Orifice Size and the Dual Scale Design for the Nonlinear Alum Doser

Abstract:

During the fall semester of 2009, the Nonlinear Chemical Dosing Team developed the dual scale, orifice-based doser in order to be able to deliver both turbulent and laminar alum flow. Like its linear predecessor, this doser must automatically increase or decrease the alum solution to maintain a target dosage set by the operator as the plant flow changes. As an additional feature, the two different scales provide the operator with additional precision through a low dosage (5-25 mg/L) and a high (20-100 mg/L) alum dosage range.

In order to meet our objectives above, we first researched and identified the nonlinear relationship between plant flow rate and alum dosage and the movement of the lever arm. We then utilized this relationship to develop the lever arm design to include the dual scales and the dual orifices. Attached is the Mathcad File that contains the calculations for our dosing system.

Our current design consists of a 80cm long lever arm with equal lengths and two orifices of 3.175mm and 1.587mm diameter, 9.525 mm PVC tubing, and other associated hydraulic components listed in our component list.

Summary of the Design Process:

In order to meet our design objectives mentioned above, we must link plant flow to alum flow coming out of our doser.
We utilized Mathcad's vector calculation ability to help us in our calculations.

Our first step in developing this dosage system was the selection of the orifice to control the flow of alum. We increased the tubing size connecting the constant head tank to the orifice to 9.525mm which is wide and smooth enough to make the head loss from the tubing negligible compared to the head loss through each orifice, making the orifice the flow control component for the dosage system. The orifice equation, shown below, demonstrates the nonlinear relationship between flow rate and the change in head loss.

Where

= Flow Rate

= Head Loss

= Area of the Orifice

= Orifice Constant
The plant itself is also controlled by the orifice. Head loss in the plant after the entrance tank occurs in the rapid mixer, the flocculation tank, and the launders. Those components are all controlled by orifices. The table below lists the major sources of head loss in the plant.

Table 1: Head Loss Through the Plant

The only source of head loss not controlled by an orifice is the weir. Because the majority of the head loss is due to the orifice, we can state that the orifice equation dominates the relationship. Therefore, we can link the flow rate of the plant with the flow rate of alum required for the plant using the same square root relationship mentioned above. In other words, the rise and fall of the water height in the entrance tank caused by the change in flow rate, is nonlinearly proportional to the alum flow of our orifice based doser.

Consequently, the lever arm must be long enough to rise and fall with the minimum and maximum water height in the entrance tank. This range is equal to the total head loss in the plant, which is 33.5 cm as shown in Table 1. Therefore, we designed an equally balanced lever arm of 0.8 m that fits in our 1 m x 1 m entrance tank as well as respond to the 33.5 cm water height difference.
Our next step consists of developing the dual nonlinear scale and the two orifices for our two sets of target alum concentrations: 5-25 mg/L and 20-100 mg/L. Given a known maximum plant flow rate(

) and Alum Stock concentration(

), we utilized the mass balance equation to determine alum flow rate required for each target alum concentration as shown below:

Where

= Flow Rate of Alum Solution

= Plant Flow Rate

= Target Alum Concentration

= Alum Concentration in the Stock Tank
Because the orifice controls the flow of this alum solution, we again use the orifice equation. This time we use it to solve for the head loss necessary to achieve these different flow rates. These head losses, or the difference in height from the orifice to the water height in the constant head tank, are calculated as shown below:

Where

= Flow Rate of Alum Solution

= Plant Flow Rate

= Head loss

= Diameter of the Orifice

= Orifice Constant
We then convert these headlosses to points along our scale via simple geometry as shown below:

Where

= distance from the pivot to a point on the scale

= head loss from the previous paragraph

= Maximum Angle Deflection
So that "scale" variable above corresponds to a specific head loss which corresponds to a specific alum flow rate, which corresponds to the target alum concentration that we want in our plant flow. Since we have nine target dosages, we utilized Mathcad to turn the nine target dosages into an array and apply the the relationships shown above to produce arrays of corresponding alum flow rates, head losses, and scale points. The array of scale points is essentially the scale for our nonlinear scale. Since all above mentioned parameters are related to one another in a nonlinear relationship, the scale that is generated is nonlinear as shown below:
Utilizing our Mathcad file, we varied the orifice diameter until we created a scale that maximized the total available length of the lever arm for the scale which for this lever arm is .4 m. We can also manipulate the alum stock concentration to affect orifice size. As the above mentioned equations show, lowering the stock alum concentration means more alum flow which means that we can use a greater orifice diameter while utilizing the same length of the scale part of the lever arm.

Results and Discussions

Currently, our orifices are 3.175 mm for an alum dosage range of 20 to 100 mg/L in 10 mg/L increments and 1.587 mm for an alum dosage range of 5 to 25 mg/L with 2.5 mg/L increments. Our lever arm is 80 cm in length with the pivot point located directly in the center of the arm. The tubing is made up of PVC has a diameter of 9.525 mm, which is wide and smooth enough to produce negligible head loss on the alum flow. The tubes length is .5 m which can be lowered. For ease of operation, whenever this lever arm is used in the field, it can be delivered to the Aguaclara plant with the dual scales already engraved on the arm. The operator simply has to calibrate the maximum dosage to the maximum flow rate and the lever arm will be ready for operation. The complete calibration procedures can be found on the float page.

We are currently conducting research on the reason why the doser in Honduras is clogging. If alum precipitation is the cause, an option to remedy the problem is to decrease the alum stock concentration which would lead to an increase in orifice size. More dilute stock concentration means less likelihood of alum precipitation while a larger orifice means less chance of alum precipitate getting lodged.

Although negligible, head loss via the tube is a source of error. At most the discrepancy between the scale generated by taking both the orifice and tube head loss into account and the scale generated using only the orifice head loss is only .409 cm, which only occurs at the maximum dosage of 100 mg/L. Currently our PVC tubing is 9.525 mm in diameter and 50 cm long. We can further reduce the error by increasing the diameter and decreasing the length.

Our upcoming goals are to build the lever arm prototype, to set up our hydraulic components and engrave our dual scale. Afterwards, we want to test the lever arm at different dosages and measure the actual flow rates to confirm that the error resulting from tube head loss is negligible.

Bibliography

• CEE4540 Flow Control Measurement Notes at https://confluence.cornell.edu/display/cee4540/Syllabus