituents, including chlorine. Under a known set of hydraulic conditions and source input patterns, a two state random walk model is developed to simulate the decay of chlorine in a single pipe by solving the advective-transport equation. The model predicts how the concentration of dissolved chlorine varies with time and space throughout the flow. Linear non-equilibrium particle transfer from water bulk phase (state 1) to pipe wall phase (state 2) is handled using stochastic analogue of two-state Markovchain process with absorbing state. The model is verified by comparison with experimental observations available in the literature, EPANET 2 (Time- driven method) and other models.
Keywords: Chlorine decay, Markov-chain, Random walk, Pipes, Stochastic, Transport equation.