Analysis of lime feeder requirements based on Mathcad

ANC CONTROL

Flow rate required in Lime-feeder

The effluent from the lime feeder will increase the alkalinity of the raw water during the coagulation process. This process will help the original carbonate system build a buffer zone to neutralize the acidity resulting from the addition of aluminum sulfate (Instead of increasing the pH, the hydrogen ion from aluminum sulfate will react with the hydroxide from lime). This will improve the quality of the treated effluent water. Our team wanted to find the relationship between the flow rate of the lime feeder, pH, and the alkalinity in raw water.

There are two major criteria in the experiment: the dosage of lime and the upflow velocity. We need to find the proper combination of dosage and flow rate to maintain the effluent pH of lime feeder at the lime saturation pH of 12.4. Our assumption is that with a continuous flow system, the dissolved lime would be washed out and provide an effluent pH of 12. Lime particles suspended in the bed would also slowly dissolve. With the proper combination of lime dosage and flow rate this function could be kept constant until all the lime comes out with effluent water, and provide us with a constant effluent pH for a relatively long time (12 hours for routine operation).

Since the effluent pH should be relatively constant under the assumption previously discussed, the way we can change the lime concentration in raw water is to change the flow rate of the lime feeder. A constant effluent pH also makes it more convenient for the operator to use the apparatus because to adjust pH and alkalinity in raw water, all he would have to do is to change 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, which is the range where coagulation is the most efficient.  <Water Quality and Treatment by Letter 1999>

Our next step is to analyze the relationship between flow rate and change in pH and alkalinity in the Marcala and Cuatro Comunidades plants based on the data from Honduras report.

To get the proper lime dosage it is necessary to know the initial total carbonate (CT) 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, 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, and we can acquire the relationship between this flow ratio and the concentration of hydroxide ion in raw water from this mass balance equation,
equation 2:

The relationship between OH- concentration and alkalinity can be calculated 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 this data and these equations  we can make a model showing the change of pH and alkalinity as the function of flow ratio between lime feeder and plant. The model which follow these relationships in 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)
 
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 alum. After we increase the flow ratio from 0 to 0.01, we can see from figure 1 that both of the plants - Cuatro Comunidades(figure 1.a) and Marcala(figure 1.b) have almost the same increasing pattern of pH and alkalinity. The increase of alkalinity has a linear relationship with an increase of flow ratio: with a higher flow ratio the lime concentration in the raw water will increase and cause the alkalinity to increase (equation 3). The change of pH is more complicated than alkalinity due to the existence of bicarbonate acting as the buffer. In order to find how the buffer affects pH we can make the model of buffer intensity in the system, as seen in figure 2: 


Figure 2: Buffer intensity in Marcala and Cuatro Comunidades

The buffer intensities in Marcala and Cuatro Comunidades are different because of different initial alkalinities. Buffer intensity is greatest at a pH of 6.3. Here the pH equals to pK1 of  carbonate systems. As pH increases from 6.3 the buffer intensity becomes weaker and the pH of the system will increase much faster, which could easily cause coagulation mechanism faliure and an undesirable effluent water quality.