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Mathematical Problems in Engineering
Volume 2018, Article ID 1040476, 13 pages
https://doi.org/10.1155/2018/1040476
Research Article

A Numerical Computation Approach for the Optimal Control of ASP Flooding Based on Adaptive Strategies

1Automation School, Beijing University of Posts and Telecommunications, Beijing 100876, China
2College of Information and Control Engineering, China University of Petroleum (East China), Qingdao 266580, China

Correspondence should be addressed to Shurong Li; nc.ude.tpub@gnoruhsil

Received 12 December 2017; Revised 28 April 2018; Accepted 3 May 2018; Published 31 May 2018

Academic Editor: Łukasz Jankowski

Copyright © 2018 Shurong Li and Yulei Ge. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A numerical computation approach based on constraint aggregation and pseudospectral method is proposed to solve the optimal control of alkali/surfactant/polymer (ASP) flooding. At first, all path constraints are aggregated into one terminal condition by applying a Kreisselmeier-Steinhauser (KS) function. After being transformed into a multistage problem by control vector parameter, a normalized time variable is introduced to convert the original problem into a fixed final time optimal control problem. Then the problem is discretized to nonlinear programming by using Legendre-Gauss pseudospectral method, whose numerical solutions can be obtained by sequential quadratic programming (SQP) method through solving the KKT optimality conditions. Additionally, two adaptive strategies are applied to improve the procedure: the adaptive constraint aggregation is used to regulate the parameter ρ in KS function and the adaptive Legendre-Gauss (LG) method is used to adjust the number of subinterval divisions and LG points. Finally, the optimal control of ASP flooding is solved by the proposed method. Simulation results show the feasibility and effectiveness of the proposed method.