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 dervied 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:

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

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

  • default (dict) –

    Default ProcessBlockData config

    Keys
    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

    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

    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 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.

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

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 transfered. This should be a tuple in the form (value, units), (default = (1000 J/s))

Returns

None