Abstract
Cellular Automata (CA) is an evolutionary computing technique that makes discrete idealizations of differential equations and represents the physical system at the mesoscopic scale. A novel CA approach for predicting the temporal and spatial variations of chlorine in Water Distribution Systems (WDSs) is presented in this paper. Random Walk Particle Tracking (RWPT), a stochastic Lagrangian technique, is used to represent the advection and dispersion processes. A one-dimensional CA-based reactive-transport model for chlorine, named as RWPT_CA model, incorporating advective-dispersive transport mechanism is developed and demonstrated. The significance of the cell dimension in the model algorithm is ascertained, and a deterministic approach is formulated for its selection. An indirect numerical solution technique is developed to improve the computational efficiency of the CA algorithm and to minimize the restrictions in the process of discretization of mass into equivalent particles. The numerical accuracy of the proposed RWPT_CA model is verified by applying it on to a benchmark problem. The RWPT_CA model provided excellent representations of the chlorine concentration profiles for low to medium range dispersion in WDSs. The model testing on a benchmark problem from the literature, well tested by researchers, revealed its effectiveness to derive the chlorine concentration patterns under dynamic hydraulic conditions. The dispersion mechanism was found significant in controlling the temporospatial distribution of chlorine at the nodes farther from the source nodes. The models which consider only advective transport mechanism were found over-predicting the chlorine concentrations, and thereby, establishing untrue representations of the quality of the delivered water.
Similar content being viewed by others
References
Abokifa AA, Yang YJ, Lo CS, Biswas P (2016) Investigating the role of biofilms in trihalomethane formation in water distribution systems with a multicomponent model. Water Res 104:208–219. https://doi.org/10.1016/j.watres.2016.08.006
Axworthy DH, Karney BW (1996) Modeling low velocity/high dispersion flow in water distribution systems. J Water Resour Plan Manag 122:218–221
Barry DA, Bajracharya K, Miller CT (1996) Alternative split-operator approach for solving chemical reaction/groundwater transport models. Adv Water Resour 19:261–275. https://doi.org/10.1016/0309-1708(96)00002-4
Bivins AW, Sumner T, Kumpel E, Howard G, Cumming O, Ross I, Nelson K, Brown J (2017) Estimating infection risks and the global burden of diarrheal disease attributable to intermittent water supply using QMRA. Environ Sci Technol 51:7542–7551. https://doi.org/10.1021/acs.est.7b01014
Boulos PF, Altman T, Jarrige PA, Collevati F (1994) An event-driven method for modelling contaminant propagation in water networks. Appl Math Model 18:84–92. https://doi.org/10.1016/0307-904X(94)90163-5
Brown D, Bridgeman J, West JR (2011) Predicting chlorine decay and THM formation in water supply systems. Rev Environ Sci Biotechnol 10:79–99. https://doi.org/10.1007/s11157-011-9229-8
Castro AP (1996) Dynamic Water Quality Modeling using Cellular Automata. Virginia Polytechnic Institute and State University
Chaudhry MH, Islam MR (1995) Water quality modeling in pipe networks. In: Improving Efficiency and Reliability in Water Distribution Systems, Cabrera E, Vela AF (eds.). Kluwer Academic Publishers, pp 369–393
Clark RM (2015) The USEPA’s distribution system water quality modelling program: A historical perspective. Water Environ J 29:320–330. https://doi.org/10.1111/wej.12132
Clark RM, Rossman LA, Wymer LJ (1995) Modeling distribution system water quality: Regulatory implications. J Water Resour Plan Manag 121:423–428. https://doi.org/10.1061/(ASCE)0733-9496(1995)121:6(423)
D’Souza CD, Kumar MSM (2010) Comparison of ANN models for predicting water quality in distribution systems. J Am Water Work Assoc 102:92−+
Digiano FA, Zhang W (2005) Pipe section reactor to evaluate chlorine-wall reaction. J Am Water Works Assoc 97:74–85. https://doi.org/10.2307/41312005
Goyal VR, Patel HM (2015) Analysis of residual chlorine in simple drinking water distribution system with intermittent water supply. Appl Water Sci 5:311–319. https://doi.org/10.1007/s13201-014-0193-7
Grayman W, Clark R, Males RM (1988) Contaminant propagation in distribution systems. J Environ Eng 114:929–943. https://doi.org/10.1061/(ASCE)0733-9372(1988)114:4(929)
Hallam NB, West JR, Forster CF, Powell JC, Spencer I (2002) The decay of chlorine associated with the pipe wall in water distribution systems. Water Res 36:3479–3488. https://doi.org/10.1016/S0043-1354(02)00056-8
Helbling DE, Vanbriesen JM (2009) Modeling residual chlorine response to a microbial contamination event in drinking water distribution systems. J Environ Eng 135:918–927
Karapiperis T (1997) Cellular automaton models of reaction-transport processes. Model. Aquat. Chem, In, pp 495–524
Karapiperis T, Blankleider B, Kaneko K (1994) Cellular automaton model of reaction-transport processes. Phys D 78:30–64. https://doi.org/10.1016/0167-2789(94)00093-X
Lachowicz M (2011) Microscopic, mesoscopic and macroscopic descriptions of complex systems. Probabilistic Eng Mech 26:54–60. https://doi.org/10.1016/j.probengmech.2010.06.007
