Flanges are designed to remain leak-free under hydrostatic test pressure (cold condition) and under operating pressure (hot condition). Flange Leakage is a function of the relative stiffnesses of the flange, gasket, and bolts.

Flange leakage is considered a serious issue in the process plant operation. It has a tremendous potential to cause a severe hazard in the process plants. Therefore, flange leakage needs to be investigated during the design stage to reduce the possibility of leakage during the testing and operation stage.

The design of ASME flanges (ASME B16.5, B16.47) does not take into account the external bending moment and axial force in the pipe. This will cause a wire drawing effect on the mating surface of the flange. Therefore, additional flexibility is to be provided when a flange joint is located near a spot with a high bending moment. So, flange leakage checking is really required.

ASME Piping Flanges (ASME B16.5, B16.47 …) are designed in accordance with ASME Boiler and Pressure Vessel Code, Section VIII, Division 1, Appendix 2, but using allowable stress and temperature limits of ASME B 31.3 code.

In general practice, the following cases need to be considered for flange leakage:

- Flanges with pressure rating 600 and above
- Flanges with pressure rating 300 and above, pipe size 16 inches and above
- Pipe flanges carrying category M fluid service
- Pipe flanges carrying hydrogen or other flammable fluid
- Flanges in PSV lines with NPS 4 inches and above
- Flanges in jacketed piping
- Flanges with stress analysis output of very high bending moment

There are various methods for determining if the flange joint is leaking, including:

- Pressure Equivalent method based on ASME B 16.5 P-T rating
- ASME BPVC Sec VIII Div.1 Appendix 2 method.
- NC 3658.3 method

In this article, we’ll explore into how to check for flange leakage by *ASME BPVC Sec VIII Div.1 Appendix 2 method *together with the application of pressure equivalent method to take into account the external force and moment.

Kellogg Method convert piping axial forces and bending moments into an equivalent pressure on the flange.

**Peq = 16Mb /πG³+ 4Fa/πG²+ Pd**

Where:

Peq = total equivalent pressure

Mb = calculated bending moment on flange

G = diameter of effective gasket reaction

Fa = axial force of flange

Pd = design pressure

Before we go to a thorough calculation, we need to point out here two distinct scenarios for the gasket group:

- case 1: for spiral-wound and ring joint gasket
- case 2: for the full-face gasket.

**1. For spiral-wound and ring joint gasket.**

K = ratio of the outside diameter of the flange to the inside diameter of the flange = A /B

K²(1 + 8.55246 log₁₀K)-1

T =

(1.04720 + 1.9448 K²)(K-1)

K² (1 + 8.55246 log₁₀K) -1

U = ~~ ~~

(1.36136(K² – 1)(K – 1)

1 K² log₁₀K

Y = ~~ ~~(0.66845+5.71690 ~~ ~~ )

K -1 K² – 1

K² + 1

Z = ~~ ~~

K² – 1

The required bolt load for the operating conditions W1:

Wm1 = H + Hp = 0.785 G² Peq + (2b x 3.14GmP)

m = gasket factor

The minimum initial bolt load required for this purpose Wm2:

Wm2= 3.14bGy

where b = b₀ when b₀ ≤ 1⁄4 inches (6 mm) and b = Cb√b₀ when b₀ > 1⁄4 inches (6 mm)

The total required bolt area shall be Am = max(Wm1/Sb, Wm2/Sa), and the Actual bolt area Ab >= Am

Sa = allowable bolt stress at atmospheric temperature

Sb = allowable bolt stress at design temperature

**Flange design bolt load:**

– For operating condition: W = Wm1

– For gasket seating condition: W = (Am + Ab) Sa /2

**Flange moment and stress:**

– For operating condition:

hD = R + 0.5g1, hG = (C-G)/2, ht = (R+g1+hG) /2

H = total hydrostatic end force = 0.785G²Peq

HD = hydrostatic end force on area inside of flange = 0.785B²Pd

HG = W – H

HT = H – HD

MD = hD * HD

MG = hG * HG

MT = hT * HT

Mᴏ = MD + MG + MT

Longitudinal hub stress SH = fMᴏ / Lg1²B

Radial flange stress SR = (1.33tₑ +1)Mᴏ /Lt²B

Tangential flange stress ST = YMᴏ/t²B – ZSR

f = hub stress correction factor for integral flanges

L = (tₑ +1)/T + t³/ d

t = flange thickness

d = Uhᴏ gᴏ²/V

e = F / hᴏ

F = flange factor

hᴏ = √Bgᴏ

– For gasket seating condition:

