Question 4 of 5: Filtration, coagulation and contaminant-removal mechanisms in water treatment

Question 4: Filtration, coagulation and contaminant-removal mechanisms in water treatment (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.

(a) Schmutzdecke and backwash in rapid sand filters (8 marks)

The question contains a deliberate trap, and the marks are in naming it. The schmutzdecke — German for "dirty skin" — is the biologically active mat of algae, bacteria, protozoa and trapped debris that develops on the surface of a slow sand filter over one to two weeks of operation. It is the defining feature of slow sand filtration and does most of the treatment: within the mat, predation and biological oxidation remove bacteria, viruses, Giardia cysts and dissolved organic carbon by mechanisms that are not available to straining alone, which is why a mature slow sand filter can produce a safe water with no coagulant at all. A slow sand filter is cleaned by draining it and scraping 20 to 40 mm off the top, and it is then out of service for the days needed for the mat to re-ripen.

A properly operated rapid sand filter has no schmutzdecke, and is deliberately designed not to develop one. Three things prevent it. The filtration rate is 5 to 15 m/h against 0.1 to 0.2 m/h for a slow filter — a factor of fifty or more — and the resulting hydraulic shear at the grain surfaces prevents a fragile biological mat from establishing. The run length is 24 to 72 hours, an order of magnitude shorter than the one to two weeks a mat needs to mature. And the design intent is opposite: a rapid filter is a depth filter, in which chemically destabilised floc is meant to penetrate and be stored throughout the full bed depth, whereas surface accumulation is a defect that causes premature headloss, mudball formation and short runs. If a rapid filter does develop a visible surface skin, the diagnosis is a coagulation problem or an over-long run, not a feature to be exploited.

Backwash is therefore the rapid filter's only cleaning mechanism, and it is a scheduled part of the process rather than maintenance. A run is terminated on whichever of three criteria arrives first: terminal headloss, typically 2.4 to 3 m; turbidity breakthrough in the filtrate; or a maximum elapsed time, imposed to prevent biological growth and floc compaction. The wash sequence then reverses the flow through the underdrain to fluidise the bed and expand it by 20 to 30 per cent, so that grains separate, attached solids are released by the combination of shear and grain collision, and the released material is carried up and out over the wash troughs. Modern practice precedes and overlaps the water wash with an air scour at 0.9 to $1.5\ \text{m}^3/\text{m}^2\!\cdot\!\text{min}$, and the ordering rule is worth stating because it is the whole logic of the sequence: air scour only works while the bed is not fluidised, because fluidisation separates the grains and abolishes the grain-to-grain abrasion that does the cleaning. Hence air alone, then air plus sub-fluidisation water, then high-rate water alone.

Given. A rapid filter runs at 5 m/h for 48 hours between washes and is washed at 0.6 m/min for 10 minutes. Find. The wash water as a fraction of production. Each square metre of bed produces $5 \times 48 = 240\ \text{m}^3$ per run and consumes $0.6 \times 10 = 6\ \text{m}^3$ of wash water, so backwash costs $\boxed{2.5\ \text{per cent}}$ of plant output. That water is recovered to the head of the plant after settling, but it carries the plant's entire pathogen load and therefore has to be equalised and returned slowly — the recycle of spent filter backwash is a regulated practice, not a housekeeping detail. The filtered-to-waste or ripening period at the start of the next run, when the freshly washed bed passes its highest turbidity, is the other operating consequence.

(b) Design and operating principle of coagulation, flocculation and settling (9 marks)

The three unit processes form one system with a single purpose: to convert the non-settleable colloidal fraction of a raw water into settleable solids and then remove them. Colloidal clay, natural organic matter and micro-organisms carry a negative surface charge, so electrostatic repulsion keeps them dispersed indefinitely; their settling velocities are in any case so small — hours to years for particles of 1 µm and below — that no buildable tank could remove them. Coagulation destroys the stability, flocculation grows the destabilised particles into aggregates large enough to settle, and sedimentation removes them.

Coagulation is the chemical step, complete in a fraction of a second. A hydrolysing metal salt — alum $\text{Al}_2(\text{SO}_4)_3\!\cdot\!14\text{H}_2\text{O}$ or ferric chloride — is dispersed into the flow, hydrolyses to positively charged polynuclear species and finally to an amorphous metal hydroxide precipitate. It acts by charge neutralisation at low dose and by sweep-floc enmeshment at higher dose, and because hydrolysis consumes alkalinity ($0.2525\ \text{mg}$ as $\text{CaCO}_3$ per mg of alum, so a 40 mg/L dose consumes 10.1 mg/L) the raw water must have enough buffer or lime must be added. The design requirement is instantaneous and complete dispersion, because the coagulant hydrolyses faster than it can be mixed; a rapid mix that is too slow lets part of the dose form inert hydroxide before it ever meets a particle.

Given. A 20 000 m³/d plant with a 45-second rapid mix at $G = 800\ \text{s}^{-1}$, three flocculation cells of 500 s each with tapered $G = 60, 35, 20\ \text{s}^{-1}$, and a settling basin at $30\ \text{m}^3/\text{m}^2\!\cdot\!\text{d}$ with 2.5 h detention; water at $15\,{}^{\circ}\text{C}$, $\mu = 1.139 \times 10^{-3}\ \text{Pa}\!\cdot\!\text{s}$. Find. The tank sizes, mixing power and the $Gt$ products that characterise each stage.

