rates: determining molar rates of chemical species

Code author: Peter Kraus

Includes functions to convert mixture compositions (concentration, mol fraction) from instantaneous flow data or continuous batch data to rates (dimension of [quantity]/[time]). The flow_to_molar() function is useful for converting gas-phase or liquid flows, while batch_to_molar() can be used to determine formation rates from the concentration profile of a batch mixture.

Functions

`batch_to_molar`(time, c, V[, t0, output])	Calculates a molar rate of species from specified volume and composition at the specified timesteps.
`flow_to_molar`(flow[, c, x, Tref, pref, output])	Calculates a molar rate of species from specified flow and composition.

dgpost.transform.rates.flow_to_molar(flow, c=None, x=None, Tref=<Quantity(273.15, 'kelvin')>, pref=<Quantity(1, 'standard_atmosphere')>, output='rate')

Calculates a molar rate of species from specified flow and composition. The units of the rate have to be either dimensionless (for unit-naive dataframes) or in dimensions of [substance]/[time].

Currently, three combinations of units are supported:

Dimensionless flow and dimensionless comp, as is the case for unit-naive dataframes. In this case, the molar flow rates of species \(r_s\) are calculated by a simple multiplication:

\[r_s = \text{flow} \times \text{comp}_s\]

Volumetric flow \(\dot{V}\) and composition comp as a concentration, as is often the case in liquid flows. In this case, the molar rates of species \(r_s\) are also a simple multiplication (accounting for unit conversion):

\[r_s = \dot{V} \times c_s\]

Volumetric flow \(\dot{V}\) and composition comp as a dimensionless molar fraction \(x_s\), in which case the flow is assumed to be gas-phase. In this case, the flow has to be converted to molar units using the ideal gas law:

\[r_s = \dot{V} \times \frac{p_\text{ref}}{RT_\text{ref}} \times x_s\]

The pressure \(p_\text{ref}\) and temperature \(T_\text{ref}\) are specifying the state at which the flow \(\dot{V}\) has been measured.

Parameters:

flow (Quantity) – The total flow of the mixture.
c (Optional[dict[str, Quantity]]) – A dictionary containing the composition of the mixture as concentration. Cannot be supplied at the same time as x.
x (Optional[dict[str, Quantity]]) – A dictionary containing the composition of the mixture as mole fraction. Assuming ideal gas-phase flow. Cannot be supplied at the same time as c.
Tref (Quantity) – Reference temperature of the flow measurement, used when composition is specified using a mol fraction. By default set to 273.15 K.
pref (Quantity) – Reference pressure of the flow measurement, used when composition is specified using a mol fraction. By default set to 1 atm.
output (str) – Prefix of the keys of the returned rate dictionary.

Return type:

dict[str, Quantity]

dgpost.transform.rates.batch_to_molar(time, c, V, t0=None, output='rate')

Calculates a molar rate of species from specified volume and composition at the specified timesteps. The units of the rate have to be either dimensionless (for unit-naive dataframes) or in dimensions of [substance]/[time].

First, the \(\delta t\) and \(\delta c(x)\) at each timestep \(n\) is calculated:

\[\delta t_n = t_n - t_{n-1} \delta c(x)_n = c(x)_n - c(x)_{n-1}\]

Then, the formation rate is calculated using the volume:

Parameters:

time (Quantity) – An array of timestamps at which the concentrations and volumes are measured.
c (dict[str, Quantity]) – A dictionary containing concentrations of species at the specified timestamps.
V (Quantity) – Volume of the batch at the timestamps.
t0 (Optional[Quantity]) – An optional timestamp representing the initial time where all concentrations are zero. If not supplied, the calculation will use the first datapoint as reference with its rates set to zero.
output (str) – Prefix of the columns where the calculated rate will be stored.

Return type:

dict[str, Quantity]