The 12th International Conference of
International Association for Computer Methods and Advances in Geomechanics (IACMAG)
1-6 October, 2008
A Statistical Model for Slurry Thickening
Environmental Systems Engineering, University of Regina, Regina, SK, Canada
Syed A. Imran
Centre for Sustainable Infrastructure Research, National Research Council, Regina, SK, Canada
Keywords: statistical model, slurry thickening, large-strain consolidation, synthetic polymers
ABSTRACT: Thickening is the first step in the design of sustainable (cost effective, environmentally friendly, and
socially viable) tailings management solutions for surface deposition, mine backfilling, and sub-aqueous
discharge. The high water content slurries are converted to materials with superior dewatering properties by
adding long-chain synthetic polymers. Given the solid and liquid composition of a slurry, a high settling rate
alongside a high solids content can be achieved by optimizing the various polymers parameters: ionic type (T),
charge density (C), molecular weight (M), and dosage (D). This paper developed a statistical model to predict
field performance of a selected metal mine slurry using laboratory test data. Results of sedimentationconsolidation
tests were fitted using the method of least squares. A newly devised polymer characteristic
coefficient (Cp) that combined the various polymer parameters correlated well with the observed dewatering
behavior as the R2 equalled 0.95 for void ratio and 0.84 for hydraulic conductivity. The various combinations of
polymer parameters resulted in variable slurry performance during sedimentation and were found to converge
during consolidation. Further, the void ratio-effective stress and the hydraulic conductivity-void ratio relationships
were found to be e = a σ′ b and k = 10 (c + e d), respectively.
Economic prosperity is influenced by the exploration of new sources of energy and materials along with the
development of existing reserves. The Canadian mining industry contributes $40 billion to the economy and
accounts for about 4% of the Gross Domestic Product. This important activity is associated with large volumes of
ever increasing mine wastes of variable nature and extent. The mine tailings (slurries generated during ore
processing) are particularly challenging because of their slow settling rates and high standing toxic waters in the
waste containment facilities (Eckert et al., 1996). Numerous tailings dam failures in different parts of the globe
have been reported to result in massive contaminant releases causing acute public distress over the conventional
practice of tailings disposal (Vick, 1983). In order to minimize its environmental footprint, the Canadian mining
industry has been quite proactive in developing novel waste management methods such as thickening of the
slurry tailings. This paper is part of the ongoing research at the University of Regina that focuses on developing
case-specific engineering solutions for base-metal mining operations by investigating the innovative method of
The conventional practice of mine waste disposal usually generates large volumes of soil slurries that must be
contained in tailings dams over a number of decades. Thickening is the initial step in the design of cost effective,
environmentally friendly, and socially viable tailings management solutions for surface deposition, mine
backfilling, and sub-aqueous discharge. Through a properly designed thickening process, the slurries can be
converted into paste-like materials and deposited on the ground requiring minimal continuous monitoring
(Robinsky, 1999). The production of thickened slurries by adding long-chain polymers as flocculating agents is
not well understood in geotechnical engineering. Complex colloid-water-polymer interactions govern the hindered
sedimentation and large-strain consolidation behaviour of such materials (Azam 2004). To develop a process that
achieves a high dewatering rate together with a high amount of water (that is, high solids content of the settled
slurry) in the gravity thickener requires screening a number of synthetic polymers in the bench-scale laboratory
tests. This allows the selection of appropriate polymers for a given slurry composition: solid particles (size
distribution, mineralogy, and surface charges) and liquid medium (pH, electrical conductivity, and electrolyte
The main objective of this paper was to develop a statistical model to understand and improve the dewatering
behaviour of a selected metal mine slurry during thickening. The test data was obtained from a comprehensive
laboratory investigation program completed earlier (Azam 2003). The synthetic polymers used in the
sedimentation-consolidation testing were characterized by their ionic type (T, -1 for anionic polymer and +1 for
cationic polymer), charge density (C), molecular weight (M, x 106 g/mol), and dosage (D, ppm). The test data
were fitted using the method of least squares in conjunction with the newly devised polymer characteristic
coefficient (Cp) that combined the various polymer parameters.
