Adjoint-Based Well-Placement Optimization Under Production Constraints
- Maarten Zandvliet (Shell International Ltd.) | Martijn Handels (D&M Schlumberger) | Gijs van Essen (Delft U. of Technology) | Roald Brouwer (Shell Intl. E&P BV) | Jan-Dirk Jansen (Delft U. of Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2008
- Document Type
- Journal Paper
- 392 - 399
- 2008. Society of Petroleum Engineers
- 5.4.1 Waterflooding, 5.5 Reservoir Simulation, 5.3.2 Multiphase Flow, 2.3 Completion Monitoring Systems/Intelligent Wells, 2.2.2 Perforating, 2.3.4 Real-time Optimization, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 5.1.5 Geologic Modeling
- 4 in the last 30 days
- 1,163 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Determining the optimal location of wells with the aid of an automated search method can significantly increase a project's net present value (NPV) as modeled in a reservoir simulator. This paper has two main contributions: first, to determine the effect of production constraints on optimal well locations and, second, to determine optimal well locations using a gradient-based optimization method. Our approach is based on the concept of surrounding the wells whose locations have to be optimized by so-called pseudowells. These pseudowells produce or inject at a very low rate and, thus, have a negligible influence on the overall flow throughout the reservoir. The gradients of NPV over the lifespan of the reservoir with respect to flow rates in the pseudowells are computed using an adjoint method. These gradients are used subsequently to approximate improving directions (i.e., directions to move the wells to achieve an increase in NPV), on the basis of which improving well locations can be determined. The main advantage over previous approaches such as finite-difference or stochastic-perturbation methods is that the method computes improving directions for all wells in only one forward (reservoir) and one backward (adjoint) simulation. The process is repeated until no further improvements are obtained. The method is applied to three waterflooding examples.
Determining the location of wells is a crucial decision during a field-development plan because it can affect a project's NPV significantly. Well placement is often posed as a discrete optimization problem (Yeten 2003) (i.e., involving integers as decision variables). Solving such problems is an arduous task; therefore, well locations often are determined manually. However, several automated well-placement optimization methods are available in the literature. They can be classified broadly into two categories. The first category consists of local methods such as finite-difference-gradient (FDG) (Bangerth et al. 2006), simultaneous-perturbation-stochastic-approximation (Bangerth et al. 2003, Spall 2003), and Nelder-Mead simplex (Spall 2003) methods. The second category consists of global methods such as simulated annealing (Beckner and Song 1995), genetic algorithms (Montes et al. 2001, Güyagüler et al. 2002, Yeten et al. 2003), and neural networks (Centilmen et al. 1999). The first category is generally very efficient, requires only a few forward reservoir simulations, and increases NPV at each iteration. However, these methods can get stuck in a local optimal solution. The second category can, in theory, avoid this problem but has the disadvantages of not increasing NPV at each iteration and requiring many forward reservoir simulations.
A rather different approach is proposed by Lui and Jalali (2006), where standard reservoir models are transformed to maps of production potential to screen regions that are most favorable for well placement.
In this paper, we present a gradient-based method that is distinct from those previously mentioned. The adjoint method used in optimal-control theory has been used previously for optimization of injection and production rates in a fixed-well configuration (Ramirez 1987, Asheim 1988, Sudaryanto and Yortsos 2001, Zakirov et al. 1996, Virnovsky 1991, Brouwer and Jansen 2004, Sarma et al. 2005, Kraaijevanger et al. 2007). In these applications, the parameters to be optimized are usually well-flow rates, bottomhole pressures (BHPs), or choke-valve settings. Because these are not mixed-integer problems, gradient-based methods are used commonly to solve them and the adjoint method efficiently generates the required gradients.
We propose to use the adjoint method for well-placement optimization. An example of well-placement optimization using optimal control theory has been proposed previously by Virnovsky and Kleppe (1995). Our approach, however, is significantly different. Moreover, two further applications of adjoint-based well-placement optimization were published recently (Wang et al. 2007, Sarma and Chen 2007.)
The outline of our paper is as follows: First, the effect of production constraints on optimal well locations is investigated. Then, an adjoint-based well-placement-optimization method is presented. Finally, the benefits of this method are demonstrated by three waterflooding examples.
|File Size||1 MB||Number of Pages||8|
Asheim, H. 1988. Maximizationof Water Sweep Efficiency by Controlling Production and Injection Rates.Paper SPE 18365 presented at the European Petroleum Conference, London, 16-19October. doi: 10.2118/18365-MS.
Aziz, K. and Settari, A. 1979. Petroleum Reservoir Simulation.London: Elsevier Applied Science Publishers.
Bangerth, W., Klie, W.H., Wheeler, M.F., Stoffa, P.L., and Sen, M.K. 2006.On optimizationalgorithms for the reservoir oil well placement problem. ComputationalGeosciences 10 (3): 303-319. doi:10.1007/s10596-006-9025-7.
