Introduction
The task of assessing the level of air pollution from the different techno sources of emission (accidents, industrial chimneys, main fans at mines, dumps of wastes, etc) [1, 2, 3, 6, 7–13] has a huge interest. The main pollution of the atmosphere by coal mining enterprises occurs during coal mining. The gas – methane released from the formations together with coal dust is emitted through the diffuser of the ventilation shaft into the atmosphere. The volumetric flow rate of the dust-gas-air mixture is 14 000 m3/min. The concentration of dust in the gas-air mixture is 5.5 mg/m3, methane – 0.1 % per ton of produced coal. When unloading coal and storing it in a warehouse, coal dust is emitted into the atmospheric air. When coal moves through a closed gallery, the rocks are periodically cleaned and spilled, which is dumped through the hatch. Inorganic dust containing silicon dioxide enters the atmospheric air. With the passage of the mine workings, a large part of the rock mass (90 %) is removed to the rock heap, and a small part (10 %) is used for laying the worked-out space. When loading and unloading the rock and forming the dump by the bulldozer, inorganic dust with a high content of silicon dioxide enters the air.
Significant role in air pollution is performed by the main ventilation fans (MVF), as they operate around the clock, discharging the exhaust mine air into the atmosphere. Mine air emissions contain gaseous impurities (CO, CO2, NOx) and solid particles of coal and rock dust. The dust emissions of the «West Donbas Mine» are about 2000 tons/year.
The pathogenic effect of dust is determined by the mass of dust, the time of its impact, the material composition and dispersion.
The material composition of coal and rock dust is determined by the composition of coal rocks. The host rocks contain: quartz, mica, hydromica, calcite, dolomite, magnesite, sulfides.
The degree of dust dispersion is influenced by the physical and mechanical properties of coal, loading and transportation of rock, the degree of turbulence in ventilation flows. The dispersed composition of dust is not constant and can vary: 5 mkm – 12 %; 5–10 mkm – 23 %; 10–30 mkm – 59 %; more than 30 mkm – 6 %.
The maximum permissible concentration for the most harmful types of industrial dust is in the range of 0.01 – 10 mg/m3, depending on the characteristics of the dust and the silicon dioxide content of SiO2; for the settlements, this concentration is lower and amounts to 0.5 – 1.5 mg/m3.
Currently, to calculate the concentration of impurities in atmospheric air experimental, empirical, analytical, numerical methods are used.
Experimental methods are effective, but they allow to take into account only accomplished events with specific meteorological parameters, they are performed locally, they require high-quality expensive equipment, and material and time costs.
Most computer programs regarding the calculation of pollutant transport in the surface layer of the atmosphere from various sources are based on the model of M. E. Berland – OND–86. This technique is very simple to implement, but it is difficult to use it to calculate the dynamics of the process, since it uses the dimensionless and empirical coefficients obtained on the basis of average annual values of the parameters of the pollution source. The results obtained by this method are somewhat underestimated, their error increases with increasing distance from the source of emission.
Analytical methods of solving allow solving differential equations taking into account real physical parameters: wind speed, diffusion coefficient, particles sedimentation rate, ejection source power. However, all these solutions are obtained according to the introduced simplifications, since the analytical solution of the three-dimensional transport equations is rather complicated.
Numerical methods of calculation take into account all the factors listed, are implemented on the basis of the Navier-Stokes equations or by finite difference methods. These methods are operational. They have a smaller calculation error, but require skills of numerical simulation.
Thus, there is a shortage of operational control methods, in particular, dust emissions, which does not allow them to assess objectively, promptly identify the reason for their increase, select the desired mode of operation based on the dust factor or carry out dust suppression measures.
Fig. 1. West Donbas Mine: 1 – main ventilation fan
Emissions from MVF pose a threat of dust pollution of atmospheric air in the areas adjacent to the mine. To assess the impact of these emissions on air pollution, it is necessary to have effective mathematical models. On the basis of such models, it is possible to predict the change in the quality of atmospheric air for different weather situations characteristic of a particular region and for different intensity of coal dust emission, which may vary during the operation of the mine.
At present, the forecast of the atmospheric air pollution level is being carried out on the basis of simplified models that do not take into account the velocity profile of the wind flow. In addition, the OND–86 model used in practice, the Gauss model and the Berland model carry out a forecast only for a permanently operating source of emissions. For practice, it is important to have mathematical models of wider use.
Purpose
The purpose of this work is to create a numerical model and software for the rapid conduct of computational experiments to analyze and predict the level of air pollution by dust emissions from the main ventilation fan. On the basis of such an assessment, the risk for the population in the zone of influence of emissions from this fan is analyzed.
Methodology
In this paper, the solution of two problems is considered related to the simulation of atmospheric air pollution from dumps.
The process of dispersion of dust from the fan
was modeled by the following equation [1, 4, 5]: (1)
where C – dust concentration (mg/m3); u, v, w – airflow components (m/s); ws – dust settling rate (m/s); = (x, y, z) – turbulent diffusion coefficients (m/s2); x0, y0, z0 – the coordinates of the point source of the main ventilation fan MVF (m); Q0 – the averaged value of the dust intensity at the location of the point source of emission (mg/s); (x x0)(y y0)(z z0) – Dirac's delta-function, which is used to simulate the arrival of dust from MVF. The values of the diffusion coefficient is calculated by dependencies x = (0.1-1)U, y = (0.1-1)U, z = k(z/z1)m, where U – wind speed (m), z – height above ground level (m), z1 – height, where wind speed is given U (m), m 1, k = 0.2.
The composition of the dust is not uniform, taking into account the settling of individual fractions of dust is achieved by setting a different sedimentation rate ws for each fraction, so the calculation on this model must be performed for each fraction. This parameter is calculated using the Stokes formula (2) or is given from еру known experimental data.
