**1. Introduction**

There are various types of rocks forming the hard coal seams in Poland. They include claystones, coal shales, mudstones, sandstones and, where the ongoing exploitation is divided into layers, also hard coal. All of these rocks have different strength properties [1,2].

So far, the strength properties of the rocks surrounding mine headings have been considered primarily in terms of their impact on the capacity to maintain the stability of mine headings [3–5]. When coal is exploited with caving, the analysis also encompasses their capacity to transform into the state of caving and to maintain the roof in a longwall heading (classification by Salustowicz [6]). The strength properties of these rocks were, therefore, mainly examined in terms of rock mass mechanics.

From the perspective of ensuring safe exploitation in longwalls, the impact of the strength of roof rocks should be considered not only in terms of maintaining the stability of the mine headings, but also in terms of the occurrence of ventilation hazards, and—more precisely—the risk of spontaneous coal combustion (endogenous fires) in the caving goaves of longwalls.

Spontaneous combustion of coal is a phenomenon that commonly occurs in hard coal mines [7–11]. It results from the self-ignition of coal following its self-heating in a mine heading or its immediate surrounding, e.g., in the goaves with caving.

Goaves with caving are a space formed after coal extraction, filled with rock rubble from the collapse of roof rocks hanging over the exploited seam. The degree to which this space is filled once the coal has been extracted depends on a number of factors. However, the most important of these is the type of roof rocks forming the goaves [12–14].

The parameter that is critical for the propensity of these rocks to transform into the state of caving is their tensile strength [15]. It determines the filling (tightness) degree of the cave-in rubble, and hence its porosity and permeability. Strong and solid roof rocks separating from the rock mass fill goaves with caving to a lesser extent than weak and brittle rocks. Therefore, goaves with caving filled with roof rocks of low tensile strength provide better filling of the space created after the mined coal (due to their lower permeability).

However, regardless of the type of rocks forming the goaves with caving, such goaves always include void spaces not filled with any rock material. These spaces, representing open contacts between chaotically arranged blocks of fractured roof rocks, form a particular type of a porous medium which allows for the flow of gases, including the air migrating from the longwalls.

The flow of air through goaves with caving results from its migration from the area of the longwall to which a stream of ventilation air is supplied. This stream is supplied to longwalls for their ventilation. There are several longwall ventilation systems, with the most common being the U-type ventilation system from the borders and the Y-type ventilation system [16] (Figure 1). Analysing both of these systems, it is possible to see a clear di fference in the flow of air through the exploited headings.

**Figure 1.** Diagram of the U-type (**a**) and Y-type ventilation systems (**b**).

The choice of a longwall ventilation system depends on a number of factors. The ventilation system must ensure proper chemical composition and temperature of the atmosphere [17–19]. One of the most important is the level of natural hazards, including gas-related risks, which occur in the region of active exploitation. In practice, there is no system that would be beneficial in the event of simultaneous occurrence of the self-combustion risk and the methane risk for the longwall under exploitation.

A system advantageous in the case of spontaneous combustion risk is less suitable for areas with methane hazard and vice versa. In longwalls with a high methane hazard which is typical of mines, it is increasingly common to use Y-type ventilation systems with air discharge along the goaves. However, this system is characterised by a significantly higher migration of air to the goaves with caving compared to the U-type ventilation system. This o ffers more favourable conditions for the self-heating of coal left in the goaves, which, in turn, may cause an endogenous fire to arise.

The research conducted by Szl ˛azak [20] revealed that the total migration of air to the goaves with caving depending on the type of roof rocks filling the goaves with caving may, in extreme cases, amount to as much as approximately 40% (for rocks with the highest value of tensile strength).

The air stream migrating to the goaves with caving poses a risk for a low-temperature process of coal oxidation to be initiated, which may lead to spontaneous combustion of the coal left in the goaves. The prerequisites for this process to be initiated, besides the presence of coal, include the flow of air with a specific speed and appropriate oxygen concentration. When these conditions are met, it is possible for the reaction of low-temperature coal oxidation to be initiated, during which heat is produced and then accumulated by the coal, thereby causing its temperature to rise. If these conditions continue for a specific period of time (the incubation time), spontaneous combustion of coal, i.e., an endogenous fire, may occur.

The most essential factor a ffecting the process of heat accumulation is the speed of the air stream flowing through the goaves with caving in the longwall. This speed depends on the type of roof rocks forming the caving (since they influence their sealing degree) as well as on the volumetric flow rate of the air supplied to the longwall. However, the issue of how the volumetric flow rate of the air supplied to the longwall impacts the risk of endogenous fires has been discussed in several publications [21–24].

Nevertheless, no conclusive range has been determined for the air speed flowing through the goaves that would contribute to the initiation and maintenance of the coal oxidation process.

