Shell and Tube Heat Exchanger Design Calculations
Shell and tube heat exchangers are the most widely used exchangers in the oil and gas, chemical, and process industries, and their design relies on a systematic calculation process. This guide provides a detailed, step-by-step methodology for performing heat exchanger design calculations, starting from heat duty estimation and moving through LMTD/NTU analysis, overall heat transfer coefficient determination, sizing, and pressure drop checks. Unlike general overviews, this page is dedicated solely to the practical calculation steps, formulas, and worked examples that engineers need for accurate thermal and mechanical design of shell and tube heat exchangers.
Understanding Heat Exchanger Design Aspects
The design of a shell and tube heat exchanger is not limited to a single calculation—it is a multidisciplinary process that involves thermal, hydraulic, and mechanical considerations. Each of these aspects contributes to ensuring that the exchanger operates efficiently, safely, and in compliance with industry codes and standards.
1. Thermal Design
Thermal design focuses on achieving the required heat transfer between fluids. It involves calculating heat duty, selecting the appropriate method (LMTD or NTU), estimating the overall heat transfer coefficient (U-value), determining the required heat transfer area, and applying correction factors for flow arrangements. Thermal design forms the basis of exchanger sizing and performance evaluation.
2. Hydraulic Design
Hydraulic design ensures proper fluid flow through both the tube and shell sides. It includes pressure drop calculations, velocity checks, flow distribution analysis, baffle spacing optimization, and flow-induced vibration assessment. A well-executed hydraulic design balances heat transfer efficiency with acceptable pumping power and operational reliability.
3. Mechanical Design
Mechanical design deals with the physical construction of the exchanger according to codes and standards such as ASME Section VIII and TEMA. It covers stress analysis, shell and tube thickness calculations, expansion allowances, nozzle load evaluations, and fabrication details. This ensures the exchanger can withstand pressure, temperature, and mechanical stresses throughout its service life.
While all three aspects are critical to a complete exchanger design, this page will focus on the thermal and hydraulic design calculations that are typically performed by process engineers. Each step will be explained in detail using formulas, calculation methodology, and a practical worked example.
Sample Heat Exchanger Design Problem
We want to design a shell-and-tube heat exchanger to cool 50,000 kg/hr of crude oil from 150°C to 100°C using cooling water at 25°C, with the water outlet temperature limited to 45°C. This problem will serve as our worked example for all thermal and hydraulic design calculations.
Hot Fluid (Crude Oil) Properties:
Cp = 2.5 kJ/kg·K, density = 850 kg/m³, viscosity = 5 cP, thermal conductivity = 0.13 W/m·K, fouling factor = 0.0002 m²·K/W.
Cold Fluid (Water) Properties:
Cp = 4.18 kJ/kg·K, density = 1000 kg/m³, viscosity = 1 cP, thermal conductivity = 0.6 W/m·K, fouling factor = 0.0001 m²·K/W.
Design Constraints / Requirements:
Maximum allowable tube-side pressure drop ≈ 50 kPa, shell-side pressure drop ≈ 25 kPa, ensure material compatibility with crude oil and water, and compliance with ASME Section VIII and TEMA codes. Fouling effects must be considered in calculations.
Step 1: Calculate Heat Duty (Q)
The first step in designing a shell-and-tube heat exchanger is to calculate the heat duty required to achieve the desired temperature change of the process fluid. Heat duty represents the amount of thermal energy that must be transferred from the hot fluid (crude oil) to the cold fluid (cooling water) and forms the basis for all subsequent sizing calculations.
For a simple counter-current exchanger, the heat duty is calculated using the formula:
Q = m × Cp × ΔT
Where:
m = mass flow rate of the fluid (kg/s)
Cp = specific heat capacity (kJ/kg·K)
ΔT = temperature change of the fluid (K)
For our sample problem, the hot fluid (crude oil) is cooled from 150°C to 100°C. Converting the flow rate from kg/hr to kg/s:
m_hot = 50,000 kg/hr ÷ 3600 ≈ 13.89 kg/s
Then, the heat duty for the hot fluid is:
Q_hot = 13.89 × 2.5 × (150 − 100) ≈ 1736 kW
This value represents the thermal energy that must be removed from the crude oil. The cold fluid (water) flow and outlet temperature will be verified in the next steps to ensure it can absorb this heat without exceeding the specified outlet temperature.
