A fractally fractional diffusion model of composite dual-porosity for multiple fractured horizontal wells with stimulated reservoir volume in tight gas reservoirs.

Abstract Based on fractal theory (FT) and fractional calculus (FC), a new fractally fractional diffusion model (FFDM) of composite dual-porosity has been developed to evaluate performance of multiple fractured horizontal wells (MFHWs) with stimulated reservoir volume (SRV) in tight gas reservoirs (TGRs). More specifically, FT is used to characterize the complex and heterogeneous fracture network (FN) both inside and outside of SRV, while anomalous behavior of diffusion processes both inside and outside of SRV is quantified by applying the temporal fractional derivatives. The FFDM is then solved by the Laplace transformation, line source function, the numerical discrete method, and superposition principle. The transient pressure responses are then inversely converted from Laplace domain into real time domain with the Stehfest algorithm, and the FFDM is also validated, and type curves are generated as well. Flow stages are subsequently identified together with analysis on characteristics of the type curves, especially the anomalous features different with those generated from the conventional Euclidean model. Sensitivity analyses of some related parameters have also been discussed as well. And the FFDM is then also matched with the real field well-testing data of a MFHW with SRV in a TGR. The proposed FFDM provides a new understanding of the performance of MFHWs with SRV in TGRs, which can be used to interpret the field pressure data more accurately and appropriately. Graphical abstract The SRV includes the main hydraulic fractures, the Euclidean matrix, and the fractal micro-fractures, while the USRV contains the Euclidean matrix and the fractal natural fractures. The flow of the gas in SRV and USRV follows the temporal fractional anomalous diffusion. By discretizing the main hydraulic fractures and applying the Laplace transformation, line source function, and superposition principle, we can obtain the pressure responses of a MFHW with SRV in a tight gas reservoir. Flow regime diagnostics and the characteristics analysis of type curves are accomplished, especially the anomalous characteristics. Image 1 Highlights • Fractal theory is used to describe the complex fracture network both in the SRV and USRV. • The anomalous diffusion both in the SRV and USRV is considered by employing the fractional derivatives. • A new FFDM of composite dual-porosity for MFHWs with SRV in tight gas reservoirs has been developed. • The PTA is then studied in depth, especially the anomalous characteristics different from that of conventional model. [ABSTRACT FROM AUTHOR]