## 1 Introduction
However, they only concerned the determination of speed distributions and oxygen concentrations in the goaves of longwallsventilated with the U-type system [26; 27; 28; 29; 30; 31; 32; 33; 34; 35]. These papers failed to take into account the type of roof rocks forming the goaves with caving, which affect 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 [PERSON] and [PERSON] [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, [PERSON] and [PERSON] [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, [PERSON] and [PERSON] [30; 31] used the permeability model of the goaves with caving, created by [PERSON] and [PERSON] [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 [PERSON] 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 different 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 [PERSON] 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, [PERSON] 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, [PERSON] and [PERSON] [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.