Flare Stack Mechanical Design Calculations by Abdel Halim Galala

DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. Abdel Halim Galala, Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter

Page : 1 of 24 REV. : 0

Date

: 4.4.2000

Location : Gulf of Seuz

Client : ABB/OPC Item : X-06-02

ELEVATED FLARE STACK SELF SUPPORTED & MULTIPLE DIAMETER

Design General Mgr.

BY

Eng. Abd El Halim Galala Design General Manager Assistance

1st issue Dated : 6.6.1985

DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK According to ASME Code, Sec. VIII, Div. Div. 1, Edition 95, Addenda 96. Designed by : Eng. Abdel Halim Galala, Design General Manager (Assistant)

Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter

Page : 2 of 24 REV. : 0

Date

: 4.4.2000



Contents Page

A. Wind Loads as Computed in Accordance with ANSI A58.1.

3

B. Allowable Shell Buckling (Compression) Stress.

5

C. Shell Plate Thickness, Design Procedure. 1. Total Uncrodded Stack W eight. 2. Computation of the Projected Area. 3. Computation of the W ind Loads. 4. Computation of the W ind Moments. 5. Required Shell Plate Thickness. 6. Anchor Bolt Chair. 7. W idth of Base Ring. 8. Base Plate Thickness. 9. Top Plate Thickness.

7 7 8 9 11 12 13 14 15 15

D. Vibration Analysis. 1. Cantilever Vibration. - Analyzing Technique. - Static Deflection. - Dynamic Deflection. 2. Ovaling Vibration. - Design of Ovaling Ring : - Critical W ind Velocity. - Required Ring Section Modulus.

16 16 17 18 19 20 22 22 22

E. References.

24

DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK According to ASME Code, Sec. VIII, Div. 1, Edition 95, Addenda 96. Designed by : Eng. Abdel Halim Galala, Design General Manager (Assistant)

Page : 3 of 24 REV. : 0


Date

: 4.4.2000



A. WIND LOADS AS COMPUTED IN ACCORDANCE WITH ANSI A58.1-1955. The procrdure for calculation of the minimum design wind load normal to the surface is as follows : 1. The geographical area of the job site (Gulf of Suez & Mostorod) is located on the wind pressure map, see Table-1. The basic wind pressure p is selected. 2. The wind design pressure pz, corresponding to tha basic wind pressure p, for various height zones above the ground are given in Table 1. 3. To calculate design wind forces from wind pressures, shape factor B shall be used.The shape factor for round objects is equal to 0.6 and is applied to the design pressure pz. 4. If the windward surface area projected on the vertical plane normal to the direction of the wind 2 is A ft , then the resultant of the wind pressure load over the area pw is assumed to act at the area centroid and is given by : pw = A B pz, lb The wind pressure forces are applied simultaneously, normal to all exposed windward surfaces of the structure. The minimum net pressure B*pz in the above formula for cylindrical vertical vessels is not less than : for L/D <= 10 13 PSF and for L/D >= 10 18 PSF Where L is the overall tangent-to-tangent length of the vessel, and D is the vessel nominal diameter. Table 1. Design Wind Pressure of the Job Site, p. Height zone Basic wind pressure, p above grade 2 Kg/m Ft M PSF 30 9 15.3612 75 32 to 46 10 to 14 20.4816 100 49 to 62 15 to 19 25.602 125 over 65 over 20 30.7224 150 1 Kg/M2 = 0.2048159 lb/Ft2

Computation of the Projected Area, A. An approach to computing A which is often used and is recommended here is to increase the vessel diameter D to the so called effective vessel diameter to approximate the combined design wind load : De = (Vessel OD + Twice insulation Thickness) x Kd The coefficient Kd is given in Table 2. The required projected area A will then be equal to : A = De Ls where Ls = length of the shell section in the zone of the uniform wind velocity.


Page : 4 of 24 REV. : 0


Date

: 4.4.2000



* The method of determining wind loads on vessels of two or more diameters is the same as for a vessel of a uniform diameter. When the conical transition section is no more than 10% of the total height, cylindrical sections can be assumed to extend to the midhight of the conical section. Otherwise, the transition section should be considered as separate section.

