4. Transient Analysis

Transient analysis¶

Prior to any transient analysis please ensure that the baseline correction and calibration have been properly performed.

While the moments describe summary statistics of the flux response, the transient analysis performs operations to the outlet flux to measure chemical quantities such as the gas concentration and reaction rate. This comes in the form of the Y-Procedure (reactor physics based) or G-Procedure (statistical based). Below are a few example of applying the Y and G procedure using tapsap.

In [1]:

# imports and reading in the data
import pandas as pd
import tapsap
import plotly
plotly.offline.init_notebook_mode()

data = pd.read_csv('../tapsap/data/irreversible_reaction.csv')
times = data['times'].values
inert_flux = data['inert_flux'].values
reactant_flux = data['A_flux'].values
rate = data['A_rate'].values
concentration = data['A_concentration'].values
# additional information needed for the concentration and rate
diffusion = 0.002
zone_lengths = {'zone0':0.018, 'zone1':1e-5, 'zone2':0.018}
zone_porosity = {'zone0':0.4, 'zone1':0.4, 'zone2':0.4}
reactor_radius = 0.002
concentration_units = zone_lengths['zone2'] / diffusion
y_smoothing = 3
y_smoothing_low = 1
y_smoothing_high = 6

The imported data comes from a simulation performed by Denis Constales. Noise has been added to the reactant flux and because this is a simulation the rate and concentration are known. In tapsap, the gas concentration can be obtained by the functions concentration_y or concentration_g. Both require the outlet flux, times and the zone lengths, but the Y-procedure allows requires the diffusion, zone porosity and smoothing amount. The diffusion parameter is a result of determining the diffusion of the inert and then scaling the value by Graham's law. The smoothing amount is critical when applying the Y-procedure. If too little smoothing is applied, then the concentration will result in just noise. Too much smoothing will alter the shape of the concentration near beginning and end of the flux. Examples of the Y and G procedure are given below:

In [2]:

estimate_y_concentration = tapsap.concentration_y(reactant_flux,times,diffusion,zone_lengths,zone_porosity,smoothing_amt= y_smoothing) * concentration_units
estimate_g_concentration = tapsap.concentration_g(reactant_flux, times, zone_lengths) * concentration_units
df = pd.DataFrame({'actual':concentration, 'y':estimate_y_concentration, 'g':estimate_g_concentration})
tapsap.plot_tap(times, df, legend = True, y_lab='Concentration')

When calculating the reaction rate, it is necessary to know whether the species is a reactant or product to account for the transport in the reactor. When the species is a product, the inert_flux is left as None in both rate functions. If the species is a reactant, then the inert_flux (scaled by Graham's Law to account for mass differences) must be included.

In [3]:

estimate_y_rate = tapsap.rate_y(reactant_flux,times,diffusion,zone_lengths,zone_porosity,inert_flux=inert_flux, smoothing_amt= y_smoothing)
estimate_g_rate = tapsap.rate_g(reactant_flux, times, zone_lengths, inert_flux=inert_flux)
df = pd.DataFrame({'actual':rate, 'y':estimate_y_rate, 'g':estimate_g_rate})
tapsap.plot_tap(times, df, legend = True, y_lab='Rate')

The G-Procedure is invariant with respect to the noise in the flux, however the rate and concentration will be slightly different from the true values. The Y-Procedure is highly dependent on the smoothing parameter and the noise. Below are a couple of additional examples where the smoothing parameter is adjusted:

With a smoothing paramter of 1:

In [4]:

estimate_y_concentration = tapsap.concentration_y(reactant_flux,times,diffusion,zone_lengths,zone_porosity,smoothing_amt= y_smoothing_low) * concentration_units
estimate_g_concentration = tapsap.concentration_g(reactant_flux, times, zone_lengths) * concentration_units
df = pd.DataFrame({'actual':concentration, 'y':estimate_y_concentration, 'g':estimate_g_concentration})
tapsap.plot_tap(times, df, legend = True, y_lab='Concentration')

In [5]:

estimate_y_rate = tapsap.rate_y(reactant_flux,times,diffusion,zone_lengths,zone_porosity,inert_flux=inert_flux, smoothing_amt= y_smoothing_low)
estimate_g_rate = tapsap.rate_g(reactant_flux, times, zone_lengths, inert_flux=inert_flux)
df = pd.DataFrame({'actual':rate, 'y':estimate_y_rate, 'g':estimate_g_rate})
tapsap.plot_tap(times, df, legend = True, y_lab='Rate')

With a smoothing parameter of 6:

In [6]:

estimate_y_concentration = tapsap.concentration_y(reactant_flux,times,diffusion,zone_lengths,zone_porosity,smoothing_amt= y_smoothing_high) * concentration_units
estimate_g_concentration = tapsap.concentration_g(reactant_flux, times, zone_lengths) * concentration_units
df = pd.DataFrame({'actual':concentration, 'y':estimate_y_concentration, 'g':estimate_g_concentration})
tapsap.plot_tap(times, df, legend = True, y_lab='Concentration')

In [7]:

estimate_y_rate = tapsap.rate_y(reactant_flux,times,diffusion,zone_lengths,zone_porosity,inert_flux=inert_flux, smoothing_amt= y_smoothing_high)
estimate_g_rate = tapsap.rate_g(reactant_flux, times, zone_lengths, inert_flux=inert_flux)
df = pd.DataFrame({'actual':rate, 'y':estimate_y_rate, 'g':estimate_g_rate})
tapsap.plot_tap(times, df, legend = True, y_lab='Rate')

Note that when performing the calculation for the concentration, the results were scaled by the ratio of the second zone length and diffusion. Rather than scaling each time the function is run, the correct units can be determined using the function concentration_units and rate_units in tapsap.

Application to a Transient object¶

The above examples can be applied in a similar fashion but to all flux within a species using the method set_rate and set_concentration. The concentration and rate both have an argument input for the Y procedure smoothing value. If the smoothing value is left as None, then the G-Procedure is used. Additionally, when setting the rate, isreactant is a boolean value for using the inert flux information or not (this means that the attribute reference_gas must be set). The Graham's Law scaling of the inert is automatically performed in this method and all of the units are automatically set.

Also, when setting the rate and concentration, the flux will be overwritten. Please use the make_copy function in the Experiment object prior to performing the analysis.

In [8]:

data = tapsap.read_tdms('../tapsap/data/argon_100C.tdms')
# set the reactor information
data.reactor.zone_lengths = {'zone0':0.018, 'zone1':1e-5, 'zone2':0.018}
data.reactor.zone_porosity = {'zone0':0.4, 'zone1':0.4, 'zone2':0.4}
data.reactor.reactor_radius = 0.002
# this specifies the reactor parameters to each species
data.set_reactor_params()
# setting the diffusion (this can also be calculated see the moments analysis examples)
data.species_data['AMU_40_1'].diffusion = 0.002
# making a copy and naming it AMU_40_1_concentration 
data.make_copy('AMU_40_1', 'AMU_40_1_concentration')
# grabbing the transient information
transient_info = data.species_data['AMU_40_1_concentration']
# baseline correcting
transient_info.baseline_correct(baseline_time_range = [4.5, 5])
# setting the concentration
transient_info.set_concentration()
tapsap.plot_tap(transient_info.times, transient_info.flux.iloc[:,10].values, y_lab='Concentration')