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[Justin Spencer]

Hi,

I'm a process EIT with a little less than 2 years of direct experience and I've been working on a calculation that has been making me think quite a bit. I have done PSV calculations before, but just to make sure I am understanding everything correctly I have been quite verbose in describing the problem. My apologies

I am working on sizing a PSV for overpressure protection of the existing piping that is being tied into. The overpressure scenario would be a rare event due to operator error where higher pressure fluid (propane) is misdirected to a lower pressure system (butane). The relief load is ultimately being discharged to a very large vessel (which is part of this lower pressure system) and the pressure of this vessel is assumed to remain constant owing to its capacity and limited duration of the relief event.

I will attempt to describe the relief scenario as a steady state system. The liquid propane system is at a certain constant pressure and reverse flows across two series checkvalves into the lower pressure system. The propane then loses roughly 0.4 psi across piping and flashes a small amount of vapour before reaching the PSV that I am sizing. After flashing across this PSV the propane remains in two-phases. The propane then loses roughly 0.2 psi before reaching the existing PSV as two-phases. After flowing through the existing PSV, the propane reaches the large vessel with negligible losses expected to occur.

I have worked through the majority of the calculation and it is just a small aspect that I am unsure how to deal with. I'll briefly overview how I have tackled the sizing so far, then point out the remaining issues.

I estimated the relief load that would occur across the double check valves as the flow through an orifice with a diameter one-tenth of the largest check valve's nominal diameter (API STD 521, 4.3.4.4). From the preliminary calculation, the fluid is still liquid downstream of the checkvalves. The upstream pressure is known and the downstream pressure used is PSV set plus the non-recoverable pressure loss. I chose the PSV set pressure rather than the maximum relieving pressure (1.1*P_set in this case) to get a more conservative estimate for the flow rate.

The design pressure of the lower pressure system is 180 psig and H/T is 270 psig. The datasheet for the existing PSV indicates that it is set at 180 psig and is a pilot operated modulating PSV with overpressure specified as "10% of set". There is a note that says "Modulating pilot operator will limit relieving capacity to maintain 180 psig + 10% overpressure". From my limited experience with pilot operated modulating PSVs, the overpressure indicated on the datasheet is the pressure at which the piston lifts to 100%. If they had specified the overpressure to be 7%, then the piston would achieve full lift at 107%; however, full rated capacity still would not be achieved until 10% overpressure (see Fig. 17 in API STD 520 PT I). I'm assuming it just happens that the values of 10% coincide, yet differ in meaning; one is the pressure at which full lift occurs, the other and more common one is the pressure at which the rated capacity must be reached.

I think that for this particular pilot operated modulating valve that at 5% overpressure, the piston will be at ~50% lift. This seems contrary to what the aforementioned note implies, but I support my claim with the quote below.

Anderson Greenwood Series 400 Piston Pilot POPRV
The main valve will open at nameplate set, but only an amount proportional to the relieving capacity required. As process pressure increases, the valve will open more and be in full lift at 110% of set.

The reason I am going into such detail here is because the set pressure higher can't be greater than the design pressure of the pipe. Well, ASME B31.2 para. 302.2.4 (with the pertinent part quoted below) may be a way around this, but I want to use that as a last resort.

(a ) 33% for no more than 10 h at any one time
and no more than 100 h/y, or
(b ) 20% for no more than 50 h at any one time
and no more than 500 h/y

So being stuck with not being able to have the set pressure greater than 180 psig, and a backpressure of 198.2 psig (180 psig * 1.1 + 0.2 psi), I can not size a PSV to flow from 198 psig to 198.4 psig. Even if the non-recoverable pressure loss of 0.2 is neglected, I would still need an infinitely large orifice to pass the required flow without exceeding the rated overpressure of 10%. In practice I could install an orifice the same size as the currently installed one and the pressure upstream would increase beyond the 10% overpressure as necessary. I would even suspect that the pressure rise would not exceed the 3% of set pressure that is allowed for non-recoverable pressure loss at the inlet as per API RP 520 II.

API RP 520 II
When a pressure-relief valve is installed on a process line, the 3 percent limit should be applied to the sum of the loss in the normally non-flowing pressure-relief valve inlet pipe and the incremental pressure loss in the process line caused by the flow through the pressure-relief valve. The pressure loss should be calculated using the rated capacity of the pressure-relief valve.

In fact, this 3% could be another way around the problem, Just size the valve for 13% accumulation instead of 10% overpressure. Well, In actuality I would take into account the non-recoverable pressure loss, which might decrease the 13% accumulation to ~12% overpressure. But I reiterate that I am not certain as to whether I can actually do this or not. If I went this route, could I calculate the non-recoverable pressure loss based on the required relieving rate or would I have to base it on rated relieving capacity? API allows built-up backpressure to be calculated based on required relieving rate. I just find it odd that API makes an exception for modulating PSV's in calculating the built-up backpressure, but not for the inlet loss.

API STD 520 PT I
4.2.2.3.2 The modulating pilot, as shown in Figure 17, opens the main valve only enough to satisfy the required
relieving capacity and can be used in gas, liquid or two-phase flow applications. A modulating pilot-operated valve, in
contrast to a pop action valve, limits the amount of relieving fluid to only the amount required to prevent the pressure
from exceeding the allowable accumulation. Since a modulating pilot only releases the required relieving rate, the
calculation of built-up backpressure may be based on the required relieving rate instead of the rated relieving capacity
of the valve.

API STD 521
Modulating pilot-operated-type pressure-relief valves generate loads that are equivalent to the required relieving
rate for a particular contingency [101].

The lateral or tailpipe from a modulating pilot-operated pressure-relief valve is
sized based upon the required relieving rate for a particular contingency.

OK, so from the preliminary calculations I have done so far, the required area of the currently installed PSV is ~35% of the actual area. As I alluded to earlier, lift percent and pressure should be linearly related as long as the spring has linear characteristics. The problem is that lift percent is not easily calculated based on area (similar to the liquid level in a horizontal cylindrical tank) and even if you used the relation for area enclosed by a chord of a circle, the cross sectional area you see on page 32 shaded in yellow would make things more complicated. Also take a look at the fully open valve on page 12.

Probably the best way to go about this is to assume that (required area)/(actual area)*100% is roughly equal to lift%, then multiply by some contingency factor of say 25%. This number would be used to interpolate between the set pressure (0% lift) and 10% overpressure (100% lift).

Recall that the existing PSV has a required area roughly 35% of the actual area (the existing PSV is a J size). depending on what value I use for lift%, I have sized the PSV for 3 cases
lift of 94.1% give a J size
lift of 84.7% gives an H size
lift of 56.7% gives a G size

so the least conservative G size still has a large (56.7%/35% = 1.61) contingency factor.



The only other option I could think of was to reduce the set pressure of the existing PSV a few psi, but when I brought that up I was told that it wasn't an option.