Blast furnace burden porosity calculation method based on Monte Carlo algorithm

Abstract

The invention discloses a blast furnace burden porosity calculation method based on a Monte Carlo algorithm, and belongs to the technical field of blast furnace ironmaking. The method comprises the steps that firstly, according to a particle size distribution probability density function, Monte Carlo random sampling is adopted to generate and initialize the particle size of furnace charge particles; then, in a three-dimensional Cartesian coordinate system, a three-ball contact geometric constraint equation set is established and solved, and spatial positions of newly-added particles in an existing accumulation system are searched; meanwhile, the search radius of the supporting particles is dynamically adjusted, and collision detection is executed; and finally, after the total number of the particles reaches a preset threshold value, calculating the total volume and the particle volume in a set spherical calculation domain, and determining the porosity by adopting a moving average and moving variance statistical method. According to the method, the limitation of a traditional experimental method and an existing numerical model is overcome, high-precision and high-efficiency calculation of the blast furnace burden porosity is realized, and a reliable theoretical tool is provided for optimizing a blast furnace burden distribution system and analyzing air permeability.

Description

Technical Field

[0001] This invention belongs to the field of blast furnace ironmaking technology, specifically relating to a method for calculating the porosity of blast furnace burden based on the Monte Carlo algorithm. Background Technology

[0002] Blast furnace ironmaking is one of the core processes in steel production, and its efficiency and quality directly affect the performance and cost of steel products. During blast furnace smelting, the porosity of the furnace charge is a key factor influencing blast furnace permeability and smelting efficiency. Porosity not only determines the distribution of airflow and heat and mass transfer efficiency within the furnace but also directly affects the stability and production efficiency of the blast furnace. Therefore, accurately calculating the porosity of the furnace charge is of great significance for optimizing blast furnace operation and improving smelting efficiency.

[0003] Traditional methods for measuring the porosity of blast furnace burdens mainly rely on experimental techniques, such as mercury intrusion porosimetry and gas adsorption. However, these methods have significant limitations in complex particulate systems, making it difficult to accurately capture the packing state and pore distribution characteristics between particles. Furthermore, experimental methods typically require substantial time, manpower, and resources, and are often insufficient to meet the needs of real-time monitoring and optimization of blast furnaces.

[0004] In recent years, with the development of computer technology and numerical simulation methods, porosity calculation methods based on numerical simulation have gradually become a research hotspot. The Monte Carlo algorithm, as a classic random sampling method, can simulate the particle packing process through a large number of random experiments and accurately calculate porosity. Compared with traditional deterministic methods, the Monte Carlo algorithm has advantages such as strong adaptability, high computational accuracy, and wide applicability, and is particularly suitable for the simulation and analysis of complex particle systems.

[0005] To address the aforementioned problems, this invention proposes a method for calculating the porosity of blast furnace burden based on the Monte Carlo algorithm. This method achieves high-precision calculation of blast furnace burden porosity by optimizing particle generation and initialization, the geometric description of particle packing, the selection and collision detection of supporting particles, and porosity calculation and statistical methods. This invention not only provides a reliable theoretical tool for optimizing blast furnace burden structure and analyzing permeability, but also provides a scientific basis for energy conservation, emission reduction, and efficient production in blast furnace ironmaking processes, possessing significant theoretical value and practical application significance. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating the porosity of blast furnace burden based on the Monte Carlo algorithm. By simulating the accumulation process of burden particles, the porosity of the burden can be accurately calculated, providing a scientific basis for the optimization of blast furnace burden structure and permeability analysis.

[0007] This invention is implemented as follows: a method for calculating the porosity of blast furnace burden based on the Monte Carlo algorithm, comprising the following steps: Step S1: On-site sampling is used to obtain the proportion data of different particle sizes. The Monte Carlo random sampling method is used to generate the particle size of the furnace charge, and the radius and center coordinates of each particle are initialized. Step S2: Based on the spherical geometry equations, in a three-dimensional Cartesian coordinate system, find a stable spatial position for the newly generated particle within the existing particle packing system. Specifically, select at least three existing particles as support points, construct a set of three-sphere contact geometric constraint equations, and solve the set of equations to obtain the center coordinates of the new particle. If the set of equations has real solutions, select one set from the solution set as the placement position of the new particle. If there are no solutions, reselect support particles and repeat the calculation until a physically realizable stable packing configuration is obtained. Step S3: Dynamically adjust the radius C of the sphere generation area used to screen the supporting particles, and after determining the temporary position of the new particle, perform collision detection to verify that the new particle and all existing particles meet the non-overlapping geometric condition; if a collision occurs, return to step S2 to reselect the supporting point; Step S4: When the total number of generated particles reaches the preset threshold, a spherical computational domain with radius S is set with the origin of the coordinate system as the center. The total volume in the computational domain and the total volume occupied by all particles in the computational domain are calculated. The porosity is determined based on the ratio of the difference between the two to the total volume of the computational domain. During the calculation process, the porosity values ​​of multiple continuously generated sub-samples are processed using moving average and moving variance statistical methods to evaluate the convergence and stability of the calculation results.

