Moving boundary analysis of fractured shale gas reservoir

Shale gas reservoirs are extremely tight, their pores are mainly nano-micron size, and their gas flow resistance is greater than that of conventional gases. Thus, the flow with low-velocity non-Darcy seepage characteristics of diffusion, slippage, and desorption needs to be solved. Moreover, the fractured reservoir has a complicated structure of pores and fractures, which causes the problem of multi-scale flow. The pressure disturbance propagates over time and does not instantaneously reach infinity. Another problem is that the moving boundary pressure disturbance of unstable seepage propagates slowly with time. Based on the above issues, in this paper, the permeability model of fractal distribution and Gaussian distribution was obtained to describe the different fracturing characteristics. Using the method of successive replacements of steady states and considering desorption, diffusion, and slippage, the mathematical model of unstable flowing pressure disturbance in a multistage fractured horizontal well was established. The moving characteristics of the different fractured conditions were compared and analyzed. The research shows that the pressure moving boundary increases with time, and the lower the permeability, the slower the pressure boundary moves. In general, the shale gas reservoir pressure propagates slowly, the natural productivity of the gas well is low, and the velocity of the pressure moving boundary of the matrix reservoir is less than the fractal distribution of the fractured reservoir and less than the Gaussian distribution of the fractured reservoir. Thus, it is necessary to carry out the large-scale fracturing treatment and reasonable control of the fracturing degree to improve the permeability as well as the development effect. When the production time is 6000 days, based on the moving boundary of the fractured horizontal well, the horizontal section length was optimized to 90 m. The optimum well distance of the well with fractal distribution permeability was 318 m, while the well with Gaussian distribution permeability was 252 m. Thus, the fracture treatment scale should be reasonably controlled to achieve optimal production and high yield.