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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 66, 2018 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Songying Zhao, Yougang Sun, Ye Zhou 
Copyright © 2018, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-63-1; ISSN 2283-9216 

Application Research of Mathematical Economic Model in 

Terms of Gas Distribution and Reconstruction of Distribution 

Field in Coal Mine Stope 

Jingguo Dua,b, Jianxun Jianga, Yongqing Wanga*, Xun Chenb, Chenjun Wangb 

a College of Oil and Natural Gas Engineering, South Pertroleum University, Suchuan 610500, China 
b College of Mining Engineering, North China University of Science and Technology, Hebei 063210, China 

carlpetrol@yeah.net 

Research of the application on Mathematical Economic Model in Terms of Gas Distribution and 

Reconstruction of Distribution Field in Coal Mine Stope The research is divided into 2 sections, the first section 

is to analyze the application of mathematical economic model in coal mine stope gas distribution; The second 

section is to analyze the application of mathematic economic model in reconstruction of coal mine stope gas 

distribution field. From the perspective of mathematic economy, when there are a lot of data samples 

participating in distribution field reconstruction, the reconstruction based on neutral network algorithm is 

slightly superior to space information statistical approach. When there are a few data samples participating in 

reconstruction, the spatial system statistical approach is obviously superior to neutral network reconstruction 

approach in terms of reconstruction result. It is essential to choose coal mine stope gas distribution field 

reconstruction method scientifically so as to reduce occurrence of gas accident. 

1. Introduction  

Gas accident is a kind of most serious accident form, and it often causes a lot of life and personal injuries and 

major economic loss. During the explosion accidents of coal mine gas, most of which happens in the recovery 

and excavation area. Recovery and excavation area roadway is the main gas discharge area, and gas 

accumulation is easy to occur here. Computer numerical simulation is mainly adopted for the gas distribution 

in the excavation roadway wind flow, and the gas distribution rule can be recognized and ventilation design 

can be optimized but it is impossible to judge and predict the gas discharge and accumulated district 

according to the concentration of field gas and effective analysis can not be also made to the gas distribution 

in the stope according to gas concentration date of coal mine actual measurement. Utilizing field gas 

concentration monitoring data to reconstruct gas distribution field can achieve quantification cognition for 

stope gas distribution to define gas discharge and accumulated areas quickly. In this way, the gas accidents 

can be further reduced to reduce economic loss and social loss arising from gas accidents.  

Therefore, the paper mainly performs theoretic and experimental analysis based on gas distribution law and 

studies reconstruction technology of gas distribution field. Only based on the distribution rule of stope gas can 

we further use related experiments to find out the frequent occurrence points of gas accidents, and propose 

basic requirements for gas monitoring of working face. And then based on the point, reconstruct the 

distribution field of gas.  

2. Literature review 

The stope is the general name for a mining area, including the mining face, the heading face, the coal seam, 

the goaf, the ventilation tunnel and the transportation lane, etc., which are the important components of the 

mine ventilation system. The ventilation flow field of stope is a composite flow field including coal mining and 

heading face and goaf. Because the geometric boundary shape of the ventilation flow field of the stope is 

extremely irregular and the distribution of the flow pattern is very irregular, the gravity action of the stope in the 

steep seam is equal to the mechanical ventilation pressure P, so the flow field in the stope is a rather 

                                

 
 

 

 
   

                                                  
DOI: 10.3303/CET1866099 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Du J., Jiang J., Wang Y., Chen X., Wang C., 2018, Application research of mathematical economic model in terms of 
gas distribution and reconstruction of distribution field in coal mine stope, Chemical Engineering Transactions, 66, 589-594  
DOI:10.3303/CET1866099   

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complicated flow field. The gas accumulation area is related to the source of gas, and is affected by the shape 

of the space, causing the joint action of local turbulence and air flow. Therefore, a simple analysis method 

cannot be used in the study. It is necessary to combine the wind flow and the gas concentration distribution 

field by combining the field theory analysis method with the test and actual field measurement and combine 

the gas migration law with the flow of the tunnel and combine the numerical simulation with the calculating 

machine to realize the quantitative research on mine gas distribution under turbulence state. 

