Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 15, No. 2, 2025 35 Research on the Calculation of Mine Ventilation Network Based on Loop Airflow Method Jun Liang1, 2 1State Key Laboratory of Coal Mine Disaster Prevention and Control, Chongqing 400037, China 2China Coal Technology and Engineering Group Chongqing Research Institute, Chongqing 400037, China Abstract: In response to the need to further explore the potential of existing mine ventilation network solutions, a mine ventilation network solution was carried out based on the loop air volume method. A computer program design framework for loop method ventilation network solution was constructed, and ventilation network solution software was developed. Combined with the ventilation data of Yuyang Coal Mine, the application solution was carried out. The research results indicate that the accuracy of the mine air volume obtained through this calculation method and the developed software is relatively high, with a total air volume error of less than 0.5. This has important theoretical and practical significance for overall control of the mine ventilation status and decision-making. Keywords: Mine ventilation; ventilation network; loop air volume method; solution; error. 1. Introduction The mine ventilation system is a critical component in ensuring safe mining operations, where the accuracy and efficiency of network resolution directly impact the reliability of ventilation control and the effectiveness of hazard prevention [1-3]. With increasing mining depths and system complexity, traditional ventilation network solution methods (such as the air volume balance method and node pressure method) have shown limitations in handling high- dimensional nonlinear systems. The loop air volume method, as a mathematical modeling approach based on pressure balance equations, significantly improves the computational efficiency and stability of complex networks by transforming ventilation network topology into independent loop equation systems [4-5]. In recent years, domestic and international scholars have conducted extensive research on the theoretical refinement, algorithmic optimization, and engineering applications of the loop air volume method. Zhong Deyun et al. [6] systematically investigated the computational principles of the loop air volume method and proposed an improved Scott-Hinsley algorithm. Tian Ziwen et al. [7] developed a rapid computational algorithm for complex ventilation networks and applied it to the iterative solution module of the "Huangfang Coal Mine Ventilation Intelligent Decision System." The results demonstrated that the air volume calculation errors were all below 5%, meeting engineering requirements. Wang Pengfei et al. [8] conducted full-scale mine ventilation network calculations based on the loop air volume method. By designing preprocessing steps for the ventilation network model and exploring different application scenarios, combined with ventilation data from the Bofang Coal Mine, they achieved a solution accuracy of over 90%, a convergence time of less than 10 seconds for networks with up to 1,000 branches, and loop resistance adjustment errors below 0.5%. However, the potential of this method in dynamic network regulation, multi-objective optimization, and intelligent computation still requires further exploration. Therefore, building upon existing research, this paper conducts a systematic analysis of the key technologies in the loop air volume method, aiming to provide theoretical support for the precise regulation of mine ventilation systems. 2. Theory of Loop Airflow Method 2.1. Basic principle of ventilation When the wind flows in the wind network, it follows the laws of conservation of mass and energy, namely Kirchhoff's law. These laws are applicable to any form of wind network, regardless of whether the air volume is distributed according to demand or naturally, and therefore serve as the theoretical basis for calculating ventilation networks. The loop air flow method is actually based on graph theory and the basic laws of air flow. It uses the Gauss Seidel iteration method to sequentially solve the corrected air flow of the mesh until a predetermined accuracy is reached, in order to obtain asymptotic quantities that approach the true solution of the system of equations. The law of air volume balance and the law of air pressure balance constitute an N-order nonlinear large-scale equation system with air volume as the unknown variable. It is very difficult to directly solve such a system of equations, and it is generally solved through linearization of nonlinear equations. If the wind pressure balance equation is expanded according to Taylor's formula and high-order terms are omitted, the K-th linear approximation calculation formula is: 1 1 1 ( ) ( ) ( ) 1 2 1 2 1 2 1 2 ( ) ( , , , ) ( , , , ) 0 K K k k k k i i n i N i i i n n f Q f Q Q Q f Q Q Q f f f Q Q Q Q Q Q                       (1) Given the following constraints on the above equation: ( ) ( ) 1 1, 2,..., N k ki i i j ji j j i f f Q Q i M Q Q          (2) Equation (1) is simplified as: 36 ( )ki i i i f Q f Q      (3) So 1 1 2 N ij j j j i i j i N i ij j j j i a R Q Q P F Q dF a R Q dQ           (4) Where, iQ is the corrected air volume of the circuit. If jQ (j=1, 2,..., N) has been assigned a certain initial value and the air volume balance equation is satisfied, but generally cannot satisfy the air pressure balance equation, then ij ia Q is used to correct jQ . However, when correcting jQ , it will also cause changes in the airflow of the common branches between circuits, thereby affecting the convergence of other circuits. Therefore, it is necessary to repeatedly correct the circuits to achieve the required accuracy. The verification formula is as follows: ( 1) ( )k k j jQ Q E   (5) Where, E is the precision indicator, E>0.001. 