2 Literature Review
Mine tailings offer unique challenges related to the design, construction, operation, and reclamation of the
containment facilities (Edil and Fox, 2000). The geological origin and the mining operation govern the
geotechnical properties of the placed materials (Morgenstern and Scott, 1995). The tailings usually segregate
during hydraulic transport and subsequent deposition. The coarse-grained fraction is used for dam construction
thereby forming a basin to store the chemical-rich water and the fine-grained materials in suspension (Vick,
1983). A slow settling rate of the fine tailings along with high standing toxic waters in the ponds require that the
containment facilities be carefully managed for a long time (Eckert et al., 1996). Several tailings dam failures
around the world resulted in huge contamination causing acute public distress over conventional tailings disposal.
The industry has been proactive in developing novel waste management methods to minimize its environmental
footprint (Concha and Burger, 2003). A sustainable innovation is slurry thickening that can produce a
nonsegregating tailings stream with bulk of the process water removed and recycled back for ore beneficiation
(Robinsky, 1999). Theoretically, the low water content engineered materials occupy a much smaller disposal area
that can be reclaimed as a useful landscape in a relatively short time. The gravity thickener (a cylindrical vessel
with inverted conical base with or without a slow rotating rake mechanism) is used to develop a tailings stream
with superior settling characteristics during sedimentation in the thickener and consolidation in the tailings pond
(Jewell et al., 2002). Developing such a slurry is the most challenging issue in the design and implementation of
an efficient tailings management program since sedimentation is governed by physicochemical interactions
whereas consolidation is primarily a load-deformation process (Chalaturnyk et al., 2002).
The dewatering slurry in a continuous thickener exhibits a clear liquid at the top, an intermediate settling zone,
and a bottom compression zone. Upward drainage allows collection of the liquid overflow at the top and of the
solid underflow at the bottom. For a given set of operating conditions, the thickener retention time largely
depends on the rate and amount of slurry dewatering (Bustos et al., 1999). The behavior of a slurry, which is
governed by ore geology and the metal extraction process, can be improved by agglomerating individual particles
and/or particle groups to develop multi-particle flocs that can settle rapidly (Torfs et al., 1996). Long-chain
polymers are generally used because of their effectiveness in flocculation and negligible environmental impact.
Based on cost-benefit analysis, an optimum flocculant is selected and added to a nonsegregating feed slurry at a
low solids content (Xu and Cymerman, 1999). These opposing prerequisites of the feed slurry help maximize
physicochemical phenomena at phase boundaries thereby resulting in a distinct microstructure (Hogg, 2000).
The initial flocculated morphology (derived from solid mineralogy, liquid chemistry, and polymer properties
including ionic type, charge density, molecular weight, and dosage) can result in an increased initial hydraulic
conductivity (Azam and Sadiq, 2006). However, a high settling rate may or may not be associated with an
increased dewatering amount during sedimentation and consolidation.
Figure 1: Schematic of a typical slurry thickener
To account for physicochemical interactions (summed up in the term β), the effective stress principle for
thickening of dilute slurries can be defined as follows (Mitchell and Soga, 2005):
σ′ = (σ − u) − β (1)
Interactive forces during sedimentation are quite large and may approach (σ – u) thereby resulting in zero
effective stress. With increasing solids content in the compression zone, the interactions gradually decrease such
that the Terzaghi effective stresses can be measured. Given their porous nature, the flocs in the slurry do not
transmit these stresses, as is the case for solid grains in a soil sediment (Terzaghi et al., 1996). The measured
values overestimate the stress state in the slurry until β can be reduced to zero. This can be achieved either by
significantly increasing the solids content (up to 60% - 70% for most slurries) or by applying a small external load
of 1 kPa - 2 kPa (Jeeravipoolvarn et al., 2006). A continuous gravity thickener precludes the development of such
conditions and generates a tailings stream that usually requires further dewatering through consolidation (Azam
et al., 2005). Similar to soft soils investigated in the classical geotechnical engineering literature (Been and Sills,
1981), consolidation of flocculated (polymer-modified) tailings is invariably slow and depends on material
properties and the thickening process. Prediction of slurry behavior in the pond requires a clear understanding of
the tailings stream design. Correlating slurry behavior with complex physicochemical interactions during the
thickening process can achieve this purpose.
