Regularization of Water Flooding Optimization

The use of smart well technology to optimize water flooding introduces a large number of control parameters both in space (well segments) and time. The problem of finding the optimal control parameters to maximize net present value as an objective function can be solved with the aid of a gradient-based optimization method. Using too many parameters may lead to a large number of local maxima in the objective function, so the gradient-based optimization method may result in suboptimal solutions. In this thesis, proper orthogonal decomposition is applied to regularize gradient-based control parameter optimization by projecting the original high dimensional control space onto a low dimensional subspace and thus reduce the number of control parameters. Since in a low dimensional subspace there are fewer local maxima, the solution is more likely to reach a local maximum that is in the close vicinity of the global solution. To evaluate the efficiency of our proposed method, ordinary multiscale parameterization as developed by Lien et al. (2005) is also applied to the optimization of the control parameters. A multiscale approach starts from optimization of a very coarse representative parameter. Then the number of parameters is gradually increased until convergence is reached. Numerical examples indicate that a regularization approach with the aid of proper orthogonal decomposition may speed up the convergence rate, and also may increase the convergence to the global solution within shorter optimization time compared to optimization without regularization technique. The method effectively reduces the control effort by grouping multiple well settings in space and time and treating them as one control parameter.Section for Petroleum EngineeringDepartment of GeotechnologyCivil Engineering and Geoscience