For Stack material Where, E = Modulus of elasticity of plate material @ operating temp. Y = Yield point stress of plate material @ operating temp. St = Allowable Tensile Strength of Plate Material @ operating temp. r = Steel Density V30 = 'Wind velocity at 30 f t height. C = Corrosion allowance

Table 2. Vessel OD including insulation MM INCH

Less than 36 36 to 60 60 to 84 84 to 108 over 108

Coefficient Kd 1.5 1.4 1.3 1.2 1.18

ASTM A285 Grade C 27600000 30000 15000 490 100 0.125

PSI PSI PSI 3 lb/ft MPH INCH

Ls1-2

50

Ls2-3

3

7850

Kg/M

3.175

MM

Ft

15240

MM

16.8

Ft

5120.64 MM

*Ls3-4

17

Ft

5181.6

MM

*Ls4-5

11

Ft

3352.8

MM

*Ls5-6

10

Ft

3048

MM

Ls6-7

10

Ft

3048

MM

114.8

Ft

34991

MM

Flare stack segment lengths, Ls

Total vessel height Figure (1)

DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 5 of 24 REV. : 0

Designed by : Eng. Abdel Halim Galala, Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter

Date

: 4.4.2000



B. ALLOWABLE SHELL BUCKLING (COMPRESSION) STRESS. Intially, some thicknesses at each section are assumed. Allowable compression stresses at each level are determined from the following formula : - For ta/d < 0.00425 Sc = (0.56 ta E)/d(1+0.004 E/Y) - For higher ta/d ratios, the allowable compression stress used is that calculated for t/d = 0.00425 where ta = assumed corroded plate thickness at each level under consideration, in. d = internal stack diameter at level under consideration, in. Stack OD1-2

20

INCH

508

MM

Stack OD2-3

20

INCH

508

MM

Stack OD3-4

20

INCH

508

MM

Stack OD4-5

28

INCH

711.2

MM

Stack OD5-6

36

INCH

914.4

MM

Stack OD6-7

36

INCH

914.4

MM

0.166142 INCH

4.22

MM

ta2-3

0.30315

7.7

MM

ta 3-4

0.492126 INCH

12.5

MM

ta 4-5

0.307087 INCH

7.8

MM

ta 5-6

0.224409 INCH

5.7

MM

ta 6-7

0.275591 INCH

7

MM

d 1-2 = OD1-2 - 2 ta1-2

19.66772 INCH

499.56

MM

d2-3

19.3937

492.6

MM

d 3-4

19.01575 INCH

483

MM

d 4-5

27.38583 INCH

695.6

MM

d 5-6

35.55118 INCH

903

MM

d 6-7

35.44882 INCH

900.4

MM

By assuming corroded thicknesses as follows: ta 1-2

Internal vessel dia. at each level,

Since the calculated ratio,

ta1-2 / d1-2

INCH

INCH

0.008447

>

0.00425

ta2-3 / d2-3

0.015631

>

0.00425

ta3-4 / d3-4

0.02588

>

0.00425

ta4-5 / d4-5

0.011213

>

0.00425

ta5-6 / d5-6

0.006312

>

0.00425

ta6-7 / d6-7

0.007774

>

0.00425



The ratio ta/d to be used in calculations shall be computed as follows : Use ta1-2 / d1-2 = Min. (Calculated value, 0.00425)

Date

: 4.4.2000



0.00425

ta2-3 / d2-3

0.00425

ta3-4 / d3-4

0.00425

ta4-5 / d4-5

0.00425

ta5-6 / d5-6

0.00425

ta6-7 / d6-7

0.00425

Therefore, the allowable buckling (compression) stress Sc shall be : Sc = (0.56 ta E) / d(1+ 0.004 E/Y) = (ta/d) (0.56 E) / (1+ 0.004 E/Y) Final allowable buckling (compression) stress, Sc 1-2

14035.9

PSI

Sc2-3

14035.9

PSI

Sc3-4

14035.9

PSI

Sc4-5

14035.9

PSI

Sc5-6

14035.9

PSI

Sc6-7

14035.9

PSI



Date

: 4.4.2000



C. SHELL PLATE THICKNESS, DESIGN PROCEDURE. 1. Total Uncrodded Stack Weights. Weights at each level are calculated by adding corrosion allowance to the thicknesses assumed above. [Uncorroded mean adding corrosion allowance ]

