Calculating TIme to Reach Desired Chemical Concentration 1

[autonub]

This should be an easy one, but how do you calculate the time it takes to raise a tank of liquid up to a certain chemical concentration given the following known parameters:

Input Tank Volume in Gallons
Output Flow Rate in Gal/hr
Concentration of Output in parts-per-million
Desired Increase in Input Tank Concentration in parts-per-million

Example: We have a 50,000 gallon tank with a chemical concentration of 3ppm, but we want to raise the concentration to 17 ppm. We have a pump with a flow rate of 9.25 gal/hr able to inject the chemical at a concentration of 35 parts-per-million. How long would it take to raise the input tank of 50,000 gallons of liquid from 3 parts per million to 17 parts per million using our pump with a flow rate of 9.25 gal/hr outputting a concentration of 35 ppm?

There's something I'm missing so I'd like to see the math if anyone would be so kind as to show it. Before anyone asks, this is job related not school related. I'm working on an excel calculator for work but I'm having difficulty wrapping my head around this one! Thanks in advance!

 

[Compositepro]

It will be a long time. Calculate how many lbs of chemical are in the tank now and how many lbs. you have to add. Then calculate how many lbs./hr you can add, and how many lbs. per hour are leaving while you are adding. The leaving concentration will be changing (close to) linearly with time, so take an average over time. A couple of iterations should get a very close answer. The trick is to use a mass balance and not concentrations for your calculation.

 

[Latexman]

It looks like you need to derive a differential balance on the "certain chemical" you are interested in, intergate it between initial and final conditions, and solve for elapsed time. A good reference would be Elementary Principles of Chemical Processes by Felder and Rousseau.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[Latexman]

Do you have a ChE resource at the site/in the company that could help? They probably have the reference cited since it's used in most ChE curriculums these days, and it should be child's play for them. It just doesn't get much easier than this - mass balance, no heat balance, no reaction.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[chicopee]

I can do this problem two ways discreetly or by integration, however, is the concentration in ppm by volume or ppm by weight?

 

[chicopee]

Please see the attachment. The problem is one that involves a logarithmic solution. The solution is based on assuming the concentration to be in ppm by weight of the medium carrying the additive which in this case I used water. Any other liquid would do as long as isothermal mixing is understood. The solution, and this is an ideal time, revealed that it would take 3,110 hours to reach the 17 ppm(W) at the outlet. Obviously, it may take a longer or shorter time to reach the 17 ppm(W) at the outlet due to an inefficient mixing process.

 

[Compositepro]

It's nice to see my answer confirmed (It will be a long time). The OP hasn't been back since he posted his question.

 

[bimr]

Here is an example of the math. Same as Chicopee above with some details.

 

[autonub]

Good Morning Gentlemen,

Thank you all for taking the time to respond. I apologize for not acknowledging your efforts sooner. It has been busy here and I was out of state on field service for over a week. We actually derived an equation by solving algebraically. Your calculations are very interesting though. It makes me wonder if ours is incorrect. We will review.

Thanks again for your time!