1D Control Volume Class¶
The ControlVolume1DBlock block is used for systems with one spatial dimension where material flows parallel to the spatial domain. Examples of these types of unit operations include plug flow reactors and pipes. ControlVolume1DBlock blocks are discretized along the length domain and contain one StateBlock and one ReactionBlock (if applicable) at each point in the domain (including the inlet and outlet).

class
idaes.core.control_volume1d.
ControlVolume1DBlock
(*args, **kwargs)¶ ControlVolume1DBlock is a specialized Pyomo block for IDAES control volume blocks discretized in one spatial direction, and contains instances of ControlVolume1DBlockData.
ControlVolume1DBlock should be used for any control volume with a defined volume and distinct inlets and outlets where there is a single spatial domain parallel to the material flow direction. This encompases unit operations such as plug flow reactors and pipes.
Parameters:  rule (function) – A rule function or None. Default rule calls build().
 concrete (bool) – If True, make this a toplevel model. Default  False.
 ctype (str) – Pyomo ctype of the block. Default  “Block”
 default (dict) –
Default ProcessBlockData config
 Keys
 dynamic
 Indicates whether this model will be dynamic, default  useDefault. Valid values: { useDefault  get flag from parent, True  set as a dynamic model, False  set as a steadystate model}
 has_holdup
 Indicates whether holdup terms should be constructed or not. Must be True if dynamic = True, default  False. Valid values: { True  construct holdup terms, False  do not construct holdup terms}
 property_package
 Property parameter object used to define property calculations, default  useDefault. Valid values: { useDefault  use default package from parent model or flowsheet, PropertyParameterObject  a PropertyParameterBlock 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.}
 auto_construct
 If set to True, this argument will trigger the auto_construct method which will attempt to construct a set of material, energy and momentum balance equations based on the parent unit’s config block. The parent unit must have a config block which derives from CONFIG_Base, default  False. Valid values: { True  use automatic construction, False  do not use automatic construciton.}
 area_definition
 Argument defining whether area variable should be spatially variant or not. default  DistributedVars.uniform. Valid values: { DistributedVars.uniform  area does not vary across spatial domian, DistributedVars.variant  area can vary over the domain and is indexed by time and space.}
 transformation_method
 Method to use to transform domain. Must be a method recognised by the Pyomo TransformationFactory.
 transformation_scheme
 Scheme to use when transformating domain. See Pyomo documentation for supported schemes.
 finite_elements
 Number of finite elements to use in transformation (equivalent to Pyomo nfe argument).
 collocation_points
 Number of collocation points to use (equivalent to Pyomo ncp argument).
 initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries described under the “default” argument above.
 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 overide the default behavior of matching the BlockData index exactly to the index in initialize.
Returns: (ControlVolume1DBlock) New instance

class
idaes.core.control_volume1d.
ControlVolume1DBlockData
(component)[source]¶ 1Dimensional ControlVolume Class
This class forms the core of all 1D IDAES models. It provides methods to build property and reaction blocks, and add mass, energy and momentum balances. The form of the terms used in these constraints is specified in the chosen property package.

add_geometry
(length_domain=None, length_domain_set=[0.0, 1.0], flow_direction=<FlowDirection.forward: 1>)[source]¶ Method to create spatial domain and volume Var in ControlVolume.
Parameters:   (length_domain_set) – domain for the ControlVolume. If not provided, a new ContinuousSet will be created (default=None). ContinuousSet should be normalized to run between 0 and 1.
  – a new ContinuousSet if length_domain is not provided (default = [0.0, 1.0]).
  argument indicating direction of material flow (flow_direction) –
 relative to length domain. Valid values:
 FlowDirection.forward (default), flow goes from 0 to 1.
 FlowDirection.backward, flow goes from 1 to 0
Returns: None

