## 1 Introduction  
With the advancement of exploration technology and the broadening of exploration scope, the buried hill reservoir situated on an uncomformity surface within a bedrock reservoir has emerged as a significant area for oil and gas exploration and accumulation [1, 2]. Large reserves have been uncovered in several oil and gas fields worldwide, including the Oiongondapan buried hill field in China, the Baihu field in the Mekong Basin of Southeast Asia and the fields in the Bongor and Sirte Basins of Africa [3, 4, 5]. Metamorphic rock buried hills mostly produce fractured condensate gas reservoirs. The amount of reserve and their level of enrichment are closely tied to the degree of fracture development and permeability [6, 7]. By examining the effectiveness of fractures, well productivity is determined by pinpointing effective reservoirs. Due to the complexity of the lithology and strong heterogeneity of reservoir in the metamorphic buried hill undergoing multi-stage tectonic movement. Traditional techniques for interpreting fractures are not appropriate for metamorphic rock reservoirs. These methods fail to meet the necessary requirements for further exploration and development. Currently, well productivity of fractured reservoir is evaluated primarily through three methods: the conventional well test productivity equation method, the analytical formula based on the seepage model, and the empirical formula based on well logging data. For instance, [PERSON] examined the effects of turbulence on gas flow within the formation and utilized the pseudo-pressure method in well testing to forecast gas well output [8]. [PERSON] et al. combined with well productivity test to obtain empirical values of the well and then used the well testing one-point method equation to predict gas well production capacity [9]. [PERSON] et al. opted for the well test productivity evaluation equation for pressure and pressure flat method to promptly calculate productivity using distinct PVT data from real gas reservoirs [10]. [PERSON] et al. also performed similar research. The authors developed analytical calculation formulas for well productivity by constructing the equivalent formation coefficient of fractured gas reservoirs using a seepage model [11]. [PERSON] et al. forecasted the production of fractured reservoirs employing the Stehfest numerical inversion technique based on the seepage and mathematical models of fractured reservoirs [12]. [PERSON] proposed an equivalent simulation method to characterize fractured reservoirs for different types of reservoir models, which guides well productivity prediction by taking into account the natural characteristics of fractured gas reservoirs [13]. [PERSON] et al. utilised geological, seismic, well logging and engineering data to define the attributes of natural fractured basement reservoirs in carbonate formations to enhance production prediction accuracy [14]. [PERSON] et al. assessed gas well productivity quantitatively by establishing a relationship between rock elastic modulus and fracture porosity, and combines it with production profile logging [15]. [PERSON] et al. established the relationship between the fracture productivity coefficient interpreted by imaging logging and meter gas production index to predict the regression formula of gas well productivity [16]. [PERSON] used the effective permeability of oil and gas reservoirs as a breakthrough point and established a method for predicting production capacity using conventional logging data before oil and gas reservoir testing [17]. The methods for predicting the productivity of fractured gas reservoirs include the one-point method, binomial equation method, productivity prediction model based on seepage mechanics, and empirical formula method based on logging data. All of these methods rely on the physical and fluid parameters of the reservoir for the prediction and evaluation of productivity.