Method for calculation of the carrying capacity of the bottomhole zone of a gas-bearing formation

This paper presents a method for calculating vertical and horizontal stresses in gas-bearing coal seams based on a set of equations developed by the authors. The method describes the experimental curve of rock pressure as a convex quadratic function, with the initial value of the function equal to the normal stress at the top of the bottom hole crack. The method also considers the variation of gas pressure as the crack moves towards the interior of the formation. In addition, the method employs the relationship between active tangential stresses at points on the edges of the bottomhole crack, derived from Coulomb’s strength criteria for brittle materials. The accuracy of the method was confirmed by experimental data on the maximum shear strength of marble and brown coal at various levels of confining pressure and pore pressure. The paper also presents analytical expressions for the strength limit of the bottomhole zone of gas-bearing coal seams as a function of gas pressure gradient.