Analysis of lime feeder requirements based on Mathcad

Flow rate required in Lime-feeder

The lime feeded by lime feeder will help to increase the Alkalinity in raw water during coagulation process, help the original carbonate system to build the buffer to neutralize the Acidity from adding Aluminum Sulfate, thus improve the quality of treated effluent water, our team want to find the relationship between flow rate of lime feeder and the pH and Alkalinity in raw water.

There are several ways to change the concentration of lime in raw water through lime feeder, such as the dosage of lime, the operation time, lime feeder velocities, lime feeder effluent pH etc. Technically, the effluent pH of lime feeder should be kept at around 12, that is the lime saturate pH, our assupmtion is that with a continously flow comes from a distribution of raw water into lime feeder 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, and 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.

Since the effluent pH should be constant based on our assumption, the way we can change the lime concentration in raw water is depend on the flow rate of lime feeder, it also create convenience for the operator to use the apparetus changing pH and AlK in raw water. The flow rate should be in certain range which could provide the pH environment in the tank 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 spanish version translated by our team member Ximena.

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 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 waterFrom mass balance equation,
equation 2:

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

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 these datas and equations now we can make the 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: 

Figure 1: The relationship between flow ratio, ANC and pH of Cuatro Comunidades(figure 1.a) and Marcala(figure 1.b)
 
Both of the two plants have almost the same increasing pattern of pH and alkalinity after we increase the flow rate ratio, and we can also notice the zero point of both plants represent when there is no lime feeded in water, and the pH and alkalinity are only affected by aluminum sulfate. What the model can show us is that the change of pH is affacted by the buffer intensity of bicarbonate, since the buffer intensity is simply the differential of alkalinity over pH, we can generate the buffer graph to show this relationship more clearly, see the buffer intensity graph in figure 2: 


Figure 2: Buffer intensity in Marcala and Cuatro Comunidades

The different buffer intensity in Marcala and Cuatro Comunidades is simply because they have 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 finally it can not control the pH increasement anymore, the pH starts increasing exponentially which would easily cause the coagulation mechanism faliure and undesirable effluent water quality, just as what the two models predict.