## 2 Construction of Productivity Prediction Method of Reservoir
### Construction of Productivity Coefficients  
For fractured reservoirs located in buried hills of metamorphic rocks, well productivity evaluation is carried out through DST testing. This method offers the benefits of fast speed and abundant data acquisition. However, it also has the disadvantage of lengthy well test section. Due to strong heterogeneity, the reservoir displays intricate seepage patterns, causing discontinuity in the vertical direction of the reservoir's effectiveness. As a result, the effective thickness of reservoir is significantly smaller than well test section. Furthermore, testing operations may face potential contamination and additional pressure at the well's bottom. Based on the aforementioned scenario, it is challenging to depict the actual production capacity of the reservoir through a comparison of the gas production index J (Equation (8)), The equation is expressed as [16]:  
\[J=\frac{Q_{\text{g}}}{(P_{\text{e}}-P_{\text{wf}})h} \tag{8}\]  
where \(J\) is the meter gas production index, (104 m\({}^{3}\cdot\)(d\(\cdot\)MPa\(\cdot\)m)\({}^{-1}\)); \(Q\)g is the daily gas production, 104 m\({}^{3}\)/d; \(P_{\text{e}}\) is the formation pressure, MPa; \(P_{\text{wf}}\) is the bottom hole flowing pressure, MPa; \(h\) is the thickness of test section, m.  
To address well productivity evaluation, this article initially utilizes imaging logging data-derived fracture parameters to form the fracture effectiveness index. Furthermore, it thoroughly analyses conventional logging and array acoustic data to establish the effective reservoir thickness. Using the skin coefficient derived from well-test data, one can determine the actual productivity coefficient of the reservoir by calculating the pressure drop. The use of the productivity coefficient Ji, as compared to the gas production index J, can improve the precision of reservoir productivity evaluation (Equation (9)). \[J_{i}=\frac{Q_{\text{g}}}{(\Delta P_{i})h_{i}} \tag{9}\]  
where \(Ji\) is the real productivity coefficient of the reservoir, (104 m\({}^{3}\cdot\)(d\(\cdot\)MPa\(\cdot\)m)\({}^{-1}\)); \(Q\)g is the daily gas production, 104 m\({}^{3}\)/d; \(\Delta p\) = \(P_{\text{e}}-P_{\text{wf}}+P_{\text{s}}\), \(P_{\text{s}}\) is the additional pressure, MPa; \(h_{i}\) is the effective reservoir thickness determined by the fracture index, m.  
The gas production capacity of fractured reservoirs heavily relies on their effective thickness and permeability. As a result, variations in the effectiveness and permeability of reservoirs occur between wells, leading to significant variances in test yields among different exploration wells. To improve the comparability of logging data in both vertical and horizontal directions between individual wells, it is essential to consider these differences. This article employs the fracture parameter ratio technique, which measures the fracture parameter ratio E between the tight section and the reservoir section (Equation (10)). By avoiding subjective evaluations and excluding the influence of good conditions, wellbore diameters, lithology and other related factors on the calculation results, this method allows for a better assessment of fracture parameters impacting on the fracture efficiency and formation permeability. By combining conventional logging, and mud logging data to verify the accuracy of reservoir effectiveness and permeability of multiple test wells,the quantitative evaluation criteria for effectiveness and permeability in the study area is achieved, The equation is expressed as [23]:  
\[E=\frac{\sum\limits_{i=1}^{N}R_{i}}{\sum\limits_{i=1}^{N}R_{O}} \tag{10}\]  
In the Equation (10) for calculating the effectiveness ratio, \(Ri\) is the fracture effectiveness index of the dense interval, dimensionless; \(Ro\) is the fracture effectiveness index of the effective formation interval, dimensionless; When calculating the permeability ratio, \(Ri\) is the permeability index of the dense interval, dimensionless; Ro is the permeability index of the effective formation interval, dimensionless.