Single-Stage Solvex Development Cortix Tech 17Nov2025
1. TBP-Diluent-H\(_2\)O-HNO\(_3\) Mixing#
Developer: Valmor F. de Almeida, PhD
Cortix Tech, Lowell, MA 01854, USA
Revision date: 17Nov25
1.1. Objectives#
Develop usecase scenario for water and nitric acid extraction by TBP without a vapor phase.
Test implementation and present results.
'''Other helpers'''
fig_count = 0
tbl_count = 0
markdown_display = True # if False code cell output is type: stream, else: markdown. Use True for in-house conversion to .md
1.2. Base System#
Single stage mixing of TBP with inert diluent and HNO3 solution.
'''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
[3365] 2025-11-18 03:03:56,289 - 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 to model and simulate the reactive mixing process.
'''Import Stage'''
from solvex import Stage
1.2.1.1. Configuration#
'''Create Base Stage and add to Base System'''
# Initialization
holdup_volume = 1*unit.L
# Aqueous phase
vol_flowrate_aqu = 500*unit.mL/unit.min
# Organic phase
vol_flowrate_org = 600*unit.mL/unit.min
# Vapor phase
vol_flowrate_vap = (0.0*vol_flowrate_org/100, 0.0*vol_flowrate_aqu/100) # percentage of (org, aqu)
vol_flowrates = [vol_flowrate_org, vol_flowrate_aqu, vol_flowrate_vap]
stg_temperature = unit.convert_temperature(40, 'C', 'K')
stg = Stage(holdup_volume, 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)
print('Vapor volume fraction = %5.3e'%stg.volume_frac_vap)
Flow residence time [s]: average = 5.455e+01
Aqueous volume fraction = 4.545e-01
Organic volume fraction = 5.455e-01
Vapor volume fraction = 0.000e+00
'''Draw the Cortix network 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
# Poor's man help
#help(solvex_ustc.stage)
1.2.2. Reaction Mechanism#
Contacting water, inert diluent and TBP, and nitric acid.
1.2.2.1. Nitric acid, water extraction example#
args_dict = {'water_activity': 1.0}
file_name = 'tbp-h2o-hno3.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)
WARNING: ReactionMechanism: user must implement a HNO3*[C4H9O]3PO(o) product partition function with signature <product>(rxn_mech, temperature, spc_molar_cc, arg_dict) function for H^+(a) + NO3^-(a) + [C4H9O]3PO(o) <-> HNO3*[C4H9O]3PO(o)
WARNING: ReactionMechanism: user must implement a HNO3*[[C4H9O]3PO]2(o) product partition function with signature <product>(rxn_mech, temperature, spc_molar_cc, arg_dict) function for H^+(a) + NO3^-(a) + 2 [C4H9O]3PO(o) <-> HNO3*[[C4H9O]3PO]2(o)
#'''User input'''
#rxn_mech.cat_input()
#'''Show Mechanism'''
# Jupyter Book does not render LaTeX through IPython.display(Markdown)
#rxn_mech.md_print()
#'''Species and Reactions Manual Output'''
# Jupyter Book does not render LaTeX through IPython.display(Markdown)
#print(len(rxn_mech.species_names), ' **Species**\n', rxn_mech.latex_species)
#print(len(rxn_mech.reactions), ' **Reactions**\n', rxn_mech.latex_rxn)
9 Species
\[\begin{align*}
&{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}, {\mathrm{H}_{2}\mathrm{O}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, {\mathrm{H}\mathrm{N}\mathrm{O}_{3}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, {\mathrm{H}\mathrm{N}\mathrm{O}_{3}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}, {\mathrm{H}^+}_\mathrm{(a)}, {\mathrm{N}\mathrm{O}_{3}^-}_\mathrm{(a)}, {[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, {[\mathrm{H}_{2}\mathrm{O}]_{2}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}, \\
& {[\mathrm{H}_{2}\mathrm{O}]_{6}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{3}}_{\mathrm{(o)}}\end{align*}\]
5 Reactions
\[\begin{align*}
{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}\ + \ {[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\ &\longleftrightarrow \ {\mathrm{H}_{2}\mathrm{O}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\\
2.0\,{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}\ + \ 2.0\,{[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\ &\longleftrightarrow \ {[\mathrm{H}_{2}\mathrm{O}]_{2}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}\\
6.0\,{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}\ + \ 3.0\,{[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\ &\longleftrightarrow \ {[\mathrm{H}_{2}\mathrm{O}]_{6}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{3}}_{\mathrm{(o)}}\\
{\mathrm{H}^+}_\mathrm{(a)}\ + \ {\mathrm{N}\mathrm{O}_{3}^-}_\mathrm{(a)}\ + \ {[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\ &\longleftrightarrow \ {\mathrm{H}\mathrm{N}\mathrm{O}_{3}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\\
{\mathrm{H}^+}_\mathrm{(a)}\ + \ {\mathrm{N}\mathrm{O}_{3}^-}_\mathrm{(a)}\ + \ 2.0\,{[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}\ &\longleftrightarrow \ {\mathrm{H}\mathrm{N}\mathrm{O}_{3}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}\\
\end{align*} \]
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 = 5
# species = 9
rank of S = 5
S is full rank.
