Transcript
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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter
Date
: 4.4.2000
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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.
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 : 4 of 24 REV. : 0
Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter
Date
: 4.4.2000
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
* 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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 6 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
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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 7 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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 8 of 24 REV. : 0
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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 9 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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
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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
Client : ABB/OPC Item : X-06-02
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
Location : Gulf of Seuz
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
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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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 12 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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
N.B. The assumed thickness must be changed untill the calculated > the assumed thickness.
tr2-3 + C.A
0.428282 INCH
10.8784
MM
For construction, use (tr2-3 + C.A)
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
N.B. The assumed thickness must be changed untill the calculated > the assumed thickness.
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
N.B. The assumed thickness must be changed untill the calculated > the assumed thickness.
tr4-5 + C.A
0.433321 INCH
11.0064
MM
For construction, use (tr4-5 + C.A)
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
N.B. The assumed thickness must be changed untill the calculated > the assumed thickness.
tr5-6 + C.A
0.352475 INCH
8.95287
MM
For construction, use (tr5-6 + C.A)
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
N.B. The assumed thickness must be changed untill the calculated > the assumed thickness.
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 13 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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
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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
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
Client : ABB/OPC Item : X-06-02
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
Location : Gulf of Seuz
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.)
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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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 16 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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
Corroded thickness tr2-3
0.308071 INCH
7.825
MM
Corroded thickness tr3-4
0.504921 INCH
12.825
MM
Corroded thickness tr4-5
0.347441 INCH
8.825
MM
Corroded thickness tr5-6
0.229331 INCH
5.825
MM
Corroded thickness tr6-7
0.308071 INCH
7.825
MM
O.D.
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 17 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
Corroded internal diameter in inches : Corroded ID1-2
Flare stack segment heights,
Date
Client : ABB/OPC Item : X-06-02
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
Location : Gulf of Seuz
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 18 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
Max. wind velocity at the top of the stack is 0.143 Vw = V30 (L / 30)
Date
: 4.4.2000
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 19 of 24 REV. : 0
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Date
: 4.4.2000
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 20 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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 21 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
At Section 5-6 :
0.5
fr5-6 = (7.58 tr5-6 E ) / 60 D
Date
Client : ABB/OPC Item : X-06-02
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
Location : Gulf of Seuz
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.
DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Page : 22 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
Client : ABB/OPC Item : X-06-02
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
Location : Gulf of Seuz
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
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
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)
Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter
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 אª
Page : 24 of 24 REV. : 0
Date
: 4.4.2000
Location : Gulf of Seuz
Client : ABB/OPC Item : X-06-02
