Numerical modelling of the self-heating process of a wet porous medium

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Abstract

In this research, the shortcomings of some advanced models for heat and fluid flow and moisture transport within and around a reactive porous medium (a coal stockpile) are numerically investigated based on a local thermal non-equilibrium approach and results are compared with experimental data. A full account of the problem is presented, including transient variation of the maximum temperature in the medium and the time required to vaporize the water content. The former is the main parameter used in the study of spontaneous self-ignition of coal stockpiles and the latter is an indication of the last step of self-heating toward self-ignition. Correlations are developed for the maximum dimensionless temperature inside the pile when the moisture content is near zero and the time that it takes from the beginning of self-heating until this time as functions of porosity, permeability, moisture content and the overall size of the porous medium.

Introduction

The role of moisture in the self-heating of porous media is a key economic and safety consideration in heat generating porous media, such as coal. Most natural products, such as hay, wool, and coal, contain moisture and their self-heating is affected by the transport of moisture. Simultaneous heat transfer due to oxidation and moisture transport through porous media occurs in areas as diverse as food processing, energy production and mining operations.

Self-heating is the process by which a temperature rise in a porous medium occurs due to internal heat generation from chemical or physical processes taking place within the reactive porous medium. When a wet porous medium is subjected to thermal drying, the main processes that occur simultaneously are the transfer of energy and the transfer of internal moisture to the surface and the subsequent evaporation of the moisture due to the energy transfer.

Dong [1] uses one dimensional mathematical modelling to determine the effect of moisture content on the maximum temperature rise in a coal pile. He included the influence of chemical exothermic reactions on phase change of the moisture during the drying process. The influence of coal stockpile height, slope angle and moisture was investigated by Akgun and Essenhigh [2]. Their model predicts that the ignition temperature is dependent on the bed porosity, pile shape, and coal type and the time to ignition is usually in excess of half a month or more. Bouddour et al. [3] simplified mathematical models of heat and mass transfer in wet porous media in the presence of evaporation and modelled them using asymptotic expansions for periodic structures. This method uses four homogenization techniques based on double scale expansions to specify the domains where the different descriptions can be used. Spontaneous combustion may happen when the heat generated within the reactive pile cannot be transferred away quickly enough to the environment by natural convection [4]. The time needed for the temperature to reach a critical value for a moist porous medium such as coal is much more than that required for a dry one [5], [6], [7], [8]. The effect of relative pressure on water diffusion/sorption into coal assuming thermal equilibrium has been reported for some specific applications [9], [10].

Self-heating of stockpiles of bulk porous materials is also affected by the penetration of water into the void volumes and the humidity of the surroundings. For example, an increase in humidity can enhance the self-heating due to heat released to the stockpile when condensation occurs [11], [12]. An experimental investigation and a simplified numerical simulation of the influence of humidity on the self-heating of combustible materials are reported by Lohrer et al. [13]. They show that a moist atmosphere may lead to a significant increase in the temperature of the medium.

The air entering the stockpile can play a major role in increasing the heat removal from the stockpile to the environment. However, increased air flow can also enhance the rates of chemical reactions, leading to an increase in the maximum temperature within the stockpile. This can then lead to spontaneous combustion. An increasing temperature within the stockpile is used as a criterion for possible spontaneous combustion. Ejlali et al. [14] show that there is a particular mass flow rate of air that leads to the lowest maximum temperature within a reacting stockpile.

There have been few studies that investigate the effects of moisture transport in reactive porous media on actual heat generation and water phase change. In the present research, numerical modelling of self-heating within coal stockpiles of typical size and physical properties has been coupled with a set of moisture transport correlations with buoyancy effects to study the transient heat transfer and moisture transport in heat generating porous media. The result is a system of non linear time-dependent equations for the flow inside and around the pile. Solutions allow the prediction of the magnitude of the maximum dimensionless temperature within the stockpile. As the solution proceeds, the water content goes to zero at different points in the stockpile at different times. The point in time when the water content first goes to zero is also of interest. The solution also gives the temperature at this point and the time at which it occurs. The former is a measure of coal self-heating. After the liquid water has evaporated inside the pile, coal enters the final step of self-heating which can result in self-ignition. The approach is quite general and, in addition to coal stockpiles, could be applied to stockpiles of any reactive material. However, the focus of this particular research is on coal stockpiles of typical sizes that would be found in the coal mining and processing industry.

Section snippets

Mathematical modelling

Fig. 1 shows a schematic diagram of the problem under consideration. A two-dimensional frustum-shaped geometry has been adopted in this study because this is representative of the typical shape of a coal stockpile. The third direction is assumed to be relatively long so that the governing equations, taken from Vafai et al. [15], [16], [17] to cover both porous and non-porous domains, reduce to a two-dimensional form. The conservation equations for moisture in liquid and vapour forms and the

Numerical procedure

The numerical calculations for the above mentioned unsteady and coupled dimensionless vorticity, stream-function, and temperature are achieved by the finite difference method using the Alternating Direction Implicit (ADI) method [27]. This method is an unconditionally stable finite difference method for solving parabolic and elliptic partial differential equations for transport of momentum, heat and moisture. The governing equations are discretized by second-order accurate central difference

Results and discussion

Validation of the code was accomplished by comparing the results from the simulations with experimental results for an industrial-scale stockpile [29] with particle sizes between 10 and 18 mm, 18% humidity, 5 m width, 3 m height and 10 m length.

To compare the results with experimental data and also in order to investigate the transient performance of the simulations, the dimensionless time, t, and dimensionless temperature, T, are replaced by the actual time and temperature in this section. Ozdeniz

Conclusions

A numerical approach has been used to study the self-heating mechanisms of wet porous media. Favourable comparisons between numerical and experimental results justify the suitability of the numerical approach. It is observed that the temperature within the porous medium increases at the start of the process mainly due to self-heating. The rate of increase in temperature slows as the simulations proceed due to phase change from liquid to vapour within the medium. The last stage of self heating

References (31)

  • M. Malow et al.

    The overall activation energy of the exothermic reactions of thermally unstable materials

    J. Loss Prev. Process Ind.

    (2004)
  • X. Dong Chen

    Effect of drying heat and moisture content on the maximum temperature rise during spontaneous heating of a moist coal pile

    Coal Preparation

    (1994)
  • A. Ejlali et al.

    Buoyancy effects on cooling a heat generating porous medium: coal stockpile

    Transp. Porous Med.

    (2011)
  • A. Arisoy, Numerical modelling of coal spontaneous combustion with moisture included, in: A.D.S. Gillies (Ed.), Eighth...
  • K. Brooks et al.

    Effect of natural convection on spontaneous combustion of coal stockpiles

    AIChE J.

    (1988)
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