S=
[[-1. 1. 0. 0. 0. 0. -1. 0. 0.]
[-2. 0. 0. 0. 0. 0. -2. 1. 0.]
[-6. 0. 0. 0. 0. 0. -3. 0. 1.]
[ 0. 0. 1. 0. -1. -1. -1. 0. 0.]
[ 0. 0. 0. 1. -1. -1. -2. 0. 0.]]
1.2.2.3. User-Provided Partition Functions#
'''Partition functions 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
# Partition function for H2O*TBP complexation
rxn_mech.data[0]['tau-partition-function'] = partition_h2o_tbp_org
# Partition function for 2H2O*2TBP complexation
rxn_mech.data[1]['tau-partition-function'] = partition_2h2o_2tbp_org
# Partition function for 6H2O*3TBP complexation
rxn_mech.data[2]['tau-partition-function'] = partition_6h2o_3tbp_org
from solvex.partition_func_local import partition_hno3_tbp_org
from solvex.partition_func_local import partition_hno3_2tbp_org
# Partition function for HNO3*TBP complexation
rxn_mech.data[3]['tau-partition-function'] = partition_hno3_tbp_org
# Partition function for HNO3*2TBP complexation
rxn_mech.data[4]['tau-partition-function'] = partition_hno3_2tbp_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 (Jupyter Book will not render)'''
#str = stg.rxn_mech.md_print('(a)')
#'''Aqueous phase (manual for Jupyter Book)'''
#print(stg.rxn_mech.md_print('(a)'))
\[\begin{align*}
&{\mathrm{H}_{2}\mathrm{O}}_\mathrm{(a)}, \ {\mathrm{H}^+}_\mathrm{(a)}, \ {\mathrm{N}\mathrm{O}_{3}^-}_\mathrm{(a)}, \ \end{align*}\]
#'''Organic phase (Jupyter Book will not render)'''
#str = stg.rxn_mech.md_print('(o)', n_species_line=5)
#'''Organic phase (manual for Jupyter Book)'''
#print(stg.rxn_mech.md_print('(o)', n_species_line=5))
\[\begin{align*}
&{\mathrm{H}_{2}\mathrm{O}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, \ {\mathrm{H}\mathrm{N}\mathrm{O}_{3}\bullet[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, \ {\mathrm{H}\mathrm{N}\mathrm{O}_{3}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}, \ {[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}}_\mathrm{(o)}, \ {[\mathrm{H}_{2}\mathrm{O}]_{2}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{2}}_{\mathrm{(o)}}, \\
& {[\mathrm{H}_{2}\mathrm{O}]_{6}\bullet[[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{O}]_{3}\mathrm{P}\mathrm{O}]_{3}}_{\mathrm{(o)}}, \ \end{align*}\]
1.2.2.6. Mass Transfer Data#
'''Adjust relaxation times for mass transfer'''
rxn_mech.data[0]['tau'] = 1.0e-0 * stg.flow_residence_time_avg
rxn_mech.data[1]['tau'] = 1.0e-0 * stg.flow_residence_time_avg
rxn_mech.data[2]['tau'] = 1.0e-0 * stg.flow_residence_time_avg
rxn_mech.data[3]['tau'] = 1.0e-0 * stg.flow_residence_time_avg
rxn_mech.data[4]['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 Hydrate'
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 of Mixer#
1.3.1. Organic Phase#
'''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
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
1.3.2. Aqueous Phase#
'''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(a)', rho_h2o_aqu)
c_hno3_aqu = 1e-3 * unit.molar # residual
h_plus_aqu = stg.aqueous_phase.get_species('H^+(a)')
rho_h_plus_aqu = c_hno3_aqu * h_plus_aqu.molar_mass
stg.aqueous_phase.set_value('H^+(a)', rho_h_plus_aqu)
no3_minus_aqu = stg.aqueous_phase.get_species('NO3^-(a)')
rho_no3_minus_aqu = c_hno3_aqu * no3_minus_aqu.molar_mass
stg.aqueous_phase.set_value('NO3^-(a)', rho_no3_minus_aqu)
1.4. Inflow Condition#
1.4.1. Aqueous Phase#
'''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)
c_hno3_aqu = 0.5 * unit.molar # low acid feed
h_plus_aqu = stg.inflow_aqueous_phase.get_species('H^+(a)')
rho_plus_aqu = c_hno3_aqu * h_plus_aqu.molar_mass
stg.inflow_aqueous_phase.set_value('H^+(a)', rho_plus_aqu)
