Solid Waste Management Methods

Step 1: Solids entering the centrifuge.

%5Ctext%7BFeed%20flow%7D%20%3D%201000%5C%20%5Ctext%7BL%2Fh%7D

%5Ctext%7BFeed%20solids%20concentration%7D%20%3D%202%5C%20%5Ctext%7Bg%2FL%7D

%5Ctext%7BSolids%20in%20feed%7D%20%3D%201000%20%5Ctimes%202%20%3D%202000%5C%20%5Ctext%7Bg%2Fh%7D

Step 2: Solids captured in thickened slurry (99% efficiency).

%5Ctext%7BCaptured%20solids%7D%20%3D%200.99%20%5Ctimes%202000%20%3D%201980%5C%20%5Ctext%7Bg%2Fh%7D

Step 3: Slurry solids concentration.
Given:

20%5C%20%5Ctext%7Bg%20per%20100%20mL%7D%20%3D%20200%5C%20%5Ctext%7Bg%20per%20L%7D

Thus slurry concentration:

C_s%20%3D%20200%5C%20%5Ctext%7Bg%2FL%7D

Slurry flow rate:

Q_s%20%3D%20%5Cfrac%7B1980%5C%20%5Ctext%7Bg%2Fh%7D%7D%7B200%5C%20%5Ctext%7Bg%2FL%7D%7D%20%3D%209.9%5C%20%5Ctext%7BL%2Fh%7D

Step 4: Supernatant flow rate.

Q_%7B%5Ctext%7Bsup%7D%7D%20%3D%20Q_%7B%5Ctext%7Bfeed%7D%7D%20-%20Q_s

Q_%7B%5Ctext%7Bsup%7D%7D%20%3D%201000%20-%209.9%20%3D%20990.1%5C%20%5Ctext%7BL%2Fh%7D

Rounded to one decimal:

%5Cboxed%7B990.1%5C%20%5Ctext%7BL%2Fh%7D%7D

Step 1: Model for continuous aeration/stripping.
For a completely mixed tank with first-order mass transfer to gas phase (with finite equilibrium), the liquid-phase concentration obeys

%5Cfrac%7BdC%7D%7Bdt%7D%3D-k%5C%2C(C-C%5E*).

Integrating from

C_%7B%5Ctext%7Bin%7D%7D

C_%7B%5Ctext%7Bout%7D%7D

t%3D%5Cfrac%7B1%7D%7Bk%7D%5Cln%5C!%5Cleft(%5Cfrac%7BC_%7B%5Ctext%7Bin%7D%7D-C%5E*%7D%7BC_%7B%5Ctext%7Bout%7D%7D-C%5E*%7D%5Cright).

Step 2: Compute the necessary hydraulic residence time $t$ .
Insert numbers (all in

%5Cmu

g/L):

t%3D%5Cfrac%7B1%7D%7B0.40%7D%5Cln%5C!%5Cleft(%5Cfrac%7B33-5%7D%7B12-5%7D%5Cright)%0A%3D2.5%5C%20%5Cln(4)%0A%3D2.5%5Ctimes%201.386294%0A%3D%20%5Cboxed%7B3.4657%5C%20%5Ctext%7Bs%7D%7D.

Step 3: Convert flow to m $%5E3$ /s and obtain volume.

Q%3D%5Cfrac%7B180%7B%2C%7D000%5C%20%5Ctext%7Bm%7D%5E3%7D%7B%5Ctext%7Bd%7D%7D%5Ctimes%20%5Cfrac%7B1%5C%20%5Ctext%7Bd%7D%7D%7B86%7B%2C%7D400%5C%20%5Ctext%7Bs%7D%7D%0A%3D%20%5Cboxed%7B2.0833%5C%20%5Ctext%7Bm%7D%5E3%2F%5Ctext%7Bs%7D%7D.

Tank volume

V%3DQ%5C%2Ct%3D2.0833%5Ctimes%203.4657%3D%5Cboxed%7B7.215%5C%20%5Ctext%7Bm%7D%5E3%7D%20%5CRightarrow%20%5Cboxed%7B7.22%5C%20%5Ctext%7Bm%7D%5E3%7D.%0A%5C%5D%20%3Cbr%3E%3Cstrong%3EStep%204%3A%20Sanity%20checks.%3C%2Fstrong%3E%3Cbr%3E

C_{\text{out}}(=12)

is%20above

C^*(=5)

so%20removal%20is%20feasible%20by%20mass%20transfer%3B%20small

arises%20due%20to%20large

(fast%20gas%E2%80%93liquid%20transfer).%20%3Cstrong%3EFinal%20Answer%3A%3C%2Fstrong%3E%5Cfbox%7B7.22%20m

^3$}

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Solid Waste Management Methods

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs