2 phase choked flow fluid dynamics

Factual Questions
1

This, my friends, is a tough one.

 I want to find a way to estimate the capacity that a pipe can carry of a 2 phase fluid mixture. For a one phase fluid, we usually use the choked critical flow equation: [http://en.wikipedia.org/wiki/Choked_flow](http://en.wikipedia.org/wiki/Choked_flow)

 At a given upstream pressure and area, there is a finite limit at how much fluid you can force through a pipe. This is because the fluid reaches it's sonic velocity. I cannot find any equations for a two phase flow. That is, a mixture of liquid and vapor. I have only heard of this being calculated using special software, of which I do not have access to at this time.

 Does anyone have any experience in calculating two phase flashing flow capacity in pipes?

As an example, consider:

  Is it possible to flow 10,000 lb/hr of 50 psig steam of 50% quality (half liquid/half vapor) through a 10" pipe? 

 The real figure I am trying to calculate is a litte more complex, but I am looking for a good place to start.

Thanks,

Leidenfrost

2

In general it is not possible to characterize two phase or multiphase flow in closed form, owing to non-linear thermodynamic interactions between the different phases. There are certain circumstances where it is possible to simplify adiabatic, frozen, steady-state two-phase flows with some empirical correction factors when the interaction between the two phases is minimal, but I doubt this can be done for steam+supercritical water in the transonic regime owing to changes in state from vaporization and condensation and pressure wave interactions that prevent it from achieving an equilibrium state. The examples of simplified two-phase flow I’m familiar with involve a small fraction of solid microparticulate condensate (<6% of total mass flow) and a low molecular weight ideal gas fluid, where the only interactions between the two flows can be simplified to convective transfer between the phases, and the momentum transfer between phases is minimal. For water and steam, which can exhibit not only rapid phase change and thermodynamic transfer, but also (in liquid form) significant viscous effects, I don’t think there is any simple set of closed-form equations for solution.

Here is an online text on multiphase fluid flow in which the author essentially says the same thing. There may be some kind of empirically-correlated general model in use by steam turbine designers to establish minimum speeds for choked two-phase flow, but that is afield from my experience.

Stranger

3

Is this not related to petrochemical processes? The oil/gas/water mixture flowing from well head to separation apparatus would seem to be a real example of multiphase flow, with minimal interaction(s) except for the possible differences in the fractional hydrocarbons. A Chemical engineer would be helpful?

4

Stranger,

  I had the suspicion that this would be the case. 2 phase flow is inherently unstable. The only equation that I know works somewhat for 2 phase flow is the Omega Method which is published by the API. This is for sizing the orifice of a relief device for flashing two phase flow. However, this is not really the same thing I am asking. I can't find a link, but API RP 520 has it. I am wondering if I can extrapolate that a certain pipe cross-sectional area would be fine for a orifice calculated of the same size? Hard to say.
5

I don’t think you can, but my experience with multiphase flow involves high temperature, low pressure near ideal gas and the general assumption of frozen, adiabatic flow through a converging-diverging nozzle or a pure hot gas generator cycle, not petroleum cracking or superheated high pressure steam cycle, so I’m no kind of expert on the type of scenario that you are looking at.

Stranger

6

Are you still interested in this problem? i’ve done a lot of research on the subject to answer the same question but for saturated 50 psi condensate that travels thru an 8" pipe to a far away atmospheric tank flashing on the way as it drops in pressure.

Firstly; The flow chokes in the sense that it does increase with pressure drop at the exit up to certain critical pressure ratio where it won’t increase any more with a further drop in pressure. But, in two-phase flow, this does not take place at any sonic velocity.

I’ve found a good paper presenting a solution procedure for saturated condensate at very low quality The paper is by Fraser and another author starting with A, 2001. The solution is iterative so it’s not simple to calculate

If your still pursuing this topic, let me know what you’ve learned and i’ll respond.