Question

We are throttling liquid CO2 stored in a cylinder at 60bar pressure. The liquid CO2 is allowed to escape through an orifice nozzle into the atmosphere. The escape causes the temperature to plunge below the triple point of CO2 causing change of phase to solid + gas.

The objective is to calculate the natural flow rate of liquid in this case and subsequently, estimate the mass flow rate of solid CO2
. I have a decent hold on the solid-gas ratio that would be obtained as a consequence of the throttling process. For now, the effects of friction offered through pipes and valves can be neglected. It would really help if you could shed light on the mass flow rate that would be achieved of the liquid in this case.

Answer 1

The mass flow rate of liquid CO2 during throttling can be estimated using the conservation of mass and energy, focusing on the enthalpy remaining constant. The phase diagram of CO2 dictates that below the triple point, CO2 will transition from liquid to dry ice and gas. Determining the mass flow rate of solid CO2 also involves considering the solid-gas ratio post-phase change.

Step-by-step explanation:

Understanding the mass flow rate of a throttling process for CO2 requires knowledge of the thermodynamic properties of the substance at the given conditions and the application of the conservation of mass and energy. When throttling occurs, the enthalpy remains constant (isenthalpic process), and the mass flow rate can be estimated by using the equation:

m⋅dot = CdA√(2ρΔP)

Here, m⋅dot represents the mass flow rate, Cd is the discharge coefficient, A is the cross-sectional area of the orifice, ρ is the density of the liquid CO2, and ΔP is the pressure drop across the orifice. As CO2 escapes into the atmosphere at a pressure below its triple point, it will transition from liquid to a mixture of solid and gas. Given the phase diagram of CO2, it's clear that under ambient pressure, solid CO2 will sublime directly to gas without going through a liquid phase, known as dry ice because of this property.

Accurate determination of the mass flow rate of the solid CO2 would also require considering the ratio of solid to gas after the phase change, which relates to the enthalpy change during sublimation and the specific conditions of the throttling process.