Theoretical model and experimental verification of seepage-transition-spontaneous imbibition in water migration of water-injected coal

Coal seam water injection is widely applied to prevent mine disasters. In the traditional water migration model of water-injected coal, from ignoring capillary force in the seepage stage to generating the capillary dynamic during the spontaneous imbibition state, no transition state exists from 0 to generating capillary force. In this paper, on the basis of theoretical analysis, an equivalent capillary term is introduced to modify the Forchheimer model, and then a seepage-transition-spontaneous imbibition model that is suitable for water migration of water-injected coal is proposed. The formulas for the upper critical point velocity v₁, lower critical point velocity v₂, and water migration range of the transition state are derived. An analysis experiment of the spontaneous imbibition state in the coal rock water injection process and a monitoring experiment of the water injection process based on nuclear magnetic resonance method are conducted to verify the accuracy of the model. The results show that the accuracy of the water migration model, which takes the transition section into account, exceeds 0.99, representing a 12% improvement compared to the fitting precision of the water injection model that does not consider the transition section. The water migration process of water-injected coal cannot be accurately reflected without considering the transition section. In this paper, the water migration model of water-injected coal is improved, which provides theoretical support for a deeper understanding of the water injection mechanism and for enhancing the extraction efficiency of the coal seam.