This worked example documents the ASME Section VIII Division 1 design of a 24 in OD vertical reactor at 1,000 psig and 200 °F, with hemispherical heads at both ends. The vessel is SA-516 Grade 70 Normalized: a 0.875 in nominal shell and 0.500 in nominal hemispherical heads, with Class 600 RFWN flanges on the four process nozzles. Vessel MAWP is 1,200 psig (shell-governed); the hemispherical heads are rated 1,360 psig at the in-service thickness.
The teaching content is the dramatic thickness contrast among the curved head types at high pressure. Section 5 example 3 compares hemispherical (0.500 in nominal, UG-32(f)), 2:1 SE (0.750 in nominal, UG-32(d)), and F&D torispherical (1.250 in nominal, UG-32(c)) on the same 24 in shell at the same 1,000 psig design point. The hemi head requires half the thickness of the SE and a quarter of the F&D, but adds 14 in of overall vessel height (D/2 per end). At this pressure the hemi is the natural choice when overall height is not a hard constraint. Pairs with the moderate-pressure head comparison on the 48 in OD vessel page.
Five sections. Each section is a collapsible block. Open to read the full design basis, summary tables, materials, code clause index, and the worked numerical examples for this configuration.
| Parameter | Value | Reference |
|---|---|---|
| Code of construction | ASME Section VIII Division 1, 2023 Edition | U-1, U-2 |
| Equipment type | Vertical reactor, hemispherical heads both ends | |
| Design pressure | 1,000 psig | UG-21 |
| Design temperature | 200 °F | UG-20(a) |
| Design MDMT | -20 °F | UG-20(b), UCS-66 |
| Corrosion allowance | 0.0625 in (internal surfaces) | UG-25 |
| Joint efficiency, shell | 1.00 (full RT long seam) | UW-12 |
| Joint efficiency, heads | 1.00 (one-piece formed hemi) | UW-12 |
| Radiography | Full RT on Cat. A welds, surface NDE on nozzle welds | UW-11, UW-50 |
| Service | Non-lethal, non-cyclic, gas-phase or supercritical reaction service | UG-22, UW-2 |
The vessel is analyzed for the loadings listed in UG-22. Governing loads for this configuration are:
Non-cyclic per UG-22(e).
The design MDMT is -20 °F at full pressure. The shell and heads are SA-516 Grade 70 Normalized, Curve D under Table UCS-66. Required MDMT at the shell thickness (0.875 in nominal) is approximately -35 °F at no impact testing, which is colder than the design MDMT requirement.
The shop hydrostatic test follows UG-99(b):
SA-516 Grade 70 does not derate below 300 °F so the material LSR is 1.00. The Class 600 RFWN flanges have a 70 °F rating of 1,500 psig, so the test pressure is just over the cold flange rating; the flange stud loading is checked in the hydrotest summary against the 0.9 S_y limit and passes by inspection.
| Component | Material | t_req (in) | t_avail (in) | MAWP (psig) | Clause |
|---|---|---|---|---|---|
| Cylindrical shell | SA-516 Gr 70 N | 0.582 | 0.703 | 1,200 | UG-27(c)(1) |
| Hemispherical heads (top and bottom) | SA-516 Gr 70 N | 0.284 | 0.388 | 1,360 | UG-32(f) |
| Cl 600 RFWN flanges (process) | SA-105 | standard | standard | 1,440 | UG-44, B16.5 Gp 1.1 at 200 F |
| NPS 2 inlet/outlet, NPS 1 instrument | SA-106 Gr B | < 0.10 | > 0.30 | matches shell | UG-27(c)(1) |
The cylindrical shell governs the vessel MAWP at 1,200 psig. The hemispherical heads are rated 1,360 psig at the same in-service thickness (0.388 in formed-corroded), 160 psig above the shell. The high-pressure design point is what makes the hemispherical head the natural choice on this vessel; an F&D head at 1,000 psig would require about 2.5 in of plate and a 2:1 SE head about 1.0 in. See worked example 3 for the comparison.
