Critical Review of the Percentage of Cumulative Oil Production with Sequential Quadratic Programming Technique for Gas Lifted Wells

Gas lift optimisation presents a complex, nonlinear constrained problem in petroleum engineering, where dynamic well interactions, multiphase flow behaviour, and stringent operational constraints pose significant computational challenges. This study systematically reviews the application of Sequential Quadratic Programming (SQP) as an advanced numerical optimisation technique for gas lift performance enhancement. SQP’s mathematical foundation, rooted in second-order approximations of the objective function and constraints, leverages Hessian approximations and Lagrange multipliers to achieve superior solution accuracy and convergence efficiency. Comparative analyses demonstrate SQP’s superiority over conventional optimisation methods such as Mixed-Integer Linear Programming (MILP) and the Augmented Lagrangian (AL) method. Unlike MILP, which struggles with nonlinear deliverability constraints, and AL, which exhibits minor constraint violations, SQP ensures strict constraint adherence while optimising gas injection rates. The method’s computational efficiency is attributed to advanced gradient estimation, parallel processing capabilities, and QR factorisation updates, making it highly effective for large-scale gas lift networks. Notably, SQP-driven optimisation has been shown to improve Net Present Value (NPV) by up to 42% and increase oil production by 45% through optimal gas allocation and stabilisation of intermittent flow regimes. Furthermore, the adaptability of SQP for real-time optimisation enables its seamless integration into industry-standard production simulation tools such as PROSPER, GAP, and OLGA, facilitating dynamic field-wide gas lift coordination. Emerging hybrid SQP frameworks, incorporating augmented Lagrangian strategies and nonlinear steady-state optimisation, further enhance solution robustness and economic performance. Crucially, SQP’s ability to model real-world constraints—including reservoir pressure limits, gas-lift performance curves, and fluctuating operational conditions— demonstrates its viability for practical implementation in complex petroleum production systems. This review establishes SQP as a transformative optimisation framework for gas lift operations, bridging theoretical advancements with real-world applicability. The findings underscore SQP’s computational and economic advantages over conventional methods while paving the way for future research into hybridised algorithms and real-time adaptive gas lift control in large-scale petroleum production networks.