Leak rate calculation through clearance between tube and tubesheet of air-finned cooler

[Eakapong]

Hi,
I am finding the calculation method for the maximum leak rate of a gas/liquid mixture through clearance between tube and tubesheet of an air-finned cooler. The fluid contains 79% H2 gas, 19% liquid hydrocarbon, and 2% liquid water at 181 barg and 168 degC. There is a 0.15 mm clearance between tube (25.4 mm OD) and its bore (25.7 mm OD). Fluid would leak through this clearance to the atmospheric.

I tried the orifice flow equation (Q = C*A*sqrt(2*(P1-P2)/Density)). As the clearance is very small comparing with the upstream area (header box), C=0.6 was assumed). By substitute P1=18.1 MPa and P2=0 MPa with average density of fluid at 42.8 kg/m3, I got flow rate 0.00664 m3/sec (6.6 litre/sec). This flow rate means the fluid is leaking at velocity of 551 m/s!!! This is unbelievable and I believe I did something wrong. Can anyone suggest please?

Thank you so much.

 

[georgeverghese]

This 0.15mm clearance between tube and tubesheet wouldnt exist in the installed tube bundle, since the tubes would be roller expanded into the tubeholes in the tubesheet - in some cases the tubes are expanded and seal welded.

 

[Eakapong]

Hi Georgeverghese, the tubes were light expanded 3-5% with seal weld. I guess the clearance is still exist more or less. So, I took it conservative with 0.15 mm clearance in the calculation.

 

[georgeverghese]

As the cooler ages, corrosion at this tube - tubesheet joint may yet occur - you could check with your safety and instrumentation engineers if gas detectors are installed above the cooler bay. Also check with your materials selection engineers if the materials selected and construction methods for the tubes and the tubesheet are good for this service - this sounds like a hydrotreating recycle gas compressor cooler, so trace components like water vapor, chlorides, H2S and ammonia may be present, and the first place where corrosion would show up is at this highly stressed tube - tubesheet joint.