[0008] As a preferred technical solution, in step S2, the initial particle packing system consists of three spherical particles with equal radii, externally tangent to each other, and whose centers are located on the same horizontal plane, forming an equilateral triangle layout.

[0009] The use of a symmetrical and stable initial core structure provides balanced mechanical support for the subsequent layer-by-layer stacking of particles, ensuring that the simulation system has good geometric symmetry and physical rationality from the initial stage, thus laying the foundation for the stability of the entire stacking process.

[0010] As a preferred technical solution, in step S2, the method for selecting support points is as follows: a sphere is generated with the origin of the coordinate system as the center and the dynamically adjusted radius C as the radius. A point P is randomly selected on the surface of the sphere, and then the three existing particles closest to point P are found as support points.

[0011] In this scheme, by adaptively adjusting the search radius, the search range can be expanded in densely populated areas to improve the success rate, while the search radius can be contracted in sparsely populated areas to improve efficiency, thus achieving a dynamic balance between physical rationality and computational efficiency in the search process.

[0012] As a preferred technical solution, in step S2, the three-ball contact geometric constraint equations are as follows:

[0013] Where r represents the radius of the newly falling particle, and the radii of the three supporting particles are r. i Where i = 1, 2, 3; (x, y, z) represents the position of the newly added particle after it is stably placed on the other particles; the center coordinates of the three supporting particles are (x, y, z). i y i , z i ).

[0014] Based on the geometric contact conditions, a set of equations was established to mathematically describe the external tangential relationship between particles, ensuring that the newly added particles and the supporting particles are in close contact without overlap, thus providing accurate mathematical model support for simulating real stacking behavior.

[0015] As a preferred technical solution, the specific strategy for dynamically adjusting the radius C of the sphere generation region in step S3 is as follows: Initially, C is set to the first preset value; When an attempt to generate a new particle fails, C is increased by one-N times the radius of the smallest particle in the current particle system, where N is an integer greater than 1. When a new particle is successfully generated, C is reduced by the value of the largest particle radius in the current particle system.

[0016] By adaptively adjusting the search radius, the search range can be expanded in densely populated areas to improve the success rate, while the search radius can be contracted in sparsely populated areas to improve efficiency, thus achieving a dynamic balance between physical rationality and computational efficiency in the search process.

[0017] As a preferred technical solution, the collision detection in step S3 is to verify whether the geometric distance between the temporary position of the new particle and all existing particles satisfies the non-overlapping condition, that is, the square of the center distance between the new particle and any existing particle is greater than the square of the sum of their radii. If there is any particle that does not meet this condition, it is determined that a volume collision has occurred, and the support point needs to be reselected and iteratively calculated until a non-overlapping and stable particle configuration is generated.

[0018] Rigorous global collision detection ensures that no geometric overlap occurs between particles during the simulation, maintaining the physical authenticity of the packing system and providing an error-free geometric basis for subsequent porosity calculations, thus significantly improving the reliability of the calculation results.

[0019] As a preferred technical solution, the collision detection method in step S3 is as follows: if the radius and coordinates of the existing particles are r... j With (x) iy i j i The determination conditions are as follows: ; If any existing particle satisfies the above inequality, it is determined to be a collision, the temporary position is discarded, and the process returns to step 2 to select a new support point.

[0020] As a preferred technical solution, in step S4, the porosity is calculated as follows: Taking the origin as the center, the calculation region is a sphere with radius S, and its total volume is: ; Let the total volume of the particles be V. b The porosity p of the packed system is calculated by summing the volumes of all particles completely within the computational domain: .

[0021] The method employs a spherical computational domain combined with volumetric accumulation to calculate porosity. This approach is intuitive and easy to implement, accurately reflecting the macroscopic porosity characteristics of the packing system and providing a reliable quantitative indicator for blast furnace permeability analysis.

[0022] As a preferred technical solution, in step S4, when calculating the total volume occupied by the particle within the computational domain, for particles that intersect with the boundary of the computational domain, the effective volume is included by calculating the volume of the spherical cap of the particle within the computational domain.

