Sludge is composed of solids and water in such a mixture that the physical appearance looks more of being composed of wet solids than being a concentrated water. Analysis of the sludge, however, will show that it is practically water containing about 99% of it.
Because of the high percentage of water that it contains, the volume of sludge produced in chemical coagulation is the biggest drawback for its use. Nevertheless, depending upon circumstances, it has to be used. Therefore, we now derive the formulas for estimating the volume of sludge produced in coagulation treatment of water.
Two sources of solids are available for the production of sludge: the suspended solids or turbidity in the raw water and the solids produced from the coagulant. The suspended solids in surface raw waters can vary from 5 to 1000 mg/L (Sincero, 1968). The aim of coagulation treatment is to produce a clear water. Thus, for practical purposes, suspended solids can be assumed to be all removed. If V is the cubic meters of water coagulated and spss are the solids, the kilograms of solids produced from the suspended solids is ([spss]mg/1000)V, where [spss]mg is in mg/L.
For convenience, the chemical reactions for the coagulants are reproduced as follows:
Al2(SO4)3 • xH2O + 3Ca(HCO3)2 ^ 2Al(OH)31 + 6CO2 + 3CaSO4 + xH2O
Al2(SO4)3 • xH2O + 3Ca(OH)2 ^ 2Al(OH)3i + 3CaSO4 + xH2O (12.87)
Al2(SO4)3 • xH2O + 3CaCO3 + 3HOH ^ 2Al(OH)31 + 3CaSO4 + 3CO2 + xH2O
FeSO4 • 7H2O + Ca(OH)2 ^ Fe(OH)2i + CaSO4 + 7H2O (12.90) Fe( OH ) 2 + 4O2 + ^O^ Fe ( OH )31 (12.91)
2FeCl3 + 3Ca(HCO3)2 ^ 2Fe(OH)31 + 6CO2 + 3CaCl2 (12.92)
Fe2(SO4)3 + 3Ca(HCO3)2 ^ 2Fe(OH)31 + 6CO2 + 3CaSO4 (12.93)
2Fe3+ + 3CaCO3 + 3H2O ^ 2Fe(OH)31 + 3Ca2+ + 3CO2 (12.96)
The solids produced from the coagulation reactions are Al(OH)3, Fe(OH)3 and CaCO3. Referring to the reactions of alum, the equivalent mass of aluminum hydroxide is 2Al(OH)3/6 = 26.0. The ferric hydroxide is produced through the use of copperas and the ferric salts. Its equivalent mass from the use of copperas [Eqs. (12.89) through (12.91)] is Fe(OH)3/2 = 53.4 and from the use of the ferric salts, its equivalent mass is 2Fe(OH)3/6 = 35.6. Calcium carbonate is produced from the reaction of copperas, Equation (12.89). From this reaction, the equivalent mass of calcium carbonate is 2CaCO3/2 = 100.
Let MAlOH be the kilogram mass of aluminum hydroxide (plus the solids coming
from the suspended solids) produced from treating V m of water and from an optimum alum dose of [Alopi]geq gram equivalents per liter or, equivalently, [Alopt]mg milligrams per liter. Also, let MFeOH FeII be the kilogram mass of ferric hydroxide (including the calcium carbonate plus the solids coming from the suspended solids) resulting from the use of an optimum dose of copperas of [FeIIopt]geq gram equivalents per liter or [FeIIopt]mg milligrams per liter, and let MpeOH Fein be the kilogram mass of ferric hydroxide (plus the solids coming from the suspended solids) resulting from the use of an optimum dose of [FeIIIopt]geq gram equivalents per liter or [FeIIIopt]mg milligrams per liter of any of the ferric salt coagulants.
[Alopt]geqV = ([ALopt]mg/1000(57.05 + 3x))V and [FeIIopt]geqV = ([FeIIopt]mg/ 1000(138.95))V. [Femopi]geqV = [FeIIIopi]mgV/1000(54.1) for FeCl3 and [FeIIIopi]geqV = [FeIIIcpi]mgV/1000(66.65) for Fe2(SO4)3. Thus,
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