2

2

3067.04

2

2

1504.943 lb

2

2

2173.824 lb

2

2

1400.718 lb

2

2

1331.634 lb

2

2

1524.498 lb

Wt 1-2 = r (3.14) [OD1-2 -(d1-2 - 2C) ] Ls1-2 Wt 2-3 = r (3.14) [OD2-3 -(d2-3 - 2C) ] Ls2-3 Wt 3-4 = r (3.14) [OD3-4 -(d3-4 - 2C) ] Ls3-4 Wt 4-5 = r (3.14) [OD4-5 -(d4-5 - 2C) ] Ls4-5 Wt 5-6 = r (3.14) [OD5-6 -(d5-6 - 2C) ] Ls5-6 Wt 6-7 = r (3.14) [OD6-7 -(d6-7 - 2C) ] Ls6-7 Total Weight

lb

11002.66 lb

Kg

By adding 15% of the calculated weight to compensate weight of piping, internals, platforms, ladders, etc., we get :

Wt 1-2

3527.096 lb

Wt 2-3

1730.685 lb

Wt 3-4

2499.898 lb

Wt 4-5

1610.826 lb

Wt 5-6

1531.379 lb

Wt 6-7

1753.173 lb

(Total Weight + 15%), Wt

12653.06 lb

Kg


Designed by : Eng. Abdel Halim Galala, Design General Manager (Assistant) Project : Design & procurement of Flare Stack According to ASME Code, Sec. VIII, Div. 1, Edition 95, Addenda 96. Dwg. No. : Stack Type : Self supported & Multiple Diameter

Date

: 4.4.2000



2. Computation of the Projected Area, A An approach to computing A which is often used and is recommended here is to increase the vessel diameter D to the so-called effective stack diameter De to approximate the combined design wind load : De = Kd [(Vessel OD + 2 insulation thk.) + (pipe OD + 2 insulation thk. + (platform + ladder)] The coefficient Kd is given in Table 2. The required projected area A will then equal to : A = De * Ls where Ls = Length of the shell section in the zone of the uniform wind velocity. De = Kd [Stack OD + Fuel Gas Pipe OD + Steam Pipe OD] N.B. In our case, the size of fuel gas and steam pipes can be neglected.

Coefficient Kd

[fromTable 2]

Kd1-2

[dia. <

36"]

Kd2-3

[dia. <

36"]

1.5

20

508

Kd3-4

[dia. <

36"]

1.5

20

508

Kd4-5

[dia. <

36"]

1.5

28

711.2

Kd5-6

[dia. = 36"]

1.4

36

914.4

Kd6-7

[dia. = 36"]

1.4

36

914.4

Effective Diameter, De = Kd * Stack OD, De1-2 = Kd1-2 * OD1-2

Projected Area, A = De * Height Ls

1.5

Stack OD INCH MM 20 508

2.5

Ft

MM

De2-3

2.5

Ft

MM

De3-4

2.5

Ft

MM

De4-5

3.5

Ft

MM

De5-6

4.2

Ft

MM

De6-7

4.2

Ft

125

Ft

A1-2 = De1-2 - Ls1-2

M

2

M

2

2

A2-3

42

Ft

A3-4

42.5

Ft

M

A4-5

38.5

Ft

M

2

2

2

A5-6

42

Ft

M

A6-7

42

Ft

M



Date

: 4.4.2000



3. Computation of Wind Loads. The resultant of the wind pressure load Pw over the area A is given by : Pw = A * B * Pz where Pw = Wind pressure load over the projected area A, lb. 2 A = Windward surface area projected on the vertical plane normal to the direction of the wind, ft . B = Shape Factor, for round objects B = 0.6 0.6 Pz = Design wind pressure, psf, depends upon the geographical area of the job site (see Table 1). B Pz = Min. net wind pressure, psf. For cylindrical vertical vessels : - For L/D <= 10, BPz not less than 13 PSF - For L/D >= 10, BPz not less than 18 PSF where, L is the overall tangent-to-tangent length of the vessel, Davg. is the vessel average diameter. =B451= (L1-2 D1-2 + L2-3 D2-3 + L3-4 D3-4 + L4-5 D4-5 + L5-6 D5-6 + L6-7 D6-7) / L