1. Rapid mix. At $Q = 0.2315\ \text{m}^3/\text{s}$ the volume is $V = Q t = 0.2315 \times 45 = 10.4\ \text{m}^3$, and the Camp–Stein velocity gradient $G = \sqrt{P/\mu V}$ inverts to $$P = G^2 \mu V = 800^2 \times 1.139\times10^{-3} \times 10.4 = \boxed{7.6\ \text{kW}}, \qquad Gt = 800 \times 45 = 36\,000$$
2. Flocculation, tapered. The total volume is $0.2315 \times 1\,500 = 347\ \text{m}^3$ in three equal cells of $116\ \text{m}^3$. The same relation gives 474 W, 161 W and 53 W in the three cells — 689 W in total, less than a tenth of the rapid-mix power — and $$Gt = (60 + 35 + 20)(500) = 57\,500$$ comfortably inside the usual 30 000 to 150 000 window. Tapering matters because $G$ governs both aggregation and floc breakup: a high gradient is needed early to bring particles into contact, but the same gradient applied to a 1 mm floc would shear it apart.
3. Sedimentation. Sizing on the overflow rate, $A = 20\,000/30 = \boxed{667\ \text{m}^2}$, and the 2.5-hour detention gives $V = 2\,083\ \text{m}^3$, hence a depth of $2\,083/667 = 3.13\ \text{m}$. These are not independent choices: for an ideal basin $\text{SOR} = H/\tau$, so fixing any two fixes the third.
4. What the overflow rate means physically. The overflow rate is a velocity: $30\ \text{m}^3/\text{m}^2\!\cdot\!\text{d}$ is $3.47\times10^{-4}\ \text{m/s}$, and every particle whose Stokes settling velocity exceeds it is removed regardless of where it enters. Inverting Stokes' law at $\rho_p = 2\,650\ \text{kg/m}^3$, $$d = \sqrt{\frac{18\mu v_s}{(\rho_p-\rho)g}} = 21\ \mu\text{m}$$ so the basin captures everything above about 21 µm — which is precisely why the raw colloids, three orders of magnitude smaller, must first be grown into floc. Depth does not appear in this result, which is the single most useful fact about clarifier design: adding a parallel basin halves the overflow rate and improves capture, whereas deepening the existing basin by the same volume does not.

(c) Mechanisms of contaminant removal in filtration (8 marks)

Granular filtration removes particles far smaller than the pores of the bed, so straining explains almost none of what a rapid filter does. The process is properly described in two sequential steps: transport, which brings a particle from the bulk flow to the surface of a grain, and attachment, which decides whether it stays there. Both must succeed. Transport is a physical, hydrodynamic question; attachment is a chemical, surface question, and it is the one the plant controls through coagulation.

Transport mechanisms. Interception captures a particle whose streamline passes within one particle radius of a grain, and grows in importance with particle size. Sedimentation lets a particle denser than water fall across streamlines onto the grain below, and also grows with size — it dominates above roughly 1 µm. Brownian diffusion carries very small particles across streamlines by random thermal motion, and grows as size decreases, dominating below about 1 µm. Hydrodynamic action from velocity gradients in the pore rotates and drifts non-spherical particles across streamlines. Straining retains only particles larger than the pore constrictions and is confined to the top few centimetres. Because two of these mechanisms strengthen with size and one strengthens as size falls, the overall single-collector efficiency passes through a minimum near 1 to 2 µm — and that is exactly the size range of Cryptosporidium oocysts and many viruses adsorbed to fine colloids. The most difficult particles for a filter to catch are neither the largest nor the smallest, and knowing where the minimum lies is what the marks are for.

Attachment mechanisms. Once transported to the grain, a particle is held by van der Waals attraction, by electrostatic interaction, by adsorption and chemical bridging through polymer or metal-hydroxide surface coatings, and by specific chemical bonding to the coating on a conditioned medium. The controlling factor is the electrical double layer: untreated colloids and quartz grains both carry a negative charge, so the repulsive barrier prevents attachment however efficient the transport, and the particle is swept on through the bed. Adequate upstream coagulation collapses that barrier. This is why filter performance is set in the rapid-mix chamber and not in the filter, and why filter-aid polymer is dosed ahead of the bed when coagulation is marginal.

Detachment is the third process and explains the end of a run: as deposits accumulate, the pore velocity rises, the shear on the deposited material rises with it, and previously captured particles are re-entrained and driven deeper — producing turbidity breakthrough while the headloss may still be acceptable. Headloss itself follows from the same geometry; for 0.75 m of 0.6 mm sand at porosity 0.40 and 5 m/h, the Carman–Kozeny expression gives $\text{Re} = 0.73$, a friction factor of 125, and a clean-bed loss of about $\boxed{0.29\ \text{m}}$, rising through the run to the 2.4 to 3 m terminal value at which the filter is washed. A dual-media bed (anthracite over sand) is the standard response: the coarse, light anthracite on top provides depth storage while the finer sand beneath provides polishing, so solids are distributed through the bed rather than concentrated at the surface, and both the run length and the headloss profile improve.