HeatExchanger

Process Description

Counter-current shell-and-tube heat exchanger for thermal energy recovery in process applications. Uses effectiveness-NTU method for heat transfer calculations with dynamic thermal response modeling. Commonly applied in crude oil preheat trains, process cooling, and heat integration systems.

Key Equations

Effectiveness-NTU Method:

\[\varepsilon = \frac{1 - \exp(-NTU(1-C_r))}{1 - C_r \exp(-NTU(1-C_r))}\]

Heat Transfer Rate:

\[Q = \varepsilon \cdot C_{min} \cdot (T_{h,in} - T_{c,in})\]

Number of Transfer Units:

\[NTU = \frac{UA}{C_{min}}\]

Thermal Dynamics:

\[\tau \frac{dT}{dt} = T_{ss} - T\]

where \(\tau = \frac{\rho V c_p}{C}\) is the thermal time constant.

Process Parameters

Parameter

Typical Range

Units

Description

Overall HTC (U)

100 - 2000

W/m²·K

Heat transfer coefficient

Heat Transfer Area (A)

10 - 500

m²

Surface area for heat exchange

Hot Flow Rate

0.5 - 100

kg/s

Hot fluid mass flow rate

Cold Flow Rate

0.5 - 100

kg/s

Cold fluid mass flow rate

Effectiveness (ε)

0.1 - 0.95

Thermal effectiveness

NTU

0.5 - 10

Number of Transfer Units

Hot Inlet Temperature

60 - 250

°C

Process heating temperature

Cold Inlet Temperature

10 - 80

°C

Cooling medium temperature

Pressure Drop

<20

kPa

Allowable pressure loss

Industrial Example

"""
Industrial Example: Crude Oil Preheat Train Heat Exchanger
Typical refinery application with realistic plant conditions and scale

This example demonstrates a shell-and-tube heat exchanger used in crude oil preheating,
a common application in petroleum refineries for energy integration and efficiency.
"""

import numpy as np
import matplotlib.pyplot as plt
import sys
import os

# Add the parent directory to the Python path to import HeatExchanger
sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..', '..'))

from sproclib.unit.heat_exchanger.HeatExchanger import HeatExchanger

# =============================================================================
# Process Conditions (Typical Industrial Scale - Crude Oil Preheat Train)
# =============================================================================

print("=" * 80)
print("INDUSTRIAL HEAT EXCHANGER EXAMPLE")
print("Application: Crude Oil Preheat Train in Petroleum Refinery")
print("Configuration: Counter-current Shell-and-Tube Heat Exchanger")
print("=" * 80)

# Heat Exchanger Design Parameters
U = 180.0               # W/m²·K - Overall heat transfer coefficient (crude oil/gas oil)
A = 450.0              # m² - Heat transfer area (typical industrial size)
m_hot = 25.0           # kg/s - Hot gas oil flow rate (90 m³/h @ 0.85 kg/L)
m_cold = 30.0          # kg/s - Cold crude oil flow rate (108 m³/h @ 0.92 kg/L)

# Fluid Properties
cp_hot = 2400.0        # J/kg·K - Gas oil specific heat capacity
cp_cold = 2100.0       # J/kg·K - Crude oil specific heat capacity
V_hot = 8.5            # m³ - Hot side volume (shell side)
V_cold = 6.2           # m³ - Cold side volume (tube side)
rho_hot = 850.0        # kg/m³ - Gas oil density at operating temperature
rho_cold = 920.0       # kg/m³ - Crude oil density at operating temperature

print(f"\nDESIGN PARAMETERS:")
print(f"Overall Heat Transfer Coefficient (U): {U:.1f} W/m²·K")
print(f"Heat Transfer Area (A): {A:.1f} m²")
print(f"Hot Side Flow Rate (Gas Oil): {m_hot:.1f} kg/s ({m_hot*3.6/rho_hot*1000:.1f} m³/h)")
print(f"Cold Side Flow Rate (Crude Oil): {m_cold:.1f} kg/s ({m_cold*3.6/rho_cold*1000:.1f} m³/h)")

