Mass balances

PFR mass balance.

class reactord.flowreactors.stationary_1d.pfr.mass_balances.MolarFlow(molar_flows_in: dict = {}, molar_flows_out: dict = {})

Bases: object

PFR Molar Flow class.

\[\frac{1}{a_t}\frac{dF_i}{dz}=r_i\]

\(a_t\): reactor’s transversal area.

\(F_i\): molar flow of the i-th substance.

\(z\): reactor’s length coordinate.

\(r_i\): reaction rate of the i-th substance.

Parameters:

• molar_flows_in (dict, optional) – Molar flow in the inlet reactor section

• molar_flows_out (dict, optional) – Molar flow in the out reactor section

property irepr

Represent for ipython.

initial_profile(reactor: PFR)

Set initial profile in PFR.

Parameters:

reactor (PFR) – PFR object

Returns:

initial mass profile in all grid

Return type:

ndarray

Raises:

• ValueError – Raise to guarantee one condition (inlet or outlet) for each substance

• ValueError – Raise to guarantee border condition

update_profile(reactor: PFR, variables)

Update profile.

border_conditions(reactor: PFR)

Set border conditions.

Parameters:

reactor (PFR) – PFR object

Returns:

array with molar flow in the inlet and outlet reactor

Return type:

ndarray

evaluate_balance(reactor: PFR)

Evaluate mass balance.

Parameters:

reactor (PFR) – PFR object

Returns:

Reaction rate of each substance on each reactor’s z

Return type:

ndarray

Energy balances

PFR energy balance.

class reactord.flowreactors.stationary_1d.pfr.energy_balances.Adiabatic(temperature_in_or_out: dict)

Bases: object

PFR Adiabatic energy balance.

\[\frac{1}{a_t}\frac{dT}{dz}=\frac{\sum\Delta{H_j}_{(TP)}r_{j}}{{c_p}_ {mix}{\sum}F_i}\]

\[\frac{dT_r}{dz}=0\]

\(a_t\): reactor’s transversal area.

\(T\): reactor’s temperature.

\(T_r\): refrigerant’s temperature.

\(z\): reactor’s length coordinate.

\(\Delta{H_j}_{(TP)}\): enthalpy of j-th reaction.

\(r_{j}\): rate of j-th reaction.

\({c_p}_{mix}\): mixture’s heat capacity.

\(F_i\): molar flow of the i-th substance.

Parameters:

temperature_in_or_out (dict) – Temperature of reactive mixture in the inlet or outlet position. Use {“in”: 200} for 200 K at inlet or {“out”: 200} for 200 K at outlet.

Raises:

• NotImplementedError –

• Both in and out border condition for temperature not implemented. –

property irepr

Represent for ipython.

initial_profile(reactor: PFR) → ndarray[Any, dtype[float64]]

Set initial energy profile in adiabatic PFR.

Parameters:

reactor (PFR) – PFR object

Returns:

initial temperature profile in all reactor’s length grid.

Return type:

NDArray[np.float64]

update_profile(reactor: PFR, variables: ndarray[Any, dtype[float64]]) → None

Update PFR’s temperature profile.

Parameters:

• reactor (PFR) – PFR object.

• variables (NDArray[np.float64]) – Variables of solve_bvp ode solver.

border_conditions(reactor: PFR) → tuple

Set border conditions.

Parameters:

reactor (PFR) – PFR object

Returns:

array with temperature in the inlet and outlet reactor.

Return type:

tuple

evaluate_balance(reactor: PFR) → ndarray[Any, dtype[float64]]

Evaluate energy balance.

Parameters:

reactor (PFR) – PFR object.

Returns:

Temperature rate of each substance on each reactor’s z.

Return type:

NDArray[np.float64]

class reactord.flowreactors.stationary_1d.pfr.energy_balances.Isothermic(temperature: float)

Bases: object

PFR isothermic energy balance.

\[\frac{dT}{dz}=0\]

\[\frac{dT_r}{dz}=0\]

\(T\): reactor’s temperature.

\(T_r\): refrigerant’s temperature.

\(z\): reactor’s length coordinate.

Parameters:

temperature (float) – Isothermic temperature

property irepr

Represent for ipython.

initial_profile(reactor: PFR) → ndarray[Any, dtype[float64]]

Set initial energy profile in isothermic PFR.

Parameters:

reactor (PFR) – PFR object

Returns:

initial temperature profile in all grid

Return type:

NDArray[np.float64]

update_profile(reactor: PFR, variables: ndarray[Any, dtype[float64]]) → None

Update PFR’s temperature profile.

Parameters:

• reactor (PFR) – PFR object.

