Mathematical Modelling Of Clean Water Treatment Works .
UNIVERSITY COLLEGE LONDONDOCTORAL THESISMathematical Modelling of CleanWater Treatment WorksFolashade AKINMOLAYANA thesis submitted in ful llment of the requirementsfor the degree of Doctor of Philosphyin theCentre for Process Systems EngineeringDepartment of Chemical Engineering2017
I, Folashade AKINMOLAYAN, con rm that the work presented in this thesis is my own.Where information has been derived from other sources, I con rm that this has beenindicated in the thesis.SignatureDatei
AcknowledgementsThrough the years, I met so many wonderful people I am thankful for seeing me throughthis journey. Firstly, I would like the thank Professor Eva Sorensen for guiding a nervousstudent. You have played so many important roles in my life, initially a supervisor, aline manager, a friend and a constant shoulder to cry on. Thank you for correcting mewhen I was wrong (spelling and grammar especially), supporting me when I was right,and taking time out of your own life to ensure I did not procrastinate. You have helpmould me into the woman I have become today and I am beyond grateful our pathscrossed. I am grateful to my secondary supervisor Professor Nina Thornhill for all theinteresting discussions and your eye for details.To the close friends before this journey: Gurbinder, Sa e, Folake, Beverley, Mickal,Bianca, Sara, Na sah, Belquis, The Lous , Vidal and Carl.To the friends I met along the way:Rema, Matt, Mithila, Ishanka, Chara, Noor,Matteo, George and Alex.You have all played a crucial role in this chapter of my life.To Eria and Vivien, thank you for the long distance encouragement and entertainment.To my lovely ladies lunch club:Emanuela, Kate, and Elpida thank you for yourcontinued words of wisdom and encouragement.Vassilis and Asif, you both are my PPSE best friends who always kept me laughing.You both understood the pains and joys of computer modelling. Thank you for yourcontinued support and random adventures.Above all I wish to thank my parents, siblings and nephews for their faith in me, theirunconditional love, their endless support and understanding throughout all these years.None of this would be possible without them and to them I am eternally grateful.Special mentions go to my dad and my brother Ore for taking care of me when Ineglected to take care of myself, for the sweet treats when I craved them but mostlyfor being there to kill the spiders whenever I needed them no matter the time of night.Dami - thank you for your constant love, motivation, encouragement, Thai food andpatience at all times.We shared this PhD journey together and you always cheeredme up, stood by me through the good, bad and the panic because I could not solve an error in my code.ii
AbstractOne of the biggest operational risks to water companies arises from their ability tocontrol the day-to-day management of their water treatment plants. With increasingpressures to remain competitive, companies are looking for solutions to be able to makepredictions on how their treatment processes can be improved. This work focuses onmathematical modelling and optimisation of clean water treatment processes. The mainmotivation is to provide tools which water companies can use to predict the performanceof their plants to enable better control of risks and uncertainties.Most modelling work within water operations has so far been based on empiricalobservations rather than on mathematically describable relationships of the process aswill be considered in this work. Mathematical models are essential to describe, predictand control the complicated interactions between the di erent parts of the treatmentprocess, a concept which is well understood within the process industry but not yetestablished within the water treatment industry. This work will also consider the levelof modelling detail actually required to accurately represent a water treatment plant.This thesis develops the conceptual understanding of clean water treatment processesutilising rst principles modelling techniques.The main objective of this work isthe consideration of a complete mathematical model of an entire water treatmentplant, which enables a wider view on how changes in one processing unit will a ectthe treatment process as a whole.The performance of the process models are rstveri ed individually and are then combined to enable the simulation of a complete watertreatment work. By using detailed modelling (especially gPROMS utilised in this work)requires specialist software knowledge. Without knowledge of advanced simulation toolsor having a background in process modelling, the detailed models developed in thiswork would not be fully utilised if implemented in the water industry, if utilised atall.A systematic framework is presented for the development of simpler surrogatemodels that can be used to predict the e uent suspended solids concentration, for agiven number of independent variables. This approach can provide valuable guidancein clean water treatment process design and operation, thus providing a tool to achievebetter day-to-day performance management.
My thesis in a drop.
