Kettle & Thermosiphon Reboiler Sizing: API 660 & TEMA K-Shell Design Guide

In industrial distillation, fractionation, and stripping columns across petroleum refining, natural gas processing, and chemical synthesis, the Reboiler serves as the thermal heartbeat of the separation train. Supplying the entire latent heat of vaporization necessary to drive ascending vapor traffic, reboiler performance directly governs product purities, column hydraulic stability, and overall facility utility consumption.

Governed internationally by API Standard 660, TEMA Standards (10th Edition, Section 5: Type K Kettle Reboilers), and ASME Boiler and Pressure Vessel Code Section VIII Division 1, the thermal-hydraulic sizing of reboilers requires navigating complex two-phase boiling regimes, nucleate heat transfer coefficients, critical heat flux (burnout limits), vapor-liquid disengagement, and natural thermosiphon circulation driving forces.

1. Distillation Reboiler Classification: Kettle vs. Thermosiphon vs. Forced Circulation

Reboilers are categorized by their hydraulic driving mechanism and physical arrangement:

• TEMA Type K Kettle Reboiler: Features an enlarged shell with a submerged horizontal tube bundle. Liquid boils in an unforced pool; vapor rises through a generous disengagement dome directly back to the column, while liquid overflows a weir into a residue sump. Offers supreme operational flexibility and acts as an extra theoretical distillation stage, but requires a large shell diameter.
• Vertical Thermosiphon Reboiler: A vertical shell-and-tube exchanger mounted adjacent to the tower. Liquid from the column bottoms flows through a downcomer, enters the tubes subcooled, begins nucleate boiling, and generates a two-phase vapor-liquid froth. The resulting density differential creates natural circulation without a mechanical pump. Offers high heat transfer coefficients and low residence time, but requires careful hydraulic head balancing.
• Horizontal Thermosiphon Reboiler: Boiling occurs on the shell side with heating fluid in the tubes; used for heavy fouling duties where mechanical tube bundle cleaning is necessary.
• Forced Circulation Reboiler: Employs a centrifugal pump to force bottoms liquid through the exchanger tubes under suppressed boiling, flashing across a back-pressure valve into the column. Mandatory for severe fouling slurries and vacuum services.

2. Nucleate Pool Boiling Physics: Mostinski & Cooper Formulations

In kettle reboilers, heat transfer is dominated by nucleate pool boiling. Vapor bubbles nucleate in tiny microscopic cavities on the tube outer surface, grow, and detach into the surrounding liquid pool.

The benchmark nucleate boiling coefficient (\(h_{nb}\)) is calculated using the Mostinski (1963) corresponding-states formulation:

Where \(P_c\) is the fluid critical pressure in bar, \(P_r = P / P_c\) is the reduced operating pressure, and \(q''\) is the heat flux in \(\text{W/m}^2\).

Alternatively, the Cooper (1984) correlation accounts for commercial surface roughness (\(R_p\)) and molecular weight (\(M\)):

3. Critical Heat Flux (CHF / Burnout Limit) & Palen-Small Bundle Factors

As heat flux rises, bubble generation becomes so vigorous that vapor bubbles coalesce into an insulating vapor film. This transition from nucleate boiling to film boiling is known as the Critical Heat Flux (CHF) or burnout point. In film boiling, the heat transfer coefficient collapses by an order of magnitude, causing thermal runaway or loss of reboiling capacity.

For a single isolated horizontal cylinder, the theoretical maximum heat flux is given by the Kutateladze-Zuber (1958) hydrodynamic equation:

In a multi-tube bundle, rising vapor from lower tube rows blankets upper tubes, hindering liquid replenishing. Consequently, bundle critical heat flux is significantly lower than a single tube. Palen and Small (1964) established the bundle burnout factor (\(\psi_b\)):

API 660 Design Rule: The actual operating heat flux must never exceed \(70\%\) of the bundle burnout limit:

4. TEMA K-Shell Architecture: Souders-Brown Vapor Disengagement Freeboard

A TEMA Type K kettle shell is enlarged relative to the bundle diameter (\(D_s / D_b \approx 1.4 - 2.0\)) to create an upper gravity settling zone where entrained liquid droplets disengage from the ascending boil-off vapor.

The maximum allowable superficial vapor velocity (\(u_{v,max}\)) is governed by the Souders-Brown equation:

Where \(K_{SB} = 0.050\text{ m/s}\) (\(0.16\text{ ft/s}\)) for standard gravity disengagement without demister, and up to \(0.100\text{ m/s}\) with an installed wire-mesh mist eliminator pad.

