Adjoint-Based Well Trajectory Optimization

Abstract

Abstract The selection of optimal well locations and trajectories is a challenging and important step in a field development plan. Selecting the optimal trajectory of a deviated well is an arduous task, which is usually done manually. In this study we demonstrate the use of a new technique to assist the determination of the optimal well trajectory with the aid of a gradient-based search method. Our approach is based on surrounding the well trajectory with side tracks to all adjacent grid blocks. These side tracks have such a small perforation and thus production rate that they hardly influence the production through the main well bore. The gradients of the side track contributions to the net present value (NPV) of the well with respect to their positions are approximated using a reservoir simulator equipped with adjoint functionality. Using the approximate gradients of the side track contributions, coordinates for a new trajectory are selected, and with these a new well trajectory is constructed. The curvature of the trajectory is restricted to stay within predefined drillability constraints expressed in terms of dog-leg severity. The process is repeated until a location with a maximum NPV is reached. The reservoir model to demonstrate the optimization technique represents a 3-dimensional heterogeneous reservoir located in a tilted anticline cut off by a fault running through the top of the anticline. It contains a thin oil rim drained by a single deviated well with a given kick-off point and a trajectory that has to be optimized within drillability constraints. The optimization results show a significant improvement in NPV of the well. Depending on the value that is assigned to the reservoir fluids (gas, oil and water) in the cost function, the well will seek a path in the reservoir that leads either away from the gas cap (in case of gas disposal), or towards the gas cap (in case of gas sales). Introduction Deciding on a well trajectory with the aim of obtaining an optimal project NPV is usually done manually. A large number of sensitivity runs in a reservoir simulator combined with geosciences and engineering insights result in a chosen well trajectory. The purpose of this paper is to propose a method to automate this process, at least to a certain extent, with an iterative gradient-based algorithm that approaches the optimal well trajectory in a reasonable number of steps. Zandvliet et al. (2008) have previously successfully used a similar approach for well location optimization, but only for 2-dimensional well placement in a relative simple reservoir. In this paper their method is extended to a three-dimensional model and a full well trajectory instead of only a surface location. The method is tested on a reservoir model for a thin oil rim with a relatively large gas cap and aquifer. In such a thin oil rim the optimal well trajectory is very important because water coning and gas cusping are likely to occur very soon and limit the oil production. The well trajectory is therefore very sensitive to minor adjustments.