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 the degree we want, while neutralizing the effect of the alum that will be shortly added to it. By calculating the alkalinity under the orginial pH we can find the total carbonate eg.CT in the system, and then we can find the relationship between the target ANC and the desired pH we want(see figure 1). The total lime dose required in tank is the sum of the amount using to neutralize the alum and to raise the raw water to the desired pH(see equation below).
After we get the required lime dose demand in raw water, we want to find the lime feeder flow rate to satisfy this dosage, under the assumption that the effluent pH of lime feeder keeps at 12.4, we know the effluent OH supply, and we suppose the plant flow rate is 50 L/min, we get the required ratio between flow rate in lime feeder and the plant with the pH requirement in raw water based on equation 1.the relationship shows in figure 2.
Figure 1: The target ANC with the pH change.
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Figure 2: The ratio of required lime flow rate and plant flow rate with the required pH in raw water.
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 3). 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, ,and we assume the same initial pH(6.5), using the same method gives a much steeper slope (see figure 4).
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 <equation 1>
final ANC of plant <equation 2>
Figure 3: Ratio of lime feeder flow rate to plant flow rate versus final ANC and pH (Alkalinity is 20mg/L, good buffer.)
Figure 4: 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)