2.2. Loop method computer program design (1) Choose an independent circuit To select an independent circuit, the first step is to obtain a tree diagram of the ventilation network and its corresponding residual tree diagram. Then, the chain branches of the residual tree diagram are added to the corresponding tree diagram one by one, forming a closed circuit with some of the branches in the tree diagram. Therefore, in order to select a reasonable independent circuit, the branches should first be sorted reasonably to ensure that the fixed air volume branch, the fan containing branch, and the high wind resistance branch are selected into the residual tree set. During the calculation process, the fixed branch and the fan containing branch should be ranked first, and the other branches should be arranged in descending order of wind resistance. The operation process of the program is equivalent to removing all branches in the wind network, leaving only all nodes, and then starting from the branch with the lowest wind resistance, adding branches to its original position on the wind network one by one to form the lowest tree. In the process of establishing the lowest tree, once a mesh or loop appears, the branch that finally forms the mesh or loop is the basic branch, that is, the highest wind resistance branch in the mesh or loop. Removing this branch will not form a mesh or loop, which is called "breaking the circle". A mesh or loop is based on a basic branch and extends in its direction until it forms a mesh or loop. The program stipulates that the direction of the mesh or loop is determined by the direction of the basic branch, so the branches in the mesh or loop that are consistent with the direction of the basic branch are called forward branches, and the branches in the opposite direction are called reverse branches, and they are recorded one by one. (2) Calculate the natural wind pressure of the mesh or circuit According to the input value of natural wind pressure, calculate the natural wind pressure of each mesh or circuit, and print the mesh or circuit numerical label as needed, including the mesh or circuit number, the number of branches within the mesh or circuit, the branch number and its direction, and the natural wind pressure value. The program allows natural wind pressure to appear on any branch. (3) Fitting of wind pressure characteristic curve of fan The wind pressure characteristics of a fan are generally characterized by a quadratic polynomial. If the data of three points on the input characteristic curve (the first point is the upper limit point for stable operation of the fan, the second point is the highest efficiency point, and the third point is the lower limit point), the quadratic spline interpolation method can be used to construct the expression formula for the characteristic curve. If the selected number of points is greater than three, non-linear fitting method is used. (4) Initial value of air volume For the mesh or circuit where the fixed air volume branch is located, the fixed air volume value can be directly assigned to the other branches of the mesh or circuit as the initial air cooling for iterative calculation. For fan branches, assign the airflow at the high-efficiency point on the fan curve to each branch of the mesh or circuit. The remaining basic branches are assigned 10, and then assigned to the remaining branches of the mesh or loop. (5) Iterative calculation Iterative calculation is the process of determining the natural distribution of airflow in a wind network, given the known wind resistance, natural wind pressure, and wind pressure characteristic curves of each branch. To ensure that the fixed air volume value remains unchanged, the computer program specifies that the mesh or circuit with a fixed air volume does not participate in the iteration. Since all branches in this type of mesh or circuit, except for the fixed air volume branch, are functional branches of other mesh or circuit branches, they actually participate in the iterative calculation. Iteration is based on the unit of mesh or loop, from the end of the chair until all mesh or loops reach the predetermined accuracy within the specified number of iterations. (6) Calculate the resistance and wind resistance values of a fixed air volume vocabulary Since the fixed air volume branch does not participate in the iteration, the resistance of the fixed air volume branch is calculated based on the wind pressure balance relationship of the circuit, that is 1 , n fix j a j j fix h h p     (6) Then calculate the air resistance of the fixed air volume manifold: 2 9/ fixfixfix QhR  ， 82 /msN  (7) Where, fixR is Fixed air volume branch air resistance value, 82 /msN  . fixh is Fixed airflow branch resistance value, ap . fixQ is Fixed air volume value， sm /3 . fixR 37 is the wind resistance value that the branch must have to ensure a fixed air volume value remains unchanged. 