MATHEMATICAL MODELS ABOUT THE CRITICAL SIZE OF COAL RESERVOIR FRACTURE MAKE OF WATER MIGRATION FOR SINGLE-PHASE COALBED METHANE WELLS

Identifying the critical size of coal reservoir fracture for single-phase water migration drained by coal bed methane (CBM) well provides the study of pressure transmission in CBM wells with theoretical basis. A geological conceptual model for coal reservoirs was established according to the characteristics of the fracture structure of coal reservoirs. Based on the elastic-plastic mechanical theory, the dynamic equilibrium equation of the water migration in coal reservoir fracture in its single-phase water flow stage was constructed. By combining effective stress principle and damage theory, the stress distribution and damage evolution around the fracture were analyzed, and the mathematical model of the critical size of coal reservoir fracture for water migration in its single-phase water flow stage was built. The calculation for the critical size of the coal reservoir fracture in Sihe mine in Jincheng showed that the critical size of water migration in coal reservoir was 0.1 μm in its original state. The result is basically in an agreement with the results of laboratory tests carried out by other scholars. Meanwhile, with the generation of water in a drainage process, the critical size of coal reservoir fracture for water migration increases slightly, which is still around 0.1 μm. The model established accurately predicts the critical size of coal reservoir fracture in varied conditions in its single-phase water flow stage, and the changing regulation of the critical size in drainage process.