Study of the CO₂ adsorption isotherms on El Hicha clay by statistical physics treatment: microscopic and macroscopic investigation

ABSTRACT

CO₂ introduction in deep aquifers based on adsorption phenomena represents geological tanks that reduce CO₂ emission. Thus, investigating carbon dioxide adsorption on rocks is becoming more interesting. In our work, carbon dioxide adsorption on El Hicha clay is extensively studied. Experimental data for CO₂ adsorption on this clay are given for the first time. All the corresponding parameters are simulated and interpreted using the multilayer model with two interaction energies. The effect of the key parameters involved in the adequate model on the isotherm curves are thus elucidated and interpreted. The formulation of this model is based on statistical physic formalism. Several hypotheses involving some physicochemical parameters which describe perfectly the adsorption process are used.

The characteristic parameters of the adsorption isotherm such as the number of carbon dioxide molecules per site (n), the receptor site densities (N_M), the number of adsorbed layers (N_L) and the energetic parameters (-ε₁) and (-ε₂) are estimated for the studied systems by a nonlinear least square regression. These parameters are discussed and interpreted considering their temperature dependence. In order to provide new macroscopic interpretations of adsorption mechanisms, three thermodynamic functions are also determined such as the entropy, the internal energy and the free enthalpy of Gibbs from experimental data. Thus, we prove theoretically and experimentally that CO₂ adsorption on El Hicha clay is feasible, spontaneous and exothermic in nature.

KEYWORDS:

• Carbon dioxide
• Tunisian El Hicha clay
• adsorption isotherm
• statistical physics
• modeling

Nomenclature

Q	=	The adsorbed quantities (g/g).
Qasat	=	The saturation adsorption quantity (g/g).
CO2	=	Carbon dioxide.
c	=	BET or GAB constant.
k	=	GAB constant.
N0	=	The average number of the adsorbed quantity
εi	=	The receptor site sorption energy.
n	=	The number of molecule per sites.
S	=	receptor sites.
μ	=	The chemical potential of receptor site.
μm	=	The chemical potential of the gaseous molecule.
Ni	=	The receptor site occupation state.
kB	=	The Boltzmann constant.
T	=	The absolute temperature.
NM	=	The receptor sites per surface unit.
1+NL	=	The number of adsorbed layers.
Pvs	=	The saturated vapor pressure.
P1 and P2	=	Pressures at the half saturation.
V	=	The volume of the gas.
ztr	=	The translation partition function.
zgc	=	The grand canonical partition function.
Zgc	=	The total grand canonical partition function.
zv	=	The translation partition function per unit of volume.
$\mathrm{\Delta }{E}_1^a$,$\mathrm{\Delta }{E}_2^a$	=	The molar adsorption energies at first, second and other layers respectively.
ΔEv	=	The vaporization energy of one adsorbed mole of water molecules.
R2	=	The coefficient of determination.
RMSE	=	The residual root mean square error
RSS	=	The residual sum of squares.
Qjcal,Qjexp	=	The calculated and experimental values.
Sa	=	The configurational entropy.
Ea	=	The internal energy.
G	=	The enthalpy of Gibbs.