In Deep-Sea Oil-Gas Separators Operating at 200 bar External Pressure, What Wall Thickness of Titanium Grade 5 Heater Tube Is Required to Resist Collapse?

Oil and gas separators, placed deep on the ocean floor at depths of between 1,500 and 2,000 meters, suffer external hydrostatic pressures of 150 to 200 bar (15 to 20 MPa). These separators have electric heating tubes which have to run at the process temperature to avoid hydrate formation and wax deposition. They are susceptible to a particular failure mode of external pressure collapse. Internal pressure failure leads to ductile bursting.External pressure collapse is an elastic instability event which occurs suddenly at a critical pressure much lower than the yield strength of the material. Due to its excellent strength-to-weight ratio and the resistance of corrosion in saltwater, titanium Grade 5 (Ti-6Al-4V) is used for deep-sea heater tubes. The article defines the minimum wall thickness of Grade 5 titanium tubes to resist a 200 bar external pressure without buckling, taking into account ovality, wall thickness tolerances and safety factors needed by pressure vessel standards.

Collapse pressure theory of cylindrical tubes
For a long cylindrical tube subjected to uniform external pressure, the critical external pressure, $P_{c}$, is determined by the classical formula for elastic collapse:

Pc = 2E 1-v2 t/Davg( )3

where E is the Young modulus (about 110 GPa at 20°C for Grade 5 titanium), ν is the Poisson's ratio (roughly 0.34), t is the tube wall thickness and D_avg is the average diameter (out diameter minus t). The formula is based on the assumption of perfect circles and constant wall thickness. The collapse pressure of real tubes is lower than the theoretical one because of the initial ovality (out-of-roundness) and wall thickness changes.

The practical collapse pressure for a tube with standard manufacturing tolerances (ovality within 0.5 % of diameter, wall thickness tolerance ±10 %) is about 60-70 % of the theoretical elastic collapse pressure. If the ratio of diameter to thickness (D/t) is less than a particular value the collapse mode changes from elastic to plastic and the calculation is different and based on tangent modulus theory.

Grade 5 Titanium - Specific Parameters
Grade 5 titanium has a yield strength of 830-900 MPa (minimum 825 MPa for annealed condition) at room temperature, much greater than the 275-345 MPa of Grade 2. This high strength allows thinner walls for internal pressure applications, but does not provide proportionally increased external collapse resistance. Collapse is essentially an elastic modulus driven process. Young's modulus for Grade 5 (110 GPa) is actually somewhat lower than for Grade 2 (105-110 GPa-similar) so that the collapse pressure for a given geometry is roughly the same regardless of grade. The grade 5 has the advantage of higher yield strength for post-collapse behaviour and better performance under combined external pressure and thermal stresses.

Wall thickness for 200 bar service
For a typical heater tube with an outer diameter of 25 mm (D = 25 mm) and an external pressure of 200 bar (20 MPa) at seabed temperatures of 4-10°C, the needed wall thickness is computed iteratively:

P_design = 200 bar x safety factor (desired design collapse pressure). Pressure vessel codes (ASME BPVC Section VIII, Division 2) require a factor of safety of 3 for collapse under external pressure. P_design = 600 bar (60 MPa).

Assumptions D=25mm, t=2.5mm, Davg=22.5mm, D/t=10.0. Theoretical elastic collapse: P_c = [2 * 110 * 10^9 / (1 - 0.34^2)] * (2.5/22.5)^3 = [2.2 * 10^11 / 0.884] * 0.00137 Then P_c = 2.49×10¹¹ × 0.00137 = 3.41×10⁸ Pa = 341 bar (34.1 MPa). After ovality drop 65%, P_c_actual = 341 × 0.65 = 222 bar (22.2 MPa) < necessary 600 bar. This D/t is not sufficient.

Increase t to 4.0 mm. Davg = 25 - 4.0 = 21.0 mm D/t= 6.25. (t/D average) = 4.0/21.0 = 0.1905. (0.1905)^3 = 0.00691. P_c = 2.49x10^11 x 0.00691 = 1.72x10^9 Pa = 1720 bar (172 MPa). Knocked down to 65% gives 1,720 x 0.65 = 1,118 bar (112 MPa) which is above the 600 bar design requirement.

Increase t to 3.0 mm. D average = 22.0 mm, D/t = 8.33. t / D_avg = 0.1364, cube = 0.00254. P_c = 2.49×10¹¹ × 0.00254 = 6.32×10⁸ Pa = 632 bar (63.2 MPa). Knockdown to 65% 632 x .65 = 411 bar (41.1 MPa)-under 600 bar requirement. The minimal t lies between 3.0 and 4.0 mm.

Solve for t = 3.5 mm. D_avg = 25 - 3.5 = 21.5 mm, D/t = 7.14. t/D_avg = 0.1628, cube = 0.00431. P_c = 2.49E11 * 0.00431 = 1.07E9 Pa = 1,070 bar (107 MPa). Knock down: 1.070 x 0.65 = 695 bar (69.5 MPa) - over 600 bar requirement.

Thus a 25 mm O.D. Grade 5 titanium tube needs minimum wall thickness of 3.5 mm to withstand collapse at 200 bar external pressure with ASME safety factors. 4.0 mm is preferred to give extra margin for ovality, manufacturing variations and possible denting during installation.

Deep Sea Heater Tube Thickness Application Matrix
Operating Depth (m) External Pressure (bar) D/t Ratio (25mm OD tube)Recommended Wall Thickness (With safety factor) Minimum Wall Thickness (25 mm OD) Depth (m) Pressure (bar) 500 m 50 bar 10.5 2.2 mm 2.5 mm 1,000 m 100 bar 8.5 2.8 mm 3.0 mm 1,500 m 150 bar 7.5 3.2 mm 3.5 mm 2,000 m 200 bar 7.0 3.5 mm 4.0 mm 2,500 m 250 bar 6.3 4.0 mm 4.5 mm 3,000 m 300 bar 5.8 4.5 mm 5.0 mm
Other Considerations for Deep-Service Heaters
The wall thickness for external pressure collapse has to be chosen considering temperature derating. At seabed temperatures of 4°C, the Young's modulus of Grade 5 is roughly 5% greater than at ambient temperature, which is helpful for collapse resistance. But during operation of heater the tube is heated up to 100-150°C from the inside while the exterior saltwater is at 4°C. The temperature gradient produces compressive stresses which add up to an external pressure. This combined loading needs to be included in finite element analysis for each design.

Titanium grade 5 can be subject to hydrogen embrittlement in seawater under cathodic protection potentials below -0.7 V vs. Ag/AgCl. Deep-sea structures are often protected cathodically with aluminium anodes. Hydrogen absorption (delayed cracking of cathodically protected structures or coated with a coating) must be prevented by means of electrical isolation of the heater tube from cathodically protected structures or coating protection. Grade 5 is less tolerant of hydrogen than grade 2

For deep-sea oil-gas separators at 200 bar external pressure, the minimum wall thickness of the 25 mm outer diameter titanium Grade 5 heating tubes is 3.5 mm, with a preference for 4.0 mm to allow for manufacturing errors and damage during installation. Engineers shall specify ASTM B861 Grade 5 tubing with tight ovality limitations (max. 0.3% of diameter), thorough radiographic inspection for wall thickness homogeneity and pressure testing to at least 300 bar external pressure. Welded tube-to-tubesheet junctions shall be designed with full penetration and stress relief to avoid stress corrosion cracking in seawater. For depths over 2,500 m the use of alternative tube geometries (lower diameters, internal stiffening rings) has to be taken into account.