add_phase_component_balances
(has_rate_reactions=False, has_equilibrium_reactions=False, has_phase_equilibrium=False, has_mass_transfer=False, custom_molar_term=None, custom_mass_term=None)[source]¶ This method constructs a set of 1D material balances indexed by time, length, phase and component.
Parameters:  has_rate_reactions – whether default generation terms for rate reactions should be included in material balances
 has_equilibrium_reactions – whether generation terms should for chemical equilibrium reactions should be included in material balances
 has_phase_equilibrium – whether generation terms should for phase equilibrium behaviour should be included in material balances
 has_mass_transfer – whether generic mass transfer terms should be included in material balances
 custom_molar_term – a Pyomo Expression representing custom terms to be included in material balances on a molar basis. Expression must be indexed by time, length domain, phase list and component list
 custom_mass_term – a Pyomo Expression representing custom terms to be included in material balances on a mass basis. Expression must be indexed by time, length domain, phase list and component list
Returns: Constraint object representing material balances

add_phase_energy_balances
(*args, **kwargs)[source]¶ Method for adding energy balances (including kinetic energy) indexed by phase to the control volume.
See specific control volume documentation for details.

add_phase_enthalpy_balances
(*args, **kwargs)[source]¶ Method for adding enthalpy balances indexed by phase to the control volume.
See specific control volume documentation for details.

add_phase_momentum_balances
(*args, **kwargs)[source]¶ Method for adding momentum balances indexed by phase to the control volume.
See specific control volume documentation for details.

add_phase_pressure_balances
(*args, **kwargs)[source]¶ Method for adding pressure balances indexed by phase to the control volume.
See specific control volume documentation for details.

add_reaction_blocks
(has_equilibrium=None)[source]¶ This method constructs the reaction block for the control volume.
Parameters:  has_equilibrium – indicates whether equilibrium calculations will be required in reaction block
 package_arguments – dictlike object of arguments to be passed to reaction block as construction arguments
Returns: None

add_state_blocks
(information_flow=<FlowDirection.forward: 1>, has_phase_equilibrium=None)[source]¶ This method constructs the state blocks for the control volume.
Parameters:  information_flow – a FlowDirection Enum indicating whether information flows from inlettooutlet or outlettoinlet
 has_phase_equilibrium – indicates whether equilibrium calculations will be required in state blocks
 package_arguments – dictlike object of arguments to be passed to state blocks as construction arguments
Returns: None

add_total_component_balances
(has_rate_reactions=False, has_equilibrium_reactions=False, has_phase_equilibrium=False, has_mass_transfer=False, custom_molar_term=None, custom_mass_term=None)[source]¶ This method constructs a set of 1D material balances indexed by time length and component.
Parameters:  has_rate_reactions – whether default generation terms for rate reactions should be included in material balances
 has_equilibrium_reactions – whether generation terms should for chemical equilibrium reactions should be included in material balances
 has_phase_equilibrium – whether generation terms should for phase equilibrium behaviour should be included in material balances
 has_mass_transfer – whether generic mass transfer terms should be included in material balances
 custom_molar_term – a Pyomo Expression representing custom terms to be included in material balances on a molar basis. Expression must be indexed by time, length domain and component list
 custom_mass_term – a Pyomo Expression representing custom terms to be included in material balances on a mass basis. Expression must be indexed by time, length domain and component list
Returns: Constraint object representing material balances

add_total_element_balances
(has_rate_reactions=False, has_equilibrium_reactions=False, has_phase_equilibrium=False, has_mass_transfer=False, custom_elemental_term=None)[source]¶ This method constructs a set of 1D element balances indexed by time and length.
Parameters:   whether default generation terms for rate (has_rate_reactions) – reactions should be included in material balances
  whether generation terms should for (has_equilibrium_reactions) – chemical equilibrium reactions should be included in material balances
  whether generation terms should for phase (has_phase_equilibrium) – equilibrium behaviour should be included in material balances
  whether generic mass transfer terms should be (has_mass_transfer) – included in material balances
  a Pyomo Expression representing custom (custom_elemental_term) – terms to be included in material balances on a molar elemental basis. Expression must be indexed by time, length and element list
Returns: Constraint object representing material balances

add_total_energy_balances
(*args, **kwargs)[source]¶ Method for adding a total energy balance (including kinetic energy) to the control volume.
See specific control volume documentation for details.

add_total_enthalpy_balances
(has_heat_of_reaction=False, has_heat_transfer=False, has_work_transfer=False, has_enthalpy_transfer=False, custom_term=None)[source]¶ This method constructs a set of 1D enthalpy balances indexed by time and phase.
Parameters:   whether terms for heat of reaction should (has_heat_of_reaction) – be included in enthalpy balance
  whether terms for heat transfer should be (has_heat_transfer) – included in enthalpy balances
  whether terms for work transfer should be (has_work_transfer) – included in enthalpy balances
  whether terms for enthalpy transfer due to (has_enthalpy_transfer) – mass transfer should be included in enthalpy balance. This should generally be the same as the has_mas_trasnfer argument in the material balance methods
  a Pyomo Expression representing custom terms to (custom_term) – be included in enthalpy balances. Expression must be indexed by time, length and phase list
Returns: Constraint object representing enthalpy balances

add_total_material_balances
(*args, **kwargs)[source]¶ Method for adding a total material balance to the control volume.
See specific control volume documentation for details.

add_total_momentum_balances
(*args, **kwargs)[source]¶ Method for adding a total momentum balance to the control volume.
See specific control volume documentation for details.

add_total_pressure_balances
(has_pressure_change=False, custom_term=None)[source]¶ This method constructs a set of 1D pressure balances indexed by time.
Parameters:   whether terms for pressure change should be (has_pressure_change) – included in enthalpy balances
  a Pyomo Expression representing custom terms to (custom_term) – be included in pressure balances. Expression must be indexed by time and length domain
Returns: Constraint object representing pressure balances

apply_transformation
()[source]¶ Method to apply DAE transformation to the Control Volume length domain. Transformation applied will be based on the Control Volume configuration arguments.

initialize
(state_args=None, outlvl=0, optarg=None, solver='ipopt', hold_state=True)[source]¶ Initialization routine for 1D control volume (default solver ipopt)
Keyword Arguments:  state_args – a dict of arguments to be passed to the property package(s) to provide an initial state for initialization (see documentation of the specific property package) (default = {}).
 outlvl – sets output level of initialization routine
 optarg – solver options dictionary object (default=None)
 solver – str indicating whcih solver to use during initialization (default = ‘ipopt’)
 hold_state – flag indicating whether the initialization routine should unfix any state variables fixed during initialization, default  True. Valid values: True  states variables are not unfixed, and a dict of returned containing flags for which states were fixed during initialization, False  state variables are unfixed after initialization by calling the release_state method.
Returns: If hold_states is True, returns a dict containing flags for which states were fixed during initialization else the release state is triggered.

model_check
()[source]¶ This method executes the model_check methods on the associated state blocks (if they exist). This method is generally called by a unit model as part of the unit’s model_check method.
Parameters: None – Returns: None

release_state
(flags, outlvl=0)[source]¶ Method to release state variables fixed during initialization.
Keyword Arguments:  flags – dict containing information of which state variables were fixed during initialization, and should now be unfixed. This dict is returned by initialize if hold_state = True.
 outlvl – sets output level of logging
Returns: None

ControlVolume1DBlock Equations¶
This section documents the variables and constraints created by each of the methods provided by the ControlVolume0DBlock class.
 \(t\) indicates time index
 \(x\) indicates spatial (length) index
 \(p\) indicates phase index
 \(j\) indicates component index
 \(e\) indicates element index
 \(r\) indicates reaction name index
Most terms within the balance equations written by ControlVolume1DBlock are on a basis of per unit length (e.g. \(mol/m \cdot s\)).
add_geometry¶
The add_geometry method creates the normalized length domain for the control volume (or a reference to an external domain). All constraints in ControlVolume1DBlock assume a normalized length domain, with values between 0 and 1.
This method also adds variables and constraints to describe the geometry of the control volume. ControlVolume1DBlock does not support varying dimensions of the control volume with time at this stage.
Variables
Variable Name  Symbol  Indices  Conditions 

length_domain  \(x\)  None  None 
volume  \(V\)  None  None 
area  \(A\)  None  None 
length  \(L\)  None  None 
Constraints
geometry_constraint:
add_phase_component_balances¶
Material balances are written for each component in each phase (e.g. separate balances for liquid water and steam). Physical property packages may include information to indicate that certain species do not appear in all phases, and material balances will not be written in these cases (if has_holdup is True holdup terms will still appear for these species, however these will be set to 0).
Variables
Variable Name  Symbol  Indices  Conditions 

material_holdup  \(M_{t,x,p,j}\)  t, x, p, j  has_holdup = True 
phase_fraction  \(\phi_{t,x,p}\)  t, x, p  has_holdup = True 
material_accumulation  \(\frac{\partial M_{t,x,p,j}}{\partial t}\)  t, x, p, j  dynamic = True 
_flow_terms  \(F_{t, x, p, j}\)  t, x, p, j  None 
material_flow_dx  \(\frac{\partial F_{t,x,p,j}}{\partial x}\)  t, x, p, j  None 
rate_reaction_generation  \(N_{kinetic,t,x,p,j}\)  t, x, p ,j  has_rate_reactions = True 
rate_reaction_extent  \(X_{kinetic,t,x,r}\)  t, x, r  has_rate_reactions = True 
equilibrium_reaction_generation  \(N_{equilibrium,t,x,p,j}\)  t, x, p ,j  has_equilibrium_reactions = True 
equilibrium_reaction_extent  \(X_{equilibrium,t,x,r}\)  t, x, r  has_equilibrium_reactions = True 
phase_equilibrium_generation  \(N_{pe,t,x,p,j}\)  t, x, p ,j  has_phase_equilibrium = True 
mass_transfer_term  \(N_{transfer,t,x,p,j}\)  t, x, p ,j  has_mass_transfer = True 
Constraints
material_balances(t, x, p, j):
\(fd\) is a flow direction term, which allows for material flow to be defined in either direction. If material flow is defined as forward, \(fd = 1\), otherwise \(fd = 1\).
The \(N_{custom, t, x, p, j}\) term allows the user to provide custom terms (variables or expressions) in both mass and molar basis which will be added into the material balances, which will be converted as necessary to the same basis as the material balance (by multiplying or dividing by the component molecular weight). The basis of the material balance is determined by the physical property package, and if undefined (or not mass or mole basis), an Exception will be returned.
material_flow_linking_constraints(t, x, p, j):
This constraint is an internal constraint used to link the extensive material flow terms in the StateBlocks into a single indexed variable. This is required as Pyomo.DAE requires a single indexed variable to create the associated DerivativeVars and their numerical expansions.
If has_holdup is True, material_holdup_calculation(t, x, p, j):
where \(\rho_{t, x, p ,j}\) is the density of component \(j\) in phase \(p\) at time \(t\) and location \(x\).
If dynamic is True:
Numerical discretization of the derivative terms, \(\frac{\partial M_{t,x,p,j}}{\partial t}\), will be performed by Pyomo.DAE.
If has_rate_reactions is True, rate_reaction_stoichiometry_constraint(t, x, p, j):
where \(\alpha_{r, p. j}\) is the stoichiometric coefficient of component \(j\) in phase \(p\) for reaction \(r\) (as defined in the PhysicalParameterBlock).
If has_equilibrium_reactions argument is True, equilibrium_reaction_stoichiometry_constraint(t, x, p, j):
where \(\alpha_{r, p. j}\) is the stoichiometric coefficient of component \(j\) in phase \(p\) for reaction \(r\) (as defined in the PhysicalParameterBlock).
add_total_component_balances¶
Material balances are written for each component across all phases (e.g. one balance for both liquid water and steam). Physical property packages may include information to indicate that certain species do not appear in all phases, and material balances will not be written in these cases (if has_holdup is True holdup terms will still appear for these species, however these will be set to 0).
Variables
Variable Name  Symbol  Indices  Conditions 

