A widely used process for remineralization of desalinated water consists of dissolution of calcite particles by flow of acidified desalinated water through a bed packed with millimeter-size calcite particles. An alternative process consists of calcite dissolution by slurry flow of micron-size calcite particles with acidified desalinated water. The objective of this investigation is to provide theoretical models enabling design of remineralization by calcite slurry dissolution with carbonic and sulfuric acids. Extensive experimental results are presented displaying the effects of acid concentration, slurry feed concentration, and dissolution contact time. The experimental data are shown to be in agreement within less than 10% with theoretical predictions based on the simplifying assumption that the slurry consists of uniform particles represented by the surface mean diameter of the powder. Agreement between theory and experiment is improved by 1-8% by taking into account the powder size distribution. Apart from the practical value of this work in providing a hitherto lacking design tool for a novel technology. The paper has the merit of being among the very few publications providing experimental confirmation to the theory describing reaction kinetics in a segregated flow system.