L/Davg. Therefore, the net wind pressure BPz shall not be less than

114.8

Ft

34991

1.962834 Ft 58.48686 > 18 PSF

MM MM

10



Date


Determining Design Wind Pressure B Pz for each Segment [based upon Table 1]. Table 3 From Table 1. Height zone

above grade M

Design Wind Pressure,

: 4.4.2000


Pz1-2

Segment

Basic height, H wind above pressure, P grade PSF M

Design wind pessure,

Pz PSF

30.722385

34.991

30.722385

25.601988

19.751

25.6019875

20.48159

14.6304

20.48159

9.4488

15.3611925

6.096

15.3611925

3.048

15.3611925

20 19 Pz2-3 15 14 Pz3-4 10 9

Pz4-5 Pz5-6 Pz6-7 Net wind pressure, NWP shall be as follows :B Pz 1-2

Use the max. following wind pressure :

15.361193 0 18.43343 PSF

B Pz2-3

15.36119 PSF

B Pz3-4

12.28895 PSF

B Pz4-5

9.216716 PSF

B Pz5-6

9.216716 PSF

B Pz6-7

9.216716 PSF

B Pz 1-2 = Max (NWP,18)

18.43343 PSF

B Pz2-3

18

PSF

B Pz3-4

18

PSF

B Pz4-5

18

PSF

B Pz5-6

18

PSF

B Pz6-7

18

PSF

Wind Load shall be as follows : Pw = A * B Pz Pw1-2 = A1-2 B Pz1-2

2304.179 lb

Kg

Pw2-3

756

lb

Kg

Pw3-4

765

lb

Kg

Pw4-5

693

lb

Kg

Pw5-6

756

lb

Kg

Pw6-7

756

lb

Kg



Date

: 4.4.2000



4. Computation of Wind Moments. In the following calculations we assumed that geographical location of the job site does not required a moment calculation for the earthquake. Therefore, the total wind moment shall be calculated as follows :

Figure (2) Moment = Wind Load x Arm 57604.47 102665.1 M3 =Pw1-2 (0.5 L1-2+L2-3)+Pw2-3(0.5L2-3) 161190.6 M4 =Pw1-2 (0.5 L1-2+L2-3+L3-4)+Pw2-3(0.5L2-3+L3-4)+ Pw3-4(0.5L3-4) M5 =Pw1-2 (0.5 L1-2+L2-3+L3-4+L4-5)+Pw 2-3(0.5L2-3+L3-4+L4-5)+ Pw3-4(0.5L3-4+L4-5)+Pw4-5(0.5 L4-5) 207079.1 M6 =Pw1-2 (0.5 L1-2+L2-3+L3-4+L4-5+L5-6)+Pw2-3(0.5L2-3+L3-4+L4-5+L5-6)+ Pw3-4(0.5L3-4+L4-5+L5-6)+ 256040.9 M7 =Pw1-2 (0.5 L1-2+L2-3+L3-4+L4-5+L5-6+L6-7)+Pw2-3(0.5L2-3+L3-4+L4-5+L5-6+L6-7)+ Pw3-4(0.5L3-4+L 312562.7 M2 = Pw1-2 (0.5 L1-2)

Load W, lb 2304.179

lb-ft lb-ft lb-ft lb-ft lb-ft lb-ft Wind Shear Q, lb

Table 4. Weight Moment @ section M, lb-ft WT, lb 3527.09562

2304.1789 57604.5 756 5257.78058 3060.1789 102665 765 7757.67823 3825.1789 161191 693 9368.50446 4518.1789 207079 756 10899.8834 5274.1789 256041 756 12653.0565 Figure (3)

6030.1789 312563



Date

: 4.4.2000



5. Required Shell Plate Thickness. The required shell plate thickness shall be computed as follows : 2 tr = (WT dr + 48 M) / 3.14 dr Sc where W T = Total weight @ Section under consideration By assuming corroded thicknesses as follows: ta 1-2

