Temporal scale-based production analysis of fractured horizontal wells with stimulated reservoir volume

After volume fracture, the permeability field is found to be varying with space. This is not only a commonly-occurring production effect, but has also become a hot research topic in the field of tight gas reservoirs. However, different flow velocities and temporal scales controlled by varying permeability field are often neglected. In this study, the temporal scale analysis for two-dimensional (2D) inhomogeneous permeability field is introduced to explain the inhomogeneity and different flow velocities in the stimulated-reservoir-volume (SRV). Firstly, a new mathematical approach for temporal scale analysis to the well response has been provided. According to the proposed approach, the solution is obtained by using finite element method in the Laplace domain. The well performance is then speared into the temporal scales, which are derived from the analytical Laplace inversion of the solution. Based on this, the temporal scale diagrams are provided for production performance analysis and comparison. Secondly, the significant differences in the well response and its temporal scale analysis from one-dimensional (1D) field have been highlighted. The results showed that the varying permeability is observed to be properly represented by two-dimensional field. In general, the shape of the temporal scale distribution stripe is different with varying pattern of the permeability, and its width and density are enhanced by the rapid variation of the permeability. The temporal scales are enhanced at higher permeability area, while their contributions are reduced by the permeability, though these are enhanced by the initial energy of their corresponding area. By analyzing the initial energy, the propagation of the pressure and the exploited area are presented in a better way. Furthermore, the exponential and power fields explain the permeability inhomogeneity better than the linear field. In spite of this, the linear field is described better by the temporal scale analysis, while multiple temporal scale is the result of permeability inhomogeneity. Last but not the least, the effect of the less permeable outer boundary is eliminated by decelerating the decline in permeability in the whole SRV. The temporal scales fail to couple in terms of both mass and energy, and their corresponding processes fail to influence each other. Finally, practical guidelines for the volume fracture techniques are derived based upon the proposed model.