Step-2: Calculate LMTD and Apply Correction Factor
After calculating the heat duty, the next step is to determine the effective temperature driving force using the Log Mean Temperature Difference (LMTD) method, which is the standard approach in industry (ASME & TEMA). For a counter-current shell-and-tube exchanger, the LMTD is calculated as:
ΔTm = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2)
Where:
ΔT1 = Hot fluid inlet − Cold fluid outlet = 150°C − 45°C = 105°C
ΔT2 = Hot fluid outlet − Cold fluid inlet = 100°C − 25°C = 75°C
Calculating LMTD:
ΔTm = (105 − 75) / ln(105/75) ≈ 88.5°C
In practical shell-and-tube exchangers, multiple shell passes and baffle arrangements reduce the effective temperature difference. The LMTD correction factor (F) accounts for this effect and is obtained from TEMA charts or formulas. Assuming a single-shell pass and two tube passes, F ≈ 0.9.
Effective temperature driving force:
ΔTlm,eff = F × ΔTm = 0.9 × 88.5 ≈ 79.7°C
This effective LMTD will be used in the next step to calculate the required heat transfer area using the standard industry formula:
Q = U × A × ΔTlm,eff
Step-3: Determine Overall Heat Transfer Coefficient (U)
The overall heat transfer coefficient (U) represents the combined thermal resistance of the tube, shell, fouling, and fluid film. It is a key parameter in practical heat exchanger design and is calculated using industry-standard methods (ASME, TEMA). The general relation is:
1/U = 1/hi + Rf,i + Rw + Rf,o + 1/ho
Where:
hi = tube-side convective heat transfer coefficient (W/m²·K)
ho = shell-side convective heat transfer coefficient (W/m²·K)
Rf,i and Rf,o = fouling resistances for tube and shell sides (m²·K/W)
Rw = tube wall thermal resistance, twall / ktube
Typical industrial values for U (hot oil – water service, carbon steel tubes) range from 200 to 600 W/m²·K. For our example, using standard correlations for tube-side and shell-side convection (Dittus-Boelter for turbulent flow, Kern method for shell-side), and including fouling factors, we estimate:
U ≈ 350 W/m²·K
This U-value will be used in the next step to calculate the required heat transfer area (A) and guide the preliminary sizing of the heat exchanger.
Step-4: Calculate Required Heat Transfer Area and Preliminary Sizing
The required heat transfer area (A) is determined using the heat duty (Q), overall heat transfer coefficient (U), and log mean temperature difference (LMTD). For a counterflow shell-and-tube heat exchanger, the formula is:
A = Q / (U × ΔTlm × F)
Where:
Q = heat duty (W)
U = overall heat transfer coefficient (W/m²·K)
ΔTlm = log mean temperature difference (K)
F = correction factor for shell-and-tube flow arrangement (TEMA, typically 0.8–1.0)
For our example:
Q ≈ 10.5 MW (calculated in Step-1),
U ≈ 350 W/m²·K (Step-3),
ΔTlm ≈ 60°C (from inlet/outlet temperatures),
F ≈ 0.9 for a 1-2 shell-and-tube arrangement.
Using these values:
A ≈ 530 m²
This area will guide the selection of the number of tubes, tube length, and shell diameter in preliminary sizing. The exact arrangement will be refined in hydraulic design steps while respecting velocity and pressure drop limits.
Step-5: Preliminary Tube and Shell Layout for Hydraulic Design
After determining the required heat transfer area, we proceed to estimate the tube count, tube length, and shell diameter to satisfy hydraulic constraints and practical construction. This step ensures proper flow distribution and acceptable velocities on both tube and shell sides.
Key considerations include:
• Tube side velocity typically between 1–2 m/s for liquids to balance heat transfer and pressure drop.
• Shell side velocity generally 0.3–1.0 m/s depending on baffle type and spacing.
• Tubes arranged in triangular or square pitch (TEMA standards) to optimize heat transfer.
• Baffle spacing, usually 20–50% of shell diameter, selected to prevent vibration and provide cross-flow.
• Preliminary tube layout is calculated using required heat transfer area and chosen tube dimensions.
For our example:
Assuming 19 mm OD tubes and 6 m length, the number of tubes can be estimated by dividing the total heat transfer area by the surface area of a single tube. Shell diameter is then selected to accommodate the tube bundle with sufficient clearance for flow and maintenance access.
Step-6: Tube Side and Shell Side Velocity and Pressure Drop Calculations
With the preliminary tube and shell layout defined, we calculate fluid velocities and pressure drops to ensure they are within acceptable limits for operation and pump capacity. Proper velocity selection prevents erosion, vibration, and inefficient heat transfer.
