Determination of pre-Darcy/Darcy/non-Darcy seepage patterns in coal around extraction boreholes

The stress concentration phenomenon in extraction drill holes easily leads to different degrees of damage to the coal body structure around the holes, and the redistribution of stress also causes the formation of a large number of pores and fissure networks around the holes. In order to accurately determine the effective extraction radius of coal seam gas and then reasonably determine the hole spacing, it is proposed to give a kind of “three-zone” gas flow pattern around the hole by accurately determining the gas flow pattern in the coal body around the extraction hole. It is proposed to give a new method for determining the gas flow pattern in the coal by accurately determining the gas flow pattern in the pore and fissure around the extraction boreholes. To this end, a variable porosity triaxial seepage test system was designed independently to determine the changing law of permeability of coal body around the extraction boreholes under different stress conditions, and the Kozney-Carman equation was applied to correct the Reynolds number Re, which is an indicator of the determination of the flow pattern, so as to obtain the critical conditions for the determination of the three typical seepage patterns (pre-Darcy, Darcy, and Forchheimer-type non-Darcy). The results show that: ① the gas seepage under low Reynolds number belongs to the pre-Darcy stage, and the penetration resistance mainly comes from the viscous force of gas itself, which exists only when the flow velocity v_s ≤ 0.062 m/s; the flow velocity curve has an inflexion point at Re_p > 15, which is a weakly inertial region, where the viscous and inertial effects co-exist. At this time, the pressure drop of the gas through the coal medium around the hole is inversely proportional to the Reynolds number, which is due to the capillary force in the coal body around the hole restricting the flow of gas. ② The seepage process of high Reynolds number is basically a turbulent state, and the test found that there is a non-linear phase of the seepage process of the coal medium around the hole, which indicates that the coal medium’s own internal structure has little effect on the flow rate of the gas, and the inertial effect of the flow is the main factor of the frictional resistance, the inertial effect is a major factor of the frictional resistance. The inertia effect during the flow process is the main factor of friction resistance, and the size of inertia resistance can be calculated by the second-order velocity correlation term in Darcy’s equation, and the inertia zone of the coal medium particles around the peripore starts from v_s > 0.086 m/s. ③ By analysing the three typical seepage patterns of the coal body pore and fissure media around the peripore, the Reynolds number calculation methods under different seepage patterns are calculated, and the critical Reynolds number value for the determination of the permeability flow pattern is given, and the value of Reynolds number for the determination of permeability flow pattern is found. When ${{Re} _{\sqrt K }}$ is greater than 3.29, the whole seepage process belongs to the non-Darcy Forchheimer state, and the value calculated at this time is the critical condition for nonlinear flow (Re_p > 0.18). Combined with the above conclusions, the radius of coal seam gas extraction can be accurately determined in coal seam gas pre-pumping work by using the improved method of calculating the seepage pattern of the coal body around the hole, so as to provide an important theoretical basis for the design of the drilling hole layout method.