The BoilerHeatExchanger model can be used to represent boiler heat exchangers in sub-critical and super critical power plant flowsheets (econmizer, primary superheater, secondary superheater, finishing superheater, reheater, etc.), the model consists of a shell and tube crossflow heat exchanger; in which the shell is used as the gas side and the tube is used as the water or steam side. Rigorous heat transfer calculations (convective and radiative heat transfer for shell side, and convective heat transfer for tube side) and shell and tube pressure drop calculations have been included.

The BoilerHeatExchanger model can be imported from idaes.unit_models.power_generation, while additional rules and utility functions can be imported from idaes.unit_models.power_generation.boiler_heat_exchanger.


The example below demonstrates how to initialize the BoilerHeatExchanger model, and override the default temperature difference calculation.

# Import Pyomo libraries
from pyomo.environ import ConcreteModel, SolverFactory, value
# Import IDAES core
from idaes.core import FlowsheetBlock
# Import Unit Model Modules
from idaes.property_models import iapws95
# import ideal flue gas prop pack
from idaes.unit_models.power_generation.IdealProp_FlueGas import FlueGasParameterBlock
# Import Power Plant HX Unit Model
from idaes.unit_models.power_generation.boiler_heat_exchanger import BoilerHeatExchanger, TubeArrangement, \
import pyomo.environ as pe # Pyomo environment
from idaes.core import FlowsheetBlock, StateBlock
from idaes.unit_models import HeatExchanger
from idaes.unit_models.heat_exchanger import delta_temperature_amtd_callback
from idaes.property_models import iapws95

# Create a Concrete Model as the top level object
m = ConcreteModel()

# Add a flowsheet object to the model
m.fs = FlowsheetBlock(default={"dynamic": False})

# Add property packages to flowsheet library
m.fs.prop_water = iapws95.Iapws95ParameterBlock()
m.fs.prop_fluegas = FlueGasParameterBlock()

# Create unit models
m.fs.ECON = BoilerHeatExchanger(default=
                          {"side_1_property_package": m.fs.prop_water,
                           "side_2_property_package": m.fs.prop_fluegas,
                           "has_pressure_change": True,
                           "has_holdup": False,
                           "delta_T_method": DeltaTMethod.counterCurrent,
                           "tube_arrangement": TubeArrangement.inLine,
                           "side_1_water_phase": "Liq",
                           "has_radiation": False})

# Set Inputs
# BFW Boiler Feed Water inlet temeperature = 555 F = 563.706 K
# inputs based on NETL Baseline Report v3 (SCPC 650 MW net, no carbon capture case)
h = iapws95.htpx(563.706, 2.5449e7)
m.fs.ECON.side_1_inlet.flow_mol[0].fix(24678.26) # mol/s
m.fs.ECON.side_1_inlet.pressure[0].fix(2.5449e7) # Pa

# FLUE GAS Inlet from Primary Superheater
FGrate = 28.3876e3  # mol/s equivalent of ~1930.08 klb/hr
# Use FG molar composition to set component flow rates (baseline report)
m.fs.ECON.side_2_inlet.temperature[0].fix(682.335) # K
m.fs.ECON.side_2_inlet.pressure[0].fix(100145) # Pa
# economizer design variables and parameters
ITM = 0.0254  # inch to meter conversion
# Based on NETL Baseline Report Rev3
m.fs.ECON.tube_di.fix((2-2*0.188)*ITM)  # calc inner diameter
#                        (2 = outer diameter, thickness = 0.188)
m.fs.ECON.tube_thickness.fix(0.188*ITM) # tube thickness
# pitch_y = (54.5) gas path transverse width /columns
m.fs.ECON.tube_length.fix(53.41*12*ITM) # use tube length (53.41 ft)
m.fs.ECON.tube_nrow.fix(36*2.5)         # use to match baseline performance
m.fs.ECON.tube_ncol.fix(130)            # 130 from NETL report
# parameters
# heat transfer resistance due to tube side fouling (water scales)
m.fs.ECON.tube_rfouling = 0.000176
# heat transfer resistance due to tube shell fouling (ash deposition)
m.fs.ECON.shell_rfouling = 0.00088
if m.fs.ECON.config.has_radiation is True:
    m.fs.ECON.emissivity_wall.fix(0.7)       # wall emissivity
# correction factor for overall heat transfer coefficient
# correction factor for pressure drop calc tube side
# correction factor for pressure drop calc shell side

# Initialize the model

Degrees of Freedom

Aside from the inlet conditions, a heat exchanger model usually has two degrees of freedom, which can be fixed for it to be fully specified. Things that are frequently fixed are two of:

  • heat transfer area,
  • heat transfer coefficient, or
  • temperature approach.

