XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 961
X
x
x
x10W
x
1
2
3
4
6
8
9
11
12
13
=
R
T
S
Sx
S
S
Sx
S Sx5W
Sx
S Sx7W
Sx
S
Sx
S
S
Sx
S
S
Sx
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W ic
IC
0
0
0
0
=
R0V
T
S
S0W
S
S
S0W
S
S
S0W
S S0W
S0W
S S0W
S
S
S0W
S
S
X
W
W
W
W
W
W
W
W
W
W
W
E
0
0
0
0
0
0
0
0
0
0
îeMS3W
MS1
MS2
=
R
T
S
Sîe
S
S
S
S
S
Sîe
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
where r is the internal recycle rate around the mixer settler,
xn is the molar flow for the nth stream, ic is the initial aque-
ous feed, and Δemsn is the mass transfer rate for the mixer
settler. Note that the vectors and matrices would need to be
reconfigured for the organic streams, and importantly the
sign on E would be reversed.
The LCA structure can be combined with the Turgeon
et al. (2023) model to create a large, but well-structured
system of equations, whereby the Δe, X, and Y values can
be solved simultaneously or in controlled iteration depend-
ing on the non-linear solver that is used. Solving the system
of equations will yield the mass flow of the aqueous and
organic, which can then be used to calculate recovery, ele-
ment mass flow, and concentration in each stream. One of
the unique abilities of this modeling process is that a solu-
tion can be determined relatively quickly and robustly com-
pared to other brute force or iterative processes. Programs
like METSIM can take months to model a complex solvent
extraction battery that includes many elements. Thus, we
have developed a process to integrate the above solution
method with METSIM using Python as an intermediary to
assist in larger plant design. METSIM passes off the solvent
extraction process to a solution method written in Python,
which solves for that process module and passes the rel-
evant information back to METSIM.
RESULTS AND DISCUSSION
To demonstrate the utility of the method in an applica-
tion example, a hypothetical scenario, incorporating five
elements and a battery of mixer settlers was simulated.
Equilibrium constants are listed in Table 2 as well as the
other inputs to the system. The initial concentration of the
organic phase was zero for this scenario. The system was
designed according to Figure 2 with 3 mixer settlers. An
internal O/A ratio of one was used for each mixer-settler
which necessitated an internal organic recycle rate of 33%
in the system.
The recovery to the organic as well as the organic con-
centrations are shown in Table 2. Likewise, the concentra-
tion and pH in each mixer settler is plotted in Figure 3.
While this process only modeled the solvent extrac-
tion process here, the same framework can be used to solve
scrubbing and stripping circuits as well.
CONCLUSION
Combining the equilibrium-based method of solvent
extraction modeling with the linear circuit analysis frame-
work yields a robust structure to model solvent extraction
systems of arbitrary complexity. The novel method can be
used to simulate solvent extraction, scrubbing, and strip-
ping and gives the user a framework to solve the entire sys-
tem simultaneously including internal recirculation loops
inside the solvent extraction batteries. Such methods are
pivotal given the increased complexity of rare earth element
separation circuit. The linear circuit analysis process with
the transfer term also has the potential for wider appli-
cation to other reactions that include a thermodynamic
based transfer term in the modeling process. Moreover, the
approach of tracking individual species with the linear cir-
cuit analysis could help expand the scope of process to glean
more information on other separation circuits. Overall, the
Table 2. Input variables for the example system
Elements
Aqueous
Concentration, g/L
Equilibrium
Constants
La 9.40 1.95 E–03
Pr 7.38 4.28 E–03
Nd 31.16 5.33 E–03
Sm 7.44 1.81 E–02
Eu 2.07 1.32 E–01
Aqueous Flow: 3 lpm
Organic Flow: 2 lpm
pH: 4.5 ||RH: 0.448v
Aqueous Recycle: 0%
Organic Recycle: 33%
Table 3. Recovery to the organic and final organic
concentration of the solved system of equations
Element Recovery
Final Organic
Concentration, g/L
La 3.6% 0.50
Pr 7.7% 0.86
Nd 9.6% 4.48
Sm 29.9% 3.34
Eu 91.7% 2.84
X
x
x
x10W
x
1
2
3
4
6
8
9
11
12
13
=
R
T
S
Sx
S
S
Sx
S Sx5W
Sx
S Sx7W
Sx
S
Sx
S
S
Sx
S
S
Sx
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W ic
IC
0
0
0
0
=
R0V
T
S
S0W
S
S
S0W
S
S
S0W
S S0W
S0W
S S0W
S
S
S0W
S
S
X
W
W
W
W
W
W
W
W
W
W
W
E
0
0
0
0
0
0
0
0
0
0
îeMS3W
MS1
MS2
=
R
T
S
Sîe
S
S
S
S
S
Sîe
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
where r is the internal recycle rate around the mixer settler,
xn is the molar flow for the nth stream, ic is the initial aque-
ous feed, and Δemsn is the mass transfer rate for the mixer
settler. Note that the vectors and matrices would need to be
reconfigured for the organic streams, and importantly the
sign on E would be reversed.
