CrossFlowHeatExchanger1D#

This model is for a cross flow heat exchanger between two gases. The gas in the shell has a straight path, while the gas in the tubes snakes back and forth across the shell’s path. Note that the finite_elements option in the shell and tube control volume configs should be set to an integer factor of number_passes in order for the discretization equations to make sense as a cross-flow heat exchanger.

Example#

import pyomo.environ as pyo

from idaes.core import FlowsheetBlock
import idaes.core.util.scaling as iscale
from idaes.models.unit_models import HeatExchangerFlowPattern
from idaes.models.properties.modular_properties import GenericParameterBlock
from idaes.models_extra.power_generation.properties.natural_gas_PR import (
    get_prop,
    EosType,
)
from idaes.models_extra.power_generation.unit_models import CrossFlowHeatExchanger1D
from idaes.core.util.model_statistics import degrees_of_freedom

optarg = {
    "constr_viol_tol": 1e-8,
    "nlp_scaling_method": "user-scaling",
    "linear_solver": "ma57",
    "OF_ma57_automatic_scaling": "yes",
    "max_iter": 350,
    "tol": 1e-8,
    "halt_on_ampl_error": "no",
}

m = pyo.ConcreteModel()
m.fs = pyo.FlowsheetBlock(dynamic=False)
m.fs.properties = GenericParameterBlock(
      **get_prop(["H2", "H2O", "Ar", "N2"], {"Vap"}, eos=EosType.IDEAL),
      doc="H2O + H2 gas property parameters",
  )
m.fs.heat_exchanger = CrossFlowHeatExchanger1D(
      has_holdup=True,
      dynamic=False,
      cold_side={
          "property_package": m.fs.h2_side_prop_params,
          "has_holdup": False,
          "dynamic": False,
          "has_pressure_change": pressure_drop,
          "transformation_method": "dae.finite_difference",
          "transformation_scheme": "FORWARD",
      },
      hot_side={
          "property_package": m.fs.h2_side_prop_params,
          "has_holdup": False,
          "dynamic": False,
          "has_pressure_change": pressure_drop,
          "transformation_method": "dae.finite_difference",
          "transformation_scheme": "BACKWARD",
      },
      shell_is_hot=True,
      flow_type=HeatExchangerFlowPattern.countercurrent,
      finite_elements=12,
      tube_arrangement="staggered",
  )

hx = m.fs.heat_exchanger

hx.hot_side_inlet.flow_mol.fix(2619.7)
hx.hot_side_inlet.temperature.fix(971.6)
hx.hot_side_inlet.pressure.fix(1.2e5)
hx.hot_side_inlet.mole_frac_comp[0, "H2"].fix(0.79715)
hx.hot_side_inlet.mole_frac_comp[0, "H2O"].fix(0.20177)
hx.hot_side_inlet.mole_frac_comp[0, "Ar"].fix(0.00086358)
hx.hot_side_inlet.mole_frac_comp[0, "N2"].fix(0.00021589)

hx.cold_side_inlet.flow_mol.fix(2619.7)
hx.cold_side_inlet.temperature.fix(446.21)
hx.cold_side_inlet.pressure.fix(1.2e5)
hx.cold_side_inlet.mole_frac_comp[0, "H2"].fix(0.36203)
hx.cold_side_inlet.mole_frac_comp[0, "H2O"].fix(0.63689)
hx.cold_side_inlet.mole_frac_comp[0, "Ar"].fix(0.00086358)
hx.cold_side_inlet.mole_frac_comp[0, "N2"].fix(0.00021589)

hx.di_tube.fix(0.0525018)
hx.thickness_tube.fix(0.0039116)
hx.length_tube_seg.fix(4.3)
hx.number_passes.fix(12)
hx.number_columns_per_pass.fix(50)
hx.number_rows_per_pass.fix(25)

hx.pitch_x.fix(0.1)
hx.pitch_y.fix(0.1)
hx.therm_cond_wall = 43.0
hx.rfouling_tube = 0.0001
hx.rfouling_shell = 0.0001
hx.fcorrection_htc_tube.fix(1)
hx.fcorrection_htc_shell.fix(1)

hx.cp_wall.value = 502.4

pp = m.fs.properties
pp.set_default_scaling("enth_mol_phase", 1e-3)
pp.set_default_scaling("pressure", 1e-5)
pp.set_default_scaling("temperature", 1e-2)
pp.set_default_scaling("flow_mol", 1e-3)

