Multi-Stream Heat Exchanger

The MultiStreamHeatExchanger2 class models heat exchangers with multiple hot and cold streams exchanging heat simultaneously. This is essential for:

Table of Contents

Overview

Property Value
Class neqsim.process.equipment.heatexchanger.MultiStreamHeatExchanger2
Package neqsim.process.equipment.heatexchanger
Max Streams Unlimited (practical limit ~10)
Unknown Outlets 1, 2, or 3 temperatures
Solver Newton-Raphson with numerical Jacobian 
         ┌─────────────────────────────────────────┐
Hot 1 ───▶│                                         │───▶ Hot 1 Out
Hot 2 ───▶│     MULTI-STREAM HEAT EXCHANGER         │───▶ Hot 2 Out
Hot 3 ───▶│                                         │───▶ Hot 3 Out
         │        Q_hot = Q_cold                   │
Cold 1 ──▶│     (Energy Balance)                   │───▶ Cold 1 Out
Cold 2 ──▶│                                         │───▶ Cold 2 Out
Cold 3 ──▶│     ΔT_min ≥ Approach Temperature      │───▶ Cold 3 Out
         └─────────────────────────────────────────┘

Mathematical Foundations

Energy Balance

The fundamental constraint is that total heat released by hot streams equals total heat absorbed by cold streams:

\[\sum_{i \in \text{hot}} \dot{m}_i \cdot (h_{in,i} - h_{out,i}) = \sum_{j \in \text{cold}} \dot{m}_j \cdot (h_{out,j} - h_{in,j})\]

Where:

Enthalpy Calculation: NeqSim performs a TP flash at each temperature to calculate enthalpy, accounting for:

The energy imbalance residual function:

\[f_E = Q_{hot} + Q_{cold} = \sum_i \dot{m}_i (h_{out,i} - h_{in,i})\]
At convergence: $ f_E < \epsilon$ (default $\epsilon = 10^{-3}$ kW)

Composite Curves

Composite curves combine all hot streams into a single “hot composite” and all cold streams into a “cold composite”. This enables visualization of heat transfer feasibility and pinch point identification.

Construction Algorithm:

  1. Collect temperature breakpoints: All inlet and outlet temperatures on each curve
  2. Sort temperatures in ascending order
  3. Calculate interval loads: For each temperature interval $[T_k, T_{k+1}]$:
\[Q_{\text{interval}} = \sum_{i \in \text{active}} \dot{m}_i \cdot C_{p,i} \cdot (T_{k+1} - T_k)\]

Where “active” streams are those spanning the interval.

  1. Accumulate loads: Starting from $Q = 0$ at the coldest point:
\[Q_k = Q_{k-1} + Q_{\text{interval},k}\]

Result: Temperature vs. cumulative heat duty for each composite curve.

Pinch Analysis

The pinch point is the location of minimum temperature approach between hot and cold composites:

\[\Delta T_{min} = \min_k \left( T_{hot,k} - T_{cold,k} \right)\]

Where temperatures are evaluated at the same cumulative heat load.

Feasibility constraint: For thermodynamically feasible heat exchange:

\[\Delta T_{min} \geq \Delta T_{approach}\]

The pinch residual function:

\[f_P = \Delta T_{min} - \Delta T_{approach}\]

UA Calculation (LMTD Method)

The overall heat transfer coefficient-area product (UA) is calculated by summing contributions from each interval:

\[UA = \sum_{k=1}^{N} \frac{Q_k}{\text{LMTD}_k}\]

Where the Log Mean Temperature Difference for interval $k$ is:

\[\text{LMTD}_k = \frac{(T_{h,in} - T_{c,in}) - (T_{h,out} - T_{c,out})}{\ln\left(\frac{T_{h,in} - T_{c,in}}{T_{h,out} - T_{c,out}}\right)}\]
For small temperature differences ($ \Delta T_1 - \Delta T_2 < 10^{-4}$):
\[\text{LMTD}_k \approx \frac{\Delta T_1 + \Delta T_2}{2}\]

Units: UA is returned in W/K (Watts per Kelvin).