# Create heat exchanger instance
hx = HeatExchanger(
    U=U, A=A,
    m_hot=m_hot, m_cold=m_cold,
    cp_hot=cp_hot, cp_cold=cp_cold,
    V_hot=V_hot, V_cold=V_cold,
    rho_hot=rho_hot, rho_cold=rho_cold,
    name="CrudeOilPreheater"
)

# =============================================================================
# Operating Conditions Analysis
# =============================================================================

# Typical operating temperatures (K)
T_hot_in = 473.15      # 200°C - Hot gas oil inlet temperature
T_cold_in = 313.15     # 40°C - Cold crude oil inlet temperature

print(f"\nOPERATING CONDITIONS:")
print(f"Hot Gas Oil Inlet Temperature: {T_hot_in-273.15:.1f}°C ({T_hot_in:.1f} K)")
print(f"Cold Crude Oil Inlet Temperature: {T_cold_in-273.15:.1f}°C ({T_cold_in:.1f} K)")
print(f"Operating Pressure: 15 bar (typical crude unit pressure)")

# Calculate steady-state performance
u_design = np.array([T_hot_in, T_cold_in])
T_outlets = hx.steady_state(u_design)
T_hot_out, T_cold_out = T_outlets

print(f"\nSTEADY-STATE RESULTS:")
print(f"Hot Gas Oil Outlet Temperature: {T_hot_out-273.15:.1f}°C ({T_hot_out:.1f} K)")
print(f"Cold Crude Oil Outlet Temperature: {T_cold_out-273.15:.1f}°C ({T_cold_out:.1f} K)")

# =============================================================================
# Heat Transfer Analysis
# =============================================================================

# Calculate heat transfer performance
Q = hx.calculate_heat_transfer_rate(T_hot_in, T_cold_in, T_hot_out, T_cold_out)
lmtd = hx.calculate_lmtd(T_hot_in, T_cold_in, T_hot_out, T_cold_out)

print(f"\nHEAT TRANSFER PERFORMANCE:")
print(f"Heat Transfer Rate (Q): {Q/1e6:.2f} MW")
print(f"Log Mean Temperature Difference (LMTD): {lmtd:.1f} K")
print(f"Heat Exchanger Effectiveness: {hx.effectiveness:.3f}")
print(f"Number of Transfer Units (NTU): {hx.NTU:.2f}")

# Dimensionless groups
C_hot = hx.C_hot
C_cold = hx.C_cold
C_min = min(C_hot, C_cold)
C_max = max(C_hot, C_cold)
C_ratio = C_min / C_max

print(f"\nDIMENSIONLESS ANALYSIS:")
print(f"Hot Side Heat Capacity Rate (C_hot): {C_hot/1e3:.1f} kW/K")
print(f"Cold Side Heat Capacity Rate (C_cold): {C_cold/1e3:.1f} kW/K")
print(f"Heat Capacity Rate Ratio (Cr): {C_ratio:.3f}")

# =============================================================================
# Energy Integration Analysis
# =============================================================================

# Calculate energy savings compared to no heat integration
Q_max_theoretical = C_min * (T_hot_in - T_cold_in)
energy_recovery_efficiency = Q / Q_max_theoretical

# Economic impact (rough estimate)
fuel_heating_value = 42e6  # J/kg - typical fuel oil heating value
fuel_cost = 0.8  # $/kg - typical fuel cost
hours_per_year = 8000  # operating hours per year
furnace_efficiency = 0.85  # typical furnace efficiency

fuel_savings_kg_h = Q / (fuel_heating_value * furnace_efficiency)  # kg/h fuel saved
annual_fuel_savings = fuel_savings_kg_h * hours_per_year * fuel_cost  # $/year

print(f"\nENERGY INTEGRATION BENEFITS:")
print(f"Maximum Theoretical Heat Transfer: {Q_max_theoretical/1e6:.2f} MW")
print(f"Energy Recovery Efficiency: {energy_recovery_efficiency:.1%}")
print(f"Fuel Savings: {fuel_savings_kg_h:.1f} kg/h")
print(f"Annual Cost Savings: ${annual_fuel_savings/1e3:.1f}k/year")

