I How to calculate the mass of gas in a tank?

[Chestermiller]

Oh, no. I plotted the gauge pressures. The absolute pressures are only in post #71.

I calculate precisely this in post #88. It is the bottom right graph.

Well, obviously there is something wrong because the mass should never increase.

 

[Chestermiller]

:(
That could change the problem significantly. I did everything assuming we're talking about absolute pressures.

Not really. The difference between absolute pressure and gauge pressure is only 0.1 MPa.

 

[Tom.G]

Probably does not matter, but:

In summary, once the pressure tank goes beyond a certain pressure limit defined by the ambient pressure and the springs, the valve will open.

Umm, not quite.

It is designed to close when the tank being filled reaches a set pressure.

Note that the outlet pressure, not the source-tank pressure, acts on the diaphragm, closing the valve.

("absperrventil", on the right, is the "shut-off valve"
'Zum Brenner' translates as 'to the burner'.)

Cheers,
Tom

 

[Leopold89]

Well, obviously there is something wrong because the mass should never increase.

Juanda got increasing masses, too.

What's the meaning of $r$?
View attachment 350506

I think I don't need it for the way I want to solve it but I'd like to know.

These are the differences between the vapour and liquid enthalpies.

 

[Leopold89]

The way this thread is going, it looks like that 'future' is rapidly approaching!

Since the tanks are from an outside source, try getting a scale for one of the tanks and have a tank delivered to it (or moved to it). Maybe you will have to make room somewhere, or put it in an inconvenient spot. Try it out to see how well it works.

You may even be able to rent a scale for testing.

Your product supplier will likely know how heavy a full tank is, and maybe an empty one too.

If your tanks are currently placed on a stand of some sort, maybe putting some strain gauges on the stand would turn them into a scale.

The strain guages measure the deflection of the stand, which is proportional to the weight.

I have also seen tanks for several thousand gallons of product being weighed by using a balance. They rest on a platform (or stand) mounted on a long bar. The pivot point is close to the tank and the bar extends several feet past the pivot. Then enough standard weights are hung on the far end of the bar to balance the tank weight. Think 'balance scale'.

Cheers,
Tom

Can anybody recommend a proper scale? One which I can connect to a (Linux) computer, can recalibrate myself and is cheap?

 

[Chestermiller]

In the earlier analysis I presented, if we include heat transfer between the tank gas and the surroundings, we obtain:
$$(F_3V-F_4m)\frac{dT}{dt}=\frac{dm}{dt}-\frac{UA}{(h_v-F_2)}(T-T_s)$$where A is the surface area of the tank, U is the overall heat transfer coefficient, and $T_s$ is the temperature of the surroundings; t is time.

 

[Tom.G]

Can anybody recommend a proper scale? One which I can connect to a (Linux) computer, can recalibrate myself and is cheap?

Not at the moment, but if somebody knew what weight range you needed, they could likely do a Google search and find a few. As you are the only one here that would have such information, who do you think would be the most appropriate to do the search? (hint, hint)

 

[Leopold89]

I have now finally completed the computation with the new model by Chestermiller. As I could not find a clever substitution to seperate this differential equation into two seperate, I instead implemented this equation as minimization problem with the mass and temperature time serieses as optimization variables. This had the unfortunate consequence that I could not compute the change over a whole day in a timely fashion. Now I had to reduce the time series to the first 200 minutes. Over the next days I will also try to complete the rest of the day.

 

[Juanda]

I have now finally completed the computation with the new model by Chestermiller. As I could not find a clever substitution to seperate this differential equation into two seperate, I instead implemented this equation as minimization problem with the mass and temperature time serieses as optimization variables. This had the unfortunate consequence that I could not compute the change over a whole day in a timely fashion. Now I had to reduce the time series to the first 200 minutes. Over the next days I will also try to complete the rest of the day.

But you're still seeing mass increments. Although the overall trend seems more realistic than previous results.
Maybe the sensors are not measuring correctly sometimes when things are happening too fast.

 

[Leopold89]

But you're still seeing mass increments. Although the overall trend seems more realistic than previous results.
Maybe the sensors are not measuring correctly sometimes when things are happening too fast.

Maybe it is not that realistic, because the gas temperature is essentially constant compared to room temperature, but the gauge pressure still rises, likely even more than justified, if you look at the plot in post #71. But I also had to adapt Chestermiller's formula a bit, because I do not have liquid phase under these conditions. I started with $U=mu_V \Rightarrow \mathrm{d} U = m\mathrm{d}u_V + u_V\mathrm{d}m$ and inserted it into $\mathrm{d}U=h_V\mathrm{d}m - \alpha A\Delta T$ and got $m(\frac{\mathrm{d}u}{\mathrm{d} p} \dot p + \frac{\mathrm{d}u}{\mathrm{d}T}\dot T) + \alpha A(\dot T - \dot T_s) = (h-u)\dot m$. Maybe my derivation is wrong.