3 Data Collection
Table 1 summarizes the material properties of the selected metal mine slurry provided by the Metallurgical
Technologies Division of Dynatec Corporation, Canada. The solids of the slurry primarily consisted of heavy iron
oxides (goethite, hematite, and maghemite) and chrysotile clay minerals, all of which cumulatively resulted in a
specific gravity (Gs) of 3.15. The exchange capacities corresponded to the mineralogy of the solids and indicated
that the latter can be flocculated with both anionic and cationic polymers. The fine grained solids together with the
near neutral water and the low dissolved ions were expected to provide favourable conditions for effective colloidwater-
polymer interactions (Farinato et al. 1999).
Table 1: Material properties of the slurry (Azam et al. 2005)
Minerals (%) Goethite (50 ± 5); Hematite (20 ± 5);
Maghemite (20 ± 5); Chrysotile (10 ± 5)
Cation Exchange Capacity, CEC (cmol(+)/kg) 7.6
Anion Exchange Capacity, AEC (cmol(-)/kg) 6.8
Electrical C Water Chemistry onductivity, EC (μS/cm) 744.0
Dissolved Ions (mg/L) Na+ (17); K+ (1.1); Ca2+ (19.5); Mg2+ (87);
Cl– (28.4); NO3
– (1.3); HCO3
– (24); SO4
Specific Gravity, Gs 3.15
Index Properties −0.075 mm (%) 93.0
−0.002 mm (%) 35.0
To determine the behaviour of underflow metal mine slurries, sedimentation-consolidation tests were conducted
using a graduated cylinder with an internal diameter of 95 mm. The initial sample height was kept as 95 mm to
facilitate visual observation of the interface through an opaque fluid. The resulting height to diameter ratio of 1.0
at the start of sedimentation was found to have no significant wall effects. To mimic process conditions and
facilitate easy comparison, the initial solids content was kept at 15% that invariably correlated with negligible
segregation (Azam 2003). Based on consultations with the chemical and mining industry, the 15% initial solids
content was the concentration at which interactions between the colloids of the selected slurry and the pore water
are at a maximum. After the completion of the sedimentation stage, the sediment was incrementally loaded in the
effective stress range of 0.5 kPa – 10 kPa that is operative in most freshly deposited tailings (Scott et al., 1986).
The loads were applied through a diaphragm arrangement and the vertical displacement of the top plate of the
cell was recorded using an automated data acquisition system. The top and bottom plates with O-rings prevented
material escape, ensured minimal side friction, and improved cell stability. To facilitate water flow during
consolidation, both plates had a network of radial and circumferential grooves, duly fastened to porous stones, and
connected to external ports. The successive load increments were applied after the complete dissipation of excess
pore pressure. Hydraulic conductivity (k) was directly measured at the end of each load using the constant head
method (according to the ASTM Standard Test Method for Permeability of Granular Soils (Constant Head)
(D2434-68(2006)) and allowing an upward drainage path (Suthaker and Scott, 1996) Test results for each load
were presented in the form of interface height-time, void ratio-time, solids content-time, excess pore pressuretime,
and water flow velocity-time. For the entire sedimentation-consolidation test, the data was defined by two
characteristic relationships, namely; the effective stress versus void ratio and the void ratio versus hydraulic
Based on 24 factorial design, T, C, M, and D were tested at two levels for the acrylamide-based anionic and
cationic polymers, provided by Ciba Specialty Chemicals Inc., Canada. Table 2 gives the average values of
polymer parameters provided by the manufacturer and used in the sedimentation-consolidation tests. The low
and high polymer dosages corresponded to 4 ppm (53 g/ton) and 12 ppm (159 g/ton), respectively, based on dry
mass of polymer and solids in the slurry. A fresh concentrated stock solution was prepared for each test by
dissolving the polymers in distilled water. To preclude the effect of polymer aging, this solution was instantly
diluted to a test solution and immediately used.