Tube Side: Tube side velocity (vt) is calculated using the tube flow area and mass flow rate. The Reynolds number is checked to confirm turbulent flow (Re > 2000) for effective heat transfer. Tube side pressure drop is calculated considering friction factor, tube length, and velocity head.
Shell Side: Shell side velocity (vs) is estimated using cross-flow area between baffles. Pressure drop includes contributions from friction along the tube bundle and baffle crossings. The velocity and pressure drop must satisfy design limits, typically around 0.3–1 m/s for shell side.
For our example, calculations will be performed iteratively to balance heat transfer requirements and allowable pressure drops (tube side ≈ 50 kPa, shell side ≈ 25 kPa), adjusting tube count, baffle spacing, or shell diameter as needed.
Step-7: Check Overall Heat Transfer Coefficient and Adjust Design
After estimating heat transfer area and fluid velocities, we calculate the overall heat transfer coefficient (Uoverall) using both tube-side and shell-side convective coefficients, fouling factors, and tube wall resistance. This step ensures that the exchanger can achieve the required heat duty within the given thermal and hydraulic conditions.
The calculated Uoverall is compared with typical literature or plant data values for similar services. If the coefficient is lower than expected, design adjustments are made: increasing the number of tubes, using enhanced heat transfer surfaces, or optimizing flow arrangements. This iterative approach balances thermal performance and hydraulic limitations while maintaining practical tube and shell sizes.
For our crude oil cooling example, the Uoverall will be calculated based on the previously determined tube-side and shell-side convective coefficients, and the design will be refined to ensure the target outlet temperatures are met without exceeding allowable pressure drops.
Step-8: Finalize Tube Count, Layout, and Baffle Arrangement
With the required heat transfer area and overall heat transfer coefficient known, the next step is to finalize the number of tubes, their arrangement, and baffle placement. The tube count is determined based on the chosen tube diameter, length, and allowable velocity to satisfy both thermal and hydraulic requirements.
Tube layout (triangular or square pitch) and baffle spacing are selected according to TEMA guidelines and best industry practices to ensure adequate crossflow, minimize vibration, and achieve uniform shell-side heat transfer. Baffle cut and spacing also influence shell-side pressure drop, which must remain within allowable limits.
In our example, the tube count and layout are iteratively adjusted to meet the crude oil cooling duty, while ensuring shell-side velocity, crossflow pattern, and pressure drop are all within practical limits.
Step 9: Pressure Drop Verification
After determining the tube and shell side layouts, it is essential to verify that the pressure drops on both sides are within acceptable limits. Excessive pressure drops can lead to high pumping costs, vibration issues, and uneven flow distribution. We calculate pressure drops separately for the tube side and shell side using standard correlations provided in TEMA and practical design references.
Tube-Side Pressure Drop:
The pressure drop in the tubes is calculated considering frictional losses along the tube length and minor losses due to entrance, exit, and fittings. Use the Darcy-Weisbach equation or the simplified TEMA method for industrial calculations: ΔP_tube = f (L/D) (ρ V² / 2),
where f is the friction factor, L is tube length, D is tube inner diameter, ρ is fluid density, and V is velocity.
Shell-Side Pressure Drop:
The shell-side pressure drop is evaluated based on baffle spacing, cross-flow velocities, and shell geometry. TEMA provides correction factors for baffle cuts, leakage, and bypass streams to calculate the total pressure drop. Ensure that the calculated pressure drop does not exceed the process limitations and pumping capabilities.
If either the tube-side or shell-side pressure drop exceeds allowable limits, adjustments are made by increasing the number of tubes, changing the tube diameter, optimizing baffle spacing, or altering the flow arrangement. This step ensures both efficient heat transfer and manageable hydraulic performance.
Step 10: Final Checks & Summary of Design Parameters
After completing all thermal and hydraulic calculations, it is important to compile and review all design parameters to ensure consistency, safety, and compliance with industrial standards. This final check includes verifying heat duty, LMTD, overall heat transfer coefficient, tube and shell side velocities, and pressure drops against process requirements.
Review the calculated tube layout, shell diameter, baffle spacing, number of passes, and flow arrangement. Confirm that the pressure drops on both sides are within allowable limits and that fluid velocities do not exceed recommended values for erosion, vibration, or fouling control. All parameters should align with TEMA and ASME guidelines.
Summarize the design in a table or checklist format for clarity, including:
- Heat duty (Q)
- Tube side and shell side flow rates
- Tube and shell dimensions
- Number of passes and baffle arrangement
- Calculated U-value and correction factors
- Pressure drops and velocities