# =============================================================================
# Process Sensitivity Analysis
# =============================================================================

print(f"\nSENSITIVITY ANALYSIS:")

# Flow rate sensitivity
flow_ratios = np.linspace(0.5, 1.5, 11)
effectiveness_vs_flow = []
Q_vs_flow = []

for ratio in flow_ratios:
    m_hot_var = m_hot * ratio
    m_cold_var = m_cold * ratio
    
    # Create temporary heat exchanger with varied flow rates
    hx_temp = HeatExchanger(
        U=U, A=A,
        m_hot=m_hot_var, m_cold=m_cold_var,
        cp_hot=cp_hot, cp_cold=cp_cold,
        V_hot=V_hot, V_cold=V_cold,
        rho_hot=rho_hot, rho_cold=rho_cold
    )
    
    effectiveness_vs_flow.append(hx_temp.effectiveness)
    
    # Calculate heat transfer at design conditions
    T_out_temp = hx_temp.steady_state(u_design)
    Q_temp = hx_temp.calculate_heat_transfer_rate(T_hot_in, T_cold_in, T_out_temp[0], T_out_temp[1])
    Q_vs_flow.append(Q_temp / 1e6)  # MW

print(f"Flow Rate Sensitivity (±50% of design):")
print(f"  50% Flow: Effectiveness = {effectiveness_vs_flow[0]:.3f}, Q = {Q_vs_flow[0]:.2f} MW")
print(f"  Design Flow: Effectiveness = {effectiveness_vs_flow[5]:.3f}, Q = {Q_vs_flow[5]:.2f} MW")
print(f"  150% Flow: Effectiveness = {effectiveness_vs_flow[10]:.3f}, Q = {Q_vs_flow[10]:.2f} MW")

# Temperature sensitivity
T_hot_variations = np.array([450, 460, 470, 480, 490]) + 273.15  # K
Q_vs_temp = []

for T_hot_var in T_hot_variations:
    u_temp = np.array([T_hot_var, T_cold_in])
    T_out_temp = hx.steady_state(u_temp)
    Q_temp = hx.calculate_heat_transfer_rate(T_hot_var, T_cold_in, T_out_temp[0], T_out_temp[1])
    Q_vs_temp.append(Q_temp / 1e6)

print(f"\nHot Inlet Temperature Sensitivity:")
for i, T_hot_var in enumerate(T_hot_variations):
    print(f"  {T_hot_var-273.15:.0f}°C: Q = {Q_vs_temp[i]:.2f} MW")

# =============================================================================
# Comparison with Perry's Handbook Correlations
# =============================================================================

print(f"\nCOMPARISON WITH HANDBOOK CORRELATIONS:")

# Calculate heat transfer coefficient from empirical correlations
# (Simplified Dittus-Boelter for turbulent flow in tubes)

# Assume tube diameter and properties for Reynolds number calculation
D_tube = 0.025  # m - typical tube diameter
mu_hot = 0.001  # Pa·s - gas oil viscosity at operating temperature
mu_cold = 0.005  # Pa·s - crude oil viscosity at operating temperature

# Velocity calculation (simplified)
A_cross_tube = np.pi * (D_tube/2)**2  # m²
n_tubes = 200  # estimated number of tubes
v_cold = m_cold / (rho_cold * n_tubes * A_cross_tube)  # m/s

# Reynolds number for cold side (crude oil in tubes)
Re_cold = rho_cold * v_cold * D_tube / mu_cold

print(f"Estimated Tube Side Velocity: {v_cold:.2f} m/s")
print(f"Tube Side Reynolds Number: {Re_cold:.0f}")

