Heater1D#

This model is for a gas trim heater modeled as gas being blown perpendicularly across banks of hollow tubes, which are heated by resistive heating. Note that the finite_elements option in the control volume config 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.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 Heater1D
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 = FlowsheetBlock(dynamic=False)
m.fs.h2_side_prop_params = GenericParameterBlock(
    **get_prop(["H2", "H2O", "Ar", "N2"], {"Vap"}, eos=EosType.IDEAL),
    doc="H2O + H2 gas property parameters",
)
m.fs.heater = Heater1D(
    property_package=m.fs.h2_side_prop_params,
    has_holdup=True,
    dynamic=False,
    has_fluid_holdup=False,
    has_pressure_change=pressure_drop,
    finite_elements=4,
    tube_arrangement="in-line",
    transformation_method="dae.finite_difference",
    transformation_scheme="BACKWARD",
)

heater = m.fs.heater

heater.inlet.flow_mol.fix(5102.5)
heater.inlet.temperature.fix(938.83)
heater.inlet.pressure.fix(1.2e5)
heater.inlet.mole_frac_comp[0, "H2"].fix(0.57375)
heater.inlet.mole_frac_comp[0, "H2O"].fix(0.42517)
heater.inlet.mole_frac_comp[0, "Ar"].fix(0.00086358)
heater.inlet.mole_frac_comp[0, "N2"].fix(0.00021589)

heater.di_tube.fix(0.0525018)
heater.thickness_tube.fix(0.0039116)
heater.pitch_x.fix(0.1)
heater.pitch_y.fix(0.1)
heater.length_tube_seg.fix(10)
heater.number_passes.fix(1)
heater.rfouling = 0.0001
heater.fcorrection_htc_shell.fix(1)
heater.cp_wall = 502.4
if pressure_drop:
    heater.fcorrection_dp_shell.fix(1)

heater.number_columns_per_pass.fix(40)
heater.number_rows_per_pass.fix(40)
heater.electric_heat_duty.fix(3.6504e06)

pp = m.fs.h2_side_prop_params
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 = heater.control_volume
iscale.set_scaling_factor(shell.area, 1e-1)
iscale.set_scaling_factor(shell.heat, 1e-6)
iscale.set_scaling_factor(shell.enthalpy_flow_dx, 1e-7)
iscale.set_scaling_factor(heater.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)

Heater 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 flow, measured from center-of-tube to center-of-tube
`pitch_y`	None	Distance between tubes perpendicular to 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 control volume
`length_flow_shell`	None	Reference to flow length on 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.

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 flow length from control volume to equal value implied by geometry
`area_flow_shell_eqn`	None	Constrains 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

Performance Equations#

Variable	Index Sets	Doc
`electric_heat_duty`	time	Electric heat duty supplied to entire heater unit
`fcorrection_htc_shell`	time, length	Correction factor for convective heat transfer
`conv_heat_transfer_coeff_shell`	time, length	Convective heat transfer coefficient
`temp_wall_shell`	time, length	Wall temperature of tube
`temp_wall_center`	time, length	Temperature at center of tube wall
`v_shell`	time, length	Flow velocity through minimum area
`N_Re_shell`	time, length	Reynolds number
`N_Nu_shell`	time, length	Nusselt number

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 Reynolds number
`conv_heat_transfer_coeff_shell_eqn`	time, length	Calculates the convective heat transfer coefficient
`N_Nu_shell_eqn`	time, length	Calculate the Nusselt number
`heat_shell_eqn`	time, length	Calculates heat transfer per unit length
`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.

Pressure Change Equations#

Parameter	Index Sets	Doc
`fcorrection_dp_shell`	None	Correction factor for pressure drop

Variable	Index Sets	Doc
`fcorrection_dp_shell`	None	Correction factor for pressure drop
`friction_factor_shell`	time, length	Friction factor

Constraint	Index Sets	Doc
`friction_factor_shell_eqn`	time, length	Calculates the friction factor
`deltaP_shell_eqn`	time, length	Sets `deltaP_shell` based on the friction factor and physical properties

Holdup Equations#

Created when has_holdup=True in the config.

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

Initialization#

A simple initialization method that first initializes the control volume without heat transfer, then adds heat transfer in and solves it again, then finally solves the entire model.

Heater1D Class#

class idaes.models_extra.power_generation.unit_models.heater_1D.Heater1D(*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}

has_fluid_holdup
Indicates whether holdup terms for the fluid should be constructed or not. default - False. Valid values: { 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.}

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 transforming domain. See Pyomo documentation for supported schemes.

finite_elements
Number of finite elements to use when discretizing length domain (default=5). Should set to the number of tube rows

collocation_points
If using collocation, number of collocation points to use per finite element when discretizing length domain (default=3)

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:

(Heater1D) New instance

Heater1DData Class#

class idaes.models_extra.power_generation.unit_models.heater_1D.Heater1DData(component)[source]#

Standard Trim Heater Model Class Class.

build()[source]#

Begin building model (pre-DAE transformation).

Parameters:: None
Returns:: None

default_initializer#: alias of Heater1DInitializer

Heater1DInitializer Class#

class idaes.models_extra.power_generation.unit_models.heater_1D.Heater1DInitializer(**kwargs)[source]#

Initializer for Heater 1D units.