Ventilation in the working face not only flows in the roadway, but also causes the corresponding gas flow in 

the adjacent goaf. Stope is not only the main place for mining, tunnelling, transportation and other related 

production activities, but also the most concentrated area of gas emission in the whole mine. The gas 

composition of the whole mine is mainly from stope. After the production activities such as coal mining and 

tunnelling, such as coal wall, roof and floor, goaf, coal and other areas gushed out, the gas in the stope is 

mixed and dispersed in the flowing stope air, accompanied by corresponding flow and diffusion. The 

movement of gas in ventilation and airflow of stope follows the law of dispersion of fluid dynamics (Pinetown, 

2014). Since 1980s, a great number of theoretical, experimental and computer simulated numerical research 

and analysis have been carried out on the research of mine gas distribution in the domestic research 

institutes, and a great number of valuable research results have been obtained, and the distribution and 

migration laws of gas under different conditions of the mine have been basically mastered. Especially with the 

progress of fluid dynamics and numerical calculation methods, the analysis and understanding of gas flow and 

gas distribution in stope have also been greatly improved. In recent years, Computational Fluid Dynamics 

(CFD) has been developed rapidly and widely used (Tanguturi and Balusu, 2014), At the same time, it also 

promoted the research and in-depth study of the air flow and gas distribution in the stope area. 

Wang and others pointed out that the domestic scholars first put forward the research method of applying 

seepage theory to the analysis of the air flow in the working face and goaf (Wang et al., 2014), a unified 

seepage mathematical model based on mass conservation principle is established. In addition, using the 

observation data obtained from the observation point in the stope and using the finite element method to 

calculate the reverse osmosis coefficient, the mathematical model is closer to the reality, and the finite 

element method is used to obtain the results. The quantitative analysis of the air flow status of the stope is a 

step further than the ideal fluid hypothesis. The mathematical model of three-dimensional steady seepage and 

gas distribution in stope and its Galerkin finite element method are further improved to further improve the 

numerical model of gas distribution in stope. Frippiat and others using the Fortran language to write a stope 

ventilation simulation system software (Simulation System for the Ventilation of Fields, referred to as SSVF), 

which can be used to simulate the natural fire sources of different positions and the diffuse state of the fire 

gas. According to the simulation results, the prevention and control schemes and measures of the phase can 

be formulated (Frippiat et al., 2015). In the study, Wang and others said that Professor Ding Guangxiang of 

China University of Mining and Technology, in view of the irregular geometric boundary and the complex 

distribution of the stope, has complicated flow field in the mining field with the complex distribution of gravity 

and mechanical pressure. The basic principle of similar theory is proposed to solve the problem of fluid 

dynamics in the field flow field. The composite Euler criterion is proposed and the characteristics of turbulence 

independence are demonstrated (Wang et al., 2015). 

Field reconstruction technology, and data visualization technology, field reconstruction technology and 

computer imaging technology belong to a category. Because the technology needs a lot of data processing 

and analysis, the technology is basically a new field of research with the development of computer technology, 

which is the computer technology, graphics and images. A variety of theories, methods, and techniques that 

can be converted into a figure or image based on a certain amount of data, which can be converted to a figure 

or image by a variety of display devices (Nazarova et al., 2014). Computed Tomography (CT) is the most 

representative of various field reconstruction techniques, and CT technology is produced in 1970s. It has been 

applied in many fields of science, such as medical diagnosis and pathology, industrial detection and non-

destructive detection. CT technology is based on projection image reconstruction technology, that is, by 

projecting multiple axes of an object and reconstructing the target image with projection. Different types of CT 

