Quantitative evaluation of cross-well interference among coalbed methanewells based on modified Kusakkin formula

The drainage of vertical coalbed methane wells in China is carried out after the reservoir reformation, and the values of the water phase permeability are different in different drainage stages. In order to more accurately and quantitatively evaluate the degree of cross-well interference in coalbed gas vertical well drainage after coal reservoir reformation, a prediction model of post-fracture permeability was constructed based on the Warren-Rut flow model and the pressure drop curve during fracturing. According to the difference of the proportion of gas/water in the process of drainage, the relative permeability model of water phase in the low-yield and stable production phases of gas/water two-phase flow was constructed. The water permeability models in different drainage stages were embedded in the classical,and the mathematical models about water pressure propagation distance in different drainage stages were obtained. Based on the interference well testing and exploration data of the typical well group in the southern block of Shizhuang, the accuracy of the theoretical model was verified. A permeability-pressure gradient-impact distance map was established based on a mathematical model. The results showed that when the reservoir pressure gradient was constant, the influence distance increased exponentially with the increase of permeability.When the permeability was constant, the influence distance increased linearly with the increase of reservoir pressure. When the reservoir pressure gradient was 0.5 MPa/hm and the permeability after fracturing was generally (0.5～8.0)×10-3μm, the influence distance in the long axis direction was 95～120 m and that in the short axis direction was 56～75 m, and the well pattern under this reservoir condition should be less than 240 m×150 m. This method can provide theoretical basis for well pattern optimization under the condition that there was no overflow recharge and coal structure is primary or fractured coal reservoir. When the coal structure was dominated by granular coal or mylonite coal and overflow recharge, the calculation results of this method can be used as a reference.