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A Calcite Dissolution Model for the Estimation of Particle Size Distribution¹

ABSTRACT

Since reactions of solid phase carbonates generally occur as surface reactions, the reactive surface area and particle size distribution become important considerations. The objective of this study was to develop and test a stochastic model for the dissolution of calcite in which particle size is treated as a random variable. When used in conjunction with pH-stat steady-state dissolution procedure, the stochastic model provides a method to obtain estimates of particle size distribution of calcite in mixed particle size systems. The stochastic model was developed from a deterministic model which is based on the equal diameter reduction hypothesis. The deterministic model differs from the stochastic model in that a uniform particle size is assumed in the former and a distribution of particle sizes in the latter. Particle distribution was expressed according to the beta function, which was selected because of its flexibility. The stochastic model represented an improvement over the deterministic model in description of the dissolution of calcite under steady-state conditions. This improvement is due to the fact that a sample of particles in nature is more realistically described according to a distribution of particle sizes than as a single particle size.

¹ Contribution of the Texas Agricultural Experiment Station, Texas A&M, College Station 77843.

² Graduate Student, Statistics Dep., and Assistant Professor and Professor, Soil & Crop Sciences and Statistics Dep., respectively, Texas A&M Univ., College Station.

Received for publication November 14, 1983. Accepted for publication October 29, 1984.