In order to capture off design conditions and heat transfer coefficients at ramp up/down or load following conditions, the BoilerHeatExanger model includes rigorous heat transfer calculations. Therefore, additional degrees of freedom are required to calculate Nusselt, Prandtl, Reynolds numbers, such as:

  • tube_di (inner diameter)
  • tube length
  • tube number of rows (tube_nrow), columns (tube_ncol), and inlet flow (nrow_inlet)
  • pitch in x and y axis (pitch_x and pitch_y, respectively)

If pressure drop calculation is enabled, additional degrees of freedom are required:

  • elevation with respect to ground level (delta_elevation)
  • tube fouling resistance (tube_r_fouling)
  • shell fouling resistance (shell_r_fouling)

Model Structure

The BoilerHeatExchanger model contains two ControlVolume0DBlock blocks. By default the gas side is named shell and the water/steam side is named tube. These names are configurable. The sign convention is that duty is positive for heat flowing from the hot side to the cold side. Aside from the sign convention there is no requirement that the hot side be hotter than the cold side.

The control volumes are configured the same as the ControlVolume0DBlock in the Heater model. The BoilerHeatExchanger model contains additional constraints that calculate the amount of heat transferred from the hot side to the cold side.

The BoilerHeatExchanger has two inlet ports and two outlet ports. By default these are shell_inlet, tube_inlet, shell_outlet, and tube_outlet. If the user supplies different hot and cold side names the inlet and outlets are named accordingly.


Variable Symbol Index Sets Doc
heat_duty \(Q\) t Heat transferred from hot side to the cold side
area \(A\) None Heat transfer area
U \(U\) t Heat transfer coefficient
delta_temperature \(\Delta T\) t Temperature difference, defaults to LMTD

Note: delta_temperature may be either a variable or expression depending on the callback used. If the specified cold side is hotter than the specified hot side this value will be negative.


The default constraints can be overridden by providing alternative rules for the heat transfer equation, temperature difference, heat transfer coefficient, shell and tube pressure drop. This section describes the default constraints.

Heat transfer from shell to tube:

\[Q = UA\Delta T\]

Temperature difference is:

\[\Delta T = \frac{\Delta T_1 - \Delta T_2}{\log_e\left(\frac{\Delta T_1}{\Delta T_2}\right)}\]

The overall heat transfer coefficient is calculated as a function of convective heat transfer shell and tube, and wall conduction heat transfer resistance.

Convective heat transfer equations:

\[\frac{1}{U}*fcorrection_{htc} = [\frac{1}{hconv_{tube}} + \frac{1}{hconv_{shell}} + r + tube_{r fouling} + shell_{r fouling}]\]
\[hconv_{tube} = \frac{Nu_{tube} k}{tube_{di}}\]
\[Nu_{tube} = 0.023 Re_{tube}^{0.8} Pr_{tube}^{0.4}\]
\[Pr_{tube} = \frac{Cp \mu}{ k Mw}\]
\[Re_{tube} = \frac{tube_{di} V \rho}{\mu}\]
\[hconv_{shell} = \frac{Nu_{shell} k_{flue gas}}{tube_{do}}\]
\[Nu_{shell} = f_{arrangement} 0.33 Re_{tube}^{0.6} Pr_{tube}^{0.3333}\]
\[Pr_{shell} = \frac{Cp \mu}{ k Mw}\]
\[Re_{shell} = \frac{tube_{do} V \rho}{\mu}\]
\[tube_{do} = 2*tube_{thickness} + tube_{di}\]

Wall heat conduction resistance equation:

\[r = 0.5 * tube_{do} * \log{(\frac{tube_{do}}{tube_{di}})}*k\]


