This article presents a mathematical model and algorithm for numerically solving a problem for studying the hydrodynamic process of in-situ leaching in a heterogeneous porous medium, taking into account mass transfer kinetics, the law of layer deformation dependent on the elastic coefficient, changes in porosity depending on pressure, and the permeability of the ore reservoir for the purpose of developing ore deposits. The developed mathematical apparatus allows for a comprehensive study of the properties of the ore seam, optimization of the location of production and injection wells, determination of changes in porosity under pressure, and analysis and provision of a factor ensuring the protection of groundwater from pollution. The model under consideration is described using a system of second-order parabolic partial differential equations with initial, boundary, and internal conditions. Since the analytical solution to this problem was too complex or impossible for numerical integration, a second-order finite-difference scheme was used.
| Mualliflar | Usmonov, L.S., Усмонов, Л.С. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2026-05-02 |
| Son | 2 |
| Betlar | 89-108 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.2_72.2026.06 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.2_72.2026.06 · Maqolaning asl sahifasi
in-situ leaching, mathematical modeling, filtration, diffusion, kinetics, useful component, numerical methods, подземное выщелачивание, математическое моделирование, фильтрация, диффузия, кинетика, полезная компонента, численные методы
| APA | Usmonov, L.S., & Усмонов, Л.С. (2026). Mathematical Modeling of the Hydrodynamic Process of In-Situ Leaching taking into account the Changes in Hydrodynamic Parameters of a Porous Medium. Ҳисоблаш ва амалий математика муаммолари, (2), 89-108. https://doi.org/10.71310/pcam.2_72.2026.06 |
|---|---|
| GOST (OAK) | Usmonov, L.S., Усмонов, Л.С. Mathematical Modeling of the Hydrodynamic Process of In-Situ Leaching taking into account the Changes in Hydrodynamic Parameters of a Porous Medium // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 2. – P. 89-108. – DOI: 10.71310/pcam.2_72.2026.06. |
| MLA | Usmonov, L.S., and Усмонов, Л.С. “Mathematical Modeling of the Hydrodynamic Process of In-Situ Leaching taking into account the Changes in Hydrodynamic Parameters of a Porous Medium.” Ҳисоблаш ва амалий математика муаммолари, (2), 89-108, 2026. https://doi.org/10.71310/pcam.2_72.2026.06 |
| Chicago | Usmonov, L.S., and Усмонов, Л.С. “Mathematical Modeling of the Hydrodynamic Process of In-Situ Leaching taking into account the Changes in Hydrodynamic Parameters of a Porous Medium.” Ҳисоблаш ва амалий математика муаммолари, (2), 89-108 (2026). https://doi.org/10.71310/pcam.2_72.2026.06 |
| Harvard | Usmonov, L.S., and Усмонов, Л.С (2026) ‘Mathematical Modeling of the Hydrodynamic Process of In-Situ Leaching taking into account the Changes in Hydrodynamic Parameters of a Porous Medium’, Ҳисоблаш ва амалий математика муаммолари, (2), 89-108. https://doi.org/10.71310/pcam.2_72.2026.06 |
| BibTeX | @article{usmonovls2026,
title = {Mathematical Modeling of the Hydrodynamic Process of In-Situ Leaching taking into account the Changes in Hydrodynamic Parameters of a Porous Medium},
author = {Usmonov, L.S. and Усмонов, Л.С.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2026},
number = {2},
pages = {89-108},
doi = {10.71310/pcam.2_72.2026.06},
url = {https://doi.org/10.71310/pcam.2_72.2026.06}
} |
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