Efficient Optimization of Production from Smart Wells Based on the Augmented Lagrangian Method

A new method for dynamic optimization of water flooding with smart wells is developed. The algorithm finds optimal injection and production well or well segment rates. In the new method, we solve a constrained optimization problem where the net present value is maximized and the reservoir flow equations are considered as constraints. The problem is formulated as finding the saddle point of the associated augmented Lagrangian functional, and solved efficiently. The method is compared with a more traditional optimal-control method, based on solving the adjoint system of equations. In the examples tested the new method obtains the same maximum profit as the adjoint method using approximately the same number of iterations. An advantage of the new method is that we do not solve the flow equations exactly at each iteration. As the optimization proceeds, the flow equations will be fulfilled at convergence. Thus, each iteration of the minimization algorithm is much cheaper than for the adjoint method. The method is tested on a small 2D model, but the results should be valid also for larger, 3D models.