Solver Modes

The solver automatically selects the solution method based on the number of unknown outlet temperatures:

Unknown Count Equations Variables Method
0 - - Direct calculation (no iteration)
1 Energy balance 1 temperature 1×1 Newton-Raphson
2 Energy + Pinch 2 temperatures 2×2 Newton-Raphson
3 Energy + Pinch + UA 3 temperatures 3×3 Newton-Raphson

Newton-Raphson Iteration

For $n$ unknowns, the system solves:

\[\mathbf{J} \cdot \Delta \mathbf{T} = \mathbf{f}\]

Where:

Jacobian calculation (numerical, with $\delta = 10^{-4}$°C):

\[J_{ij} = \frac{f_i(T_j + \delta) - f_i(T_j)}{\delta}\]

Damping: Updates are damped to improve stability:

\[T_j^{new} = T_j^{old} - \alpha \cdot \Delta T_j\]

Default damping factor $\alpha = 1.0$.

Usage Examples

Basic Usage

import neqsim.process.equipment.heatexchanger.MultiStreamHeatExchanger2;
import neqsim.process.equipment.stream.Stream;
import neqsim.process.processmodel.ProcessSystem;
import neqsim.thermo.system.SystemSrkEos;

// Create fluid
SystemSrkEos fluid = new SystemSrkEos(273.15 + 50.0, 50.0);
fluid.addComponent("methane", 0.90);
fluid.addComponent("ethane", 0.05);
fluid.addComponent("propane", 0.03);
fluid.addComponent("n-butane", 0.02);
fluid.setMixingRule("classic");

// Create hot streams
Stream hot1 = new Stream("Hot-1", fluid.clone());
hot1.setTemperature(100.0, "C");
hot1.setFlowRate(20000.0, "kg/hr");

Stream hot2 = new Stream("Hot-2", fluid.clone());
hot2.setTemperature(80.0, "C");
hot2.setFlowRate(15000.0, "kg/hr");

// Create cold streams
Stream cold1 = new Stream("Cold-1", fluid.clone());
cold1.setTemperature(10.0, "C");
cold1.setFlowRate(25000.0, "kg/hr");

Stream cold2 = new Stream("Cold-2", fluid.clone());
cold2.setTemperature(20.0, "C");
cold2.setFlowRate(10000.0, "kg/hr");

// Create multi-stream heat exchanger
MultiStreamHeatExchanger2 mshx = new MultiStreamHeatExchanger2("MCHE-100");

// Add streams: (stream, type, outletTemp)
// outletTemp = null means "solve for this"
mshx.addInStreamMSHE(hot1, "hot", 40.0);     // Known outlet: 40°C
mshx.addInStreamMSHE(hot2, "hot", 35.0);     // Known outlet: 35°C
mshx.addInStreamMSHE(cold1, "cold", null);   // Unknown - solve
mshx.addInStreamMSHE(cold2, "cold", 60.0);   // Known outlet: 60°C

// Set approach temperature
mshx.setTemperatureApproach(5.0);  // Minimum ΔT = 5°C

// Build process and run
ProcessSystem process = new ProcessSystem();
process.add(hot1);
process.add(hot2);
process.add(cold1);
process.add(cold2);
process.add(mshx);
process.run();

// Get results
System.out.println("Cold-1 outlet: " + mshx.getOutStream(2).getTemperature("C") + " °C");
System.out.println("UA value: " + mshx.getUA() + " W/K");
System.out.println("Pinch ΔT: " + mshx.getTemperatureApproach() + " °C");

One Unknown Temperature

When only one outlet is unknown, the solver uses energy balance alone:

MultiStreamHeatExchanger2 mshx = new MultiStreamHeatExchanger2("HX-1");

// All outlets known except one
mshx.addInStreamMSHE(hot1, "hot", 50.0);    // Known
mshx.addInStreamMSHE(hot2, "hot", 45.0);    // Known
mshx.addInStreamMSHE(cold1, "cold", null);  // Unknown - energy balance determines this
mshx.addInStreamMSHE(cold2, "cold", 70.0);  // Known

