## 1 Introduction  
Gas flow in porous media has recently attracted much attention and stimulated great interest in the development of oil and gas reservoirs [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. In the past decades, many gas reservoirs with stress-sensitive permeability have been discovered and developed around the world. During the development process of stress-sensitive reservoirs, the continuously decreasing formation pressure leads to the decrease of the formation permeability. Therefore, it is critical to investigate the effect of the stress sensitivity of the permeability on the production. Recently, lots of models have been established to study the performance of various wells in stress-sensitive reservoirs [16; 17; 18].  
On the other hand, in order to obtain economic benefit, hydraulic fracturing has been widely applied in the development of low-permeability gas reservoirs. A great variety of seepage models of vertical fractured wells have been proposed and the characteristic of pressure response has been studied in detail. [PERSON] et al. [19] established a seepage model of a vertical fractured well with two symmetrical infinite-conductivity hydraulic fractures, which can be used to identify the linear flow. Later, by considering the effect of the fluid flow within the hydraulic fractures, a seepage model of a vertical fractured well with two symmetrical finite-conductivity hydraulic fractures was established [20; 21], which can identify the bilinear flow. Some researchers pointed out the existence of two asymmetrical hydraulic fractures in practice and established some seepage models of vertical fractured wells with two asymmetrical hydraulic fractures [22; 23; 24; 25; 26; 27]. In fact, massive hydraulic fracturing usually creates fractured network or several main hydraulic fractures near the wellbore instead of two symmetrical/asymmetrical hydraulic fractures [28; 29; 30; 31]. Recently, seepage models of vertical fractured wells with multiple hydraulic fractures have received more attention. [PERSON] et al. [32] proposed a numerical model of a vertical fractured well with multiple hydraulic fractures and investigated the pressure behavior of a vertical fractured well. [PERSON] and [PERSON] [33] and [PERSON] et al. [34] established semi-analytical models of a vertical fractured well with multiple infinite-conductivity hydraulic fractures. [PERSON] and [PERSON] [35] and [PERSON] and [PERSON] [36] proposed semi-analytical models of a vertical fractured well with multiple finite-conductivity hydraulic fractures. Compared with the pressure behavior of vertical fractured wells with two hydraulic fractures, the pressure response of vertical fractured wells with multiple hydraulic fractures is very complex. Although the effect of relevant parameters on the pressure response of vertical fractured wells with multiple hydraulic fractures has been studied, and the characteristics of the type of curves is not clearly understood. More important, little work has focused on vertical fractured wells with multiple hydraulic fractures in stress-sensitive gas reservoirs. In particular, the effect of relevant parameters on the error caused by neglecting the stress sensitivity has not been recognized clearly.  
In this paper, we propose a seepage model of vertical fractured wells with multiple finite-conductivity hydraulic fractures. Type curves are identified and analyzed. The effects of relevant parameters on type curves and the error caused by neglecting the stress sensitivity are discussed in detail. This work can enrich the understanding of the influence of stress sensitivity on the performance of vertical fractured wells with multiple hydraulic fractures.