ContentsDeclaration of Authorship . . . . . . . . . . . . . . . . . . . . . . . . . .iAcknowlegdements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iiAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iiiList of Figures1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviiiList of Notationxxiii. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .General introduction11.1Scope11.2Water Industry: raw water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4. . . . . . . . . . . . . . . . . . . . . . . . .51.3Clean water treatment process . . . . . . . . . . . . . . . . . . . . . . .71.4Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101.5Objectives and contributions of this thesis. . . . . . . . . . . . . . . .131.6Organisation of this thesis. . . . . . . . . . . . . . . . . . . . . . . . .131.2.1Raw water sourcesv
viCONTENTS2Literature review2.1Introduction2.2What is Process Systems Engineering (PSE)?2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15162.2.1Fundamentals and methodologies of PSE. . . . . . . . . . . .172.2.2Enterprise-wide optimisation . . . . . . . . . . . . . . . . . . . .20Mathematical modelling - clean water industry . . . . . . . . . . . . . .212.3.1Turbidity vs. Suspended solids concentration. . . . . . . . . .232.3.2Coagulation and occulation. . . . . . . . . . . . . . . . . . .242.3.3Clari cation. . . . . . . . . . . . . . . . . . . . . . . . . . . .332.3.3.12.3.42.3.5Flotation tank studiesFiltration2.3.4.1. . . . . . . . . . . . . . . . . .43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48One-dimensional modelling. . . . . . . . . . . . . . .51. . . . . . . . . . . . . . . . . . . . . . . . . . . . .59Kinetic model . . . . . . . . . . . . . . . . . . . . . . .60Disinfection2.3.5.13152.4Challenges and opportunities. . . . . . . . . . . . . . . . . . . . . . .652.5Overall concluding remarks. . . . . . . . . . . . . . . . . . . . . . . .662.6Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68Modelling of clean water treatment units703.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .703.2Modelling of coagulation and occulation . . . . . . . . . . . . . . . . .713.2.1Unit principle713.2.2Model development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72
viiCONTENTS3.33.443.2.3Numerical simulation and validation. . . . . . . . . . . . . . .803.2.4Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . .85Modelling of clari cation process. . . . . . . . . . . . . . . . . . . . .85. . . . . . . . . . . . . . . . . . . . . . . . . . .863.3.1Unit principle3.3.2Model development. . . . . . . . . . . . . . . . . . . . . . . .863.3.3Model simulation and validation . . . . . . . . . . . . . . . . . .903.3.4Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . .93Modelling of ltration. . . . . . . . . . . . . . . . . . . . . . . . . . .943.4.1Unit principle. . . . . . . . . . . . . . . . . . . . . . . . . . .943.4.2Model development3.4.3Model simulation and validation. . . . . . . . . . . . . . . . .1023.4.4Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . .1073.5General discussion of model development . . . . . . . . . . . . . . . . .1073.6Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108. . . . . . . . . . . . . . . . . . . . . . . .Complete model of clean water treatment941104.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1104.2Unit con gurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1114.2.11114.3Integration of units . . . . . . . . . . . . . . . . . . . . . . . . .Overall plant performance. . . . . . . . . . . . . . . . . . . . . . . . .1134.3.1Scenario 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1134.3.2Scenario 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1184.3.3Scenario 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1224.4Computational statistics. . . . . . . . . . . . . . . . . . . . . . . . . .1284.5Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129
viiiCONTENTS5Surrogate models for process integration1315.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1315.2Surrogate modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1325.2.1Arti cial neural network1335.2.2Polynomial response surface methodology. . . . . . . . . . . .1345.2.3Full factorial design . . . . . . . . . . . . . . . . . . . . . . . . .135Coagulation- occulation surrogate model . . . . . . . . . . . . . . . . .1375.3.1Results and validation. . . . . . . . . . . . . . . . . . . . . . .1435.3.2Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . .150Clari cation surrogate model . . . . . . . . . . . . . . . . . . . . . . . .1505.4.1Results and validation. . . . . . . . . . . . . . . . . . . . . . .1545.4.2Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . .160Filtration surrogate model . . . . . . . . . . . . . . . . . . . . . . . . .1615.5.1Results and validation. . . . . . . . . . . . . . . . . . . . . . .1645.5.2Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . .1675.35.45.55.65.7. . . . . . . . . . . . . . . . . . . . . .Disinfection surrogate model. . . . . . . . . . . . . . . . . . . . . . .1675.6.1Results and validation. . . . . . . . . . . . . . . . . . . . . . .1715.6.2Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . .177Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179
ixCONTENTS6Conclusions and recommendations6.16.26.3Review of project deliverables180. . . . . . . . . . . . . . . . . . . . . . .6.1.1Critical assessment of the current state-of art6.1.2Dynamic modelling of conventional clean water treatment work1816.1.3Surrogate model development of clean water treatment work . .1836.1.4Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . .183Direction for future research . . . . . . . . . . . . . . . . . . . . . . . .1846.2.1Use of numerical simulation tools in drinking water treatment.1846.2.2Plant optimisation. . . . . . . . . . . . . . . . . . . . . . . . .1866.2.3Model calibration . . . . . . . . . . . . . . . . . . . . . . . . . .1896.2.4Broader recommendations. . . . . . . . . . . . . . . . . . . . .190Summary and main contributions . . . . . . . . . . . . . . . . . . . . .191List of Communications. . . . . . . . . .180. . . . . . . . . . . . . . . . . . . . . . . . . . .A181194219A.1General introductionA.1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . .Water quality regulations. . . . . . . . . . . . . . . . . . . . .B219219222B.1Modelling the conventional clean water treatment process unitsB.1.1Modelling coagulation and occulation unit. . . .222. . . . . . . . . . .222C224C.1Implementation of SST model . . . . . . . . . . . . . . . . . . . . . . .224C.1.1224Approximation of convective ux. . . . . . . . . . . . . . . . .