Beckner, B.L. and Song, X. 1995. Field Development Planning UsingSimulated Annealing--Optimal Economic Well Scheduling and Placement. PaperSPE 30650 presented at the SPE Annual Technical Conference and Exhibition,Dallas, 22-25 October. doi: 10.2118/30650-MS.
Brouwer, D.R. and Jansen, J.D. 2004. Dynamic Optimization of WaterFlooding With Smart Wells Using Optimal Control Theory. SPEJ9 (4): 391-402. SPE-78278-PA. doi: 10.2118/78278-PA.
Centilmen, A., Ertekin, T., Grader, A.S. 1999. Applications of Neural Networks inMultiwell Field Development. Paper SPE 56433 presented at the SPE AnnualTechnical Conference and Exhibition, Houston, 3-6 October. doi:10.2118/56433-MS.
Güyagüler, B., Horne, R.N., Rogers, L., Rosenzweig, J.J. 2002. Optimization of Well Placement in aGulf of Mexico Waterflooding Project. SPEREE 5 (3): 229-236.SPE-78266-PA. doi: 10.2118/78266-PA.
Kraaijevanger J.F.B.M., Egberts P.J.P., Valstar, J.R., and Buurman, H.W.2007. Optimal Waterflood DesignUsing the Adjoint Method. Paper SPE 105764 presented at the SPE ReservoirSimulation Symposium, Houston, 26-28 February. doi: 10.2118/105764-MS.
Lui, N. and Jalali, Y. 2006. Closing the Loop Between Reservoir Modeling andWell Placement and Positioning. Paper SPE 98198 presented at the SPEIntelligent Energy Conference and Exhibition, Amsterdam, 11-13 April.
Montes, G., Bartolome, P., and Udias, A.L. 2001. The Use of Genetic Algorithms in WellPlacement Optimization. Paper SPE 69439 presented at the SPE Latin Americanand Caribbean Petroleum Engineering Conference, Buenos Aires, 25-28 March. doi:10.2118/69439-MS.
Ramirez, W.F. 1987. Application of Optimal Control Theory to EnhancedRecovery. Amsterdam: Developments in Petroleum Science series, ElsevierScience.
Sarma, P. and Chen, W.H. 2007. Efficient Well PlacementOptimization With Gradient-Based Algorithms and Adjoint Models. Paper SPE112257 presented at the SPE Intelligent Energy Conference and Exhibition,Amsterdam, 25-27 February. doi: 10.2118/112257-MS.
Sarma, P., Aziz, K., and Durlofsky, L.J. 2005. Implementation of Adjoint Solutionfor Optimal Control of Smart Wells. Paper SPE 92864 presented at the SPEReservoir Simulation Symposium, Houston, 31 January-2 February. doi:10.2118/92864-MS.
Spall, J.C. 2003. Introduction to Stochastic Search and Optimization:Estimation, Simulation, and Control. Hoboken, New Jersey:Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons.
Sudaryanto, B. and Yortsos, Y.C. 2001. Optimization of Displacements inPorous Media Using Rate Control. Paper SPE 71509 presented at the SPEAnnual Technical Conference and Exhibition, New Orleans, 30 September-3October. doi: 10.2118/71509-MS.
van Essen, G.M., Zandvliet, M.J., van den Hof, P.M.J., Bosgra, O.H., andJansen, J.D. 2006. RobustWaterflooding Optimization of Multiple Geological Scenarios. Paper SPE102913 presented at the SPE Annual Technical Conference and Exhibition, SanAntonio, Texas, USA, 24-27 September. doi: 10.2118/102913-MS.
Virnovsky, G.A. 1991. Waterflooding strategy design using optimal controltheory. Paper presented at the 6th European IOR Symposium, Stavanger, 21-23May.
Virnovsky, G.A. and Kleppe, H. 1995. Application of control theory tooptimize horizontal well location producing from thin oil zone. Paper presentedat the 8th European IOR Symposium, Vienna, Austria, 15-17 May.
Wang, C., Li, G., and Reynolds, A.C. 2007. Optimal Well Placement forProduction Optimization. Paper SPE 111154 presented at the Eastern RegionalMeeting, Lexington, Kentucky, USA, 17-19 October. doi: 10.2118/111154-MS.
Yeten B. 2003. Optimum deployment of nonconventional wells. PhDdissertation, Stanford University, Stanford, California.
Yeten, B., Durlofsky, L.J., and Aziz, K. 2003. Optimization of Nonconventional WellType, Location, and Trajectory. SPEJ 8 (3): 200-210.SPE-86880-PA. doi: 10.2118/86880-PA.
Zakirov, I.S., Aanonsen, S.I., Zakirov, E.S., and Palatnik, B.M. 1996.Optimization of reservoir performance by automatic allocation of well rates.Proc., 5th European Conference on the Mathematics of Oil Recovery,Leoben, Austria.