0.166142 INCH

4.22

MM

ta2-3

0.30315

7.7

MM

ta 3-4

0.492126 INCH

12.5

MM

ta 4-5

0.307087 INCH

7.8

MM

ta 5-6

0.224409 INCH

5.7

MM

0.275591 INCH

7

MM

0.166173 INCH

4.2208

MM MM

ta 6-7 2

tr1-2 = (WT1-2 dr1-2 + 48 M2) / PI( ) dr1-2 Sc1-2

INCH

N.B. The assumed thickness must be changed untill the calculated > the assumed thickness.

tr1-2 + C.A

0.291173 INCH

7.3958

For construction, use (tr1-2 + C.A)

0.314961 INCH

8

2

0.303282 INCH

7.70337 MM

tr2-3 = (WT2-3 dr2-3 + 48 M3) / PI( ) dr2-3 Sc2-3


tr2-3 + C.A

0.428282 INCH

10.8784

MM


0.433071 INCH

11

MM

0.4945

12.5603 MM

2

tr3-4 = (WT3-4 dr3-4 + 48 M4) / PI( ) dr3-4 Sc3-4

INCH


tr3-4 + C.A

0.6195

For construction, use (tr3-4 + C.A) 2

tr4-5 = (WT4-5 dr4-5 + 48 M5) / PI( ) dr4-5 Sc4-5

15.7353

MM

0.629921 INCH

16

MM

0.308321 INCH

7.83136 MM

INCH


tr4-5 + C.A

0.433321 INCH

11.0064

MM


0.472441 INCH

12

MM

2

0.227475 INCH

5.77787 MM

tr5-6 = (WT5-6 dr5-6 + 48 M6) / PI( ) dr5-6 Sc5-6


tr5-6 + C.A

0.352475 INCH

8.95287

MM


0.354331 INCH

9

MM

2

0.278855 INCH

7.08291 MM

tr6-7 = (WT6-7 dr6-7 + 48 M7) / PI( ) dr6-7 Sc6-7


tr6-7 + C.A For construction, use (tr6-7 + C.A)

0.403855 INCH

0.433071 INCH N.B. Since there is no appreciable change in calculated thicknesses, the weights based on the required thicknesses are almost the same as previouslyestimated.

10.2579

MM

11

MM



Date

: 4.4.2000



6. Ancor Bolt Chair. Anchor bolt material Assume No. of anchor bolts, N Bolt Circle Dia, DBC

ASTM A36 16 BOLTS 43.93701 INCH

Max. Allowable stress of Anchor Bolt Material, SB

15000

MM

PSI

The total tension in each anchor bolt is determined from the relationship: W B = (48 M / N DBC) - Wt / N

20550.83 lb

Thus, the anchor bolt area required at the root of the thread shall be: AB = WB / SB

1.370055 INCH

0.5

1116

Kg

2

2

883.905 MM

Diameter of the anchor bolt at the root of thread, D = (4 AB /3.14)

1.320761 INCH

33.5473

MM

Use 16 holding down bolts with a dia. of , d Each bolt shall be provided with two hex heavy nuts and washer. - Length of threaded portion, l - Radius, R - Length, L - Bolt projection - Total length, M

1.75

INCH

44.45

MM

INCH INCH INCH INCH INCH

150 90 350

MM MM MM MM MM

Figure (4)

Figure (5)

1085



7. Width of Base Ring, C. Assume width of base ring, C Bearing pressure on concrete foundation is calculated from the following formula : 2 Pb = (48 M / PI D b C) + (Wt / 3.14 D b C)

where

Db = OD at bottom of stack

Date


11.10236 INCH

282

MM

341.9775 PSI SAFE

<

500

36

914.4

MM

INCH

Assume C, and note that the value of Pb is limited to : - For 3000 lb concrete - For 2000 lb concrete

: 4.4.2000


750 500

N.B. If the calculated Pb exceeds the above limit, the value of C is modified so that Pb falls within the allowable limit.

PSI PSI

(Max.) (Max.)



