Analysis of lime feeder requirements based on Mathcad

ANC CONTROL

Flow rate required in Lime-feeder

The lime fed by lime feeder will help to increase the alkalinity in the raw water during the coagulation process, help the original carbonate system to build the buffer to neutralize the (This is a closed system, how will the system buffer with respect to the carbonate system if you are adding hydroxide?) acidity from adding aluminum sulfate, and thus, improve the quality of the treated effluent water. Our team wants to find the relationship between flow rate of lime feeder, pH ,and alkalinity in raw water.

There are several ways to change the concentration of lime in raw water through the lime feeder, such as changing the dosage of lime, the operation time (I'm not sure how this is different than the upflow velocity.), lime feeder velocities. Technically, the effluent pH of lime feeder should be kept at around a lime saturation pH of 12.4. Our assupmtion is that with a continuously flow system, the previously dissolved lime would be washed out and provide the effluent pH at around 12, it follows more and more settled lime become dissolvable in water. With a proper combination of lime dosage and flow rate this function could be kept until all the settled lime dissolve in water and come out with effluent water, thus provide us the constant effluent pH for a relatively long time, we hope it can achieve 12 hours for routine opertation.
(Please revise the structure of this sentence. I could not follow it completely.)+

Since the effluent pH should be relatively constant under our assumption previously discussed, the way we can change the lime concentration in raw water is to change the flow rate of lime feeder. The constant effluent pH also creates convenience for the operator to use the apparatus adjusting pH and AlK in raw water by simply changing the flow rate of lime feeder. The flow rate should be in a certain range which could  maintain plant pH between 6.5 to 7.5, it is the range coagulation  will be most efficient.  <Water Quality and Treatment by Letter 1999>

Our next step is to build the model between flow rate of lime feeder and the change in pH, alkalinity in plant Marcala and Cuatro Comunidades based on the data from Honduras report.(Please edit sentences before you submit them on the wiki.)

To get the proper lime doseage it is necessary to know the initial total carbonate in the system. e.g CT, from the initial Alkalinity and pH of Marcala and Cuatro Comunidades. We can find the CT based on equation 1, and because we assume this is a closed system so the CT will not change during the process, so that the relationship between Alkalinity and pH can be also measured with equation 1:
equation 1:

In the next step, considering the flow rate of the plant will also change, the team would like to use the ratio between the lime feeder flow rate and the plant flow rate to get a more practical function

When this flow ratio changes, lime concentration will also change, we can acquire the relationship between this flow ratio and the concentration of hydroxide ion in raw water. From mass balance equation,
equation 2:

The relationship between OH- concentration and alkalinity can be caculated with equation 3:
equation 3

The premise of using the above equation is that we have to know the equivalent of proton created by adding aluminum sulfate, which can be measured from the difference of initial alkalinity and final alkalinity from our data.     
Based on all this  data and equations  we can make a model showing the change of pH and alkalinity as the funcion of flow ratio between lime feeder and plant. The model which predict these relationships of Marcala and Cuatro Comunidades are shown in figure 1:  (Remind us what was different about Marcala versus Cuatro Comunidades)

Figure 1: The relationship between flow ratio, ANC and pH of Cuatro Comunidades(figure 1.a) and Marcala(figure 1.b)
 
The zero point of both plants represent when there is no lime fed into the water, and the pH and alkalinity are only affected by aluminum sulfate. After we increase the flow ratio from 0 to 0.01, we can see from figure 1 that both of the two plants have almost the same increasing pattern of pH and alkalinity. The increase of alkalinity has a linear relationship with the increse of flow ratio: with higher flow ratio the lime concentration in the raw water will increase, and cause the alkalinity increase(equation 3). The change of pH is more complicated than alkalinity due to the exist of bicarbonate acting as the buffer. In order to find how does the buffer affect on the pH we can make the model of buffer intensity in the system, see graph in figure 2:  (What did you assume about the alkalinity in these cases?)


Figure 2: Buffer intensity in Marcala and Cuatro Comunidades

The different buffer intensity in Marcala and Cuatro Comunidades is because of different initial alkalinity. As the initial pH starts from 6, it just locate in the zone which the buffer intensity is greatest(the highest point is when pH equals to pK1 of  carbonate system), as the pH continously increase the buffer intensity becomes weak and the pH begin to increase much more faster, which would easily cause the coagulation mechanism faliure and undesirable effluent water quality, just as what the two models predict. (Proofread this sentence as well.)