List of Figures1.1Breakdown of the water availability in the world. . . . . . .21.2Public water supply, England and Wales . . . . . . . . . . . . .31.3EU per capita water consumption (DEFRA, 2014).41.4Illustration to show how water enters the unsaturated zone. . . . . .(soil moisture) and the saturated zone (groundwater) (Environment and Climate Change Canada, 2013).1.5. . . . . . . . .6Illustration to show an artesian well, which has been drilledinto a con ned aquifer, and a water table well. The brownlayer represents an impermeable layer (Environment andClimate Change Canada, 2013). . . . . . . . . . . . . . . . . . .71.6Main technologies available for water treatment processes.82.1Graphical representation of the modelling process. Adapted. . . . . . . . . . . . .19with permissions from Sargent (2005).2.2Integrated framework for PSE in a clean water treatmentplant.2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Typical process diagram for clean water treatment plant (withexamples of variations).2.421. . . . . . . . . . . . . . . . . . . . . .22Possible particle collision trajectories. (a) Rectilinear model.(b) Curvilinear model. Adapted with permissions from Hanand Lawler (1992). . . . . . . . . . . . . . . . . . . . . . . . .x27
xiLIST OF FIGURES2.5Cross-section of solid-contact clari er (AWWA CommitteeReport, 1951).2.6. . . . . . . . . . . . . . . . . . . . . . . . . . . .Schematic overview of an ideal one-dimensional clari er. Adaptedwith permissions from Burger et al. (2011). . . . . . . . . .2.7Schematic overview of a dissolved air otation unit.2.8Typical curve showing lter performance over di erent stages2.935. . . . .3944of transient ltration. . . . . . . . . . . . . . . . . . . . . . . . .51Filtration: Porous medium element.52. . . . . . . . . . . . . . .2.10 Basic transport mechanisms in a granular lter (Binnie andKimber, 2009; Tobiason et al., 2010). . . . . . . . . . . . . .2.11 Particle attachment to lter media and to other particles.3.1. .5455Schematic impressions of a) coagulation and occulation owsheet,b) oc formation chamber. . . . . . . . . . . . . . . . . . . .3.2Schematic diagram of multi-compartment occulator. . . .3.3Sensitivity analysis: Relationship between the velocity gradient, G, and the total hydraulic retention (residence) time,7374τ,for two di erent case studies ( occulation chamber with oneand four compartments, respectively) for two di erent valuesof collision constant,KA and break-up constant, KB .a) Collision constant KA 5.1 10 5 and break-up constantKB 1.1 10 7b) Smaller collision constant KA 1.8 10 5 and break-upconstant KB 0.8 10 7 . . . . . . . . . . . . . . . . . . . . . . .3.483Sensitivity analysis: Relationship between primary particlesforming suspended particles ( ocs) in a rapid mixing unitand how the system would react to speci c changes.disturbances are implemented (black dotted line):Two1) 10%increase in the primary particle concentration, and 2) 20%decrease in the impeller speed or velocity gradient. . . . . .84
xiiLIST OF FIGURES3.5Schematic impression of an ideal secondary settling tank (SST)unit.3.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87A dynamic simulation of the convection-di usion clari er modelstarting at steady state with the parameters found in Table3.3.a) literature simulation with 10 discretised points (Burgeret al., 2012).b) literature reference simulation, both are reproduced fromliterature with permission (Burger et al., 2012).c) simulation using the model shown in Equation 3.3.1 with10 discretised points.3.7. . . . . . . . . . . . . . . . . . . . . . . .92A steady state simulation of the sedimentation clari cationunit using the parameters in Table 3.3.The concentrationpro le of di erent discretisation levels:10, 20 and 30 areshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .933.8Schematic of rapid gravity ltration unit. . . . . . . . . . . . .953.9The changes in relative suspended particle concentration withltration time at 3 di erent positions in space (z 0.045 m,z 0.45 m and z 0.85 m). The lter column has a depthof 0.9m has been simulated with 100 discretised layers.a) shows the graph reproduced with permissions from literature (Han et al., 2008).b) show the graph obtained from modelling in gPROMS. . . .1043.10 Relative e uent suspended solids concentration and headlossthrough the lter column during the ltration. The values ofthe transitional speci c deposit valuemg/L (black) to 600 mg/L (red).σc ,is changed from 300. . . . . . . . . . . . . . . . . . .1053.11 The e ect of ow rates (4 m/s, 5 m/s, 6 m/s and 7 m/s) onrelative e uent suspended solids concentration. . . . . . . .106. . . . . . . . . . . . .1124.1Illustration of plug ow reactor model.4.2Illustration of the individual mathematical model connectionswith the pipeline model. . . . . . . . . . . . . . . . . . . . . .113
