Karst collapse columns (KCCs) are naturally formed geological structures that are widely observed in North China. Given their influence on normal mining operations and the progress of mining work, collapse columns pose a hidden danger in coal mining under the influence of manual mining. By communicating often with the aquifer, the water inrush from KCCs poses a serious threat to construction projects. This paper adopts three flow field models, namely, Darcy aquifer laminar flow, Forchheimer flow, and Navier–Stokes turbulent flow, based on the changes in the water inrush flow pattern in the aquifer and laneway, and uses COMSOL Multiphysics software to produce the numerical solutions of these models. As the water inrush flow velocity increases, the Forchheimer flow shows the effect of additional force (inertial resistance) on flow in KCCs, in addition to the effect of viscous resistance. After the joint action of viscous resistance and inertial resistance, the inertial resistance ultimately dominates and gradually changes the water inrush from the KCCs to fluid seepage. Forchheimer flow can comprehensively reflect the nonlinear flow process in the broken rock mass of KCCs, demonstrate the dynamic process from the Darcy aquifer to the final tunnel turbulence layer, and quantitatively show the changes in the flow patterns of the water inrush from KCCs.

This paper investigates the dynamic behavior of non-Darcy seepage systems in post-failure rock. A one-dimensional non-Darcy seepage evolution equation is established, and a 6-dimensional nonlinear ordinary differential system is derived via the spectral truncation method. Eigenvalue analysis is adopted to determine the instability and bifurcation conditions, with the bifurcation diagram plotted. The fourth-order Runge–Kutta method is used to obtain phase trajectory patterns under different initial values. The results confirm the existence of transcritical bifurcations and fold bifurcations. The dynamic response of the system is discontinuous with control parameters, and phase trajectory symmetry breaking occurs with the increase in nonlinear terms. The reduced-order model shows diverse phase trajectories including equilibrium, periodic, chaotic attractors and unstable states. The system is sensitive to initial values, which significantly affect phase trajectory behaviors. The system may lose stability and trigger water inrush hazards under critical conditions. The bifurcation diagram and critical parameters obtained can provide a theoretical basis for the early warning, risk assessment and prevention of coal mine water inrush hazards.

Heat stimulation of coalbed methane (CBM) reservoirs has remarkable promotion to gas desorption that enhances gas recovery. However, coalbed deformation, methane delivery and heat transport interplay each other during the stimulation process. This paper experimentally validated the evolutions of gas sorption and coal permeability under variable temperature. Then, a completely coupled heat-gas-coal model was theoretically developed and applied to a computational simulation of CBM thermal recovery based on a finite element approach of COMSOL with MATLAB. Modeling and simulation results show that: Although different heat-gas-coal interactions have different effects on CBM recovery, thermal stimulation of coalbed can promote methane production effectively. However, CBM thermal recovery needs a forerunner heating time before the apparent enhancement of production. The modeling and simulation results may improve the current cognitions of CBM thermal recovery.