imaging techniques, such as transmission fault imaging, emission tomography, magnetic resonance imaging, 

ultrasonic tomography, reflection tomography, etc., are developed according to the different projection 

reconstruction methods (Huang et al., 2015). Hua and others use the transformation method and iterative 

reconstruction method, which are based on Radon transform, and develop a variety of transform algorithms, 

such as filter back projection algorithm and convolution back projection algorithm and form new algorithms 

based on two methods to be used in different industrial fields (Hua et al., 2015). The feature information 

contained in the sampled data should be made full use of the feature information contained in the sampled 

data in the interpolation calculation and estimation of the region valuation, so that the unknown spatial 

estimation of the output can fully reflect the role of these characteristics, and the estimation model which is as 

consistent as the real model is constructed. 

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3. Method  

3.1 Gas distribution of coal mine stope  

In order to ensure safe production of coal mines, basic requirement for gas motoring of working face in terms 

of coal mine safe procedure, mine safe monitoring system and detecting instrument use management rules is 

proposed. U-type ventilation way is generally used for long wall coal face, and the gas monitoring sensor 

should be set according to figure 1 and it is required to set gas monitoring instrument on the three positions 

including upper corner, working face and working face air return way (T0, T1 and T2 in the figure). In order to 

whole non-intrinsically safe electrical equipment which can not control inlet air way of the whole coal mining 

working face for coal and gas outburst mine and gas sensor T1, one set of gas monitor should be newly-

added in the inlet air way. For the low gas and high gas mines which are applied tandem ventilation way in the 

working face, one set of gas monitor can be newly-added in the inlet air way of working face (see T4 in the 

figure). The setting of gas monitor in the working face under the ventilation way of H, Y, Z and W -type is 

basically the same.  

 

Figure 1: Settings of Gas Sensor Under U-shaped Ventilation Mode 

The setting position of gas monitor in the excavating working face is shown in figure 2. There are 3 setting 

positions: 1. Working face mixed wind flow location (T1); 2. Working face return wind flow location (T2); 3. In 

front of local fan in the excavating working face of tandem ventilation (T3). When dual-way excavation is 

adopted and the mine is high gas, coal and gas outburst mine, then gas monitor should be set according to 

figure 3. There are 3 setting positions: 1. Mining working face(T1) 2. Air return lane (T2) 3. Working face mixed 

return wind flow location (T3); In the coal mine safety regulations, coal mine safety monitoring systems and 

testing instrument use management specifications, not only detailed provisions have been made for the 

setting positions and number of gas monitors, but also the suspension height, suspension method, alarm, and 

power-off concentration, re-test period for gas monitors are required as well. For example, it is required to 

suspend the gas monitors on the position with stable wind flow in the upper of roadway vertically, and the 

distance cannot be larger than 300mm from roof (top beam), also not be lower than 200mm from side wall of 

roadway, and it should be convenient for installment and maintenance and the pedestrians and travelling 

cranes cannot be influenced. It is stipulated that an alarm will be given when the gas concentration in the 

working face is generally equal or larger than 1%, and it will be powered-off when the gas concentration is 

equal or larger than 1.5% and then it will restore when the gas concentration is less than 1.5%. In some 

special locations, the alarming and power-off concentration is slightly different.  

   

Figure 2: Gas Sensor Setting in Heading Face 

 

