Question 5 of 5: The Rapid Sand Filter — Principle, Ripening, Backwash and Air Scour

Question 5: The Rapid Sand Filter — Principle, Ripening, Backwash and Air Scour (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. No data are supplied, so a representative Canadian conventional filtration plant is carried through the discussion: a design flow of 10 000 m³/d, a filtration rate of 5 m/h (120 m³/m²·d), a 0.75 m bed of silica sand of 0.55–0.60 mm effective size with a porosity of 0.42 and a sphericity of 0.85, a 48-hour filter run, and a backwash at 0.6 m/min for 10 minutes preceded by air scour at 1.2 m³/m²·min.

Find. The working principle and operating cycle of the rapid sand filter, the correct treatment of the term "schmutzdecke", and the role and design basis of backwash and air scour — supported by the filter area, the clean-bed head loss and the wash-water fraction for the representative plant.

Working principle

The rapid gravity sand filter is a depth filter, and that phrase is the heart of the answer. Unlike a strainer or a membrane, it does not work by having pores smaller than the particles it removes: the pore openings of a 0.55 mm sand are of the order of 80–100 µm, while the particles being captured — alum floc fragments, clay colloids, algal cells, Giardia cysts and Cryptosporidium oocysts — are one to fifty micrometres across. Removal happens within the depth of the bed, in two sequential stages.

First, transport carries a particle from the bulk flow in a pore to the surface of a grain. The mechanisms are interception (a particle following a streamline that passes within one particle radius of the grain), sedimentation (a particle denser than water settling out of its streamline onto the top of a grain), and Brownian diffusion (which dominates for particles below about 1 µm); hydrodynamic action and inertia contribute at the margins. These mechanisms have opposite dependence on size, which produces the well-known minimum in removal efficiency near 1–2 µm — awkwardly close to the size of a Cryptosporidium oocyst, and one of the reasons filtration is credited with only about 2 to 2.5 log removal and must be backed by disinfection.

Second, attachment holds the particle once it has arrived. This is a surface-chemistry step, not a hydraulic one. Both natural particles and quartz grains carry a negative surface charge at natural pH and repel one another, so an unconditioned particle simply bounces off. This is why a rapid filter cannot be operated without upstream chemical conditioning: coagulation with alum or a ferric salt, aided where necessary by a polymer filter aid, must destabilise the particles before they reach the bed. A rapid filter operating on a poorly coagulated water passes turbidity straight through even though its head loss builds normally — the classic sign of chemical rather than hydraulic failure.

Flow is downward under gravity, driven by a submergence of 1.0–1.5 m of water standing over the bed. The design filtration rate is 5–12 m/h (120–300 m³/m²·d) for a conventional single-medium plant, one to two orders of magnitude higher than the slow sand filter with which it is contrasted below. For the representative plant:

1. Size the filter area from the design rate. $$A = \frac{Q}{v} = \frac{10\,000\ \text{m}^3/\text{d}}{5\ \text{m/h} \times 24\ \text{h/d}} = \boxed{83.3\ \text{m}^2}$$ Provided as four cells of 20.8 m² each (about 4.5 m by 4.6 m), so that one cell can be out of service for backwash while the remaining three carry the flow at 6.7 m/h — still within the design envelope. A minimum of four cells is the normal rule for exactly this reason.
2. Compute the clean-bed head loss from the Carman–Kozeny equation. With $v = 5$ m/h $= 1.389\times10^{-3}$ m/s, $L = 0.75$ m, $d = 0.60$ mm, porosity $e = 0.42$, sphericity $\varphi = 0.85$ and $\nu = 1.003\times10^{-6}$ m²/s at 20 °C, the grain Reynolds number is $$Re = \frac{\varphi d v}{\nu} = \frac{0.85 \times 6.0\times10^{-4} \times 1.389\times10^{-3}}{1.003\times10^{-6}} = 0.706$$ so the friction factor is $$f' = \frac{150(1-e)}{Re} + 1.75 = \frac{150 \times 0.58}{0.706} + 1.75 = 124.9$$ and $$h_L = f'\,\frac{1-e}{e^3}\,\frac{L}{\varphi d}\,\frac{v^2}{g} = 124.9 \times 7.829 \times 1\,470.6 \times 1.966\times10^{-7}$$ $$\boxed{h_L = 0.283\ \text{m clean bed}}$$ The filter is taken out of service when the accumulated loss reaches a terminal value of 2.0–2.5 m, or when filtrate turbidity breaks through, whichever comes first.
3. Compute the wash-water penalty. Over a 48-hour run the filter produces $5 \times 48 = 240$ m³ of filtrate per m². A wash at 0.6 m/min for 10 minutes consumes $0.6 \times 10 = 6.0$ m³ per m², so $$\text{wash-water fraction} = \frac{6.0}{240} = \boxed{2.5\ \text{per cent of production}}$$ Design practice keeps this between 1 and 4 per cent; above about 5 per cent the plant is effectively washing away its own capacity, and either the run length or the wash regime needs revisiting.