Date

: 4.4.2000



8. Base Plate Thickness, Tb Base plate thickness Tb is calculated from the following equation: Tb = e SQRT(3 Pb / 20000)

1.480195 INCH

37.5969

MM

where e = A + B A B

6.535433 INCH

166 101 65

MM MM MM

Use Tb

1.771654 INCH

45

MM

TT = SQRT[ 3 * W B * 6 / (4 * 20000 * e)]

0.841141 INCH

21.365

MM

where W B = Total tension in each bolt

20550.83 PSI

Use TT

1.181102 INCH

30

MM

Figure (6) 9. Top Plate Thickness, TT



Date

: 4.4.2000



D. VIBRATION ANALYSIS. 1. Cantilever vibration. The following criteria is used to establish need for vibration analysis of stacks with Lc/L ratio not exceeding 0.5 : 2 - W / L Dr <= 20 vibration analysis must be performed 9.443917 < 20 vibration analysisis required 2 - 20 < W / L Dr <= 25 vibration analysis should be performed 2 - 25 < W / L Dr vibration analysis need not be performed Where

Wt = Total corroded stack weight (see next page). Le = Total length of stack. Dr = Average internal dia. of top half of stack. Lc = Total length of conical section(s) of stack. Conical section height 28"/20" Conical section height 36"/28" We note that Lc / L < 0.5

8071.981 114.8 2.72862 4.002625

lb ft ft ft

2.001312 ft 2.001312 ft

610 610

MM MM

0.034866 OK

Stack OD1-2

20

INCH

508

MM

Stack OD2-3

20

INCH

508

MM

Stack OD3-4

20

INCH

508

MM

Stack OD4-5

28

INCH

711.2

MM

Stack OD5-6

36

INCH

914.4

MM

Stack OD6-7

36

INCH

914.4

MM

Corroded thickness tr1-2

0.189961 INCH

4.825

MM


0.308071 INCH

7.825

MM


0.504921 INCH

12.825

MM


0.347441 INCH

8.825

MM


0.229331 INCH

5.825

MM


0.308071 INCH

7.825

MM

O.D.



Corroded internal diameter in inches : Corroded ID1-2

Flare stack segment heights,

Date


19.62008 INCH

Corroded ID2-3

19.38386 INCH

Corroded ID3-4

18.99016 INCH

Corroded ID4-5

27.30512 INCH

Corroded ID5-6

35.54134 INCH

Corroded ID6-7

35.38386 INCH

L1-2

: 4.4.2000


50

Ft

15240

MM

L2-3

16.8

Ft

5120.64

MM

L3-4

17

Ft

5181.6

MM

L4-5

11

Ft

3352.8

MM

L5-6

10

Ft

3048

MM

L6-7

10

Ft

3048

MM

Total Corroded Stack Weights. Weights at each l evel are calculated, without taking into account adding corrosion allowance to the thicknesses assumed above. Corroded mean neglecting corrosion allowance. 2

2

2011.418 lb

912.365

Kg

2

2

1089.511 lb

494.194

Kg

2

2

1788.879 lb

811.423

Kg

2

2

1129.776 lb

512.459

Kg

2

2

876.9458 lb

397.776

Kg

2

2

1175.45

lb

533.176

Kg

8071.981 lb

3661.39

Kg

Wt 1-2 = r (PI/4) [do -di ]1-2 L1-2 Wt 2-3 = r (PI/4) [do -di ]2-3 L2-3 Wt 3-4 = r (PI/4) [do -di ]3-4 L3-4 Wt 4-5 = r (PI/4) [do -di ]4-5 L4-5 Wt 5-6 = r (PI/4) [do -di ]5-6 L5-6 Wt 6-7 = r (PI/4) [do -di ]6-7 L6-7 Total corroded stack Weight, Wt Analyzing technique. Period of vibration is determined as follows : 2 0.5 T = 1.648 (Le ) / Dr E 'where Le = effective length of stack

1.515107 second 114.8

ft

Natural frequency of stack vibration, f = 1 / T

0.660019 cps

Critical wind velocity, Vc = 3 f Dr

5.402825 MPH



Max. wind velocity at the top of the stack is 0.143 Vw = V30 (L / 30)

Date

: 4.4.2000



121.1556 MPH

V30 = Wind velocity at 30 f t height (basic wind velocity) Max. gust velocity = 1.3 Vw

100

MPH

157.5022 MPH

Since the critical wind velocity, Vc falls within max. gust velocity, the stack must be checked further for K. In that case, corroded stack weight must be > 15 times the wind force at critical velocity or expressed as a formula, the ratio K should be less than 1/15. 5

