Well placement optimization according to field production curve using gradient-based control methods through dynamic modeling

Abstract Determination of optimal well locations plays an important role in field development. Therefore in recent years, there has been an increasing consideration to solve the problem through systematic methods. The problem usually defined as finding well locations such that maximum profit is achieved. Usually there is an industrial demand for oil and gas production in oil and gas companies with respect to consumers' needs. In such cases tracking the required production curve could be a good choice. For this purpose, in this paper optimal well placement problem is formulated as an optimal control one. In this case, well locations and the field oil production total/rate are input and output variables, respectively. The target is to locate wells such that the output can track a desired pre-specified curve. The curve can be determined according to the industrial gas and oil companies' seasonal need. To our best knowledge this is the first contribution that define well placement as a tracking problem in an optimal control frame work. The first step in solving such problems is modeling. No one can ever deny the significance of an appropriate model. According to reservoir complexity usually neural network and neuro-fuzzy modeling were used. However, because of reservoir uncertainties, dynamical approaches where the model would be updated during the process, could be more helpful. This study presents an approach where a Dynamic Fuzzy Neural Network (DFNN) is applied to generate a model which can perform dynamically. The model will be updated at each iteration due to current reservoir information. On the other hand, since the network starts with no hidden units, there is no need to generate input–output set of data for training purposes for which hundreds of costly and time-consuming simulations are required so simulator runs will be decreased significantly. In the optimization step, gradient based approaches as one of the most common methods in control field are employed. These methods perform the search without being obliged to use the simulator several times and usually are faster due to increment of cost function at each iteration. Finally, the proposed method is evaluated by applying to a 3D 3-phase synthetic reservoir for three different scenarios of well location determination. Simulation results show how a desired curve can be tracked through the method with only few numbers of simulator run and confirm the abilities of the proposed procedure in both modeling and tracking control.