Calculating Fill Time for Pressure Vessels: Inlet Parameters & Mass Flow Rate

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Discussion Overview

The discussion revolves around calculating the fill time for a pressure vessel, focusing on the parameters affecting the mass flow rate and the complexities introduced by pressure differentials during the filling process. Participants explore theoretical and practical aspects of the calculation, including the effects of gas compression and the use of differential equations.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant outlines the parameters known for the pressure vessel and attempts to calculate the fill time using mass flow rate, but finds the result unrealistic.
  • Another participant inquires whether the fluid is a gas or a liquid, leading to clarification that it is air at 520R.
  • Concerns are raised about whether the initial calculations consider the effects of compression and the pressure differential between the empty tank and the inlet pressure.
  • Participants discuss the rapid expansion of gas to fill the tank and the longer time required to reach the desired pressure, indicating a misunderstanding of the initial assumptions.
  • One participant expresses the need to calculate the time to pressurize the vessel to 420 psig and questions the necessity of using a differential equation for this calculation.
  • Another participant suggests that the flow rate will decrease as the pressure in the tank rises, emphasizing the role of pressure differential in determining flow rate.
  • A participant shares a screenshot of their calculations in Mathcad and seeks verification of their validity, expressing doubt about their correctness.
  • Discussion includes the consideration of constant mass flow in the case of a screw compressor and the implications for fill time calculations.
  • One participant points out a potential error in using SCFM for fill time calculations, suggesting the need to determine the actual fill volume at different pressures or to use ACFM for accurate estimates.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions made regarding gas behavior during filling, the necessity of differential equations, and the appropriate methods for calculating fill time. No consensus is reached on the best approach to solve the problem.

Contextual Notes

Limitations include the dependence on the definitions of flow rates (SCFM vs. ACFM) and the unresolved nature of the mathematical steps involved in the calculations. The discussion reflects varying assumptions about gas behavior and pressure effects.

Juanka
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I am needing to calculate the fill time of a pressure vessel. I know the following parameters regarding the vessel:

Volume, Temperature, Properties of the fluid media, inlet pipe diameter, flow rate of the inlet, pressure of the inlet.

I tried calculating the mass flow rate of the inlet then dividing the capacity of the tank (lbm) by the mass flow to find a time of fill. However, this number was extremely small (unrealistically small).

I know as the vessel fills the fill rate is going to go down until S.S. is finally reached. However do I have to implement a D.E. to calculate the time for the vessel to fill?
 
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Is this a gas or a liquid.
 
Air at 520R
 
So does your calc take into consideration the effects of compression? i.e. inlet pressure differential between empty tank and tank at desired pressure.
Air will expand to "fill" the tank really quickly. But it will take longer to get the tank up to the desired pressure.
 
Yes, I am assuming my vessel pressure to be 0 psig while inlet pressure to be 420 psig.
 
Yet that obviously isn't true the instant any air enters the tank.

As I said, the gas will expand to fill the tank. The "fill" time is extremely short. The time it takes to fill to the desired pressure is another story, and your initial assumption does not hold.
 
I am needing to calculate the time required to pressurize the vessel to the inlet pressure of 420 psig. I am working on a DE at the moment however I do not seem to be making much progress. Is it possible to solve this without a DE? (I am thinking it is not).
 
Not that I am aware of. The driving force behind the flow rate will be the pressure differential (for most compressors) thus the fill rate will decrease differentially as the pressure rises in the tank.
 
I have attached a screenshot of my work described in Mathcad. I would like it if someone could verify whether the calculation is valid or not. (As cited before I believe it is not, I just want an outside opinion).
 

Attachments

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    Capture.JPG
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  • #10
Though, if it is a screw compressure with positive displacement, then you can treat your mass flow as constant, unless I'm mistaken...
 
  • #11
The mass flow inlet can be assumed constant, the inlet to this vessel occupies <5% of the capacities of the compressors supplying the flow. However, I know it takes much longer than the 30 seconds to fill this vessel, for that reason I know there is an error and I am trying to work out a DE to find a solution I just wanted to rule out the non Diff-Eq method before proceeding.
 
  • #12
Oh, I see one mistake, your flow is in SCFM and that should not be used to determine the fill time of your tank. Either you must determine the actual fill volume of your tank (a 6000 ft3 tank holds quite a bit more volume at 380 psig than it does at 1 atm), and divide by the SCFM flowrate to estimate your fill time, or you must determine the ACFM and use the geometric tank volume (6000 gt3).
 
  • #13
Good catch, this looks more like it.

Thanks
 

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