New mathematical model of horizontal well production for coalbed methane

Based on the Langmuir equation,Fick unsteady diffusion law and Darcy equation,the partial differential equations and the definite conditions which describe the mechanism of coal gas and water flow were established in consideration of gravity and compression.The method of finite difference was presented to solve the equations.It can be concluded that the model and algorithm are available on predicting the productivity of coalbed methane horizontal well.According to the productivity results under different fissure permeability,we can conclude that the peak time will be artificially shortened and the peak gas rate will be exaggerated,the energy of gas expansion is decreased and the productivity is underestimated if the unsteady diffusion and the compression are ignored.The higher fissure permeability is,the greater the effect of permeability reversion on productivity.The shorter the duration of peak gas rate is,the faster the decline rate will be.In order to reduce the disadvantage of the effect of permeability reversion,a thoughtful bottom hole flowing pressure should be set during production to establish a reasonable pressure system.