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Urban Water

Department of Hydro Sciences, Institute for Urban Water Management. Global water aspects Introduction to urban water management Basics for systems description Water transport Matter transport Introduction to water supply Water extraction Water purification Water distribution

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Urban Water

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  1. Department of Hydro Sciences, Institute for Urban Water Management • Global water aspects • Introduction to urban water management • Basics for systems description • Water transport • Matter transport • Introduction to water supply • Water extraction • Water purification • Water distribution • Introduction to wastewater disposal • Urban drainage • Wastewater treatment • Sludge treatment Urban Water Peter Krebs Dresden, 2010

  2. Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 4 Matter transport 4.1 Introduction to transport phenomena 4.2 Transport processes 4.3 Reactor approach 4.4 Advection-dispersion approach

  3. Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 4 Matter transport 4.1 Introduction to transport phenomena 4.2 Transport processes 4.3 Reactor approach 4.4 Advection-dispersion approach

  4. Characteristics of compounds Passive solubles Travel ~ with water Often used to indicate velocity and residence-time distribution Solids Transport decoupled from flow Suspended solids and gravel Sedimentation and Erosion Reactive matter Can be solubles or solids Residence time and conditions in reactor important Reaction must be known for balancing

  5. Quiescent conditions Stirring Milk and sugar in a cup of coffee Molecular diffusion Turbulent diffusion

  6. L, t Tracer in a full pipe • Transport with flow • Longitudinal extension of tracer cloud • Decrease of peak concentration

  7. Residence-time distribution in a clarifier

  8. Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 4 Matter transport 4.1 Introduction to transport phenomena 4.2 Transport processes 4.3 Reactor approach 4.4 Advection-dispersion approach

  9. Example: Transport of compound with constant concentration C in a tube with cross section A: Advection Transport with water flow  no relative movement Flux

  10. Molecular diffusion Transport in the direction of decreasing concentration  1st Fick law • 1D approach; it also applies in a 2D or 3D system • Dmd,M is a specific value for a certain compound M • Dmd,M is a function of temperature

  11. C Diffusive flux x Turbulent diffusion Process similar to molecular diffusion, but some orders of magnitude more efficient • Dtd is dependant on flow and state of turbulence, not on the compound itself • Concentration gradients decrease !!

  12. Dispersion Dispersion is not transport relative to water, but inhomogeneous advection  In 1D formulation, dispersion “collapses on diffusion”

  13. v Sedimentation flux vS Sedimentation • Suspended particles have a transport component in gravity direction • In reactors this effect is used for particle separation • In transport systems, a sink or source term - depending on the operation conditions - is needed Examples: - 1D clarifier model - Sewer sediments

  14. Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 4 Matter transport 4.1 Introduction to transport phenomena 4.2 Transport processes 4.3 Reactor approach CSTR Plug-flow reactor CSTR in series 4.4 Advection-dispersion approach

  15. Q Q V C Cin C r Mass balance Continuously stirred tank reactor (CSTR) • Constant volume • Immediate mixing • Complete mixing  no concentration gradients • CReactor = COutlet

  16. 0-order reaction 1st-order reaction CSTR: steady state Mass balance

  17. Mass balance No input, no reaction CSTR: residence-time distribution (RTD) Tracer pulse is introduced to the inlet tracer concentration is measured in the outlet

  18. Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 4 Matter transport 4.1 Introduction to transport phenomena 4.2 Transport processes 4.3 Reactor approach CSTR Plug-flow reactor CSTR in series 4.4 Advection-dispersion approach

  19. A x dx Mass balance Plug-flow reactor • Constant volume • Constant cross section • No mixing (ev. lateral) • Concentration gradients along flow axes

  20. Plug-flow reactor: steady state Outlet concentrations: with x = L L/v =  Mass balance 0-order 1st order

  21. Plug-flow reactor: RTD Tracer pulse is introduced to the inlet tracer pulse appears in the outlet unchanged !!

  22. Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 4 Matter transport 4.1 Introduction to transport phenomena 4.2 Transport processes 4.3 Reactor approach CSTR Plug-flow reactor CSTR in series 4.4 Advection-dispersion approach

  23. Q Q Q Q Q r r r C2 Ci-1 Ci Cn-1 Cn V2 C2 Vi Ci Vn Cn 1st order reaction Reactor i CSTR cascade Q Q r Cin C1 V1 C1

  24. 2 Reactors n Reactors CSTR cascade: 1st order reaction (i) n = number of reactors Total volume

  25. n Reactors CSTR cascade: 1st order reaction (ii)

  26. 2nd reactor i-th reactor CSTR cascade: RTD (i) Initial condition in 1st reactor c0,1 as reference concentration 1st reactor

  27. Mean value Variance Peak value at time CSTR cascade: RTD (ii) Solving the coupled equations with Laplace transformation yields

  28. CSTR cascade: RTD (iii)

  29. Peter Krebs Department of Hydro Sciences, Institute for Urban Water Management Urban Water 4 Matter transport 4.1 Introduction to transport phenomena 4.2 Transport processes 4.3 Reactor approach 4.4 Advection-dispersion approach

  30. Analytical solution for a tracer pulse u = mean velocity Ddisp = dispersion coefficient m = total amount of tracer introduced A = cross-section area t = time from dosage Advection-dispersion approach (i)

  31. Advection-dispersion approach (ii) Standard deviation Dispersion coefficient Shear velocity cf = Fischer coefficient = 0.011 (-) b = width of water surface h = water depth Sf = friction slope

  32. Advection Dispersion, estimated by diffusion approach   Standard deviation A-D approach: effect of dispersion/diffusion

  33. A-D approach: tracer curves

  34. 1 tracer model 2 3 4 5 0 50 100 150 200 250 300 350 400 450 Time (minutes) A-D approach: dispersion in a river Boeije (1999)

  35. Peclet number A-D approach: reactor approximation (i) Normalisation by length L of reactor Pe large  Advection dominant  plug flow behaviour Pe small  Diffusion dominant  CSTR behaviour small < Pe < large  CSTR cascade or A-D approach

  36. A-D approach: reactor approximation (ii) Relation of turbulence/dispersion and standard deviation Simplification for Pe > 100 (applies to conditions in sewers and rivers) CSTR approximation, „hydrologic model“  Turbulence can be estimated from RTD (i.e. )

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