Flow rate in a sand column is proportional to the cross-sectional area of the sand and the
Darcy’s Law explained
Darcy studied how water flows through sand, and came up with the following equation: Q = K (Ah/L) where:
- Q is the discharge, or flow
- K is the hydraulic conductivity in m/hour (which itself is a product of both the properties of the fluid (viscosity and density) and the sand)
- A is the cross-sectional area
- h is the head loss, and
- L is the distance through which the water travels
pressure head (hydraulic loading) of water on top of the sand. Flow rate is also affected by the length of the sand column, as well as by the properties of the fluid (viscosity, density and raw water quality) and the sand characteristics. For example, colder water should result in a slower flow rate, and over time, a higher turbidity raw water can affect flow rate by clogging the sand pores in the top centimetres of sand. In the same way, porosity and specific yield, which are both dependent on the type of sand in the filter, can both affect the hydraulic conductivity – that is, how much water passes through an area of sand in a particular time.
Increasing the surface area or hydraulic loading, improving the raw water quality prior to filtration, using a filter in the tropics as opposed to cold climates, decreasing the sand height or changing the sand type to a coarser sand can all result in a higher flow rate. A drum filter will therefore give a higher flow rate than the concrete filter due to the increased surface area available.
Traditionally, flow rates in slow sand filters should be between 0.1 - 0.4 m/hour. Note that this is a compaction of m3/m2/hour and sometimes the unit is in days and not hours. For the concrete filter, this equates to a maximum of 22 to 25 litres per hour depending on if the filter is round or square.
Research done by Elliott et al (2008 [ref 05]) using chemical tracer tests, revealed that the intermittently-operated biosand filter operates under near-plug flow conditions. What this means is that all parcels of water travelling through the sand medium seem to travel at the same speed, and residence time for each parcel of water is almost the same.
Effect of flow rates on bacteriological quality
Within a range, however, flow rates do not seem to affect bacteriological effluent quality in continually-operated sand filters. Huisman and Wood (1974 [ref_01]) reported the use of higher filtration rates in the Netherlands (0.25 and 0.45 m/hr) without any marked difference in effluent quality in continually-operated sand filters. Also research done in India for continually-operated sand filters found no significant difference in faecal coliform reductions with flow rates of 0.1, 0.2 and 0.3 m/hour (NEERI, 1982 [ref 02]). However, it is possible to increase the filtration rate considerably if effective pretreatment is given and if an effective disinfection stage follows the filtration (Ellis, 1987 [ref 03]).
Recent research carried out by Jenkins et al (2009, [ref 06]; 2011, [ref 07]) on intermittently-operated sand filters has highlighted the importance of sand size and hydraulic loading (both of which directly affect flow rates) in microbiological removal. They tested filters with varying levels of hydraulic loading above the sand surface (10, 20 and 30 cm) and two sand sizes (0.17 mm and 0.52 mm). They found that bacteria and virus removal was significantly better for filters with finer sand and those with lower head, independently from each other and for both short and long term residence times, but results were enhanced with longer residence times. The best combination was 0.17 mm sand with 10 cm head over longer residence times. What this shows is that slower flow rates are preferable regarding microbiological removal rates for intermittently-operated filters, and that sand size and hydraulic loading are major factors causing these slower flows.
So with the exception of the factor of sand area, lower flow rates are generally preferable in terms of microbiological removal. This is because of the following reasons:
- Contact time
A slower flow allows an increased pathogen removal, which is especially important in colder climates where biological activity is more time-dependent (Huisman and Wood, 1974 [ref 01]).
- Depth of bacteria
With higher flow rates, bacteria will be found at deeper depths as their food supply is carried deeper (Huisman and Wood, 1974 [ref 01]) and so to ensure water quality, sand bed depth would need to be increased. Lower flow rates are preferable to keep the bed depth within reasonable limits.
Lower flow rates that result from lower hydraulic loadings also ensure that other pathogens (such as Cryptosporidium oocysts) are not pushed through to deeper depths, and that organic matter does not break through.
- Biofilm development
Lower flow rates may allow biofilms to become better developed.
Slow sand filter designs should therefore incorporate an acceptable combination of hydraulic loading, sand size, sand height and sand area for effective pathogen removal with a range of raw water qualities. Some discussion on the recent research on the design of the concrete sand filter is available here.
Effect of flow rates on turbidity and colour removal
Turbidity and colour removal efficiency decline considerably with higher filtration rates in continually-operated sand filters, although the filtrate quality remains reasonably good. Filtration rates higher than the conventional one can therefore be adapted in slow sand filters if using a good quality of raw water (Muhammad et al, 1996 [ref 04]).
References: (jump back)
Ref 01: Huisman, L; Wood, W.E. (1974). Slow Sand Filtration. WHO, Geneva, Switzerland. p.44. Available from IRC
Ref 02: National Environmental Engineering Research Institute (NEERI). (1982) Slow sand filtration. Final project report, Nagpur, India.
Ref 03: Ellis, K.V. (1987). 'Slow Sand Filtration', WEDC J. Developing World Water, Vol 2, pp 196-198.
Ref 04: Muhammad, N.; Ellis, K.; Parr, J.; Smith, M.D. Optimization of slow sand filtration. Reaching the unreached: challenges for the 21st century. 22nd WEDC Conference New Delhi, India, 1996. pp.283-5.
Ref 05: Elliott, M.A.; Stauber, C.E.; Koksal, F.; DiGiano, F.A.; Sobsey, M.D. (2008). Reductions of E. coli, echovirus type 12 and bacteriophages in an intermittently operated household-scale slow sand filter. Water Research Vol 42 (10-11) pp.2662 – 2670. (DOI: 10.1016/j.watres.2008.01.016). Available here.
Ref 06: Jenkins, M.W.; Tiwari, S.K.; Darby, J.; Nyakash, D.; Saenyi, W.; Langenbach, K. (2009). The BioSand Filter for Improved Drinking Water Quality in High Risk Communities in the Njoro Watershed, Kenya. Research Brief 09-06-SUMAWA, Global Livestock Collaborative Research Support Program. University of California, Davis, USA. Available here.
Ref 07: Jenkins, M.W.; Tiwari, S.K.; Darby, J. (2011) Bacterial, viral and turbidity removal by intermittent slow sand filtration for household use in developing countries: Experimental investigation and modeling. Final draft of submitted paper. Dept of Civil & Environmental Engineering, University of California, Davis, USA. The draft is available here, and the published article is available at http://www.sciencedirect.com/science/article/pii/S0043135411005410. A poster submitted at a household water treatment conference in 2008 also illustrates the findings well, and is available here.