Additives rich in Si and Al such as kaolin may be applied in PF biomass boilers to fix alkali metals in species that are more benign than the alkali salts released in biomass combustion. In this study, models for the reaction of gas-phase potassium salts with kaolin particles are developed for the conditions appearing in PF boilers such as short residence times, high temperatures, and small size of the additive particles. The reaction between gaseous potassium components and kaolin particles has been modeled with a shrinking core model (SCM) and a uniform conversion model (UCM). The SCM takes into account the effects of chemical kinetics, diffusion in a gas film surrounding the particle, diffusion in a product layer, and thermochemical equilibrium on the reaction progress. The UCM covers diffusion in a gas film surrounding the particles, chemical kinetics, and thermochemical equilibrium. Both models are able to accommodate the effects of change in temperature, particle size, reaction time, and potassium component concentration. Literature data from experiments in an entrained flow-reactor (EFR) at 800–900 °C were used to derive the chemical kinetic rate coefficients of the reaction between kaolin and KOH. The models were then evaluated against experimental data for alkali salts of KCl, KOH, K2CO3, and K2SO4 covering temperatures of 800–1450 °C, kaolin particle sizes of 4–14 μm, residence times of 0.8–1.9 s, and salt/additive molar ratios of 0.05–0.96. The evaluation indicated that both SCM and UCM were suitable for a wide range of conditions, but the UCM captured the effect of particle size better. The modeling outcomes suggested that if the reaction time was long enough, the thermochemical equilibrium would be the major limitation in capturing potassium by kaolin at high temperatures and high potassium concentrations. At lower temperatures, however, the conversion was mainly limited by chemical kinetics. The mass-transfer limitation was less critical under the investigated conditions. The developed models can account for the reaction of gas-phase potassium salts with kaolin at local conditions relevant to PF boilers using biomass.