Mathematical model of the formation of barite-lead mineralization of the Ushkatyn III deposit (Central Kazakhstan)

The genesis of stratiform deposits of lead and barite in sedimentary rocks is of great interest from the point of view of replenishing reserves of polymetallic ores. The aim of the work is to establish the regularity of the hydrogenic formation of ores in limestones, taking into account the influence of the nanosurface of pores and cracks based on a mathematical model of the movement and characteristics of ore-bearing solutions in the pores. The thicknesses of the surface layer of limestones and minerals included in the ore-containing strata and sulfide minerals are calculated. The results indicate that they are nanostructures with special physical properties different from the rest of the substance, which is confirmed by the regularity of the formation of a heavy sulfur isotope in ores of various textural types. The influence of hydrotherms with different densities, kinematic viscosity, and velocity on the intensity of mineralization formation in cracks and pores of limestone, as well as the occurrence of new feathering cracks around the fractures of dismemberment, is estimated. The dependence of the hydrothermal flow density on the diffusion of the liquid is established. The equation of kinematic viscosity is derived from the pressure in the solution flow, the velocity of its movement, the mass of particles of ore-forming elements, and sulfur isotopes under thermodynamic conditions of determined Gibbs energies. The relationship of the viscosity of the solution with the surface tension of the nanolayer of limestone particles in cracks and pores is shown, indicating that the greater this energy, the greater the velocity of movement of ore-forming solutions, the fewer branches of newly formed cracks around the dissection crack. The mathematical model is applicable for the numerical analysis of the regularity of mineralization in cracks, taking into account the influence of the nanostructural layer of cracks and pores of limestone in the thermodynamic conditions of the occurrence of an ore-bearing formation.