Process and mechanical design of shell-and-tube heat exchangers

Process and mechanical design of shell-and-tube exchangers: TEMA types, fluid allocation, tube layout, passes and the F factor, baffles, the area–tube count–velocity procedure, overall coefficient with fouling, bundle diameter and mechanical considerations.

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Why it matters

Shell-and-tube exchangers are the workhorses of process plants: coolers, heaters, condensers, reboilers and feed–effluent exchangers. Designing one means two linked jobs. The process (thermal) design fixes the duty, area, tube count, passes and baffles so that the required heat is transferred within the allowed pressure drops; the mechanical design makes the shell, tubesheets, channels and tubes safe at the design pressures and temperatures while allowing thermal expansion and cleaning.

Key ideas

Construction and TEMA types. A bundle of tubes is held at each end in tubesheets; one fluid passes through the tubes, the other through the shell around them, guided by baffles. TEMA describes each exchanger with three letters: front head (e.g. A channel with removable cover, B bonnet), shell type (E single pass — most common; F two-pass; J divided flow; K kettle reboiler; X cross flow) and rear head. The three common constructions are:

  • Fixed tubesheet (L, M, N rear heads): cheapest; shell side cannot be mechanically cleaned; large shell–tube temperature differences need an expansion bellows in the shell.
  • U-tube: tubes bent into U's with a single tubesheet; free expansion and a removable bundle, but the inside of the bends is hard to clean.
  • Floating head (S split-ring, T pull-through, P packed): one tubesheet floats, so the bundle expands freely and can be pulled for cleaning both sides; the most expensive and has a larger bundle-to-shell clearance.

Which fluid goes where. Put on the tube side: the more corrosive fluid (only tubes and channels need alloy), the more fouling fluid (tubes are easier to clean), the higher-pressure fluid (small-diameter tubes hold pressure cheaply), and cooling water. Put on the shell side: viscous fluids and condensing vapours (cross-flow gives better coefficients), and the stream with the tighter pressure-drop limit.

Tubes and layout. Common outside diameters are 19.05 mm (3/4 in) and 25.4 mm (1 in), with wall thickness given by BWG gauge and standard lengths such as 2.44, 3.66, 4.88 and 6.1 m. The tube pitch is typically 1.25 times the outside diameter. Triangular pitch packs more tubes into a shell; square pitch leaves straight lanes for mechanical cleaning of the shell side.

Passes and the F factor. Several tube passes raise tube velocity (and the coefficient) but make the flow partly co-current, so the log-mean temperature difference is corrected by a factor F read from charts (functions of the temperature ratios R and P). Designs normally keep F above about 0.75–0.8; below that, use more shells in series.

Baffles. Single-segmental baffles with about 25 % cut are the norm, spaced between roughly 0.2 and 1.0 times the shell diameter. Closer spacing raises the shell-side coefficient and pressure drop; the maximum spacing is limited by the unsupported tube span to avoid sagging and flow-induced vibration.

Design procedure (Kern/Sinnott style). Duty from an energy balance → LMTD and F → assume U → area → number of tubes → passes for a sensible tube velocity (liquids about 1–2.5 m/s) → bundle and shell diameter → film coefficients on each side → calculated U including fouling and wall → compare with the assumed U and iterate → check pressure drops on both sides.

Mechanical design. Shell and channel thickness follow the pressure-vessel formulas; tube wall is checked for internal and external pressure; tubesheet thickness, flanges and expansion joints follow TEMA and the pressure-vessel code (take the tubesheet formulas and factors from TEMA/your code book). Tube-to-tubesheet joints are expanded (rolled), welded or both. Allow for differential thermal expansion between shell and tubes, especially in fixed-tubesheet units.

Formulas

Q = m·cp·ΔT (duty from either stream, W) ΔT_lm = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2) (counter-current terminal differences) Q = U·A·F·ΔT_lm A = N_t·π·d_o·L (outside area of N_t tubes of length L) 1/U_o = 1/h_o + R_do + d_o·ln(d_o/d_i)/(2·k_w) + (d_o/d_i)·R_di + (d_o/d_i)·(1/h_i) u_t = m_t / (ρ·(N_t/N_p)·(π/4)·d_i²) (tube-side velocity) D_b = d_o·(N_t / K1)^(1/n1) (bundle diameter; K1, n1 from data book for pitch type and passes) Nu = 0.023·Re^0.8·Pr^0.4 (tube-side turbulent heating, Re > 10⁴; use the viscosity correction for viscous fluids)

  • Q in W; m = mass flow (kg/s); cp (J/kg·K); U, h = coefficients (W/m²·K); A in m²; F = LMTD correction factor (–); R_d = fouling resistances (m²·K/W, from data book or TEMA); k_w = tube wall conductivity (W/m·K); d_o, d_i = tube outside and inside diameters (m); N_p = number of tube passes; D_b in the same unit as d_o.