no3_minus_aqu = stg.inflow_aqueous_phase.get_species('NO3^-(a)')
rho_no3_minus_aqu = c_hno3_aqu * no3_minus_aqu.molar_mass
stg.inflow_aqueous_phase.set_value('NO3^-(a)', rho_no3_minus_aqu)
1.4.2. Organic Phase#
'''Organic phase in the inflow'''
# Set the same mass concentration as the initial condition in the mixer
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, 10*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
[3365] 2025-11-18 03:03:56,852 - cortix - INFO - Launching Module <solvex.stage.Stage object at 0x7ff2001c9a90>
[14546] 2025-11-18 03:03:58,068 - cortix - INFO - Stg-1::run():time[m]=0.0
[14546] 2025-11-18 03:03:58,244 - cortix - INFO - Stg-1::run():time[m]=0.6
Total mass rate density (mixture volume) residual [g/L-s]= -1.38778e-16
total mass inflow rate [g/min] = 6.868e+02
total mass outflow rate [g/min] = 6.815e+02
net total mass flow rate [g/min] = -5.337e+00
[14546] 2025-11-18 03:03:58,327 - cortix - INFO - Stg-1::run():time[m]=1.0 (et[s]=0.3)
[3365] 2025-11-18 03:03:58,512 - cortix - INFO - run()::Elapsed wall clock time [s]: 2.22
[3365] 2025-11-18 03:03:58,513 - cortix - INFO - Closed Cortix object.
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T E R M I N A T I N G
_____________________________________________________________________________
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https://cortix.org
_____________________________________________________________________________
[3365] 2025-11-18 03:03:58,514 - cortix - INFO - close()::Elapsed wall clock time [s]: 2.22
'''Recover stage'''
stg = system_net.modules[0]
n_startup = len(stg.organic_phase.time_stamps)
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.
Note depletion of free TBP in the organic phase.
Note corresponding complexation of TBP with H2O and HNO3.
Note orders of magnitude of mass concentration in the mixer.
Experimental measurements would be instrumental to help calibrate and validate the model.
'''Organic phase mass density'''
import matplotlib.pyplot as plt
quant = stg.mass_density_history('organic')
quant.plot(title='Organic Phase Mass 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+r'$-\rho_\text{diluent}$'
' ['+quant.unit+']', show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Organic phase mass density history at start-up.')
Figure 2: Organic phase mass density history at start-up.
tbl_count += 1
print(f'Table {tbl_count}: Organic phase mass density history at start-up.')
print('Time [s] Organic Phase Mass Density [g/L]')
print(quant.value[::5].apply(lambda x: round(x,2)))
Table 1: Organic phase mass density history at start-up.
Time [s] Organic Phase Mass Density [g/L]
0.000000 291.75
18.181818 295.11
36.363636 296.35
54.545455 296.93
Name: Organic Phase Mass Density [g/L]; Time History in [s], dtype: float64
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 3: Aqueous phase species history dashboard at start-up.
The inflow feed increases the concentration of all species in the aqueous phase of the mixer.
'''Aqueous phase mass density'''
import matplotlib.pyplot as plt
quant = stg.mass_density_history('aqueous')
quant.plot(title='Aqueous Phase Mass 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+']', show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Aqueous phase mass density history at start-up.')
Figure 4: Aqueous phase mass density history at start-up.
tbl_count += 1
print(f'Table {tbl_count}: Aqueous phase mass density history at start-up.')
print('Time [s] Aqueous Phase Mass Density [g/L]')
print(quant.value[::5].apply(lambda x: round(x,2)))
Table 2: Aqueous phase mass density history at start-up.