# Thermal boundary layer considerations
Pr_cold = mu_cold * cp_cold / 0.14  # Prandtl number (k = 0.14 W/m·K for crude oil)
print(f"Tube Side Prandtl Number: {Pr_cold:.1f}")

if Re_cold > 2300:
    print("Flow Regime: Turbulent (typical for industrial heat exchangers)")
else:
    print("Flow Regime: Laminar (unusual for industrial scale)")

# =============================================================================
# Scale-up Considerations
# =============================================================================

print(f"\nSCALE-UP CONSIDERATIONS:")
print(f"Current Heat Duty: {Q/1e6:.1f} MW")
print(f"Heat Flux: {Q/A:.0f} W/m² (within typical range: 5,000-50,000 W/m²)")
print(f"Area Density: {A/V_hot:.1f} m²/m³ (shell side)")

# Fouling considerations
fouling_factor = 0.0002  # m²·K/W - typical for crude oil service
U_clean = 1 / (1/U - fouling_factor)
print(f"Clean Overall HTC (U_clean): {U_clean:.0f} W/m²·K")
print(f"Design U with Fouling: {U:.0f} W/m²·K")
print(f"Fouling Margin: {(U_clean - U)/U_clean:.1%}")

# =============================================================================
# Performance Monitoring Recommendations
# =============================================================================

print(f"\nPERFORMANCE MONITORING RECOMMENDATIONS:")
print(f"Key Process Variables to Monitor:")
print(f"  • Inlet/Outlet temperatures (±2°C accuracy)")
print(f"  • Flow rates (±5% accuracy)")
print(f"  • Pressure drop across exchanger (<20 kPa typical)")
print(f"  • Fouling rate (effectiveness degradation)")

print(f"\nMaintenance Indicators:")
print(f"  • Effectiveness drop below {hx.effectiveness*0.9:.3f} indicates fouling")
print(f"  • LMTD increase above {lmtd*1.2:.1f} K suggests performance degradation")

print(f"\nExample completed successfully!")
print(f"Results demonstrate typical industrial heat exchanger performance")
print(f"with realistic crude oil processing conditions and scale.")
print("=" * 80)

Results

================================================================================
INDUSTRIAL HEAT EXCHANGER EXAMPLE
Application: Crude Oil Preheat Train in Petroleum Refinery
Configuration: Counter-current Shell-and-Tube Heat Exchanger
================================================================================

DESIGN PARAMETERS:
Overall Heat Transfer Coefficient (U): 180.0 W/m²·K
Heat Transfer Area (A): 450.0 m²
Hot Side Flow Rate (Gas Oil): 25.0 kg/s (105.9 m³/h)
Cold Side Flow Rate (Crude Oil): 30.0 kg/s (117.4 m³/h)

OPERATING CONDITIONS:
Hot Gas Oil Inlet Temperature: 200.0°C (473.1 K)
Cold Crude Oil Inlet Temperature: 40.0°C (313.1 K)
Operating Pressure: 15 bar (typical crude unit pressure)

STEADY-STATE RESULTS:
Hot Gas Oil Outlet Temperature: 106.8°C (380.0 K)
Cold Crude Oil Outlet Temperature: 128.7°C (401.9 K)

HEAT TRANSFER PERFORMANCE:
Heat Transfer Rate (Q): 5.59 MW
Log Mean Temperature Difference (LMTD): 69.0 K
Heat Exchanger Effectiveness: 0.582
Number of Transfer Units (NTU): 1.35

DIMENSIONLESS ANALYSIS:
Hot Side Heat Capacity Rate (C_hot): 60.0 kW/K
Cold Side Heat Capacity Rate (C_cold): 63.0 kW/K
Heat Capacity Rate Ratio (Cr): 0.952

ENERGY INTEGRATION BENEFITS:
Maximum Theoretical Heat Transfer: 9.60 MW
Energy Recovery Efficiency: 58.2%
Fuel Savings: 0.2 kg/h
Annual Cost Savings: $1.0k/year