• variables (NDArray[np.float64]) – Variables of solve_bvp ode solver.

border_conditions(reactor: PFR) → tuple

Set border conditions.

Parameters:

reactor (PFR) – PFR object

Return type:

isothermic temperature

evaluate_balance(reactor: PFR) → ndarray[Any, dtype[float64]]

Evaluate energy balance.

Parameters:

reactor (PFR) – PFR object

Returns:

Temperature rate of each substance on each reactor’s z This is zero in a isothermic balance.

Return type:

NDArray[np.float64]

class reactord.flowreactors.stationary_1d.pfr.energy_balances.NoIsothermicAllConstant(temperature_in_or_out: dict, refrigerant_in_temperature: float, heat_exchange_coefficient: float)

Bases: object

PFR noisothermic energy balance.

Refrigerant’s temperature and heat exchange coefficient U remains constant.

\[\frac{1}{a_t}\frac{dT}{dz}=\frac{Ua(T_r-T)+\sum\Delta{H_j}r_{j}}{{c_p}_ {mix}{\sum}F_i}\]

\[\frac{dT_r}{dz}=0\]

\(a_t\): reactor’s transversal area.

\(U\): heat exchange coefficient.

\(a\): reactor’s heat exchange area per reactor’s volume.

\(T\): reactor’s temperature.

\(T_r\): refrigerant’s temperature.

\(z\): reactor’s length coordinate.

\(\Delta{H_j}_{(TP)}\): enthalpy of j-th reaction.

\(r_{j}\): rate of j-th reaction.

\({c_p}_{mix}\): mixture’s heat capacity.

\(F_i\): molar flow of the i-th substance.

Parameters:

• temperature_in_or_out (dict) – Temperature of reactive mixture in the inlet or outlet position. Use {“in”: 200} for 200 K at inlet or {“out”: 200} for 200 K at outlet.

• refrigerant_in_temperature (float) – Refrigerant temperature. [K]

• heat_exchange_coefficient (float) – Heat exchange coefficient. [J/K/s/m²]

property irepr

Represent for ipython.

initial_profile(reactor: PFR) → ndarray[Any, dtype[float64]]

Set initial energy profile in noisothermic PFR.

Parameters:

reactor (PFR) – PFR object

Returns:

initial temperature profile in all grid

Return type:

NDArray[np.float64]

update_profile(reactor: PFR, variables: ndarray[Any, dtype[float64]]) → None

Update the reactor’s temperature profile.

Parameters:

• reactor (PFR) – PFR object.

• variables (NDArray[np.float64]) – Variables of solve_bvp ode solver.

border_conditions(reactor: PFR) → tuple

Set border conditions.

Parameters:

reactor (PFR) – PFR object

Return type:

temperature at in and out condition

evaluate_balance(reactor: PFR) → ndarray[Any, dtype[float64]]

Evaluate energy balance.

Parameters:

reactor (PFR) – PFR object

Returns:

Temperature rate of each substance on each reactor’s z.

Return type:

NDArray[np.float64]

class reactord.flowreactors.stationary_1d.pfr.energy_balances.NoIsothermicUConstant(temperature_in_or_out: dict, refrigerant_in_temperature: float, heat_exchange_coefficient: float, refrigerant_mix: AbstractMix, refrigerant_composition: ndarray[Any, dtype[float64]], refrigerant_pressure: float, refrigerant_molar_flow: float, heat_exchange_arrangement: str = 'co-current')

Bases: NoIsothermicAllConstant

PFR noisothermic energy balance.

Heat exchange coefficient U remains constant. Refrigerant’s pressure profile, composition profile and volumetric flow are assumed constant.

\[\frac{1}{a_t}\frac{dT}{dz}=\frac{Ua(T_r-T)+\sum\Delta{H_j}r_{j}}{{c_p}_ {mix}{\sum}F_i}\]

\[\text{Co-current refrigerant energy balance: } \frac{1}{a_t}\frac{dT_r}{dz}=\frac{Ua(T-T_r)}{{c_p}_{r}{\sum}F_i}\]

\[\text{Counter-current refrigerant energy balance: } \frac{1}{a_t}\frac{dT_r}{dz}=\frac{Ua(T_r-T)}{{c_p}_{r}{\sum}F_i}\]

\(a_t\): reactor’s transversal area.

\(U\): heat exchange coefficient.

\(a\): reactor’s heat exchange area per reactor’s volume.

\(T\): reactor’s temperature.

\(T_r\): refrigerant’s temperature.

\(z\): reactor’s length coordinate.

\(\Delta{H_j}_{(TP)}\): enthalpy of j-th reaction.

\(r_{j}\): rate of j-th reaction.

