In: Chemistry
We stated at the start of the course that any separation unit is generally more expensive if it has a higher separation factor. Carefully explain whether the correlation from Perry’s logically matches that statement for treating a given wastewater feed.
Solution
Separation factors, recall, are defined so that
where i and j are selected so that Sij > 1.
A given feed implies the physical properties are fixed, which implies the terminal settling velocity is constant (note: a misconception that some people have is the TSV changes with an increased tank diameter; we explicitly learned this is not the case, else we wouldn’t be able to scale up from lab tests to industrial scale). So if we are treating a given wastewater feed, by increasing the tank diameter we expect the following logic to hold:
• we will pay more for a larger diameter tank, (based on the correlation), so a
• larger tank diameter, implies
• larger tank area, implies
• slower horizontal velocity component for a given throughput Q, implying
• more time for solids to settle (i.e. a longer residence time), implying
• x_solid,under increases and x_solid,over decreases, implying
• S in the above equation gets larger and larger.
This sequence of logical events matches our expectation.