Factorial design and statistical analysis of smectite clay treatment by hydrocyclone

Gama, A. J. A.; Figueirêdo, J. M. R.; Brito, A. L. F.; Gama, M. A.; Neves, G. A.; Ferreira, H. C.

doi:10.1590/0366-69132018643692196

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Articles • Cerâmica 64 (369) • Jan-Mar 2018 • https://doi.org/10.1590/0366-69132018643692196 copy

Factorial design and statistical analysis of smectite clay treatment by hydrocyclone

Planejamento fatorial e análise estatística do tratamento de argilas esmectitícas por hidrociclone

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Bentonite clays are materials composed by one or more smectite clay minerals and some accessory minerals, mainly quartz, cristobalite, mica, feldspars and other clay minerals such as kaolinite. These contaminants present in clays have a large distribution of particle sizes which severely restrict their industrial applications, with the use of hydrocyclone as a likely solution for their reduction. This study aims to analyze the treatment of smectite clays from the state of Paraíba using modeling, simulation and optimization of the variable average particle diameter in relation to various process variables related to the hydrocyclone. In this study, the average diameter of smectite clays was evaluated as a function of the factors: pressure, apex diameter and vortex diameter of the hydrocyclone. Complete factorial design and addition in the central points were used to model the hydrocycloning process. The results evidenced reduction in equivalent average particle size of approximately 19.2%. Regarding the simulations, the optimum point with the lowest value was found for the average diameter of 4.033 µm, with a pressure of 4.3 bar, apex opening of 5.3 mm, and vortex opening of 6.3 mm, all at a 95% confidence level.

Keywords:
modeling; simulation; hydrocyclone; smectite

Table I - Factors and factor levels.

Factor	Low level (-1)	Center point (0)	High level (+1)
Apex diameter (mm)	3.0	4.0	5.0
Vortex diameter (mm)	5.0	5.5	6.0
Pressure (bar)	3.0	3.5	4.0

Table II - Analysis of variance (ANOVA) for 3 factors.

Source of variation	D.F.	Square sum (SS)	Adjusted mean square (MS)	F value¹
Main effects	2	SS main effects	MS main effects	-
Interaction	1	SS interaction	MS interaction	-
Curvature	1	SS curvature	MS curvature	-
Error	2	SS error residual	MS error
Total	6	SS total	-
R²	R²max	R

Table III - Average diameter of particle sizes after hydrocycloning.

Essay	Apex, A (mm)	Vortex, B (mm)	Pressure, C (bar)	Average diameter (µm)
1	3	5	3	4.61
2	5	5	3	4.85
3	3	6	3	4.96
4	5	6	3	4.31
5	3	5	4	4.58
6	5	5	4	4.65
7	3	6	4	4.68
8	5	6	4	4.24
9	4	5.5	3.5	4.81
10	4	5.5	3.5	4.82
11	4	5.5	3.5	4.83

Table IV - Analysis of variance (ANOVA) for three factors of average diameter (µm).

Source of variation	D.F.	Square sum (SS)	Adjusted mean square (MS)	F value
Apex	1	0.076050	0.076050	760.501
Vortex	1	0.076050	0.031250	312.501
Pressure	1	0.042050	0.042050	420.501
Apex^*Vortex	1	0.245000	0.245000	2450.001
Apex^*Pressure	1	0.000200	0.000200	2.002
Vortex^*Pressure	1	0.001800	0.001800	18.001
Apex^Vortex^Pressure	1	0.018050	0.018050	180.501
Curvature	1	0.000200	0.096218	962.181
Error	2	0.000200	0.000200
Total	10	0.510818
R² = 99.96%		R²max = 99.96%	R = 0.998

Table V - Simulated values: optimum point region (average diameter in µm).

Simulation	Apex factor	Vortex factor	Pressure factor	Adjusted value (y_s )
1	4	5	8.0	4.155 µm
2	4	5	8.5	4.097 µm
3	4	5	9.0	4.040 µm
4	4	5	9.5	3.982 µm
5	4	5	10.0	3.925 µm
6	4	5	10.1	3.913 µm
7	4	5	10.2	3.902 µm
8	4	5	10.3	3.890 µm
9	4	5	10.4	3.879 µm
10	4	5	10.5	3.867 µm
11	4.9	5.9	3.9	4.309 µm
12	4.8	5.8	3.8	4.377 µm
13	4.7	5.7	3.7	4.443 µm
14	5.1	6.1	4.1	4.169 µm
15	5.2	6.2	4.2	4.100 µm
16	5.3	6.3	4.3	4.033 µm
17	5.0	5.9	3.9	4.289 µm
18	5.0	5.8	3.8	4.341 µm
19	4.9	6.0	3.9	4.270 µm
20	4.8	6.0	3.8	4.302 µm

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[TFN1] Notes: 1 - significant effect (F Cal was >F Tab ); non-significant effect (F Cal was ≤F Tab ); D.F. - degrees of freedom; R 2 - coefficient of determination; R 2 max - maximum explainable variation.