*The Lime dosage required in the Lime-feeder *
For our experiment, the lime feeder water flow rate required was calculated in a MathCad file.
The variables required in the analysis, such as the dosage of lime, the operation time, water velocities, water pH etc. were taken from the values in the previous team's report. Hence the raw water was assumed to have a hardness of 0.02gm/L and an initial pH of 6.5.
The lime dosage we want should be able to increase the pH of water to 7, while neutralizing the effect of the alum that will be shortly added to it. By calculating the alkalinity under the orginial pH and a pH of 7, we can find the hydrogen demand to raise to this ANC. The amount of lime consumed to neutralize the alum can be calculated using the relationship between the equivalent weight of Alum and Lime.
The total lime required is the sum of these two parts, the equations are shown below.
The relationship between the ratio of flow rates and pH
Under actual plant conditions, we cannot keep the flow rate of water in the lime feeder constant. The water flow rate entering the lime feeder will keep changing in proportion to the actual plant flow rate because the doage of lime required in the plant will change as per the amount of water entering the plant. So the calculations must be based on the variable 'ratio' i.e. the fraction of plant flow rate entering the lime feeder.
The effect of this ratio on the ANC and pH are illustrated in the MathCad file.
It was assumed that the effluent pH of limefeeder is constant at 12.4, and the ratio of the flow rate between lime feeder and plant changes from 10^(-5) to 0.01. Other values in the calculations were kept the same as in the previous calculation.
A hardness of 0.02g/L acts as a good buffer for the system (see figure 1). From figure 1 it is observed that when the flow rate changes, the change of pH is not so dramatic but the case is much different if the hardness decreases. For instance, for the raw water of CUATRO COMUNIDADES for which the inital ANC is 7.65mg/L, using the same method gives a much steeper slope (see figure 2).
NOTE: For the present calculations, it has been assumed that water will remian neutral even after the addition of alum so the final ANC is affetced only by the initial ANC (caused by the hardness of raw water) and the hydroxide provided by the lime feeder. But in reality, the alum addition will contribute to a further decrease in the pH of water and so one of our future tasks is to re-calculate the effluent pH required to negate the effect of the alum dose.
The equation to calculate balance OH ions in plant and the final ANC are also shown below:
balance OH in plant
final ANC of plant
Figure 1: Ratio of lime feeder flow rate to plant flow rate versus final ANC and pH (Alkalinity is 20mg/L, good buffer.)
Figure 2: Ratio of lime feeder flow rate to plant flow rate versus final ANC and pH (Raw water in Cuatro Comunidades, Alkalinity is 7.65mg/L)