Particle Technology- Filtration


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The fifth lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics.

Filtration covers the modification of Darcys law to predictive filtration design equations as well as ones used for test data analysis. Examples of industrial equipment for filtration are included.

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Particle Technology- Filtration

  1. 1. Filtration<br />Chapter 4 in Fundamentals<br />Watch this lecture at<br />Visit for further resources.<br />Course details: <br />Particle Technology, <br />module code: CGB019 and CGB919, <br />2nd year of study.<br />Professor Richard Holdich<br /><br />
  2. 2. Filtration<br /><ul><li> Types
  3. 3. Cake filtration mechanism
  4. 4. Modification of Darcy's law
  5. 5. Constant pressure filtration
  6. 6. Constant rate filtration
  7. 7. Variable rate & pressure filtration
  8. 8. Industrial equipment</li></li></ul><li>Types of filtration<br />Deep bed - clarification<br />Normally batch (in duplicate) but some continuous ones:<br />Image supplied by DynaSand and Hydro International (Wastewater) Ltd.<br />
  9. 9. Types - membrane<br />Clarification on filtering membranes<br />
  10. 10. Types - Clarification<br />Cartridge and candle filtration<br />
  11. 11. Cake filtration mechanism<br /><ul><li>Multifilament filter cloth p. 40</li></li></ul><li>Cake filtration mechanism<br /><ul><li>Monofilament filter cloth</li></li></ul><li>Cake filtration mechanism<br /><ul><li>Monofilament open filter cloth/mesh</li></li></ul><li>Cake filtration mechanism p.31<br />Why can’t we simply measure Rm for each medium?<br />
  12. 12. Cake filtration mechanism – reality p 41<br />Why can’t we simply measure Rm for each medium?<br />i.e. Rm = f(material to be filtered)<br />
  13. 13. Modification of Darcy's law<br /><ul><li>Porosity or voidage
  14. 14. and Concentration</li></li></ul><li>Modification of Darcy's law<br />Darcy’s law:<br />Flow rate<br />Kozeny-Carman equation:<br />Pressure/L<br />use:<br />
  15. 15. Modification of Darcy's law<br />Volume liquid<br />Flow rate<br />Darcy’s law/Kozeny:<br />Pressure/L<br />Time<br />What do the graphs tell us about these equations? <br />How will this vary for filtration? <br />Think about a given material and filter in these equations – what is constant, what varies, look at the graph…<br />What are the independent and dependent variables?<br />
  16. 16. Modification of Darcy's law – p.29<br />At constant pressure drop:<br />Q is constant - permeation<br />Darcy’s law:<br />Filtrate volume<br />Q decreases - filtration<br />Time<br />
  17. 17. Modification of Darcy's law – p. 32<br />Build up of incompressible filter cake:<br />Filter cake<br />formation<br />Filter medium<br />
  18. 18. Modification of Darcy's law<br />
  19. 19. Modification of Darcy's law<br />Pressure drops are additive:<br />Pcake<br />Pmedium<br />
  20. 20. Modification of Darcy's law<br />Pressure drops are additive:<br />P<br />Ratio: <br />cake volume:filtrate = constant = <br />
  21. 21. Modification of Darcy's law<br />Ratio: <br />cake volume:filtrate = constant = <br />What does<br />Represent – in English, see the graph…<br />What does<br />Represent – in English<br />
  22. 22. Modification of Darcy's law – p.36<br />where cis the dry cake mass per unit volume of filtrate:<br />sis feed slurry mass fraction andmis the moisture ratio of the cake (mass cake wet/mass cake dry - or sample). In some instances one can assume m=1; i.e. neglect liquid in cake.<br />and  is the specific resistance to filtration (m/kg).<br />
  23. 23. Modification of Darcy's law – p.36<br />Considering Rc & alpha some more:<br />w is dry mass/unit area solids:<br />Rc<br />alpha = Rc/w<br />so:<br />w<br />
  24. 24. Modification of Darcy's law – equation (4.11)<br />General filtration equation:<br />
  25. 25. Constant pressure filtration<br />Constant P filtration - integrate general equation:<br />Time over filtrate volume<br />to give:<br />a<br />b<br />i.e:<br />Filtrate volume<br />
  26. 26. Constant pressure filtration<br />summary:<br />Need to know:<br />viscosity, pressure, and filter area <br />& slurry mass fraction, liquid density (and cake moisture - if poss.)<br />Time over filtrate volume<br />a<br />b<br />Need to calculate:<br />c then <br />and Rm<br />Filtrate volume<br />
  27. 27. Constant pressure filtration<br /><ul><li>General filtration equation:
  28. 28. Constant pressure:</li></ul>y = m x + c<br />
