Nonlinear Chemical Dose Controller
Abstract
The nonlinear chemical doser (CD) is designed for turbulent chemical does flow rates to be used in conjunction with the Rapid Mix Chamber Design in contrast to the linear CD which requires that the chemical flow in the dosing tube be laminar. The linear CD uses the relationship between laminar flow and major losses in the doser tube to maintain a constant chemical dose with varying plant flow rates. However, when the flow in the dosing tube is turbulent, the linear relationship no longer exists. In this case, a nonlinear CD, one that uses minor losses to control flow rates, can be used to maintain a constant chemical dose with the varying plant flow rates. By using an orifice to control chemical flow, the CD will have the same nonlinear response to increasing flow as the plant flow rate which is controlled by a rectangular orifice. A float in the grit chamber controls the height of a lever arm. The dosing orifice is located at the opposite end of the lever arm. As plant flow rates increase, the float rises, and the dosing orifice falls making more head available to power chemical flow. As the flow rate decreases so does the available head and the chemical flow rate slows down. The lever arm has holes drilled into the top of it so that the dosing orifice may be inserted into one of these holes to adjust dosage for changes in turbidity. Since the dosing orifice flows directly into the lever arm, the alum will always be dispersed into the same spot, no matter the dose.
The advantage to designing a nonlinear CD is that higher chemical flow rates can be used. With an alum stock solution of 500 grams per liter the linear flow controller can deliver a maximum chemical dose of 90 mg/L to plants with flow rates as high as 2000 L/min. In larger water treatment plants higher chemical flow rates are necessary to dose alum and chlorine. A flow control module with a higher capacity than the linear CDC flow control module is necessary for the nonlinear doser. Head loss through the float valve orifice limits the flow control moduleto chemical flows less than 400 ml/min. Otherwise, the chemical stock tank needs to be placed excessively far above the FCM. This maximum chemical flow is been adequate for La 34, Ojojona, Tamara, and Four Communities given their flow rates. Two flow controllers are used to achieve the necessary alum dose at Marcala. As the demand for larger AguaClara plants grows, larger chemical dose flow rates will be required.
Theory
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 orifice is related to the available head by the equation:
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$$Q_c = K h^
Unknown macro: {n_c }
$$
where
- Q c is the chemical flow rate
- K is the minor loss coefficient for an orifice
- h is the available head
- n c is an unknown power
The entrance to the rapid mix tank is a rectangular orifice. The relationship between flow rate and head is governed by the equation:
Unknown macro: {latex}
$$Q_p = K h^
Unknown macro: {n_p }
$$
where
- Q c is the chemical flow rate
- n c is an unknown power
The chemical dose to the plant can be determined by a simple mass balance:
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$$C_p = {{C_c Q_c } \over {Q_p }}$$
where
- C c is the chemical stock concentration
- C p is the chemical dose
The CD uses a lever arm to relate head in the rectangular plant entrance orifice to head in the dosing orifice. This means that the available head for the dosing orifice is the same as the head controlling the plant flow rate. The increase in head links the chemical flow rate to the plant flow rate and the chemical dose will be constant as long as n p = n c.
The dosing tube is designed to minimize major losses. This tube must be flexible to accommodate lever arm motion. Flow will be channeled through the dose control orifice into the lever arm. Holes must be drilled in the lever arm so that the flexible tubing with the dosing orifice can be moved to different locations along the lever arm. The arm will deposit chemical flow into the same position in the rapid mixer regardless of the corresponding dosing location on the lever arm.
Methods
Flexible Dosing Tube
The dosing tube was designed to minimize major losses and to give a maximum chemical dose of 90 mg/L. The maximum flow rate through the tube was found using the stock concentration and the desired maximum chemical dose in a simple mass balance of water flowing through the plant. The stock concentration was assumed to be 120 grams per liter although concentrations as high as 500 grams per liter were considered. Then the head loss through the tube was set to be 2 centimeters. The tubing diameter was chosen as the minimum available diameter with the desired head loss at a flow rate greater than or equal to the calculated maximum chemical dose flow rate. In the initial calculations it was assumed that the dosing tube would be 40 cm long (half the length of the lever arm plus ten centimeters of slack). The current CDC design places the flow control module and chemical stock tanks on the opposite side of a walkway from the lever arm, requiring much longer flexible dosing tube. A constant chemical dose is not well maintained with tubing longer than half a meter. A combination of wide tubing to deliver the chemical dose to the plant and the flexible tubing must be designed to minimize head loss if the stock tank and flow control module must be placed far apart.
