Mixed H∞/Passivity controller design through LMI approach applicable for waterflooding optimization in the presence of geological uncertainty

Waterflooding is one of the most popular techniques which are generally used to increase oil recovery factor in mature reservoirs. A challenging issue in conducting the waterflooding process is how to handle the effects of exiting reservoir uncertainties. To this aim, in this paper an optimization algorithm based on Mixed H-infinity/passivity controller design is introduced. The presented approach is capable to systematically take into account the unpredicted influences of inherent geological uncertainties on the production regime, while guaranteeing the stability and disturbance attenuation in the closed-loop system. In addition, this technique expresses energy transition between system states and disturbances, which are representatives of the uncertainty effects. In this study, the optimization problem has been formulated such that the gained profit (here, the net present value: npv) is maximized, while dealing with the operational constraints and also the uncertainty impacts. The defined performance index is able to simultaneously achieve the H-infinity performance and the passivity property, in the presence of inherent uncertainties. The optimization problem has been solved by Linear Matrix Inequality (LMI) approach. The developed algorithm has been simulated on 10th SPE-model#2 as a well-known case study, by generating hypothetical uncertainty in the permeability grids. The obtained results have shown that the designed controller can appropriately adjust the water injection profile, known as the manipulated variable, to achieve the maximum feasible npv in the presence of uncertainty and operational constraints. Finally, further analysis has been provided to compare the introduced methodology with conventional robust optimization approach. (C) 2020 Elsevier Ltd. All rights reserved.