Tracer concentration + effective residence time for a basin

[maistral]

I'm very sorry for the lengthy post. I'm actually not sure as to how to deal with this as this is the first time I've been assigned to these kinds of problems; I need to be sure. Thanks in advance.

So I have this large basin-like structure whose water naturally has K⁺ ions dissolved in it; let's call this constant A. This basin only has one stream as the feedstream and another one for the effluent. I wanted to measure the effective residence time for this "basin" which I think I can deal with alone.

So I intended to use something like potassium carbonate or potassium chloride to measure the effective residence time. I injected around 0.005 kilomoles of potassium carbonate (so that's around 0.01 kilomoles of K⁺ ions). My problems began from here actually.

1. My sensor detects K⁺ ions. Obviously, it would detect a gradual increase, then a decrease (typical reactor RTD). What I initially thought is that if I subtract the number of K⁺ ions initially from the dataset of K⁺ ions I have generated from the effluent's sensor (basically subtracting the constant A from the entire dataset), and I would add all these values, I should be getting the total 0.01 kilomoles of K⁺ ions detected by the tracer. This did not happen (I mean, I did not get all of the 0.01 kmols of K⁺ ions). Where could have they run off to? After subtracting initial K⁺ ion concentration A from the dataset and adding all of the values I ended up detecting around 0.0003 kmols of K⁺ ions only.
2. (Connected to #1) For curiosity's sake I wanted to take the recovery of potassium carbonate. Is it still 0.0003/0.01 * 100 = 3%? Is this even realistic? Or am I doing something wrong; and there is a different formula for this?

Thanks for reading this lengthy post. I hope someone can answer as I'm at a total loss.

 

[Bystander]

If you rewrite the problem in terms of concentrations, apply a step function perturbation of the concentration, watch the relaxation rate, ... hmmm?

 

[Chestermiller]

Let’s see a graph of your conc vs time. Are you sure you are using the correct flow rate in and out? Does the outflow match the inflow?

 

[maistral]

Ah, I figured out that I have to integrate the concentration vs. time then multiply it to the measured flowrate. I'll have to integrate the flowrate vs time as well to get the mean flow rate.

I resolved the issue. Thanks!