Worked examples

Example 1 (standard): area, tube count and passes Given: oil 20 kg/s, cp = 2.5 kJ/kg·K, cooled 150 → 90 °C by water (cp = 4.18 kJ/kg·K, ρ = 995 kg/m³) heated 30 → 50 °C. Assume U = 400 W/m²·K and F = 0.92 (from chart). Tubes 19.05 mm OD, 14.83 mm ID, 4.88 m long.

  1. Duty: Q = 20 × 2.5 × (150 − 90) = 3000 kW; water m = 3000 / (4.18 × 20) = 35.9 kg/s.
  2. ΔT1 = 150 − 50 = 100 K, ΔT2 = 90 − 30 = 60 K; ΔT_lm = 40 / ln(1.667) = 78.3 K.
  3. Area: A = 3 × 10⁶ / (400 × 0.92 × 78.3) = 104.1 m².
  4. One tube: π × 0.01905 × 4.88 = 0.292 m²; N_t = 104.1 / 0.292 = 356.5 → 358 tubes (even number for 2 passes).
  5. Water in tubes, 2 passes: flow area = 179 × (π/4) × 0.01483² = 0.0309 m²; u_t = 35.9 / (995 × 0.0309) = 1.17 m/s — acceptable. Answer: about 104 m², 358 tubes, 2 tube passes.

Example 2 (GATE level): checking U and sizing the bundle Given (same exchanger): h_i = 4000 W/m²·K, h_o = 800 W/m²·K, R_di = 0.0002, R_do = 0.0003 m²·K/W, k_w = 45 W/m·K; triangular pitch 1.25 d_o, 2 passes: K1 = 0.249, n1 = 2.207 (data-book constants).

  1. Terms of 1/U_o (m²·K/W): 1/h_o = 0.00125; R_do = 0.0003; wall = 0.01905 × ln(1.2846) / 90 = 0.000053; (d_o/d_i)·R_di = 1.2846 × 0.0002 = 0.000257; (d_o/d_i)/h_i = 1.2846/4000 = 0.000321.
  2. Sum = 0.002181, so U_o = 458 W/m²·K — above the assumed 400, giving about 15 % margin. ✓
  3. Bundle: D_b = 19.05 × (358 / 0.249)^(1/2.207) = 514 mm.
  4. Shell ID ≈ 514 mm plus the bundle-to-shell clearance read from the data-book chart for the head type (larger for a floating head than for a fixed tubesheet).

Common mistakes

  • Using LMTD without the F correction for multi-pass exchangers.
  • Mixing inside and outside areas in U (refer every resistance to the same area).
  • Putting the corrosive or fouling fluid on the shell side.
  • Choosing too many passes, giving velocities above erosion limits or F below 0.75.
  • Forgetting fouling resistances and so undersizing the area.
  • Picking a fixed-tubesheet unit for a large shell–tube temperature difference without an expansion joint.

For GATE CH

Expect numericals on duty, LMTD and the F-corrected area, number of tubes, tube-side velocity, overall coefficient from individual resistances, and conceptual questions on TEMA types, fluid allocation, baffle spacing and pitch layouts. Practise the full chain from energy balance to tube count.

Quick check

  1. Which fluid would you put in the tubes: corrosive acid or clean steam?
  2. Why use square pitch?
  3. ΔT1 = 40 K and ΔT2 = 20 K. What is ΔT_lm?
  4. What does a U-tube design avoid that a fixed tubesheet does not?

Answers: 1. The corrosive acid. 2. To allow mechanical cleaning lanes on the shell side. 3. 20 / ln 2 = 28.9 K. 4. Thermal-expansion stress between shell and tubes (the bundle expands freely).

Interview questions

All Process Equipment Design interview questions

Try answering each one aloud before you open it.

