Plant average
Worst lane
State point diagram
Solids flux against concentration for one clarifier surface. Underflow lines run from the applied flux on the vertical axis, through the state point, down to the predicted RAS concentration.
Loading and limits
| Quantity | Average | Worst lane |
|---|
Headroom
How far each lever can move before the clarifiers fail, others held.
| Limit | Average | Worst lane |
|---|
Time to overflow
Flows and MLSS held at current values.
| Blanket | Average | Worst lane |
|---|
Operating envelope
Maximum forward flow the clarifiers can carry at each MLSS. The lower of the two curves governs.
How it works
Settling model
Zone settling velocity follows Vesilind, Vs = V₀·e−K·X, with X in g/L (= kg/m³). In SVI mode the parameters come from the correlation
With the default α–δ and SVI 120 this gives V₀ ≈ 5.6 m/h and K ≈ 0.54 L/g. Use the SVI basis the coefficients were fitted on (SVI, DSVI or SSVI). If your coefficients belong to a different equation form, switch to Direct V₀ & K.
Reading the diagram
- Gravity flux is
G = X·V₀·e−KX: the solids the sludge can carry down by settling alone. - The state point sits at MLSS on the overflow line, whose slope is the surface overflow rate
q = Q/A. - The underflow line has slope −
QRAS/A. It cuts the vertical axis at the applied solids flux(Q+QRAS)·X/Aand the horizontal axis at the RAS concentration the mass balance predicts. - Thickening failure: the underflow line crosses the falling limb of the gravity curve. The clarifier cannot thicken to the RAS concentration demanded, so the blanket rises. The red dashed line is the steepest-allowable case, drawn tangent to the falling limb; its intercept is the limiting flux.
- Clarification failure: the state point lies above the gravity curve, meaning overflow rate exceeds what the sludge settles at that MLSS.
Time to overflow
In thickening failure the clarifier receives more solids than it can pass to the underflow. The surplus builds a blanket at the limiting concentration XL, sitting under a dilute zone at Xd, where the total flux curve on its rising limb equals the applied flux. The interface between them rises at
dh/dt = (applied flux − limiting flux) / (X_L − X_d)Time to overflow is the sidewater depth divided by that rate, taking the blanket from the floor to the water surface. Flows and MLSS stay at their current values, so in reality the drawdown of MLSS into the blanket slows the rise and the true time is longer.
Assumptions
- Steady state. Flow splits evenly across the clarifiers in service. WAS and effluent solids are ignored in the mass balance.
- The worst-lane factor scales MLSS for the most heavily loaded clarifiers at the same flows. It approximates channel imbalance and does not model the runaway that develops over time.
- A thickening failure here is an instantaneous verdict. In the plant the blanket stores solids, draws MLSS down and can rebalance. That dynamic is for phase two.
- If QRAS/A exceeds V₀/e², the total flux curve has no minimum, so thickening does not limit.