## 1 Introduction  
Whether CO2 geological sequestration, disposal of high-level radioactive waste, or exploitation of geothermal and hydrocarbon resources, all of them are associated with fractured reservoirs [1; 2; 3]. Therefore, it is increasingly significant to understand fluid flow behavior through naturally fractured reservoir in hydrology, environment, and petroleum engineering. Especially, with the development of natural gas exploration and exploitation in the world, the proven reserves and production of naturally fractured gas reservoirs are increasing year by year [4]. The majority of naturally fractured gas reservoirs exhibit abnormally high-pressured as a result of disequilibrium compaction [5]. In China, Kela-2 gas field in Tarim Basin and Moxi gas field in Sichuan Basin which have been developed for several years are both abnormally high-pressured fractured gas reservoirs. Due to the characteristics of abnormal pressure, the rock and fluid properties of naturally fractured gas reservoirs are commonly pressure-dependent. With microseismic monitoring and transient pressure analysis, it is demonstrated that some naturally fractured gas reservoirs may exhibit composite properties in the radial direction. That is, a large number of natural fractures exist near the wellbore area while the outer region far away from well has fewer ones [6]. Therefore, a composite model is appropriate to analyze the production performance of the well. Composite reservoir models were originally targeted to model special reservoir configuration consisting of two or more concentric zones with different diffusivities or fluid properties. As early as 1960, [PERSON] [7] developed the analytical solution for radially composite reservoirs in which the storativity ratio between two regions are identical. Two decades later, [PERSON] and [PERSON] [8; 9] proposed an analytical solution to analyze pressure transient behavior for wells in finite composite reservoir system. Besides the composite formation with single porosity media in inner and outer regions, many researchers [10; 11; 12; 13; 14] also developed the mathematical model for composite dual-porosity reservoirs. Subsequently, [PERSON] and [PERSON] [15] solved fluid flow problems in composite reservoirs by reflection and transmission theory of electromagnetics. In recent years, composite model is applied to describe stimulated region volume around well in unconventional reservoirs [16; 17; 18]. Unfortunately, most literature aimed at studying fully penetrated wells in composite reservoirs. Nevertheless, some wells in actual fields were partially penetrated especially in thick formations. For the research of partially penetrated wells, extensive works were carried out in hydrology and petroleum engineering. [PERSON] [19] first investigated steady flow through porous media for partially penetrated vertical well. [PERSON] [20] and [PERSON] and [PERSON] [21] studied the effect of partial penetration on the pressure drawdown and buildup of oil wells in an isotropic layer with no-flow boundary conditions at the top and bottom of the layer. [PERSON] [22] established the steady-state flow model of partially penetrated well by Fourier transforms. [PERSON] and [PERSON] [23] studied the combined effect of anisotropy and stratification with crossflow on pressure response for partially penetrated well. With Laplace and Hankel transforms, [PERSON] [24; 25; 26] solved the unsteady-state flow problems for partially penetrated well. The Laplace transform was also used by [PERSON] and [PERSON] [27] to analyze hydraulics problem for a partially penetrated well in a dual-porosity reservoir. [PERSON] et al. [28] developed an analytical solution to analyze transient pressure behavior of partially penetrated wells in naturally fractured reservoirs with infinite radial extent. Based on the solution of [PERSON] et al. [28], a set of pressure derivative type curves were generated by [PERSON] and [PERSON] [29]. Recently, [PERSON] et al.