Probabilistic modeling using bivariate normal distributions for identification of flow and displacement intervals in longwall overburden

Gob gas ventholes (GGV) are used to control methane emissions in longwall mines by capturing it within the overlying fractured strata before it enters the work environment. In order for GGVs to effectively capture more methane and less mine air, the length of the slotted sections and their proximity to top of the coal bed should be designed based on the potential gas sources and their locations, as well as the displacements in the overburden that will create potential flow paths for the gas.In this paper, an approach to determine the conditional probabilities of depth-displacement, depth-flow percentage, depth-formation and depth-gas content of the formations was developed using bivariate normal distributions. The flow percentage, displacement and formation data as a function of distance from coal bed used in this study were obtained from a series of borehole experiments contracted by the former US Bureau of Mines as part of a research project. Each of these parameters was tested for normality and was modeled using bivariate normal distributions to determine all tail probabilities. In addition, the probability of coal bed gas content as a function of depth was determined using the same techniques. The tail probabilities at various depths were used to calculate conditional probabilities for each of the parameters. The conditional probabilities predicted for various values of the critical parameters can be used with the measurements of flow and methane percentage at gob gas ventholes to optimize their performance.