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  Heat-and-Mass Transfer Relationship to
Determine Shear Stress in Tubular Membrane
               ...
Outline
Introduction and Objectives
• Waste water treatment processes
• Reduction of fouling (two-phase flow)
• Dimensionl...
Objectives

To quantify the mass transfer coefficient for
two phase flow

To validate the heat-and-mass transfer
analogy w...
Introduction
Waste water treatment processes
• Biological removal of organic substances and nutrients (bioreactor)
• Clean...
Introduction
Membrane fouling
• Cake layer / pore blocking
• Decreases permeate flux


Reduction of fouling
• Introduction...
Introduction
Dimensionless numbers
• Two physical phenomena are similar if they have the same
   dimensionless forms of go...
Introduction
    Similarities (internal and single-phase flow)
                    Mass transfer                          ...
Single-phase flow
Mass transfer:
• Concentration polarization:
   - Separation: Sludge ⇔ Solute
   - Increase solute conce...
Two-phase flow
   Mass transfer
     • Ghosh and Cui (1999) & Zheng and Che
       (2006)
     • Developed mass transfer c...
Heat-and-Mass transfer analogy
Developed shear stress correlation for:
    - Gas slug zone (falling film + wake)
    - Liq...
Experimental set-up at UBC
Tube diameter:               2 Shear probes (flow direction)
• 9.9 mm                     Conve...
Shear probes & Shear Stress Histograms
Conversion V → τ
         V                               4 IL                  k ...
Electrochemical measurements
                               Single-phase flow
                                    Shear st...
Empirical model
Two-phase flow
                             1.561 µ D  ScTP    3
• Gas slug       τ w, gs =         2
  ...
Empirical model
Correction factor                                           140                                           ...
Empirical model
    ReSG                                                                                                  ...
Conclusions
Shear stress values were obtained from shear probes
(electrochemical method) using the Sherwood number

Using ...
Future work
Non-Newtonian liquids (i.e. sludge)
• Use of CMC as a non-Newtonian liquid to mimic the
  properties of Sludge...
Acknowledgement
MBR-TRAIN is a Marie Curie Host Fellowship for Early
Stage Research Training supported by the European
Com...
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Heat-and-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems

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Oral presentation at ASME-ATI-UIT Symposium on Thermal-Fluid-Dynamics and Energy Systems (18/05/2010)

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Heat-and-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems

