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

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.

[1]  Ping Wang,et al.  The Combination of Adaptive Pseudospectral Method and Structure Detection Procedure for Solving Dynamic Optimization Problems with Discontinuous Control Profiles , 2014 .

[2]  Louis J. Durlofsky,et al.  Production Optimization With Adjoint Models Under Nonlinear Control-State Path Inequality Constraints , 2008 .

[3]  H. H. Spain,et al.  Limitations on Pressure Predictions for Water-Drive Reservoirs , 1958 .

[4]  Alexey F. Izmailov,et al.  Some composite-step constrained optimization methods interpreted via the perturbed sequential quadratic programming framework , 2015, Optim. Methods Softw..

[5]  Wolfgang Marquardt,et al.  Dynamic optimization using adaptive control vector parameterization , 2005, Comput. Chem. Eng..

[6]  Zohreh Fathi,et al.  Use of optimal control theory for computing optimal injection policies for enhanced oil recovery , 1986, Autom..

[7]  Shurong Li,et al.  An approximate dynamic programming method for the optimal control of Alkai-Surfactant-Polymer flooding , 2018 .

[8]  Anil V. Rao,et al.  Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method , 2006 .

[9]  J. S. Aronofsky,et al.  A Linear Programming Model for Scheduling Crude Oil Production , 1958 .

[10]  Usman Ali,et al.  Multiple Shooting Technique for Optimal Control Problems with Application to Power Aware Networks , 2015, ADHS.

[11]  Lorenz T. Biegler,et al.  Dynamic Process Optimization through Adjoint Formulations and Constraint Aggregation , 1999 .

[12]  Yu Hu,et al.  New results on pseudospectral methods for optimal control , 2016, Autom..

[13]  John Matthew Santosuosso,et al.  Dynamic optimization of batch processing , 2003 .

[14]  Yang Lei,et al.  Spatial-Temporal ARX Modeling and Optimization for Polymer Flooding , 2014 .

[15]  Sebastian Engell.  Feedback control for optimal process operation , 2007 .

[16]  Shurong Li,et al.  A Novel Empirical Equation for Relative Permeability in Low Permeability Reservoirs , 2014 .

[17]  Salvador Pintos,et al.  An Optimization Methodology of Alkaline-Surfactant-Polymer Flooding Processes Using Field Scale Numerical Simulation and Multiple Surrogates , 2005 .

[18]  J. Jansen,et al.  A Stochastic Simplex Approximate Gradient (StoSAG) for optimization under uncertainty , 2017 .

[19]  Jishun Qin,et al.  Application and enlightenment of carbon dioxide flooding in the United States of America , 2015 .

[20]  Miguel A. Mariño,et al.  Optimal Control of Ground‐Water Quality Management: Nonlinear Programming Approach , 1994 .

[21]  Zohreh Fathi,et al.  Optimal injection policies for enhanced oil recovery: Part 1-Theory and computational strategies , 1984 .

[22]  Sam Huang,et al.  IMPROVED OIL RECOVERY BY ADSORPTION–DESORPTION IN CHEMICAL FLOODING , 2004 .

[23]  Paul M.J. Van den Hof,et al.  Model-based control of multiphase flow in subsurface oil reservoirs , 2008 .

[24]  Gamal N. Elnagar,et al.  The pseudospectral Legendre method for discretizing optimal control problems , 1995, IEEE Trans. Autom. Control..

[25]  V. V. Karelin.  Penalty Functions in a Control Problem , 2004 .

[26]  William W. Hager,et al.  A unified framework for the numerical solution of optimal control problems using pseudospectral methods , 2010, Autom..

[27]  R. Sargent,et al.  Solution of a Class of Multistage Dynamic Optimization Problems. 2. Problems with Path Constraints , 1994 .

[28]  Tomoki Ohsawa.  Contact geometry of the Pontryagin maximum principle , 2015, Autom..

[29]  Qiang Zhang,et al.  Optimal control of polymer flooding based on mixed-integer iterative dynamic programming , 2011, Int. J. Control.

[30]  Anil V. Rao,et al.  Direct Trajectory Optimization Using a Variable Low-Order Adaptive Pseudospectral Method , 2011 .

[31]  Lorenz T. Biegler,et al.  New strategies for flexibility analysis and design under uncertainty , 2000 .

[32]  Albert C. Reynolds,et al.  Optimal control of ICV's and well operating conditions for the water-alternating-gas injection process , 2017 .

[33]  Amir H. Mohammadi,et al.  Efficient screening of enhanced oil recovery methods and predictive economic analysis , 2014, Neural Computing and Applications.