Hi,
I have performed Flange Leakage calculation in CAESAR II by using Press. Equ. method for 10"/900# DSS-Flange and found the result of Ratio % exceeds minor, which is 100.15, hence i have performed flange rigidity calculation with the below inputs

Externally Applied Moment ..... (optional) ....(N.m. ) 13360.000
Externally Applied Force ...... (optional) .......(N. ) 3947.000
Pressure [P]...............................(kg./sq.cm.) 140.000


And the result of Rigity method is that, it is ok (pass) in Operating and fails in Seating as below

CALCULATED STRESSES (kg./sq.cm.)
OPERATING ALLOW SEATING ALLOW
--------- ----- ------- -----
Longitudinal Hub .. 1513 2710 3436 2710 *
Radial Flange ..... 1367 1807 3102 1807 *
Tangential Flange . 1028 1807 2333 1807 *
Maximum Average ... 1440 1807 3269 1807 *
Bolting ........... 1544 1498 6174 1498 *
"*" Indicates Failure for an item.
STRESS SAFETY FACTOR: (If less than one then joint
failure is predicted.) (Allowed/Actual)
OPERATING SEATING
--------- -------
Longitudinal Hub .... 1.79 0.79
Radial Flange ....... 1.32 0.58
Tangential Flange ... 1.76 0.77
Maximum Average ..... 1.25 0.55
Bolting ............. 0.97 0.24

Please help me the way to proceed.

IMO, ASME VIII (Taylor Forge) method is not a checking method; gasket seating force and operating force are rather minimum gasket forces to assure a quality joint.
I think we force this reality by trying to adapt this procedure for flange checking case; the logic is we can propose the geometry of a standardized flange as candidate for ASME design procedure considering the operating/design pressure and temperature.

If you decide to go ahead with this method, you need to pass both cases.
In case one step of method is negative (as your seating condition) you cannot pretend the method is fulfilled. It means the flange will leak? IMO, you cannot say "yes, there is leakage"; it means you haven't tools to prove will leak or not.

About the PEq method which not pass by decimals; is 140 bar the design pressure or operating pressure? Is 394.7 daN a tensile force or compressive force? Maybe you can adjust some parameters to formally pass this conservative method. Of course, you have the option to change piping routing...

If you do an ASME VIII Div 1 or 2 flange 'stress analysis' for most 150# and 300# rated flanges, at the max pressure allowed by B16.5 and using a spiral wound gasket, the design will fail the 'bolt-up' but pass the 'operating' case.

Clearly there are countless such flanges out there, not leaking, just doing their job properly. The basic equations that generate the 'bolt-up' case loads are too conservative in my view.

In case the criterion is the real world (leaking or not leaking?), the "bolt-up" ASME VIII theory is conservative, exactly as MoverZ says.

In case the criterion is the ASME VIII/ "Taylor-Forge" theory, I would say that the operating gasket load is nonconservative taken. In fact in the original Taylor-Forge bulletin 502 one can find that "the gasket load is 2b(PI)GmP where gasket factor m relates the required gasket stress at design pressure [...] For example an m factor of 3 means that the residual gasket stress at P must be at least 3P for the joint to be tight". True, however evaluating stress with a gasket load "at least" a given value, you risk to find a value of stress flange "at least" the result of calculation.

A paragraph below, Taylor Forge says that the gasket reaction load is generally assumed to decrease as internal pressure is applied. True again, but why we evaluate stress with a gasket load which increases as internal pressure is applied?

For these reasons, I avoid qualifying flanges which do not pass integrally ASME VIII calculation; that theory is weak enough (and in the same time it provides good quality flanges) and I don't need to improve it relaxing the steps of its calculation.

Best regards.