Water Treatment Processes - Mathematics and Statistics for the Environment - page 628

23.5.7 d etermining l lime d osage ( mg /l)
During the alum dosage process, lime is sometimes added to provide adequate alkalinity (HCO 3 - )
in the solids contact clarification process for the coagulation and precipitation of the solids. To
determine the lime dose required, in mg/L, three steps are required. In Step 1, the total alkalinity
required to react with the alum to be added and provide proper precipitation is determined using
the following equation:

Total alkalinity required = Alkalinity reacting with alum + Alkalinity in the water (23.55)

↑

(1 mg/L alum reacts with 0.45 mg/L alkalinity)

■ EXAMPLE 23.56
Problem: Raw water requires an alum dose of 45 mg/L, as determined by jar testing. If a residual
30-mg/L alkalinity must be present in the water to ensure complete precipitation of alum added,
what is the total alkalinity required (in mg/L)?

Solution: First calculate the alkalinity that will react with 45 mg/L alum:

0.45 mg/L alkalinity
1mg/Lalum

= x

linity
45 mg/L alum

mg/L alka

04545 . ×= x

x = 20.25 mg/L al kalinity

Then calculate the total alkalinity required:

Total alkalinity required = Alkalinity reacting with alum + Alkalinity in the water

= 20.25 mg/L + 30 mg/L = 50.25 mg/L

■ EXAMPLE 23.57
Problem: Jar tests indicate that 36 mg/L alum is optimum for a particular raw water. If a residual
30-mg/L alkalinity must be present to promote complete precipitation of the alum added, what is
the total alkalinity required (in mg/L)?

Solution: First calculate the alkalinity that will react with 36-mg/L alum:

0.45 mg/L alkalinity
1mg/Lalum

= x

linity
36 mg/L alum

mg/L alka

04536 . ×= x

x = 16.2 mg/L alk alinity

Then calculate the total alkalinity required:

Total alkalinity required = 16.2 mg/L + 30 mg/L = 46.2 mg/L