Dimension TEMA Type K kettle reboilers for chemical columns, refinery splitters, and vaporizers. Solves bundle boiling heat flux, Mostinski nucleate pool boiling coefficients, Palen-Small & Fair critical heat flux (CHF) burnout limits, Souders-Brown vapor-liquid disengagement surface velocities, and shell dome diameters to prevent liquid carryover.
1. Thermal Duty & Fluid Properties
2. Tube Bundle Dimensions & Layout
3. Sizing & Safety Validation
[ Submerged Tube Bundle: DB ] → [ Liquid Weir & Overflow Spillage Compartment ] → [ Liquid Residence / Bottoms Outlet ]
Mathematical Foundations & TEMA Engineering Derivations
Kettle reboiler design combines pool boiling two-phase mechanics with aerosol disengagement hydrodynamics. The sizing calculation follows standard TEMA, API 660, and GPSA standards:
$$dot{m}_v = rac{Q}{Delta H_{vap}}$$ $$Q_v = rac{dot{m}_v}{3600 cdot ho_v}$$ Determines the total volumetric gas release exiting the liquid pool.
$$q_{max,1} = 0.131 Delta H_{vap} ho_v^{0.5} [sigma g ( ho_L - ho_v)]^{0.25}$$ $$psi_B = 3.14 left( rac{D_B L}{A_{tot}} ight) left[1 + 0.1 left( rac{D_B}{D_o} ight) ight]^{-1}$$ Bundle critical flux $q_{max,B} = psi_B cdot q_{max,1}$. Safe limit $q le 0.70 q_{max,B}$.
$$u_{allow} = K_{SB} sqrt{ rac{ ho_L - ho_v}{ ho_v}}$$ $K_{SB} = 0.055 ext{ m/s}$ (gravity), $0.090 ext{ m/s}$ (demister mesh). Prevents entrainment.
$$A_{dis} = W_{surf} cdot L_{eff} ge rac{Q_v}{u_{allow}}$$ $$D_{shell} ge max(1.4 D_B, sqrt{D_B^2 + 4 A_{dis} / pi})$$ Ensures droplet fall-back velocity exceeds upward vapor velocity.
5 Fatal Traps in Kettle Reboiler Sizing & Operation
Using standard 30° or 60° triangular tube layouts to maximize surface area in a reboiler is a catastrophic mistake. In boiling services, vapor generated at bottom rows must rise through the bundle. Triangular patterns lack straight vertical chimney channels; bubbles collide with adjacent tubes, coalesce, and create a stagnant vapor vapor blanket across upper rows. This causes premature transition into film boiling (heat transfer coefficient plunges by 80-90%). Always specify 90° square or 45° rotated square tube pitch with $P/D_o ge 1.30$.
Selecting an undersized shell diameter ($D_{shell} / D_B < 1.4$) to cut shell capital costs reduces the liquid surface disengagement area. When superficial vapor velocity exceeds the Souders-Brown terminal velocity of 100-micron droplets, violent foaming and droplet carryover contaminate column bottom draw trays and flood overhead condensers. TEMA K standards mandate minimum freeboard disengagement heights of 300 to 600 mm (12-24 in) above the boiling pool.
The internal overflow weir establishes the liquid level across the tube bundle. If the weir crest is set flush with or below the top tube row, hydraulic crest oscillations and surface wave action expose top tubes directly to vapor. Exposed tubes bake dry, rapidly forming hard pyrolytic coking or scale that accelerates localized thermal stress cracking. The weir crest must be positioned at least 50 to 120 mm (2 to 5 in) above the uppermost tube bundle tangent.
Single-tube nucleate boiling correlations (like clean Mostinski or Forster-Zuber) predict very high heat flux. However, inside industrial bundles, heavy fraction accumulation, multicomponent distillation boiling ranges, and fouling resistance ($R_f approx 0.0003 - 0.0005 ext{ m}^2 ext{K/W}$) depress effective temperature difference and suppress nucleation sites. Designing a reboiler without bundle correction factors results in columns failing to achieve target boilup rates under dirty operational conditions.