  1. 1.What is a shell-and-tube heat exchanger and where is it commonly used?Concept

    It is a bundle of tubes held in tubesheets inside a cylindrical shell: one fluid flows through the tubes and the other flows over them in the shell, guided by baffles, and heat passes through the tube walls. It is robust, can be built for high pressures and temperatures in many materials, and can be made cleanable, so it is used for coolers, heaters, condensers, reboilers and feed–effluent exchangers throughout refineries, chemical plants and power stations.

  2. 2.Explain the basic working principle of a shell-and-tube heat exchanger.Concept

    In a shell-and-tube heat exchanger, one fluid flows through the tubes while another fluid flows around the tubes within the shell. Heat is transferred from the hot fluid to the cold fluid through the tube walls. The design allows for efficient heat exchange by maximizing the surface area for heat transfer and enabling counterflow or parallel flow configurations.

  3. 3.Why are baffles used in shell-and-tube heat exchangers?Application

    Baffles are used in shell-and-tube heat exchangers to direct the flow of fluid across the tubes rather than allowing it to flow straight through the shell. This increases the turbulence of the fluid, enhancing the heat transfer coefficient and improving the overall efficiency of the heat exchanger. Baffles also help support the tubes and prevent vibration.

  4. 4.What happens if the tube side fluid velocity is too low in a shell-and-tube heat exchanger?Application

    The film coefficient falls (it varies roughly as velocity to the 0.8 power in turbulent flow, and drops sharply if flow becomes laminar), so the exchanger underperforms. Low velocity also lets suspended solids settle and fouling build up faster, especially with cooling water, which is typically kept above about 1 m/s. The usual remedy is more tube passes, accepting a higher pressure drop and checking the F factor.

  5. 5.How does the choice of tube material affect the performance of a shell-and-tube heat exchanger?Application

    The choice of tube material affects the heat exchanger's thermal conductivity, corrosion resistance, and mechanical strength. Materials with high thermal conductivity, like copper, enhance heat transfer. Corrosion-resistant materials, such as stainless steel, extend the lifespan of the exchanger in corrosive environments. The material must also withstand the operating pressures and temperatures.

  6. 6.Why is it important to consider thermal expansion in the design of shell-and-tube heat exchangers?Application

    Thermal expansion is important because different materials expand at different rates when heated. In a shell-and-tube heat exchanger, if the tubes and shell expand at different rates, it can lead to mechanical stress and potential failure. Designing for thermal expansion ensures the integrity and longevity of the heat exchanger under varying temperature conditions.

  7. 7.What is the purpose of using a floating head in a shell-and-tube heat exchanger?Application

    A floating head allows one end of the tube bundle to move freely, accommodating thermal expansion and contraction without causing stress on the tubes. This design is particularly useful in applications with significant temperature differences between the shell and tube sides, as it prevents tube damage and leakage.

  8. 8.Calculate the overall heat transfer coefficient U given h_i = 500 W/m²·K, h_o = 700 W/m²·K and fouling factors 0.0002 (tube side) and 0.0003 m²·K/W (shell side), neglecting wall resistance and area differences.Numerical

    With thin tubes, 1/U = 1/h_i + 1/h_o + R_di + R_do = 0.002000 + 0.001429 + 0.0002 + 0.0003 = 0.003929 m²·K/W, so U = 1/0.003929 ≈ 255 W/m²·K. For an accurate design the inside terms are multiplied by d_o/d_i and the wall resistance d_o·ln(d_o/d_i)/(2k_w) is added.

  9. 9.Determine the log mean temperature difference (LMTD) for a counterflow shell-and-tube heat exchanger with inlet temperatures of 150°C (hot fluid) and 30°C (cold fluid), and outlet temperatures of 90°C (hot fluid) and 60°C (cold fluid).Numerical

    The LMTD for a counterflow heat exchanger is calculated using the formula: LMTD = (ΔT1 - ΔT2) / ln(ΔT1/ΔT2), where ΔT1 = Th,in - Tc,out and ΔT2 = Th,out - Tc,in. Substituting the given values: ΔT1 = 150 - 60 = 90°C, ΔT2 = 90 - 30 = 60°C. LMTD = (90 - 60) / ln(90/60) ≈ 74.1°C.

  10. 10.Explain the significance of the tube pitch in the design of a shell-and-tube heat exchanger.Concept

    Tube pitch is the center-to-center distance between adjacent tubes in a heat exchanger. It affects the heat exchanger's compactness, pressure drop, and heat transfer efficiency. A smaller tube pitch increases the heat transfer area but may lead to higher pressure drops and potential maintenance challenges. The choice of tube pitch balances these factors based on the specific application requirements.

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