Nonlinear Theory
The nonlinear chemical doser is part of the evolution of the alum dosing methods in AguaClara plants. Previous linear chemical dosers have relied upon the major head losses caused by the friction of the dosing tube to control the flow of alum. The important point is recognizing the relationship between head loss and the flow rate of alum in the two dosing methods. In previous linear dosing designs, the flow of alum is proportional to Q. If the flow rate of alum were to increase into the turbulent range then the head loss is proportional to the flow rate squared, which causes errors in the linear dosing scheme. In order to allow there to be turbulent alum flow, which will allow us to scale up AguaClara plants, an orifice controlled nonlinear doser is now being used. In the nonlinear orifice controlled doser, the majority of the head losses is due to the orifice, with the flow rate of alum being proportional to the square root of h.
|
Laminar |
Turbulent |
|---|---|---|
Linear doser |
$$Q\alpha h$$ |
$$Q^2 \alpha h$$ |
Orifice doser |
$$Q\alpha h$$ |
$$Q\alpha h$$ |
The nonlinear doser uses a dosing orifice (minor losses) instead of a dosing tube (major losses) to control the relationship between changing plant flow rates and chemical dose. The flow rate through the Chemical Dose Controller (CDC) is related to the available head by the equation:
Unknown macro: {latex}
$$Q_
Unknown macro: {Cdc}
= K_
Unknown macro: {orifice}
\sqrt {2gh_
} $$
where
- Unknown macro: {latex}is the chemical flow rate
$$Q_
Unknown macro: {Cdc}$$
- Unknown macro: {latex}is the orifice coefficient
$$ K_
Unknown macro: {orifice}$$
- h is the available head
The desired chemical dose to the plant can be determined by a mass balance:
Unknown macro: {latex}
$$C_p = {{C_c Q_
Unknown macro: {Cdc}
} \over {Q_
Unknown macro: {Plant}
}}$$
where
- C c is the chemical stock concentration
- C p is the chemical dose
The water leaves the entrance tank through the Rapid Mix Tube and the alum is dosed directly into the tube. An orifice is located in the tube to generate small-scale mixing.
The relationship between flow rate and head loss is governed by the orifice equation:
Unknown macro: {latex}
$$ Q_
Unknown macro: {Plant}
= K_
Unknown macro: {orifice}
\sqrt {2gh_
Unknown macro: {EtOrifice}
} $$
where
- Unknown macro: {latex}is the plant flow rate
$$ Q_
Unknown macro: {Plant}$$
- Unknown macro: {latex}is the height of water above the entrance tank orifice
$$ h_
Unknown macro: {EtOrifice}$$
The CDC uses a lever arm with a float and counterweight to relate the dosing to the changes in the entrance tank water level, which is a function of the influent flow rate chosen by the operator. An increase in head loss links the chemical flow rate to the plant flow rate and the chemical dose (mg/L) will be constant as plant flow varies.
The dosing tube must be designed to minimize major losses so that minor losses dominate head loss. The dosing tube must be flexible to accommodate the lever arm motion and dose adjustment. There will be two dosing tubes from the constant head tank to the level arm (one for each scale and one tube from the lever arm to the rapid mix tube.