The LCA structure can be combined with the Turgeon
et al. (2023) model to create a large, but well-structured
system of equations, whereby the Δe, X, and Y values can
be solved simultaneously or in controlled iteration depend-
ing on the non-linear solver that is used. Solving the system
of equations will yield the mass flow of the aqueous and
organic, which can then be used to calculate recovery, ele-
ment mass flow, and concentration in each stream. One of
the unique abilities of this modeling process is that a solu-
tion can be determined relatively quickly and robustly com-
pared to other brute force or iterative processes. Programs
like METSIM can take months to model a complex solvent
extraction battery that includes many elements. Thus, we
have developed a process to integrate the above solution
method with METSIM using Python as an intermediary to
assist in larger plant design. METSIM passes off the solvent
extraction process to a solution method written in Python,
which solves for that process module and passes the rel-
evant information back to METSIM.
RESULTS AND DISCUSSION
To demonstrate the utility of the method in an applica-
tion example, a hypothetical scenario, incorporating five
elements and a battery of mixer settlers was simulated.
Equilibrium constants are listed in Table 2 as well as the
other inputs to the system. The initial concentration of the
organic phase was zero for this scenario. The system was
designed according to Figure 2 with 3 mixer settlers. An
internal O/A ratio of one was used for each mixer-settler
which necessitated an internal organic recycle rate of 33%
in the system.
The recovery to the organic as well as the organic con-
centrations are shown in Table 2. Likewise, the concentra-
tion and pH in each mixer settler is plotted in Figure 3.
While this process only modeled the solvent extrac-
tion process here, the same framework can be used to solve
scrubbing and stripping circuits as well.
CONCLUSION
Combining the equilibrium-based method of solvent
extraction modeling with the linear circuit analysis frame-
work yields a robust structure to model solvent extraction
systems of arbitrary complexity. The novel method can be
used to simulate solvent extraction, scrubbing, and strip-
ping and gives the user a framework to solve the entire sys-
tem simultaneously including internal recirculation loops
inside the solvent extraction batteries. Such methods are
pivotal given the increased complexity of rare earth element
separation circuit. The linear circuit analysis process with
the transfer term also has the potential for wider appli-
cation to other reactions that include a thermodynamic
based transfer term in the modeling process. Moreover, the
approach of tracking individual species with the linear cir-
cuit analysis could help expand the scope of process to glean
more information on other separation circuits. Overall, the
Table 2. Input variables for the example system
Elements
Aqueous
Concentration, g/L
Equilibrium
Constants
La 9.40 1.95 E–03
Pr 7.38 4.28 E–03
Nd 31.16 5.33 E–03
Sm 7.44 1.81 E–02
Eu 2.07 1.32 E–01
Aqueous Flow: 3 lpm
Organic Flow: 2 lpm
pH: 4.5 ||RH: 0.448v
Aqueous Recycle: 0%
Organic Recycle: 33%
Table 3. Recovery to the organic and final organic
concentration of the solved system of equations
Element Recovery
Final Organic
Concentration, g/L
La 3.6% 0.50
Pr 7.7% 0.86
Nd 9.6% 4.48
Sm 29.9% 3.34
Eu 91.7% 2.84