# Heat Exchangers (1D)¶

Heat Exchanger models represents a unit operation with two material streams which exchange heat. The IDAES 1-D Heat Exchanger model is used for detailed modeling of heat exchanger units with variations in one spatial dimension. For a simpler representation of a heat exchanger unit see Heat Exchanger (0-D).

## Degrees of Freedom¶

1-D Heat Exchangers generally have 7 degrees of freedom.

Typical fixed variables are:

• shell length and diameter,
• tube length and diameter,
• number of tubes,
• heat transfer coefficients (at all spatial points) for both shell and tube sides.

## Model Structure¶

The core 1-D Heat Exchanger Model unit model consists of two ControlVolume1DBlock Blocks (named shell and tube), each with one Inlet Port (named shell_inlet and tube_inlet) and one Outlet Port (named shell_outlet and tube_outlet).

## Construction Arguments¶

1-D Heat Exchanger units have construction arguments specific to the shell side, tube side and for the unit as a whole.

Arguments that are applicable to the heat exchanger unit are as follows:

• flow_type - indicates the flow arrangement within the unit to be modeled. Options are:

• ‘co-current’ - (default) shell and tube both flow in the same direction (from x=0 to x=1)
• ‘counter-current’ - shell and tube flow in opposite directions (shell from x=0 to x=1 and tube from x=1 to x=0).
• finite_elements - sets the number of finite elements to use when discretizing the spatial domains (default = 20). This is used for both shell and tube side domains.

• collocation_points - sets the number of collocation points to use when discretizing the spatial domains (default = 5, collocation methods only). This is used for both shell and tube side domains.

• has_wall_conduction - option to enable a model for heat conduction across the tube wall:
• ‘none’ - 0D wall model
• ‘1D’ - 1D heat conduction equation along the thickness of the tube wall
• ‘2D’ - 2D heat conduction equation along the length and thickness of the tube wall

Arguments that are applicable to the shell side:

• property_package - property package to use when constructing shell side Property Blocks (default = ‘use_parent_value’). This is provided as a Physical Parameter Block by the Flowsheet when creating the model. If a value is not provided, the ControlVolume Block will try to use the default property package if one is defined.
• property_package_args - set of arguments to be passed to the shell side Property Blocks when they are created.
• transformation_method - argument to specify the DAE transformation method for the shell side; should be compatible with the Pyomo DAE TransformationFactory
• transformation_scheme - argument to specify the scheme to use for the selected DAE transformation method; should be compatible with the Pyomo DAE TransformationFactory

Arguments that are applicable to the tube side:

• property_package - property package to use when constructing tube side Property Blocks (default = ‘use_parent_value’). This is provided as a Property Parameter Block by the Flowsheet when creating the model. If a value is not provided, the ControlVolume Block will try to use the default property package if one is defined.
• property_package_args - set of arguments to be passed to the tube side Property Blocks when they are created.
• transformation_method - argument to specify the DAE transformation method for the tube side; should be compatible with the Pyomo DAE TransformationFactory
• transformation_scheme - argument to specify the scheme to use for the selected DAE transformation method; should be compatible with the Pyomo DAE TransformationFactory

Additionally, 1-D Heat Exchanger units have the following construction arguments which are passed to the ControlVolume1DBlock Block for determining which terms to construct in the balance equations for the shell and tube side.

Argument Default Value
dynamic useDefault
has_holdup False
material_balance_type ‘componentTotal’
energy_balance_type ‘enthalpyTotal’
momentum_balance_type ‘pressureTotal’
has_phase_equilibrium False
has_heat_transfer True
has_pressure_change False

1-D Heat Exchanger models write the following additional Constraints to describe the heat transfer between the two sides of the heat exchanger. Firstly, the shell- and tube-side heat transfer is calculated as:

$Q_{shell,t,x} = - N_{tubes} \times (\pi \times U_{shell,t,x} \times D_{tube,outer} \times (T_{shell,t,x}-T_{wall,t,x}))$

where $$Q_{shell,t,x}$$ is the shell-side heat duty at point $$x$$ and time $$t$$, $$N_{tubes}$$ $$D_{tube}$$ are the number of and diameter of the tubes in the heat exchanger, $$U_{shell,t,x}$$ is the shell-side heat transfer coefficient, and $$T_{shell,t,x}$$ and $$T_{wall,t,x}$$ are the shell-side and tube wall temperatures respectively.

$Q_{tube,t,x} = N_{tubes} \times (\pi \times U_{tube,t,x} \times D_{tube,inner} \times (T_{wall,t,x}-T_{tube,t,x}))$

where $$Q_{tube,t,x}$$ is the tube-side heat duty at point $$x$$ and time $$t$$, $$U_{tube,t,x}$$ is the tube-side heat transfer coefficient and $$T_{tube,t,x}$$ is the tube-side temperature.

