Heat Exchanger using the NTU Method#

The HeatExchangerNTU model can be imported from idaes.models.unit_models, and models a heat exchanger using the effectiveness-NTU method. This model derived from the

Degrees of Freedom#

Aside from the inlet conditions, an NTU heat exchanger model has three degrees of freedom which must be fixed for it to be fully specified. Additionally, users may include a pressure change in the unit which adds two additional degrees of freedom.

Standard design variables are:

  • heat transfer area,

  • heat transfer coefficient, and

  • effectiveness.

If pressure change is included, additional degrees of freedom are:

  • hot and cold side pressure changes.

Model Structure#

The HeatExchanger model contains two ControlVolume0DBlock blocks named hot_side and the cold side. These names are configurable using the hot_side_name and cold_side_name configuration arguments, in which case aliases are assigned to the control volumes and associated Ports using the names provided (note that hot_side and cold_side will always work). 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 HeatExchanger has two inlet ports and two outlet ports. By default these are hot_side_inlet, cold_side_inlet, hot_side_outlet, and cold_side_outlet. If the user supplies different hot and cold side names the inlet and outlets are named accordingly.

Variables#

Variable

Symbol

Index Sets

Doc

heat_duty

\(Q\)

t

Heat transferred from hot side to the cold side

area

\(A\)

None

Heat transfer area

heat_transfer_coefficient

\(U\)

t

Heat transfer coefficient

effectiveness

\(\epsilon\)

t

Effectiveness factor

Expressions#

The following Expressions are constructed by the model and can be used in correlations to determine the effectiveness factor.

Minimum heat capacitance:

\[C_{min} = min((F_{mol, hot} \times c_{p, mol, hot}), (F_{mol, hot} \times c_{p, mol, hot}))\]

Maximum heat capacitance:

\[C_{max} = max((F_{mol, hot} \times c_{p, mol, hot}), (F_{mol, hot} \times c_{p, mol, hot}))\]

Min and max operators are implemented using smooth approximation using the \(\epsilon_{cmin}\) parameter.

Heat capacitance ratio:

\[C_{ratio} = \frac{C_{min}}{C_{max}}\]

Number of theoretical heat transfer units:

\[NTU = \frac{U \times A}{C_{min}}\]

Constraints#

The effectiveness-NTU method is a method to approximate the heat transferred in a heat exchanger using the following calculation:

\[Q_{cold} = \epsilon \times C_{min} \times (T_{hot} - T_{cold})\]

where \(Q_{cold}\) is the heat transferred from the hot side to the cold side, \(\epsilon\) is the effectiveness factor for the heat exchanger, \(C_{min}\) is the minimum heat capacitance between the hot and cold inlet streams and \(T_{hot}\) and \(T_{cold}\) are the temperatures of the hot and cold inlet streams respectively.

Additionally, and overall energy balance constraint is written:

\[Q_{hot} = -Q_{cold}\]

Initialization#

class idaes.models.unit_models.heat_exchanger_ntu.HXNTUInitializer(**kwargs)[source]#

Initializer for NTU Heat Exchanger units.

constraint_tolerance

Tolerance for checking constraint convergence

output_level

Set output level for logging messages

solver

Solver to use for initialization

solver_options

Dict of options to pass to solver

writer_config

Dict of writer_config arguments to pass to solver

default_submodel_initializer

Default Initializer object to use for sub-models. Only used if no Initializer defined in submodel_initializers.

always_estimate_states

Whether initialization routine should estimate values for state variables that already have values. Note that if set to True, this will overwrite any initial guesses provided.

initialization_routine(model, plugin_initializer_args=None, copy_inlet_state=False, duty=<pyomo.core.expr.numeric_expr.NPV_ProductExpression object>)[source]#

Common initialization routine for NTU Heat Exchangers.

This routine starts by initializing the hot and cold side properties. Next, the heat transfer between the two sides is fixed to an initial guess for the heat duty (provided by the duty argument), the associated constraint deactivated, and the model is then solved. Finally, the heat duty is unfixed and the heat transfer constraint reactivated followed by a final solve of the model.

Parameters:
  • model (Block) – Pyomo Block to be initialized

  • plugin_initializer_args (dict) – dict-of-dicts containing arguments to be passed to plug-in Initializers. Keys should be submodel components.

  • copy_inlet_state (bool) – bool (default=False). Whether to copy inlet state to other states or not (0-D control volumes only). Copying will generally be faster, but inlet states may not contain all properties required elsewhere.

  • duty – initial guess for heat duty to assist with initialization. Can be a Pyomo expression with units.

Returns:

Pyomo solver results object

Class Documentation#

class idaes.models.unit_models.heat_exchanger_ntu.HeatExchangerNTU(*args, **kwds)#
Parameters:
  • rule (function) – A rule function or None. Default rule calls build().

