Vertical Thermosyphon Reboiler Hydraulics
Rigorous hydraulic loop balance for vertical natural circulation reboilers. Includes dynamic elevation sketching, pressure drop, and vaporization checks.
1. Project Data
2. Process Conditions & Fluid Properties
3. Elevations & Geometry
System Elevations
Piping & Exchanger Geometry
4. Detailed Hydraulics & Parametric Analysis
Detailed Hydraulic Results
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| ① Inlet Piping — Liquid Phase | |||
| Velocity | vin | — | ft/s |
| Reynolds Number | Rein | — | — |
| Frictional Pressure Drop | ΔPin | — | psi |
| ② Exchanger Tubes — Two-Phase Boiling | |||
| Inlet Velocity (liquid) | vtube | — | ft/s |
| Reynolds Number | Retube | — | — |
| Mean Two-Phase Density | ρ̄tp | — | lb/ft³ |
| Tube L/D Ratio | L/D | — | — |
| Frictional Pressure Drop | ΔPtube | — | psi |
| ③ Outlet Piping — Two-Phase Return | |||
| Velocity | vout | — | ft/s |
| Reynolds Number | Reout | — | — |
| Exit Two-Phase Density | ρtp,out | — | lb/ft³ |
| Frictional Pressure Drop | ΔPout | — | psi |
All values update automatically. ΔP values are frictional losses only per segment.
Parametric Sweep Analysis
Engineering Reference & Technical Basis
1. Heat & Mass Balance
Exit vapor fraction ($x$) based on total heat duty ($Q$) and mass circulation rate ($W$):
Homogeneous two-phase density ($\rho_{tp}$) at reboiler exit:
Mean exchanger density uses a linear quality profile (uniform heat flux assumption): $$\bar{\rho}_{exch} = \frac{2\,\rho_L\,\rho_{tp}}{\rho_L + \rho_{tp}}$$ where $\rho_{tp}$ is the homogeneous exit density. Note: all calculations are performed internally in SI units (Pa, kg, m, s); inputs are converted before calculation and results converted back for display.
2. Hydraulic Driving Head
Static pressure difference between the descending liquid leg and the ascending two-phase riser:
The liquid column from $H_B$ to $H_L$ provides the driving force. The two-phase riser from $H_B$ to $H_R$ is the resistance. Net $\Delta P_{drive}$ must equal total frictional losses at steady state.
Important: Fluid densities and latent heat must be evaluated at the actual operating pressure and bubble-point temperature. The operating pressure input is for documentation only.
3. Frictional Losses
Total pressure drop sums inlet piping (liquid), exchanger tubes (two-phase), and outlet piping (two-phase):
Friction factor $f$ by flow regime and selected method:
- Laminar (Re < 2300): $f = 64 / Re$
- McAdams (turbulent, smooth, Darcy form): $f = 0.184 / Re^{0.2}$ — calibrated for Re > 10,000 (fully turbulent). This is the Darcy–Weisbach friction factor as used in $\Delta P = f(L/D)(\rho v^2/2)$. Use Churchill/Moody for transitional flow (2,300–10,000) or rough pipes.
- Churchill/Moody (turbulent, with roughness $\varepsilon$): explicit Colebrook approximation valid for all Re and relative roughness.
Two-phase outlet viscosity uses the McAdams homogeneous blend: $1/\mu_{tp} = x/\mu_V + (1-x)/\mu_L$, where $\mu_V$ is the vapour viscosity input.
Circulation Ratio = $W_{total}/W_{vapour}$ = $1/x$ — total mass flow per unit of vapour generated. Values below 3 indicate unstable circulation; above 10 indicates oversized driving head.
4. Loop Convergence
The bisection solver iterates mass flow $W$ until driving head balances friction (relative tolerance 1% of driving head):
Convergence criterion: $|\Delta P_{drive} - \Delta P_{fric}| < \max(1\,\text{Pa},\; 0.01 \times |\Delta P_{drive}|)$ — 1% relative tolerance with 1 Pa absolute floor. Up to 60 bisection steps over $W \in [0.1,\,2000]$ kg/s. Head margin is reported as $(\Delta P_{drive} - \Delta P_{fric}) / \Delta P_{drive} \times 100\%$ at convergence.
