Please cite this article in press as: Forouzanfar, F., Reynolds, A.C., Joint optimization of number of wells, well locations and controls using a gradient-based algorithm. Chem. Eng. Res. Des. (2013), http://dx.doi.org/10.1016/j.cherd.2013.11.006 ARTICLE IN PRESS CHERD-1412; No. of Pages 14 chemical engineering research and design x x x ( 2 0 1 3 ) xxx–xxx Contents lists available at ScienceDirect Chemical Engineering Research and Design j ourna l h omepage: www.elsevier.com/locate/cherd Joint optimization of number of wells, well locations and controls using a gradient-based algorithm Fahim Forouzanfar * , A.C. Reynolds The University of Tulsa, 800 South Tucker Drive, Tulsa, OK 74104, United States a b s t r a c t This paper presents a detailed algorithm for solving the general well-placement optimization problem in which the number of wells, their locations and rates are simultaneously optimized with an efficient gradient-based algorithm. The proposed well-placement optimization algorithm begins by placing a large number of wells in the reservoir, where, the well rates are the optimization variables. During iterations of the algorithm, most of the wells are elimi- nated by setting their rates to zero. The remaining wells and their controls determine the optimal number of wells, their optimum locations and rates. The well-placement algorithm consists of two optimization stages. In the initial- ization stage, the appropriate total reservoir production rate (or the total injection rate) for the set of to-be-optimized producers (or injectors) is estimated by maximizing the net-present-value for the specified operational life of the reservoir. In the second stage, a modified net-present-value functional which also considers the drilling cost of the wells is maximized subject to the a total rate constraint determined in the initialization stage. Both stages of the algorithm use gradient projection to enforce the linear and bound constraints, where the required gradients are computed with the adjoint method. The bottomhole pressure constraints on the wells are enforced using a practical approach. The applicability and robustness of our well-placement algorithm is discussed through several example problems. © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Optimal well-placement; Well control optimization; Joint optimization; Adjoint gradient; Gradient projec- tion; Bottomhole pressure constraint 1. Introduction Determining the optimal number of the producers and injec- tors and their optimal locations is a critical step in preparing the development plan for a reservoir. The general well- placement optimization problem considers simultaneously optimizing the number of wells, well types, well locations and trajectories and well operating conditions for life cycle of the reservoir. To the best of our knowledge the general well-placement problem is far from solved, although many researchers have focused on solving individual components of the problem. Most papers on optimal well-placement assume the number of wells are fixed and the well operating condi- tions, wellbore pressures or rates, and the reservoir life are ∗ Corresponding author at: McDougall School of Petroleum Engineering, University of Tulsa, Tulsa, OK 74104, United States. Tel.: +1 918 6254404. E-mail address: fahim-forouzanfar@utulsa.edu (F. Forouzanfar). Received 3 September 2012; Received in revised form 9 May 2013; Accepted 10 November 2013 specified and fixed when optimizing well locations and tra- jectories (completions). We should mention, however, that in the optimization procedures used by Handels et al. (2007) and Emerick et al. (2009) the optimal number of wells may change by a very small number during the optimization process, and, in the optimization procedures proposed by Yeten et al. (2002) and Onwunalu and Durlofsky (2010), the number of laterals of a multi-lateral well is optimized during the optimization process. Beckner and Song (1995) proposed an algorithm to optimize the schedule of the wells (the time to bring the wells online) and with the algorithms proposed by Yeten et al. (2002), Emerick et al. (2009), Onwunalu and Durlofsky (2010) and Nwankwor et al. (2013) the types of the wells (injection or pro- duction) are also optimized. Recently, the joint optimization 0263-8762/$ – see front matter © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cherd.2013.11.006