Determination of compressibility-permeability parameters of mineral
sediments using analytical photocentrifuge
M. Loginov1, 2, E. Vorobiev1, N. Lebovka1, 2 and O. Larue1
1Unité
Transformations Intégrées de la Matière Renouvelable, Université de
Technologie de Compiègne, Centre de Recherches de Royallieu, B.P. 20529-60205
Compiègne Cedex, France
(E-mail : eugene.vorobiev@utc.fr)
2Institute of Biocolloidal Chemistry named after F.D. Ovcharenko, NAS of Ukraine,
42, blvd. Vernadskogo, Kyiv, 03142, Ukraine
(E-mail : lebovka@gmail.com)
Abstract
This work discusses applications of analytical photocentrifuge LUMiSizer for estimation of the low-pressure
compression-permeability characteristics of sediments. Two methods for determination of compressibilitypermeability parameters were proposed. These methods are based on analysis of equilibrium height of
sediment versus centrifugal acceleration (1) and kinetics of consolidation (2). Aqueous suspensions of
calcium carbonate with different concentrations of dispersant were tested. The values of specific resistance
and compressibility coefficient (both local and average) of sediments were estimated.
Keywords. Analytical centrifugation – consolidation – compressibility – suspension – calcium carbonate.
INTRODUCTION
Dependencies of compressibility and permeability on applied pressure are important factors determining
dewatering behaviour of suspensions. Conventional way of estimating these characteristics of sediments and
filter cakes requires a set of experiments using a special compression-permeability cell. However, it was
recently shown that the low-pressure compressibility of sediments may be estimated from centrifugal
sedimentation experiments carried out in analytical photocentrifuge [Lerche, 2007, Curvers, 2009; Iritani,
2007].
METHODS
Aqueous mineral suspensions, prepared from colloidal calcium carbonate (OMYA, France) and chemical
dispersant (sodium polyacrylate DV834, COATEX, France), were used in this study. The dispersant
concentration in suspensions varied within cd = 0–1 % (wt dispersant /wt solids). Mean size of particles
(d, μm) and their specific surface area (S0, m–1) in the suspensions were determined using a laser diffraction
instrument (Mastersizer X 6618, Malvern Instruments GmbH, UK).
Samples of suspensions with initial solid volume fraction φ = 0.0827 and mass 1.81 g were subjected to
centrifugation in an analytical photocentrifuge (LUMiSizer 610.0–135, L.U.M Gmbh, Germany).
Centrifugation experiments were carried at different rotor speeds ( = 320–4000 rpm). The two type of
experiments were done. In the first type experiments, position of the sediment surface in the centrifugal cell
in the course of sedimentation was measured and evolution of the sediment height (H, mm) with time (t, s)
was recorded. Experiments were finished when constant equilibrium sediment height H was reached. In the
second type experiments, kinetics of consolidation (sedimentation) was studied. The experiments were
carried out using pre-consolidated sediments directly prepared in centrifugal cells from initial suspensions (by
means of sedimentation at sufficiently low rotation speed 320 rpm, corresponding to 15g acceleration). Then,
rotation speed was increased up to 4000 rpm (2320g), and consolidation curve was registered at a constant
high speed. The average consolidation ratio Uc was calculated as follows:
Uc(t) = (H0 – H)/(H0 – H)
where H0 is the initial height of pre-consolidated sediment.
RESULTS
Compressibility characteristics of sediments were estimated by means of two different methods. First method
analysed dependence of the equilibrium height of sediment (H) on rotation speed (). It was assumed that
relation between the equilibrium local solid volume fraction of sediment (φ) and local solid pressure (ps)
, 1 % disp.
2
6
Ce, 0 % disp.
4
1.5
Ce, 1 % disp.
2
, 0 % disp.
1
0.5
0
20
40
60
0
local solids pressure, ps (kPa)
Figure 1. Calculated values of local specific
resistance () and local consolidation coefficient
(Ce) at various values of solid pressure ps.
1
average consolidation ratio, Uc
10
8
local consolidation coeff., Ce (10-6 m2/s)
local specific resistance,  (1010 m/kg)
follows the Tiller’s constitutive equation:
(1)
φ = φ0(1+ps/pa)
where φ0 is a gel point, pa and  are parameters of Tiller’s equation. The experimental data were fitted by
means of Eq.1 using the numerical method proposed in [Curvers, 2009]. It was observed that Eq.1
sufficiently fits experimental dependencies of H on  for different dispersant concentrations. The calculation
showed that addition of the dispersant transformed the mineral suspension from poorly compressible
( = 0.177, pa = 70.7 Pa at cd = 0 %) to almost incompressible ( = 0.05, pa = 0.1 Pa at cd = 1 %).
The local specific resistance of the sediment () was calculated from Kozeny’s equation:
(2)
 = K0S02φ/{s(1 – φ)3}
where s is the solid density. Here, K0 is Kozeny constant estimated using Happel’s equation [Iritani, 2007].
Finally, Eq.1 and Eq.2 were used for estimation of the local consolidation coefficient (Ce) defined as [Iritani,
2009]:
(3)
(Ce)–1 = s(–de/dps)
where e=(1–φ)/φ and  is viscosity of the aqueous media. The calculated dependences of  and Ce versus
ps in suspensions with cd = 0% and cd = 1 % are shown in Fig.1.
0.8
0.6
– exp. 0 % disp.
0.4
– exp. 1 % disp.
– fitting by Eg.4
for Ce* = 2·10-7 m2/s
0.2
0
0
10
20
30
sedimentation time, t (s)
Figure 2. Kinetics of consolidation at rotation speed
4000 rpm (corresponds to the average solid
pressure ps = 36 kPa).
In the second method, dependencies of consolidation ratio Uc versus time t were determined. It was shown
that if (H0–H) << R (where R is the distance between rotation axis and bottom of sediment), kinetics of
centrifugal sedimentation may be satisfactory described by gravitational sedimentation equations derived in
[Iritani, 2009], and average consolidation ratio may be presented as:
Uc  1 
n 1
2
2
*
32  ( 1)
 ( 2n  1)  Ce 

exp


t

3
3
2 
 1 ( 2n  1)
4
w0 

(4)
where w0 is the total height of solids, Ce* is the average consolidation coefficient (which is assumed to be
constant inside the sediment). Experimental data for Uc fitted by Eq.4 are presented in Fig.2.
CONCLUSION
Two methods of analysis of the centrifugal sedimentation data allow estimation of the permeability and
compressibility of mineral sediments at low compressive pressure.
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