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 work, 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.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

Keywords:

regularization , ordinary multiscale parameterization , proper orthogonal decomposition , water flooding , closed-loop reservoir management , smart wells