# Membrane separations experimental set up

1. Oct 3, 2015

### Maylis

Hello,

I will be doing an experiment to separate N2 from O2 in air using membrane separations. I need to write my own experimental procedure to find the objectives of the experiment.

Here is our experimental set up

I'm trying to figure out how to do objective i. I need to figure out the selectivity of the membrane for oxygen over nitrogen. It says I should calculate the transmissibility of the two species. the transmissibility, $k_{pi}$ is defined
$$k_{pi} = \frac {\mathcal{P}_{i}}{L_{m}}$$

Where $\mathcal{P}_{i}$ is the permeability of species $i$, and $L_{m}$ is the length of the membrane. You can calculate the molar flux, $J_{i}$

$$J_{i} = k_{pi}(P_{ir}-P_{ip})$$

Where $P_{ir}$ is the retentate pressure (feed pressure), and $P_{ip}$ is the permeate pressure. I get I can find the feed pressure from the first gauge, but from the diagram there is no pressure gauge for the permeate. I figured I could calculate the molar flux because the permeate flow rate is equal to the area of the membrane times the average molar flux

$$V_{p} = A_{T} \langle J_{i} \rangle$$

So I could use the rotameter to find $V_{p}$, then knowing $A_{T}$ I can calculate the $\langle J_{i} \rangle$. Once I have $\langle J_{i} \rangle$, I would do

$$\langle J_{i} \rangle = k_{pi}(P_{feed}-P_{permeate})$$

But I run again into the problem of not knowing $P_{permeate}$. If I can get that, then I know the selectivity is trivial

$$\alpha_{ij} = \frac {k_{pi}}{k_{pj}}$$

Any ideas how I might be able to do this? One thought is using the temperature of the permeate to find the permeate pressure with the ideal gas law.

Last edited: Oct 3, 2015
2. Oct 3, 2015

### Staff: Mentor

As you release the filter products into the air again without additional pumps, I would expect a pressure close to atmospheric pressure behind the membrane (no needle valve at the middle line).

3. Oct 3, 2015

### Maylis

I read on wikipedia that a needle valve is used for precise flow measurements. How does that relate to your expectation of a pressure neat atmospheric pressure?

4. Oct 3, 2015

### Staff: Mentor

It is unrelated because my comment refers to the line without it.

5. Oct 3, 2015

### Maylis

Right, but I'm interpreting your meaning as the lack of a needle valve implies atmospheric pressure. If this is the correct interpretation, I'm curious how that is so.

6. Oct 3, 2015

### Staff: Mentor

I don't see anything that could change the pressure. It's basically an open pipe.

The needle valve can maintain a pressure difference between its sides.

7. Oct 3, 2015

### Maylis

Okay, sounds good. Thank you! I will come back if I get stuck on the other objectives.

8. Oct 3, 2015

### Maylis

I have to admit, something strange in the lab manual procedure

I don't understand why I would need the temperature to determine the flow rate of the permeate if I have a flow meter, as seen in the diagram. Here is an overall diagram. The one I posted earlier is just for one module (co-current flow). I included the whole lab manual so I don't have to just give you vague details without anyone knowing the whole context of the experiment.

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9. Oct 4, 2015

### Staff: Mentor

Density depends on temperature and pressure. I don't know your flow meter, if it just measures volumetric flow you need the density of the medium to calculate mass flow.
Even it measures mass flow directly, its measurement will still depend on temperature a bit. Better flow meters have internal thermometers and software to correct for that.

10. Oct 4, 2015

### Maylis

This bit of information may help from the lab manual
Permeate
I figure I will read from the rotameter the volume and divide by time to get volumetric flow rate. Then I need the temperature to know the density of the gas. From the figure in my OP, whats the purpose of having both a rotameter and a flow meter?

11. Oct 4, 2015

### Staff: Mentor

And pressure. Yes, that's the point.
I don't know.

12. Oct 5, 2015

### Maylis

Turns out the volumetric flow meter range is too small, so it maxes out even at small flow rates