Calculating pressure in 2-phase closed systems

[Near Critical]

I have a closed pressure vessel that is partially filled with water and the head space has been purged with He and charged to about 100 psi. What I wish to know is how to calculate the overall pressure in this vessel after heating it to a given temperature (e.g., 300 or 400 C). I know the volume of water and the head space at ambient temperature.

I think I am having difficulties because I keep wanting to apply an equation of state such as the Redlich-Kwang, BWR, or Soave but these are for gases and in my case I have a liquid and a gas. It is likely that all of the liquid will exist in the vapor state at an end temperature of 400 C but likely it will be a saturated vapor/liquid mix at 300 C.

 

[LightHero]

Do I need to calculate the vapor pressure of the water at 300 C or 400 C?The answer to your question depends on what type of equation of state you are using. If you are using an equation of state designed for a two-phase system (gas and liquid in equilibrium), then you would have to calculate the vapor pressure of the water at the desired temperature. However, if you are using an equation of state that is designed for a single-phase system (either gas or liquid) then you would not need to calculate the vapor pressure of the water. In this case, you would simply use the equation of state to calculate the overall pressure in the vessel.

 

[astrokreng]

I would first like to commend you for your careful consideration and use of equations of state in your calculations. However, in this case, as you have correctly identified, the presence of both a liquid and a gas in your closed system makes it more complex than a simple gas-only system.

To accurately calculate the overall pressure in your closed vessel after heating, you will need to use a two-phase equilibrium calculation. This involves considering the vapor and liquid phases separately and then combining their individual pressures to determine the overall pressure. The specific equations and methods used will depend on factors such as the properties of your particular system and the temperature and pressure conditions involved.

One approach to this calculation is to use the Antoine equation, which relates the vapor pressure of a liquid to its temperature. This equation can be used to determine the vapor pressure of the water at your given temperatures of 300 and 400 C. The partial pressure of the helium gas in the head space can also be calculated using the ideal gas law. Then, using Dalton's law of partial pressures, the overall pressure in the vessel can be determined by adding the vapor pressure of the water and the partial pressure of helium.

Alternatively, you could also use a thermodynamic property calculation software or program, which will take into account the properties of both the liquid and gas phases and perform the two-phase equilibrium calculation for you.

In summary, to accurately calculate the overall pressure in your two-phase closed system, you will need to use a two-phase equilibrium calculation, taking into account the properties of both the liquid and gas phases and using appropriate equations or software. I hope this helps guide you in your calculations.