Continuously Stirred Tank Reactor with Injection

This CSTR with injection unit model is based on the IDAES CSTR with the addition of mass transfer terms. The model makes the following assumptions:

• is 0-dimensional

• supports a single liquid phase only

• supports steady-state only

Degrees of Freedom

Aside from the inlet feed state variables (i.e. temperature, pressure, component flowrates), the CSTR with injection model has two degree of freedoms, and additional degrees of freedom may need to be specified depending on the configuration options.

• volume OR hydraulic retention time

• injection rates for all components

If heat transfer is included:

• heat duty

If pressure change is included:

• change in pressure (ΔP)

If aeration is included, the following degrees of freedom could replace the oxygen injection rate:

• lumped mass transfer coefficient for oxygen (KLa)

• dissolved oxygen concentration at equilibrium (\(S_{O, eq}\))

Model Structure

The CSTR with injection unit model consists of a single ControlVolume0D (named control_volume) with one inlet port (named inlet) and one outlet port (named outlet).

Sets

Description	Symbol	Indices
Time	\(t\)	[0]
Inlet/outlet	\(x\)	[‘in’, ‘out’]
Phases	\(p\)	[‘Liq’]
Components	\(j\)	[‘H2O’, ‘NaCl’]*

*Solute depends on the imported property model; example shown here is for the NaCl property model.

Variables

Description	Symbol	Variable Name	Index	Units
Hydraulic retention time	\(HRT\)	hydraulic_retention_time	[t]	\(\text{s}\)
Dissolved oxygen concentration at equilibrium	\(S_{O, eq}\)	S_O_eq	None	\(\text{kg/}\text{m}^3\)
Component injection	\(I\)	injection	[t, p, j]	\(\text{kg/hr}\)
Electricity intensity	\(E_{I}\)	energy_electric_flow_vol_inlet	None	\(\text{kWh/}\text{m}^3\)

Equations and Relationships

Description	Equation
CSTR retention time	\(HRT = V / Q_{in}\)
Oxygen mass transfer	\(I_{O} = KLa * V * (S_{O, eq} - C_{O})\)
Electricity consumption (without aeration)	\(E = E_{I} * Q_{in}\)
Electricity consumption (with aeration)	\(E = \frac{S_{O, eq}}{1.8} * V * KLa\)

Class Documentation

class watertap.unit_models.cstr_injection.CSTR_Injection(*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}

  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_heat_transfer

  Indicates whether terms for heat transfer should be constructed, default - False. Valid values: { True - include heat transfer terms, False - exclude heat transfer terms.}

  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_equilibrium_reactions

  Indicates whether terms for equilibrium controlled reactions should be constructed, default - True. Valid values: { True - include equilibrium reaction terms, False - exclude equilibrium reaction terms.}

  has_phase_equilibrium

  Indicates whether terms for phase equilibrium should be constructed, default = False. Valid values: { True - include phase equilibrium terms False - exclude phase equilibrium terms.}

  has_heat_of_reaction

  Indicates whether terms for heat of reaction terms should be constructed, default - False. Valid values: { True - include heat of reaction terms, False - exclude heat of reaction terms.}

  property_package

  Property parameter object used to define property calculations, default - useDefault. Valid values: { useDefault - use default package from parent model or flowsheet, PhysicalParameterObject - a PhysicalParameterBlock object.}

  property_package_args

  A ConfigBlock with arguments to be passed to a property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}

  reaction_package

  Reaction parameter object used to define reaction calculations, default - None. Valid values: { None - no reaction package, ReactionParameterBlock - a ReactionParameterBlock object.}

  reaction_package_args

  A ConfigBlock with arguments to be passed to a reaction block(s) and used when constructing these, default - None. Valid values: { see reaction package for documentation.}

  electricity_consumption

  Indicates whether electricity consumption is fixed by the user or excluded default - ElectricityConsumption.none. Valid values: { ElectricityConsumption.none - no electricity consumption within the unit, ElectricityConsumption.fixed - calculate electricity consumption based on assumed electricity intensity in kWh/m3, ElectricityConsumption.aeration_calculation - calculate electricity consumption based on aeration energy}

  has_aeration

  Indicates whether terms for aeration terms should be expected, default - False. Valid values: { True - include aeration terms, False - exclude aeration terms.}

• 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:

(CSTR_Injection) New instance