(94b) A Comprehensive Study of the Ionic Mass Transfer and Proton Adsorption inside -Alumina Pores with Charged Surfaces

1. Introduction

Gamma alumina solids are used in industry as supports for hydrotreatment catalysts prepared by impregnation (Catita et al., 2021) and as adsorbents for the decontamination of industrial water effluents from heavy metals (Srivastava et al., 2011). The refining industries are focusing their efforts on designing more active and selective catalysts for hydrotreatment processes with enhanced performances, as a result of the increasing worldwide demand for cleaner transportation fuels. This can be done by optimizing the metal distribution profiles obtained during impregnation (Jolivet, 2020). alumina adsorbents used in water treatment processes suffer from low metal adsorption efficiencies (Srivastava et al., 2011). Not to mention that the effect of the operating conditions, especially the pH of the solution, on both applications is unclear (Nagashima & Blum, 1999). Understanding the mass transfer and adsorption physicochemical phenomena governing these processes remains challenging (Corral Valero et al., 2019).

The objective of this study is to rationalize the mass transfer and adsorption phenomena occurring during impregnation and water decontamination processes by developing a predictive model based on experimental findings. In a first attempt, the adsorption of protons from acidic solutions at different pH values on the charged and heterogeneous surface of alumina pores, is evaluated in the absence of metallic species.

2. Methodology

2.1. Modeling Approach

The interactions between an acid solution containing protons, nitrate, and hydroxide ions with a fixed mass of cylindrical alumina extrudates is modeled here in a batch system with a fixed liquid volume. Material balances are written for the different species in each domain of the system, including:

• The extra-granular liquid with a mass transfer flux at the interface between the extra-granular and intra-granular liquids.
• The intra-granular liquid with a molecular diffusion flux in the direction parallel to the pore surface and a mass transfer flux at the interface between the intra-granular liquid and the liquid/solid interface. This molecular diffusion flux is expressed using the extended Fick model including a supplementary term for the electrostatic potential generated due to the differences in the charges and the self-diffusivities of the species in solution. The electrostatic potential gradient is determined by the zero-current method as described by (Krishna, 2016).
• The electrostatic double layer (or EDL) formed at the liquid/solid interface to neutralize the charges on the pore surface. Inside this layer, the species are distributed based on their charges and an electrostatic potential is generated in the direction perpendicular to the pore surface. The structure of the EDL is determined using the Poisson-Boltzmann equation based on the work of (Ichikawa, 2022).
• The solid surface on which only protons can adsorb. The heterogeneity of the alumina pore surface is accounted for: protons can adsorb on three different types of sites present on the pore surface with the adsorption/desorption mechanisms described in Table 1. The Langmuir adsorption isotherm is used to describe the proton adsorption on each of the three sites, with distinct maximal adsorption capacities and equilibrium constants.

Table 1. Adsorption/desorption mechanisms of the active sites present on the alumina pore surface and accounted for in the model [retrieved from (Corral Valero et al., 2019)].

2.2. Experimental Procedure

Some of the model parameters are unknown. They are determined by minimizing the error between the simulation data and the results of batch adsorption experiments conducted with nitric acid solutions at different initial pH values. During these experiments, pre-wetted alumina extrudates are contacted with the acid solution for , during which the extra-granular liquid phase is homogeneously stirred, and its pH and electrical conductivity are measured in-situ.

3. Results and Discussion

3.1. Simulations vs Experimental Data

The parameter estimation shows the parameters to be highly dependent, though the values estimated are comparable with values found in literature. The simulations agree very well with the experiments, as shown in Figure 1 for an initial pH of 2.

Figure 1. Comparison of the simulation and experimental data for a) the proton concentration and b) the electrical conductivity in the extra-granular liquid phase when the initial pH of the solution is 2

In this case, the proton concentration in the extra-granular liquid decreases with time and never stabilizes. The protons penetrate inside the solid pores as soon as they are contacted with the alumina extrudates. In parallel, the electrical conductivity keeps decreasing due to the depletion of the protons from the solution.

