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# API520 Part II 2-Phase Reaction Force Equation

## API520 Part II 2-Phase Reaction Force Equation

(OP)
The 2-phase equation in Part II of API 520 latest edition does not seem to provide results consistent with the API 520 gas/vapor or ASME B31.1 App. 2 steam equation, when the vapor fraction goes to 1.0. I get results about 5 orders of magnitude higher with the API 2-phase equation (seems out of the ball park). When vapor fraction goes to zero, the liquid force is about 1/2 order of magnitude higher than the API liquid reaction force equation (seems in the ball park).

For example the API vapor/gas reaction force equation, and the ASME App. 2 equation gives me about a 2600 to 2800 lb force. And the left half of the API 2-phase equation gives me about 2200 lb force (close to the other results), but when I multiply by the resulting factor from the right side of the equation (the mass fraction ratios) I get about 10,000 lbs. If I look at a mass vapor fraction at 1.0, the force becomes 288,000 lbs!

Q1: Could someone refer me the source of this equation? There is no footnote reference in API.

Q2: Does anyone routinely use this equation, and verified it against other approaches to calculating the reaction force for 2-phase flow?

### RE: API520 Part II 2-Phase Reaction Force Equation

you should verify the values for Vs (sum of specific volumes of all phases), in SI m3/Kg , for (all liquid streams) it's the specific volume of liquid while for (all vapor streams) it's the specific volume of vapor, the correlation itself is simple :

F (N or Kg M / S*S ) = K * (W*W / A) * Vs +AP

with W Kg/s , A M2 , Vs M3/Kg

for two phase flow, where required, take care to estimate correctly the speed of sound (and critical conditions) , I use the HEM method available in Prode Properties with GERG 2008 or a similar accurate EOS , see this thread for some additional information

https://www.cheresources.com/invision/topic/16336-...

### RE: API520 Part II 2-Phase Reaction Force Equation

(OP)
Are you saying API 520, Part II, Equation (2), is derived from the correlation you presented?
Is the correlation from API, ASME or related standard, or from basic fluids?

I'm not clear on the correlation presented. It looks like:

(force) / (speed of sound, squared) = K * (mass flow rate of the bulk phase, squared) * Vs + AP

Is that correct? Is "K" a constant to adjust for the units used, or something else?

### RE: API520 Part II 2-Phase Reaction Force Equation

the basic equation is Mass Flow * velocity

the formula simply converts from mass flow, area and specific volume to Mass Flow * velocity

W * W * Vs / A

(Kg/s) * (Kg/s) * (M3/Kg) * (1/M2) -> (Kg/s) * (M/s)

you can add K to convert to different Units of Measurement and the static contribute (AP)

### RE: API520 Part II 2-Phase Reaction Force Equation

(OP)
Thank you, apetri, got it. Back to the basics.
Yes, that gives the same results for momentum portion of the reaction force (10,000 lbs), in API Part 2 two-phase equation.

I conclude, then, the reason that the two-phase force is so much higher than the force for the vapor alone is that the bulk flow, with the homogeneous flow assumption, is carrying the liquid mass at such a high velocity with the vapor as to result in much more force. If I were to be able to calculate the phase slip, then the actual reaction force would be (much ?) lower.

### RE: API520 Part II 2-Phase Reaction Force Equation

correct,
you can consider homogeneous flow (the HEM model discussed in my previous post) or different models and obtain different results,
in general, HEM gives conservative results and I prefer that at high relative speeds, near critical flow condition.

### RE: API520 Part II 2-Phase Reaction Force Equation

(OP)
Thank you, apetri, I will consider and review the adv/disadv of some other methods for calculating the reaction force.

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