Figure 3: Settings of Gas Sensor Under Double Tunneling Face 

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A certain amount of gas concentration monitoring data is needed to achieve construction of gas distribution 

field in the working face. And a certain amount of gas monitoring points need to be increased, the existing 

wide-used wired data transmission way is hard to meet the requirements, and it is more convenient to adopt 

wireless data transmission gas sensor in terms of wiring, installing and monitoring substation coordination 

compared to tradition wired way. Currently there are a lot of wireless communication methods which are used 

maturely, such as Zig Bee, Bluetooth, GPRS, RFID and so on. Among them, what is proper for being used for 

monitoring in the environment under the coal well are mainly Zig Bee and RFID. RFID is currently applied in 

personnel location system and equipment management under the well, and Zig Bee is a more proper wireless 

transmission method. Zig Bee wireless network technology is a kind of new wireless connection technology, 

and the wireless connection technology mainly resolves the equipment networking application with low cost, 

low power consumption, low complexity, low transmission rate and near distance. Zig Bee standard was 

established based on 802.15.4 protocol stack and it is equipped with powerful equipment networking function 

and supports three major self-organizing wireless network types, that is, star configuration, net structure and 

cluster tree, especially the mesh structure, which is applied multiple-jumping route communication with big 

network capacity, which can span big physical space and it is proper for structure with a long distance and 

rather scattered. Mesh network topology owns powerful functions, and all of entities in the network can 

communicate with each other only if they are within the scope of communication. If there is no direct path, the 

communication can also be performed through the way of “multiple-class jumping” and the topological 

structure can also constitute network which is rather complex. In addition, the network is also equipped with 

self-organizing and self-healing functions. It owns powerful network robustness and system reliability. There 

are 2 types which constitute the network equipment of Zig Bee: Fully function equipment(FFD)and simplified 

function equipment(RFD). FFD is taken as the router or application equipment in the whole network, while 

RFD is taken as the application equipment in the network and can communicate with FFD and owns the 

function of taking over route. The distance between two Zig Bee nodes is generally 150 to 200m, utilizing its 

function of taking over route can achieve data transmission for a longer distance by adopting relaying 

communication method. Stope gas monitoring system topological graph is shown in figure 4. The stope gas 

monitoring network based on Zig Bee technology includes distributed self-powered Zig Bee gas sensor 

monitoring node and Zig Bee central node. Mesh network structure is adopted so as to ensure reliability of 

data transmission fully. The gas monitoring system firstly obtains the gas concentration of the unit through a 

Zig Bee gas monitoring node set up on the working face, and then transmits the monitoring data to the Zig 

Bee central node. Finally, transmitting to the ground monitoring data management center by the coal mine 

safety supervision and communication system to be displayed and saved. Because each gas monitoring 

nodes are connected by adopting wireless network, the quantity of gas sensor can be established flexibly 

according to the length of working face and actual situation.  

 

Figure 4: Topology of Gas Monitoring System in Stope 

3.2 Reconstruction of coal mine stope distribution field  

The length of the working face for reconstructing gas distribution field is approx. 110m, and the goaf area is 

about 5m away from the front of the coal wall. The gas concentration should be measured according to 

mensuration of improved unit, and 1 measuring unit should be set every other 10m from the beginning of air 

inlet side, and 11 measuring units are set in total. A group of actual gas concentration measurement data is 

list in Table 1. 

 

 

 

 

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Table1: Measured Data of Gas Concentrations in Coal Face 

 X=  

10 20 30 40 50 60 70 80 90 100 110 

Y=1 0.01 0.06 0.08 0.1 0.14 0.35 0.58 0.72 0.85 0.98 1.12 

Y=2 0.01 0.06 0.06 0.11 0.16 0.33 0.49 0.52 0.65 0.78 0.98 

Y=3 0.01 0.05 0.07 0.32 0.38 0.51 0.6 0.75 0.89 0.85 0.91 

Y=4 0.01 0.08 0.11   0.42 0.48  0.66 0.82 0.91 1.14 1.02 1.05 

 

Firstly, utilizing MATLAB software to draw gas concentration distribution drawing of the working face, as 

shown in figure 5 (X-direction refers to the working face direction from air inlet side to air return side, Y-

direction refers to the direction from goaf area to coal wall surface, the same below)  

 

