Heater1D ======== .. index:: pair: idaes.models_extra.power_generation.unit_models.heater_1D;Heater1D .. module:: idaes.models_extra.power_generation.unit_models.heater_1D 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 ------- .. code-block:: python 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 -------------- .. autoclass:: Heater1D :members: Heater1DData Class ------------------ .. autoclass:: Heater1DData :members: Heater1DInitializer Class ------------------------- .. autoclass:: Heater1DInitializer :members: