# 0D Control Volume Class¶

The ControlVolume0DBlock block is the most commonly used Control Volume class, and is used for systems where there is a well-mixed volume of fluid, or where variations in spatial domains are considered to be negligible. ControlVolume0DBlock blocks generally contain two StateBlocks - one for the incoming material and one for the material within and leaving the volume - and one StateBlocks.

class idaes.core.control_volume0d.ControlVolume0DBlock(*args, **kwds)

ControlVolume0DBlock is a specialized Pyomo block for IDAES non-discretized control volume blocks, and contains instances of ControlVolume0DBlockData.

ControlVolume0DBlock should be used for any control volume with a defined volume and distinct inlets and outlets which does not require spatial discretization. This encompases most basic unit models used in process modeling.

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

• 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 steady-state 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.}

• 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

(ControlVolume0DBlock) New instance

class idaes.core.control_volume0d.ControlVolume0DBlockData(component)[source]

0-Dimensional (Non-Discretised) ControlVolume Class

This class forms the core of all non-discretized 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.

Method to create volume Var in ControlVolume.

Parameters

None

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 0D material balances indexed by time, 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, 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, phase list and component list

Returns

Constraint object representing material balances

Method for adding energy balances (including kinetic energy) indexed by phase to the control volume.

See specific control volume documentation for details.

Method for adding enthalpy balances indexed by phase to the control volume.

See specific control volume documentation for details.

Method for adding momentum balances indexed by phase to the control volume.

See specific control volume documentation for details.

Method for adding pressure balances indexed by phase to the control volume.

See specific control volume documentation for details.

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 – dict-like object of arguments to be passed to reaction block as construction arguments

Returns

None

This method constructs the inlet and outlet state blocks for the control volume.

Parameters
• information_flow – a FlowDirection Enum indicating whether information flows from inlet-to-outlet or outlet-to-inlet

• has_phase_equilibrium – indicates whether equilibrium calculations will be required in state blocks

• package_arguments – dict-like 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 0D material balances indexed by time and component.

Parameters
• rate (has_rate_reactions - whether default generation terms for) – reactions should be included in material balances

• for (has_equilibrium_reactions - whether generation terms should) – chemical equilibrium reactions should be included in material balances

• phase (has_phase_equilibrium - whether generation terms should for) – equilibrium behaviour should be included in material balances

• be (has_mass_transfer - whether generic mass transfer terms should) – included in material balances

• to (custom_mass_term - a Pyomo Expression representing custom terms) – be included in material balances on a molar basis. Expression must be indexed by time, phase list and component list

• to – be included in material balances on a mass basis. Expression must be indexed by time, phase list and component list

Returns

Constraint object representing material balances

This method constructs a set of 0D element balances indexed by time.

Parameters
• rate (has_rate_reactions - whether default generation terms for) – reactions should be included in material balances

• for (has_equilibrium_reactions - whether generation terms should) – chemical equilibrium reactions should be included in material balances

• phase (has_phase_equilibrium - whether generation terms should for) – equilibrium behaviour should be included in material balances

• be (has_mass_transfer - whether generic mass transfer terms should) – included in material balances

• custom (custom_elemental_term - a Pyomo Expression representing) – terms to be included in material balances on a molar elemental basis. Expression must be indexed by time and element list

Returns

Constraint object representing material balances

Method for adding a total energy balance (including kinetic energy) to the control volume.

See specific control volume documentation for details.

This method constructs a set of 0D enthalpy balances indexed by time and phase.

Parameters
• should (has_heat_of_reaction - whether terms for heat of reaction) – be included in enthalpy balance

• be (has_work_transfer - whether terms for work transfer should) – included in enthalpy balances

• be – included in enthalpy balances

• to (has_enthalpy_transfer - whether terms for enthalpy transfer due) – mass transfer should be included in enthalpy balance. This should generally be the same as the has_mass_transfer argument in the material balance methods

• representing (custom_term - a Python method which returns Pyomo expressions) – custom terms to be included in enthalpy balances. Method should accept time and phase list as arguments.

Returns

Constraint object representing enthalpy balances

Method for adding a total material balance to the control volume.

See specific control volume documentation for details.

Method for adding a total momentum balance to the control volume.

See specific control volume documentation for details.

This method constructs a set of 0D pressure balances indexed by time.

Parameters
• be (has_pressure_change - whether terms for pressure change should) – included in enthalpy balances

• representing (custom_term - a Python method which returns Pyomo expressions) – custom terms to be included in enthalpy balances. Method should accept time as an arguments.

Returns

Constraint object representing pressure balances

build()[source]

Build method for ControlVolume0DBlock blocks.

Returns

None

initialize(state_args=None, outlvl=0, optarg=None, solver=None, hold_state=True)[source]

Initialization routine for 0D control volume.

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 log level of initialization routine

• optarg – solver options dictionary object (default=None, use default solver options)

• solver – str indicating which solver to use during initialization (default = None)

• 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.

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

## ControlVolume0DBlock Equations¶

This section documents the variables and constraints created by each of the methods provided by the ControlVolume0DBlock class.

• $$t$$ indicates time index

• $$p$$ indicates phase index

• $$j$$ indicates component index

• $$e$$ indicates element index

• $$r$$ indicates reaction name index

The add_geometry method creates a single variable within the control volume named volume indexed by time (allowing for varying volume over time). A number of other methods depend on this variable being present, thus this method should generally be called first.

Variables

Variable Name

Symbol

Indices

Conditions

volume

$$V_t$$

t

None

Constraints

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

$$M_{t,p,j}$$

t, p, j

has_holdup = True

phase_fraction

$$\phi_{t,p}$$

t, p

has_holdup = True

material_accumulation

$$\frac{\partial M_{t,p,j}}{\partial t}$$

t, p, j

dynamic = True

rate_reaction_generation

$$N_{kinetic,t,p,j}$$

t, p ,j

has_rate_reactions = True

rate_reaction_extent

$$X_{kinetic,t,r}$$

t, r

has_rate_reactions = True

equilibrium_reaction_generation

$$N_{equilibrium,t,p,j}$$

t, p ,j

has_equilibrium_reactions = True

equilibrium_reaction_extent

$$X_{equilibrium,t,r}$$

t, r

has_equilibrium_reactions = True

phase_equilibrium_generation

$$N_{pe,t,p,j}$$

t, p ,j

has_phase_equilibrium = True

mass_transfer_term

$$N_{transfer,t,p,j}$$

t, p ,j

has_mass_transfer = True

Constraints

material_balances(t, p, j):

$\frac{\partial M_{t, p, j}}{\partial t} = F_{in, t, p, j} - F_{out, t, p, j} + N_{kinetic, t, p, j} + N_{equilibrium, t, p, j} + N_{pe, t, p, j} + N_{transfer, t, p, j} + N_{custom, t, p, j}$

The $$N_{custom, t, p, j}$$ 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.

If has_holdup is True, material_holdup_calculation(t, p, j):

$M_{t, p, j} = \rho_{t, p, j} \times V_{t} \times \phi_{t, p}$

where $$\rho_{t, p ,j}$$ is the density of component $$j$$ in phase $$p$$ at time $$t$$

If dynamic is True:

Numerical discretization of the derivative terms, $$\frac{\partial M_{t,p,j}}{\partial t}$$, will be performed by Pyomo.DAE.

If has_rate_reactions is True, rate_reaction_stoichiometry_constraint(t, p, j):

$N_{kinetic, t, p, j} = \alpha_{r, p, j} \times X_{kinetic, t, r}$

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, p, j):

$N_{equilibrium, t, p, j} = \alpha_{r, p, j} \times X_{equilibrium, t, r}$

where $$\alpha_{r, p. j}$$ is the stoichiometric coefficient of component $$j$$ in phase $$p$$ for reaction $$r$$ (as defined in the PhysicalParameterBlock).

Material balances are written for each component across all phases (e.g. one balance for both liquid water and steam). Most terms in the balance equations are still indexed by both phase and component however. 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

$$M_{t,p,j}$$

t, p, j

has_holdup = True

phase_fraction

$$\phi_{t,p}$$

t, p

has_holdup = True

material_accumulation

$$\frac{\partial M_{t,p,j}}{\partial t}$$

t, p, j

dynamic = True

rate_reaction_generation

$$N_{kinetic,t,p,j}$$

t, p ,j

has_rate_reactions = True

rate_reaction_extent

$$X_{kinetic,t,r}$$

t, r

has_rate_reactions = True

equilibrium_reaction_generation

$$N_{equilibrium,t,p,j}$$

t, p ,j

has_equilibrium_reactions = True

equilibrium_reaction_extent

$$X_{equilibrium,t,r}$$

t, r

has_equilibrium_reactions = True

mass_transfer_term

$$N_{transfer,t,p,j}$$

t, p ,j

has_mass_transfer = True

Constraints

material_balances(t, j):

$\sum_p{\frac{\partial M_{t, p, j}}{\partial t}} = \sum_p{F_{in, t, p, j}} - \sum_p{F_{out, t, p, j}} + \sum_p{N_{kinetic, t, p, j}} + \sum_p{N_{equilibrium, t, p, j}} + \sum_p{N_{pe, t, p, j}} + \sum_p{N_{transfer, t, p, j}} + N_{custom, t, j}$

The $$N_{custom, t, j}$$ 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.

If has_holdup is True, material_holdup_calculation(t, p, j):

$M_{t, p, j} = \rho_{t, p, j} \times V_{t} \times \phi_{t, p}$

where $$\rho_{t, p ,j}$$ is the density of component $$j$$ in phase $$p$$ at time $$t$$

If dynamic is True:

Numerical discretization of the derivative terms, $$\frac{\partial M_{t,p,j}}{\partial t}$$, will be performed by Pyomo.DAE.