[0023] By accurately calculating the spherical cap volume of intersecting particles at the boundary, the statistical bias introduced by the traditional "all or nothing" method is avoided, significantly improving the accuracy of porosity calculation in the boundary region, and is especially suitable for statistical evaluation in finite-size calculation domains.

[0024] As a preferred technical solution, the radius S of the computational domain set in step 4 is not less than 50 times the diameter of the largest particle, and the distance between the boundary of the computational domain and the nearest particle is not less than 10 times the diameter of the smallest particle, so as to eliminate the interference of boundary effects and edge packing non-uniformity on the porosity statistical results and ensure that the statistical region is in the approximately uniform core area of ​​the packing.

[0025] The technical effects of this invention are as follows: 1. This invention uses Monte Carlo simulation to quickly reconstruct three-dimensional stacked structures in a computer, completing experimental analyses that previously took days or even weeks in just a few hours. It can also perform unlimited repeated calculations and comparisons, thereby obtaining high-precision porosity results quickly and stably. This provides unprecedented analytical efficiency and data support for blast furnace production, overcoming the inherent limitations of traditional experimental methods. 2. The porosity of the furnace charge is a key parameter that determines the permeability of the blast furnace and the uniformity of the gas flow distribution. The precise porosity data provided by this invention is the basis for studying the gas-solid two-phase heat and mass transfer process in the blast furnace. Based on this, the gas flow, pressure distribution and reduction reaction in the blast furnace can be simulated and analyzed more accurately. This allows for precise diagnosis and early warning of furnace condition fluctuations caused by poor furnace charge structure, such as deterioration of permeability and uneven gas flow distribution. It also guides operators to make timely adjustments to ensure the stable and smooth operation of the blast furnace.

[0026] 3. The core modeling principle of this method is based on general principles of spherical geometry and probability statistics, and does not depend on the chemical properties of specific materials, thus exhibiting good versatility. It can be seamlessly extended to the porosity analysis of different furnace charges (such as sinter, pellets, and coke) and their mixtures in the iron and steel smelting field. Furthermore, the theoretical framework of this method is also applicable to the study of complex particulate system packing structures in other industrial fields (such as chemical and pharmaceutical industries), demonstrating broad application potential. Attached Figure Description

[0027] Figure 1 The diagram illustrates the particle accumulation process during the calculation. (a) shows the existing furnace charge; (b) shows the random point P generated on the spherical shell S, with the furnace charge particle closest to P serving as the support point; and (c) shows the solution for the location of newly added furnace charge. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0029] Example 1 To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0030] A method for calculating the porosity of blast furnace burden based on the Monte Carlo algorithm includes the following steps: Step 1: On-site sampling is used to obtain the proportion data of different particle sizes. The Monte Carlo random sampling method is used to generate the particle size of the furnace charge particles, and the center coordinates (x,y,z) and radius r of each particle are initialized. This step ensures that the particle size distribution meets the preset conditions and provides basic data for subsequent steps. For example, if the proportion of 40-25mm particles is 20%, then particles with a mass percentage of 20% in the 40-25mm range will be randomly generated. Step 2: Based on the spherical geometric equations, solve for the stable spatial position of the new particle on the existing particle system in a three-dimensional Cartesian coordinate system. By selecting at least three existing particles as support points, construct a set of three-sphere contact geometric constraint equations and solve the set of equations to obtain the center coordinates of the new particle. If the set of equations has real solutions, randomly select a set from the solution set as the placement position of the new particle. If there are no solutions, reselect support particles and repeat the calculation until a physically realizable stable stacking configuration is obtained.

[0031] In step 2, the geometric equation of a single sphere is defined in a three-dimensional Cartesian coordinate system as follows: ; In step 2, the initial stacking core consists of three spherical particles with equal radii and externally tangent to each other. Their centers are located on the same horizontal plane and form an equilateral triangle layout. This core structure serves as the physical support point for the subsequent layer-by-layer stacking of particles, ensuring the geometric symmetry and mechanical balance of the entire simulation system.

[0032] The selection of support points is as follows: First, generate a sphere with radius C centered at the origin; randomly select a point P on the surface of this sphere, and then find the three existing particles closest to P as support points. By repeating this process, a packing system can be gradually generated. The initial state consists of a packing core composed of three particles in contact with each other.

