XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2117
where St is the degree of absorption per gram during a given
time, Se is the maximum absorption degree [g of water/g of
SAP], t is the absorption time [s], r is constant [s] and b is
constant.
This model characterizes SAP kinetics with three
parameters. To ascertain these parameters, the Excel solver
minimizes the squared differences using the least squares
method between the calculated and experimental values.
Once the equation dictating the polymer absorption kinet-
ics is identified, it becomes feasible to ascertain the mass of
water absorbed per gram of polymer as a function of time.
The mathematical efficacy of the model is commend-
able however, establishing a clear physical interpretation
for the coefficients b and r in the context of water absorp-
tion kinetics proves to be abstract. Nevertheless, the model
effectively correlates with the peak water absorption, mea-
sured in grams per gram of SAP. Various kinetic models are
documented in the literature, and among them, the Pseudo
Second-Order (PSO) model stands out for its effectiveness
in modeling water absorption kinetics by the superabsor-
bent polymer (Zafar et al., 2015).
St =(k2 Se2 t)/(1+ k2 Se t)
where k2 is the absorption reaction rate constant.
In Figure 1, one can observe the three kinetics models
and their compatibility with the data measured within the
developed protocol.
The second-order model, enriched with an additional
degree of freedom, demonstrates the higher coefficient of
determination. Nevertheless, the determination of this sup-
plementary coefficient encounters practical intricacies, as
previously discussed. Conversely, the pseudo second-order
model displays a comparable coefficient of determination
and adeptly aligns with the data calculated within the opti-
mal fitting model, as elucidated in the Table 1.
Based on the results obtained through the developed
protocol for SAP within ore kinetics, a correlation has been
established between the screen efficiency, resulting from
apparent moisture reduction, and the SAP kinetics for water
absorption defined in the previously equation. Delving
into the particle size distribution (PSD) outcomes for SAP
dosage at 900g/t incorporated into ore at a 12% moisture
content, an expected trend appears: as the incorporation
time lengthens, a greater presence of particles undersizing
10 mm is observed. The calculation of normalized screen
50
75
100
125
150
175
200
0 1000 2000 3000 4000 5000 6000
Time [s]
Second-order degree (A) Second-order degree with extra degree of freedom (B) Pseudo Second Order (C) Measured Points
(A) St =Se (1 – e-t/r)
R2 =0,90
(B) St =Se (1− e-[t^(1/b)]/r)
R2 =0,99
(C) St =(k
2 Se2 t)/(1+ k
2 Se t)
R2 =0,98
Figure 1. SAP kinetics models with water absorption through time
]g/g[noitprosbaretaW
where St is the degree of absorption per gram during a given
time, Se is the maximum absorption degree [g of water/g of
SAP], t is the absorption time [s], r is constant [s] and b is
constant.
This model characterizes SAP kinetics with three
parameters. To ascertain these parameters, the Excel solver
minimizes the squared differences using the least squares
method between the calculated and experimental values.
Once the equation dictating the polymer absorption kinet-
ics is identified, it becomes feasible to ascertain the mass of
water absorbed per gram of polymer as a function of time.
The mathematical efficacy of the model is commend-
able however, establishing a clear physical interpretation
for the coefficients b and r in the context of water absorp-
tion kinetics proves to be abstract. Nevertheless, the model
effectively correlates with the peak water absorption, mea-
sured in grams per gram of SAP. Various kinetic models are
documented in the literature, and among them, the Pseudo
Second-Order (PSO) model stands out for its effectiveness
in modeling water absorption kinetics by the superabsor-
bent polymer (Zafar et al., 2015).
St =(k2 Se2 t)/(1+ k2 Se t)
where k2 is the absorption reaction rate constant.
In Figure 1, one can observe the three kinetics models
and their compatibility with the data measured within the
developed protocol.
The second-order model, enriched with an additional
degree of freedom, demonstrates the higher coefficient of
determination. Nevertheless, the determination of this sup-
plementary coefficient encounters practical intricacies, as
previously discussed. Conversely, the pseudo second-order
model displays a comparable coefficient of determination
and adeptly aligns with the data calculated within the opti-
mal fitting model, as elucidated in the Table 1.
Based on the results obtained through the developed
protocol for SAP within ore kinetics, a correlation has been
established between the screen efficiency, resulting from
apparent moisture reduction, and the SAP kinetics for water
absorption defined in the previously equation. Delving
into the particle size distribution (PSD) outcomes for SAP
dosage at 900g/t incorporated into ore at a 12% moisture
content, an expected trend appears: as the incorporation
time lengthens, a greater presence of particles undersizing
10 mm is observed. The calculation of normalized screen
50
75
100
125
150
175
200
0 1000 2000 3000 4000 5000 6000
Time [s]
Second-order degree (A) Second-order degree with extra degree of freedom (B) Pseudo Second Order (C) Measured Points
(A) St =Se (1 – e-t/r)
R2 =0,90
(B) St =Se (1− e-[t^(1/b)]/r)
R2 =0,99
(C) St =(k
2 Se2 t)/(1+ k
2 Se t)
R2 =0,98
Figure 1. SAP kinetics models with water absorption through time
]g/g[noitprosbaretaW