In recent years, Shallow water Christmas trees have made a significant breakthrough internationally. It fills technological gaps, alleviates energy shortages, and offers innovative solutions for global shallow - water oil and gas development. However, this development faces challenges like special wellbore structures, complex temperature - pressure systems, and downhole operation uncertainties. These issues lead to poor wellbore pressure control and high well - control risks. Traditional steady - state models assume constant flow parameters. They fail to accurately depict wellbore dynamics, ignoring gas - liquid slippage and transient effects. As result, conventional commercial well control software exhibits significant calculation discrepancies, which hinders the design of effective well kill operations. This study introduces a semi-discrete relaxation strategy to address simulation challenges in shallow water environments. By reformulating gas-liquid two-phase flow equations into a semi-linear model with relaxation coefficients, numerical stability is enhanced. The system's dynamic evolution is analyzed using the Chapman-Enskog asymptotic expansion, while the FVS algorithm decomposes source terms to improve accuracy. Flow directions and boundary conditions are determined by solving the characteristic lines of the Jacobian matrix, enabling precise parameter calculation for the Driller’s Method. Practical applications confirm that this method significantly improves the stability and accuracy of transient wellbore simulations, offering an optimized strategy for well control operations. • Algorithmic Integration Innovation For the first time, the semi-discrete method is integrated with the FVS algorithm for solving gas-liquid two-phase flow models. The semi-discrete method transforms the nonlinear hyperbolic system into a semi-linear model, after which the FVS algorithm decomposes the source terms. This integration enables precise capture of the complex dynamic behaviors of fluid flow within the wellbore, significantly enhancing computational accuracy and numerical stability. It breaks through the limitations of traditional algorithms in resolving small-scale flow features. • Engineering Research Innovation This study conducts the first systematic research on well-killing operations in the development mode of shallow-water Christmas tree equipment, filling a gap in both theoretical and engineering practice. By thoroughly analyzing the unique wellbore structures, complex temperature-pressure systems, and operational uncertainties in shallow water, it proposes targeted well-killing strategies, providing a new technical approach and practical guidance for global shallow-water oil and gas development. • Boundary Condition Solution Innovation Through solving the characteristic lines of the Jacobian matrix to analyze the propagation of boundary physical quantities, this research achieves precise solutions for the boundary conditions during well-killing operations in shallow-water wellbores. Compared with the traditional first-order extrapolation method, which often causes numerical oscillations, this approach accurately determines the inflow and outflow directions of fluids and precisely calculates key parameters such as pressure and velocity. As a result, it significantly improves the reliability and engineering practicability of well-killing operation simulations.
Xiao et al. (Sun,) studied this question.