Liou CP, Kroon JR (1987) Modeling the propagation of waterborne substances in distribution networks. J Am Water Works Assoc 79:54–58
Mahrous YM, Al-Ghamdi AS, Elfeki AMM (2016) A two-state random walk approach for modeling chlorine decay in water distribution network. Int J Civ Environ Eng 15:39–47
Monteiro L, Figueiredo D, Dias S, Freitas R, Covas D, Menaia J, Coelho ST (2014) Modeling of chlorine decay in drinking water supply systems using EPANET MSX. Procedia Eng 70:1192–1200. https://doi.org/10.1016/j.proeng.2014.02.132
Morale D, Capasso V, Oelschläger K (2005) An interacting particle system modelling aggregation behavior: From individuals to populations. J Math Biol 50:49–66. https://doi.org/10.1007/s00285-004-0279-1
Munavalli GR, Mohan Kumar MS (2005) Water quality parameter estimation in a distribution system under dynamic state. Water Res 39:4287–4298. https://doi.org/10.1016/j.watres.2005.07.043
Munavalli GR, MohanKumar MS (2004) Dynamic simulation of multicomponent reaction transport in water distribution systems. Water Res 38:1971–1988. https://doi.org/10.1016/j.watres.2004.01.025
Naser G, Karney BW (2007) A 2-D transient multicomponent simulation model : Application to pipe wall corrosion. J Hydro-Environment Res 1:56–69. https://doi.org/10.1016/j.jher.2007.04.004
Nikolopoulos D, Risva K, Makropoulos C (2018) A cellular automata urban growth model for water resources strategic planning. In: HIC 2018. 13th International Conference on Hydroinformatics Engineering. pp 1557–1545
Palanichamy J, Schüttrumpf H, Palani S (2008) A probabilistic cellular automaton for two dimensional contaminant transport simulation in ground water. Water Sci Technol 58:2083–2092. https://doi.org/10.2166/wst.2008.824
Peirovi Minaee R, Afsharnia M, Moghaddam A, Ebrahimi AA, Askarishahi M, Mokhtari M (2019) Calibration of water quality model for distribution networks using genetic algorithm, particle swarm optimization, and hybrid methods. MethodsX 6:540–548. https://doi.org/10.1016/j.mex.2019.03.008
Powell JC, Hallam NB, West JR, Forster CF, Simms J (2000) Factors which control bulk chlorine decay rates. Water Res 34:117–126. https://doi.org/10.1016/S0043-1354(99)00097-4
Prickett TA, Naymik TG, Lonnquist CG (1981) A “Random-Walk” Solute Transport Model for Selected Groundwater Quality Evaluations. Bull (State Illinois) 65:108
Rossman LA (1994) EPANET Users Manual. Natl. Risk Manag. Res. Lab. US Environ. Prot. Agency, Cincinatti
Rossman LA (2000) EPANET 2: users manual. Natl. Risk Manag. Res. Lab. US Environ. Prot. Agency, Cincinatti
Rossman LA, Boulos PF (1996) Numerical methods for modeling water quality in distribution systems: a comparison. J Water Resour Plan Manag 122:137–146. https://doi.org/10.1061/(ASCE)0733-9496(1996)122:2(137)
Rossman LA, Boulos PF, Altman T (1993) Discrete volume-element method for network water-quality models. J Water Resour Plan Manag 119:505–517
Rossman LA, Clark RM, Grayman WM (1994) Modeling chlorine residuals in drinking-water distribution systems. J Environ Eng 120:803–820
Salamon P, Fernandez-Garcia D, Gomez-Hernandez JJ (2006) A review and numerical assessment of the random walk particle tracking method. J Contam Hydrol 87:277–305
Sattar AMA (2014) Gene expression models for the prediction of longitudinal dispersion coefficients in transitional and turbulent pipe flow. J Pipeline Syst Eng Pract 5:04013011. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000153
Seyoum AG, Tanyimboh TT (2017) Integration of hydraulic and water quality modelling in distribution networks: EPANET-PMX. Water Resour Manag 31:4485–4503. https://doi.org/10.1007/s11269-017-1760-0
Taylor G (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proc R Soc A Math Phys Eng Sci 219:186–203. https://doi.org/10.1098/rspa.1953.0139
Tian Y, Guo H, Wang Y, Liu Y, Shan J (2017) Behaviour of haloacetic acids in drinking water distribution systems. Trans Tianjin Univ 23:93–99. https://doi.org/10.1007/s12209-016-0026-x
Vasconcelos JJ, Rossman LA, Grayman WM, Boulos PF, Clark RM (1997) Kinetics of chlorine decay. J Am Water Works Assoc 89:54–65. https://doi.org/10.1002/j.1551-8833.1997.tb08259.x
Zhang GR, Kiene L, Wable O, Chan US, Duguet JP (1992) Modelling of chlorine residual in the water distribution network of Macao. Environ Technol 13:937–946. https://doi.org/10.1080/09593339209385229
Zhang W, Miller CT, DiGiano FA (2004) Bacterial regrowth model for water distribution systems incorporating alternating split-operator solution technique. J Environ Eng 130:932–941. https://doi.org/10.1061/(ASCE)0733-9372(2004)130:9(932)
Zhang WD, DiGiano FA (2002) Comparison of bacterial regrowth in distribution systems using free chlorine and chloramine: a statistical study of causative factors. Water Res 36:1469–1482. https://doi.org/10.1016/S0043-1354(01)00361-X
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors have declared that no competing interests exist.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Abhijith, G.R., Mohan, S. Random Walk Particle Tracking Embedded Cellular Automata Model for Predicting Temporospatial Variations of Chlorine in Water Distribution Systems. Environ. Process. 7, 271–296 (2020). https://doi.org/10.1007/s40710-019-00406-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40710-019-00406-6