,
(2)
where d
– the
equivalent particle diameter of the pollutant (m);
p
– particle
density of the pollutant (mg/m3);
a –
air density (mg/m3);
cx = 24/Re + 4/
– the
dependence of the drag coefficient on the Reynolds number.
An extremely important feature of this model is taking into account the stability of the atmosphere due to the task according to M.E. Berland of different values of the vertical diffusion coefficient z. It should be noted that the normative methodology of OND-86 does not allow to take into account the different stratification of the atmosphere.
Two approaches are used.
The first approach is based on splitting of the model equations into four fractional steps. At each splitting step, two physical processes are taken into account: convective transport and atmospheric diffusion; in addition, at each splitting step, the influence of the dust emission source on the formation of the contaminated zone is taken into account.
To build a numerical model, an implicit alternating triangular difference scheme is used, approximating the modeling equation (1). It is built on a rectangular differential grid. The concentration is determined in the center of the difference cells, the components of the air velocity vector are set at the boundaries of the difference cells [5]. For approximation of time derivatives the formula is used:
.
Prior to discretization, convective derivatives are written as the sum of signed variables:
,
,
,
where
,
,
,
,
,
.
Difference approximations of the first derivatives are written as:
,
,
,
,
,
where
etc. –
notation
for difference operators in the approximation of convective
derivatives.
Difference approximations of second order derivatives are written this way:
,
,
.
The following notation is used to shorten the writing of difference equations:
,
.
Applying the introduced notation of difference operators, the transport equation takes the following form:
At the next stage of the construction of the difference scheme, the splitting of this difference equation into four steps is performed with integrating over the time interval dt:
– in the first splitting step k = 1/4:
– in the second splitting step k = n + 1/2; c = n + 1/4:
– in the third splitting step k = n + 3/4; c = n + 1/2:
– in the fourth splitting step k = n + 1; c = n + 3/4:
In discrete form, the Dirac delta function is «distributed» to a single difference cell so as to preserve the total amount qi of the contaminant that is placed in the cell. Moreover, the function l that is used in difference expressions is not zero only in the cells where the source of dust emission is located. Using the above splitting scheme allows us to obtain difference equations of a simpler form, which makes it possible to carry out their software implementation.
The initial condition for each splitting equation is as follows [10–11]:
,
,
,
,
where,
,
– is
the impurity concentration value at one or another calculation step.
The boundary condition of non-leakage is realized due to the use of dummy cells. Based on the constructed numerical model, the software package «Dust source pollution 3D» has been developed.
In addition to the considered difference scheme, a different numerical model is used, its feature is the splitting of the modeling equation so that at each fractional step only one physical process is taken into account: convection, atmospheric diffusion, action of the emission source.
,
,
(3)
.
Such splitting allows you to calculate separately the process of dust dispersion when there is calm, in this case it is necessary to solve the second equation from system (3).
Findings
The developed program allowed to carry out computational experiments to calculate the dust dispersion in the atmospheric air contained in the emissions of the fan of the main airing in the «West Donbas Mine» based on the following characteristics of the MVF and its release:
– emitted substance – coal dust;
– dispersed composition – polydisperse dust with particle sizes from 1 mkm toо 60–100 mkm;
– the average density of the dust substance – 1900 kg/m3;
– temperature of emission is 24С, so cold ejection is considered;
– the intensity of dust emission Q0 = 61.6 g/s;
– height of the mouth of the diffuser above ground level – 6.5 m;
– the width of the mouth of the source – 6 m;
– the length of the mouth of the source – 6 m;
– average ejection velocity – 11.9 m/s;
– the volume of gas-air mixture 430 m3/s.
The calculation was performed with the following parameters: the size of the computational area was 4 km by 2 km, the wind speed was U = 4 m/s with the direction indicated by the arrow (Fig. 2).
Fig. 2. Distribution of dust concentration from MVF of the «West Donbas Mine», C [mg/m3]
As can be seen from Figure 2 zones of air pollution cover nearby villages. Obviously, when the meteorological situation changes, the position of the pollution zones will change, but these territories will fall to some extent into the pollution radius.
Figure 3 shows the concentration distribution at 1.7 m, which corresponds to the position of the human respiratory system. As can be seen from this figure, if we take MPCdust = 10mg/m3, then at a distance of 300m there is a violation of the MPC. When the MPC is reduced to 10mg/m3, the unfavorable zone increases.
Fig. 3. Distribution of dust concentration along the plume axis, C [mg/m3]
Originality and practical value
Numerical models were developed to predict atmosphere pollution from main ventilator fan. The model is based on equation of dust convective – diffusive transfer. For the numerical integration of modeling equation, the implicit difference scheme of splitting was used. The developed model can be used for quick computing of influence of mine ventilator fan on the settlements, which are situated near mines.
Conclusions
As a result of research we obtained the following.
1. Developed numerical model for predicting the level of air pollution in the zone of influence of MVF based on the three-dimensional impurity transport equation, which is solved by finite-difference methods.
2. The forecast can be performed on the basis of two numerical models. The models differ in the used splitting patterns. Both splitting schemes allow to calculate quickly the concentration of dust in ambient air. Calculation time is 10 s.
3. The developed numerical models take into account almost all the physical factors affecting the formation of pollution zones in the event of emission from MVF.
4. These models are implemented in the form of the «Dust Source Pollution 3D» program code, in which the transition to the calculation using one model for any meteorological conditions and the other, which is realized in the case of a calm situation, is foreseen.
Carrying out this class of calculations is a necessary tool for the practical assessment of a safe environmental situation during the operation of a public year survey, whose activity is related to the entry of dust into the atmosphere.