Critical volumes for spontaneous ignition of dry and wet coals

Abstract

Coal oxidizes even at low temperatures, emitting heat. If this heat is dispersed more slowly than it is generated, the coal may ultimately become so hot that it catches fire. The generation of heat by the oxidation of coal depends on the properties of the coal and on the amount of oxygen available to it. The dispersion of the heat depends on the properties of the coal, and also on the size and shape of the volume of coal being oxidized and on the conditions of heat exchange at its boundaries. In particular, the properties of the coalwill depend on its water content.We will call the temperature above which the coal can catch fire the critical temperature. We will call the lowest volume for which this temperature can be reached the critical volume.In this article we establish an approximate relation between the critical volume for spontaneous ignition of the coal and the water content. For this purpose we will consider the conditions of stability of the temperature field in a volume of oxidizing coal and the relation between the critical volume and the thermal characteristics of the coal. On the basis of the relation between the thermal characteristics and water content of the coal, we will investigate how the water content affects the critical volume.In our mathematical study of the temperature field we will make the following assumptions: i) the coal in the volume initially has homogeneous properties; ii) the oxygen in the mine air can reach any point in the volume equally easily, and does so in excess. With these postulates we can formulate the problem.In a region r bounded by a surface r~ we have to find a function u(x, y, z, t) which satisfies the equationon the conditions .J,:0 ~f(x,y,z) 0.; u+/el 0~_u +k2=0 on E, OnHere u is the temperature, a is the thermal diffusivity, c is the specific heat of the coal, p is the density of the coal, t is the time, x, y, and z are Cartesian coordinates, g(x, y, z, t, u) is a function which determines the rate of heat emission, k 1 and kz are quantities (in general not constant) which characterize heat exchange at the boundary surface, and n is the normal to the surface E.In the general case, the solution to this problem is very complicated. For this reason we will make some additional assumptions. Let us assume that the region r is a rectangular parallelepiped with its faces parallel to the coordinate planes, and that some fixed temperature is maintained on each face. Let us also assume that the rate of heat emission, expressed by the function g, is proportional to the rate of oxidation of the coal.According to Veselovskii [1], before the coal catches fire the temperature dependence of the rate of oxidation can be expressed to a first approximation by a straight-line segment. We therefore put g= ~'u + b,where ~' and b are constants.-~ "* Deceased. 1" We will consider this relation from the initial natural temperature of the coal to its ignition point.Eastern Scientific Research Institute.

Use of a model of a fissured porous medium for solving problems of liquid and gas filtration in a coal seam

“…They must be selected in such a way that the idealized model represents as faithfully as possible the actual pattern of transfer of liquid or gas in the seam. In other words, an imaginary fissured medium, the properties of which enable us to take account (albeit partially) of the essential characteristics of a coal seam as a filtering medium, is contrasted with a real medium (a coal seam) [4,5], Let us consider in general form the formulation of certain problems of liquid and gas transfer in a coal seam, taking account of the proposed model. The actual problems are the degassing of a coal seam and its wetting by water or special liquids.…”