Table 2: Average values of polymer parameters used in the sedimentation-consolidation tests
Polymer Type, T Charge Density, C Molecular Weight, M × 106
Dosage, D (ppm)
5 1 24
5 1 24
4 Statistical Modeling
The sedimentation-consolidation test data were fitted using the method of least squares. Regression models
were developed to understand the effect of T, C, M, and D on the dewatering behaviour of the slurry. The various
polymer parameters were combined in a single term called as the polymer characteristic coefficient (Cp) that
was defined as follows:
Cp = (T x M x D) / (C) (2)
Figure 2 and Figure 3 plot the modeled void ratio against the measured void ratio and the modeled hydraulic
conductivity versus the measured hydraulic conductivity, respectively. Good correlations were obtained in both
cases as indicated by the corresponding R2 values of 0.95 and 0.84. Table 3 summarizes the results of the
statistical modeling. Using the least square constants determined above, the governing equations describing the
effective stress-void ratio and the void ratio-hydraulic conductivity relationships were developed.
Table 3: Summary of statistical modeling results
Governing Relationship Least Square Constants
e = a σ′ b ab == – 00..00061992 CCpp –+ 06..10531806
k = 10 (c + e d) cd == – 00..00044822 CCpp +– 06..38185776
Figure 4 illustrates the effective stress versus void ratio relationships on a semi-logarithmic plot for the polymeradded
slurries. The various combinations of polymer parameters were found to result in variable slurry
performance during sedimentation as indicated by the large variation in void ratios at σ′ ≤ 1 kPa. However, the
predicted behaviour for all of the slurries during consolidation was found to be the same and converged to e = 2 ±
0.2 at σ′ = 1000. Therefore, the influence of physicochemical interactions is overcome by the application of
Figure 5 gives the void ratio versus hydraulic conductivity on a semi-logarithmic plot for the polymer-added
slurries. The figure indicates that the hydraulic conductivity varies linearly by six orders of magnitude over the
entire range of void ratio from 0 through 20. This means that the hydraulic conductivity is independent of the
polymer parameters and the flow of water through the porous media (voids between flocs and voids within the
flocs) generally followed the Darcy’s law.
0 5 10 15 20
Measured Void Ratio
Modeled Void Ratio
Line of Equality
emod = 0.9872 emeas
R2 = 0.95
Figure 2: Modeled versus measured void ratio
-8 -6 -4 -2 0
Measured (Log10 k)
Modeled (Log10 k)
Line of Equality
(Log10 k)mod = 1.0874 (Log10 k)meas
R2 = 0.84
Figure 3: Modeled versus measured hydraulic conductivity
0.001 0.01 0.1 1 10 100 1000
Effective Stress (kPa)
Figure 4: Effective stress versus void ratio relationships
0 4 8 12 16 20
Hydraulic Conductivity (cm/s)
Figure 5: Void ratio versus hydraulic conductivity relationships
5 Summary and Conclusion
A statistical model was developed to understand the thickening behaviour of polymer-added slurries. The various
polymers parameters including ionic type, charge density, molecular weight, and dosage were combined in the
polymer characteristic coefficient (Cp). Based on sedimentation-consolidation test data, the model correlated well
with the observed dewatering behavior as the R2 equalled 0.95 for void ratio and 0.84 for hydraulic conductivity.
The various combinations of polymer parameters resulted in variable slurry performance during sedimentation
and were found to converge during consolidation. Further, the void ratio-effective stress and the hydraulic
conductivity-void ratio relationships were found to be e = a σ′ b and k = 10 (c + e d), respectively.