All components meet UG-16(b) by wide margins.
| Component | Calc Stress at 1,560 psig (psi) | 0.9 × S_y at 70 °F (psi) | Status |
|---|---|---|---|
| Shell, UG-99 Note 35 | 25,330 | 32,400 (SA-516-70 N) | PASS |
| Hemispherical heads | 22,750 | 32,400 | PASS |
| Cl 600 flange (B16.5 rating) | 1,560 psig (above 1,500 cold rating) | standard product | PASS (stud check) |
| Component | Specification | S at 200 °F (psi) | UCS-66 Curve | Form |
|---|---|---|---|---|
| Shell | SA-516 Grade 70, normalized | 20,000 | D | 0.875 in plate, rolled and welded long seam |
| Top and bottom hemispherical heads | SA-516 Grade 70, normalized | 20,000 | D | 0.500 in plate, one-piece formed, hemispherical to a 24 in OD skirt |
| Nozzle necks | SA-106 Grade B, seamless | 17,100 | B | NPS 2 / 1 Schedule 80 or thicker |
| Flanges | SA-105 | 17,500 | B | ASME B16.5 RFWN Class 600, all process nozzles |
| Bolting | SA-193 Gr B7 studs, SA-194 Gr 2H nuts | 25,000 | n/a | standard B16.5 stud-and-nut sets |
| Support lugs | SA-516 Grade 70 plate | n/a | n/a | Two welded lugs at the lower head-to-shell circumferential weld |
| Tag | Function | Size and Class | Location | Type | Weld |
|---|---|---|---|---|---|
| N1 | Process inlet | NPS 2 Cl 600 RFWN, Sch 160 neck | Top hemi head | Set-in radial, no repad (UG-37 PASS) | Full pen + fillet per UW-16(f) |
| N2 | Process outlet | NPS 2 Cl 600 RFWN, Sch 160 neck | Bottom hemi head | Set-in radial, no repad | Full pen + fillet per UW-16(f) |
| N3 | Pressure relief (PSV) | NPS 1 Cl 600 RFWN, Sch 160 neck | Shell, top | Set-in radial, exempt UG-36(c)(3)(a) | Full pen + fillet per UW-16(f) |
| N4 | Instrument tap | NPS 1 Class 6000 threaded coupling | Shell | Set-on, exempt UG-36(c)(3)(a) | Full pen + fillet per UW-16(f) |
All openings are below the UG-36(c)(3)(a) 3.5 in finished-diameter exemption limit on a 0.703 in corroded shell. The NPS 2 inlet and outlet (2.067 in finished bore) are well within the exemption.
Category A welds (long seam and head-to-shell circumferentials) are fully radiographed per UW-11(a)(1). The hemispherical-to-shell joint is a Category A circumferential and receives 100% RT plus surface NDE on the OD per UW-50 to confirm full penetration. Nozzle attachment welds are MT or PT per UW-50.
| Item | Value |
|---|---|
| Shell OD | 24.000 in |
| Shell wall, nominal | 0.875 in |
| Shell wall, mill-min (-12.5%) | 0.766 in |
| Shell wall, corroded (mill-min less CA) | 0.703 in |
| Shell tangent-to-tangent length | 60 in (5 ft) |
| Head nominal thickness, hemispherical | 0.500 in |
| Head minimum corroded (after 10% forming thinning + CA) | 0.388 in |
| Head inside depth, D/2 hemispherical | 11.30 in |
| Overall tangent-to-crown height (shell + 2 hemi heads) | 60 + 2 × 11.30 = 82.6 in |
| Internal volume, new (shell + 2 hemi heads) | 30,000 in³ (130 US gal) |
| Empty weight, new | 1,180 lb |
| Empty weight, corroded | 1,090 lb |
| Test weight, water-filled | 2,265 lb |
Every clause applied. The hemispherical-head walkthrough (UG-32(f)) is the central content.
| Clause | Component | Use |
|---|---|---|
| UG-16(b) | All | Minimum 0.0625 in |
| UG-23 | All | Allowable stresses at design temperature |
| UG-25 | All | Corrosion allowance 0.0625 in |
| UG-27(c)(1) | Cylindrical shell | Internal pressure, circumferential stress |
| UG-32(c) | Comparison only (F&D option) | Reference in head-comparison summary |
| UG-32(d) | Comparison only (2:1 SE option) | Reference in head-comparison summary |
| UG-32(f) | Hemispherical heads (as-built) | Required thickness, L = inside crown radius |
| Clause | Use |
|---|---|
| UG-36(c)(3)(a) | Exempts all NPS 2 and NPS 1 openings from detailed UG-37 |
| UG-37 | Area replacement, run as verification on the NPS 2 inlet (PASS by large margin) |
| UG-43(a) | Threaded openings on the instrument tap |
| UG-44 | Cl 600 RFWN flanges accepted at 1,440 psig at 200 F |
| UG-45 | Nozzle min thickness check |
| Clause | Use |
|---|---|
| UW-9 / UW-11(a)(1) / Table UW-12 | Cat. A weld design, full RT, E = 1.00 |
| UW-15 / UW-16 / UW-50 | Nozzle attachment welds and NDE |
| UCS-66 / UCS-66.1 | MDMT qualification |
| UG-99(b) / Note 35 | Hydrotest at 1,560 psig, stress under 0.9 S_y |
| UG-116 / UG-118 / UG-120(c) | Nameplate, location, U-1A |
Five worked examples. The hemispherical-head calc (example 2) and the head-type comparison at 1,000 psig (example 3) are the central teaching content.
