Question 2 (20 pts): The secondary clarifier surface overflow rate, QIA, has bee

Question

Question 2 (20 pts): The secondary clarifier surface overflow rate, QIA, has been fixed at 24 m2/m2 d. The return sludge recycle rate, QR is equal to 75% of Q. (Hint: underflow rate Ub-QR/A). Assume that the solids wasting rate Qw is negligible compared to OR. The following settling data for activated sludge suspension are given. Initial settling MLSS, g/m velocity, 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 m/h 6.246 3.203 1.642 0.842 0.432 0.221 0.113 0.058 0.015 0.008 0.004 0.002 0.001 1. Calculate the gravity solids flux (SF CV), underflow solids flux (SF- CUb), and total solids flux (SF-SF+ SF) in terms of kg/m2-h for each MLSS concentration

Explanation / Answer

Activated sludge entering the secondary clarifier from the activated sludge basin settles towards the bottom of the clarifier by two velocity components;

(i) Initial settling velocity that results from gravitational forces (Vs) and

(ii) A velocity component resulting from the removal of sludge from the bottom of the clarifier, (Ub= QR/A), where A is the clarifier surface area and QR is defined as the Clarifier Underflow rate.

The solids flux that results from Initial settling velocity (Vs) is termed Gravity Solid flux (SFg), which is defined as Multiplication of the initial settling velocity by the concentration yields of the solids

I.e. SFg = CiVsi, Where Ci is concentration and Vsi is initial settling velocity at a particular instant

The flux resulting from underflow flow rate is termed as Underflow Solid flux (SFu), which is the product of underflow velocity (Ub) and concentration.

I.e. SFu = CiVbi, Where Ci is concentration and Vbi is underflow velocity at a particular instant.

From the question, we have

Concentration (Ci) given in the table as MLSS, in g/m3

Initial settling velocity (Vsi) for different concentration is also in the table in m/h

We have,

Surface Overflow Rate, Q/A = 24 m3/ m2.h and Return Sludge Cycle Rate, QR = 0.75 Q

Therefore, QR/A = 0.75 * 24 m3/ m2.h

Underflow Velocity is given by, Ub= QR/A = 0.75 * 24 m3/ m2.h = 0.75* 24 m/ 24 h       {1 day = 24 hrs.}

                                                                            = 0.75 m/h

The total Solid flux is the sum of Gravity Solid Flux (SFg) and Underflow Solid flux (SFu).

I.e. SFt = SFg + SFu

Since, values of Solid flux is required in Kg/m2.h , convert the concentration (MLSS) from g/m3 to Kg/m3 by dividing by 1000.

For, MLSS = 1000 g/m3 = 1 Kg/m3 and Vs = 6.246 m/h ; SFg = 1 * 6.246 = 6.246 Kg/ m2.h

SFu = 0.75 * 1 = 0.750 Kg/m2.h and Total Solid Flux, SFt = SFg + SFu = 6.246 + 0.750 = 6.996 Kg/m2.h.

Similarly, for all values of concentration, Gravity flux , Underflow Flux and Total solid flux has been calculated and summarised in the table below.

Calculation of Gravity Solid Flux , Underflow Solid Flux and Total Flux 1 2 3 4 5 6 7 S.No Concentration Initial Settling Velocity Gravity Solid Flux Underflow Rate Underflow Solid Flux Total solid flux (Ci) (Vsi) (SFg = Ci* Vsi) (Ub) (Sfu) (SFt = SFg + Sfu) Unit Kg/m3 m/h Kg/m2.h m/h Kg/m2.h Kg/m2.h 2*3 2*5 4+6 1 1 6.246 6.246 0.75 0.750 6.996 2 2 3.203 6.406 0.75 1.500 7.906 3 3 1.642 4.926 0.75 2.250 7.176 4 4 0.842 3.368 0.75 3.000 6.368 5 5 0.432 2.160 0.75 3.750 5.910 6 6 0.221 1.326 0.75 4.500 5.826 7 7 0.113 0.791 0.75 5.250 6.041 8 8 0.058 0.464 0.75 6.000 6.464 9 9 0.030 0.270 0.75 6.750 7.020 10 10 0.015 0.150 0.75 7.500 7.650 11 11 0.008 0.088 0.75 8.250 8.338 12 12 0.004 0.048 0.75 9.000 9.048 13 13 0.002 0.026 0.75 9.750 9.776 14 14 0.001 0.014 0.75 10.500 10.514

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