Owing to the limitations of physical experiments on heavy oil, this study establishes a mathematical model for heavy oil–water two-phase flow based on the theory of multiphase flow, considering factors such as heavy oil viscosity, mixed flow velocity, and inlet water cut. Through transient calculations of 650 groups of heavy oil–water two-phase flows based on this model, six typical heavy oil–water two-phase flow patterns were identified by monitoring flow pattern cloud images, liquid holdup, and the probability density function (PDF) of liquid holdup: water-in-oil bubble flow, transitional flow, water-in-oil slug flow, oil-in-water bubble flow, oil-in-water very fine dispersed flow, and water-in-oil core-annular flow. Five sets of flow pattern maps for a heavy oil–water two-phase flow with different viscosities were established based on the inlet water cut and mixed flow velocity. The results showed that different heavy oil viscosities lead to different oil–water two-phase flow patterns. When the heavy oil viscosity is 100 mPa·s, the flow patterns include water-in-oil bubble flow, transitional flow, water-in-oil slug flow, oil-in-water bubble flow, and oil-in-water very fine dispersed bubble flow. When the heavy oil viscosity reaches 600 mPa·s, a water-in-oil core-annular flow appears, and the oil-in-water very fine dispersed bubble flow disappears. After the heavy oil viscosity exceeds 1100 mPa·s, the oil-in-water bubble flow disappears. Among the different flow patterns, the range of the water-in-oil slug flow is most affected by the viscosity and flow velocity. The greater the heavy oil viscosity, the larger the range. When the viscosity remained constant, a larger flow velocity resulted in a smaller range. The accuracy of the flow pattern predictions in the maps was verified by comparing them with field production data, confirming that the research results can provide a theoretical basis for understanding oil–water two-phase flow patterns in heavy oil wellbores.

As one of the main numerical methods, the boundary element method boasts the advantages of fast computation speed and high accuracy. Based on the considerations of the influence of pressure drop, perforation height, skin coefficient, reservoir coefficient, and reservoir radius on the seepage law, a novel three-dimensional seepage model for vertical wells was established using the Laplace transform method and Stehfest numerical inversion method. The model was utilized to examine the velocity of pressure propagation and drop amplitude, revealing that the near-well area experienced faster propagation and drop than the far-well area. During dimensional analysis, it was observed that neglecting the effects of formation pressure change could lead to a substantial increase in the dimensional error of bottom hole pressure, with a maximum error of 9.45% recorded in this study. Additionally, a sensitivity analysis was conducted on perforation length, wellbore reservoir coefficient, skin coefficient, and reservoir radius to further elucidate the seepage law of vertical wells. This study provides theoretical guidance for oil and gas production. The original contribution of this research lies in the incorporation of formation pressure changes into the three-dimensional seepage model of vertical wells for the first time, which significantly enhances the model’s accuracy and practicality.