"Schmutzdecke" — and why it is not a feature of the rapid sand filter

The question names the schmutzdecke explicitly, and the correct engineering answer is to identify it as the defining feature of the slow sand filter and to explain why the rapid filter deliberately has none. Stating this distinction is the substance of this part of the question; inventing a schmutzdecke inside a rapid filter is the trap.

In a slow sand filter, operating at 0.1–0.4 m/h, the top 10–25 mm of the bed develops over one to two weeks into a schmutzdecke (German for "dirt blanket"): a biologically active mat of algae, bacteria, protozoa, diatoms, rotifers and their extracellular polymer, bound together with the trapped inorganic silt. This layer is a living treatment stage. It strains particles physically, but more importantly it predates on bacteria, degrades dissolved organic carbon, and achieves 2–4 log removal of coliforms with no coagulant at all. A slow sand filter is cleaned by draining the bed and scraping off the top 20 mm — the schmutzdecke itself — after which the filter must re-ripen before it performs fully again.

A rapid sand filter cannot form a schmutzdecke, and is designed so that it does not, for three reasons.

• Hydraulic. At 5–12 m/h the shear at the bed surface is ten to a hundred times that in a slow filter. Any incipient surface mat is either sheared away or, if it does form, blinds the surface, drives the head loss to its terminal value within hours, and ends the run — a condition called surface blinding or mudballing, which is an operating fault, not a treatment mechanism.
• Operational. The rapid filter is backwashed every 24–72 hours, and the whole point of the backwash is to strip the accumulated deposit from every grain in the bed. No layer survives to mature biologically; a schmutzdecke needs one to two weeks of undisturbed operation.
• By design intent. The rapid filter is a depth filter whose capacity is the pore volume distributed through 0.75 m of media. Concentrating removal at the surface would waste that storage. This is precisely why dual-media beds (0.45–0.60 m of 1.0–1.2 mm anthracite, specific gravity 1.5, over 0.20–0.30 m of 0.5 mm sand, specific gravity 2.65) are so common: the coarse light medium sits on top after backwash and provides coarse-to-fine filtration in the direction of flow, driving the deposit deeper into the bed, extending the run and roughly doubling the solids storage before terminal head loss.

Two secondary consequences follow and are worth stating. First, the rapid filter removes essentially no dissolved organic carbon and provides little biological treatment, so it depends entirely on upstream coagulation and downstream disinfection — whereas a slow sand filter can serve a small, protected supply almost unaided. Second, the one biological analogue a rapid filter does exhibit is ripening: for the first 15–60 minutes after a wash, the clean grains have not yet acquired the deposit that improves attachment, and filtrate turbidity spikes. Because that spike coincides with the highest pathogen passage of the whole cycle, modern practice is to run the first 15–30 minutes to waste (filter-to-waste), or to dose a low polymer concentration to shorten the ripening period.