5. Design Guidelines & Operating Targets
The following ranges are widely used for initial sizing and operability assessment of vertical thermosyphon reboilers (Kern 1950; Fair 1960; HEDH):
| Parameter | Typical Range | Flag if Outside | Notes |
|---|---|---|---|
| Exit vapor fraction $x$ | 10–30 wt% | <5% or >35% | Ensures nucleate boiling; avoids film boiling and dry-out |
| Circulation ratio $W/W_{vap}$ | 3–10 | <3 or >10 | Below 3: unstable; above 10: oversized driving head |
| Inlet pipe velocity (liquid) | 0.5–2.0 m/s (1.6–6.6 ft/s) | <0.3 m/s | Minimum to prevent settling; maximum to limit erosion |
| Tube inlet velocity (liquid) | 0.3–2.0 m/s | <0.2 m/s | Minimum for complete tube wetting |
| Outlet velocity (two-phase) | 3–15 m/s (10–50 ft/s) | >20 m/s | Avoid slug flow and piping vibration at high velocity |
| Tube L/D ratio | 50–200 | <50 | Short tubes give poor natural circulation; model less accurate |
| Driving head margin | >20% | <10% | Reserve for fouling, operating variation, and flow maldistribution |
| Return nozzle elevation | $H_R \geq H_T$ | $H_R < H_T$ | Return must be above top tube sheet for proper loop geometry |
6. Model Assumptions & Limitations
- Homogeneous two-phase flow assumed throughout — no slip between vapour and liquid phases. Conservative for driving head; may under-predict friction at high quality (>30%).
- Uniform heat flux along tube length — linear quality profile used for mean exchanger density.
- Acceleration (momentum) ΔP is not included — conservative (small for low quality, <5% of friction ΔP at $x$ < 0.2).
- Nucleate boiling regime assumed — departure from nucleate boiling (DNB) and film boiling are not predicted.
- Single-pass vertical shell-and-tube only — not applicable to horizontal, kettle, or multi-pass configurations.
- Subcooled liquid feed assumed — no flash at the exchanger inlet.
- Tube roughness affects friction factor when Churchill/Moody method is selected; McAdams assumes hydraulically smooth tubes.
- Tube-side friction factor is evaluated using liquid-only Reynolds number at the tube inlet ($Re = \rho_L v_{tube} D / \mu_L$). This is conservative for a boiling channel where vapour generation reduces the effective fluid viscosity along the tube length.
- Vapour viscosity ($\mu_V$) is used only in the outlet two-phase friction calculation (McAdams homogeneous blend). It does not affect driving head or tube-side friction.
- Operating pressure is recorded for documentation only. All fluid properties must be supplied at actual operating pressure and temperature.
7. References
- Kern, D.Q. (1950). Process Heat Transfer. McGraw-Hill. — Thermosyphon fundamentals and loop balancing.
- Fair, J.R. (1960). Vaporizer and reboiler design. Chemical Engineering Progress, 56(7), pp.49–56; and Petroleum Refiner, 39(2), pp.105–123. — Driving head and two-phase correlations for vertical thermosyphons.
- Hewitt, G.F. (Ed.) (1992). Heat Exchanger Design Handbook (HEDH), Section 3.7. Hemisphere. — Comprehensive two-phase reboiler design.
- Bell, K.J. & Mueller, A.C. Wolverine Heat Transfer Engineering Data Book II. Wolverine Tube Inc. — Boiling correlations and design practice.
- McAdams, W.H. (1954). Heat Transmission, 3rd Ed. McGraw-Hill. — Darcy–Weisbach friction factor correlation $f = 0.184/Re^{0.2}$ for turbulent flow in smooth pipes.
- Churchill, S.W. (1977). Friction-factor equation spans all fluid-flow regimes. Chemical Engineering, 84(24), pp.91–92. — Explicit friction factor for all Re and roughness.