The authors are grateful to the University of Regina and the National Research Council for providing computer
facilities to conduct statistical modeling.
Azam S. 2004. Thickening of mine waste slurries. Geotechnical News. 22(4), 40-43.
Azam S. 2003. Solid-Liquid Separation of Laterite Slurries, Ph.D. Dissertation, University of Alberta, Edmonton, Alberta,
Azam S., Sadiq R. 2006. Evaluation of slurry settling rate using fuzzy rule-based modeling. Acta Geotechnica. 1(3), 149-156.
Azam S., Chalaturnyk R., Scott J.D. 2005. Geotechnical characterization and sedimentation behavior of laterite slurries.
Geotechnical Testing Journal, 28(6), 523-533.
Been K., Sills G.C. 1981. Self-weight consolidation of soft soils-an experimental and theoretical study. Geotechnique. 31, 519-
Bustos M.C., Concha F., Burger R., Tory E.M. 1999. Sedimentation and Thickening–Phenomenological Foundation and
Mathematical Theory. Kluwer Academic (The Netherlands).
Chalaturnyk R.J., Scott J.D., Özüm B. 2002. Management of oil sands tailings. Petroleum Science and Technology. 20(9-10),
Concha F., Burger R. 2003. Thickening in the 20th Century: a historical perspective. Mineral & Metallurgical Processing. 20, 57-
Eckert W.F., Masliyah J.H., Gray M.R., Fedorak P.M. 1996. Prediction of sedimentation and consolidation of fine tails.
American Institute of Chemical Engineers Journal. 42, 960-972.
Edil T.B., Fox P.J. 2000. Geotechnics of High Water Content Materials. ASTM, Pennsylvania (USA).
Farinato R.S., Huang S.Y., Hawkins P. 1999. Polyelectrolyte assisted dewatering. Colloid-Polymer Interaction-From Theory to
Practice, Farinato, R.S and Dubin P.L. Editors. John Wiley & Sons Inc. New York (USA).
Hogg R. 2000. Flocculation and dewatering. International Journal of Mineral Processing. 58(1-4), 223-236.
Jeeravipoolvarn S., Scott J.D., Chalaturnyk R.J. 2006. Three ten meter high standpipe tests on tailings. Proceedings, 59th
Canadian Geotechnical Conference, Vancouver (Canada), 1078-1085.
Jewell R.J., Fourie A.B., Lord E.R. 2002. Paste and Thickened Tailings–A Guide. Uniprint (Australia).
Mitchell J.K., Soga K. 2005. Fundamentals of Soil Behavior. 3rd ed. Wiley, New York (USA).
Morgenstern N.R., Scott J.D. 1995. Geotechnics of fine tailings management. Proceedings, Specialty Conference on
Geotechnical Practice in Waste Disposal, Los Angeles (USA). 2, 1663-1683.
Robinsky E.I. 1999. Thickened Tailings Disposal in the Mining Industry. Quebecor Printpak, Ontario (Canada).
Scott J.D., Dusseault M.B., Carrier W.D. 1986. Large-scale self-weight consolidation testing. ASTM Special Technical
Suthaker N.N., Scott J.D. 1996. Measurement of hydraulic conductivity in oil sand tailings slurries. Canadian Geotechnical
Journal. 33(4), 642-653.
Terzaghi K., Peck R.B., Mesri G. 1996. Soil Mechanics in Engineering Practice. 3rd ed. Wiley, New York (USA).
Torfs H., Mitchener H., Huysentruyt H., Toorman E. 1996. Settling and consolidation of mud/sand mixtures. Coastal
Engineering. 29, 27-45.
Vick S.G. 1983. Planning, Design, and Analysis of Tailings Dams. Wiley, New York (USA).
Xu Y., Cymerman G. 1999. Flocculation of fine oil sand tails. Proceedings, 3rd UBC-McGill Bi-Annual International Symposium
on Fundamentals of Mineral Processing, Quebec (Canada), 591-604.
The 12th International Conference of