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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.

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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, ,and we assume the same initial pH(6.5), using the same method gives a much steeper slope (see figure 2).

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