Optimal Rate Control Under Geologic Uncertainty

Abstract

Abstract Waterflood optimization via rate control is receiving increased interest because of rapid developments in the smart well completions and i-field technology. The use of inflow control valves (ICV) allows us to optimize the production/injection rates of various segments along the wellbore, thereby maximizing sweep efficiency and delaying water breakthrough. A major challenge for practical field implementation of this technology is dealing with geologic uncertainty. In practice, the reservoir geology is known only in a probabilistic sense; hence, the optimization of smart wells should be carried out in a stochastic framework to account for geologic uncertainty. We propose a practical and efficient approach for computing optimal injection and production rates accounting for geological uncertainty. The approach relies on equalizing arrival time of the waterfront at all producers using multiple geologic realizations. The main objective is to improve sweep efficiency and thereby improve oil production and recovery. We account for geologic uncertainty using two optimization schemes. The first one is to formulate the objective function in a stochastic form which relies on a combination of expected value and standard deviation combined with a risk attitude coefficient. The second one is to minimize the worst case scenario using a min-max problem formulation. The optimization is performed under operational and facility constraints using a sequential quadratic programming approach. A major advantage of our approach is the analytical computation of the gradient and Hessian of the objective function which makes it computationally efficient and suitable for large field cases. Multiple examples are presented to support the robustness and efficiency of the proposed optimization scheme. These include 2D synthetic examples for validation and a 3D field-scale application. The role of geologic uncertainty in the outcome of the optimization is demonstrated both during the early stage and also, later stages of waterflooding when substantial production history is available. Introduction The recent increase in oil demand worldwide combined with the decreasing number of new discoveries has underscored the need to efficiently produce existing oil fields. The maturity of most of the existing large fields requires prudent reservoir management and development strategies to maximize recovery. With this goal in mind, the use of smart/complex wells and completions are becoming increasingly common place. Among the various improved recovery schemes, waterflooding is by far the most widely used (Craig 1971; Lake et al., 1992). In spite of its many appealing characteristics, the presence of heterogeneity such as high permeability streaks might yield unfavorable results, causing premature breakthrough, poor sweep and consequently reduce oil production and recovery (Sudaryanto and Yortsos 2001; Brouwer and Jansen 2004; Alhuthali et al., 2007). Various methods have been suggested to mitigate this problem. Among these is smart well completion where the production or the injection section is divided into several intervals (Arenas and Dolle 2003; Glandt 2005). The flow rate at each interval can be independently controlled by inflow control valves (ICVs), making it possible to manage the flood front in highly heterogeneous reservoirs.