3

K = Pc Dr Le / W s = 0.0077 Dr E / Le Ws

0.002632

<

l / 15

0.06666667

7.71321

MM

Therefore, the stack is free from cantilever vibration. N.B. For lined stacks, W can be used in place of Ws in order to reduce vibration. Design modifications are required, if K in the above equation exceeds 1/15. Static deflection. The computed dynamic loading is applied as a stagnant pressure to the stack. Assuming it to be a cantilever beam, amplitude at the top is approximated by : Static Deflection, where,

Pc

4

3

Ds = Pc Dr (Le) (12) / 8 E I

0.303669 INCH

= Total wind force at critical velocity 2 = C1 pair (1.467 Vc) / 2

0.074756 psf

C1 = Lift coefficient (usually taken as1) pair = mass density of air

1 0.00238

I = Moment of inertia of top half of stack 3 = 3.14 * r * t r = Average internal radius of top half of stack t = Average corroded plate thick. of top half of stack

913.0678 INCH 9.679528 INCH 0.320472 INCH

2

lb.sec /ft 4

4

4

38004.8 CM 245.86 MM 8.14 MM



Date

: 4.4.2000



Dynamic deflection. At a critical wind velocity, the structure vibrates at resonant frequency, and thus the amplitude of vibration is magnified greatly. The dynamic coefficient, which is a ratio of dynamic amplitude to static amplitude, is called the magnification factor. This is a function of the lining, stiffness of the soil and several other factors. The amount of static deflection must be multiplied by the magnification factor to determine dynamic deflection. Approximate value of magnification factors for different types of stacks as suggested by DeGhetto and Long are listed in Table 3. Table 5. Magnification factors Types of stacks

Lined stacks Unlined stacks Using a magnification factor of Dynamic deflection = Static Deflection * Magnification factor = Ds * Magnification factor

Spread footings on soft soil (Bearing < 1500 psi)

Piled foundations

on medium and spread

(1500 psi < footings Bearing > on stiff soil 3000 psi) and rocks

5

30

50

30

60

90

30 Allowed deflection

9.110085 INCH NotT Good

N.B. For dynamic deflection, It is assumed to be within the allowable limits when allowing about 7-inch deflection per 100 feet* of height of stack. * "Shortcut method for calculating tower deflection", Hydrocarbon Processing 47. No. 11, Nov. 1968, p 230.

Allowed deflection of stack under consideration = 7 x L / 100

Spread footings

8.036

INCH

>

8.036



Date

: 4.4.2000



2. Ovaling vibration. Natural frequency of the free ring is given by : 0.5 2 fr = (7.58 tr E ) / 60 D Vortex shedding frequency is given by : fv = 0.2 V / D Where V = wind velocity for v ortex shedding is 45 MPH or 66 fps as recommended by Dickey and Woodruff for most economical and safe stack design as far as vibration is concerned.

45 66

MPH fps

Both these frequencies should be calculated at each level using the corresponding thicknesses and diameters. Corroded internal diameters in feet, D

D1-2

1.635007 1.615322 1.582513 2.275427 2.961778 2.948655

D2-3 D3-4 D4-5 D5-6 D6-7

At Section 1-2 :

0.5

fr1-2 = (7.58 tr1-2 E ) / 60 D

2 1-2

fv1-2 = 0.2 V / D1-2

Ft Ft Ft Ft Ft Ft

47.16253 cps 8.073362 cps

2 fv1-2

16.14672 cps Since fr > 2 fv , no ovaling rings are required, and the stack is free from ovaling vibration. N.B. t calculated upon corroded thk. & V = 66 fps. At Section 2-3 :

0.5

fr2-3 = (7.58 tr2-3 E ) / 60 D

2 2-3

fv2-3 = 0.2 V / D2-3

78.36194 cps 8.171748 cps

2 fv2-3

16.3435 cps Since fr > 2 fv , no ovaling rings are required, and the stack is free from ovaling vibration. At Section 3-4 :

0.5

fr3-4 = (7.58 tr3-4 E ) / 60 D

2 3-4

fv3-4 = 0.2 V / D3-4

133.814

cps

8.341163 cps

2 fv3-4 16.68233 cps Since fr > 2 fv , no ovaling rings are required, and the stack is free from ovaling vibration. At Section 4-5 :

0.5

fr4-5 = (7.58 tr4-5 E ) / 60 D fv4-5 = 0.2 V / D4-5 2 fv4-5

2 4-5

44.53771 cps 5.80111

cps

11.60222 cps Since fr > 2 fv , no ovaling rings are required, and the stack is free from ovaling vibration.

