# Modeling air temperature and pressure in an open system (decompressing tank)

• fflachowski
In summary, the conversation discusses the need to accurately model an open system that includes a tank with a volume of 1320 gallons and an exit pipe with a diameter of 3 inches. The tank is compressed from atmospheric conditions to a final pressure of 100 psig and then decompressed by opening a valve at the exit. The initial temperature of the air in the tank is 400 F and 100 psig, and both the pressure and temperature decrease as the tank decompresses. The challenge is to model this temperature change in addition to the pressure change, taking into account choke conditions, isentropic behavior, and perfect insulation. The most accurate approach involves utilizing differential equations to determine the mass flow rate out of the tank as a

#### fflachowski

I am trying to determine how to accurately model an open system which includes:

A tank: Volume = 1320 gallons
An exit pipe from tank: Diameter = 3 inches

The tank is compressed from atmospheric conditions to a final pressure of 100 psig. Then the tank is allowed to decompress by opening a valve at the exit (blow down test).

The air in the tank is initially at 400 F and 100 psig.

The temperature in the tank decreases as pressure decreases. How do I model the temperature change in the tank as well as pressure.

Keep in mind choke conditions at the pipe exit. Assume isentropic behavior and perfect insulation. Ignore frictional losses of the exit pipe and bends.

Hope you guys can help me with this. Thanks!

FYI: The problem I am having is that, we known, PV=mRT but the pressure changes with the temperature, but the mass also changes due to decompression (open system).

Joule–Thomson effect on Wikipedia along with the equations

There are a couple of different ways to approach the problem, the more accurate of which utilize differential equations. You basically need to look at the mass flow rate out of the tank as a function of pressure, which in turn is a function of time. It isn't straightforward, but it can be done.

The basic form of the relationship would be something like this:
$\frac{d}{dt}m(t)=-m_{dot}$

Where m.dot is the flow rate out of the orifice, and dependent on p(t) and rho(t).

$m_{dot}(t)=C*A*\sqrt{2*\rho(t)*(P_{ambient}-P_{tank}(t))}$

Oops also noticed this thread is almost a year old and was never followed-up on by the OP. Thanks emerhawk.

Yes it has been almost a year since I received a response. If other ideas/ methods keep rolling in, I appreciate them. Thank you.

## 1. How does air temperature and pressure change in an open system when the tank is being depressurized?

As the tank is being depressurized, the volume of the system increases, causing the air molecules to spread out and the pressure to decrease. This decrease in pressure also results in a decrease in temperature, according to the ideal gas law (PV = nRT). This is because the air molecules have less energy to transfer as heat due to the decrease in pressure.

## 2. Can you model the change in air temperature and pressure accurately?

Yes, the change in air temperature and pressure in an open system can be accurately modeled using the ideal gas law and other thermodynamic equations. However, the accuracy of the model depends on the assumptions made and the accuracy of the initial data.

## 3. How does the rate of depressurization affect the change in air temperature and pressure?

The rate of depressurization does not significantly affect the change in air temperature and pressure in an open system. As long as the tank is allowed to depressurize gradually, the change in temperature and pressure will follow the same trend as described by the ideal gas law.

## 4. What factors can affect the accuracy of the model for air temperature and pressure in an open system?

The accuracy of the model can be affected by various factors such as the initial conditions of the system, the assumptions made in the model, and any external factors that may impact the system (e.g. heat transfer to or from the surroundings). It is important to carefully consider these factors when developing a model for air temperature and pressure in an open system.

## 5. Are there any limitations to modeling air temperature and pressure in an open system?

Yes, there are some limitations to modeling air temperature and pressure in an open system. The ideal gas law assumes that the gas molecules are point masses with no volume, and that there are no intermolecular forces between them. In reality, these assumptions may not hold true for all gases. Additionally, the model may not accurately predict the behavior of the system if it experiences sudden changes or extreme conditions.