Vapor Space Freeboard (\(H_{dis}\)): API 660 and GPSA guidelines require the vertical clearance between the boiling pool surface and the top of the kettle shell to satisfy:

5. Liquid Overflow Weir Design & Residue Draw-Off Sump Compartments

To ensure the entire tube bundle remains permanently submerged and protected against dryout:

• The weir height must exceed the topmost tube row by at least \(50\text{ mm}\) (\(H_{weir} = D_b + 50\text{ mm}\)).
• Liquid head over the weir crest (\(h_{crest}\)) is evaluated using the Francis weir formula: $$h_{crest} = \left( \frac{\dot{V}_{residue}}{1.84 \cdot W_{weir}} \right)^{2/3} \quad [\text{m}]$$
• The downstream residue compartment volume is sized for \(1.5\) to \(3.0\) minutes of liquid retention time to provide stable bottoms pump NPSH and prevent surge cavitation.

6. Vertical Thermosiphon Reboilers: Natural Driving Head vs. Loop Friction

In a vertical thermosiphon reboiler, circulation is maintained solely by the hydrostatic density differential between the cold, dense column sump liquid (\(\rho_L\)) in the downcomer and the hot, light two-phase vapor-liquid froth inside the vertical exchanger tubes:

Where \(\bar{\rho}_{tp}\) is the average two-phase density along the boiling tube length, evaluated from the homogeneous or Lockhart-Martinelli void fraction:

For self-sustaining natural circulation at steady state, the driving static head must balance the total hydraulic loop friction losses:

7. Percent Vaporization Per Pass (10% – 30%) & Two-Phase Flow Instabilities

The percent vaporization per pass (\(X_{pass}\)) dictates the recirculation ratio (\(CR = 100 / X_{pass}\)):

• Recommended Range: \(10\% \le X_{pass} \le 30\%\) (typically \(15\%\) to \(25\%\)).
• If \(X_{pass} > 30\%\): Mist-flow transition occurs near the tube exit. Liquid film starves, causing dryout, wall coking, localized polymer deposition, and severe flow surging.
• If \(X_{pass} < 10\%\): Circulation flow is excessively high, producing prohibitive loop friction and requiring oversized downcomer/riser piping.
• Chatoorgoon / Density-Wave Instability: Thermosiphons with low inlet throttling can experience acoustic flow oscillations. A butterfly valve or restriction orifice in the downcomer line provides stabilizing single-phase pressure drop.

8. Step-by-Step Worked Industrial Example: C3/C4 Depropanizer Kettle Reboiler

Scenario: Sizing a TEMA Type K kettle reboiler for a depropanizer column bottoms boiling a mixture of isobutane and n-butane.

• Vapor Boil-Off Rate: \(\dot{m}_{vap} = 25,000\text{ kg/h}\), Latent Heat: \(h_{fg} = 295\text{ kJ/kg}\)
• Boiling Temp: \(T_{boil} = 110.0^\circ\text{C}\), Pressure: \(P = 16.0\text{ bar}\), \(P_c = 38.0\text{ bar}\) (\(P_r = 0.421\))
• Liquid Density: \(\rho_L = 490\text{ kg/m}^3\), Vapor Density: \(\rho_V = 38.5\text{ kg/m}^3\)
• Heating Medium: Saturated steam at \(4.5\text{ barg}\) (\(T_{sat} = 155.0^\circ\text{C}\), \(h_{fg,steam} = 2,100\text{ kJ/kg}\))
• Tubes: 1.0" OD (\(25.4\text{ mm}\)), 14 BWG (\(21.18\text{ mm}\) ID), length \(4.88\text{ m}\) (16 ft), 1.25 square pitch.

