279689 Optimal Planning of Drilling and Production in Oil Reservoirs
The oil demand is increasing and therefore oil companies have increased their drilling activities to meet this demand. However, oil reservoirs are limited and mostly are depleting. Hence, in order to reduce drilling costs and increase the efficiency of oil recovery, it is inevitable to focus on optimal well placement and optimal production planning. To do so, all three technical elements of upstream production should be considered in a unified manner. That includes multiphase flow (a) in the reservoir, (b) through the well and (c) into the surface facilities. The production efficiency strongly depends on all these three elements and economic constraints of the problem. In our previous work , we focused on the subsurface section as the first above element and the main source of the oil phase. We developed a non-convex MINLP model and modified an outer approximation algorithm to solve that. In this study, we extend our previous work to include the remaining elements (b) and (c). The main objective is to design a state-of-art model that locates the most promising drilling sites for the new/infill oil producers and decides the optimal number of wells. Additionally, it should decide the optimal injection and production flow rates to maximize the net present value (NPV) of the overall (drilling and production) project. Although there have been attempts to address similar problems using evolutionary methods [2,3] or derivative based algorithms , we use the power of mathematical programming, which enables us to rigorously model, analyse and solve the problem. In contrast, the first two approaches rely mostly on the numerical reservoir simulators as black box models.
Developing a mathematical model that thoroughly captures sub-surface, well string and surface elements of upstream production is very challenging. It is different from combining several software packages, each specialized for a specific task and phenomenon. The former is a complex task but it can provide much flexibility and has a wide scope; the latter is more straightforward, however it has limited scope. A holistic model should offer very versatile and general formulation that can accommodate different possible events. That is truly a complicated task. This complexity is due to several contributors including: the different nature of spatial grids with and without wells in the reservoir, highly combinatorial nature of the problem and strong nonlinearity of the multiphase flow in the porous media and then through the wells. We have attempted to overcome most of these challenges and we have considered all the three aforementioned elements in the current extended non-convex, dynamic and multi-period MINLP model. Since the problem is inherently very large in size, we have also ensured that the model remains as sparse as possible. That can help both the MILP and NLP solvers.
We tested our extended model using two case studies for two synthetic reservoirs. Both are infill-drilling problems with old producer and injector wells already active in the reservoir. It is targeted to drill up to 8 and 11 wells for the first and second case studies respectively. For comparison purpose, we also defined a base case where no new wells are drilled and old wells continue the production. Our method successfully located 5 wells for the first example and achieved NPV of $ 5.96x108 (even by considering the drilling cost of 5 new wells) whereas the base case only obtained $4.50x108 . It also suggested to drill 3 new producer wells for the second test to yield NPV of $ 4.31x108. The base case NPV is $ 3.69x108 where no new wells are drilled. In both examples, the optimizer has effectively determined and distributed the production and injection flow rate level of different wells. Moreover, their flow rate profile confirmed the effective responses from the injectors at the event of water breakthrough to maximize the NPV.
We would like to appreciate National University of Singapore and SINGA program for the financial support of this research. We are also thankful to Mr. David Baxendale from RPS Energy Limited and Professor Sh. Ayatollahi from Shiraz University for their valuable industrial and academic insights. Finally, we would like to extend our gratitude to Schlumberger for the provision of the ECLIPSE software package to aid us in our work.
 M.S. Tavallali, I.A. Karimi, & K.M. Teo, 2011, Dynamic Optimal Well Placement in Oil Reservoirs, Annual Meeting of AICHE, Minneapolis, USA.
 B. Yeten, L.J. Durlofsky & A. Khalid, 2003, Optimization of Nonconventional Well Type, Location, and Trajectory, SPE Journal, Volume 8(3), Pages 200-210.
 Onwunalu JE, Durlofsky LJ, 2009, Application of a particle swarm optimization algorithm for determining optimum well location and type, Computational Geosciences:1-16
 Forouzanfar, F., G. Li, & A.C. Reynolds (2010). A Two-Stage Well Placement Optimization Method Based on Adjoint Gradient. SPE Annual Technical Conference and Exhibition. Florence, Italy.
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