This study established an analytical method for simplified productivity equations based on field-measured reservoir PVT data and gas testing data from 17 wells in the Xihu Sag, and systematically investigated the application conditions of the p-binomial and p2-binomial equations. The results indicate that the core of the applicable pressure intervals for the two simplified equations lies in the pressure ranges on the natural gas \(\overline{m }\left(p\right)\) ~p and \(\overline{m }\left(p\right)\) ~p2 curves that pass through the test points of gas wells and exhibit an approximately linear relationship. The deviation of these curves from the straight line in the low-pressure stage is the primary cause of computational deviations. Further quantification resulted in the establishment of the following applicable criteria. For the p2-binomial, the applicable conditions are a test pressure difference (pr – pwf) ≤ 18 MPa and a formation pressure pr < 40.06 MPa. Specifically, when pr ≤ 18 MPa, it enables the calculation of complete IPR curves including the absolute open flow; when 18 MPa < pr < 40.06 MPa, it is only applicable to the interval (pr - 18 MPa) ≤ pwf ≤ pr. For the p-binomial, the applicable conditions are a test flowing pressure pwf ≥ 22.06 MPa and a formation pressure pr ≥ 40.06 MPa, and it is only applicable to the interval 22.06 MPa ≤ pwf ≤ pr. Selecting simplified productivity equations based on these criteria can effectively mitigate IPR curve deviations caused by improper model selection, particularly in the low-pressure stage. The research findings provide technical support for accurate productivity evaluation of gas wells in the Xihu Sag and serve as a reference quantitative standard for the application of simplified equations in other small-to-medium-sized reservoirs lacking PVT data in China, thereby holding significant engineering practical value.