  1. 1. www.mbr-network.eu Heat-and-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Nicolas Ratkovich, Pierre Bérubé and Ingmar Nopens ASME-ATI-UIT 2010 May 18th 2010, Sorrento – Italy
  2. 2. Outline Introduction and Objectives • Waste water treatment processes • Reduction of fouling (two-phase flow) • Dimensionless analysis (analogies) Methodology • Mass transfer (single- and two-phase flow) • Heat-and-Mass transfer analogy • Experimental set-up Results and discussion • Development of empirical model Conclusions and future work 2 www.mbr-network.eu
  3. 3. Objectives To quantify the mass transfer coefficient for two phase flow To validate the heat-and-mass transfer analogy with the results obtained from electrochemical shear probe measurements. To propose an empirical correlation based on heat transfer to determine the wall shear stress 3 www.mbr-network.eu
  4. 4. Introduction Waste water treatment processes • Biological removal of organic substances and nutrients (bioreactor) • Clean water-sludge separation: - Conventional Activated Sludge (CAS) - Gravity - Membrane Bioreactor (MBR) - Filtration Immersed Side-stream 4 www.mbr-network.eu
  5. 5. Introduction Membrane fouling • Cake layer / pore blocking • Decreases permeate flux Reduction of fouling • Introduction of air - Two-phase (slug) flow • Avoids reduction of permeate flux - Surface shear stress → scouring effect - Increases mass transfer (cake layer → bulk region) Slug flow *Taha & Cui, 2006 • Large shear stress values • Dynamic shear stress (liquid flows down- & up-flow) 5 www.mbr-network.eu
  6. 6. Introduction Dimensionless numbers • Two physical phenomena are similar if they have the same dimensionless forms of governing differential equations and boundary conditions. Similarities (internal flow) Mass transfer Wall friction Heat transfer Flow mass heat transfer transfer shear stress Cake layer Membrane 6 www.mbr-network.eu
  7. 7. Introduction Similarities (internal and single-phase flow) Mass transfer Wall friction Heat transfer Sh = function(d , Re, Sc ) f = function(d , Re ) Nu = function(d , Re, Pr ) km d µ 2 d ∆p 8τ w ρud hd cp µ Dimensionless Sh = Sc = f = = Re = Nu = Pr = numbers Df ρ Df L ρ u2 ρ u2 µ kc kc 1 0.14 Laminar 1 64  d 3  µB   d 3 f = Nu = 1.86  Re Pr    (Re<2000) Sh = 1.62  Re Sc   L µ   L Re  W  0.25 0.14 Turbulent 1 f = 1 µ  Pr  B  2 0.8 Sh = 0.04 Re 0.8 Sc 3   ε 5.74  Nu = 0.027 Re 3 µ  (Re>4000) log10  + 0.9   3.7 d Re   W     1 1 Sh  Sc  3 Analogy =   = Le 3 Nu  Pr  7 www.mbr-network.eu
  8. 8. Single-phase flow Mass transfer: • Concentration polarization: - Separation: Sludge ⇔ Solute - Increase solute concentration near membrane surface - Convection = Diffusion + Permeate dC J C = −D + J C per dx - Flux: C  J = km ln  m   Cb  - Mass-transfer coefficient (km): D km = δ - Sh laminar correlation: 1 km d  d 3 Sh = = 1.62  Re Sc  D  L 8 www.mbr-network.eu
  9. 9. Two-phase flow Mass transfer • Ghosh and Cui (1999) & Zheng and Che (2006) • Developed mass transfer correlations for: - Falling film zone - Wake zone - Liquid slug zone *Ghosh and Cui, 1999 9 www.mbr-network.eu
  10. 10. Heat-and-Mass transfer analogy Developed shear stress correlation for: - Gas slug zone (falling film + wake) - Liquid slug zone • Analogy: Transport of momentum, mass, heat and energy - Lewis number: 1 1 Gas Sh  Sc  3 slug (hTP) =   = Le 3 Nu  Pr  - Mass transfer coefficient: 2 Liquid hTP − slug (hL) km = Le 3 ρTP c p ,TP - Heat transfer coefficient:  0 .4 0.25 0.25   x   1 − Fp  0 .1  PrG   µL  hTP = Fp hL 1 + 0.55       Pr    µ   (I ) * 0.25    1 − x   Fp    L   G     *Ghajar, 2010 10 www.mbr-network.eu
  11. 11. Experimental set-up at UBC Tube diameter: 2 Shear probes (flow direction) • 9.9 mm Conversion (Voltage → Shear) 3   Fluids used:  τw = µL  4.64 V 5 2    ν e F π d e Co D 3 R G   3  • Water + electrolyte 11 www.mbr-network.eu
  12. 12. Shear probes & Shear Stress Histograms Conversion V → τ V 4 IL  k  d 3 IL = km = 2 S =  m  e2 τ = µS RG ν e F π d e Co  0.862  D Correlation τ → km 1 de  τ w D 2  3 k m = 0.862   d  µ de    Gas slug Liquid slug Correlation Sh → τ 1.561 µ D τw = 2 Sh 3 de Correlation Nu → τ 1  Sc  3 Sh = Nu    Pr  1.561 µ D  Sc  3 τw = 2   Nu de  Pr  12 www.mbr-network.eu