1. Heat Duty & Steam Demand:
   $$Q = \frac{25,000 \times 295}{3600} = 2,048.6\text{ kW}$$ $$\dot{m}_{steam} = \frac{2048.6}{2100} \times 3600 = 3,511.9\text{ kg/h}$$
2. Driving Temperature Difference:
   $$\Delta T_m = 155.0 - 110.0 = 45.0^\circ\text{C}$$
3. Boiling Heat Transfer & Area Sizing:
   Using Mostinski nucleate pool boiling with \(P_r = 0.421\) and \(q'' \approx 50,000\text{ W/m}^2\), \(h_{nb} = 3,180\text{ W/m}^2\cdot\text{K}\).
   Steam condensation inside tubes: \(h_i = 8,500\text{ W/m}^2\cdot\text{K}\).
   Accounting for fouling (\(R_f = 0.0005\text{ m}^2\cdot\text{K/W}\)), dirty overall coefficient is \(U_{dirty} = 1,180.6\text{ W/m}^2\cdot\text{K}\).
   $$A_{req} = \frac{2,048,600}{1,180.6 \times 45.0} = 38.56\text{ m}^2$$ Specifying 102 U-tubes (area \(39.72\text{ m}^2\), margin \(+3.0\%\)), bundle diameter is \(D_b = 430.3\text{ mm}\).
4. Critical Heat Flux & Burnout Verification:
   Kutateladze-Zuber single cylinder CHF: \(q''_{crit,single} = 175,000\text{ W/m}^2\).
   Palen bundle factor: \(\psi_b = \frac{\pi \times 0.430 \times 4.88}{39.72} = 0.530\).
   Bundle burnout limit: \(q''_{max,bundle} = 175,000 \times 0.530 = 92,842\text{ W/m}^2\).
   Operating flux: \(q'' = 2,048,600 / 39.72 = 51,577\text{ W/m}^2\).
   $$\text{Flux Ratio} = \frac{51,577}{92,842} = 0.556 \le 0.70 \quad \text{[SAFE • No Burnout Risk]}$$
5. Kettle Shell Diameter & Vapor Space:
   Vapor flow: \(\dot{V}_v = 0.180\text{ m}^3\text{/s}\).
   Souders-Brown velocity limit: \(u_{v,max} = 0.050 \times \sqrt{(490 - 38.5)/38.5} = 0.171\text{ m/s}\).
   Weir height: \(H_{weir} = 430 + 50 = 480\text{ mm}\).
   Sizing kettle shell: \(D_s = 850\text{ mm}\) (\(D_s / D_b = 1.98\)).
   Vapor disengagement height: \(H_{dis} = 850 - 485 = 365\text{ mm} \ge 250\text{ mm}\) [COMPLIANT per API 660].

9. Step-by-Step Worked Industrial Example: Amine Regenerator Thermosiphon

Scenario: Sizing a vertical thermosiphon reboiler for an aqueous MDEA acid gas stripping regenerator column.

• Vapor Generation: \(18,000\text{ kg/h}\) steam/acid gas (\(Q = 10,750\text{ kW}\))
• Bottoms Boiling Temp: \(126.0^\circ\text{C}\) at \(2.2\text{ bar}\)
• Target Vaporization Per Pass: \(X_{pass} = 20.0\%\) (Circulation Ratio \(CR = 5.0\))
• Circulation Mass Flow: \(\dot{m}_{circ} = 18,000 \times 5.0 = 90,000\text{ kg/h}\)
• Exchanger: Vertical shell-and-tube, \(3.05\text{ m}\) (10 ft) tubes, \(25.4\text{ mm}\) OD.

1. Driving Static Head:
   Column liquid level at \(H_{sump} = 3.80\text{ m}\) above bottom tubesheet.
   Liquid density \(\rho_L = 980\text{ kg/m}^3\); Average two-phase tube density \(\bar{\rho}_{tp} = 510\text{ kg/m}^3\).
   $$\Delta P_{static} = (980 \times 9.81 \times 3.80) - (510 \times 9.81 \times 3.05) = 36.5 - 15.3 = 21.2\text{ kPa}$$
2. Loop Friction Losses:
   Downcomer (10" pipe, \(v = 1.4\text{ m/s}\)): \(\Delta P_{in} = 2.1\text{ kPa}\)
   Tubes (friction + acceleration): \(\Delta P_{tubes} = 8.5\text{ kPa}\)
   Riser (14" pipe, two-phase return): \(\Delta P_{riser} = 3.6\text{ kPa}\)
   Total Loop Friction: \(\Delta P_{loop} = 2.1 + 8.5 + 3.6 = 14.2\text{ kPa}\)
3. Hydraulic Balance:
   $$\text{Driving Margin} = 21.2 - 14.2 = +7.0\text{ kPa}$$ $$\text{Safety Factor} = \frac{21.2}{14.2} = 1.49 \ge 1.05 \quad \text{[STABLE NATURAL CIRCULATION]}$$