Random distribution of porosity in the combustion space area of underground coal fire

Through statistical analysis of random experiments, there is a function of porosity 3lnφ-2ln(1-φ) that approximately follows a normal distribution. In the test particle size range of 30 to 180 ram, the expectation and variance of this function value increase with an increase in grain size of rock blocks. On the basis of deriving the subsidence hypersurface equation of a basic roof, a continuous inhomogeneous distribution model and a random inhomogeneous distribution model of porosity in the combustion space area (CSA) are deduced. For a rectangular coal fire space, the porosity in the shallow and edge side of CSA is large, but in the middle region is small. In the x-y plane, the porosity contour appears a side lying U-shaped distribution, and the porosity presents negative exponent attenuation with an increase in distance entering CSA along the x axis. In addition, the overall trend of the porosity of continuous distribution and random distribution is the same, but the difference is that the porosity described by the random distribution model has a certain stochastic volatility. The random distribution model of porosity has been used in a numerical simulation of the temperature field in a fire zone, and the accuracy of simulation and the applicability of this porosity model are verified by infrared temperature measurements.