Figure 5: Gas Density Distribution Figure Based on Measured Data 

It can be seen from the gas concentration distribution drawing of the group of measurement data and its 

contour map, the features of gas concentration in the coal mining working face are as follows: (1) The gas 

concentration gradually rises up from air inlet side to air return side, this is because the wind flow is mixed with 

gas of high concentration constantly leaked from the coal wall, top baseboard and goaf area; (2) The gas 

concentration in the goaf area side (left side) is lower than the gas concentration of coal wall side (right side) 

in the same measurement unit, and this is mainly as a result of influences of gas concentration newly 

discharged from the coal wall side; (3) The gas concentration at the position 9 (X=90, Y=4 location) of the 

measurement unit for upper corner and coal wall side is obviously higher than the other positions. In practice, 

Figure 6 can be used to make the coal mine staff have a preliminary understanding of the gas distribution in 

the coal mine working face, but it is relatively rough and not accurate, especially in the case that it is 

impossible to set so many measurement points and data are missing, it is very difficult to accurately grasp the 

gas distribution in the working face. Utilizing the limited data obtained from field actual measurement, the 

research on achieving reconstruction technology of gas distribution field based on neural network algorithm 

will make the research on the gas distribution of stope more perfect and accurate. 

4. Result and discussion 

In order to verify and evaluate the reconstruction method of the gas distribution field in the previous paper, the 

study performs gas distribution field reconstruction for a group of field actual measurement data based on 

adopting neutral network algorithm and space information statistical approach method respectively. In order to 

verify the data adaptability of the two methods, 30, 20, and 10 data were randomly selected from 56 measured 

data respectively. The reconstructing and comparative analysis of the gas distribution field was performed by 

adopting these two methods. It is shown in the error of the reconstruction results that when there are a lot of 

data samples participating in distribution field reconstruction, the reconstruction based on neutral network 

algorithm is slightly superior to space information statistical approach. When there are a few data samples 

participating in reconstruction, the spatial system statistical approach is obviously superior to neutral network 

reconstruction approach in terms of reconstruction result.  

The reconstruction technology based on space information statistics technology (geostatistics) in the stope 

gas distribution field proposed in this paper has the features of high reconstruction accuracy and strong data 

adaptability, and can be used to solve the problem of coal mine gas distribution field reconstruction. On the 

basis of just adding a small number of gas monitoring devices, this technology can be used to achieve a gas 

distribution field reconstruction with satisfactory accuracy. Via setting an alarm threshold for the reconstructed 

field data, it is possible to alarm the area that exceeds the hazardous gas concentration, and display 

transfinite gas and accumulation area.  

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5. Conclusion 

During coal mine production, one of the most serious accidents is the gas accident. The gas accident will 

cause extremely major economic loss and life and personnel injuries, which influences the normal production 

of coal mines and corporate image seriously. According to practice, most of the mine coal gas explosions 

occur in the roadway of the recovery and excavation area, because this is the area where gas is discharged. 

Therefore, the study applies mathematical economic model, via field gas monitoring system, obtaining field 

gas concentration of coal mine and performing reconstruction research for stope gas distribution field. The 

paper performs analysis for achieving gas testing network in the stope and  gas concentration in the stope is 

measured, also, performing mathematic interpolation analysis for the data obtained from measurement. The 

research achievement supplies theoretic basis for reconstruction of coal mine gas distribution field, and is 

beneficial to reducing gas accident during the production process of coal mine and reducing economic loss 

and life and personnel injuries resulting from gas accident so as to ensure normal production of coal mine and 

establish good corporate image of coal mine enterprises. 

Acknowledgement 

(1) Chinese national major science and technology special project (2016ZX05042004-003)—Research on 

improving the production technology of single well production of coal bed gas; 

(2) Hebei science and technology project project (15273616) - Research on magnetization and anti scaling 

technology of injection water in Gaoshangpu;  

(3) Innovation Fund of North China University of Science and Technology (X2013008) - Laboratory study on 

stress sensitivity of coalbed gas reservoir 

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