MULTIPHYSICS MODELING OF ELECTROKINETIC

PHENOMENA IN UNSATURATED FINEGRAINED

SOILS
Cristina Jommi1 , Fabio Cattaneo2 , Guido Musso3
Claudio Tamagnini4 , and Diana Salciarini4
1
Dipartimento di Ingegneria Strutturale
Politecnico di Milano, Italy
e-mail: jommi@stru.polimi.it
2
Dipartimento di Ingegneria Civile, Architettura, Territorio e Ambiente
Universit`a degli Studi di Brescia, Italy
e-mail: fcattaneo@stru.polimi.it
3
Dipartimento di Ingegneria Strutturale e Geotecnica
Politecnico di Torino, Italy
e-mail: guido.musso@polito.it
4
Dipartimento di Ingegneria Civile e Ambientale
Universit`a degli Studi di Perugia, Italy
e-mail: tamag@unipg.it, diana@unipg.it

Summary. A multiphysics model for the analysis of coupled deformation and reactive
flow of pore fluids, chemical species and electric current has been developed to assess
the influence of the geochemical reactions taking place within the soil mass on the
effectiveness of electrokinetic remediation treatments. The results of FE simulations
have shown that the presence of carbonates in the solid phase may give rise to gas
production, significant changes in the degree of saturation and buffering effects with
respect to the pore water pH. Under such conditions, the efficiency of the electrokinetic
treatment can be significantly reduced.

Keywords: electrokinetic phenomena, electrokinetic remediation, reactive transport

and deformation.

1 INTRODUCTION
In the past twenty years, electrokinetic phenomena occurring in clayey soils upon
the application of an electric field have been the subject of an intense research activity,
aimed at exploring their potential in geoenvironmental applications, such as remedia-
tion of contaminated soils [1, 2] and contaminant diffusion control by means of active
barriers for waste disposal facilities or electrokinetic fences for the control of contami-
nant plumes in polluted areas [3, 4]. All such applications rely crucially on the ability
of the electric field to transport (ionic or nonpolar) contaminants by means of electro-
osmosis and ionic migration.
The effectiveness of environmental applications of electrokinetic phenomena
particularly when high current densities and long duration times are requireddepends
on the complex interactions between the transport phenomena in the pore fluid (of mass

R.I. Borja (Ed.): Multiscale and Multiphysics Processes in Geomechanics, SSGG, pp. 8992.
springerlink.com !c Springer-Verlag Berlin Heidelberg 2011
90 C. Jommi et al.

of pore fluids and ionic species and of the electric charge), the deformation of the solid
skeleton and the geochemical reactions (precipitation, dissolution, sorption, aqueous
phase reactions, electrolysis) taking place in the soil mass and at the electrodes. As
pointed out by Acar and his coworkers [1, 2], the development of an acid front moving
from the anode to the cathode due to water electrolysis is highly beneficial in elec-
trokinetic extraction of contaminants in finegrained soils, since it promotes the solu-
bilization/desorption of contaminant species from the solid particles and increases the
electrical conductivity of the soil.
Recent experimental observations by Airoldi et al. [5] on natural clay soils have
shown that the presence of carbonates in the solid skeleton can have adverse effect
on the electrokinetic treatment of a natural soil, mainly due to CO2 generationwhich
reduces both electroosmotic and electrical conductivitiesand the buffering effect with
respect to pH changes. The aim of this work is to develop a multiphysics model for the
analysis of coupled deformation and reactive flow of pore fluids, chemical species and
electric current, which could be used to assess quantitatively the impact of carbonates
geochemistry on the efficiency of electrokinetic remediation.

2 MULTIPHYSICS MODEL FOR LONGDURATION EK PROCESSES

The governing equations of the multiphysics model for long-duration electroki-
netic treatments considering reactive transport of carbonates are derived based on the
assumptions of (i) deformable three-phase solid skeleton; (ii) incompressible solids;
(iii) negligible streaming currents and electrophoresis; (iv) isothermal conditions. As-
sumption (i) represents an original contribution to the analysis of electrokinetic pro-
cesses, which are typically modeled assuming fully saturated conditions and rigid solid
skeleton.
In presence of carbonates, the chemical reactions taking place in the soil can be
summarized as follows [6]:

H2 O H+ + OH (1)
CO2(g) + H2 O H2 CO3 H2 CO3 = CO2(aq) + H2 CO3 (2)
H2 CO3 H ++
HCO
3 HCO
3 H +
+
CO2
3 (3)
CaCO3 Ca + CO2
+2
3 (4)