_mf_scale = {
    "H2": 1,
    "H2O": 1,
    "N2": 10,
    "Ar": 10,
}
for comp, s in _mf_scale.items():
    pp.set_default_scaling("mole_frac_comp", s, index=comp)
    pp.set_default_scaling("mole_frac_phase_comp", s, index=("Vap", comp))
    pp.set_default_scaling("flow_mol_phase_comp", s * 1e-3, index=("Vap", comp))

shell = hx.hot_side
tube = hx.cold_side
iscale.set_scaling_factor(shell.area, 1e-1)
iscale.set_scaling_factor(shell.heat, 1e-6)
iscale.set_scaling_factor(tube.area, 1)
iscale.set_scaling_factor(tube.heat, 1e-6)
iscale.set_scaling_factor(shell._enthalpy_flow, 1e-8)  # pylint: disable=W0212
iscale.set_scaling_factor(tube._enthalpy_flow, 1e-8)  # pylint: disable=W0212
iscale.set_scaling_factor(shell.enthalpy_flow_dx, 1e-7)
iscale.set_scaling_factor(tube.enthalpy_flow_dx, 1e-7)
iscale.set_scaling_factor(hx.heat_holdup, 1e-8)

iscale.calculate_scaling_factors(m)

initializer = m.fs.heat_exchanger.default_initializer(
      solver="ipopt",
      solver_options=optarg
)
initializer.initialize(m.fs.heat_exchanger)

Heat Exchanger Geometry#

Variable	Index Sets	Doc
`number_columns_per_pass`	None	Number of columns of tube per pass
`number_rows_per_pass`	None	Number of rows of tube per pass
`number_passes`	None	Number of tube banks of `nrow_tube * ncol_inlet` tubes
`pitch_x`	None	Distance between tubes parallel to shell flow, measured from center-of-tube to center-of-tube
`pitch_y`	None	Distance between tubes perpendicular to shell flow, measured from center-of-tube to center-of-tube
`length_tube_seg`	None	Length of tube segment perpendicular to flow in each pass
`area_flow_shell`	None	Reference to flow area on shell control volume
`length_flow_shell`	None	Reference to flow length on shell control volume
`area_flow_shell_min`	None	Minimum flow area on shell side
`di_tube`	None	Inner diameter of tubes
`thickness_tube`	None	Thickness of tube wall.
`area_flow_tube`	None	Reference to flow area on tube control volume
`length_flow_tube`	None	Reference to flow length on tube control volume

Expression	Index Sets	Doc
`nrow_tube`	None	Total number of rows of tube
`do_tube`	None	Outer diameter of tube (equal to `di_tube+2*thickness_tube`)
`pitch_x_to_do`	None	Ratio of `pitch_x` to `do_tube`
`pitch_y_to_do`	None	Ratio of `pitch_y` to `do_tube`
`area_wall_seg`	None	Total cross-sectional area of tube per pass
`total_heat_transfer_area`	None	Total heat transfer area, as measured on outer surface of tubes

Constraint	Index Sets	Doc
`length_flow_shell_eqn`	None	Constrains shell flow length from control volume to equal value implied by geometry
`area_flow_shell_eqn`	None	Constrains shell flow cross-sectional area from control volume to equal value implied by geometry
`area_flow_shell_min_eqn`	None	Constraints `area_flow_shell_min` to equal value determined by geometry
`length_flow_tube_eqn`	None	Constrains tube flow length from control volume to equal value implied by geometry
`area_flow_tube_eqn`	None	Constrains tube flow cross-sectional area from control volume to equal value implied by geometry

Performance Equations#

Variable	Index Sets	Doc
`fcorrection_htc_shell`	time, length	Correction factor for shell convective heat transfer
`conv_heat_transfer_coeff_shell`	time, length	Shell-side convective heat transfer coefficient
`temp_wall_shell`	time, length	Shell-side wall temperature of tube
`temp_wall_center`	time, length	Temperature at center of tube wall
`v_shell`	time, length	Flow velocity on shell side through minimum area
`N_Re_shell`	time, length	Reynolds number on shell side
`N_Nu_shell`	time, length	Nusselt number on shell side
`heat_transfer_coeff_tube`	time, length	Tube-side heat transfer coefficient
`temp_wall_tube`	time, length	Tube-side wall temperature of tube
`v_tube`	time, length	Flow velocity of gas in tube
`N_Re_tube`	time, length	Reynolds number in tube
`N_Nu_tube`	time, length	Nusselt number on tube side

Parameter	Index Sets	Doc
`therm_cond_wall`	None	Thermal conductivity of tube wall
`density_wall`	None	Mass density of tube wall metal
`cp_wall`	None	Tube wall heat capacity (mass basis)
`rfouling_shell`	None	Fouling resistance on shell side
`f_arrangement`	None	Adjustment factor depending on `tube_arrangement` in config

Constraint	Index Sets	Doc
`v_shell_eqn`	time, length	Calculates velocity of flow through shell using `area_flow_shell_min`
`N_Re_shell_eqn`	time, length	Calculates the shell-side Reynolds number
`conv_heat_transfer_coeff_shell_eqn`	time, length	Calculates the shell-side convective heat transfer coefficient
`v_tube_eqn`	time, length	Calculates gas velocity in tube
`N_Re_tube_eqn`	time, length	Calculates the tube-side Reynolds number
`heat_transfer_coeff_tube_eqn`	time, length	Calculates the tube-side heat transfer coefficient
`N_Nu_shell_eqn`	time, length	Calculate the shell-side Nusselt number
`N_Nu_tube_eqn`	time, length	Calculate the tube-side Nusselt number
`heat_tube_eqn`	time, length	Calculates heat transfer per unit length
`heat_shell_eqn`	time, length	Calculates heat transfer per unit length
`temp_wall_tube_eqn`	time, length	Calculate the wall temperature of the inner tube
`temp_wall_shell_eqn`	time, length	Calculate the wall temperature of the outer tube
`temp_wall_center_eqn`	time, length	Overall energy balance on tube metal