[0033] When generating new particles, it is assumed that several supporting particles already exist in the pile. To ensure the stable stacking of the new particles, at least three support points are required; where r represents the radius of the falling new particle, and the radii of the three supporting particles are r. i Where i = 1, 2, 3; (x, y, z) represents the position of the newly added particle after it is stably placed on the other particles; the center coordinates of the three supporting particles are (x, y, z). i y i , z i ).

[0034] To determine (x, y, z), the following system of equations should be solved: ; If the system of equations has real solutions, a set is randomly selected from the solution set as the spatial location of the new particle; if there are no solutions, three supporting particles are selected again and the calculation is repeated until a stable solution is obtained.

[0035] S3. Dynamically adjust the radius C of the sphere generation area to screen supporting particles and perform collision detection. By dynamically adjusting the radius of the generation area, volume collisions between particles are effectively avoided, ensuring the compactness and rationality of particle stacking.

[0036] The present invention employs a strategy of dynamically adjusting the radius C of the generated region: initially, C is set to 0.01m, and the value of C increases by r each time an attempt to generate a new particle fails. min / 3. When a new sphere is successfully generated, the value of C decreases by r. max ;r min This refers to the radius of the smallest particle in the current particle. The strategy of dynamically adjusting the radius C of the generated region in step 3 effectively avoids the failure to select support points in areas with high particle density due to an excessively small search range, while preventing the introduction of long-distance invalid particles in sparse areas due to an excessively large search range, thus achieving synergistic optimization of search efficiency and physical rationality.

[0037] After obtaining the temporary position of the new particle, a rigorous collision detection must be performed to verify whether its geometric distances with all existing particles satisfy the non-overlap condition. This means the square of the distance between the center of the new particle and any existing particle is greater than the square of the sum of their radii. If any particle does not meet this condition, a volume collision is determined, and support points must be reselected and iterative calculations repeated until a non-overlapping and stable particle configuration is generated. The collision detection method is as follows: If the radius and coordinates of the existing particles are r... j With (x) i y i j i The determination conditions are as follows: ; If any existing particle satisfies the above inequality, it is determined to be a collision, the temporary position is discarded, and the process returns to step 2 to select a new support point.

[0038] In step 3, collision detection is not only for newly generated particles and directly supporting particles, but also for all neighboring particles within the range of the two adjacent layers. The detection range is quickly located by constructing a three-dimensional spatial grid index structure, which significantly reduces computational complexity and allows the algorithm to be extended to large-scale simulation scenarios with thousands of particles.

[0039] This collision detection logic ensures the geometric non-overlap of the particle system, which is a key step in guaranteeing the physical accuracy of porosity calculation.

[0040] S4. The porosity of the spherical furnace charge is calculated using moving average and moving variance statistical methods. This step improves the stability and accuracy of porosity calculation through statistical methods, providing reliable data support for subsequent analysis.

[0041] Once the number of particles generated in the system reaches a set threshold (typically several thousand to tens of thousands of spheres), the packing tends to stabilize, and porosity calculation can be performed. With the origin as the center, the calculation region is a sphere with radius S, and its total volume is: ; Let the total volume of the particles be V b , which is obtained by accumulating the volumes of all particles completely within the computational domain. Then, the formula for calculating the porosity p of the packing system is: ; The radius S of the computational domain set in step 4 is not less than 50 times the maximum particle diameter, and the distance between the computational domain boundary and the nearest particle is not less than 10 times the minimum particle diameter, so as to eliminate the interference of boundary effects and edge packing non-uniformity on the porosity statistical results and ensure that the statistical region is in the approximate uniform core area of the packing body.

[0042] For a particle with center at P and radius r, if it is completely within the domain (i.e., |P| + r ≤ S), then its volume (4 / 3)πr³ is fully included in V b ; if it is completely outside the domain (|P| - r ≥ S), it is not included; if there is partial intersection, the volume of the spherical cap needs to be calculated. Let d = |P| be the distance from the particle center to the origin, then the height h of the spherical cap is h = r - (d + r - S) = S - d, which holds when d < S < d + r. The volume V of the spherical cap is V = (πh²(3r - h)) / 3, which is the effective volume of the particle within the computational domain.

[0043] The specific implementation mode of the present invention realizes high-precision simulation of the blast furnace burden stacking process and porosity calculation through the blast furnace burden porosity calculation method based on the Monte Carlo algorithm. This method not only overcomes the limitations of traditional experimental methods but also provides a reliable theoretical tool for the optimization of blast furnace burden structure and permeability analysis. The specific implementation steps are clear and the operation is simple, and it can be widely applied to the optimization and improvement of the blast furnace ironmaking process. The present invention provides important technical support for the green and low-carbon transformation and high-quality development of the steel industry by improving the blast furnace operation efficiency, reducing energy consumption and emissions.