Interestingly, other simulations with higher initial pH values show a faster penetration of protons inside pores.

3.2. Surface Charge

The model can predict the evolution of the charge on the pore surface, as shown in Figure 2 when the initial pH is 2. Near the extrudate edges, the surface charge (with an initial negative value) increases rapidly with time and stabilizes at a positive value. This is due to the proton adsorption, which follows a similar trend as the surface charge. The surface charge maintains its initial negative value at the center of the extrudates where the protons are not able to reach due to their strong adsorption near the extrudate edges.

Figure 2. Evolution of a) the surface charge and b) the total concentration of protons adsorbed on the pore surface when the initial pH is 2.

3.3. Concentration Profiles

The concentration profiles of the different species are also determined by the model in the different domains of the system (Figure 3). The negatively charged nitrate ions seem to follow the positively charged protons in the extra-granular and intra-granular liquids to maintain the electrical neutrality of the solution.

Moreover, the protons are repelled by the positively charged pore surface to the intra-granular liquid phase, while the nitrate and hydroxide ions are attracted towards the EDL.

Figure 3. Concentration of a) protons (or H), b) nitrate ions (or NO3), and c) hydroxide ions (or OH) in 1) the extra-granular liquid, 2) the intra-granular liquid, and 3) the EDL when the initial pH is 2. Each circular plot is an image of the radial profile of the concentration of a species in a certain domain at t1= 0 min, t2= 2000 min, and t3= 4000 min.

4. Conclusion

The model accurately predicts the distribution of species outside and inside the extrudates, including inside the EDL formed at the liquid/solid interface. It also computes the surface charge and the adsorption and mass transfer parameters, which are very difficult to determine experimentally. The surface charge seems to play a critical role in driving the mass transfer in the extra-granular and intra-granular liquids.

Finally, this model provides a more rational understanding of the interactions of gamma alumina with acid solutions at different pH levels, which could prove useful in optimizing impregnation and water treatment processes.

5. References

[1] Catita, L., Jolimaitre, E., Quoineaud, A.-A., Delpoux, O., Pichon, C., & Schweitzer, J.-M. (2021). Mathematical modeling and Magnetic Resonance Imaging experimental study of the impregnation step: A new tool to optimize the preparation of heterogeneous catalysts. Microporous and Mesoporous Materials, 312, 110756. https://doi.org/10.1016/j.micromeso.2020.110756

[2] Corral Valero, M., Prelot, B., & Lefèvre, G. (2019). MUSIC Speciation of γ-Al ₂ O ₃ at the Solid Liquid Interface: How DFT Calculations Can Help with Amorphous and Poorly Crystalline Materials. Langmuir, 35(40), 12986–12992. https://doi.org/10.1021/acs.langmuir.9b02788

[3] Ichikawa, T. (2022). Theory of Ionic Diffusion in Water-saturated Porous Solid with Surface Charge. Journal of Advanced Concrete Technology, 20(7), 430–443. https://doi.org/10.3151/jact.20.430

[4] Jolivet, L. (2020). Apport de la spectroscopie de plasma induit par laser pour la modélisation des procédés de raffinage [PhD Dissertation]. Université de Lyon.

[5] Krishna, R. (2016). Highlighting coupling effects in ionic diffusion. Chemical Engineering Research and Design, 114, 1–12. https://doi.org/10.1016/j.cherd.2016.08.009

[6] Nagashima, K., & Blum, F. D. (1999). Proton Adsorption onto Alumina: Extension of Multisite Complexation (MUSIC) Theory. Journal of Colloid and Interface Science, 217(1), 28–36. https://doi.org/10.1006/jcis.1999.6355

[7] Srivastava, V., Weng, C. H., Singh, V. K., & Sharma, Y. C. (2011). Adsorption of Nickel Ions from Aqueous Solutions by Nano Alumina: Kinetic, Mass Transfer, and Equilibrium Studies. Journal of Chemical & Engineering Data, 56(4), 1414–1422. https://doi.org/10.1021/je101152b