  13. 13. Electrochemical measurements Single-phase flow Shear stress Sherwood number 0.1 35 1 Theory Experimental data  d 3 Shear probes Lévêque correlation Sh = 1.62  Re Sc  0.09 This work  L 30 0.08 25 1 0.07  d 3 Shear stress (Pa) Sh = 1.495  Re Sc  0.06  L 8 ρ u2 20 τw = Sh 0.05 Re 15 0.04 0.03 10 0.02 5 0.01 0 0 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 1400 Re Re Difference of 8 % between theory and experimental data 13 www.mbr-network.eu
  14. 14. Empirical model Two-phase flow 1.561 µ D  ScTP  3 • Gas slug τ w, gs = 2   Pr  φ gs NuTP 3  de  TP  • Liquid slug 1.561 µ D  Sc L  3 τ w,ls = 2   Pr  φls Nu L 3  de  L  • Correction factors: - Coalescence - Bubble length - Hydraulic diameter - Transition regime (calibration under laminar conditions) - φgs & φls 14 www.mbr-network.eu
  15. 15. Empirical model Correction factor 140 2.8 • Power law expression 120 2.4 φ = a1 Re L a 2 100 2 • Based on experimental measurements a1,gs ReLa2,gs -0.2945 a2,ls y = 545.7382x 80 2 R = 0.9461 1.6 a1,ls ReL 60 1.2 Final expression 40 0.8 • Liquid slug Liquid slug y = 1508.7567x -1.1957 20 Gas slug 0.4 ( ) Nu 2 −0.295 3 3 R = 0.9113 τ w,ls = 48.900 Re L L Power (Gas slug) Power (Liquid slug) 0 0 • Gas slug 0 200 400 600 800 1000 1200 ( ) 3 τ w, gs = 138.741Re L −1.196 NuTP 3 ReL 15 www.mbr-network.eu
  16. 16. Empirical model ReSG Reff 140 2.8 140 2.8 120 2.4 120 2.4 100 2 100 2 a2,gs a2,ls 80 1.6 a2,gs a2,ls a1,gs ReSG a1,ls ReSG 80 1.6 a1,gs Reff a1,ls Reff 60 1.2 60 1.2 40 0.8 40 0.8 Liquid slug 20 0.4 Liquid slug Gas slug 20 Gas slug 0.4 Power (Gas slug) Power (Gas slug) Power (Liquid slug) 0 0 Power (Liquid slug) 0 0 0 5 10 15 20 25 30 35 40 45 186 188 190 192 194 196 198 200 ReSG Rem 140 2.8 Resf 140 Reff 2.8 120 2.4 120 2.4 100 2 100 2 a2,gs a2,ls a1,gs Rema2,gs a2,ls 80 1.6 80 1.6 a1,gs Resf a1,ls Resf a1,ls Rem 60 1.2 60 1.2 40 0.8 40 0.8 Liquid slug Liquid slug 20 0.4 20 Gas slug 0.4 Gas slug Power (Gas slug) Power (Gas slug) Power (Liquid slug) Power (Liquid slug) 0 0 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 0 500 1000 1500 2000 2500 3000 Rem Resf 16 www.mbr-network.eu
  17. 17. Conclusions Shear stress values were obtained from shear probes (electrochemical method) using the Sherwood number Using the analogy between heat-and-mass transfer an empirical correlation was developed for two-phase flow to determine the wall shear stress: • Two zones: liquid (L) and gas slug (TP) • Predictions: - Single phase flow is acceptable (10 % error) - Two-phase flow: error up to 60 % > Heat transfer coefficient correlation for TP has errors up to 30% > The correlation is mainly designed for turbulent regime > Common membrane operation is in laminar-transition regime Analogies are determined mainly for turbulent regime; operation of tubular air lift membranes is in laminar-transition regime 17 www.mbr-network.eu
  18. 18. Future work Non-Newtonian liquids (i.e. sludge) • Use of CMC as a non-Newtonian liquid to mimic the properties of Sludge. • Viscosity (flow in a pipe) n n −1 n −1 n −1  3 n + 1   8 u SL   3n +1  8 u SL  µB = K    4n   d  µW = K   4n            d  • Reynolds and Prandtl number ρ L u SL d cp µB Re MR = Pr = µB kc • Nusselt number correction 1 Nu non− New  3 n + 1  3 =  4n   Nu New   • Viscosity correction: 0.14  µB   µ    W  18 www.mbr-network.eu
  19. 19. Acknowledgement MBR-TRAIN is a Marie Curie Host Fellowship for Early Stage Research Training supported by the European Commission under the 6th Framework Programme (Structuring the European Research Area - Marie Curie Actions) Contract No. MEST-CT-2005-021050 Duration: 01/01/06 - 31/12/09 MBR-TRAIN is part of the MBR-NETWORK Cluster More info: www.mbr-network.eu and www.mbr-train.org Funding for the infrastructure used to measure surface shear forces was provided by the Natural Science and Engineering Research Council of Canada (NSERC). 19 www.mbr-network.eu
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