material_holdup  \(M_{t,x,p,j}\)  t, x, p, j  has_holdup = True 
phase_fraction  \(\phi_{t,x,p}\)  t, x, p  has_holdup = True 
material_accumulation  \(\frac{\partial M_{t,x,p,j}}{\partial t}\)  t, x, p, j  dynamic = True 
_flow_terms  \(F_{t, x, p, j}\)  t, x, p, j  None 
material_flow_dx  \(\frac{\partial F_{t,x,p,j}}{\partial x}\)  t, x, p, j  None 
rate_reaction_generation  \(N_{kinetic,t,x,p,j}\)  t, x, p ,j  has_rate_reactions = True 
rate_reaction_extent  \(X_{kinetic,t,x,r}\)  t, x, r  has_rate_reactions = True 
equilibrium_reaction_generation  \(N_{equilibrium,t,x,p,j}\)  t, x, p ,j  has_equilibrium_reactions = True 
equilibrium_reaction_extent  \(X_{equilibrium,t,x,r}\)  t, x, r  has_equilibrium_reactions = True 
mass_transfer_term  \(N_{transfer,t,x,p,j}\)  t, x, p ,j  has_mass_transfer = True 
Constraints
material_balances(t, x, p, j):
\(fd\) is a flow direction term, which allows for material flow to be defined in either direction. If material flow is defined as forward, \(fd = 1\), otherwise \(fd = 1\).
The \(N_{custom, t, x, j}\) term allows the user to provide custom terms (variables or expressions) in both mass and molar basis which will be added into the material balances, which will be converted as necessary to the same basis as the material balance (by multiplying or dividing by the component molecular weight). The basis of the material balance is determined by the physical property package, and if undefined (or not mass or mole basis), an Exception will be returned.
material_flow_linking_constraints(t, x, p, j):
This constraint is an internal constraint used to link the extensive material flow terms in the StateBlocks into a single indexed variable. This is required as Pyomo.DAE requires a single indexed variable to create the associated DerivativeVars and their numerical expansions.
If has_holdup is True, material_holdup_calculation(t, x, p, j):
where \(\rho_{t, x, p ,j}\) is the density of component \(j\) in phase \(p\) at time \(t\) and location \(x\).
If dynamic is True:
Numerical discretization of the derivative terms, \(\frac{\partial M_{t,x,p,j}}{\partial t}\), will be performed by Pyomo.DAE.
If has_rate_reactions is True, rate_reaction_stoichiometry_constraint(t, x, p, j):
where \(\alpha_{r, p. j}\) is the stoichiometric coefficient of component \(j\) in phase \(p\) for reaction \(r\) (as defined in the PhysicalParameterBlock).
If has_equilibrium_reactions argument is True, equilibrium_reaction_stoichiometry_constraint(t, x, p, j):
where \(\alpha_{r, p. j}\) is the stoichiometric coefficient of component \(j\) in phase \(p\) for reaction \(r\) (as defined in the PhysicalParameterBlock).
add_total_element_balances¶
Material balances are written for each element in the mixture.
Variables
Variable Name  Symbol  Indices  Conditions 