Filter backwash

Backwash reverses the flow through the bed at a velocity high enough to fluidise it, expanding the sand by 20–40 per cent so that the grains are lifted apart and the deposit can be carried away in the rising water and discharged over the wash-water troughs to waste. The governing condition is that the upward velocity must exceed the minimum fluidisation velocity of the largest grain, which for a 0.6 mm sand is roughly 0.5–0.7 m/min (30–40 m/h); design rates are 0.5–0.75 m/min for sand and up to 0.9 m/min for a dual-media bed, for 8–15 minutes.

Three design points deserve emphasis. The expansion must be controlled. Too little and the bed does not fluidise, so the deposit is not released and the filter never fully recovers; too much and the media is carried into the wash-water troughs and lost, so the troughs must be set high enough to clear the expanded bed — the usual rule is a trough lip at least 0.15 m above the fully expanded surface. Water temperature matters. Cold Canadian water is more viscous and more dense, so a wash rate set in summer over-expands the bed in winter and can float media out; rate controllers are normally temperature-compensated or seasonally reset. The gravel support must not be disturbed. If the wash rate lifts the supporting gravel layers, they intermix, the underdrain distribution becomes uneven, and the filter develops permanent jets and dead zones — a failure that requires the bed to be dug out and rebuilt.

The fundamental limitation of water-only backwash is that fluidisation separates the grains. Once a bed is fluidised, the grains no longer touch, so there is no abrasion between them, and the only cleaning force acting on an individual grain is fluid shear — which is weak relative to the strength of a well-attached alum floc deposit. Water-only washing therefore leaves residual attached material, which accumulates cycle after cycle into mudballs: agglomerates of sand and floc, heavy enough to sink through the bed to the gravel interface, where they block flow, cause the bed to crack and short-circuit, and progressively remove media from service. This is exactly the problem air scour exists to solve.

Air scouring

Air scour injects compressed air, typically 1.0–1.5 m³/m²·min at 35–50 kPa, through the underdrain and up through the media. Rising bubbles set up violent local turbulence and, crucially, cause the grains to collide with one another. This grain-to-grain abrasion is a far more powerful cleaning mechanism than fluid shear alone; it removes the tenaciously attached film that water-only washing leaves behind, and it breaks up mudballs before they can form.

The essential operating rule is a consequence of the mechanism: air scour is only effective while the bed is not fluidised, because fluidisation separates the grains and abolishes the very grain-to-grain contact that does the cleaning. The standard sequence therefore is:

1. Drain down and scour with air alone. The water level is lowered to just above the media and air is applied at 1.0–1.5 m³/m²·min for 1–3 minutes. The bed is unfluidised and the grains grind against one another.
2. Apply simultaneous air and low-rate water. Air continues while water is introduced at roughly 0.15–0.30 m/min — deliberately below the fluidisation velocity, so the abrasion continues while the released material begins to be carried upward. This collapse-pulsing phase is the most effective part of the wash and typically runs 3–8 minutes. The air must be stopped before the rate rises, or air will be entrained into the underdrain and can lift the gravel or damage the nozzles.
3. High-rate water wash alone. The air is shut off and the water rate is raised to the full 0.6 m/min for 5–10 minutes to fluidise the bed, carry the liberated solids to the troughs, and re-stratify the media. In a dual-media bed this final phase is what restores the anthracite-over-sand layering.
4. Refill, ripen and return to service. The filter is refilled slowly from below to avoid trapping air pockets in the bed (which cause air binding and negative head), then run to waste for 15–30 minutes until the filtrate turbidity falls below about 0.1–0.3 NTU.

A complementary or alternative approach is a surface wash, using fixed or rotating nozzle arms 50–75 mm above the media discharging at 0.05–0.10 m³/m²·min and 350–550 kPa, which attacks the surface deposit specifically. Air scour is generally preferred in new plants because it cleans the full bed depth rather than just the top layer, and it reduces wash-water consumption by 25–50 per cent relative to water-only washing — a direct operating saving, since wash water is finished water sent to waste.