# Pressure drop saturated vapor (VLE)

I'm trying to find a formula for the pressure drop of a vapor flowing through an orifice which opens at a certain value of the temperature (or pressure). Let's assume that we have a system like this: If the system is in VLE, one can calculate the pressure of the system by using Antoine's equation. So if one heats up the system, the pressure will increase. But what happens with the pressure when the orifice above opens? The equilibrium conditions are not there anymore, so the Antoine equation is not valid anymore (or is it?). So I guess that the ideal gas law will apply, but how do I connect the two pressures, if I want to determine the mass flow due to the pressure difference?

I was thinking of something like this: $$P = P_{sat} - \frac{m_vRT\theta}{V}$$

where $$m_v$$ is the mass of the vapor, $$R$$ is the gas constant, $$T$$ is the temperature, $$\theta$$ is the vapor fraction and $$V$$ is the volume occupied by the vapor.

Is this formula correct, considering that $$P_{sat}$$ is dependent on the temperature (which does not go to 0, therefore vanishing the $$P_{sat}$$ term). Can anyone help me with this?

• if you have something more specific in mind than what you posted, such as your liquid exists in a flash drum with a rupture disk as a safety device, please say so. Without knowing how much "disengagement space" is available, I can't be certain that my answer matches your problem. However, don't go so far as to publish proprietary company information, as that's a big NO NO. – David White Nov 22 '16 at 16:55