Expression	Index Sets	Doc
`total_heat_transfer_coeff_shell`	time	Returns `conv_heat_transfer_coeff_shell`. Could be extended to include radiation.
`total_heat_duty`	time	Created only if not `dynamic`. Gives total heat transferred over entire exchanger
`log_mean_delta_temperature`	time	Created only if not `dynamic`. Gives the log mean temperature difference (LMTD).
`overall_heat_transfer_coefficient`	time	Created only if not `dynamic`. Calculated from total heat transfer, area, and LMTD.

Pressure Change Equations#

Parameter	Index Sets	Doc
`fcorrection_dp_shell`	None	Correction factor for shell side pressure drop
`kloss_uturn`	None	Loss coefficient of a tube u-turn
`fcorrection_dp_tube`	None	Correction factor for tube side pressure drop

Variable	Index Sets	Doc
`fcorrection_dp_shell`	None	Correction factor for shell side pressure drop
`friction_factor_shell`	time, length	Friction factor on shell side
`friction_factor_tube`	time, length	Friction factor on tube side
`deltaP_tube_friction`	time, length	Change of pressure in tube due to friction
`deltaP_tube_uturn`	time, length	Change of pressure in tube due to U turns

Constraint	Index Sets	Doc
`friction_factor_shell_eqn`	time, length	Calculates the shell-side friction factor
`deltaP_shell_eqn`	time, length	Sets `deltaP_shell` based on the friction factor and shell properties
`friction_factor_tube_eqn`	time, length	Calculates the tube-side friction factor
`deltaP_tube_friction_eqn`	time, length	Sets `deltaP_tube_friction` based on friction factor
`deltaP_tube_uturn_eqn`	time, length	Sets `deltaP_tube_uturn` based on `kloss_uturn`
`deltaP_tube_eqn`	time, length	Sets `deltaP_tube` by summing `deltaP_tube_friction` and `deltaP_tube_uturn`

Holdup Equations#

Created when has_holdup=True in the config.

Variable	Index Sets	Doc
`heat_holdup`	time, length	Energy holdup per unit length of shell flow path

Constraint	Index Sets	Doc
`heat_holdup_eqn`	time, length	Defines heat holdup in terms of geometry and physical properties

Dynamic Equations#

Created when dynamic=True in the config.

Derivative Variable	Index Sets	Doc
`heat_accumulation`	time, length	Energy accumulation in tube wall per unit length of shell flow path per unit time

CrossFlowHeatExchanger1D Class#

class idaes.models_extra.power_generation.unit_models.cross_flow_heat_exchanger_1D.CrossFlowHeatExchanger1D(*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 side config arguments

hot_side

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}

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.}

has_phase_equilibrium
Argument to enable phase equilibrium. - 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.

cold_side
cold side config arguments

cold_side

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}

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.}

has_phase_equilibrium
Argument to enable phase equilibrium. - 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: hot and cold flows from 0 to 1 (default) - HeatExchangerFlowPattern.countercurrent: hot side flows from 0 to 1 cold side flows from 1 to 0

hot_side_name
Hot side name, sets control volume and inlet and outlet names. Default = None.

cold_side_name
Cold side name, sets control volume and inlet and outlet names. Default = None.

shell_is_hot
Boolean flag indicating whether shell side contains hot fluid (default=True). If True, shell side will be the hot_side, if False shell side will be cold_side.

tube_arrangement
tube arrangement could be in-line or staggered
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:

(CrossFlowHeatExchanger1D) New instance

CrossFlowHeatExchanger1DData Class#

class idaes.models_extra.power_generation.unit_models.cross_flow_heat_exchanger_1D.CrossFlowHeatExchanger1DData(component)[source]#

Standard Cross Flow Heat Exchanger Unit Model Class.

build()[source]#

Begin building model (pre-DAE transformation).

Parameters:: None –
Returns:: None

default_initializer#: alias of CrossFlowHeatExchanger1DInitializer

CrossFlowHeatExchanger1DInitializer Class#

class idaes.models_extra.power_generation.unit_models.cross_flow_heat_exchanger_1D.CrossFlowHeatExchanger1DInitializer(**kwargs)[source]#

Initializer for Cross Flow Heat Exchanger 1D units.

First, the shell and tube control volumes are initialized without heat transfer. Next the total possible heat transfer between streams is estimated based on heat capacity, flow rate, and inlet/outlet temperatures. The actual temperature change is set to be half the theoretical maximum, and the shell and tube are initialized with linear temperature profiles. Finally, temperatures besides the inlets are unfixed and the performance equations are activated before a full solve of the system model.

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
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.

initialize_main_model(model, copy_inlet_state=False)[source]#

Initialization routine for the main Cross Flow Heat Exchanger 1D model (as opposed to submodels like costing, which presently do not exist).