Compliance

Worked examples, with every step shown.

Five calculations: a true PlutoHX girth flange calculation to Appendix 2, and four teaching examples on a shell like the reference one, each with its formula, inputs, steps, and result.

Examples C and D on the teaching shell: the MAWP of the 1/2 in shell, 313 psi, and its hydrostatic test of about 407 psi; and the 2:1 ellipsoidal head of the shell cover, at least 1/2 in after forming; with a longitudinal section of the shell end and its head. — Open the drawing at full size

The examples

From the flange to a change of design pressure.

The girth flange and its bolting

Mandatory Appendix 2

Am = max(Wm1 / Sb, Wm2 / Sb)

G: 42.38 in. Gasket reaction diameter
P: 464 psi. Design pressure
b: 0.25 in. Effective gasket width, equal to b0 as b0 is not over 1/4 in
m, y: 3 and 10,000 psi. Gasket factor and seating stress
Sb: 25,000 psi. Allowable bolt stress, operating and seating

H = (π/4) G² P = 654,400 lbf
Hp = 2 b π G m P = 92,650 lbf
Wm1 = H + Hp = 747,000 lbf
Wm2 = π b G y = 332,800 lbf
Am = 747,000 / 25,000 = 29.88 in²

Required bolt area, Am	29.88 in²
Provided, 60 × 1 in bolts	33.06 in²
Flange thickness	1.875 in

A true PlutoHX calculation, from the girth flange example. With 60 bolts of 7/8 in, the 25.14 in² provided is below the required area; 72 bolts of 7/8 in give 30.17 in² and meet the requirement again.

Shell under internal pressure

UG-27(c)(1)

t = P R / (S E - 0.6 P)

P: 300 psi. Internal design pressure
R: 20.125 in. Inside radius: 20 in plus the 0.125 in corrosion allowance
S: 20,000 psi. Allowable stress, SA-516 Grade 70, ASME Section II, Part D, up to 650°F
E: 0.85. Joint efficiency, spot radiography

t = 300 × 20.125 / (20,000 × 0.85 - 0.6 × 300)
t = 6,037.5 / 16,820
t = 0.359 in

Required thickness	0.359 in
Plus corrosion allowance	0.125 in
Total	0.484 in
Plate	1/2 in

The rule applies while t is not over R/2 and P is not over 0.385 S E.

The MAWP of that shell, and its hydrostatic test

UG-27(c)(1), UG-99(b)

P = S E t / (R + 0.6 t)

t: 0.375 in. The 1/2 in plate less the 0.125 in corrosion allowance (corroded condition)
R: 20.125 in. Inside radius, corroded
S: 20,000 psi. Allowable stress, as before
E: 0.85. Joint efficiency, as before

P = 20,000 × 0.85 × 0.375 / (20.125 + 0.6 × 0.375)
P = 6,375 / 20.35
MAWP = 313 psi

MAWP	313 psi
Design pressure	300 psi
Hydrostatic test, 1.3 × MAWP	about 407 psi

The MAWP is a little above the 300 psi design pressure, as expected from rounding up to a 1/2 in plate. The hydrostatic test to UG-99(b) is at least 1.3 × MAWP × the stress ratio; with the same allowable stress at test and design temperature the ratio is 1.

The 2:1 ellipsoidal head of the shell cover

UG-32

t = P D / (2 S E - 0.2 P)

P: 300 psi. Internal design pressure
D: 40.25 in. Inside diameter, corroded: 40 in plus 2 × 0.125 in
S: 20,000 psi. Allowable stress, as before
E: 0.85. Joint efficiency, as before

t = 300 × 40.25 / (2 × 20,000 × 0.85 - 0.2 × 300)
t = 12,075 / 33,940
t = 0.356 in

Required thickness	0.356 in
Plus corrosion allowance	0.125 in
Total	0.481 in
After forming	at least 1/2 in

The plate is ordered a little thicker than 1/2 in, to allow for thinning in forming.

A design change: the same shell at 400 psi

UG-27(c)(1)

t = P R / (S E - 0.6 P)

P: 400 psi. The new design pressure
R: 20.125 in. Inside radius, as before
S: 20,000 psi. Allowable stress, as before
E: 0.85. Joint efficiency, as before

t = 400 × 20.125 / (20,000 × 0.85 - 0.6 × 400)
t = 8,050 / 16,760
t = 0.480 in

Required thickness	0.480 in
Plus corrosion allowance	0.125 in
Total	0.605 in
Plate	5/8 in

When a design condition changes, PlutoHX runs the dependent checks again (shell, heads, nozzles, flanges and bolting, and tubesheets) and shows what changed. Here the shell goes from a 1/2 in to a 5/8 in plate.

About these examples

Where the values come from.

Example 1 is the girth flange calculation that PlutoHX makes for the reference exchanger. Examples 2 to 5 are teaching examples: they use a 40 in shell of SA-516 Grade 70 with a 0.125 in corrosion allowance, and they are not the design data of HX-123.