In the paper by Cheng et al., this value was assumed to range from 0.004 to 0.0016 m/s [21]. Chumak et al. [22], on the other hand, assumed that the critical speed value ranges from 0.015 to 0.0017 m/s, whereas Szl ˛azak reported that this value is between 0.015 and 0.0015 m/s [23]. On the other hand, Wang et al. [24] indicated that this value ranges from 0.001 to 0.02 m/s. The speed ranges indicated are quite extensive. Therefore, the present paper assumes that this speed ranges from 0.02 m/s to 0.0015 m/s.

In the case of the oxygen concentration in the air flowing through goaves with caving, it has been demonstrated that the lower limit for self-combustion of coal is 8%. The results of the tests carried out by Buchwald [25] indicate that no spontaneous combustion of coal occurs below this value due to the insu fficient concentration of oxygen.

Coal oxidation in the goaves with caving may occur only in the area of the goaves which meets both of the above conditions, namely the presence of crushed coal susceptible to spontaneous combustion and the air flowing through the goaves at a specific speed and with a specific oxygen concentration. This area could be termed as the zone with a particularly high risk of endogenous fires. In this zone, the physical and chemical parameters of the air reach values conducive to the initiation of the oxidation process.

This was used as the basis for formulating the risk criterion for spontaneous coal combustion (endogenous fire) in the goaves with caving, which includes:


Works involving determination of the distribution of physical and chemical parameters of the air flowing through the goaves with caving have already been published. However, they only concerned the determination of speed distributions and oxygen concentrations in the goaves of longwalls ventilated with the U-type system [26–35]. These papers failed to take into account the type of roof rocks forming the goaves with caving, which a ffect their permeability, and hence the possibility of air to migrate inside the goaves, and the distributions of parameters.

One of the first papers dedicated to a three-dimensional analysis of air flow through the goaves of a longwall with caving was by T. Ren and R. Balusu [24]. In this paper, a spatial model was used to present the results of numerical tests concerning the distribution of oxygen concentration in the goaves of a longwall with caving after inertisation. The subsequent works of the same authors [27,28] also present the distribution of oxygen concentration in the goaves with caving. However, the determination of this distribution served as an introduction to numerical tests related to various methods for supplying an inert gas both into longwall headings and through the holes drilled from the surface.

On the other hand, Esterhuizen and Karacan [29], using their own model for determining the permeability of goaves with caving, carried out numerical research and determined the speed of the air flowing through the goaves. They concluded that this speed reaches the highest value at the borderline of the goaves (at the starting line of the longwall and behind the longwall lining).

For their own model-based tests, Yuan and Smith [30,31] used the permeability model of the goaves with caving, created by Esterhuizen and Karacan [29]. These tests were related to the self-heating of coal left in the goaves with caving and to the determination of the temperature in those goaves. The tests were based on chemical reactions during which heat is released into the atmosphere upon contact of coal with oxygen. This served as the basis for determining the dependency between the oxidation rate and temperature, and oxygen concentration.

Another work which attempted to examine the flow of air through a three-dimensional model of goaves with caving was the one by Dai et al. [32]. It presented the distributions of the air speed in the goaves of a longwall with caving ventilated by means of the U-type system at two di fferent flow heights, namely 1.5 m and 3.0 m from the floor of the exploited seam. In this work, the dangerous speed value of the air flowing through the goaves with caving, conducive to the self-heating of coal, was assumed to be equal to 0.004 m/s.

Tests on the flow of air through goaves with caving of a longwall, using a three-dimensional model, were also carried out by Xie et al., who presented the results of such tests in the paper [30]. They built a numerical model reflecting a real-world longwall and goaves with caving. The tests they conducted helped them to determine the distribution of air speed in the goaves with caving and the distribution of air pressure.

On the other hand, Shi et al., in the paper [34], presented the results of model-based tests on the distribution of oxygen concentrations in the goaves of a longwall with caving. They conducted these tests on a three-dimensional model which made it possible to determine the distribution of oxygen concentration in the goaves with the values from 8% to 18%. This concentration poses a risk that the oxidation process of the coal left in the goaves with caving could be initiated.

On the other hand, Brodny and Tutak [35] determined the impact of the volumetric flow rate of the air stream supplied to the longwall on the speed of the air filtrating through goaves and on the concentration of oxygen in this air.

Analysing the papers published to date, it is possible to conclude that none of them has determined how the type of the roof rocks forming the goaves with caving impact the formation of the zone with a particularly high risk of spontaneous coal combustion. This zone has also not been considered in terms of the Y-type ventilation system.

Therefore, the Authors conducted model-based tests whose purpose was to determine the impact of the type of roof rocks forming the goaves with caving on the formation of the zone with a particularly high risk of spontaneous combustion of the coal left in the goaves of longwalls ventilated with the Y-type system.