  • concrete (bool) – If True, make this a toplevel model. Default - False.

  • ctype (class) –

    Pyomo ctype of the block. Default - pyomo.environ.Block

    Config args

    dynamic

    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.}

    has_holdup

    Indicates whether holdup terms should be constructed or not. Must be True if dynamic = True, default - False. Valid values: { useDefault - get flag from parent (default = False), True - construct holdup terms, False - do not construct holdup terms}

    hot_side

    Hot fluid config arguments

    hot_side
    material_balance_type

    Indicates what type of mass balance should be constructed, default - MaterialBalanceType.useDefault. Valid values: { MaterialBalanceType.useDefault - refer to property package for default balance type **MaterialBalanceType.none - exclude material balances, MaterialBalanceType.componentPhase - use phase component balances, MaterialBalanceType.componentTotal - use total component balances, MaterialBalanceType.elementTotal - use total element balances, MaterialBalanceType.total - use total material balance.}

    energy_balance_type

    Indicates what type of energy balance should be constructed, default - EnergyBalanceType.useDefault. Valid values: { EnergyBalanceType.useDefault - refer to property package for default balance type **EnergyBalanceType.none - exclude energy balances, EnergyBalanceType.enthalpyTotal - single enthalpy balance for material, EnergyBalanceType.enthalpyPhase - enthalpy balances for each phase, EnergyBalanceType.energyTotal - single energy balance for material, EnergyBalanceType.energyPhase - energy balances for each phase.}

    momentum_balance_type

    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.}

    has_pressure_change

    Indicates whether terms for pressure change should be constructed, default - False. Valid values: { True - include pressure change terms, False - exclude pressure change terms.}

    property_package

    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.}

    property_package_args

    A ConfigBlock with arguments to be passed to property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}

    cold_side

    Cold fluid config arguments

    cold_side
    material_balance_type

    Indicates what type of mass balance should be constructed, default - MaterialBalanceType.useDefault. Valid values: { MaterialBalanceType.useDefault - refer to property package for default balance type **MaterialBalanceType.none - exclude material balances, MaterialBalanceType.componentPhase - use phase component balances, MaterialBalanceType.componentTotal - use total component balances, MaterialBalanceType.elementTotal - use total element balances, MaterialBalanceType.total - use total material balance.}

    energy_balance_type

    Indicates what type of energy balance should be constructed, default - EnergyBalanceType.useDefault. Valid values: { EnergyBalanceType.useDefault - refer to property package for default balance type **EnergyBalanceType.none - exclude energy balances, EnergyBalanceType.enthalpyTotal - single enthalpy balance for material, EnergyBalanceType.enthalpyPhase - enthalpy balances for each phase, EnergyBalanceType.energyTotal - single energy balance for material, EnergyBalanceType.energyPhase - energy balances for each phase.}

    momentum_balance_type

    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.}

    has_pressure_change

    Indicates whether terms for pressure change should be constructed, default - False. Valid values: { True - include pressure change terms, False - exclude pressure change terms.}

    property_package

    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.}

    property_package_args

    A ConfigBlock with arguments to be passed to property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}

    hot_side_name

    Hot side name, sets control volume and inlet and outlet names

    cold_side_name

    Cold side name, sets control volume and inlet and outlet names

  • initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries with config arguments as keys.

  • 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 override the default behavior of matching the BlockData index exactly to the index in initialize.

Returns:

(HeatExchangerNTU) New instance

class idaes.models.unit_models.heat_exchanger_ntu.HeatExchangerNTUData(component)[source]#

Heat Exchanger Unit Model using NTU method.

build()[source]#

General build method for UnitModelBlockData. This method calls a number of sub-methods which automate the construction of expected attributes of unit models.

Inheriting models should call super().build.

Parameters:

None

Returns:

None

default_initializer#

alias of HXNTUInitializer

initialize_build(hot_side_state_args=None, cold_side_state_args=None, outlvl=0, solver=None, optarg=None, duty=None)[source]#

Heat exchanger initialization method.

Parameters:
  • hot_side_state_args – a dict of arguments to be passed to the property initialization for the hot side (see documentation of the specific property package) (default = None).

  • cold_side_state_args – a dict of arguments to be passed to the property initialization for the cold side (see documentation of the specific property package) (default = None).

  • outlvl – sets output level of initialization routine

  • optarg – solver options dictionary object (default=None, use default solver options)

  • solver – str indicating which solver to use during initialization (default = None, use default solver)

  • duty – an initial guess for the amount of heat transferred. This should be a tuple in the form (value, units), (default = (1000 J/s))

Returns:

None