A Study of Analytical Solution for the Special Dissolution Rate Model of Rock Salt

Abstract

By calculating the concentration distributions of rock salt solutions at the boundary layer, an ordinary differential equation for describing a special dissolution rate model of rock salt under the assumption of an instantaneous diffusion process was established to investigate the dissolution mechanism of rock salt under transient but stable conditions. The ordinary differential equation was then solved mathematically to give an analytical solution and related expressions for the dissolved radius and solution concentration. Thereafter, the analytical solution was fitted with transient dissolution test data of rock salt to provide the dissolution parameters at different flow rates, and the physical meaning of the analytical formula was also discussed. Finally, the influential factors of the analytical formula were investigated. There was approximately a linear relationship between the dissolution parameters and the flow rate. The effects of the dissolution area and initial volume of the solution on the dissolution rate equation of rock salt were computationally investigated. The results showed that the present analytical solution gives a good description of the dissolution mechanism of rock salt under some special conditions, which may provide a primary theoretical basis and an analytical way to investigate the dissolution characteristics of rock salt.

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“…Mineral densities and dissolution properties are provided in Table 1. The dissolution rate k max strongly depends on the hydrodynamic boundary conditions: it increases with flow velocity [21] and reaches values under turbulent flow conditions that are at least one order of magnitude higher than that for laminar flow [16,19]. This is due to most salt minerals showing transport-controlled dissolution behavior, i.e., k max is controlled by the thickness of the diffusive boundary layer at the mineral surface [19,22,23].…”