Flashing Liquids Source Models
Flashing Liquids • Adiabatic Flashing • Adiabatic Flashing through hole • Isothermal Flashing through hole • Liquid pool boiling
Flashing Liquids • We have considered source models in terms of liquids leaking through a hole or pipe and vapors leaking through a hole or pipe. • For liquids stored under pressure above their normal boiling points, we need to consider flashing.
Adiabatic Flashing • Liquids stored under pressure above normal boiling point. • Large release of pressure (i.e. ruptured vessel). • Energy to vaporize comes from liquid
Adiabatic Flashing Excess energy in superheated liquid Separate variables
Adiabatic Flashing Cp,l & hv are functions of T. If you assume they are constant at an average value
Adiabatic Flashing • Determining the fraction of liquid vaporized • Substitute back in average between Tb and T1
Adiabatic Flashing Design equation for fraction vaporized
Flashing Liquids • Adiabatic Flashing • Adiabatic Flashing through hole • Isothermal Flashing through hole • Liquid pool boiling
Adiabatic Flashing through holes Liquids stored above saturation pressure
Adiabatic Flashing through holes • If L < 10 cm, assume incompressible liquid is flowing. • If L>10 cm, assume choked flow with P2=Psat. Then design equation becomes: Where Psat is at ambient conditions
Flashing Liquids • Adiabatic Flashing • Adiabatic Flashing through hole • Isothermal Flashing through hole • Liquid pool boiling
Isothermal Flashing through a hole • For liquids stored at saturation pressure, P1=Psat. • Assume choked two-phase mass flow v is specific volume (1/density)
Isothermal Flashing through a hole • The two-phase specific volume is • vfg is difference in specific volume between liquid (fluid) and vapor (gas) • vf is the liquid (fluid) specific volume • fv is the mass fraction of vapor
Isothermal Flashing through a hole • Differentiate with respect to pressure • From before we determined
Isothermal Flashing through a hole • All vapor formed is from liquid • Substitute in
Isothermal Flashing through a hole • Now substituted dfv into dv/dP relationship • Clausius-Clapyron equation give dT/dP
Isothermal Flashing through a hole • Substitute in the inverse of the Clausius-Clapyron relationship • Substitute into final relationship
Isothermal flashing through holes • Reduce to get design equation for vapor mass flow rate flashing through a hole • When flashing at or near Psat small droplets of liquid are entrained with the vapor. Typically design assumption is that liquid mass is the same as the mass of the vapor formed from flashing
Flashing Liquids • Adiabatic Flashing • Adiabatic Flashing through hole • Isothermal Flashing through hole • Liquid pool boiling
Liquid Pool Boiling or Evaporating • Use same relationship derived previously for evaporation Where K the mass transfer coefficient is estimated from
ChE 258Chemical Process SafetyIn Class Problem • Calculate the mass flux (kg/m2s) of sulfur dioxide that is leaking from a storage tank that holds liquid sulfur dioxide at its vapor pressure at 25°C • Vapor pressure=0.39x106Pa • Heat of vaporization=3.56x105J/kg • vfg=0.09m3/kg • Heat capacity=1.36x103J/kgK
Solution • Use relationship derived in class • Flux is
Solution cont. • Substitute in values
Solution cont • Finish reducing the units
Solution continued • If we assume that entrained liquid droplets are being carried out with the flashing liquid then • Total flux
ChE 258Chemical Process SafetyIn Class Problem • Calculate the mass flux (kg/m2s) of sulfur dioxide that is leaking from a storage tank that holds liquid sulfur dioxide at 300 psia and at 25°C. The wall thickness is 15 cm. • Vapor pressure at 25 °C =0.39x106Pa • Heat of vaporization=3.56x105J/kg • Heat capacity=1.36x103J/kgK • Liquid density=1.455gm/cm3
Solution • Use relationship derived in class • Flux is
Solution continued • Get common units
Solution cont. • Substitute in values
Solution Continued • C0 has value of 0.61 for sharp edges, 1.0 for worst case • Approximately 10 times greater than when stored at saturation pressure
