fixed_bed_0D.rst

Fixed Bed 0D Reactor

The IDAES Fixed Bed 0D Reactor (FixedBed0D) model represents a unit operation where a gas stream passes through a solid phase bed. The FixedBed0D mathematical model is a 0-D time variant model with two phases (gas and solid). The model captures the gas-solid interaction between both phases through reaction, mass and heat transfer.

Assumptions:

• There is assumed to be no axial or radial variation in solid composition.
• Excess gas flowrate and ideal gas behavior are assumed.
• The reactor is assumed to be isothermal, and the reaction is one-way (no equilibrium).

Requirements:

• Property packages contain temperature and pressure variables.

Degrees of Freedom

FixedBed0D Reactors generally have at least 2 (or more) degrees of freedom, including the reactor bed diameter and height.

Model Structure

The FixedBed0D model assumes a single control volume, and writes a set of material and energy balances for the solid phase. The gas phase conditions are considered to be fixed at the inlet values.

Construction Arguments

The IDAES FixedBed0D model has construction arguments specific to the whole unit and to the individual regions.

Arguments that are applicable to the FixedBed0D unit as a whole are:

• dynamic - indicates whether the model will be dynamic or not, must be True (default = True).
• has_holdup - indicates whether holdup terms are constructed or not, must be True (default = True).
• energy_balance_type - indicates what type of energy balance should be constructed (default = enthalpyTotal):
  • 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

Arguments that are applicable to a specific region:

• gas_property_package - property package to use when calculating properties for the gas phase (default = 'None'). This is provided as a Physical Parameter Block by the Flowsheet when creating the model.
• gas_property_package_args - set of arguments to be passed to the gas phase Property Blocks when they are created (default = 'None').
• solid_property_package - property package to use when calculating properties for the solid phase (default = 'None'). This is provided as a Physical Parameter Block by the Flowsheet when creating the model.
• solid_property_package_args - set of arguments to be passed to the solid phase Property Blocks when they are created (default = 'None').
• reaction_package - reaction package to use when calculating properties for solid phase reaction (default = None). This is provided as a Reaction Parameter Block by the Flowsheet when creating the model.
• reaction_package_args - set of arguments to be passed to the Reaction Blocks when they are created (default = None).

Constraints

In the following, the subscripts g and s refer to the gas and solid phases, respectively. FixedBed0D units write the following Constraints:

Reaction and Mass/Heat Transfer Constraints

Volume of the bed:

V_bed = πL_bed(0.5D_bed)²

Volume of the solid:

V_s, t = V_bed(1 − ϵ_s)

Solid material holdup:

j_{mass, s, t, j} = V_sρ_{mass, s, t}x_{mass, s, t, j}

Solid material accumulation:

j̇_{mass, s, t, j} = V_sMW_s, jΣ_rr_s, t, rν_s, j, r

Total mass of solids:

M_s, t = V_sΣ_jρ_{mass, s, t, j}

Sum of component mass fractions:

$${\Sigma_{j}} {x_{mass,s,t,j}} = 1 \space \space \space \forall \space t$$

if self.config.energy_balance_type != EnergyBalanceType.none:

Solid energy holdup:

q_{energy, s, t} = V_sρ_{mass, s, t}H_{mass, s, t}

Solid energy accumulation:

q̇_{energy, s, t} =  − V_sΣ_rr_s, t, rH_{rxn, s, t, r}

Isothermal solid phase:

T_s, t = T_{s, t = 0}

List of Variables

Variable	Description	Reference to
Dbed	Reactor bed diameter	bed_diameter
Hmass, s, t	Solid phase mass enthalpy	solids.enth_mass
Hrxn, s, t, r	Solid phase reaction enthalpy	solids.reactions.dh_rxn
jmass, s, t, j	Material holdup, solid phase	solids.solids_material_holdup
j̇mass, s, t, j	Material accumulation, solid phase	solids.solids_material_accumulation
Lbed	Reactor bed height	bed_height
Ms, t	Total mass of solids	solids.mass_solids
qenergy, s, t	Energy holdup, solid phase	solids.energy_material_holdup
q̇energy, s, t	Energy accumulation, solid phase	solids.solids_energy_accumulation
rs, t, r	Solid phase reaction rate of reaction r	solids.reactions.reaction_rate
Ts, t	Solid phase temperature	solids.temperature
xmass, s, t, j	Mass fraction of component j, solid phase	solids.mass_frac_comp
Vbed	Total volume of the bed	volume_bed
Vs, t	Total volume of solids	solids.volume_solid
Greek letters
ρmass, s, t	Density of solid particles	solids.dens_mass_particle

List of Parameters

Parameter	Description	Reference to
ϵs	Void fraction of the solid	solids._params.voidage
MWs, j	Molecular weight of solid component j	solids._params.mw_comp
νs, j, r	Stoichiometric coefficients	solids.reaction_package.rate_reaction_stoichiometry

Initialization

The initialization method for this model will save the current state of the model before commencing initialization and reloads it afterwards. The state of the model will be the same after initialization, only the initial guesses for unfixed variables will be changed. For the FixedBed0D model, the initialization method is a general purpose routine for simple unit models where a single control volume is initalized followed by attempting to solve the entire unit.

The model allows for the passing of a dictionary of values of the state variables of the gas and solid phases that can be used as initial guesses for the state variables throughout the time domain of the model. This is optional but recommended. A typical guess could be values of the gas and solid inlet port variables at time t = 0.

The model initialization proceeds through a sequential hierarchical method where the model equations are deactivated at the start of the initialization routine, and the complexity of the model is built up through activation and solution of various sub-model blocks and equations at each initialization step. At each step the model variables are updated to better guesses obtained from the model solution at that step.

The initialization routine proceeds as follows:

• Step 1: Initialize the thermo-physical model blocks.
• Step 2: Initialize the reaction properties.

FixedBed0D Class

idaes.gas_solid_contactors.unit_models.fixed_bed_0D

FixedBed0D

FixedBed0DData Class

FixedBed0DData