SENSITIVITY ANALYSIS:
Flow Rate Sensitivity (±50% of design):
  50% Flow: Effectiveness = 0.742, Q = 3.56 MW
  Design Flow: Effectiveness = 0.582, Q = 5.59 MW
  150% Flow: Effectiveness = 0.479, Q = 6.90 MW

Hot Inlet Temperature Sensitivity:
  450°C: Q = 14.33 MW
  460°C: Q = 14.68 MW
  470°C: Q = 15.02 MW
  480°C: Q = 15.37 MW
  490°C: Q = 15.72 MW

COMPARISON WITH HANDBOOK CORRELATIONS:
Estimated Tube Side Velocity: 0.33 m/s
Tube Side Reynolds Number: 1528
Tube Side Prandtl Number: 75.0
Flow Regime: Laminar (unusual for industrial scale)

SCALE-UP CONSIDERATIONS:
Current Heat Duty: 5.6 MW
Heat Flux: 12423 W/m² (within typical range: 5,000-50,000 W/m²)
Area Density: 52.9 m²/m³ (shell side)
Clean Overall HTC (U_clean): 187 W/m²·K
Design U with Fouling: 180 W/m²·K
Fouling Margin: 3.6%

PERFORMANCE MONITORING RECOMMENDATIONS:
Key Process Variables to Monitor:
  • Inlet/Outlet temperatures (±2°C accuracy)
  • Flow rates (±5% accuracy)
  • Pressure drop across exchanger (<20 kPa typical)
  • Fouling rate (effectiveness degradation)

Maintenance Indicators:
  • Effectiveness drop below 0.524 indicates fouling
  • LMTD increase above 82.8 K suggests performance degradation

Example completed successfully!
Results demonstrate typical industrial heat exchanger performance
with realistic crude oil processing conditions and scale.
================================================================================

Process Behavior

Heat exchanger process behavior showing effectiveness-NTU curves, temperature profiles, and operating windows

The process behavior plots demonstrate:

  • Effectiveness-NTU relationship for different heat capacity ratios with marked operating point

  • Heat transfer rate vs flow rate showing performance optimization and effectiveness trade-offs

  • Temperature profiles along exchanger length illustrating counter-current heat exchange

  • Operating window with pressure-temperature limits and heat duty contours for safe operation

Sensitivity Analysis

Detailed parameter sensitivity analysis and design optimization for heat exchanger

The detailed analysis includes:

  • Heat transfer coefficient vs area design space showing performance sensitivity

  • Effectiveness vs Reynolds number correlation for turbulent flow optimization

  • Economic optimization balancing capital cost against energy savings over equipment lifetime

  • Fouling impact analysis demonstrating performance degradation and maintenance requirements

Engineering Applications

Process Industries: - Crude oil preheat trains (200°C hot oil, 5-15 MW duty) - Chemical reactor cooling systems (exothermic reaction heat removal) - Distillation column condensers and reboilers (phase change applications) - Gas processing heat recovery (natural gas treatment plants)

Design Considerations: - Minimum temperature approach: 10-20 K for economic operation - Fouling allowance: 15-25% reduction in clean U-value - Pressure drop limits: <10% of operating pressure - Thermal stress management for temperature cycling

Scale-up Guidelines: - Heat flux range: 5,000-50,000 W/m² for liquid-liquid service - Velocity limits: 0.5-3 m/s shell side, 1-5 m/s tube side - Area density: 100-500 m²/m³ for compact designs

References

  1. Incropera, F.P. & DeWitt, D.P. “Fundamentals of Heat and Mass Transfer”, 7th Edition, Wiley (2011) - Chapter 11: Heat Exchangers - comprehensive treatment of effectiveness-NTU method

  2. Shah, R.K. & Sekulic, D.P. “Fundamentals of Heat Exchanger Design”, Wiley (2003) - Detailed design methodology and thermal-hydraulic analysis for industrial applications

  3. Perry’s Chemical Engineers’ Handbook, 8th Edition, McGraw-Hill (2008) - Section 11: Heat Transfer - practical correlations and design guidelines for process equipment