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Abstract

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Introduction

In recent decades, hydraulic stimulation of coal seams has become a widely used method in the mining industry. This process is used to improve formation permeability, improve coal mining efficiency and ensure operational safety. However, to achieve the best results, not only adequate planning and hydraulic skills are required, but also a thorough understanding of the physical processes occurring in coal seams. In this context, mathematical modeling and parameter calculation are important tools. Mathematical modeling allows one to create virtual models of the geological and geophysical parameters of a coal seam and understand complex processes such as fluid propagation within the seam, changes in pressure and permeability. Using models, it is possible to evaluate the effectiveness of hydraulic impact and determine the optimal impact parameters.

Calculation of the hydraulic impact process parameters allows us to determine the optimal pressure, volume, speed and time of impact on coal seams. This is important for achieving maximum coal mining productivity and ensuring mining safety. Calculations can also take into account the peculiarities of geological conditions and the structure of formations, which helps to anticipate possible problems and risks.In general, mathematical modeling and calculation of the process parameters of hydraulic stimulation of coal seams are important tools for optimizing coal production. Their use helps to predict the results and take the necessary measures to ensure the efficiency and safety of the hydraulic stimulation process.

1. Basic principles of hydraulic influence on coal seams

Coal seam hydraulic stimulation is a process in which fluid, usually water or solutions, is injected under pressure into coal seams to improve their permeability and increase the productivity of coal mining. Hydraulic stimulation of coal seams has several purposes, including:

1. Increasing formation permeability: fluid injected under pressure can penetrate into the cracks and pores of the coal seam, expanding them and improving permeability. This allows you to increase the productivity of coal mining.

Facilitate drainage of gases: Hydraulic action can help remove gases from the coal seam, creating a path for them to escape and reducing the risk of accidents.

Facilitate coal mining: The injection of pressurized fluid can help penetrate hard-to-reach areas of the formation and improve the efficiency of coal mining. Hydraulic impact on coal seams requires special calculations and modeling to determine the optimal impact parameters, such as pressure, fluid volume, speed and duration of impact. Accurate hydraulic planning and control help improve coal mining productivity and process safety

2. Mathematical modeling of the hydraulic impact process

When modeling the process of hydraulic impact on coal seams, various equations and models are used that describe the physical processes occurring in the seam. Here are some basic equations and models used in coal seam modeling:

1. Darcy's Equation: Darcy's equation is used to describe the flow of fluid through a porous medium such as a coal seam. It relates the speed of fluid flow to the pressure gradient and permeability of the medium.

2. Fracture model: Under hydraulic influence, cracks can form or expand within the formation. To model this process, fracture models are used that describe the characteristics of fractures (length, width, direction) and their effect on the permeability of the formation.

3. Conservation of Mass Equation: The conservation of mass equation is used to describe the distribution and movement of fluid within a formation during hydraulic stimulation. It takes into account fluid inputs and outputs, as well as distribution in time and space.

4. Equation of conservation of momentum: The equation of conservation of momentum describes the change in the speed and direction of fluid motion under the influence of external forces, including pressure and resistance of a porous medium. This equation allows the dynamic aspects of fluid flow to be taken into account.

5. Permeability Equation: The permeability equation relates the flow of fluid through a porous medium to the permeability of the formation. It takes into account various factors such as pore geometry, fluid viscosity and pore sizes.

6. Coal Seam Behavior Model: The coal seam behavior model describes its mechanical and hydrodynamic properties such as elasticity, strength, porosity and permeability. It allows you to predict the behavior of the formation under the influence of hydraulic load. These are just some of the basic equations and models used in modeling the process of hydraulic influence on coal seams. They help analyze and predict impact results, optimize process parameters and make informed decisions for the efficient operation of coal deposits.

3. Practical application of mathematical modeling and calculation of parameters

In the mining industry, mathematical modeling of coal seams plays an important role. Here are some examples of its use:

1. Coal Seam Fluid Flow Modeling: Mathematical models are used to analyze and predict fluid flow within coal seams. This makes it possible to determine the optimal hydraulic parameters, such as pressure, flow rate and fluid flow rate, to improve the permeability of the formations and the efficiency of coal mining.

2. Modeling the interaction of cracks with coal seams: Under hydraulic influence, cracks can form or expand inside coal seams. Mathematical models make it possible to analyze and predict the interaction of fractures with formations, determine the impact parameters and evaluate the effectiveness of this process.

3. Modeling Pressures and Stresses in Coal Seams: Mathematical modeling is used to estimate the pressures and stresses that occur in coal seams under the influence of hydraulic pressure. This makes it possible to predict possible deformations and destruction of formations, and thus determine safe production parameters.

4. Modeling gas migration in coal seams: Coal seams can be sources of gas, which can migrate and form reservoir gas deposits. Mathematical modeling allows you to study gas migration processes, determine its working areas and assess the potential for reservoir gas production.

5. Modeling of hydrodynamic processes in wells: Mathematical modeling is used to analyze and optimize hydrodynamic processes in wells of coal seams. This includes analyzing fluid flow inside the well, determining optimal crew parameters, and modeling drainage processes and reservoir pressure.

These are just some examples of the use of mathematical modeling in the coal seam mining industry. They help optimize coal mining processes, predict the behavior of seams and ensure safe operations.

Conclusion

In conclusion, it can be noted that mathematical modeling and calculation of the parameters of the process of hydraulic stimulation of coal seams are important tools in the mining industry. They make it possible to predict and optimize the results of hydraulic action, improve the productivity of coal mining, ensure work safety and process efficiency. Mathematical modeling allows you to create virtual models that describe the physical processes occurring in coal seams.

It allows you to analyze fluid flows, formation permeability, fracture interaction and other factors affecting the effectiveness of hydraulic stimulation. Calculation of the parameters of the hydraulic stimulation process allows you to determine the optimal values of pressure, flow rate, speed and time of influence. This helps to achieve maximum formation permeability, improve production productivity, reduce the risk of formation destruction and ensure operational safety.

However, to achieve the best results, it is necessary to take into account the realism and accuracy of data, calibrate and validate models, and use sensitivity analysis to determine important parameters. In general, the use of mathematical modeling and calculations in hydraulic stimulation of coal seams can significantly improve the efficiency and safety of mining processes coal These tools help you make informed decisions, optimize parameters and achieve better results in the mining industry

This master's work is not completed yet. Final completion: May 2024. The full text of the work and materials on the topic can be obtained from the author or his head after this date.

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