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1D Shell and Tube Heat Exchanger

The IDAES Shell and Tube Heat Exchanger model is an extension of the standard 1-D Heat Exchanger model <reference_guides/model_libraries/generic/unit_models/heat_exchanger_1D:Heat Exchangers (1D)> model which includes the effects of wall temperature and geometry of co- and counter-current flow shell and tube type heat exchangers.

Degrees of Freedom

1-D Shell and Tube Heat Exchangers generally have 5 + 2 times number of finite elements degrees of freedom.

Typical fixed variables are:

  • heat exchanger length,
  • shell diameter,
  • tube inner and outer diameters,
  • number of tubes,
  • hot and cold side heat transfer coefficients (at all spatial points).

Model Structure

The core 1-D Heat Exchanger Model unit model consists of two ControlVolume1DBlock Blocks named hot_side and cold_side, each with one Inlet Port (named hot_side_inlet and cold_side_inlet) and one Outlet Port (named hot_side_outlet and cold_side_outlet). 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). If custom names are not provided, then default names of shell and tube will be used based on the shell_is_hot configuration argument.

Construction Arguments

Shell and Tube Heat Exchanger units have construction arguments specific to the hot and cold sides 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.
  • hot_side_name
  • cold_side_name
  • shell_is_hot - (bool) indicates whether the shell will be mapped to the hot side of the heat exchanger or the cold side.

Arguments that are applicable to the hot and cold sides:

  • 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

Additionally, Shell and Tube Heat Exchanger units have the following construction arguments for each side which are passed to the ControlVolume1DBlocks for determining which terms to construct in the balance equations for the hot and cold sides.

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

Variables

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

Variable Name Notes
L length Reference to hot_side.length
Dshell shell_diameter Diameter of shell
Dtube, inner tube_inner_diameter Inner diameter of tubes

Dtube, outer Ntubes

tube_outer_diameter number_of_tubes

Outer diameter of tubes

Twall Uhot, t, x Ucold, t, x

temperature_wall hot_side_heat_transfer_coefficient cold_side_heat_transfer_coefficient

Temperature of tube wall material

Additional Constraints

1-D Shell and TubeHeat Exchanger models write the following additional Constraints to describe the heat transfer between the two sides of the heat exchanger.

Firstly, heat transfer for the hot and cold sides to the tube wall is calculated as:


Qhot, t, x =  − Uhott, x × Ntubes × π × Dtube, outer × (Thot, t, x − Twall, t, x))


Qcold, t, x = Ucoldt, x × Ntubes × π × Dtube, inner × (Twall, t, x − Tcold, t, x))

where Qhot, t, x and Qcold, t, x are the hot -and cold-side heat duties at point x and time t.

Next, overall heat conservation is enforced by the following constraint:


Qcold, t, x =  − Qhot, t, x

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


Lhot = Lcold

where Lhot and Lcold are the length of the hot and cold side respectively.

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

$$A_{tube} = N_{tubes} \times \pi \times \frac{D_{tube,inner}^2}{4}$$

where Ashell and Atube are the cross-sectional areas of the shell and tube side control volumes respectively.

ShellAndTube1D Class

idaes.models.unit_models.shell_and_tube_1d

ShellAndTube1D

ShellAndTube1Data Class

ShellAndTube1DData