element_holdup  \(M_{t,x,e}\)  t, x, e  has_holdup = True 
phase_fraction  \(\phi_{t,x,p}\)  t, x, p  has_holdup = True 
element_accumulation  \(\frac{\partial M_{t,x,e}}{\partial t}\)  t, x, e  dynamic = True 
elemental_mass_transfer_term  \(N_{transfer,t,x,e}\)  t, x, e  has_mass_transfer = True 
elemental_flow_term  \(F_{t,x,e}\)  t, x, e  None 
Constraints
elemental_flow_constraint(t, x, e):
where \(n_{j, e}\) is the number of moles of element \(e\) in component \(j\).
element_balances(t, x, e):
\(fd\) is a flow direction term, which allows for material flow to be defined in either direction. If material flow is defined as forward, \(fd = 1\), otherwise \(fd = 1\).
The \(N_{custom, t, x, e}\) term allows the user to provide custom terms (variables or expressions) which will be added into the material balances.
If has_holdup is True, elemental_holdup_calculation(t, x, e):
where \(\rho_{t, x, p ,j}\) is the density of component \(j\) in phase \(p\) at time \(t\) and location \(x\).
If dynamic is True:
Numerical discretization of the derivative terms, \(\frac{\partial M_{t,x,p,j}}{\partial t}\), will be performed by Pyomo.DAE.
add_total_enthalpy_balances¶
A single enthalpy balance is written for the entire mixture at each point in the spatial domain.
Variables
Variable Name  Symbol  Indices  Conditions 

energy_holdup  \(E_{t,x,p}\)  t, x, p  has_holdup = True 
phase_fraction  \(\phi_{t,x,p}\)  t, x, p  has_holdup = True 
energy_accumulation  \(\frac{\partial E_{t,x,p}}{\partial t}\)  t, x, p  dynamic = True 
_enthalpy_flow  \(H_{t,x,p}\)  t, x, p  None 
enthalpy_flow_dx  \(\frac{\partial H_{t,x,p}}{\partial x}\)  t, x, p  None 
heat  \(Q_{t,x}\)  t, x  has_heat_transfer = True 
work  \(W_{t,x}\)  t, x  has_work_transfer = True 
enthalpy_transfer  \(H_{transfer,t,x}\)  t, x  has_enthalpy_transfer = True 
Expressions
heat_of_reaction(t, x):
where \(Q_{rxn, t, x}\) is the total enthalpy released by both kinetic and equilibrium reactions, and \(\Delta H_{rxn, r}\) is the specific heat of reaction for reaction \(r\).
Parameters
Parameter Name  Symbol  Default Value 

scaling_factor_energy  \(s_{energy}\)  1E6 
Constraints
enthalpy_balance(t):
\(fd\) is a flow direction term, which allows for material flow to be defined in either direction. If material flow is defined as forward, \(fd = 1\), otherwise \(fd = 1\).
The \(E_{custom, t, x}\) term allows the user to provide custom terms which will be added into the energy balance.
enthalpy_flow_linking_constraints(t, x, p):
This constraint is an internal constraint used to link the extensive enthalpy flow terms in the StateBlocks into a single indexed variable. This is required as Pyomo.DAE requires a single indexed variable to create the associated DerivativeVars and their numerical expansions.
If has_holdup is True, enthalpy_holdup_calculation(t, x, p):
where \(u_{t, x, p}\) is the internal density (specific internal energy) of phase \(p\) at time \(t\) and location \(x\).
If dynamic is True:
Numerical discretization of the derivative terms, \(\frac{\partial E_{t,x,p}}{\partial t}\), will be performed by Pyomo.DAE.
add_total_pressure_balances¶
A single pressure balance is written for the entire mixture at all points in the spatial domain.
Variables
Variable Name  Symbol  Indices  Conditions 

pressure  \(P_{t,x}\)  t, x  None 
pressure_dx  \(\frac{\partial P_{t,x}}{\partial x}\)  t, x  None 
deltaP  \(\Delta P_{t,x}\)  t, x  has_pressure_change = True 
Parameters
Parameter Name  Symbol  Default Value 

scaling_factor_pressure  \(s_{pressure}\)  1E4 
Constraints
pressure_balance(t, x):
\(fd\) is a flow direction term, which allows for material flow to be defined in either direction. If material flow is defined as forward, \(fd = 1\), otherwise \(fd = 1\).
The \(\Delta P_{custom, t, x}\) term allows the user to provide custom terms which will be added into the pressure balance.
pressure_linking_constraint(t, x):
This constraint is an internal constraint used to link the pressure terms in the StateBlocks into a single indexed variable. This is required as Pyomo.DAE requires a single indexed variable to create the associated DerivativeVars and their numerical expansions.