Question 2 of 5: Discrete Particle Settling and the Trickling Filter

Question 2: Discrete Particle Settling and the Trickling Filter (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) Discrete-Particle (Type I) Settling — Surface Area Governs, Not Depth

Given. A rectangular (or equivalent) sedimentation tank of surface area $A_s$, depth $H$, treating a flow $Q$, so the horizontal (through) velocity is $v_H=Q/(A_s H/H)=Q/A_s\times(H/H)$; more directly, the hydraulic retention time is $t_d=\forall/Q=(A_sH)/Q$. A discrete particle entering at the water surface settles at its own terminal (Stokes) velocity $v_s$, independent of any other particle and unaffected by the tank’s presence (Type I, non-flocculent settling).

Find. Show algebraically that the removal condition for a discrete particle depends only on $Q/A_s$ (the surface overflow rate), and cancels out of the depth $H$.

Approach. Track a particle entering at the surface at the inlet; it is captured if and only if it reaches the tank floor before the water carrying it reaches the outlet, i.e. before its residence time in the tank elapses.

1. Time available for settling. A particle entering at the surface at the inlet is carried through the tank at the mean horizontal velocity in the time it takes the water itself to traverse the tank, $t_d=\dfrac{\forall}{Q}=\dfrac{A_sH}{Q}$ — the tank volume $\forall=A_sH$ divided by the flow.
2. Vertical distance travelled by the particle in that time. Settling at its own terminal velocity $v_s$, the particle falls a vertical distance $z=v_s\,t_d=v_s\dfrac{A_sH}{Q}$ before the water parcel carrying it exits.
3. Capture condition. The particle is 100% removed if it reaches the floor before exiting, i.e. $z\ge H$: $$v_s\frac{A_sH}{Q}\ge H.$$ The depth $H$ appears on both sides of the inequality and cancels exactly, leaving $$\boxed{v_s\ge \frac{Q}{A_s}=v_o}$$ where $v_o=Q/A_s$ is the surface overflow rate (also called the surface loading rate, units of velocity, e.g. m³/m²·d). Any particle with a settling velocity at or above $v_o$ is removed regardless of tank depth — the critical settling velocity is a pure surface-area criterion.
4. Partial removal of slower particles. For a particle with $v_s

(b) Trickling Filter — Working Principle and Operation

A trickling filter is a fixed-film (attached-growth) secondary biological treatment process: settled wastewater is distributed continuously over the top of a bed of coarse, highly permeable media (traditionally crushed rock, 25–100 mm, in a bed 1–3 m deep; modern high-rate designs use corrugated plastic media in towers up to 6–12 m tall) and trickles downward through the void spaces under gravity. A biofilm of bacteria, fungi and higher organisms (worms, insect larvae, snails) grows attached to the media surface; as wastewater flows over the film, soluble and colloidal organic matter diffuses into the biofilm and is oxidized by the attached organisms, which draw make-up oxygen from air moving through the bed — typically by natural draft driven by the temperature difference between the wastewater and ambient air, aided by open underdrain vents (no mechanical aeration is normally required). As the biofilm thickens beyond what the diffusing substrate/oxygen can sustain, the innermost (anaerobic, substrate-starved) layer loses adhesion and sloughs off the media, carrying the removed organic mass out with the filter effluent as suspended solids (“humus”); this sloughed material is captured in a downstream secondary (humus) clarifier and either wasted or, in some configurations, recycled. Distribution across the bed is normally by a rotary distributor — a set of radial arms fed from a central influent riser, rotated by the reaction thrust of the wastewater jetting from orifices along the arms (no motor needed at typical hydraulic loadings) — which doses the whole bed surface intermittently as the arm sweeps past. A portion of filter effluent is commonly recirculated back to the influent (recirculation ratios roughly 0.5:1 to 4:1 depending on standard-rate vs. high-rate design) to maintain a minimum wetting rate over the media (keeping the biofilm from drying and sloughing prematurely), dilute strong or shock-loaded influent, and re-seed the top of the bed with active organisms.