It is practically impossible to determine the zone with a particularly high risk of spontaneous coal combustion in real-world conditions because this zone is formed in an inaccessible area of the goaves. The attempts to measure the ventilation parameters in the goaves made to date have been unsuccessful in the majority of cases. For this reason, this zone was demarcated using model-based tests, which are successfully used for variant analyses of the processes related to ventilation of underground mine headings, as well as for analyses of emergency states occurring in these headings [36–38].

The tests were conducted for the actual layout of headings in one of the longwalls of a hard coal mine. The tests were based on the geometry of this longwall and the ventilation parameters registered during its exploitation. The tests (boreholes in the roof) also helped to define the strength parameters of the roof rocks forming the caving.

The main purpose of the works performed was to develop a methodology of model-based tests for spatial analysis of the ventilation phenomenon related to the identification of the area in the goaves with caving, where it is possible for spontaneous coal combustion, i.e., an endogenous fire, to occur.

In order to specify the impact of the type of roof rocks forming the goaves with caving on the location and extent of the zone with a particularly high risk of spontaneous coal combustion in the goaves, additional analyses were also conducted for five di fferent tensile strengths of the rocks. The analysis was based on the geometry and ventilation parameters of the longwall in question. A total of six variants were considered for the tensile strength of roof rocks, and the dependency between this strength and the zone with a particularly high risk of spontaneous coal combustion in the goaves were determined.

### **2. Materials and Methods**

#### *2.1. The Porosity and Permeability of Goaves with Caving*

One of the most important properties of roof rocks determining their ability to transform into caving is the tensile strength. This strength is the natural ability of the rock mass to resist stratification and caving of the roof rocks into the space (void) left after the mined coal as a result of vertical forces [39,40].

The value of the tensile strength of the roof rocks is determined by means of a down-hole penetrometer or the direct method—by stretching the sections of the vertical core of the borehole in the direction of the longitudinal axis of the borehole, and then it is determined from the following relationship:

$$R\_{\rm rii} = 0.8 \frac{F}{d^2} \tag{1}$$

where *Rrri* is tensile strength of the rocks (Pa), *F* is the applied axial load (N) and *d* is core diameter (m2).

This value depends on the type of roof rocks forming the caving. The maximum value of the tensile strength of rocks in Polish mines amounts to approximately 8 MPa [1,2]. In practice, however, such value is rare. Table 1 presents the types of roof rocks and the values of their tensile strength, as well as the characteristics of the roofs formed by these rocks.


**Table 1.** The types of roof rocks and the values of their tensile strength (own study based on [1,2]).

After such calculation of the tensile strength of roof rocks, it is possible to determine the permeability coe fficient of goaves with caving, using the following equation [41]:

$$k(\mathbf{x}) = \frac{\mu\_{\text{g}}}{r\_0 + a\mathbf{x}^2} \text{ for } 0 \le \mathbf{x} \le 2/3 \cdot l \tag{2}$$

*Appl. Sci.* **2019**, *9*, 5315

as well as the equation:

$$k(\mathbf{x}) = \frac{\mu\_{\mathcal{S}}}{r\_0 + a\left(\frac{4}{3}l - \mathbf{x}\right)^2} \text{ for } 2/3 \cdot l \le \mathbf{x} \le l \tag{3}$$

where *k(x)* is permeability (m2), μ*g* is the coe fficient of dynamic viscosity of air (Nsm−2), *l* the total length of the longitudinal longwalls (m), *r*0 we determine from dependence *r*0 = μ *k*0 and *a* we determine from dependence *a* = 6 · <sup>10</sup><sup>9</sup>*Rrrs*−1.74.

The value of the permeability coe fficient of caving goaves *k*0 behind the front of the longwall is determined from the following equation [41]:

$$k\_0 = \frac{\mu\_\mathcal{g}}{6} \cdot 10^{-10} R\_{rrs}^{-1,44} \tag{4}$$

The porosity of goaves varies on the basis of "O-zone theory" [42]. The porosity distribution along the strike direction in the middle of the working face goaves is determined from the following equation [41]:

$$m\_{\rm x} = 0.2 \varepsilon^{-0.0223 \rm x} + 0.1\tag{5}$$

where *nx* is the porosity distribution along the middle line of working face of longwall in goaves (%); *x* is the x position of the goaves (m).

The porosity of goaves in dip distribution can be determined from the following equation [43]:

$$m\_y = e^{-0.015y} + 1 \text{ for } 0 < y < \frac{L}{2} \tag{6}$$

$$m\_{\mathcal{Y}} = e^{-0.015(L-y)} + 1 \text{ for } \frac{L}{2} < y < L \tag{7}$$

where *ny* is the porosity distribution along dip direction (%), *y* is the y position of the goaves (m); *L* is the length of the working face of longwall (m).
