How to calculate the mass of gas in a tank?

[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.