  • hconv_tube : convective heat transfer resistance tube side (fluid water/steam) (W / m2 / K)
  • hconv_shell : convective heat transfer resistance shell side (fluid Flue Gas) (W / m2 / K )
  • Nu : Nusselt number
  • Pr : Prandtl number
  • Re : Reynolds number
  • V: velocity (m/s)
  • tube_di : inner diameter of the tube (m)
  • tube_do : outer diameter of the tube (m) (expression calculated by the model)
  • tube_thickness : tube thickness (m)
  • r = wall heat conduction resistance (K m^2 / W)
  • k : thermal conductivity of the tube wall (W / m / K)
  • \(\rho\) : density (kg/m^3)
  • \(\mu\) : viscocity (kg/m/s)
  • tube_r_fouling : tube side fouling resistance (K m^2 / W)
  • shell_r_fouling : shell side fouling resistance (K m^2 / W)
  • fcorrection_htc: correction factor for overall heat trasnfer
  • f_arrangement: tube arrangement factor

Note: by default fcorrection_htc is set to 1, however, this variable can be used to match unit performance (i.e. as a parameter estimation problem using real data). This variable is also called cleanniness factor (when = 1, its considered a clean tube with no fouling).

Tube arrangement factor is a config argument with two different type of arrangements supported at the moment: 1.- In-line tube arrangement factor (f_arrangement = 0.788), and 2.- Staggered tube arrangement factor (f_arrangement = 1). f_arrangement is a parameter that can be adjusted by the user.

The BoilerHeatExchanger includes an argument to compute heat tranfer due to radiation of the flue gases. If has_radiation = True the model builds additional heat transfer calculations that will be added to the hconv_shell resistances. Radiation effects are calculated based on the gas gray fraction and gas-surface radiation (between gas and shell).

\[Gas_{gray frac} = f (gas_{emissivity})\]
\[frad_{gas gray frac} = f (wall_{emissivity}, gas_{emissivity})\]
\[hconv_{shell_rad} = f (k_{boltzmann}, frad_{gas gray frac}, T_{gas in}, T_{gas out}, T_{fluid in}, T_{fluid out})\]

Note: Gas emissivity is calculated with surrogate models (see more details in Radiation = True when flue gas temperatures are higher than 700 K (for example, when the model is used for units like Primary superheater, Reheater, or Finishing Superheater; while Radiation = False when the model is used to represent the economizer in a power plant flowsheet).

If pressure change is set to True, \(deltaP_{uturn} and friction_{factor}\) are calculated

Tube side:

\[\Delta P_{tube} = \Delta P_{tube friction} + \Delta P_{tube uturn} - elevation * g *\frac{\rho_{in} + \rho_{out}}{2}\]
\[\Delta P_{tube friction} = f( tube_{di} \rho, V_{tube}, number of tubes, tube_{length})\]
\[\Delta P_{tube uturn} = f(\rho, v_{tube}, k_{loss uturn})\]


  • \(k_{loss uturn}\) : pressure loss coeficient of a tube u-turn
  • g : is the acceleration of gravity 9.807 (m/s^2)

Shell side:

\[\Delta P_{shell} = 1.4 \Delta P_{shell friction} \rho V_{shell}^2\]

\(\Delta P_{shell friction}\) is calculated based on the tube arrangement type:

In-line: \(\Delta P_{shell friction} = \frac{ 0.044 + \frac{0.08 ( \frac{P_x}{tube_{do}} ) } {(\frac{P_y}{tube_{do}}-1)^{0.43+\frac{1.13}{(\frac{P_x}{tube_{do}})}}}}{Re^{0.15}}\)

Staggered: \(\Delta P_{shell friction} = \frac{ 0.25 + \frac{0.118}{(\frac{P_y}{tube_{do}} -1)^{1.08}} }{Re^{0.16}}\)

Figure. Tube Arrangement


Tube Arrangement

Class Documentation


The hot_side_config and cold_side_config can also be supplied using the name of the hot and cold sides (shell and tube by default) as in the example.