Designing vapor outlet nozzles solely based on standard piping velocity guidelines without checking momentum flux ($ ho_v v^2$) creates severe local pressure drops and aspirates liquid bulk from the pool directly into the nozzle mouth. TEMA guidelines dictate that vapor nozzle inlet momentum $ ho_v v^2$ should not exceed 1,500 Pa ($1,000 ext{ lb}/( ext{ft}cdot ext{s}^2)$), or an internal impingement baffle / vapor disengagement bonnet must be installed.
Step-by-Step Worked Engineering Example
Application: Hydrocarbon Debutanizer Column Bottoms Kettle Reboiler.
- Thermal Duty: $Q = 2,800 ext{ kW} = 2.80 ext{ MW}$.
- Fluid: De-ethanized butane/pentane bottoms at $P_{op} = 3.2 ext{ bar a}$, $T_{sat} = 115^circ ext{C}$.
- Properties: $Delta H_{vap} = 340 ext{ kJ/kg}$, $ ho_L = 780 ext{ kg/m}^3$, $ ho_v = 4.2 ext{ kg/m}^3$, $sigma = 18.5 ext{ mN/m}$, $P_{crit} = 38.5 ext{ bar a}$.
- Geometry: 1.0 in (25.4 mm) tubes, $L = 4.8 ext{ m}$, 90° square pitch ($P/D_o = 1.33$), $D_B = 850 ext{ mm}$.
Step 1: Vapor Flow Generation:
$$dot{m}_v = rac{2800 ext{ kW}}{340 ext{ kJ/kg}} = 8.235 ext{ kg/s} = 29,647 ext{ kg/h}$$ $$Q_v = rac{8.235 ext{ kg/s}}{4.2 ext{ kg/m}^3} = 1.961 ext{ m}^3/ ext{s}$$Step 2: Tube Bundle Heat Transfer Area:
$$ ext{Tube Pitch } P = 1.33 imes 25.4 ext{ mm} = 33.78 ext{ mm}$$ $$ ext{Estimated Tubes } N_t approx 0.785 imes left( rac{850}{33.78} ight)^2 approx 497 ext{ tubes}$$ $$A_{tot} = N_t imes pi imes D_o imes L = 497 imes 3.1416 imes 0.0254 imes 4.8 = 190.4 ext{ m}^2$$ $$ ext{Heat Flux } q = rac{2800 ext{ kW}}{190.4 ext{ m}^2} = 14.71 ext{ kW/m}^2$$Step 3: Zuber-Fair Critical Heat Flux Evaluation:
$$q_{max,1} = 0.131 imes 340000 imes sqrt{4.2} imes [0.0185 imes 9.81 imes (780 - 4.2)]^{0.25} = 312.4 ext{ kW/m}^2$$ $$ ext{Bundle factor } psi_B = 3.14 imes left( rac{0.850 imes 4.8}{190.4} ight) left[1 + 0.1 imes left( rac{850}{25.4} ight) ight]^{-1} = 0.0673 imes rac{1}{4.346} = 0.0155 ightarrow q_{max,B} approx 38.6 ext{ kW/m}^2$$ $$ ext{Operating Ratio: } rac{q}{q_{max,B}} = rac{14.71}{38.6} = 38.1% quad (le 70% implies ext{ extbf{Safe Nucleate Boiling}})$$Step 4: Souders-Brown Vapor Disengagement & Shell Diameter:
$$u_{allow} = 0.055 imes sqrt{ rac{780 - 4.2}{4.2}} = 0.055 imes 13.59 = 0.747 ext{ m/s}$$ $$ ext{Required Disengagement Area } A_{dis,min} = rac{1.961 ext{ m}^3/ ext{s}}{0.747 ext{ m/s}} = 2.625 ext{ m}^2$$ $$ ext{Required Liquid Surface Width } W_{surf} = rac{2.625 ext{ m}^2}{4.8 ext{ m}} = 0.547 ext{ m} = 547 ext{ mm}$$ $$ ext{With } D_B = 850 ext{ mm}, ext{ TEMA K recommends } D_{shell} ge 1.60 imes D_B = 1,360 ext{ mm}$$ $$ ext{Selected Shell: } D_{shell} = 1,400 ext{ mm} implies rac{D_{shell}}{D_B} = 1.65 quad ( ext{Vapor superficial velocity } u_v = 0.35 ext{ m/s} ll 0.747 ext{ m/s}).$$