Production Optimization Using Gradient-Free Methods
O. Isebor and L. Durlofsky
The determination of optimum well controls represents a challenging optimization problem which is an integral component of the more general closed-loop approach to reservoir management. A very efficient technique that has been used to address this problem is the adjoint method, which provides gradients of the objective function (cumulative oil production, net present value, etc.) with respect to the well controls. Having these gradients, an appropriate gradient-based optimization algorithm can be used to maximize the objective function. A limitation of this technique is that it is difficult to implement and requires linkage to the simulator at the level of source code for the calculation of the gradients. This can be very restrictive if using commercial simulators, or if an entire workflow is involved in the computations and one needs to obtain gradients from multiple applications. In addition, the adjoint method converges to local minima. For these reasons, it is useful to investigate alternative methods that treat the simulator as a black box and are also easy to implement.
Figure 1. Synthetic 2D reservoir used to
assess performance of methods.
This work involves a study of some gradient-free alternatives to the adjoint method for the purpose of solving the production optimization problem. The optimization methods considered thus far are genetic algorithms (GAs), general pattern search (GPS), and mesh adaptive direct search (MADS). The performance of these methods, together with the adjoint method, is compared for a synthetic reservoir under waterflood (See Figures 1 and 2).
As expected, the adjoint method significantly outperforms the gradient-free procedures, typically achieving better optimum solutions in hundreds of simulations as compared to thousands of simulations for the gradient-free methods. However, it must be kept in mind that the gradient-free methods can be easily parallelized and require much less effort to implement.
Figure 2. Comparison of evolution of NPV for the different methods.
In addition to comparing different algorithms, we also investigate using proxies to improve the performance of the GA, as well as hybridization methodologies that combine aspects of the GA and adjoint procedures. It has been shown that the use of a neural network proxy with the GA substantially improves its performance, and that the hybridization of the GA and adjoint methods represents a viable means for providing different initial guesses for the adjoint procedure. Current work is geared towards improving the performance of the above mentioned gradient-free methods, as well as looking into other methods.