5. Diffusion

Diffusion¶

This set of examples show how to calculate the residence time bsed on the diffusion, transform flux via Graham's Law, and the standard diffusion curve. All of which are necessary in manipulating the inert flux information to describe the transport of the reactant gas.

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.csv')
times = data['times'].values
inert_flux = data['inert_flux'].values
reactant_flux = data['A_flux'].values
# setting the reactor parameters
zone_residence_time = {'zone0':0.5, 'zone1':1e-5, 'zone2':0.5}
zone_lengths = {'zone0':0.5, 'zone1':1e-5, 'zone2':0.5}
zone_porosity = {'zone0':0.5, 'zone1':0.5, 'zone2':0.5}
zone_diffusion = {'zone0':0.5, 'zone1':0.5, 'zone2':0.5}

Calculating the residence time¶

This is a basic function to determine the residence time of each zone based on the reactor parameters. This function is used in calculating the reactivities.

In [2]:

temp_residence_time = tapsap.calculate_residence_time(zone_lengths, zone_porosity, zone_diffusion)
print(temp_residence_time)

{'zone0': 0.5, 'zone1': 1e-05, 'zone2': 0.5}

Graham's Law¶

This function scales a flux within time by the square root of the ratio of masses. This is useful in transforming an inert flux to look like a reactant species where only transport is occuring. This function is needed in the Y/G Procedure.

In [3]:

inert_graham = tapsap.grahams_law(inert_flux, times, 40, 32)
df = pd.DataFrame({'inert':inert_flux, 'Grahams transformed':inert_graham})
tapsap.plot_tap(times, df, legend=True)

Standard diffusion curve¶

The standard diffusion curve takes a residence time and determines what the outlet response should look like in only transport conditions. This function is useful in visually determining if an inert response is within the Knudsen diffusion regime. Poor fits of the standard diffusion curve to the inert flux may indicate potential sticking on the material in the reactor or some amount of advection. The first example shows the differences in the standard diffusion curve given multiple residence times. The second example uses the function opt_sdc (requires an initial residence time) to optimize the residence time of an outlet flux to the standard diffusion curve.

In [4]:

# difference in standard diffusion curves
sdc_0_5 = tapsap.standard_diffusion_curve(0.5, times)
sdc_0_25 = tapsap.standard_diffusion_curve(0.25, times)
sdc_0_75 = tapsap.standard_diffusion_curve(0.75, times)

df = pd.DataFrame({'sdc 0.5':sdc_0_5, 'sdc 0.25':sdc_0_25, 'sdc 0.75':sdc_0_75})
tapsap.plot_tap(times, df, legend=True)

In [5]:

# optimizing the standard diffusion curve based on an inert flux
opt_flux = tapsap.opt_sdc(0.2, inert_flux, times)
print('The optimal residence time')
print(opt_flux['residence_time'])
print('The actual value is 0.5')

The optimal residence time
0.5002016007337162
The actual value is 0.5

In [6]:

# comparing the sdc with the inert flux
# they should be right on top of one another
df = pd.DataFrame({'flux':inert_flux, 'sdc':opt_flux['flux']})
tapsap.plot_tap(times, df, legend=True)