Abstract: To address the limitation of existing models that cannot simultaneously characterize the fractal features of hydraulic fracture networks in tight reservoirs,the fractal characteristics of the matrix system and the effects of stress sensitivity,fractal theory was employed to characterize the complex morphology of fracture networks within the hydraulically stimulated region and the heterogeneity of the matrix system in the unstimulated region.An analytical well test model for a stress-sensitive tight reservoir subjected to volumetric fracturing in a vertical well was established.Dimensionless pressure and pressure-derivative type curves were generated,characteristic flow regimes were identified and sensitivity analyses of relevant parameters were conducted.The results indicate that fluid flow in a volumetrically fractured vertical well completed in a fractal tight reservoir can be classified,into six typical flow regimes,according to well test curve characteristics:wellbore storage,early transition flow,linear flow,early pseudo-radial flow,inter-region transition flow between inner and outer zones,and second radial flow.The fractal parameters of the stimulated region exert a pronounced influence on the well test curves during the linear flow regime and subsequent stages.The fractal parameters of the unstimulated region primarily affect the characteristics of the well test curves during the inter-region transition flow and the second radial flow stages.The stress sensitivity effect mainly influences the mid-to late-time bottom-hole pressure response.These findings provide important guidance for evaluating hydraulic fracturing performance in vertical wells in heterogeneous tight gas reservoirs and for determining dynamic reservoir parameters.

Key words: hydraulic fracturing, vertical well, tight gas reservoir, fractal theory, stimulated region, stress sensitivity, transient pressure behavior