CHAPTER 6 Pressure (Welded) Vessel Design - ChE 192

1 CHAPTER 6 Pressure ( welded ) Vessel Design Pressure Vessel is a closed Vessel having an internal Pressure between 15 psig to 3000 psig (Perry and Green, 1997). Whereas, atmospheric and low Pressure tanks are designed to operate at pressures between atmospheric to psig, and, to 15 psig respectively (Kohan, 1987). The American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code contains rules for the Design , fabrication and inspection of boilers and Pressure vessels. ASME Code is acceptable in most of the States in the US and all Canadian provinces.

2 Section VIII Division I of ASME Boiler and Pressure Vessel Code deals specifically with Pressure vessels. Most Pressure vessels used in the process industry in the US are designed in accordance with the specification of this section. Pressure vessels may include reflux drum, storage tanks, heat exchangers, chemical reactors, distillation columns, absorption tower, stripping columns and many more. SHELL THICKNESS In general, the minimum wall thickness of welded metal plates subject to Pressure , excluding corrosion allowances, should not be less than mm (Peters et al.)

3 , 2004). To provide for the Vessel sufficient rigidity especially at low pressures, the minimum wall thickness at different cylindrical shell diameters should be (Seider, 2004). Vessel inside diameter (ft) Minimum wall thickness (inch) Up to 4 4-6 5/16 6-8 3/8 8-10 7/16 10-12 1/2 In practical designation, the shell is considered thin if the ratio of circumferential radius of curvature to wall thickness is greater than 10. Many Pressure vessels are relatively thin, having radius of thickness ratio between 10 to 500 (Bhaduri, 1984).

4 Shell Thickness Working Equations The needed Shell thickness of Pressure vessels is a function of the ultimate tensile strength of the metal at operating temperature, operating Pressure , Vessel diameter and welding joint efficiency (Peters et al, 2004). In the recent American Society of Mechanical Engineers (ASME) Code (VIII-I), the working equation for the determination of shell thickness of cylinder subjected to internal Pressure based on inside diameter is given as: eq 6-1 Pressure welded Vessel Design 2 where tp = shell thickness required (inch) [m] P = Internal gauge Pressure (psig) [kN/m2] R = Inside Radius (inch) [m] S = Allowable stress (psi) [kN/m2] E = Joint efficiency factor (Table 6-4) C = Corrosion allowance (inch) [m] Provided that 1.

5 Tp less than or equal to 2R and 2. Pressure is less than or equal to SE (Jawad and Farr, 1988). Alternative ASME equation based on outside diameter of a cylindrical shell is given as: eq 6-2 ASME Pressure Vessel Code formula excludes corrosion, wind and earthquake allowances (Mulet, 1981) as cited by (Seider, 2004). The recommended wall thickness, tv, requirement of vertical Pressure Vessel or tower incorporating wind load based on wind velocity of 140 miles/hr, which is substantially sufficient to handle additional earthquake load is, tv = tp [ + E ( L/Di)2/Pd } eq 6-3 The above equation is applicable for 10 > ( L/Di)2/ Pd > If the ratio is less than , then tv = tp Table 6-1.]

6 Design equations and data for Pressure vessels based on the ASME Boiler and Pressure Vessel /Code. Adapted from ASME as cited by Peters et al., 2004. Recommended Design equations for vessels Under internal Pressure Limiting conditions For cylindrical shells ci1 For spherical shells ci1 Pressure welded Vessel Design 3 For ellipsoidal head For torispherical (spherically dished) head For hemispherical head Same as for spherical shells with ri = La (minor axis)

7 0 = r = knuckle radius = 6% of inside crown radius and is not less than 3t **Nomenclature for Table 6-1 a = 2 for thickness < m and 3 for thickness m Cc = allowance for corrosion, m Da = major axis of an ellipsoidal head, before corrosion allowance is added, m EJ = efficiency of joints expressed as a fraction IDD = inside depth of dish, m La = inside radius of hemispherical head or inside crown radius of torispherical head, before corrosion allowance is added, m n = for D , for D = m, for D = m, and for D > m OD = outside diameter, m P = maximum allowable internal Pressure , kPa (gauge) r = knuckle radius, m ri = inside radius of shell, before corrosion allowance is added, m S = maximum allowable working stress, kPa t = minimum wall thickness, m = density of metal, kg/m3 +See the latest ASME Boiler and Pressure Vessel Code for further details.

8 Shell Wall thickness for vacuum vessels may be calculated (Kalis, 1986) with this equation eq 6-4 where Pc = Collapsing Pressure (psi) Te = Thickness to withstand external Pressure (inch) Do = Outside diameter (inch) Em = Material s modulus of elasticity Te must be high enough so that Pc is five times greater than the difference between atmospheric Pressure and Design vacuum Pressure Pressure welded Vessel Design 4 Mulet et al , 1981, as cited by Seider, 2004, presented an alternative equation for the calculation of cylindrical wall thickness at vacuum, tE, tE = ( PdL/EMDo )

9 4 eq 6-5 a correction factor is added ,tEC tEC = L ( ) x 10 -5- eq 6-6 Thus, the wall thickness of vessels at vacuum incorporating wind and earthquake loads is, tV = tE + tEC eq 6-7 tp = wall thickness (for internal Pressure ) Di = inside diameter L = cylindrical shell length Pd = internal Design gauge Pressure S = maximum allowable stress 2inlb E = fractional weld efficiency Po = operating gauge Pressure tv = wall thickness of vessels or tower incorporating wind and earthquake loads tE = wall thickness of Vessel or tower @ vacuum tEC = correction added to tE, , (tV = tE + tEC) To include corrosion allowance, tc, Seider (2004) recommended 1/8 inch for noncorrosive conditions.

10 Backhurst and Harker (1973) recommended 1/8 up to 3/16 corrosion allowance for noncorrosive and for corrosive environments. ts = tV + tc eq 6-8 where ts = cylindrical wall thickness incorporating wind, earthquake and corrosion allowances. For Spherical Shell, ASME code as cited by Kohan (1987) provide for equation to calculate the maximum allowable internal working Pressure . eq 6-9 where P = internal working gauge Pressure (psig) R = Inside Radius (inch) tp = Minimum required thickness (inch) E = Lowest joint efficiency S = Max allowable stress (psi) Pressure welded Vessel Design 5 Material of Construction In a noncorrosive environment, carbon steel and low alloy steel are commonly used material of construction for Pressure Vessel at low temperature (-20 to 650oF)