| Symbol | Value | Source |
|---|---|---|
| P | 1,000 psig | Design pressure |
| R | 11.297 in | Inside radius, corroded: (24 - 2 × 0.703) / 2 |
| S | 20,000 psi | SA-516 Gr 70 at 200 °F |
| E | 1.00 | Full RT long seam |
Required thickness with CA is 0.645 in. Mill-min supplied is 0.766 in (0.875 nom less 12.5%), corroded to 0.703 in. PASS with 0.058 in margin. Shell MAWP at corroded thickness is 1,200 psig.
| Symbol | Value | Source |
|---|---|---|
| P | 1,000 psig | Design pressure |
| L | 11.297 in | Inside crown radius (equals shell R_corr for a hemi head) |
| S | 20,000 psi | SA-516 Gr 70 at 200 °F |
| E | 1.00 | One-piece formed head |
Required thickness with CA is 0.346 in. Nominal head ordered at 0.500 in; after 10% forming thinning and CA, the in-service minimum is 0.388 in. PASS with 0.042 in margin.
The same shell could be closed by any of three curved heads. At the 1,000 psig design pressure of this vessel, the contrast is dramatic:
| Head type | Clause | t_req (in) | t_nom selected (in) | Head depth (in) | Single-head weight (lb) |
|---|---|---|---|---|---|
| Hemispherical (as-built) | UG-32(f), t = PL/(2SE - 0.2P) | 0.284 | 0.500 | 11.3 | ~120 |
| 2:1 SE | UG-32(d), t = PDK/(2SE - 0.2P) | 0.568 | 0.750 | 5.6 | ~160 |
| F&D (L = OD, r = 6% OD) | UG-32(c), t = MPL/(2SE - 0.2P), M = 1.75 | 1.055 | 1.250 | 4.2 | ~280 |
The hemispherical head is half the required thickness of the 2:1 SE and a quarter of the F&D. Adding the corrosion allowance and the formed-min discount makes the practical selected nominal thickness 0.500 in for hemi, 0.750 in for SE, and 1.250 in for F&D. The hemi head is also 25 to 60 percent lighter despite being deeper. The trade-off is the overall vessel height: 11.3 in of extra height per end for hemi vs 5.6 in for SE vs 4.2 in for F&D, so the hemi adds about 14 in of overall stack height on this 5 ft tan-to-tan vessel. For a process where height is unconstrained (open-air skid mounting, reactor in a structural frame), the hemi is the natural choice at this pressure. For a process where overall height is a hard constraint (transport-by-truck, indoor mezzanine clearance), the SE or F&D is selected and the thickness penalty is accepted.
The NPS 2 inlet on the top hemispherical head is well below the UG-36(c)(3)(a) exemption limit. A UG-37 area calc is shown as verification only.
| Symbol | Value |
|---|---|
| d (NPS 2 ID corroded) | 2.192 in |
| t_r (head, from example 2) | 0.284 in |
| t (head, corroded formed) | 0.388 in |
| F (radial in hemispherical head) | 1.00 |
PASS by 70% margin even with conservative A2 estimation. The exemption under UG-36(c)(3)(a) is the code basis; the UG-37 calc above confirms the exemption is non-binding.
| Component | Stress at test (psi) | 0.9 × S_y at 70 °F (psi) | Status |
|---|---|---|---|
| Shell (hoop) | 1,560 × 11.297 / 0.703 = 25,070 | 32,400 (SA-516-70 N) | PASS |
| Hemi head (membrane) | 1,560 × 11.297 / (2 × 0.388) = 22,710 | 32,400 | PASS |
| Cl 600 flange stud loading at 1,560 psig (above 1,500 cold rating) | 20,800 (stud root area) | 32,400 | PASS |
Test pressure stresses are below the 0.9 S_y limit for all pressure-boundary components. The Class 600 flange stud loading at the 1,560 psig test pressure (slightly above the 1,500 psig cold rating of the flange) is checked against the SA-193 B7 stud allowable, with the standard B16.5 stud arrangement passing by 35%.
24 in OD vertical reactors at 1,000 psig are common as small batch reactors, supercritical-fluid contactors, and high-pressure separator vessels in research and pilot-scale skids. The configuration uses hemispherical heads because the high design pressure makes the thickness savings of the hemi shape (about 50% lighter than 2:1 SE and 75% lighter than F&D at this pressure) outweigh the added height. The teaching value of the example is the side-by-side thickness comparison among the three curved head types at high pressure, which makes the case for hemi heads above approximately 600 psig on vessels in this size range.