[0044] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for calculating the porosity of blast furnace burden based on the Monte Carlo algorithm, characterized in that, Includes the following steps: Step S1: On-site sampling is used to obtain the proportion data of different particle sizes. The Monte Carlo random sampling method is used to generate the particle size of the furnace charge, and the radius and center coordinates of each particle are initialized. Step S2: Based on the spherical geometry equations, in a three-dimensional Cartesian coordinate system, find a stable spatial position for the newly generated particle within the existing particle packing system. Specifically, select at least three existing particles as support points, construct a set of three-sphere contact geometric constraint equations, and solve the set of equations to obtain the center coordinates of the new particle. If the set of equations has real solutions, select one set from the solution set as the placement position of the new particle. If there are no solutions, reselect support particles and repeat the calculation until a physically realizable stable packing configuration is obtained. Step S3: Dynamically adjust the radius C of the sphere generation area used to screen the supporting particles, and after determining the temporary position of the new particles, perform collision detection to verify that the new particles and all existing particles meet the non-overlapping geometric condition. If a collision occurs, return to step S2 to select a new support point; Step S4: When the total number of generated particles reaches the preset threshold, a spherical computational domain with radius S is set with the origin of the coordinate system as the center. The total volume in the computational domain and the total volume occupied by all particles in the computational domain are calculated. The porosity is determined based on the ratio of the difference between the two to the total volume of the computational domain. During the calculation process, the porosity values ​​of multiple continuously generated sub-samples are processed using moving average and moving variance statistical methods to evaluate the convergence and stability of the calculation results.

2. The calculation method according to claim 1, characterized in that, In step S2, the initial particle packing system consists of three spherical particles with equal radii, externally tangent to each other, and whose centers are located on the same horizontal plane, forming an equilateral triangle layout.

3. The calculation method according to claim 1, characterized in that, In step S2, the method for selecting support points is as follows: a sphere is generated with the origin of the coordinate system as the center and the dynamically adjusted radius C as the radius. A point P is randomly selected on the surface of the sphere, and then the three existing particles closest to point P are found as support points.

4. The calculation method according to claim 3, characterized in that, The geometric constraint equations for the three-ball contact are as follows: Where r represents the radius of the newly falling particle, and the radii of the three supporting particles are r. i Where i = 1, 2, 3; (x, y, z) represents the position of the newly added particle after it is stably placed on the other particles; the center coordinates of the three supporting particles are (x, y, z). i y i , z i ).

5. The calculation method according to claim 1, characterized in that, The specific strategy for dynamically adjusting the radius C of the sphere generation region in step S3 is as follows: Initially, C is set to the first preset value; When an attempt to generate a new particle fails, C is increased by one-N times the radius of the smallest particle in the current particle system, where N is an integer greater than 1. When a new particle is successfully generated, C is reduced by the value of the largest particle radius in the current particle system.

6. The calculation method according to claim 1, characterized in that, The collision detection in step S3 is to verify whether the geometric distance between the temporary position of the new particle and all existing particles satisfies the non-overlap condition, that is, the square of the distance between the center of the new particle and any existing particle is greater than the square of the sum of their radii. If there is any particle that does not meet this condition, it is determined that a volume collision has occurred, and the support point needs to be reselected and iteratively calculated until a non-overlapping and stable particle configuration is generated.

7. The calculation method according to claim 6, characterized in that, The collision detection method is as follows: If the radius and coordinates of the existing particles are r... j With (x) i y i j i The determination conditions are as follows: ； If any existing particle satisfies the above inequality, it is determined to be a collision, the temporary position is discarded, and the process returns to step 2 to select a new support point.

8. The calculation method according to claim 1, characterized in that, In step S4, the porosity is calculated as follows: With the origin as the center, the calculation region is a sphere with radius S, and its total volume is: ； Let the total volume of the particles be V. b The porosity p of the packed system is calculated by summing the volumes of all particles completely within the computational domain: 。 9. The calculation method according to claim 1, characterized in that, In step S4, when calculating the total volume occupied by the particles within the computational domain, for particles that intersect with the boundary of the computational domain, their effective volume is included by calculating the volume of the spherical cap of the particle within the computational domain.

10. The calculation method according to claim 1, characterized in that, In step 4, the radius S of the computational domain is set to be no less than 50 times the diameter of the largest particle, and the distance between the boundary of the computational domain and the nearest particle is no less than 10 times the diameter of the smallest particle.

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