If has_rate_reactions is True,, rate_reaction_stoichiometry_constraint(t, p, j):

$N_{kinetic, t, p, j} = \alpha_{r, p, j} \times X_{kinetic, t, r}$

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, p, j):

$N_{equilibrium, t, p, j} = \alpha_{r, p, j} \times X_{equilibrium, t, r}$

where $$\alpha_{r, p. j}$$ is the stoichiometric coefficient of component $$j$$ in phase $$p$$ for reaction $$r$$ (as defined in the PhysicalParameterBlock).

Material balances are written for each element in the mixture.

Variables

Variable Name

Symbol

Indices

Conditions

element_holdup

$$M_{t,e}$$

t, e

has_holdup = True

phase_fraction

$$\phi_{t,p}$$

t, p

has_holdup = True

element_accumulation

$$\frac{\partial M_{t,e}}{\partial t}$$

t, e

dynamic = True

elemental_mass_transfer_term

$$N_{transfer,t,e}$$

t, e

has_mass_transfer = True

Expressions

elemental_flow_in(t, p, e):

$F_{in,t,p,e} = \sum_j{F_{in, t, p, j}} \times n_{j, e}$

elemental_flow_out(t, p, e):

$F_{out,t,p,e} = \sum_j{F_{out, t, p, j}} \times n_{j, e}$

where $$n_{j, e}$$ is the number of moles of element $$e$$ in component $$j$$.

Constraints

element_balances(t, e):

$\frac{\partial M_{t, e}}{\partial t} = \sum_p{F_{in, t, p, e}} - \sum_p{F_{out, t, p, e}} + \sum_p{N_{transfer, t, e}} + N_{custom, t, e}$

The $$N_{custom, t, e}$$ 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, e):

$M_{t, e} = V_{t} \times \sum_{p, j}{\phi_{t, p} \times \rho_{t, p, j} \times n_{j, e}}$

where $$\rho_{t, p ,j}$$ is the density of component $$j$$ in phase $$p$$ at time $$t$$

If dynamic is True:

Numerical discretization of the derivative terms, $$\frac{\partial M_{t,e}}{\partial t}$$, will be performed by Pyomo.DAE.

A single enthalpy balance is written for the entire mixture.

Variables

Variable Name

Symbol

Indices

Conditions

energy_holdup

$$E_{t,p}$$

t, p

has_holdup = True

phase_fraction

$$\phi_{t,p}$$

t, p

has_holdup = True

energy_accumulation

$$\frac{\partial E_{t,p}}{\partial t}$$

t, p

dynamic = True

heat

$$Q_{t}$$

t

has_heat_transfer = True

work

$$W_{t}$$

t

has_work_transfer = True

enthalpy_transfer

$$H_{transfer,t}$$

t

has_enthalpy_transfer = True

Expressions

heat_of_reaction(t):

$Q_{rxn, t} = sum_r{X_{kinetic, t, r} \times \Delta H_{rxn, r}} + sum_r{X_{equilibrium, t, r} \times \Delta H_{rxn, r}}$

where $$Q_{rxn, t}$$ 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

$$s_{energy}$$

1E-6

Constraints

enthalpy_balance(t):

$s_{energy} \times \sum_p{\frac{\partial E_{t, p}}{\partial t}} = s_{energy} \times \sum_p{H_{in, t, p}} - s_{energy} \times \sum_p{H_{out, t, p}} + s_{energy} \times Q_t + s_{energy} \times W_t + + s_{energy} \times H_{transfer,t} +s_{energy} \times Q_{rxn, t} + s_{energy} \times E_{custom, t}$

The $$E_{custom, t}$$ term allows the user to provide custom terms which will be added into the energy balance.

If has_holdup is True, enthalpy_holdup_calculation(t, p):

$E_{t, p} = u_{t, p} \times V_{t} \times \phi_{t, p}$

where $$u_{t, p}$$ is the internal energy density (specific internal energy) of phase $$p$$ at time $$t$$

If dynamic is True:

Numerical discretization of the derivative terms, $$\frac{\partial E_{t,p}}{\partial t}$$, will be performed by Pyomo.DAE.

A single pressure balance is written for the entire mixture.

Variables

Variable Name

Symbol

Indices

Conditions

deltaP

$$\Delta P_{t}$$

t

has_pressure_change = True

Parameters

Parameter Name

Symbol

Default Value

scaling_factor_pressure

$$s_{pressure}$$

1E-4

Constraints

pressure_balance(t):

$0 = s_{pressure} \times P_{in, t} - s_{pressure} \times P_{out, t} + s_{pressure} \times \Delta P_t + s_{pressure} \times \Delta P_{custom, t}$

The $$\Delta P_{custom, t}$$ term allows the user to provide custom terms which will be added into the pressure balance.