498.35 492.35 482.35 693.55 902.75 898.75

MM MM MM MM MM MM

cps = cycle per second



At Section 5-6 :

0.5

fr5-6 = (7.58 tr5-6 E ) / 60 D

Date


2 5-6

fv5-6 = 0.2 V / D5-6

17.3512

cps

4.456782 cps

2 fv5-6

8.913564 cps Since fr > 2 fv , no ovaling rings are required, and the stack is free from ovaling vibration. At Section 6-7 :

0.5

fr6-7 = (7.58 tr6-7 E ) / 60 D fv6-7 = 0.2 V / D6-7 2 fv6-7

: 4.4.2000


2 6-7

23.51664 cps 4.476618 cps

8.953235 cps Since fr > 2 fv , no ovaling rings are required, and the stack is free from ovaling vibration.



Date


Design of Ovaling Rings. If, at any section, fr < 2fv, ovaling rings are required to stiffen that section. Section modulus of the rings, whenever required, can be determined as follows : - Critical wind velocity at the section under consideration is : Vo = ( 60 fr D ) / 2 S where fr = Natural frequency S = Strouhal number, is 0.2 over a wide range of Reynolds numbers. D = Intenal vessel dia. (corroded) at level under consideration.

Critical wind velocity at Section, Vo1-2 = ( 60 fr1-2 D1-2 ) / 2 S

FPM cps

0.2 Ft

11566.66 FPM

Vo2-3 = ( 60 fr2-3 D2-3 ) / 2 S

18986.96 FPM

Vo3-4 = ( 60 fr3-4 D3-4 ) / 2 S

31764.36 FPM

Vo4-5 = ( 60 fr4-5 D4-5 ) / 2 S

15201.34 FPM

Vo5-6 = ( 60 fr5-6 D5-6 ) / 2 S

7708.563 FPM

Vo6-7 = ( 60 fr6-7 D6-7 ) / 2 S

10401.37 FPM

Required Section Modulus of the Ring. Now, the section modulus of stiffeners at section under consideration can be found from the formula as used by Moody : -7 2 2 3 Sm = [ (7)10 (Vo) D (Hr) ] / St INCH Where, Vo = Critical wind velocity at section of consideration Hr = Spacing throughout the length of the section under considerat 0.5 Ls St = Allowable tensile strength of stiffener material 15000 -7

Sm1-2 = [ (7)10

2

2

(Vo1-2) D1-2 Hr1-2) ] / St

-7

2

2

-7

2

2

-7

2

2

-7

2

2

-7

2

2

Sm2-3 = [ (7)10 (Vo2-3) D2-3 Hr2-3) ] / St Sm3-4 = [ (7)10 (Vo3-4) D3-4 Hr3-4) ] / St Sm4-5 = [ (7)10 (Vo4-5) D4-5 Hr4-5) ] / St Sm5-6 = [ (7)10 (Vo5-6) D5-6 Hr5-6) ] / St Sm6-7 = [ (7)10 (Vo6-7) D6-7 Hr6-7) ] / St

: 4.4.2000


FPM Ft PSI 3

0.417255 INCH 3 0.368735 INCH 1.002306 INCH 3 0.307085 INCH 0.121627 INCH 0.219485 INCH

3

Stiffeners having section modulus equal to or greater than Sm should be provided at spacing Hr throughout the length of the section under consideration. If stiffeners are required for more than one section, different size and spacing should be used for economy, if possible.

DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. Abdel Halim Galala, Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter

Notes

Page : 23 of 24 REV. : 0

Date

: 4.4.2000





E. REFERENCES. 1. ANSI A58.1-1955. 2. ASCI 7-1988. 3. Pressure Vessel Design Handbook-2nd Edition, by Henry H. Bednar. 4. Flare stack paper research.

‫د א‬ª

Page : 24 of 24 REV. : 0

Date

: 4.4.2000



Flare Stack Mechanical Design Calculations by Abdel Halim Galala

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