3. Ventilation Network Example Solution 3.1. Experimental mine Yuyang Coal Mine adopts the inclined shaft stage stone gate development method, and the industrial square, main and auxiliary inclined shafts, and return air adit are built in Jinjiyan. A secondary industrial square is set up in Yangdiwan, with a pair of auxiliary shafts (for pedestrian and gangue transportation) and a 310 main return air inclined shaft. The transportation roadway is located in the Maokou Formation limestone about 40 meters below the M12 coal seam. The mining method is inclined longwall layout. Medium thick coal seams are fully mechanized, while thin coal seams are high-grade conventional mining. The approved production capacity of the mine in 2007 was 1.05 million tons per year. The mine adopts a mixed ventilation method of extraction, with air intake from the main and auxiliary inclined shafts of Jinjiyan, Yangdiwan lifting, pedestrian inclined shaft, and coal transportation inclined shaft of Anding Power Plant, and air return from Jinjiyan and Yangdiwan air shafts. The Jinjiyan air shaft is equipped with two BD-II-8-No24 ventilation fans, one for backup and one for operation. Each fan is equipped with a synchronous motor with a rated power of 370KW and a speed of 742 r/min. The motor rotates in reverse direction. The fan was put into operation in February 2005. Currently, the blade installation angle of the fan is -5°, the longest ventilation route is 6649m, the fan exhaust volume is 5759m/min, the negative pressure is 1600Pa, and the motor output power is 219.04KW. The Yangdiwan wind shaft is equipped with two 2K58No24 ventilation fans, one in operation and one as backup. Each fan is equipped with a synchronous motor with a rated power of 450KW and a speed of 740 r/min, and the motor rotates in reverse direction. At present, the installation of the fan blades is 37.5°, the longest ventilation route is 8848m, the fan exhaust volume is 5944 m3/min, the negative pressure is 1207Pa, and the motor output power is 204.72KW. 3.2. Comparison of software development and solution results Based on the actual situation of Yuyang Coal Mine, the ventilation system diagram of Yuyang Coal Mine was obtained, as shown in Figure 1. According to the process of computer program design using the loop method, a ventilation network calculation software was developed, with the interface shown in Figure 2. Figure 1. Ventilation system diagram of Yuyang Coal Mine Figure 2. Ventilation network calculation function interface 38 After measuring the ventilation resistance parameters of Yuyang coal mine, the developed ventilation network calculation software was used to simulate the ventilation system of Yuyang mine. Firstly, based on the ventilation system diagram of the mine, the network diagram of the mine ventilation system is obtained through appropriate simplification. In this ventilation network diagram, there are 289 branches and 178 nodes. Then, the measured ventilation resistance parameters are entered into the corresponding branch attributes in the system, and the solution results are obtained through topology reconstruction, error checking, and iterative calculation. In the final calculation result, the total air volume of the mine is 211.9m3/s, the wind pressure of Yangdiwan fan is 1755Pa, and the wind pressure of Jinjiyan fan is 2013Pa. The measured total air volume of the mine is 212.9 m3/s, with an error of 0.47%. The wind pressure of Yangdiwan fan is 1676.2Pa, with an error of 4.5%, while the wind pressure of Jinjiyan fan is 1958.3Pa, with an error of 2.7%. The calculation errors of other main ventilation tunnels are shown in Table 1. According to Table 1, the maximum relative error of air volume at 36 measuring points in the main ventilation tunnels of Yuyang Coal Mine is 23.6%, the minimum is 0, and the average error is 3.6%. Table 1. Calculation results of main ventilation tunnels in Yuyang Coal Mine Lane branch number Starting point Ending point Windage (Ns2/m8) Measure volume(m3/s) Calculate volume(m3/s) Relative error(％) 1 1 2 .03412 49 49.7 1.41 2 2 3 .01993 72.9 74 1.49 3 6 7 .00364 82.7 84.8 2.48 4 14 15 1.9594 11.99 10.7 12.06 5 15 16 2.26225 9.1 9.3 2.15 6 16 18 .00227 66.4 67.2 1.19 7 19 20 .02285 118 115.3 2.34 8 20 21 .03507 118.15 118.2 0.04 9 1 2 .14355 23.9 24.2 1.24 10 28 29 .418007 22.1 21.8 1.38 11 29 30 .25093 15.35 15 2.33 12 36 37 .002023 40 39.7 0.76 13 42 43 .03985 75 78.7 4.70 14 44 45 .03031 94.4 93.7 0.75 15 49 50 .004211 58 54.8 5.84 16 51 52 .030966 18.7 16.2 15.43 17 59 60 .05811 22 23.6 6.78 18 1 61 .1783 36.7 36.6 0.27 19 61 62 .14023 30 29.9 0.33 20 67 68 .002211 16 15.3 4.58 21 75 76 .01025 7 7.1 1.41 22 76 37 1.9911 5.2 5.2 0.00 23 72 96 .44512 20.5 21.3 3.76 24 14 100 .0011 11 8.9 23.60 25 107 108 19.99 4.9 4.7 4.26 26 132 133 .02717 4.2 4.2 0.00 27 132 134 .18511 6.7 6.4 4.69 28 133 134 .1526 5.1 5.6 8.93 29 127 93 2.4111 4.6 4.4 4.55 30 29 150 .1276 7 6.8 2.94 31 150 151 16.9911 4.3 4.3 0.00 32 155 157 .00706 25 23.7 5.49 33 149 153 .04308 4.8 4.8 0.00 34 21 1 .000254 118.9 118.2 0.59 35 45 1 .00024 94 93.7 0.32 36 66 147 9.9911 4.95 4.9 1.02 4. Conclusion A mine ventilation network calculation software was developed based on the loop air volume method, and a ventilation network calculation model using the loop air volume method was implemented. The measured total air volume of the Yuyang mine was 212.9 m3/s, with an error of 0.47%. The average relative error of air volume at 36 measuring points in the main ventilation roadway is 3.6%. It indicates that the calculation of mine ventilation network can be carried out, and the calculation error is within the allowable range, which can be applied to actual mine ventilation network calculation. Acknowledgments The study was supported by the Key Project of Science and 39 Technology Innovation and Entrepreneurship Fund of Tiandi Technology Co., Ltd. Under 2022-2-TD-ZD010. References [1] Liu Qingrun, Yin Qiangqiang, Zheng Kai. Analysis of Current Status and Development Trends of Mine Ventilation Systems[J]. China Nonferrous Metals, 2024, (S2): 288-290. [2] Li Nan. 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