class idaes.unit_models.power_generation.boiler_heat_exchanger.BoilerHeatExchanger(*args, **kwargs)
  • rule (function) – A rule function or None. Default rule calls build().
  • concrete (bool) – If True, make this a toplevel model. Default - False.
  • ctype (str) – Pyomo ctype of the block. Default - “Block”
  • default (dict) –

    Default ProcessBlockData config

    Indicates whether this model will be dynamic or not, default = useDefault. Valid values: { useDefault - get flag from parent (default = False), True - set as a dynamic model, False - set as a steady-state model.}
    Indicates whether holdup terms should be constructed or not. Must be True if dynamic = True, default - False. Valid values: { True - construct holdup terms, False - do not construct holdup terms}
    Property parameter object used to define property calculations, default - useDefault. Valid values: { useDefault - use default package from parent model or flowsheet, PhysicalParameterObject - a PhysicalParameterBlock object.}
    A ConfigBlock with arguments to be passed to a property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}
    Property parameter object used to define property calculations, default - useDefault. Valid values: { useDefault - use default package from parent model or flowsheet, PhysicalParameterObject - a PhysicalParameterBlock object.}
    A ConfigBlock with arguments to be passed to a property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}
    Indicates what type of material balance should be constructed, default - MaterialBalanceType.componentPhase. Valid values: { MaterialBalanceType.none - exclude material balances, MaterialBalanceType.componentPhase - use phase component balances, MaterialBalanceType.componentTotal - use total component balances, MaterialBalanceType.elementTotal - use total element balances, - use total material balance.}
    Indicates what type of energy balance should be constructed, default - EnergyBalanceType.enthalpyTotal. Valid values: { EnergyBalanceType.none - exclude energy balances, EnergyBalanceType.enthalpyTotal - single ethalpy balance for material, EnergyBalanceType.enthalpyPhase - ethalpy balances for each phase, EnergyBalanceType.energyTotal - single energy balance for material, EnergyBalanceType.energyPhase - energy balances for each phase.}
    Indicates what type of momentum balance should be constructed, default - MomentumBalanceType.pressureTotal. Valid values: { MomentumBalanceType.none - exclude momentum balances, MomentumBalanceType.pressureTotal - single pressure balance for material, MomentumBalanceType.pressurePhase - pressure balances for each phase, MomentumBalanceType.momentumTotal - single momentum balance for material, MomentumBalanceType.momentumPhase - momentum balances for each phase.}
    Indicates whether terms for pressure change should be constructed, default - False. Valid values: { True - include pressure change terms, False - exclude pressure change terms.}


    Flag indicating type of flow arrangement to use for delta T calculations (default = ‘counter-current’)

    • ’counter-current’ : counter-current flow arrangement
    Tube arrangement could be in-line and staggered
    Define water phase for property calls
    Define if side 2 gas radiation is to be considered
  • initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries described under the “default” argument above.
  • idx_map (function) – Function to take the index of a BlockData element and return the index in the initialize dict from which to read arguments. This can be provided to overide the default behavior of matching the BlockData index exactly to the index in initialize.

(BoilerHeatExchanger) New instance

class idaes.unit_models.power_generation.boiler_heat_exchanger.BoilerHeatExchangerData(component)[source]

Standard Heat Exchanger Unit Model Class


Build method for Boiler heat exchanger model

initialize(state_args_1={}, state_args_2={}, outlvl=0, solver='ipopt', optarg={'tol': 1e-06})[source]

General Heat Exchanger initialisation routine.

Keyword Arguments:
  • state_args_1 – a dict of arguments to be passed to the property package(s) for side 1 of the heat exchanger to provide an initial state for initialization (see documentation of the specific property package) (default = {}).
  • state_args_2 – a dict of arguments to be passed to the property package(s) for side 2 of the heat exchanger to provide an initial state for initialization (see documentation of the specific property package) (default = {}).
  • outlvl

    sets output level of initialisation routine

    • 0 = no output (default)
    • 1 = return solver state for each step in routine
    • 2 = return solver state for each step in subroutines
    • 3 = include solver output infomation (tee=True)
  • optarg – solver options dictionary object (default={‘tol’: 1e-6})
  • solver – str indicating whcih solver to use during initialization (default = ‘ipopt’)



Model checks for unit - calls model checks for both control volume Blocks.