Dosing Orifice
The dosing orifice was designed to give twenty centimeters of head loss at the maximum chemical flow rate through the dosing tube. The minor loss coefficient through the orifice was solved for using the equation for headloss through the orifice:
Unknown macro: {latex}
$$
h_l = K_
Unknown macro: {DoseOrifice}
{{V_
Unknown macro: {DoseTube}
^2 } \over {2g}}
$$
where
- h l is the head loss
- K DoseOrifice is the minor loss coefficient through the orifice
- V DoseTube is the velocity in the dosing tube
This head loss is equal to headloss in the vena contracta. Headloss in the vena contracta is modeled by the equation:
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$$
h_l = K_
Unknown macro: {Extension}
{{V_
Unknown macro: {VenaContracta}
^2 } \over {2g}}
$$
where
- h l is the head loss
- K Extension is the minor loss coefficient through the vena contracta
- V VenaContracta is the velocity in the vena contracta
K Extension is equal to one. The flow rate through the dosing tube is known and velocities in the vena contracta can be found using mass conservation:
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$$
A_
Unknown macro: {DoseTube}
V_
= K_
Unknown macro: {Orifice}
A_
Unknown macro: {DoseOrifice}
V_
$$
where
K orifice is the orifice minor loss coefficient equal to 0.6
The headlosses in the vena contracta are equal. Using the three equations above a relationship for the velocities can be found:
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$$
K_
Unknown macro: {DoseOrifice}
= \left[ {{1 \over {K_
Unknown macro: {Orifice}
}}\left( {{{V_
Unknown macro: {DoseTube}
} \over {V_
}}} \right)^2 } \right]^2
$$
Unknown macro: {float}
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Figure 2: Alum and Plant Flows
K DoseOrifice is used to solve for the flow rate in the alum tube with varying available head. A comparison of chemical flow rate and plant flow rate as available head increases is shown in figure 2. n c is not exactly equal to n p as can be seen in figure 2. Decreasing the difference between the two would create a more robust chemical doser.
Lever Arm and Float
Since the length of the lever arm does not effect the head loss, the same arm will be used as for the Linear CD. The PVC of length 68 cm is being used out of simplicity. In the future, a longer lever arm could be used that would allow for more flexibility in dosing with changes in turbidity. The lever arm will need to have a large enough diameter so that holes that are the same diameter as the flexible tubing may be drilled into the top of it, without effecting the flow through the lever arm. This will allow for changes in dosage with changing levels of turbidity.
The size of the float can be determined using a moment balance around the pivot of the lever arm. This is to ensure that a change of 20 cm in head in the entrance tank will cause a similar change in the relative height of the float. The float was sized using the same float sizing algorithm used by the linear CDC. For flows between 600 and 25,000 L/min the float diameter ranged between 6 and 16 in. Filling the float with a more dense material should be investigated for a more practical design at high plant flow rates.
Flow Control module
To reduce head loss through the float valve orifice, a new flow controller is being used in the design. The module being used is a PT 75 LS
Kerick Valve. When choosing what size float valve to use, the constraints are the allowable flow rate through the valve, the head loss through the valve, and the size of the valve. In this case, a valve was needed that would allow a flow rate over 400 mL/min, the constraining flow rate for the float valve in the linear CDC flow control module. Chemical flow rates higher 400 ml/min require that the chemical stock tank be elevated to an unreasonable height due to head loss through the float valve orifice. To minimize head loss, a 3/4 inch orifice was chosen. The flow controller will be mounted in a tub, so it cannot be too large. The float valve that fit all of these constraints was the PT 75 LS.
Functional Range
With an alum stock concentration of 500 mg/L, the design for the linear CDC can be extended to plants with a flow rate of 2000 L/min. At 25,000 L/min, head loss through the float valve orifice reaches 1 m. This is a potential constraint for plants this large and a float valve with a larger orifice might be considered. The constant chemical dose begins to fail at most flow rates when flow is around 45% of the design flow rate (the sharp increase in dose in figure 4). Further investigation into the optimal relationship between flow rate, chemical stock concentration, available head and dosing tube length might extend the range of functionality.