// No need to set approach or UA - only energy balance is solved
mshx.run();

Two Unknown Temperatures

With two unknowns, the solver uses energy balance + pinch constraint:

MultiStreamHeatExchanger2 mshx = new MultiStreamHeatExchanger2("HX-2");

mshx.addInStreamMSHE(hot1, "hot", null);    // Unknown
mshx.addInStreamMSHE(hot2, "hot", 80.0);
mshx.addInStreamMSHE(hot3, "hot", 60.0);
mshx.addInStreamMSHE(cold1, "cold", 10.0);
mshx.addInStreamMSHE(cold2, "cold", null);  // Unknown
mshx.addInStreamMSHE(cold3, "cold", 30.0);

// REQUIRED: Set approach temperature
mshx.setTemperatureApproach(5.0);

mshx.run();

// Solver finds temperatures that satisfy:
// 1. Energy balance: Q_hot = Q_cold
// 2. Pinch: ΔT_min = 5.0°C

Three Unknown Temperatures

With three unknowns, the solver needs energy + pinch + UA:

MultiStreamHeatExchanger2 mshx = new MultiStreamHeatExchanger2("HX-3");

mshx.addInStreamMSHE(hot1, "hot", null);    // Unknown
mshx.addInStreamMSHE(hot2, "hot", 80.0);
mshx.addInStreamMSHE(hot3, "hot", 60.0);
mshx.addInStreamMSHE(cold1, "cold", null);  // Unknown
mshx.addInStreamMSHE(cold2, "cold", null);  // Unknown
mshx.addInStreamMSHE(cold3, "cold", 30.0);

// REQUIRED for 3 unknowns: Both approach AND UA
mshx.setTemperatureApproach(5.0);
mshx.setUAvalue(70000.0);  // W/K

mshx.run();

// Solver finds temperatures satisfying:
// 1. Energy balance: Q_hot = Q_cold
// 2. Pinch: ΔT_min = 5.0°C
// 3. UA: calculated UA = 70000 W/K

Python Examples

Basic Multi-Stream Heat Exchanger

from neqsim import jneqsim

# Import classes
SystemSrkEos = jneqsim.thermo.system.SystemSrkEos
Stream = jneqsim.process.equipment.stream.Stream
MultiStreamHeatExchanger2 = jneqsim.process.equipment.heatexchanger.MultiStreamHeatExchanger2
ProcessSystem = jneqsim.process.processmodel.ProcessSystem

# Create fluid
fluid = SystemSrkEos(273.15 + 50.0, 50.0)
fluid.addComponent("methane", 0.85)
fluid.addComponent("ethane", 0.10)
fluid.addComponent("propane", 0.05)
fluid.setMixingRule("classic")

# Create streams
hot1 = Stream("Hot-1", fluid.clone())
hot1.setTemperature(100.0, "C")
hot1.setFlowRate(20000.0, "kg/hr")

hot2 = Stream("Hot-2", fluid.clone())
hot2.setTemperature(90.0, "C")
hot2.setFlowRate(20000.0, "kg/hr")

cold1 = Stream("Cold-1", fluid.clone())
cold1.setTemperature(0.0, "C")
cold1.setFlowRate(20000.0, "kg/hr")

cold2 = Stream("Cold-2", fluid.clone())
cold2.setTemperature(10.0, "C")
cold2.setFlowRate(10000.0, "kg/hr")

# Create MSHE
mshx = MultiStreamHeatExchanger2("LNG-MCHE")

# Add streams (stream, type, outlet_temp)
# Use None for unknown outlet temperatures
mshx.addInStreamMSHE(hot1, "hot", None)      # Unknown
mshx.addInStreamMSHE(hot2, "hot", 80.0)      # Known: 80°C
mshx.addInStreamMSHE(cold1, "cold", None)    # Unknown
mshx.addInStreamMSHE(cold2, "cold", 85.0)    # Known: 85°C

