Production performance analysis model of partially penetrated fractured vertical well in reservoir with high formation-saturation pressure difference

As the changes of oil properties and stress-sensitive formation permeability, the flow governing equations for early-stage depletion development in reservoirs with high formation-saturation pressure difference is strong nonlinear. By the definition of pseudo-pressure function and pseudo-time factor and considering partially penetrated vertical fracture wells in such reservoirs, the mathematical model was established. Using Laplace transform, finite Fourier cosine transform, and the point sink superposition principle, the bottomhole pressure solution for a partially penetrated infinite-conductivity vertical fracture well was obtained. By incorporating the conductivity influence function, Duhamel's convolution principle and material balance equation of closed reservoir, the production solution for a finite-conductivity fracture well was further derived. Parameter sensitivity analysis demonstrates that: for reservoirs with high formation-saturation pressure difference exhibiting stress sensitivity, implementing a rational production strategy can effectively avoid both formation permeability damage caused by excessive drawdown and the risk of dissolved gas liberates due to rapid pressure decline. The objectives should be central fracture placement within the reservoir and a vertical penetration ratio exceeding 0.5 when fracturing designing. Besides, the optimal fracture half-length and permeability should be determined based on geological characteristics and operational constraints. This study provides a methodology for forecasting production performance and inverting formation parameters of partially penetrated wells in reservoirs with high formation-saturation pressure difference. It also offers a theoretical basis for optimizing production strategies and determining the timing for formation energy replenishment in such reservoirs.