\({c_p}_{mix}\): mixture’s heat capacity.

\({c_p}_{r}\): refrigerant’s heat capacity.

\(F_i\): molar flow of the i-th substance.

Parameters:

• temperature_in_or_out (dict) – Temperature of reactive mixture in the inlet or outlet position. Use {“in”: 200} for 200 K at inlet or {“out”: 200} for 200 K at outlet.

• refrigerant_in_temperature (float) – Refrigerant temperature. [K]

• heat_exchange_coefficient (float) – Heat exchange coefficient. [J/K/s/m²]

• refrigerant_mix (AbstractMix) – Refrigerant mixture.

• efrigerant_composition (NDArray[np.float64]) – Mole fractions of the refrigerant mixture substances.

• refrigerant_pressure (float) – Refrigerant’s pressure. [Pa]

• refrigerant_moalr_flow (float) – Refrigerant’s molar flow. [mol/s]

• heat_exchange_arrangement (str, optional) – Options: ‘co-current’, ‘counter-current’, by default ‘co-current’.

border_conditions(reactor: PFR) → tuple

Set border conditions.

Parameters:

reactor (PFR) – PFR object

Return type:

temperature at in and out condition.

evaluate_balance(reactor: PFR) → ndarray[Any, dtype[float64]]

Evaluate energy balance.

Parameters:

reactor (PFR) – PFR object

Returns:

Temperature rate of each substance on each reactor’s z.

Return type:

NDArray[np.float64]

Pressure balances

PFR pressure balance.

class reactord.flowreactors.stationary_1d.pfr.pressure_balances.Ergun(pressure: dict, porosity: float, particle_diameter: float)

Bases: object

PFR Ergun energy balance class.

\[\frac{dP}{dz}=-\frac{G}{{\rho}D_p}\left(\frac{1-\phi}{\phi^3} \right)\left[\frac{150(1-\phi)\mu}{D_p}+1.75G\right]\]

Parameters:

• pressure (dict) – pressure of each substance in the inlet or outlet position.

• porosity (float) – Packed bed porosity float between 0 and 1.

• particle_diameter (float) – Diameter of particle of packed bed. [m]

Raises:

ValueError – Only inlet or outlet border condition for pressure are allowed.

property irepr

Represent for ipython.

initial_profile(reactor: PFR) → ndarray[Any, dtype[float64]]

Set initial pressure profile in non-isobaric PFR.

Parameters:

reactor (PFR) – PFR object

Returns:

initial pressure profile in all grid

Return type:

NDArray[np.float64]

update_profile(reactor: PFR, variables: ndarray[Any, dtype[float64]]) → None

Update th reactor’s presure profile.

Parameters:

• reactor (PFR) – PFR object.

• variables (NDArray[np.float64]) – Variables of solve_bvp ode solver.

border_conditions(reactor: PFR) → ndarray[Any, dtype[float64]]

Set border conditions.

Parameters:

reactor (PFR) – PFR object

Returns:

array with pressure in the inlet and outlet reactor.

Return type:

NDArray[np.float64]

evaluate_balance(reactor: PFR) → ndarray[Any, dtype[float64]]

Evaluate pressure balance.

Parameters:

reactor (PFR) – PFR object

Returns:

Pressure rate of each substance on each reactor’s z.

Return type:

NDArray[np.float64]

class reactord.flowreactors.stationary_1d.pfr.pressure_balances.Isobaric(pressure: float)

Bases: object

PFR isobaric energy pressure class.

\[\frac{dP}{dz}=0\]

\(P\): reactor’s pressure.

\(z\): reactor’s length coordinate.

Parameters:

pressure (float) – Isobaric pressure.

property irepr

Represent for ipython.

initial_profile(reactor: PFR) → ndarray[Any, dtype[float64]]

Set initial pressure profile in non-isobaric PFR.

Parameters:

reactor (PFR) – PFR object.

Returns:

initial pressure profile in all grid.

Return type:

NDArray[np.float64]

update_profile(reactor: PFR, variables: ndarray[Any, dtype[float64]]) → None

Update th reactor’s presure profile.

Parameters:

• reactor (PFR) – PFR object.

• variables (NDArray[np.float64]) – Variables of solve_bvp ode solver.

border_conditions(reactor: PFR) → tuple

Set border conditions.

Parameters:

reactor (PFR) – PFR object

Returns:

array with pressure in the inlet and outlet reactor

Return type:

tuple

evaluate_balance(reactor: PFR) → ndarray[Any, dtype[float64]]

Evaluate pressure balance.

Parameters:

reactor (PFR) – PFR object

Returns:

Isobaric pressure of each substance on each reactor’s z

Return type:

NDArray[np.float64]