# Set constraints
mshx.setTemperatureApproach(5.0)  # 5°C minimum approach

# Build and run process
process = ProcessSystem()
process.add(hot1)
process.add(hot2)
process.add(cold1)
process.add(cold2)
process.add(mshx)
process.run()

# Results
print(f"Hot-1 outlet: {mshx.getOutStream(0).getTemperature('C'):.1f} °C")
print(f"Cold-1 outlet: {mshx.getOutStream(2).getTemperature('C'):.1f} °C")
print(f"UA value: {mshx.getUA():.0f} W/K")

Extracting Composite Curves for Plotting

import matplotlib.pyplot as plt

# After running the heat exchanger...
composite_data = mshx.getCompositeCurve()

# Extract hot and cold curves
hot_curve = composite_data.get("hot")
cold_curve = composite_data.get("cold")

# Convert to lists for plotting
hot_loads = [float(p.get("load")) for p in hot_curve]
hot_temps = [float(p.get("temperature")) for p in hot_curve]
cold_loads = [float(p.get("load")) for p in cold_curve]
cold_temps = [float(p.get("temperature")) for p in cold_curve]

# Plot composite curves
plt.figure(figsize=(10, 6))
plt.plot(hot_loads, hot_temps, 'r-o', label='Hot Composite', linewidth=2)
plt.plot(cold_loads, cold_temps, 'b-o', label='Cold Composite', linewidth=2)
plt.xlabel('Heat Load (kW)')
plt.ylabel('Temperature (°C)')
plt.title('Composite Curves')
plt.legend()
plt.grid(True)
plt.show()

API Reference

Constructor

MultiStreamHeatExchanger2(String name)

Key Methods

Method Description
addInStreamMSHE(StreamInterface stream, String type, Double outletTemp) Add a stream. type = “hot” or “cold”. outletTemp = null for unknown.
setTemperatureApproach(double approach) Set minimum approach temperature (°C)
setUAvalue(double ua) Set UA constraint (W/K) - required for 3 unknowns
run() Execute the solver
getOutStream(int index) Get outlet stream by index (order of addition)
getUA() Get calculated UA value (W/K)
getTemperatureApproach() Get approach temperature setting
getCompositeCurve() Get composite curve data for plotting

Solver Configuration

Method Description Default
setTolerance(double tol) Convergence tolerance 1e-3
setMaxIterations(int max) Maximum iterations 1000
setJacobiDelta(double delta) Numerical derivative step 1e-4
setDamping(double factor) Newton step damping 1.0

Best Practices

1. Stream Ordering

Add streams in a logical order (all hot first, then all cold) for easier result interpretation:

// Recommended ordering
mshx.addInStreamMSHE(hot1, "hot", ...);   // Index 0
mshx.addInStreamMSHE(hot2, "hot", ...);   // Index 1
mshx.addInStreamMSHE(cold1, "cold", ...); // Index 2
mshx.addInStreamMSHE(cold2, "cold", ...); // Index 3

2. Reasonable Initial Guesses

The solver initializes unknown temperatures based on the approach temperature. For difficult cases, provide more known temperatures to improve convergence.

3. Physical Feasibility

Ensure your specification is physically feasible:

4. UA Estimation

For 3-unknown cases, estimate UA from:

\[UA \approx \frac{Q}{\Delta T_{lm}}\]

Where $Q$ is the expected duty and $\Delta T_{lm}$ is an estimated LMTD.

5. Check Composite Curves

Always visualize composite curves to verify:

Troubleshooting

“Failed to converge after maxIterations”

Causes:

  1. Infeasible specification (temperatures physically impossible)
  2. Poor initial guess
  3. Stiff problem near pinch

Solutions:

“Jacobian is singular”

Causes:

  1. Two unknowns have identical effect on residuals
  2. System at or near degenerate point

Solutions:

Negative ΔT in Composite Curves

Cause: Temperature crossover (cold above hot) - thermodynamically infeasible.

Solutions:

Very Large UA Values

Cause: Small LMTD in one or more intervals.

Solutions: