A quantum computing-based numerical method of mixed-integer optimal control problems under uncertainty for alkali–surfactant–polymer flooding

Abstract

ABSTRACT This article presents a numerical method based on quantum computing to solve two unresolved key issues for alkali–surfactant–polymer (ASP) flooding in oil exploitation: uncertainties affecting development planning and a switch control regarding injection oil wells. First, a fuzzy multi-objective mixed-integer optimal control model describing the mechanism of ASP flooding is established. Then, an improved possibilistic programming algorithm is presented to remove fuzziness and transform the model into a deterministic single-objective mixed-integer nonlinear programming (MINLP) model. On this basis, a bi-level quantum computing algorithm including quantum annealing and quantum ant colony algorithm is proposed to solve the MINLP and acquire the optimal mixed-integer control variables. The superiority of the proposed algorithm is verified by testing a number of benchmark examples. Finally, the numerical method based on quantum computing is adopted to solve successfully a mixed-integer optimal control problem for ASP flooding under uncertainty.