Rapid Sand Filtration

SOLUTION

The effect of increase in certain rapid sand filter and influent particle characteristics on time (T_B) for reaching particle breakthrough (turbidity > 2.5 NTU) in the effluent, and time (T_H) of reaching terminal head-loss (>3 m) across filter bed are given below. Explain the results based on you understanding of filter operation and particle removal mechanisms operative in rapid sand filters. Assume that when one characteristic is changed, all other characteristics remain fixed.

Parameter	Time to Breakthrough TB	Time to Terminal Headloss TH
Filter Depth (L)	Increase	Decrease
Superficial Velocity (Vs), (m^3/m^2/h)	Decrease	Decrease
Influent Particle Concentration, (Co), mg/L)	Decrease	Decrease
Floc Strength	Increase	Decrease
Collector diameter (d), m	Decrease	Increase
Porosity, a	Decrease	Increase
Particles not Destabilized by Addition of Coagulants	Decrease	Increase

Solution:

Effect of Increase in Filter Depth (L):

T_B: T_B will increase since particles in water will have the opportunity to potentially interact with more collectors, and hence the chance for particle attachment to a collector is more.

T_H: Since bed depth is more, water is encounter more resistance is passing through the bed. Hence T_H will decrease.

Effect of Increase in Superficial Velocity (V_s):

T_B: Since pore velocity is more, the shear forces experienced by collected particles will be more. Hence particle detachment will be more, leading to a decrease in T_B.

T_H: Since particle loading rate on the filter and rate of particle collection in the filter will increase, the porosity of the filter bed will decrease more rapidly, leading to more rapid head-loss buildup and hence a decrease in T_H.

Effect of Increase in Influent Particle Concentration (C_o):

T_B: Particle loading rate on the filter, rate of particle collection and hence porosity of the filter bed will decrease more rapidly. Thus pre velocity in the filter bed will increase more rapidly, leading to more rapid particle detachment. This will lead to decrease in T_B.

T_H: Since particle loading rate on the filter and rate of particle collection in the filter will increase, the porosity of the filter bed will decrease more rapidly, leading to more rapid head-loss buildup and hence a decrease in T_H.

Effect of Increase in Floc Strength:

T_B: Particle detachment due to shear forces will become less prominent leading to increase in T_B.

T_H: Since particle retention in the filter will be more, the porosity of the filter bed will decline faster leading to faster buildup of head-loss and hence T_H will decrease.

Effect of Increase in Collector Diameter (d):

T_B: Increase in collector diameter will mean the presence of a lesser number of collectors in the filter media. This will result is lesser number of potential interaction between a particle and a collector. Thus TB is expected to decrease.

T_H: Since lesser number of particles will be collected as mentioned above, the rate of head-loss buildup will be lower, leading to increase in T_H.

Effect of Increase in porosity (a):

It must be realized that porosity of the filter media does not depend on particle size, but on grading of particles. Well-graded sand, i.e., with a broader particle size distribution will have less porosity, as compared to poorly graded sand with a narrower particle size distribution.

T_B: In case poorly graded sand (with more porosity) is used as the filter media, the influent particles will potentially encounter lesser number of collectors and will not be collected efficiently. Hence T_B will decrease.

T_H: Increase in porosity of sand and poor particle collection as described above will result in lower rate of head-loss build-up and hence increase in T_H.

Effect of Non-Addition of Coagulant:

T_B: If no coagulants are added, the particles will be stable and hence will not attach efficiently to the filter media. Hence T_B will decrease.

T_H: Since rate of particle collection in the filter media will be lower as described above, the rate of head-loss buildup will also be lower, leading to an increase in T_H.