Modeling the dissolution rate of reactive phosphate rock in New Zealand pastoral soils

Abstract

Equations are proposed that describe the dissolution rate of phosphate rock (PR) incorporated at maintenance rates into pastoral soil. They are restricted to PR particles of equal-sized, equivalent spheres dissolving independently of each other. The rate-limiting step is considered to be steady-state diffusion through a concentric shell of soil around the PR particles. Models are examined in which the shell is either of a fixed outer diameter or of a fixed thickness. Both permit analytical solutions to the diffusion equation. They are consistent with the Kirk and Nye model for dicalcium phosphate dihydrate under appropriate conditions, and also with field dissolution of PRs applied alone, mixed with elemental sulfur or as the unreacted component in partially acidulated PRs.