Fracture geometries and drainage radius are important parameters for developing a reasonable development plan of a single fractured well. In some unconventional gas reservoir, some scholars observed the phenomenon of single well controlled reserves increasing through the material balance curve, and put forward the idea of district supply. In addition, owing to fracture hits, the fracture geometries of fractured wells are sometimes more complex. Thus, those complex factors bring challenges for parameter estimations. In order to study the variation of the drainage radius and complex fracture geometries in the single model, a well testing based model for a finite-conductivity fractured vertical well in radial composite reservoirs with dynamic supply and fracture networks is established. Based on "successive steady state method", the point source function, pressure superposition principle and boundary element method are used to solve the reservoir model, and the methods of discrete fracture and pressure superposition are used to solve the fracture model. By introducing the rate normalized pseudo-pressure and material balance time, the variable fluid flux is equivalent to the constant fluid flux. Combined with the inversion idea of well test, the drainage radius value and fracture geometries are solved by fitting the log-log curves of pressure response, and case studies are performed. The results show that the drainage radius increases with the increase of production time and finally tends to a certain value, and it has a good exponential relationship with time. Also, the fracture geometries of the typical well are multiple-radial fracture networks. Through the study of dynamic drainage radius, the controlled reserves of single well in unconventional gas reservoir can be better determined, and it can also provide theoretical basis for fracture evaluation, productivity prediction and enhanced recovery study of the same type of unconventional gas reservoir.