A modified shrinking core model for the reaction between acid and hetero-granular rough mineral particles

• A modified shrinking core model was studied, considering the effects of the surface roughness and the size distribution of the mineral particles.
• Fractal geometry principles were applied to characterize the area and volume of the rough rock particles.
• The surface fractal dimension of the particles has the most significant influence on the extent of leaching.
• The accuracy of the traditional kinetic theory of acid rock reaction for matrix acidizing was improved.

The liquid–solid heterogeneous non-catalytic reaction between acid and minerals is the foremost principle of matrix acidizing. Previous mathematical models failed to describe the acid etching issue of rock particle clusters with the property of fractal surface in a three-dimensional space. We apply fractal geometry principles to characterize the area and volume of the rough rock particles on the basis of a mathematical model of a single particle. Based on chemical reaction kinetics and mass transfer theory, we present a modified shrinking core model for the acid–rock reaction of a mineral particle cluster that is undergoing a surface reaction. Using logarithmic normal distribution functions to describe the grain distribution of rocks, we describe the variations of the extent of leaching under surface reaction control. Our analysis indicates that clusters with larger fractal dimensions, smaller mean sizes and less disperse particles will be less dissolved when most of the other factors are kept constant.