Time [s] Aqueous Phase Mass Density [g/L]
0.000000 992.06
18.181818 996.95
36.363636 1001.84
54.545455 1005.72
Name: Aqueous Phase Mass Density [g/L]; Time History in [s], dtype: float64
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 5: Stage efficiency history at start-up.
tbl_count += 1
print(f'Table {tbl_count}: Stage efficiency history at start-up.')
print('Time [s] (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 3: Stage efficiency history at start-up.
Time [s] (Stage. Eff., +-std) [%]
0.00 0.000 0.000
0.06 4.876 2.000
0.12 9.457 3.849
0.18 13.695 5.472
0.24 17.550 6.846
0.30 20.987 7.945
0.36 24.059 8.818
0.42 26.768 9.465
0.48 29.147 9.913
0.55 31.231 10.188
0.61 33.053 10.316
0.67 34.649 10.323
0.73 36.047 10.231
0.79 37.277 10.060
0.85 38.362 9.828
0.91 39.324 9.549
0.97 40.179 9.236
'''Individual reaction efficiency'''
quant = stg.efficiency_history()
quant.plot(title='Reaction 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+']', legend=stg.rxn_mech.reactions, show=True, figsize=[10,3])
fig_count += 1
print(f'Figure {fig_count}: Reaction efficiency history at start-up.')
Figure 6: Reaction efficiency history at start-up.
'''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 4: Reaction efficiency history at start-up.
Time [min] Rxn Eff. [%]
r0 r1 r2 r3 r4
0.00 0.000 0.000 0.000 0.000 0.000
0.06 6.372 6.506 6.645 2.416 2.443
0.12 12.132 12.583 13.058 4.712 4.802
0.18 17.274 18.119 19.025 6.943 7.114
0.24 21.816 23.063 24.417 9.099 9.356
0.30 25.784 27.351 29.114 11.174 11.512
0.36 29.247 31.098 33.208 13.165 13.576
0.42 32.244 34.304 36.682 15.069 15.541
0.48 34.829 37.023 39.587 16.889 17.409
0.55 37.050 39.311 41.987 18.625 19.180
0.61 38.954 41.224 43.947 20.280 20.860
0.67 40.584 42.817 45.533 21.858 22.451
0.73 41.977 44.136 46.803 23.361 23.960
0.79 43.167 45.226 47.811 24.793 25.390
0.85 44.183 46.123 48.604 26.156 26.746
0.91 45.050 46.860 49.221 27.454 28.032
0.97 45.790 47.464 49.696 28.689 29.253
1.6. Steady-State Simulation#
Pick up from where it left from the past run() and continue to a longer 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 += 5 * stg.flow_residence_time_avg
time_step = 5 * stg.flow_residence_time_avg / 15
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
[3365] 2025-11-18 03:04:01,796 - cortix - INFO - Launching Module <solvex.stage.Stage object at 0x7ff1bff43c50>
[14576] 2025-11-18 03:04:03,065 - cortix - INFO - Stg-1::run():time[m]=1.0
[14576] 2025-11-18 03:04:03,226 - cortix - INFO - Stg-1::run():time[m]=4.0
Total mass rate density (mixture volume) residual [g/L-s]= -1.04083e-17
total mass inflow rate [g/min] = 6.868e+02
total mass outflow rate [g/min] = 6.868e+02
net total mass flow rate [g/min] = -3.344e-02
[14576] 2025-11-18 03:04:03,297 - cortix - INFO - Stg-1::run():time[m]=5.5 (et[s]=0.2)
[3365] 2025-11-18 03:04:03,470 - cortix - INFO - run()::Elapsed wall clock time [s]: 7.18
[3365] 2025-11-18 03:04:03,471 - cortix - INFO - Closed Cortix object.
_____________________________________________________________________________
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_____________________________________________________________________________
[3365] 2025-11-18 03:04:03,472 - cortix - INFO - close()::Elapsed wall clock time [s]: 7.18
'''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 7: Organic phase species history dashboard at steady-state.
'''Organic phase mass density'''
import matplotlib.pyplot as plt
quant = stg.mass_density_history('organic')
quant.plot(title='Organic Phase Mass 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+r'$-\rho_\text{diluent}$'
' ['+quant.unit+']', show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Organic phase mass density history at steady-state.')