Equation (1) describes water auto-ionization; eq. (2) controls the solubility of CO2 in
the pore water as a function of its pressure, while eqs. (3) and (4) describe the dissoci-
ation of carbonic acid and the calcite dissolution/precipitation on the solid phase. The
kinetics of the reactions taking place in the aqueous phase is assumed to be sufficiently
fast to be considered almost instantaneous, with the exception of reaction (4), for which
an appropriate kinetic velocity is adopted.
In a 1-dimensional setting, the balance of mass equations for pore water, pore gas
and chemical species are given by
 MULTIPHYSICS MODELING OF ELECTROKINETIC PHENOMENA 91

Sw n dw dSw v s wxw
+n + Sw x + =0 (5)
w dt dt x x
s
n(Sg + HSw ) dg nHSw dw dSg v wxg mCO2
+n + Sg x + = RCO2 (6)
g dt w dt dt x x g
(nci ) Jx,i
+ Ri = 0 (7)
t x
MCaCO3
+ RCaCO3 MCaCO3 = 0 (8)
t

The term on the RHS of eq. (6) represents a source of gas production, proportional to
the reaction rate of the reaction (2). Equation (8) provides the mass balance equation
for the solid calcite; the quantity RCaCO3 appearing in the second term represents the
calcite production/consumption rate. The set of balance equations is completed by the
balance of electric charge and momentum (in quasistatic conditions):

jx Qe x
+ =0; + bx = 0 ; x := x!! (Sw pw + Sg pg ) (9)
x t x
where Qe is the soil-specific capacitance, and x!! is the constitutive stress, linked to the
skeleton deformation by the constitutive equation of the material.
Finally, the constitutive equations for the coupled flows of water, gas, chemical
species and electric charge are given by
! "
1 pw V
wxw = kw,rel w bx ke,rel e (10)
w x z
! " # ! " $
1 pg 1 pw V
wxg = kg,rel g bx + H kw,rel w bx ke,rel e
g x w x x
(11)
ci
Jx,i = Di zi ci ui + ci wxw (12)
x
N
%
V
jx = = s + zi F ui ci (13)
x i=1

where the hydraulic and electroosmotic conductivities are expressed by means of their
intrinsic values ( and e ) and the relative conductivities depending on the degree of
saturation Sr ; Di and ui are the effective diffusion coefficient and ionic mobility of
species i, and is the effective electric conductivity, sum of a the superficial con-
ductivity of the skeleton s and of a Faraday term proportional to ionic mobility and
charged species concentration.

3 NUMERICAL SIMULATIONS
The model described in the previous section has been implemented in the FE code
COMSOL Multiphysics, and has been used to simulate an ideal 1d electrokinetic fil-
tration test on a natural silty clay. A constant pw of 5 kPa above the reference gas
pressure was imposed at both the anode and the cathode. Constant electric current
density was imposed at the anode, while a reference null potential was assumed at the
92 C. Jommi et al.

Fig. 1. Evolution with position and time of degree of saturation (left) and pore water pH (right).

cathode. No inward flux was allowed for the chemical species at the anode. At the
cathode the species were allowed to flow outwards by convection only. The measured
value of pH was imposed at the anodic boundary. At the cathodic boundary, an inward
flux of OH - was imposed, calculated on the basis of the current density and on the
water autoionization. The model parameters were assigned where possible based
on direct experimental information [5] or taken from the literature.
Some selected results of the numerical simulation are shown in Fig. 1. The calcite
dissolution produces the development of gaseous CO2 which induces a significant drop
in the degree of saturation of the specimen. Moreover, the consumption of H+ ions
due to calcite dissolution prevents the motion of the pH front towards the cathode and
maintains the pH close to the anode above 4.55. This result is in agreement with the
experimental data reported in [5].

REFERENCES
[1] Hamed, J., Acar, Y.B., Gale, R.: Pb(II) removal from kaolinite by electrokinetics. ASCE-
JGGE 117, 241271 (1991)
[2] Alshawabkeh, A.N., Acar, Y.B.: Electrokinetic remediation. II: Theoretical model. J.
Geotech. Engng., ASCE 122, 186196 (1996)
[3] Mitchell, J.K.: Conduction phenomena: From theory to geotechnical practice.
Geotechnique 41, 229340 (1991)
[4] Yeung, A.T., Sadek, S.M., Mitchell, J.K.: A new apparatus for the evaluation of electrokinetic
processes in hazardous waste management. Geotech. Testing J. 15, 207216 (1992)
[5] Airoldi, F., Jommi, C., Musso, G., Paglino, E.: Influence of calcite on the electrokinetic
treatment of a natural clay. J. Applied Electrochemistry 39, 22272237 (2009)
[6] Appelo, C.A., Postma, D.: Geochemistry, groundwater and pollution. Balkema, Leiden
(2005)

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