On Improving Algorithm Efficiency of Gas-Kick Simulations toward Automated Influx Management: A Robertson Differential-Algebraic-Equation Problem Approach

Improved numerical efficiency in simulating wellbore gas-influx behaviors is essential for realizing real-time model-prediction-based gas-influx management in wells equipped with managed-pressure-drilling (MPD) systems. Currently, most solution algorithms for high-fidelitymultiphase-flow models are highly time consuming and are not suitable for real-time decision making and control. In the application of model-predictive controllers (MPCs), long calculation time can lead to large overshoots and low control efficiency. This paper presents a drift-flux-model (DFM)-based gas-influx simulator with a novel numerical scheme for improved computational efficiency. The solution algorithm to a Robertson problem as differential algebraic equations (DAEs) was used as the numerical scheme to solve the control equations of the DFM in this study. The numerical stability and computational efficiency of this numerical scheme and the widely used flux-splitting methods are compared and analyzed. Results show that the Robertson DAE problem approach significantly reduces the total number of arithmetic operations and the computational time compared with the hybrid advection-upstream-splitting method (AUSMV) while maintaining the same prediction accuracy. According to the “Big-O notation” analysis, the Robertson DAE approach shows a lower-order growth of computational complexity, proving its good potential in enhancing numerical efficiency, especially when handling simulations with larger scales. The validation of both the numerical schemes for the solution of the DFM was performed using measured data from a test well drilled with water-based mud (WBM). This study offers a novel numerical solution to the DFM that can significantly reduce the computational time required for gas-kick simulation while maintaining high prediction accuracy. This approach enables the application of high-fidelity two-phase-flow models in model-prediction-based decision making and automated influx management with MPD systems.