Performance of multi-stage fractured horizontal wells with stimulated reservoir volume in tight gas reservoirs considering anomalous diffusion

Horizontal well combined with volume fracturing technology has been extensively employed in the development of tight gas reservoirs. The disordered distribution of the induced and natural fractures in the reservoirs leads to the existence of the anomalous diffusion, so the conventional Darcy law has some limitations in describing the fluid flow under this circumstance. This paper introduces the fractional Darcy law to take into account the effect of the anomalous diffusion and then extends the conventional model of the multi-stage fractured horizontal (MSFH) well with the presence of the stimulated reservoir volume (SRV). The generated point source model for dual-porosity composite system includes the fractional calculus and its solution in Laplace space is derived. The superposition principle and the numerical discrete method are applied to obtain the solution for the MSFH well with SRV. Stehfest inversion method is used to transform the pseudo-pressure and production rate from Laplace space to real space. Type curves for pseudo-pressure and production rate are presented and analyzed. The influence of the relevant parameters on pseudo-pressure behavior and production rate decline is discussed in detail. The proposed model enriches the flow models of the MSFH well with SRV and can be used to more accurately interpret and forecast the transient pressure and transient rate.