  29. 29. Constant pressure filtration<br /><ul><li>Filtration Testing in the Laboratory:</li></ul>High permeability: vacuum leaf<br />Low permeability: pressure bomb<br />Tests:<br /><ul><li>effect of pressure,
  30. 30. different cloths or media,
  31. 31. slurry agitation,
  32. 32. filter aids and flocculants
  33. 33. effect of slurry pre-concentration</li></li></ul><li>Constant pressure filtration<br /><ul><li>Filtration Testing in the Laboratory:</li></ul>High permeability: vacuum leaf<br />Low permeability: pressure bomb<br />To obtain values of:<br /><ul><li>specific resistance - possibly as f(pressure),
  34. 34. medium resistance
  35. 35. cake concentration - possibly as f(pressure) or moisture ratio</li></li></ul><li>Constant pressure filtration<br /><ul><li>Filtration Testing in the Laboratory:</li></ul>High permeability: vacuum leaf<br />Low permeability: pressure bomb<br />Also required for scale-up or simulation:<br /><ul><li>Liquid viscosity
  36. 36. filtration pressure
  37. 37. filter area
  38. 38. Slurry mass fraction
  39. 39. liquid density
  40. 40. solid density - if cake height is required</li></li></ul><li>Constant pressure filtration p. 41 – vacuum filter leaf<br />Experimental characterisation<br />
  41. 41. Constant pressure filtration<br />
  42. 42. Constant rate filtration – p. 36<br /><ul><li>General filtration equation:</li></ul>Filtration pressure<br /><ul><li>Constant rate:</li></ul>a<br />b<br />Filtrate volume<br />
  43. 43. Variable rate & pressure filtration<br /><ul><li>General filtration equation:
  44. 44. Variable pressure and rate equation:</li></ul>numerical integration of:<br />plot<br />
  45. 45. Industrial equipment – p. 35<br />Rotary vacuum filter (continuous)<br /><ul><li>Stages
  46. 46. cake formation in slurry tank (F)
  47. 47. drying and/or washing (D and W)
  48. 48. discharge - then back to formation (D & Di)</li></ul>W<br />D<br />D & Di<br />F<br />
  49. 49. Industrial equipment<br /><ul><li>Constant pressure:
  50. 50. Rearrange for a quadratic:</li></li></ul><li>Industrial equipment – p. 36<br /><ul><li>Simulation of Rotary Vacuum Filter:</li></ul>i.e. aV2 + bV - t = 0<br />where ‘form’ timet = F/n(submergence/speed)<br />
  51. 51. Industrial equipment<br /><ul><li>per cycle of drum:</li></ul>Calculate volume, hence:<br /><ul><li>Mass dry cake deposited = cV (kg)
  52. 52. Mass wet cake deposited = mcV (kg)
  53. 53. mass slurry filtered = mcV + V (kg)</li></ul>All above is per cycle, hence 3600/tfor output per hour.<br />
  54. 54. Industrial equipment<br />Vacuum belt filter (continuous)<br />Image appears courtesy of Polyfilters UK Limited<br />
  55. 55. Industrial equipment<br />Vacuum belt filter (continuous)<br />Image supplied courteousy of BHS-Sonthofen GmbH, Germany<br />
  56. 56. Industrial equipment<br />Vacuum disc filter (continuous)<br />Image courtesy of FLSmidth, Inc.<br />
  57. 57. Industrial equipment<br />Tube pressure filter (batch)<br />Image courtesy of Mesto Minerals (Sala) AB<br />
  58. 58. Filtration<br /><ul><li> Types
  59. 59. Cake filtration mechanism
  60. 60. Modification of Darcy's law
  61. 61. Constant pressure filtration
  62. 62. Constant rate filtration
  63. 63. Variable rate & pressure filtration
  64. 64. Industrial equipment</li></li></ul><li>This resource was created by Loughborough University and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.<br />Slide 3. Image of a DynaSand® is provided courtesy of Hydro International (wastewater) Limited. See for more details.<br />Slide 37. The image of a vacuum belt filter (continuous is provided with the permission of Polyfilters (UK) Limited. See for more details.<br />Slide 38. Image provided courtesy of BHS-Sonthofen GmbH. See for more details. <br />Slide 39. Image provided courtesy of FLSmidth Inc. See for more details.<br />Slide 40. Image of a tube press discharge, provided courtesy of Mesto Minerals (Sala) AB. See$File/Tube_Press_ES.pdf for more details.<br />© 2009 Loughborough University<br />This work is licensed under a Creative Commons Attribution 2.0 License. <br />The name of Loughborough University, and the Loughborough University logo are the name and registered marks of Loughborough University. To the fullest extent permitted by law Loughborough University reserves all its rights in its name and marks, which may not be used except with its written permission.<br />The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence.  All reproductions must comply with the terms of that licence.<br />The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher.<br />