Figure 8: Organic phase mass density history at steady-state.
tbl_count += 1
print(f'Table {tbl_count}: Organic phase mass density history at steady-state.')
print('Time [s] Organic Phase Mass Density [g/L]')
print(quant.value[::5].apply(lambda x: round(x,2)))
Table 5: Organic phase mass density history at steady-state.
Time [s] Organic Phase Mass Density [g/L]
0.000000 291.75
18.181818 295.11
36.363636 296.35
54.545455 296.93
130.909091 297.83
221.818182 298.11
312.727273 298.17
Name: Organic Phase Mass Density [g/L]; Time History in [s], dtype: float64
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 9: Aqueous phase species history dashboard at steady-state.
'''Aqueous phase mass density'''
import matplotlib.pyplot as plt
quant = stg.mass_density_history('aqueous')
quant.plot(title='Aqueous Phase Mass 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+']', show=True, figsize=[10,3], error_data=False)
fig_count += 1
print(f'Figure {fig_count}: Aqueous phase mass density history at Steady-State.')
Figure 10: Aqueous phase mass density history at Steady-State.
tbl_count += 1
print(f'Table {tbl_count}: Aqueous phase mass density history at steady-state.')
print('Time [s] Aqueous Phase Mass Density [g/L]')
print(quant.value[::5].apply(lambda x: round(x,2)))
Table 6: Aqueous phase mass density history at steady-state.
Time [s] Aqueous Phase Mass Density [g/L]
0.000000 992.06
18.181818 996.95
36.363636 1001.84
54.545455 1005.72
130.909091 1013.36
221.818182 1015.34
312.727273 1015.71
Name: Aqueous Phase Mass Density [g/L]; Time History in [s], dtype: float64
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 11: Stage efficiency history steady-state.
tbl_count += 1
print(f'Table {tbl_count}: Stage efficiency history at steady-state.')
print('Time [s] (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 7: Stage efficiency history at steady-state.
Time [s] (Stage. Eff., +-std) [%]
0.00 0.000 0.000
0.06 4.876 2.000
0.12 9.457 3.849
0.18 13.695 5.472
0.24 17.550 6.846
0.30 20.987 7.945
0.36 24.059 8.818
0.42 26.768 9.465
0.48 29.147 9.913
0.55 31.231 10.188
... ... ...
2.79 48.755 1.679
3.09 49.106 1.214
3.39 49.359 0.875
3.70 49.540 0.630
4.00 49.670 0.453
4.30 49.764 0.325
4.61 49.831 0.233
4.91 49.879 0.167
5.21 49.913 0.120
5.52 49.938 0.086
'''Individual reaction efficiency'''
quant = stg.efficiency_history()
quant.plot(title='Reaction 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+']', legend=stg.rxn_mech.reactions, show=True, figsize=[10,3])
fig_count += 1
print(f'Figure {fig_count}: Reaction efficiency history at steady-state.')
Figure 12: Reaction efficiency history at steady-state.
'''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 8: Reaction efficiency history at steady-state.
Time [min] Rxn Eff. [%]
r0 r1 r2 r3 r4
0.00 0.000 0.000 0.000 0.000 0.000
0.06 6.372 6.506 6.645 2.416 2.443
0.12 12.132 12.583 13.058 4.712 4.802
0.18 17.274 18.119 19.025 6.943 7.114
0.24 21.816 23.063 24.417 9.099 9.356
0.30 25.784 27.351 29.114 11.174 11.512
0.36 29.247 31.098 33.208 13.165 13.576
0.42 32.244 34.304 36.682 15.069 15.541
0.48 34.829 37.023 39.587 16.889 17.409
0.55 37.050 39.311 41.987 18.625 19.180
... ... ... ... ... ...
2.79 50.039 50.046 50.284 46.624 46.780
3.09 50.045 50.036 50.205 47.561 47.683
3.39 50.041 50.027 50.147 48.242 48.335
3.70 50.034 50.020 50.106 48.735 48.805
4.00 50.027 50.015 50.076 49.091 49.143
4.30 50.021 50.011 50.055 49.347 49.386
4.61 50.015 50.008 50.039 49.531 49.560
4.91 50.011 50.005 50.028 49.664 49.685
5.21 50.008 50.004 50.020 49.759 49.774
5.52 50.006 50.003 50.014 49.827 49.838
1.7. References#
[1] V. F. de Almeida, Cortix, Network Dynamics Simulation, Cortix Tech, Lowell, MA, USA.