xiiiLIST OF FIGURES4.3Illustrative owsheet of a conventional clean water treatmentwork that will be used in the simulations for scenario 1 and 2. 1144.4Scenario 1:model.4.54.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Scenario 2:model.Simulation of complete clean water treatment116Simulation of complete clean water treatment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120Illustrative owsheet of a conventional clean water treatmentwork that will be used in the simulations for scenario 3 & 4incorporating a sludge recycle unit. . . . . . . . . . . . . . . . .4.7Scenario 3:Simulation of complete clean water treatmentmodel incorporating a sludge recycle unit.4.8Scenario 4:123. . . . . . . . . . .124Simulation of complete clean water treatmentmodel incorporating multiple processing units for clari cationand ltration incorporating a sludge recycle unit.5.1126Typical structure of a feedforward arti cial neural network(ANN).5.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133Rapid mixing: surrogate versus detailed modelling responsesfor e uent concentration for a) normal model responses andb)"logged" model responses. The dashed line represent thex y line on a parity plot. . . . . . . . . . . . . . . . . . . . . . .5.3144Coagulation/ occulation via rapid mixing: 2D graphical domain representation of the ranges for the variables and thedata used for veri cation in Table 5.5.5.4. . . . . . . . . . . . .145Flocculation in compartments: surrogate versus detailed modelling responses for e uent concentration for a) normal modelresponses and b)"logged" model responses. The dashed linerepresent the x y line on a parity plot.5.5. . . . . . . . . . . . .148Sedimentation clari cation: surrogate versus detailed modelling responses for e uent suspended solids concentrationfor a) normal model responses and b)"logged" model responses.The dashed line represent the x y line on a parity plot. . . .155
xivLIST OF FIGURES5.6Clari cation: 3D graphical domain representation of the rangesfor the runs within the ranges (blue dots) and outside of theranges (black dots) and the data used for veri cation in Tables5.10 and 5.11.5.7. . . . . . . . . . . . . . . . . . . . . . . . . . . .156Sedimentation clari cation: surrogate versus detailed modelling responses for under ow suspended solids concentrationfor a) normal model responses and b) "logged" model responses. The dashed line represent the x y line on a parityplot.5.8. . . . . . . . . . . . .
mathematical modelling and optimisation of clean water treatment processes. The main motivation is to provide tools which water companies can use to predict the performance of their plants to enable better control of risks and uncertainties. Most modelling work within water operations has so far been based on empirical
Mathematical modelling, the socio-critical perspective and the reflexive discussions * 133 . Jonei Cerqueira Barbosa . Mathematical modelling and environmental education 145. Ademir Donizeti Caldeira . Mathematical models in
Mathematical Modelling and Mathematical Competencies: The case of Biology students. . benefits associated with engaging students in mathematical modeling. There is a ‘red thread’ . These studies include an international comparison of secondary school students’ competence pro
So, I say mathematical modeling is a way of life. Keyword: Mathematical modelling, Mathematical thinking style, Applied 1. Introduction: Applied Mathematical modeling welcomes contributions on research related to the mathematical modeling of e
Common sense (19), mathematical knowledge and experience in modelling (7), both modelling experience and common sense (3), the given information (1), idea of spread of disease (1), I have never seen such problems in mathematical context before, so I don’t
Reinhard Illner et al. (2005): “Mathematical modelling is a subject without boundaries in every conceivable sense.” Andrew Fowler (1997): “Mathematical modelling is a subject that is difficult to teach . one learns it by practice: There are no set rules, and an understanding of the ‘right’ way to model can only be
Note 3: Physical Systems Modelling XMUT315 - Note 3 - 2 Figure 1: Modelling of a physical system with scaled physical model On the other hand, to represent the physical system in addition to scaled model, we often use mathematical and numerical models. Mathematical model is described as function and variable in mathematical equation.
through MM processes not provide direct solutions. Theoretical Background Lingefjärd (2007) stated that “mathematical modelling is not a body of mathematical knowledge but rather a collection of general principles which experience has proved to be helpful in the process of applying mathematical know-how to analyze problems” (p. 476).
Agile describes a set of guiding principles that uses iterative approach for software development Agile is a practice that helps continuous iteration of development and testing in the software development process. In this model, development and testing activities are concurrent, unlike the Waterfall model. This mindset allows more communication .
