Optimizing smart well controls under geologic uncertainty Ahmed H. Alhuthali a,b , Akhil Datta-Gupta a, ⁎, Bevan Yuen b , Jerry P. Fontanilla b a Petroleum Engineering Department, TAMU 3116, Texas A&M University, College Station, TX 77843-3116, USA b Saudi Aramco, Dhahran 31311, Saudi Arabia abstract article info Article history: Received 17 December 2008 Accepted 15 May 2010 Keywords: optimal rate control geologic uncertainty time-of-flight arrival time sensitivity sequential quadratic programming 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, the later stages of waterflooding when substantial production history is available. © 2010 Elsevier B.V. All rights reserved. 1. 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 in- creasingly 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. The advantages of the smart well technology have also inspired the development of efficient algorithms to optimize production/injection along the intervals of smart wells, and thereby improved sweep efficiency. Two broad classes of optimization algorithms have been used, namely gradient-based algorithms and stochastic algorithms (Brouwer and Jansen, 2004; Tavakkolian et al., 2004). The gradient- based algorithms require an efficient estimation of the gradient of the objective function with respect to the control variables. In contrast, the stochastic algorithms such as the genetic algorithm require multiple forward simulations to explore the search space of the control variables. The advantage of stochastic optimization is its ability to search for a global solution while the gradient-based optimizations typically converge to a local solution. However, the stochastic optimization methods can be computationally demanding, especially when the number of control variables is large. Journal of Petroleum Science and Engineering 73 (2010) 107–121 ⁎ Corresponding author. Fax: + 1 979 845 1307. E-mail address: datta-gupta@pe.tamu.edu (A. Datta-Gupta). 0920-4105/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2010.05.012 Contents lists available at ScienceDirect Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol