Base Solvex Development Cortix Tech 03Oct2025
1. Use-Case 02: TBP-Diluent-H\(_2\)O Mixing#
Developer: Valmor F. de Almeida, PhD
Cortix Tech, Lowell, MA 01854, USA
Revision date: 02Dec25
1.1. Objectives#
Develop usecase scenario for water extraction by TBP without a vapor phase.
Test implementation and present results.
Use AI assistants to help with information and reporting.
AI requests below may need to be executed multiple times if the result is not satisfactory or incorrect.
'''AI Assistance options'''
# Set all to False if you do not have access to OpenAI API and/or AI codes below
cortix_ai = False
stage_ai = False
'''Generate proprietary knowledge database?'''
db_save = False # set this to false if going public (online) with this notebook
'''Other Helpers'''
fig_count = 0
tbl_count = 0
1.2. Base System#
Single stage mixing of water, and TBP with inert diluent.
'''Setup the Base System'''
from cortix import Cortix
from cortix import Network
from cortix import Units as unit
from cortix import ReactionMechanism
from cortix import Quantity
system = Cortix(use_mpi=False, splash=True) # System top level
system_net = system.network = Network() # Network
[13917] 2025-12-02 13:51:51,807 - cortix - INFO - Created Cortix object
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L A U N C H I N G
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https://cortix.org
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1.2.1. Stage#
Instantiate a single stage.
'''Import Stage'''
from solvex import Stage
'''Create Base Stage and add to Base System'''
from solvex import Stage
# Initialization
mixing_volume = 1*unit.L
# Aqueous phase
mixing_vol_flowrate_aqu = 500*unit.mL/unit.min
# Organic phase
mixing_vol_flowrate_org = 600*unit.mL/unit.min
# Vapor phase
mixing_vol_flowrate_vap = (0.0*mixing_vol_flowrate_org/100, 0.0*mixing_vol_flowrate_aqu/100) # percentage of (org, aqu)
mixing_vol_flowrates = [mixing_vol_flowrate_org, mixing_vol_flowrate_aqu, mixing_vol_flowrate_vap]
stg_temperature = unit.convert_temperature(40, 'C', 'K')
stg = Stage(mixing_volume, mixing_vol_flowrates, stg_temperature) # Create solvent extraction module
system_net.module(stg)
print('Flow residence time [s]: average = %5.3e'%stg.flow_residence_time_avg)
print('Aqueous volume fraction = %5.3e'%stg.volume_frac_aqu)
print('Organic volume fraction = %5.3e'%stg.volume_frac_org)
Flow residence time [s]: average = 5.455e+01
Aqueous volume fraction = 4.545e-01
Organic volume fraction = 5.455e-01
'''Draw system'''
system_net.draw(engine='circo', node_shape='folder', ports=True)
'''For help purposes'''
import solvex.stage
Documentation options:
Live in this notebook run on code cell:
help(solvex_ustc.stage)On the web: source
#help(solvex.stage)
1.2.2. Reaction Mechanisms#
1.2.2.1. Water extraction example#
args_dict = {'water_activity': 1.0}
file_name = 'tbp-h2o.txt'
rxn_mech = ReactionMechanism(file_name=file_name, order_species=True, args_dict=args_dict)
WARNING: ReactionMechanism: user must implement a H2O*[C4H9O]3PO(o) product partition function with signature <product>(rxn_mech, temperature, spc_molar_cc, arg_dict) function for [C4H9O]3PO(o) + H2O(a) <-> H2O*[C4H9O]3PO(o)
WARNING: ReactionMechanism: user must implement a [H2O]2*[[C4H9O]3PO]2(o) product partition function with signature <product>(rxn_mech, temperature, spc_molar_cc, arg_dict) function for 2 [C4H9O]3PO(o) + 2 H2O(a) <-> [H2O]2*[[C4H9O]3PO]2(o)
WARNING: ReactionMechanism: user must implement a [H2O]6*[[C4H9O]3PO]3(o) product partition function with signature <product>(rxn_mech, temperature, spc_molar_cc, arg_dict) function for 3 [C4H9O]3PO(o) + 6 H2O(a) <-> [H2O]6*[[C4H9O]3PO]3(o)
#'''User input'''
#rxn_mech.cat_input()
#'''Show Mechanism'''
# Jupyter Book does not render LaTeX through IPython.display(Markdown)
#rxn_mech.md_print()
5 Species
\[\begin{align*}
&{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}, {\mathrm{H}_{2}\mathrm{O}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, {[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, {[\mathrm{H}_{2}\mathrm{O}]_{2}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}, {[\mathrm{H}_{2}\mathrm{O}]_{6}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{3}}_{\mathrm{(o)}}\end{align*}\]
3 Reactions
\[\begin{align*}
{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}\ + \ {[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\ &\longleftrightarrow \ {\mathrm{H}_{2}\mathrm{O}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\\
2.0\,{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}\ + \ 2.0\,{[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\ &\longleftrightarrow \ {[\mathrm{H}_{2}\mathrm{O}]_{2}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}\\
6.0\,{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}\ + \ 3.0\,{[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\ &\longleftrightarrow \ {[\mathrm{H}_{2}\mathrm{O}]_{6}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{3}}_{\mathrm{(o)}}\\
\end{align*}\]
#'''Species and Reactions Manual Output'''
#print(len(rxn_mech.species_names), ' **Species**\n', rxn_mech.latex_species)
#print(len(rxn_mech.reactions), ' **Reactions**\n', rxn_mech.latex_rxn)
1.2.2.2. Sanity check#
'''Data Check'''
print('Is mass conserved?', rxn_mech.is_mass_conserved())
rxn_mech.rank_analysis(verbose=True, tol=1e-8)
print('S=\n', rxn_mech.stoic_mtrx)
Is mass conserved? True
# reactions = 3
# species = 5
rank of S = 3
S is full rank.
S=
[[-1. 1. -1. 0. 0.]
[-2. 0. -2. 1. 0.]
[-6. 0. -3. 0. 1.]]
1.2.2.3. User-provided partition functions#
'''Equilibrium constants involved in the reaction mechanism'''
from solvex.partition_func_local import partition_h2o_tbp_org
from solvex.partition_func_local import partition_2h2o_2tbp_org
from solvex.partition_func_local import partition_6h2o_3tbp_org
# Equilibrium constant for H2O*TBP complexation
rxn_mech.data[0]['tau-partition-function'] = partition_h2o_tbp_org
# Equilibrium constant for 2H2O*2TBP complexation
rxn_mech.data[1]['tau-partition-function'] = partition_2h2o_2tbp_org
# Equilibrium constant for 6H2O*3TBP complexation
rxn_mech.data[2]['tau-partition-function'] = partition_6h2o_3tbp_org
1.2.2.4. Add reaction mechanism to stage#
stg.add_reaction_mechanism(rxn_mech)
1.2.2.5. Verify Species Groups#
#'''Aqueous phase'''
#str = stg.rxn_mech.md_print('(a)')
#'''Show aqueous phase'''
# Jupyter Book does not render LaTeX through IPython.display(Markdown)
#print(str)
\[\begin{align*}
&{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}, \ \end{align*}\]
#'''Organic phase'''
#str = stg.rxn_mech.md_print('(o)', n_species_line=5)
#'''Show organic phase'''
# Jupyter Book does not render LaTeX through IPython.display(Markdown)
#print(str)
\[\begin{align*}
&{\mathrm{H}_{2}\mathrm{O}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, \ {[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, \ {[\mathrm{H}_{2}\mathrm{O}]_{2}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}, \ {[\mathrm{H}_{2}\mathrm{O}]_{6}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{3}}_{\mathrm{(o)}}, \ \end{align*}\]
1.2.2.6. Mass transfer data#
'''Adjust relaxation times for mass transfer'''
stg.rxn_mech.data[0]['tau'] = 1.0e-0 * stg.flow_residence_time_avg
stg.rxn_mech.data[1]['tau'] = 1.0e-0 * stg.flow_residence_time_avg
stg.rxn_mech.data[2]['tau'] = 1.0e-0 * stg.flow_residence_time_avg
1.2.2.7. Meta data#
'''Names and info of interest for species'''
tbp_org_name = '[C4H9O]3PO(o)'
tbp_org = stg.organic_phase.get_species(tbp_org_name)
tbp_org.info = 'Free TBP'
tbp_monomer_org_name = 'H2O*[C4H9O]3PO(o)'
tbp_monomer_org = stg.organic_phase.get_species(tbp_monomer_org_name)
tbp_monomer_org.info = 'TBP Monomer Hydrate'
tbp_dimer_org_name = '[H2O]2*[[C4H9O]3PO]2(o)'
tbp_dimer_org = stg.organic_phase.get_species(tbp_dimer_org_name)
tbp_dimer_org.info = 'TBP Dimer'
tbp_trimer_hexahydrate_org_name = '[H2O]6*[[C4H9O]3PO]3(o)'
tbp_trimer_hexahydrate_org = stg.organic_phase.get_species(tbp_trimer_hexahydrate_org_name)
tbp_trimer_hexahydrate_org.info = 'TBP Trimer Hexahydrate'
1.3. Initial Conditions#
'''Organic phase in the mixer (diluent is inert)'''
vol_frac_tbp_org = 30/100 # free tbp
#TODO: look this up at 40 C # W: TODO: look this up at 40 C
rho_tbp = 972.5 * unit.gram/unit.L # pure liquid TBP
stg.rxn_mech.args_dict['rho-tbp'] = rho_tbp # for future use in the reaction mechanism
tbp_mass_cc_org = rho_tbp * vol_frac_tbp_org # per volume of organic phase in the mixture
stg.organic_phase.set_value(tbp_org_name, tbp_mass_cc_org)
print('mass_cc_tbp_org [g/L] =', tbp_mass_cc_org)
print('molar_cc_tbp_org [M] = %1.5e'%(tbp_mass_cc_org/tbp_org.molar_mass/unit.molar))
mass_cc_tbp_org [g/L] = 291.75
molar_cc_tbp_org [M] = 1.09551e+00
'''Aqueous phase in the mixer'''
h2o_aqu = stg.aqueous_phase.get_species('H2O(a)')
h2o_aqu.info = 'Water'
#TODO look this up at 40 C # W: TODO look this up at 40 C
rho_h2o_aqu = 992 * unit.gram/unit.L # per volume of aqueous phase in the mixture
stg.aqueous_phase.set_value(h2o_aqu.name, rho_h2o_aqu)
1.4. Inflow Parameters#
'''Aqueous phase in the inflow'''
#TODO here the concentration must be larger than in the initial condition in the mixer for lower temp # W: Line too long (105/100)
# look this up later, 1.01 factor may be incorrect
stg.inflow_aqueous_phase.set_value('H2O(a)', 1.0 * rho_h2o_aqu)
'''Organic phase in the inflow'''
stg.inflow_organic_phase.set_value(tbp_org_name, tbp_mass_cc_org)
1.5. Start-up Simulation#
Define the start-up simulation period as one flow residence time.
'''Getting ready to run'''
end_time = 1 * stg.flow_residence_time_avg
import numpy as np
ave_tau = np.mean([data['tau'] for data in stg.rxn_mech.data])
time_step = ave_tau / 15
show_time = (True, 5*time_step)
stg.name = 'Stg-1'
stg.save = True
stg.verbose = True
stg.perturb_flowrates = False
stg.time_step = time_step
stg.end_time = end_time
stg.show_time = show_time
'''Run system in parallel'''
stg.monitor_mass_flowrates = False
stg.monitor_mass_conservation_residual = False
stg.mass_bal_rate_dens_res_tol = 1.e-8 * unit.micro*unit.gram/unit.L/unit.second
system.run()
system.close() # Shutdown Cortix
[13917] 2025-12-02 13:51:52,390 - cortix - INFO - Launching Module <solvex.stage.Stage object at 0x7f7a380b56a0>
[13958] 2025-12-02 13:51:53,759 - cortix - INFO - Stg-1::run():time[m]=0.0
[13958] 2025-12-02 13:51:53,837 - cortix - INFO - Stg-1::run():time[m]=0.3
[13958] 2025-12-02 13:51:53,900 - cortix - INFO - Stg-1::run():time[m]=0.6
Total mass rate density (mixture volume) residual [g/L-s]= -1.38778e-17
total mass inflow rate [g/min] = 6.710e+02
total mass outflow rate [g/min] = 6.711e+02
net total mass flow rate [g/min] = 1.041e-13
[13958] 2025-12-02 13:51:53,977 - cortix - INFO - Stg-1::run():time[m]=1.0 (et[s]=0.2)
[13917] 2025-12-02 13:51:54,169 - cortix - INFO - run()::Elapsed wall clock time [s]: 2.36
[13917] 2025-12-02 13:51:54,170 - cortix - INFO - Closed Cortix object.
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T E R M I N A T I N G
_____________________________________________________________________________
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"888. :" "Y" "Y" "Y" R888" ` "Y Y"
`""***~"` ""
https://cortix.org
_____________________________________________________________________________
[13917] 2025-12-02 13:51:54,171 - cortix - INFO - close()::Elapsed wall clock time [s]: 2.36
'''Recover stage'''
stg = system_net.modules[0]
1.5.1. Organic Phase Results#
'''Plot organic phase'''
# TODO: time axis normalized by phase flow residence time.
stg.organic_phase.plot(title='Organic Phase Start-Up', legend='Organic Phase', nrows=2,ncols=3, show=True, figsize=[12,6])
fig_count += 1
print(f'Figure {fig_count}: Organic phase species history dashboard at start-up.')
Figure 1: Organic phase species history dashboard at start-up.
'''Compute molar concentration of TBP species'''
import numpy as np
tbp_mass_cc_org_history = stg.organic_phase.get_column(tbp_org_name)
tbp_molar_cc_org_history = np.array(tbp_mass_cc_org_history)/tbp_org.molar_mass
tbp_monomer_mass_cc_org_history = stg.organic_phase.get_column(tbp_monomer_org_name)
tbp_monomer_molar_cc_org_history = np.array(tbp_monomer_mass_cc_org_history)/tbp_monomer_org.molar_mass
tbp_dimer_mass_cc_org_history = stg.organic_phase.get_column(tbp_dimer_org_name)
tbp_dimer_molar_cc_org_history = np.array(tbp_dimer_mass_cc_org_history)/tbp_dimer_org.molar_mass
tbp_trimer_hexahydrate_mass_cc_org_history = stg.organic_phase.get_column(tbp_trimer_hexahydrate_org_name)
tbp_trimer_hexahydrate_molar_cc_org_history = np.array(tbp_trimer_hexahydrate_mass_cc_org_history)/tbp_trimer_hexahydrate_org.molar_mass
time_stamps = np.array(stg.organic_phase.time_stamps)
n_startup = len(time_stamps)
tbl_count += 1
print(f'Table {tbl_count}: Molarity history of TBP in the organic phase at start-up.')
print('Time [min] | Free TBP [M] | TBP Monomer [M] | TBP Dimer [M] | TBP Trimer Hexahydrate [M] | balance |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
for t,a,b,c,d in zip(time_stamps[::5]/unit.min,
tbp_molar_cc_org_history[::5]/unit.molar,
tbp_monomer_molar_cc_org_history[::5]/unit.molar,
tbp_dimer_molar_cc_org_history[::5]/unit.molar,
tbp_trimer_hexahydrate_molar_cc_org_history[::5]/unit.molar):
balance = a+b+2*c+3*d - tbp_mass_cc_org/tbp_org.molar_mass/unit.molar
print(' %1.2e %1.3f %1.3e %1.3e %1.3e %+1.3e'%(t, a, b, c, d, balance))
Table 1: Molarity history of TBP in the organic phase at start-up.
Time [min] | Free TBP [M] | TBP Monomer [M] | TBP Dimer [M] | TBP Trimer Hexahydrate [M] | balance |
0.00e+00 1.096 0.000e+00 0.000e+00 0.000e+00 +0.000e+00
3.03e-01 0.939 2.419e-02 5.303e-02 8.904e-03 -4.441e-16
6.06e-01 0.885 3.443e-02 7.103e-02 1.124e-02 +0.000e+00
9.09e-01 0.867 3.892e-02 7.730e-02 1.177e-02 +0.000e+00
'''Volume fraction of TBP at start-up'''
tbl_count += 1
print(f'Table {tbl_count}: Volume fractions of free and total TBP in the organic phase at start-up.')
print('Time [min] | Free TBP vol frac [%] | Total TBP vol frac [%] |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
total_tbp_molar_cc_org_history = tbp_molar_cc_org_history + tbp_monomer_molar_cc_org_history + \
2*tbp_dimer_molar_cc_org_history + 3*tbp_trimer_hexahydrate_molar_cc_org_history
total_tbp_mass_cc_org_history = total_tbp_molar_cc_org_history * tbp_org.molar_mass
for t,a,b in zip(time_stamps[::5]/unit.min,
np.array(tbp_mass_cc_org_history[::5])/rho_tbp*100, total_tbp_mass_cc_org_history[::5]/rho_tbp*100):
print(' %1.2e %1.3f %1.3f'%(t, a, b))
Table 2: Volume fractions of free and total TBP in the organic phase at start-up.
Time [min] | Free TBP vol frac [%] | Total TBP vol frac [%] |
0.00e+00 30.000 30.000
3.03e-01 25.701 30.000
6.06e-01 24.244 30.000
9.09e-01 23.734 30.000
'''Total water extracted'''
water_molar_cc_org_history = tbp_monomer_molar_cc_org_history \
+ 2*tbp_dimer_molar_cc_org_history \
+ 6*tbp_trimer_hexahydrate_molar_cc_org_history
water_mass_cc_org_history = water_molar_cc_org_history * h2o_aqu.molar_mass
tbl_count += 1
print(f'Table {tbl_count}: Mass concentration and molarity history of water in the organic phase at start-up.')
print('Time [s] | [M] | [g/L] |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
for a,b,c in zip(time_stamps[::5], water_molar_cc_org_history[::5]/unit.molar, water_mass_cc_org_history[::5]):
print('%1.2e %1.3e %1.3e'%(a, b, c))
Table 3: Mass concentration and molarity history of water in the organic phase at start-up.
Time [s] | [M] | [g/L] |
0.00e+00 0.000e+00 0.000e+00
1.82e+01 1.837e-01 3.309e+00
3.64e+01 2.439e-01 4.394e+00
5.45e+01 2.641e-01 4.758e+00
1.5.2. Aqueous Phase Results#
'''Plot aqueous phase'''
# TODO: time axis normalized by phase flow residence time.
stg.aqueous_phase.plot(title='Aqueous Phase Start-Up', legend='Aqueous Phase', nrows=2,ncols=3, show=True, figsize=[12,6])
fig_count += 1
print(f'Figure {fig_count}: Aqueous phase species history dashboard at start-up.')
Figure 2: Aqueous phase species history dashboard at start-up.
1.5.3. Overall Stage Efficiency#
Stage efficiency measures how close to chemical equilibrium the system is as a whole. This is a direct result of the reaction relaxation time which is dependent on the mass transfer coefficients of the system. Much more needs to be investigated in this project with various degrees of theory but these results represent the beginning of a solid development.
'''Stage overall efficiency'''
quant = stg.efficiency_history(mean=True)
quant.plot(title='Stage Efficiency @ %2.1f C Start-Up'%unit.convert_temperature(stg_temperature,
'K','C'), x_scaling=1/stg.flow_residence_time_avg, x_label=r'Time [$\bar{\tau}$]', y_label=quant.latex_name+
' ['+quant.unit+']', show=True, figsize=[10,3], error_data=True)
fig_count += 1
print(f'Figure {fig_count}: Stage efficiency history at start-up.')
Figure 3: Stage efficiency history at start-up.
tbl_count += 1
print(f'Table {tbl_count}: Stage efficiency history at start-up.')
print('Time [min] Stage. Eff.(+-std) [%]')
time_name = ''
import pandas as pd
df = (quant.value.apply(pd.Series).mul(1)
.rename(index=lambda i: round(i/unit.min,2))
.set_axis(['',''], axis=1).rename_axis(time_name)
.round(3))
print(df.to_string(max_rows=20, min_rows=20))
Table 4: Stage efficiency history at start-up.
Time [min] Stage. Eff.(+-std) [%]
0.00 0.000 0.000
0.06 6.507 0.111
0.12 12.589 0.377
0.18 18.131 0.711
0.24 23.077 1.052
0.30 27.417 1.359
0.36 31.171 1.611
0.42 34.380 1.797
0.48 37.096 1.919
0.55 39.378 1.982
0.61 41.282 1.994
0.67 42.862 1.965
0.73 44.167 1.904
0.79 45.242 1.820
0.85 46.125 1.720
0.91 46.848 1.610
0.97 47.439 1.495
'''Individual reaction efficiency'''
quant = stg.efficiency_history()
tbl_count += 1
print(f'Table {tbl_count}: Reaction efficiency history at start-up.')
print('Time [min] Rxn Eff. [%]')
col_names = [f'r{i}' for i in range(len(stg.rxn_mech.reactions))]
time_name = ''
df = (quant.value.apply(pd.Series).mul(1)
.rename(index=lambda i: round(i/unit.min,2))
.set_axis(col_names, axis=1).rename_axis(time_name)
.round(3))
print(df.to_string(max_rows=20, min_rows=20))
Table 5: Reaction efficiency history at start-up.
Time [min] Rxn Eff. [%]
r0 r1 r2
0.00 0.000 0.000 0.000
0.06 6.372 6.506 6.644
0.12 12.131 12.581 13.054
0.18 17.270 18.111 19.012
0.24 21.807 23.042 24.383
0.30 25.779 27.366 29.107
0.36 29.232 31.105 33.176
0.42 32.218 34.303 36.618
0.48 34.790 37.011 39.488
0.55 36.997 39.288 41.849
0.61 38.886 41.190 43.768
0.67 40.501 42.772 45.312
0.73 41.880 44.080 46.542
0.79 43.055 45.160 47.512
0.85 44.058 46.048 48.270
0.91 44.912 46.776 48.855
0.97 45.641 47.373 49.302
1.5.3.1. Total water extracted in equilibrium#
From reference: 1994 Naganawa and Tachimori Anal. Sci. 10 p 607
[H2O]_o,E = 0.4265 M
h2o_e_molar = water_molar_cc_org_history[-1]/unit.molar
print('Total H2O extracted [M] = %1.4f'%h2o_e_molar)
print('Error (compared to measurement) [%%] = %1.2f'%((h2o_e_molar-0.4265)/0.4265*100))
Total H2O extracted [M] = 0.2661
Error (compared to measurement) [%] = -37.60
1.5.4. Reaction Rate Density#
This quantity only makes sense per volume of the mixture.
'''Reaction rate density'''
import matplotlib.pyplot as plt
quant = stg.r_vec_history() # mole/m^3-s
quant.plot(title='Reaction Rate Density @ %2.1f C Start-Up'%unit.convert_temperature(stg_temperature,
'K','C'), x_scaling=1/stg.flow_residence_time_avg, x_label=r'Time [$\bar{\tau}$]', y_label=quant.latex_name+
' ['+quant.unit+']', legend=stg.rxn_mech.reactions, show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Reaction rate density history at start-up.')
Figure 4: Reaction rate density history at start-up.
tbl_count += 1
print(f'Table {tbl_count}: Reaction rate density history at start-up.')
print('Time [min] r [mM/s]')
import pandas as pd
col_names = [f'r{i}' for i in range(len(stg.rxn_mech.reactions))]
time_name = 't [min]'
df = (quant.value.apply(pd.Series).mul(1)
.rename(index=lambda i: round(i/unit.min,2))
.set_axis(col_names, axis=1).rename_axis(time_name)
.round(4))
print(df.to_string(max_rows=20, min_rows=20))
Table 6: Reaction rate density history at start-up.
Time [min] r [mM/s]
r0 r1 r2
t [min]
0.00 1.0955 2.6403 0.4865
0.06 0.9820 2.2626 0.3985
0.12 0.8889 1.9681 0.3330
0.18 0.8122 1.7365 0.2836
0.24 0.7490 1.5533 0.2459
0.30 0.6966 1.4076 0.2169
0.36 0.6532 1.2912 0.1944
0.42 0.6171 1.1980 0.1770
0.48 0.5870 1.1231 0.1633
0.55 0.5620 1.0627 0.1527
0.61 0.5411 1.0141 0.1444
0.67 0.5235 0.9748 0.1378
0.73 0.5088 0.9430 0.1327
0.79 0.4965 0.9173 0.1287
0.85 0.4862 0.8964 0.1256
0.91 0.4774 0.8795 0.1232
0.97 0.4701 0.8658 0.1213
1.5.5. Species Generation Rate Density#
This quantity is on the basis of mixing volume so all species generation values can be compared.
'''Species generation rate density'''
import matplotlib.pyplot as plt
quant = stg.g_vec_history() # mole/m^3-s
quant.plot(title='Species Generation Rate Density @ %2.1f C Start-Up'%unit.convert_temperature(stg_temperature,
'K','C'), x_scaling=1/stg.flow_residence_time_avg, x_label=r'Time [$\bar{\tau}$]', y_label=quant.latex_name+
' ['+quant.unit+']', legend=stg.rxn_mech.species_names, show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Species generation rate density history at start-up.')
Figure 5: Species generation rate density history at start-up.
tbl_count += 1
print(f'Table {tbl_count}: Species generation rate density history at start-up.')
print('Time [min] g [mM/s]')
import pandas as pd
col_names = [f'a{i}' for i in range(len(stg.rxn_mech.species_names))]
time_name = 't [min]'
df = (quant.value.apply(pd.Series).mul(1)
.rename(index=lambda i: round(i/unit.min,2))
.set_axis(col_names, axis=1).rename_axis(time_name)
.round(4))
print(df.to_string(max_rows=20, min_rows=20))
Table 7: Species generation rate density history at start-up.
Time [min] g [mM/s]
a0 a1 a2 a3 a4
t [min]
0.00 -9.2949 1.0955 -7.8355 2.6403 0.4865
0.06 -7.8984 0.9820 -6.7028 2.2626 0.3985
0.12 -6.8231 0.8889 -5.8240 1.9681 0.3330
0.18 -5.9866 0.8122 -5.1359 1.7365 0.2836
0.24 -5.3306 0.7490 -4.5931 1.5533 0.2459
0.30 -4.8128 0.6966 -4.1623 1.4076 0.2169
0.36 -4.4020 0.6532 -3.8188 1.2912 0.1944
0.42 -4.0748 0.6171 -3.5439 1.1980 0.1770
0.48 -3.8132 0.5870 -3.3232 1.1231 0.1633
0.55 -3.6037 0.5620 -3.1456 1.0627 0.1527
0.61 -3.4354 0.5411 -3.0023 1.0141 0.1444
0.67 -3.3002 0.5235 -2.8866 0.9748 0.1378
0.73 -3.1912 0.5088 -2.7930 0.9430 0.1327
0.79 -3.1035 0.4965 -2.7173 0.9173 0.1287
0.85 -3.0327 0.4862 -2.6559 0.8964 0.1256
0.91 -2.9756 0.4774 -2.6061 0.8795 0.1232
0.97 -2.9296 0.4701 -2.5657 0.8658 0.1213
1.6. Steady-State Simulation#
Pick up from where it left from the past run() and continue to the fully developed state of 5 flow residence time. This demonstrates how to continue a simulation from where it was interrupted. Note that the state of the system is automatically used as the initial condition for the next run().
end_time += 4 * stg.flow_residence_time_avg
time_step = 4 * stg.flow_residence_time_avg / 10
show_time = (True, 10*time_step)
stg.time_step = time_step
stg.initial_time = stg.end_time
stg.end_time = end_time
stg.show_time = show_time
'''Run system in parallel'''
stg.monitor_mass_flowrates = False
stg.monitor_mass_conservation_residual = False
system.run()
system.close() # Shutdown Cortix
[13917] 2025-12-02 13:51:56,791 - cortix - INFO - Launching Module <solvex.stage.Stage object at 0x7f79dd878a50>
[13985] 2025-12-02 13:51:58,019 - cortix - INFO - Stg-1::run():time[m]=1.0
Total mass rate density (mixture volume) residual [g/L-s]= -9.02056e-17
total mass inflow rate [g/min] = 6.710e+02
total mass outflow rate [g/min] = 6.711e+02
net total mass flow rate [g/min] = 1.041e-13
[13985] 2025-12-02 13:51:58,127 - cortix - INFO - Stg-1::run():time[m]=4.6 (et[s]=0.1)
[13917] 2025-12-02 13:51:58,300 - cortix - INFO - run()::Elapsed wall clock time [s]: 6.49
[13917] 2025-12-02 13:51:58,301 - cortix - INFO - Closed Cortix object.
_____________________________________________________________________________
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_____________________________________________________________________________
[13917] 2025-12-02 13:51:58,301 - cortix - INFO - close()::Elapsed wall clock time [s]: 6.49
'''Recover stage'''
stg = system_net.modules[0]
1.6.1. Organic Phase Results#
'''Plot organic phase'''
# TODO: time axis normalized by phase flow residence time.
stg.organic_phase.plot(title='Organic Phase Steady-State', legend='Organic Phase', nrows=2,ncols=3, show=True, figsize=[12,6])
fig_count += 1
print(f'Figure {fig_count}: Organic phase species history dashboard at steady-state.')
Figure 6: Organic phase species history dashboard at steady-state.
'''Compute molar concentration of TBP species'''
import numpy as np
tbp_mass_cc_org_history = stg.organic_phase.get_column(tbp_org_name)
tbp_molar_cc_org_history = np.array(tbp_mass_cc_org_history)/tbp_org.molar_mass
tbp_monomer_mass_cc_org_history = stg.organic_phase.get_column(tbp_monomer_org_name)
tbp_monomer_molar_cc_org_history = np.array(tbp_monomer_mass_cc_org_history)/tbp_monomer_org.molar_mass
tbp_dimer_mass_cc_org_history = stg.organic_phase.get_column(tbp_dimer_org_name)
tbp_dimer_molar_cc_org_history = np.array(tbp_dimer_mass_cc_org_history)/tbp_dimer_org.molar_mass
tbp_trimer_hexahydrate_mass_cc_org_history = stg.organic_phase.get_column(tbp_trimer_hexahydrate_org_name)
tbp_trimer_hexahydrate_molar_cc_org_history = np.array(tbp_trimer_hexahydrate_mass_cc_org_history)/tbp_trimer_hexahydrate_org.molar_mass
time_stamps = np.array(stg.organic_phase.time_stamps)
tbl_count += 1
print(f'Table {tbl_count}: Molarity history of TBP in the organic phase at steady-state.')
print('Time [min] | Free TBP [M] | TBP Monomer [M] | TBP Dimer [M] | TBP Trimer Hexahydrate [M] | balance |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
for t,a,b,c,d in zip(time_stamps[n_startup::5]/unit.min,
tbp_molar_cc_org_history[n_startup::5]/unit.molar,
tbp_monomer_molar_cc_org_history[n_startup::5]/unit.molar,
tbp_dimer_molar_cc_org_history[n_startup::5]/unit.molar,
tbp_trimer_hexahydrate_molar_cc_org_history[n_startup::5]/unit.molar):
balance = a+b+2*c+3*d - tbp_mass_cc_org/tbp_org.molar_mass/unit.molar
print(' %1.2e %1.3f %1.3e %1.3e %1.3e %+1.3e'%(t, a, b, c, d, balance))
Table 8: Molarity history of TBP in the organic phase at steady-state.
Time [min] | Free TBP [M] | TBP Monomer [M] | TBP Dimer [M] | TBP Trimer Hexahydrate [M] | balance |
1.33e+00 0.859 4.144e-02 7.991e-02 1.180e-02 +2.220e-16
3.15e+00 0.856 4.280e-02 8.068e-02 1.163e-02 +0.000e+00
'''Volume fraction of TBP at start-up'''
tbl_count += 1
print(f'Table {tbl_count}: Volume fractions of free and total TBP in the organic phase at steady-state.')
print('Time [min] | Free TBP vol frac [%] | Total TBP vol frac [%] |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
total_tbp_molar_cc_org_history = tbp_molar_cc_org_history + tbp_monomer_molar_cc_org_history + \
2*tbp_dimer_molar_cc_org_history + 3*tbp_trimer_hexahydrate_molar_cc_org_history
total_tbp_mass_cc_org_history = total_tbp_molar_cc_org_history * tbp_org.molar_mass
for t,a,b in zip(time_stamps[::5]/unit.min,
np.array(tbp_mass_cc_org_history[::5])/rho_tbp*100, total_tbp_mass_cc_org_history[::5]/rho_tbp*100):
print(' %1.2e %1.3f %1.3f'%(t, a, b))
Table 9: Volume fractions of free and total TBP in the organic phase at steady-state.
Time [min] | Free TBP vol frac [%] | Total TBP vol frac [%] |
0.00e+00 30.000 30.000
3.03e-01 25.701 30.000
6.06e-01 24.244 30.000
9.09e-01 23.734 30.000
2.42e+00 23.455 30.000
4.24e+00 23.453 30.000
'''Total water extracted'''
water_molar_cc_org_history = tbp_monomer_molar_cc_org_history \
+ 2*tbp_dimer_molar_cc_org_history \
+ 6*tbp_trimer_hexahydrate_molar_cc_org_history
water_mass_cc_org_history = water_molar_cc_org_history * h2o_aqu.molar_mass
tbl_count += 1
print(f'Table {tbl_count}: Mass concentration and molarity history of water in the organic phase at steady-state.')
print('Time [s] | [M] | [g/L] |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
for a,b,c in zip(time_stamps[n_startup::5], water_molar_cc_org_history[n_startup::5]/unit.molar, water_mass_cc_org_history[n_startup::5]):
print('%1.2e %1.3e %1.3e'%(a, b, c))
Table 10: Mass concentration and molarity history of water in the organic phase at steady-state.
Time [s] | [M] | [g/L] |
8.00e+01 2.721e-01 4.901e+00
1.89e+02 2.739e-01 4.935e+00
1.6.2. Aqueous Phase Results#
'''Plot aqueous phase'''
# TODO: time axis normalized by phase flow residence time.
stg.aqueous_phase.plot(title='Aqueous Phase Steady-State', legend='Aqueous Phase', nrows=2,ncols=3, show=True, figsize=[12,6])
fig_count += 1
print(f'Figure {fig_count}: Aqueous phase species history dashboard at steady-state.')
Figure 7: Aqueous phase species history dashboard at steady-state.
1.6.3. Overall Stage Efficiency#
'''Stage overall efficiency'''
quant = stg.efficiency_history(mean=True)
quant.plot(title='Stage Efficiency @ %2.1f C Steady-State'%unit.convert_temperature(stg_temperature,
'K','C'), x_scaling=1/stg.flow_residence_time_avg, x_label=r'Time [$\bar{\tau}$]', y_label=quant.latex_name+
' ['+quant.unit+']', show=True, figsize=[10,3], error_data=True)
fig_count += 1
print(f'Figure {fig_count}: Stage efficiency history steady-state.')
Figure 8: Stage efficiency history steady-state.
tbl_count += 1
print(f'Table {tbl_count}: Stage efficiency history at steady-state.')
print('Time [min] Stage. Eff.(+-std) [%]')
time_name = ''
import pandas as pd
df = (quant.value.apply(pd.Series).mul(1)
.rename(index=lambda i: round(i/unit.min,2))
.set_axis(['',''], axis=1).rename_axis(time_name)
.round(3))
print(df.to_string(max_rows=20, min_rows=20))
Table 11: Stage efficiency history at steady-state.
Time [min] Stage. Eff.(+-std) [%]
0.00 0.000 0.000
0.06 6.507 0.111
0.12 12.589 0.377
0.18 18.131 0.711
0.24 23.077 1.052
0.30 27.417 1.359
0.36 31.171 1.611
0.42 34.380 1.797
0.48 37.096 1.919
0.55 39.378 1.982
... ... ...
1.33 49.276 0.855
1.70 49.800 0.437
2.06 49.947 0.211
2.42 49.987 0.099
2.79 49.997 0.046
3.15 50.000 0.021
3.52 50.000 0.010
3.88 50.000 0.004
4.24 50.000 0.002
4.61 50.000 0.001
'''Individual reaction efficiency'''
quant = stg.efficiency_history()
tbl_count += 1
print(f'Table {tbl_count}: Reaction efficiency history at steady-state.')
print('Time [min] Rxn Eff. [%]')
col_names = [f'r{i}' for i in range(len(stg.rxn_mech.reactions))]
time_name = ''
df = (quant.value.apply(pd.Series).mul(1)
.rename(index=lambda i: round(i/unit.min,2))
.set_axis(col_names, axis=1).rename_axis(time_name)
.round(3))
print(df.to_string(max_rows=20, min_rows=20))
Table 12: Reaction efficiency history at steady-state.
Time [min] Rxn Eff. [%]
r0 r1 r2
0.00 0.000 0.000 0.000
0.06 6.372 6.506 6.644
0.12 12.131 12.581 13.054
0.18 17.270 18.111 19.012
0.24 21.807 23.042 24.383
0.30 25.779 27.366 29.107
0.36 29.232 31.105 33.176
0.42 32.218 34.303 36.618
0.48 34.790 37.011 39.488
0.55 36.997 39.288 41.849
... ... ... ...
1.33 48.246 49.241 50.339
1.70 49.274 49.784 50.343
2.06 49.692 49.940 50.210
2.42 49.867 49.984 50.110
2.79 49.942 49.996 50.054
3.15 49.974 49.999 50.026
3.52 49.989 50.000 50.012
3.88 49.995 50.000 50.005
4.24 49.998 50.000 50.002
4.61 49.999 50.000 50.001
1.6.3.1. Total water extracted in equilibrium#
From reference: 1994 Naganawa and Tachimori Anal. Sci. 10 p 607
[H2O]_o,E = 0.4265 M
Comparison to steady state:
h2o_e_molar = water_molar_cc_org_history[-1]/unit.molar
print('Total H2O extracted [M] = %1.4f'%h2o_e_molar)
print('Error (compared to measurement) [%%] = %1.2f'%((h2o_e_molar-0.4265)/0.4265*100))
Total H2O extracted [M] = 0.2739
Error (compared to measurement) [%] = -35.77
1.6.4. Reaction Rate Density#
This quantity only makes sense per volume of the mixture.
'''Reaction rate density'''
import matplotlib.pyplot as plt
quant = stg.r_vec_history()# mole/m^3-s
quant.plot(title='Reaction Rate Density @ %2.1f C Steady-State'%unit.convert_temperature(stg_temperature,
'K','C'), x_scaling=1/stg.flow_residence_time_avg, x_label=r'Time [$\bar{\tau}$]', y_label=quant.latex_name+
' ['+quant.unit+']', legend=stg.rxn_mech.reactions, show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Reaction rate density history at steady-state.')
Figure 9: Reaction rate density history at steady-state.
tbl_count += 1
print(f'Table {tbl_count}: Reaction rate density history at steady-state.')
print('Time [min] r [mM/s]')
import pandas as pd
col_names = [f'r{i}' for i in range(len(stg.rxn_mech.reactions))]
time_name = 't [min]'
df = (quant.value.apply(pd.Series).mul(1)
.rename(index=lambda i: round(i/unit.min,2))
.set_axis(col_names, axis=1).rename_axis(time_name)
.round(4))
print(df.iloc[n_startup:].to_string(max_rows=20, min_rows=20))
Table 13: Reaction rate density history at steady-state.
Time [min] r [mM/s]
r0 r1 r2
t [min]
1.33 0.4445 0.8237 0.1164
1.70 0.4348 0.8117 0.1157
2.06 0.4310 0.8082 0.1158
2.42 0.4294 0.8072 0.1160
2.79 0.4287 0.8070 0.1161
3.15 0.4284 0.8069 0.1162
3.52 0.4283 0.8069 0.1162
3.88 0.4283 0.8069 0.1162
4.24 0.4282 0.8069 0.1162
4.61 0.4282 0.8069 0.1162
1.6.5. Species Generation Rate Density#
This quantity is on the basis of mixing volume so all species generation values can be compared.
'''Species generation rate density'''
import matplotlib.pyplot as plt
quant = stg.g_vec_history() # mole/m^3-s
quant.plot(title='Species Generation Rate Density @ %2.1f C Steady-State'%unit.convert_temperature(stg_temperature,
'K','C'), x_scaling=1/stg.flow_residence_time_avg, x_label=r'Time [$\bar{\tau}$]', y_label=quant.latex_name+
' ['+quant.unit+']', legend=stg.rxn_mech.species_names, show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Species generation rate density history at steady-state.')
Figure 10: Species generation rate density history at steady-state.
tbl_count += 1
print(f'Table {tbl_count}: Species generation rate density history at steady-state.')
print('Time [min] g [mM/s]')
import pandas as pd
col_names = [f'a{i}' for i in range(len(stg.rxn_mech.species_names))]
time_name = 't [min]'
df = (quant.value.apply(pd.Series).mul(1)
.rename(index=lambda i: round(i/unit.min,2))
.set_axis(col_names, axis=1).rename_axis(time_name)
.round(4))
print(df.iloc[n_startup:].to_string(max_rows=20, min_rows=20))
Table 14: Species generation rate density history at steady-state.
Time [min] g [mM/s]
a0 a1 a2 a3 a4
t [min]
1.33 -2.7903 0.4445 -2.4411 0.8237 0.1164
1.70 -2.7523 0.4348 -2.4052 0.8117 0.1157
2.06 -2.7423 0.4310 -2.3948 0.8082 0.1158
2.42 -2.7398 0.4294 -2.3918 0.8072 0.1160
2.79 -2.7392 0.4287 -2.3909 0.8070 0.1161
3.15 -2.7392 0.4284 -2.3907 0.8069 0.1162
3.52 -2.7392 0.4283 -2.3906 0.8069 0.1162
3.88 -2.7392 0.4283 -2.3906 0.8069 0.1162
4.24 -2.7392 0.4282 -2.3906 0.8069 0.1162
4.61 -2.7392 0.4282 -2.3906 0.8069 0.1162
1.6.5.1. Species generation rate density at steady-state:#
g_vec = stg.g_vec()
columns = stg.rxn_mech.species_names
print('Generation sources [mM/s]')
print(pd.DataFrame([list(g_vec)], columns=columns).T
.rename(columns={0:'g [mM/s]'}).to_string(float_format='{:.6f}'.format))
Generation sources [mM/s]
g [mM/s]
H2O(a) -2.739244
H2O*[C4H9O]3PO(o) 0.428233
[C4H9O]3PO(o) -2.390595
[H2O]2*[[C4H9O]3PO]2(o) 0.806856
[H2O]6*[[C4H9O]3PO]3(o) 0.116216
1.7. Shut-down Simulation#
From steady-state, shutdown in two flow residence times.
end_time += 2 * stg.flow_residence_time_avg
time_step = 2 * stg.flow_residence_time_avg / 20
show_time = (True, 10*time_step)
stg.time_step = time_step
stg.initial_time = stg.end_time
stg.end_time = end_time
stg.show_time = show_time
'''Organic phase in the inflow'''
tbp_mass_cc_org = 0.0
stg.inflow_organic_phase.set_value(tbp_org_name, tbp_mass_cc_org)
'''Run system in parallel'''
stg.monitor_mass_flowrates = False
stg.monitor_mass_conservation_residual = False
system.run()
system.close() # Shutdown Cortix
[13917] 2025-12-02 13:52:00,870 - cortix - INFO - Launching Module <solvex.stage.Stage object at 0x7f79d9bf9090>
[14007] 2025-12-02 13:52:02,142 - cortix - INFO - Stg-1::run():time[m]=4.6
[14007] 2025-12-02 13:52:02,296 - cortix - INFO - Stg-1::run():time[m]=5.6
Total mass rate density (mixture volume) residual [g/L-s]= 1.73472e-18
total mass inflow rate [g/min] = 4.960e+02
total mass outflow rate [g/min] = 5.196e+02
net total mass flow rate [g/min] = 2.364e+01
[14007] 2025-12-02 13:52:02,423 - cortix - INFO - Stg-1::run():time[m]=6.4 (et[s]=0.3)
[13917] 2025-12-02 13:52:02,636 - cortix - INFO - run()::Elapsed wall clock time [s]: 10.83
[13917] 2025-12-02 13:52:02,637 - cortix - INFO - Closed Cortix object.
_____________________________________________________________________________
T E R M I N A T I N G
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https://cortix.org
_____________________________________________________________________________
[13917] 2025-12-02 13:52:02,638 - cortix - INFO - close()::Elapsed wall clock time [s]: 10.83
'''Recover stage'''
stg = system_net.modules[0]
1.7.1. Organic Phase Results#
'''Plot organic phase'''
# TODO: time axis normalized by phase flow residence time.
stg.organic_phase.plot(title='Organic Phase Shut-Down', legend='Organic Phase', nrows=2,ncols=3, show=True, figsize=[12,6])
fig_count += 1
print(f'Figure {fig_count}: Organic phase species history dashboard at shut-down.')
Figure 11: Organic phase species history dashboard at shut-down.
'''Compute molar concentration of TBP species'''
import numpy as np
tbp_mass_cc_org_history = stg.organic_phase.get_column(tbp_org_name)
tbp_molar_cc_org_history = np.array(tbp_mass_cc_org_history)/tbp_org.molar_mass
tbp_monomer_mass_cc_org_history = stg.organic_phase.get_column(tbp_monomer_org_name)
tbp_monomer_molar_cc_org_history = np.array(tbp_monomer_mass_cc_org_history)/tbp_monomer_org.molar_mass
tbp_dimer_mass_cc_org_history = stg.organic_phase.get_column(tbp_dimer_org_name)
tbp_dimer_molar_cc_org_history = np.array(tbp_dimer_mass_cc_org_history)/tbp_dimer_org.molar_mass
tbp_trimer_hexahydrate_mass_cc_org_history = stg.organic_phase.get_column(tbp_trimer_hexahydrate_org_name)
tbp_trimer_hexahydrate_molar_cc_org_history = np.array(tbp_trimer_hexahydrate_mass_cc_org_history)/tbp_trimer_hexahydrate_org.molar_mass
time_stamps = np.array(stg.organic_phase.time_stamps)
tbl_count += 1
print(f'Table {tbl_count}: Molarity history of TBP in the organic phase at shut-down.')
print('Time [min] | Free TBP [M] | TBP Monomer [M] | TBP Dimer [M] | TBP Trimer Hexahydrate [M] | balance |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
for t,a,b,c,d in zip(time_stamps[n_startup::5]/unit.min,
tbp_molar_cc_org_history[n_startup::5]/unit.molar,
tbp_monomer_molar_cc_org_history[n_startup::5]/unit.molar,
tbp_dimer_molar_cc_org_history[n_startup::5]/unit.molar,
tbp_trimer_hexahydrate_molar_cc_org_history[n_startup::5]/unit.molar):
balance = a+b+2*c+3*d - tbp_mass_cc_org/tbp_org.molar_mass/unit.molar
print(' %1.2e %1.3f %1.3e %1.3e %1.3e %+1.3e'%(t, a, b, c, d, balance))
Table 15: Molarity history of TBP in the organic phase at shut-down.
Time [min] | Free TBP [M] | TBP Monomer [M] | TBP Dimer [M] | TBP Trimer Hexahydrate [M] | balance |
1.33e+00 0.859 4.144e-02 7.991e-02 1.180e-02 +1.096e+00
3.15e+00 0.856 4.280e-02 8.068e-02 1.163e-02 +1.096e+00
4.70e+00 0.754 4.251e-02 8.015e-02 1.142e-02 +9.913e-01
5.15e+00 0.420 3.526e-02 6.210e-02 7.264e-03 +6.012e-01
5.61e+00 0.253 2.577e-02 3.783e-02 3.492e-03 +3.647e-01
6.06e+00 0.158 1.787e-02 2.049e-02 1.506e-03 +2.212e-01
'''Volume fraction of TBP at start-up'''
tbl_count += 1
print(f'Table {tbl_count}: Volume fractions of free and total TBP in the organic phase at start-up.')
print('Time [min] | Free TBP vol frac [%] | Total TBP vol frac [%] |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
total_tbp_molar_cc_org_history = tbp_molar_cc_org_history + tbp_monomer_molar_cc_org_history + \
2*tbp_dimer_molar_cc_org_history + 3*tbp_trimer_hexahydrate_molar_cc_org_history
total_tbp_mass_cc_org_history = total_tbp_molar_cc_org_history * tbp_org.molar_mass
for t,a,b in zip(time_stamps[::5]/unit.min,
np.array(tbp_mass_cc_org_history[::5])/rho_tbp*100, total_tbp_mass_cc_org_history[::5]/rho_tbp*100):
print(' %1.2e %1.3f %1.3f'%(t, a, b))
Table 16: Volume fractions of free and total TBP in the organic phase at start-up.
Time [min] | Free TBP vol frac [%] | Total TBP vol frac [%] |
0.00e+00 30.000 30.000
3.03e-01 25.701 30.000
6.06e-01 24.244 30.000
9.09e-01 23.734 30.000
2.42e+00 23.455 30.000
4.24e+00 23.453 30.000
4.97e+00 14.373 20.110
5.42e+00 8.425 12.197
5.88e+00 5.206 7.398
6.33e+00 3.277 4.487
'''Total water extracted'''
water_molar_cc_org_history = tbp_monomer_molar_cc_org_history \
+ 2*tbp_dimer_molar_cc_org_history \
+ 6*tbp_trimer_hexahydrate_molar_cc_org_history
water_mass_cc_org_history = water_molar_cc_org_history * h2o_aqu.molar_mass
tbl_count += 1
print(f'Table {tbl_count}: Mass concentration and molarity history of water in the organic phase at shut-down.')
print('Time [s] | [M] | [g/L] |')
np.set_printoptions(precision=3, suppress=True, linewidth=100)
for a,b,c in zip(time_stamps[n_startup::5], water_molar_cc_org_history[n_startup::5]/unit.molar, water_mass_cc_org_history[n_startup::5]):
print('%1.2e %1.3e %1.3e'%(a, b, c))
Table 17: Mass concentration and molarity history of water in the organic phase at shut-down.
Time [s] | [M] | [g/L] |
8.00e+01 2.721e-01 4.901e+00
1.89e+02 2.739e-01 4.935e+00
2.82e+02 2.713e-01 4.888e+00
3.09e+02 2.030e-01 3.658e+00
3.36e+02 1.224e-01 2.205e+00
3.64e+02 6.788e-02 1.223e+00
1.7.2. Aqueous Phase Results#
'''Plot aqueous phase'''
# TODO: time axis normalized by phase flow residence time.
stg.aqueous_phase.plot(title='Aqueous Phase Shut-Down', legend='Aqueous Phase', nrows=2,ncols=3, show=True, figsize=[12,6])
fig_count += 1
print(f'Figure {fig_count}: Aqueous phase species history dashboard at shut-down.')
Figure 12: Aqueous phase species history dashboard at shut-down.
1.7.3. Reaction Rate Density#
This quantity only makes sense per volume of the mixture.
'''Reaction rate density'''
import matplotlib.pyplot as plt
quant = stg.r_vec_history()
quant.plot(title='Reaction Rate Density @ %2.1f C Shut-Down'%unit.convert_temperature(stg_temperature,
'K','C'), x_scaling=1/stg.flow_residence_time_avg, x_label=r'Time [$\bar{\tau}$]', y_label=quant.latex_name+
' ['+quant.unit+']', legend=stg.rxn_mech.reactions, show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Reaction rate density history at shut-down.')
Figure 13: Reaction rate density history at shut-down.
1.7.4. Species Generation Rate Density#
This quantity is on the basis of mixing volume so all species generation values can be compared.
'''Species generation rate density'''
import matplotlib.pyplot as plt
quant = stg.g_vec_history()
quant.plot(title='Species Generation Rate Density @ %2.1f C Shut-Down'%unit.convert_temperature(stg_temperature,
'K','C'), x_scaling=1/stg.flow_residence_time_avg, x_label=r'Time [$\bar{\tau}$]', y_label=quant.latex_name+
' ['+quant.unit+']', legend=stg.rxn_mech.species_names, show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Species generation rate density history at shut-down.')
Figure 14: Species generation rate density history at shut-down.
1.8. References#
[1] V. F. de Almeida, Cortix, Network Dynamics Simulation, Cortix Tech, Lowell, MA.