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Mathematics
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Mathematical Modelling and Numerical Simulation in Mining Engineering
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Mathematical Modelling and Numerical Simulation in Mining Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 7857

Special Issue Editors

Prof. Dr. Lev Levin

E-Mail Website
Guest Editor
Mining Institute of the Ural Branch of the Russian Academy of Sciences, 614007 Perm, Russia
Interests: mining engineering; mine ventilation; artificial ground freezing; numerical simulation; geotechnology
Dr. Mikhail Semin

E-Mail Website
Guest Editor
Mining Institute of the Ural Branch of the Russian Academy of Sciences, 614007 Perm, Russia
Interests: artificial ground freezing; heat and mass transfer; numerical simulation; thermal monitoring; mine shaft; underground mine; mine ventilation systems; dust–air mixture
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Presently in the mining industry, there is a clear trend towards an increase in the intensity of mining operations, the expansion of mine fields and the development of mineral deposits at ever greater depths. In this situation, mines are becoming more and more complex systems in which many interconnected natural and technological processes take place. The analysis of such systems becomes impossible without a comprehensive consideration of various interconnected physical processes, the development of coupled mathematical models and the computer simulation of these processes in various normal and emergency situations.

The purpose of this Special Issue is to highlight various problems in the mining industry for which successful solutions are achieved using modern mathematical methods and numerical techniques.

The relevance of such studies is due to the need to ensure safe and energy-efficient mining operations in complex geological conditions. The safety and energy efficiency of mining processes are achievable with a comprehensive theoretical analysis of physical processes in mines using verified mathematical models, the parameters of which are adjusted according to experimental measurements.

Prof. Dr. Lev Levin
Dr. Mikhail Semin
Guest Editors

Manuscript Submission Information

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Keywords

  • geotechnical engineering
  • geomechanics
  • geotechnology
  • mine ventilation
  • mathematical modelling
  • numerical simulation
  • digital mine

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Published Papers (4 papers)