Mᴏ = W(C-G)/2

Longitudinal hub stress SH = fMᴏ / Lg1²B

Radial flange stress SR = (1.33 tₑ +1)Mᴏ / Lt²B

Tangential flange stress Sᴛ = YMᴏ/t²B – ZSR

f = hub stress correction factor for integral flanges

L = (tₑ +1)/T + t³/d

t = flange thickness

d = Uhᴏgᴏ²/V

e = F /hᴏ

F = flange factor

hᴏ = √Bgᴏ

**2. For full-face gasket.**

b = (C-B)/4

G = C- 2hɢ

hɢ = (C-B)(2B+C)/6(B+C)

hɢ’ = (A-C)(2A+C)/6(A+C)

hɢ” = hɢ*hɢ’/(hɢ + hɢ’)

The required bolt load for the operating conditions Wm1:

Wm1 = H + Hp = 0.785G²Peq+(2bx3.14GmP)(1+hɢ/hɢ’)

m = gasket factor

The minimum initial bolt load required for this purpose is Wm2:

Wm2= 3.14bGy(1+hɢ/hɢ’)

Total required bolt area Am = max(Wm1/Sb,Wm2/Sa), and Actual bolt area Ab >= Am

Sa = allowable bolt stress at atmospheric temperature

Sb = allowable bolt stress at design temperature

**Flange design bolt load:**

– For operating condition: W = Wm1

– For gasket seating condition: W = (Am+Ab) Sa /2

**Flange moment and stress:**

– For operating condition:

hᴅ =(C-B)/2, hɢ = (C-G)/2, hᴛ =((C-B)/2+hɢ) /2

H = total hydrostatic end force = 0.785G²Peq

Hᴅ = hydrostatic end force on area inside of flange = 0.785B²Pd

Hɢ = W – H

Hᴛ = H- Hᴅ

Mᴅ = hᴅ * Hᴅ

Mᴛ = hᴛ * Hᴛ

Mᴏ = Mᴅ + Mᴛ

Longitudinal hub stress SH = fMᴏ/Lg1²B

Radial flange stress SR = (1.33tₑ+1)Mᴏ/Lt²B

Tangential flange stress ST =YMᴏ /t²B – ZSR

Radial stress at bolt circle SRAD = 6Mᴏ/t²(πC-nd1)

f = hub stress correction factor for integral flange

L = (tₑ +1)/T + t³/ d

t = flange thickness

d = Uhᴏgᴏ²/V

e = F/hᴏ

F = flange factor

hᴏ = √Bgᴏ

n = number of bolt

d1 = bole hole diameter

– For gasket seating conditions:

Mᴏ = Hɢ * hɢ”

Longitudinal hub stress SH = fMᴏ/Lg1²B

Radial flange stress SR = (1.33tₑ+1)Mᴏ/Lt²B

Tangential flange stress ST = YMᴏ/t²B-ZSR

Radial stress at bolt circle SRAD = 6Mᴏ/t²(πC-nd1)

f = hub stress correction factor for integral flange

L = (tₑ +1)/T+t³/d

t = flange thickness

d = Uhᴏgᴏ²/V

e = F/hᴏ

F = flange factor

hᴏ = √Bgᴏ

n = number of bolt

d1 = bole hole diameter

**Database inputs for Flange Leakage App:**

- Piping database ASME B36.10, B36.19
- Flange dimension ASME B16.5,ASME B16.47
- Gasket dimension ASME B16.20, ASME B16.21
- Flange specification and allowable stress as ASME B31.3
- Bolt specification and allowable stress as ASME B31.3
- Gasket properties as ASME Section VIII div.1 and Flexitallic catalog

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