The study of oil and gas flow patterns after perforation completion is essential for well productivity prediction and solutions optimization. Due to the multi-scale flow characteristics of production fluids after perforation completion, we have developed a multi-scale coupled flow model incorporating Darcy, Brinkman, and Navier/Stokes equations based on mass conservation and pressure equilibrium principles. The oil and gas flow after perforation completion is simulated, and the multi-scale coupled model is solved by numerical methods, revealing the flow law of oil and gas in the multi-scale space formed by perforation. Additionally, sensitivity analysis on factors influencing perforation completion productivity was conducted. Results indicate that the most influential parameters on well productivity, in descending order, are: blocking perforation permeability > perforation diameter > perforation density > perforation depth > perforation phase > crushed zone thickness. The selection of appropriate internal flow models for perforations is critical for accurate well productivity estimation. Given the significant impact of perforation permeability on completion productivity, measures should be taken to prevent perforation blockage during production, and clear blockages promptly upon detection. This research provides a theoretical foundation for rational selection of perforation methods, gun bullets, perforation parameters, and completion techniques.
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