Flow behavior of a coupled model between horizontal well and fractal reservoir

Many research findings have proven that the system of porous medium reservoirs exhibits different heterogeneous structures at various scales, demonstrating some form of self-similarity with fractal characteristics. In this paper, fractal theory is incorporated into the reservoir to investigate coupled flow between reservoir and horizontal well. By examining the pore structure of highly heterogeneous reservoirs, the fractal dimension can be determined. Analytical methods are utilized to solve the Green function of a point source in a reservoir with fractal characteristics. Employing Green's function and the principle of spatial superposition, a finite flow model for a horizontal well coupled with a fractal reservoir is developed to calculate the flow rate and flow profile of the horizontal well. The model also accounts for the impact of wellbore friction and is solved numerically. A specific example is used for calculation to analyze the influence of fractal parameters on the production and flow rate of the horizontal well. When considering the fractal characteristics of oil reservoirs, the flow rate of the horizontal well is lower than that in Euclidean space. As the fractal dimension increases, the connectivity of pores in the reservoir improves, making it easier to drive the fluid into the wellbore, and the flow distribution along the wellbore becomes more uniform. Conversely, as the anomalous diffusion index increases, the connectivity between pores deteriorates, thus the distribution of flow rate along the wellbore becomes more uneven.