A multi-scale flow model for production performance analysis in shale gas reservoirs with fractal geometry

Shale gas reservoirs can be divided into three regions, including hydraulic fracture regions, stimulating reservoir volume regions (SRV regions), and outer stimulating reservoir volume regions (OSRV regions). Due to the impact of hydraulic fracturing, induced fractures in SRV regions are often irregular. In addition, a precise description of secondary fractures in SRV regions is of critical importance for production analysis and prediction. In this work, the following work is achieved: (1) the complex fracture network in the SRV region is described with fractal theory; (2) a dual inter-porosity flow mechanism with sorption and diffusion behaviors is considered in both SRV and OSRV regions; and (3) both multi-rate and multi-pressure solutions are proposed for history matching based on fractal models and Duhamel convolution theory. Compared with previous numerical and analytic methods, the developed model can provide more accurate dynamic parameter estimates for production analysis in a computationally efficient manner. In this paper, type curves are also established to delineate flow characteristics of the system. It is found that the flow can be classified as six stages, including a bi-linear flow regime, a linear flow regime, a transition flow regime, an inter-porosity flow regime from the matrix to the fractures in the inner region, inter-porosity flow regime from matrix to fractures in the outer region, and a boundary dominant flow regime. The effects of the fracture and matrix properties, fractal parameters, inter-porosity flow coefficients, and sorption characteristics on type curves and production performance were studied in detail. Finally, production performance was analyzed for Marcellus and Fuling shale gas wells, in the U.S.A. and China, respectively.