*2.1. Physical Model*

In this physical model, a horizontal well is located in the center of a homogeneous reservoir with an elongated elliptical boundary. The whole drainage area consists of several di fferent flow patterns in four contiguous flow regions, as sketched in Figure 2, including (1) the hydraulic fractures, (2) the inner stimulated rock volume (SRV) region impacted by hydraulic fracturing, (3) the outer linear region beyond the extent of the SRV, and (4) the outer elliptical region beyond the tips of the horizontal wellbore.

**Figure 2.** Schematic of the compound elliptical-flow model representing four contiguous regions for a multiple-fractured horizontal well (MFHW). SRV, stimulated rock volume.

Different from the anisotropic characteristics in a naturally fractured reservoir, where a large number of nature fractures are uniformly and globally distributed [33–35], this paper assumes that the reservoir is stimulated by several hydraulic fractures, so the resulting hydraulically fractured reservoir is regarded as isotropic. In addition, there are some necessary assumptions, as follows:

