Estimating mass flow in likely two-phase relief scenario

[LaSalle1940]

Let's assume that the heat input to a blocked-in vessel is known (e.g., calculated from a known external area assuming a pool fire). Note that the vessel is completely full of liquid (that is, could essentially be considered as a wide spot in a pipeline). Let's also assume (setting aside any considerations of fire alarms and so forth) that sufficient time has passed that the liquid is at its saturation temperature at the relieving pressure.

Now: I believe that the relation for relieving rate for thermal expansion would no longer apply exclusively since the onset of boiling would be imminent; likewise, the boiling relation using the heat of vaporization does not capture the entire scenario since some thermal expansion would continue. How does one account for these simultaneous phenomena so that there's a reasonable estimate of the mass flow to be relieved? This would be used in conjunction with (let's say) the homogeneous equilibrium model to size a relief valve orifice.

 

[dcasto]

see thread1203-180139

I always ask how can you get a completely full pressure vessel witha product that has a vapor pressure over 15 psia?

Next, a relief valve of a fixed size (area) will relieve a whole bunch more liquid than it can a vapor, so the vapor will become a controlling case.

 

[LaSalle1940]

I should have pointed out that the liquid in question is an aqueous solution (typical process temperature ~120°F), and that the vessel in question is essentially a large filter, where a manual vent valve will be opened on startup to ensure complete liquid filling. Thus, it seems to me that you'd have what amounts to a wide spot in the pipeline under normal circumstances, wherein an external heat source would yield thermal expansion to the point at which a small amount of liquid discharges.

As a sidebar, I did a rough estimate of the time it would take to get to the boiling point at the relieving pressure assuming a steady heat input but varying physical properties; in the case of the filter vessel in question, I came up with something on the order of about 45 minutes, which one would think would be sufficient time to have firefighting measures well underway.

 

[Latexman]

45 minutes is not very long if this filter is in a low traffic area in a large chemical plant on the midnight shift over a holiday weekend, unless there is a detection system or two that announces into a manned area, like a control room, or into a site-wide emergency response system, usually run by security. If it's in a high traffic area in a small plant, the odds of discovering the fire faster are much better, but small plants usually cannot afford an emergency response team and rely heavily on the community systems, which means more waiting.

Once a fire is discovered, we usually *plan* to fight a fire for a duration that is proportional to the risk of the fire area. That duration ranges from 2-6 hours, except for small pilot scale operations usually found in R&D. The shortest fire duration there is probably 30 minutes if there is not much risk to the area.

I have no idea where this filter fits in to what I discussed, but that's my experience.

As for estimating the mass flow rate of this two-phase scenario, I have some experience doing that. There are two basic approaches I am familiar with, and it will simplify matters if you'd express a preference based on your personal choice or one that is closest to the tools (software) you have in hand. The first way, my favorite, is to calculate the minimum required nozzle area and then select a commercially available PSV that is larger. The other way is to select or guess a commercially available PSV and size and see if it's big enough. Both ways are dynamic in nature, but I prefer the first way because it is mathmatically smoother than dealing with discrete sizes of PSVs and the open/closed/open closed nature of a PSV larger than the minimum required nozzle area. But, at the end of the day, the calcs. have to be run on the selected PSV and size to check out the inlet dP, outlet dP, backpressure limitations, etc.



Good luck,
Latexman