Hybrid FDG optimization method and kriging interpolator to optimize well locations

As the number of new significant oilfields discoveries are reduced and as production operations become more challenging and expensive, the efficient development of oil reservoirs in order to satisfy increasing worldwide demand for oil and gas becomes crucial. A key decision engineers must make is where to drill wells in the reservoir to maximize net present value or some other objectives. Since the number of possible solutions that depend on the size of reservoir can be very large, the use of an optimization algorithm is necessary. Optimization methods are divided into two main categories: non-gradient-based and gradient-based algorithms. In the former, the search strategy is to find global optimum while they need a great number of reservoir simulation runs. On the other hand, gradient-based optimization algorithms search locally but require fewer reservoir simulations. The computational cost of optimization method in the optimal well placement problem is substantial. Thus, in practical problems with large models, implying the gradient-based method is preferable. In the present paper, finite difference gradient (FDG) algorithm as one of the easy implemented gradient-based family is used. The main disadvantage of the mentioned technique is its dependency on the number of decision variables. The major contribution of this paper is to hybrid the FDG method and kriging interpolator. This interpolator is used as a proxy to decrease the required number of function evaluations and estimate the direction of movements in the FDG algorithm. Moreover, the idea of local grid refinement is proposed to eliminate the mixed integer problem of well placement. Then, the method is applied to some sample reservoirs and the simulation results verify the performance of the proposed method.