If a OD wall model is used for the tube wall conduction, the following constraint is implemented to connect the heat terms on the shell and tube side:

$N_{tubes} \times Q_{tube,t,x} = - Q_{shell,t,x}$

Finally, the following Constraints are written to describe the unit geometry:

$4 \times A_{tube} = \pi \times D_{tube}^2$
$4 \times A_{shell} = \pi \times (D_{shell}^2 - N_{tubes} \times D_{tube}^2)$

where $$A_{shell}$$ and $$A_{tube}$$ are the shell and tube areas respectively and $$D_{shell}$$ and $$D_{tube}$$ are the shell and tube diameters.

## Variables¶

1-D Heat Exchanger units add the following additional Variables beyond those created by the ControlVolume1DBlock Block.

Variable Name Notes
$$L_{shell}$$ shell_length Reference to shell.length
$$A_{shell}$$ shell_area Reference to shell.area
$$D_{shell}$$ d_shell
$$L_{tube}$$ tube_length Reference to tube.length
$$A_{tube}$$ tube_area Reference to tube.area
$$D_{tube}$$ d_tube
$$N_{tubes}$$ N_tubes
$$T_{wall,t,x}$$ temperature_wall
$$U_{shell,t,x}$$ shell_heat_transfer_coefficient
$$U_{tube,t,x}$$ tube_heat_transfer_coefficient

## HeatExchanger1dClass¶

class idaes.unit_models.heat_exchanger_1D.HeatExchanger1D(*args, **kwargs)
Parameters: 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 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: { True - construct holdup terms, False - do not construct holdup terms} shell_side shell side config arguments 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: { True - construct holdup terms, False - do not construct holdup terms} material_balance_type Indicates what type of mass balance should be constructed, default - MaterialBalanceType.componentTotal. 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, MaterialBalanceType.total - use total material balance.} energy_balance_type Indicates what type of energy balance should be constructed, default - EnergyBalanceType.enthalpyTotal. Valid values: { 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.} has_phase_equilibrium Argument to enable phase equilibrium on the shell side. - True - include phase equilibrium term - False - do not include phase equilibrium term property_package Property parameter object used to define property calculations (default = ‘use_parent_value’) - ‘use_parent_value’ - get package from parent (default = None) - a ParameterBlock object property_package_args A dict of arguments to be passed to the PropertyBlockData and used when constructing these (default = ‘use_parent_value’) - ‘use_parent_value’ - get package from parent (default = None) - a dict (see property package for documentation) transformation_method Discretization method to use for DAE transformation. See Pyomo documentation for supported transformations. transformation_scheme Discretization scheme to use when transformating domain. See Pyomo documentation for supported schemes. tube_side tube side config arguments 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: { True - construct holdup terms, False - do not construct holdup terms} material_balance_type Indicates what type of mass balance should be constructed, default - MaterialBalanceType.componentTotal. 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, MaterialBalanceType.total - use total material balance.} energy_balance_type Indicates what type of energy balance should be constructed, default - EnergyBalanceType.enthalpyTotal. Valid values: { 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.} has_phase_equilibrium Argument to enable phase equilibrium on the shell side. - True - include phase equilibrium term - False - do not include phase equilibrium term property_package Property parameter object used to define property calculations (default = ‘use_parent_value’) - ‘use_parent_value’ - get package from parent (default = None) - a ParameterBlock object property_package_args A dict of arguments to be passed to the PropertyBlockData and used when constructing these (default = ‘use_parent_value’) - ‘use_parent_value’ - get package from parent (default = None) - a dict (see property package for documentation) transformation_method Discretization method to use for DAE transformation. See Pyomo documentation for supported transformations. transformation_scheme Discretization scheme to use when transformating domain. See Pyomo documentation for supported schemes. finite_elements Number of finite elements to use when discretizing length domain (default=20) collocation_points Number of collocation points to use per finite element when discretizing length domain (default=3) flow_type Flow configuration of heat exchanger - HeatExchangerFlowPattern.cocurrent: shell and tube flows from 0 to 1 (default) - HeatExchangerFlowPattern.countercurrent: shell side flows from 0 to 1 tube side flows from 1 to 0 has_wall_conduction Argument to enable type of wall heat conduction model. - WallConductionType.zero_dimensional - 0D wall model (default), - WallConductionType.one_dimensional - 1D wall model along the thickness of the tube, - WallConductionType.two_dimensional - 2D wall model along the lenghth and thickness of the tube 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. (HeatExchanger1D) New instance

## HeatExchanger1dDataClass¶

class idaes.unit_models.heat_exchanger_1D.HeatExchanger1DData(component)[source]

Standard Heat Exchanger 1D Unit Model Class.

build()[source]

Begin building model (pre-DAE transformation).

Parameters: None – None
initialize(shell_state_args=None, tube_state_args=None, outlvl=1, solver='ipopt', optarg={'tol': 1e-06})[source]

Initialisation routine for the unit (default solver ipopt).

Keyword Arguments:

• state_args – a dict of arguments to be passed to the property package(s) 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’)
Returns:

None