In the paper the results of investigations aimed at further identification of the phenomena occurring in abandoned workings and connected with the flow of air-gas (methane, carbon dioxide, nitrogen, oxygen and carbon oxidation products) mixture with taking into consideration the impact of supplied mineral substances on the processes of self-heating of the coal left in goaves were presented. The known and successfully used method for the prevention of fires in abandoned workings is the technology of filling goaf with an ash-air mixture, which also raises the issue of the effective use of that mixture. The computer, i.e. digital simulation methods being developed and intended for the purpose of the process discussed here are a good complement of the use of that technology. A developed mathematical model describing the process of additional sealing of gob with wet slurry supplied with three pipelines is based on the balance of volume of the supplied mixture and contained in the body created in goaves. The form of that body was assessed on the basis of the observation results available in literature and the results of model investigations. The calculation examples carried out for the the longwall area and its goaf ventilated with the “U” system allow to state that the introduced modification of the mathematical model describing the flow of the mixture of air, gases, and wet slurry with consideration of the coal burning process in the fire source area was verified positively. The digital prognostic simulations have confirmed a vital impact of the wet slurry supplied into the goaf on the processes of coal burning and also the change of rate and volume flow rate of the air mixture in goaf. As a complement to the above it should be noted that such elements as the place of the slurry supply in comparison with the longwall inclination or fire source area location is of great importance for the effectiveness of the fire prevention used. The development of computer/ digital simulation methods requires further investigations of the model adopted in this study. Those investigations should be aimed at making credible the theoretical model of the mixture flow through porous medium and the supplied mineral material. Such investigations will allow to verify the body form based on the mixture parameters such as humidity, viscosity, and fluidity and depending on the properties of the porous medium. Further development of the modelling of the phenomena discussed in this paper should be based on the methods of use of the description of the flow of fluids and slurry on the basis of 3D models.