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Environmental Engineering DISCUSSION
I am doing a preliminary design for a treatment plant with an average flow of 10,000 m³/day. Design guides give criteria for clarifiers as a surface overflow rate, a surface loading rate, a solids loading rate, a detention time and a weir loading, and I am unsure which of these are the same thing and which controls the size.
How do I get from the flow to a tank diameter and depth for a primary clarifier, and what is different when sizing the secondary clarifier after the aeration tank?
Surface overflow rate and surface loading rate are the same quantity under two names: flow divided by the plan area of the tank, Q / A, in m³/m²·day. It has the units of a velocity, and that is its meaning. In an ideal settling tank, every particle whose settling velocity is greater than Q / A reaches the bottom before the water leaves, regardless of the tank depth. Particles settling more slowly are removed in proportion to their velocity divided by Q / A.
An overflow rate of 40 m³/m²·day is 40 m/day, or about 0.46 mm/s. Area, not volume, is what determines which particles are captured; depth and detention time mainly provide room for sludge storage and protect against short-circuiting and scour.
Primary clarifier sizing for your flow. Typical overflow rates are 30 to 50 m³/m²·day at average flow. Taking 40: A = 10,000 / 40 = 250 m². For a circular tank, D = √(4 × 250 / π) = 17.8 m, say 18 m. With a side water depth of 3.5 m the volume is about 875 m³, and the detention time is 875 / 10,000 = 0.0875 day, or 2.1 hours, which is inside the usual 1.5 to 2.5 hour range.
Then check peak flow. If the peak is 2.5 times the average, the overflow rate becomes 100 m³/m²·day, which is within the 80 to 120 commonly allowed at peak. Use at least two tanks so one can be taken out of service.
Weir loading is a separate check on the outlet: flow divided by the total length of the effluent weir. A peripheral weir on a 17.8 m tank is π × 17.8 = 56 m long, giving 10,000 / 56 = about 180 m³/m·day, comfortably inside the range of roughly 125 to 500 found in design guides. If it were too high, the approach velocity at the weir would pull settled solids up and over, and the remedy is more weir length, for example an inboard launder with weirs on both sides.
Compared with the overflow rate, weir loading has a modest effect on performance in tanks of normal depth, so it seldom controls the size.
The secondary clarifier has a second criterion because the feed is mixed liquor with several grams of solids per litre, which settles as a blanket and has to be thickened. Solids loading rate = (Q + Q_r) × X / A, where Q_r is the return sludge flow and X the mixed liquor suspended solids. Note that the return flow counts here, while the overflow rate uses only Q, since the return flow leaves through the bottom.
Example: Q = 10,000 m³/day, Q_r = 5,000 m³/day, X = 3 kg/m³ and A = 400 m² give 15,000 × 3 / 400 = 112 kg/m²·day, about 4.7 kg/m²·h, within the typical 4 to 6 at average flow. The overflow rate is 10,000 / 400 = 25 m³/m²·day. Calculate the area from both criteria and use the larger.
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