Mathematics Model and Programming Realization of the Varying-Rate Gas Drainage Process for a Sealed Lane

The production process of a coal mine can often be interrupted by all kinds of events scheduled or unscheduled and thus often needs gas drainage for a temporary or long-term sealed area. Gas drainage has a relatively high risk, therefore attention must be paid to its design to keep the process safe. Based on the conservation laws of mass and constituents, and under the conditions of the allowable gas concentration limit in the return air route, the relationship between gas concentration and gas drainage flow rate as a function of time during the drainage process is discussed in detail to build a mathematical model of gas drainage from a sealed area. With respect to the gas drainage process, two different conditions need to be considered: one with a methane free fresh air supply, the other with a low gas concentration. This paper presents the derived mathematical models for these situations and then shows that they can be incorporated into one model with some modification. This combined model can be employed to determine the optimum gas drainage flow rate with the shortest drainage time. The application is coded using the C# programming language within the .NET framework. Finally, the application program developed by the author is used to validate the mathematical model through an example of gas drainage with varying rate.