Modeling the precipitation distribution by radius and pore size during drying of an impregnated sphere

TL;DR

This work addresses the distribution of a catalyst precursor precipitate during the drying of an impregnated porous sphere by extending the Whitaker drying model with a precipitation term. It solves for the radial and temporal evolution of the mobile liquid fraction $\epsilon_l(r,t)$, dissolved salt $\gamma_m(r,t)$, precipitated salt $\epsilon_m(r,t)$, and temperature $T(r,t)$ under dynamic liquid–vapor equilibrium with fixed gas pressure, using a capillary-bundle representation to couple capillary pressure and liquid velocity to the pore-size distribution. A key contribution is the explicit inclusion of $r_{pr}$-controlled precipitation rate $r_{pr} = k_{pr}\max(0,\gamma_m-\gamma_m^*)$ and the demonstration of how final salt distributions concentrate toward the sphere surface, with larger near-surface salt loading when $k_{pr}$ increases or the initial salt content is higher. The model provides quantitative insight into precipitation patterns during drying, informing optimization of impregnation-drying steps for improved catalyst durability and performance in industrial reactors.

Abstract

The process of preparing heterogeneous catalysts on porous supports includes a drying stage, in which the porous material, impregnated with an aqueous solution of the catalyst precursor, is dried, and the precursor is precipitated on the pore walls. The precipitate distribution throughout the support volume strongly influences the catalyst performance and durability within industrial reactors. This paper presents a mathematical model for simulating the precipitation distribution during the drying of a porous sphere. Examples of calculations are given demonstrating the influence of some parameters on the distribution by space and by pore size.17

Figures (7)

• Figure 1: Drying at $T_{ex}$ = 40°C. Initial salt mass fraction in liquid $\gamma_{m,0}$ = 0.2. Rate constant of precipitation $k_{pr}$ = 50 kg/(s$\cdot$m$^3$). Drying time -- 52 min. Lines on the surfaces were drawn at 4-minute intervals.
• Figure 2: Change in the total mass of substances during drying.
• Figure 3: Details of the solution of system (1)-(4) at time $t_*$ = 15 min.
• Figure 4: Distribution of precipitation by radius at the end of drying depending on the initial mass fraction of salt.
• Figure 5: Distribution of precipitation by radius at the end of drying depending on (a) the drying temperature $t_{ex}$, (b) the value of constant $k_{pr}$.