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Research

21 pages, 7067 KiB  
Article
Deep Graph Learning-Based Surrogate Model for Inverse Modeling of Fractured Reservoirs
by Xiaopeng Ma, Jinsheng Zhao, Desheng Zhou, Kai Zhang and Yapeng Tian
Mathematics 2024, 12(5), 754; https://doi.org/10.3390/math12050754 - 2 Mar 2024
Viewed by 1237
Abstract
Inverse modeling can estimate uncertain parameters in subsurface reservoirs and provide reliable numerical models for reservoir development and management. The traditional simulation-based inversion method usually requires numerous numerical simulations, which is time-consuming. Recently, deep learning-based surrogate models have been widely studied as an [...] Read more.
Inverse modeling can estimate uncertain parameters in subsurface reservoirs and provide reliable numerical models for reservoir development and management. The traditional simulation-based inversion method usually requires numerous numerical simulations, which is time-consuming. Recently, deep learning-based surrogate models have been widely studied as an alternative to numerical simulation, which can significantly improve the solving efficiency of inversion. However, for reservoirs with complex fracture distribution, constructing the surrogate model of numerical simulation presents a significant challenge. In this work, we present a deep graph learning-based surrogate model for inverse modeling of fractured reservoirs. Specifically, the proposed surrogate model integrates the graph attention mechanisms to extract features of fracture network in reservoirs. The graph learning can retain the discrete characteristics and structural information of the fracture network. The extracted features are subsequently integrated with a multi-layer recurrent neural network model to predict the production dynamics of wells. A surrogate-based inverse modeling workflow is then developed by combining the surrogate model with the differential evolutionary algorithm. Numerical studies performed on a synthetic naturally fractured reservoir model with multi-scale fractures illustrate the performance of the proposed methods. The results demonstrate that the proposed surrogate model exhibits promising generalization performance of production prediction. Compared with tens of thousands of numerical simulations required by the simulation-based inverse modeling method, the proposed surrogate-based method only requires 1000 to 1500 numerical simulations, and the solution efficiency can be improved by ten times. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Simulation in Mining Engineering)
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14 pages, 2114 KiB  
Article
Study of the Water Build-Up Effect Formation in Upcast Shafts
by Evgeniy Kolesov, Boris Kazakov, Andrey Shalimov and Artem Zaitsev
Mathematics 2023, 11(6), 1288; https://doi.org/10.3390/math11061288 - 7 Mar 2023
Cited by 1 | Viewed by 1732
Abstract
A theoretical study of the formation of water build-up, or water blanketing, and its influence on the ventilation of mine upcast shafts was carried out. Two scenarios for droplet moisture accumulation in the shaft were considered: condensation from saturated air rising up the [...] Read more.
A theoretical study of the formation of water build-up, or water blanketing, and its influence on the ventilation of mine upcast shafts was carried out. Two scenarios for droplet moisture accumulation in the shaft were considered: condensation from saturated air rising up the shaft and groundwater inflows through the leaky shaft lining. Analytical dependencies of the pressure drop due to the influence of water build-up versus the outgoing air flow velocity and the height of the groundwater source were obtained, taking into account the fractional composition of the droplet moisture. Practical arrangements are proposed to reduce the influence of the effect of water build-up in upcast shafts in the case of groundwater inflows through the leaky shaft lining. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Simulation in Mining Engineering)
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15 pages, 1784 KiB  
Article
Mathematical Modeling of Air Distribution in Mines Considering Different Ventilation Modes
by Mikhail Semin and Lev Levin
Mathematics 2023, 11(4), 989; https://doi.org/10.3390/math11040989 - 15 Feb 2023
Cited by 7 | Viewed by 2479
Abstract
The calculation of air distribution in large mine ventilation networks is usually carried out by numerically solving a system of equations representing Kirchhoff’s circuit laws. This formulation of the problem traditionally only considers the frictional air resistance of straight sections of mine airways. [...] Read more.
The calculation of air distribution in large mine ventilation networks is usually carried out by numerically solving a system of equations representing Kirchhoff’s circuit laws. This formulation of the problem traditionally only considers the frictional air resistance of straight sections of mine airways. However, when analyzing the changing ventilation modes, it is also important to correctly consider the shock losses, which sufficiently affect the redistribution of airflows. The reason is that the shock loss factor strongly depends on the airflow rates at the junctions of mine airways. This paper presents a mathematical model of a ventilation network that considers shock losses. The model considers steady-state air distribution as well as natural draft. The significance of the shock was confirmed with a practical example; we describe the application of the proposed mathematical model for the analysis of air distribution in the ventilation network of a potash mine during planned airflow reversal. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Simulation in Mining Engineering)
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19 pages, 5837 KiB  
Article
Analysis of Stress and Deformation on Surrounding Rock Mass of a Trapezoidal Roadway in a Large Inclination Coal Seam and Novel High Yielding Prop Support: A Case Study
by Yang Hao, Chunhui Liu, Yu Wu, Hai Pu, Kai Zhang and Lingling Shen
Mathematics 2023, 11(2), 319; https://doi.org/10.3390/math11020319 - 7 Jan 2023
Cited by 1 | Viewed by 1461
Abstract
Trapezoidal roadways in large inclination coal seams show asymmetrical tectonic characteristics, while there is still a lack of theoretical results on stress, deformation, and efficient and effective supporting methods on high walls. In this paper, based on the geological characteristics of a large, [...] Read more.
Trapezoidal roadways in large inclination coal seams show asymmetrical tectonic characteristics, while there is still a lack of theoretical results on stress, deformation, and efficient and effective supporting methods on high walls. In this paper, based on the geological characteristics of a large, inclined coal seam roadway, a mechanical model for stress–deformation analysis of trapezoidal section roadway was established. Complex analysis and a comfort map were employed to investigate the stress and deformation distribution on the roadway surface, and a novel yielding prop with high load capacity and constant working resistance was employed to support a high wall side based on analytical results. The results are as follows: (1) The deformation of the high wall is larger than that of the low wall, and the deformation of the roof is larger than that of the floor. The overall deformation of the surrounding rock shows that the rib closure is larger than the roof-to-floor closure. (2) The stress of the surrounding rock shows that both horizontal and vertical stresses are highest in the upper corner, indicating that the broken zone is most likely to occur at this location. (3) A new support employed with a high-yielding prop and a high-strength cable in a large, inclined angle roadway is proposed. On-site experiments were conducted in a large 5-1081 roadway of a coal mine in Shanxi, China. Under the influence of mining disturbance, the deformations at the top corner decreased by 40% compared with before. The test results show that the new support scheme can effectively control the development of roadway deformation and damage during the mining process. The new support also shows friendly environmental support and fast installation. Full article
(This article belongs to the Special Issue Mathematical Modelling and Numerical Simulation in Mining Engineering)
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