- Boolean operators
- This OR that
This AND that
This NOT that
- Must include "This" and "That"
- This That
- Must not include "That"
- This -That
- "This" is optional
- This +That
- Exact phrase "This That"
- "This That"
- (this AND that) OR (that AND other)
- Specifying fields
- publisher:"Publisher Name"
author:(Smith OR Jones)
Sequential Quadratic Programming for Solving Constrained Production Optimization--Case Study From Brugge Field
- Vahid Dehdari (University of Alberta) | Dean S. Oliver (Uni Research)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2012
- Document Type
- Journal Paper
- 874 - 884
- 2012. Society of Petroleum Engineers
- 5.7.2 Recovery Factors, 4.3.4 Scale, 2.3 Completion Monitoring Systems/Intelligent Wells, 5.4.2 Gas Injection Methods
- 3 in the last 30 days
- 454 since 2007
- Show more detail
Normally only approximately 30% of the oil in a reservoir is extracted during primary production, but using secondary-production methods such as water or gas injection, it is often possible to increase that percentage significantly and maintain the production rate of a reservoir over a longer period of time. In reservoirs under water or gas injection, additional gains can be obtained through an efficient strategy for management of front movement and reservoir sweep. The objective of reservoir production optimization is to maximize an outcome such as sweep efficiency or net present value (NPV) through the control of completion rates or pressures. Using optimization methods, it is possible to compute control settings that result in increased oil production and decreased water production compared with production from standard practices. In this paper, we focus on optimization using sequential quadratic programming (SQP) with an ensemble-based approach to estimate the gradient for the optimization. Although uncertainty in reservoir properties is usually important for the computation of optimal controls, here we use a single realization of the reservoir to evaluate the efficiency of the optimization algorithm.
The most expensive aspect of gradient-based optimization is usually the computation of gradients. Most practical production-optimization problems involve large-scale, highly complex reservoir models with thousands of constraints, which makes numerical calculation of the gradient time consuming. Here, we use an ensemble-based approach for finding gradients and use localization to improve estimation of the gradient from a small number of realizations. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used for maximizing the objective function, with the Hessian estimated from a sequence of estimates of the gradient. Improving the gradient approximation using localization results in improvement to the Hessian approximation. A second important aspect of the efficiency of the method is the identification of active constraints. In this paper, we use a method for eliminating nonnegativity constraints to decrease computation time and an updating procedure to solve each iteration of SQP much faster than the base case. Both the speed of the algorithm and the final NPV were increased significantly.
We evaluate the method by applying it to optimization of control settings in the Brugge field. Brugge is a 3D synthetic model designed by TNO with 20 vertical producers and 10 vertical peripheral water injectors. All of the producers and injectors are smart wells whose downhole chokes must be adjusted to optimize NPV. The total number of completion flow rates to be controlled is 84 at each timestep, with 40 timesteps (every 6 months). There are 1,200 inequality constraints on total well liquid rates and 3,360 nonnegativity constraints on completion liquid rates. There are also inequality constraints on the bottomhole pressure (BHP) for wells at each time period.
Antoniou, A. and Lu, W.-S. 2007. Practical Optimization: Algorithms andEngineering Applications. New York: Springer Science+Business Media.
Asheim, H. 1988. Maximization of Water Sweep Efficiency by ControllingProduction and Injection Rates. Paper SPE 18365 presented at the EuropeanPetroleum Conference, London, 16-19 October. http://dx.doi.org/10.2118/18365-MS.
Asheim, H. 1987. Optimal Control of Water Drive. Paper SPE 15978 availablefrom SPE, Richardson, Texas.
Bangerth, W., Klie, H., Wheeler, M.F., Stoffa, P.L., and Sen, M.K. 2006. Onoptimization algorithms for the reservoir oil well placement problem.Comput. Geosci. 10 (3): 303-319. http://dx.doi.org/10.1007/s10596-006-9025-7.
Björck, Å. 1996. Numerical Methods for Least Square Problems.Philadelphia, Pennsylvania: SIAM.
Brouwer, D.R. and Jansen, J.-D. 2004. Dynamic Optmization of Water FloodingWith Smart Wells Using Optimal Control Theory. SPE J. 9(4): 391-402. SPE-78278-PA. http://dx.doi.org/10.2118/78278-PA.
Chaudhri, M.M., Phale, H.A., Liu, N., and Oliver, D.S. 2009. An ImprovedApproach for Ensemble-Based Production Optimization. Paper SPE 121305 presentedat the SPE Western Regional Meeting, San Jose, California, USA, 24-26 March. http://dx.doi.org/10.2118/121305-MS.
Chen, C., Wang, Y., Li, G., and Reynolds, A. 2010. Closed-loop reservoirmanagement on the Brugge test case. Comput. Geosci. 14 (4):691-703. http://dx.doi.org/10.1007/s10596-010-9181-7.
Chen, Y. and Oliver, D.S. 2010. Ensemble-Based Closed-Loop OptimizationApplied to Brugge Field. SPE Res Eval & Eng 13 (1):56-71. SPE-118926-PA. http://dx.doi.org/10.2118/118926-PA.
Chen, Y. and Oliver, D.S. 2011. Localization of ensemble-based controlsetting updates for production optimization. SPE J. 17 (1):122-136. SPE-125042-PA. http://dx.doi.org/10.2118/125042-PA.
Chen, Y., Oliver, D.S., and Zhang, D. 2009. Efficient Ensemble-BasedClosed-Loop Production Optimization. SPE J. 14 (4):634-645. SPE-112873-PA. http://dx.doi.org/10.2118/112873-PA.
Davidson, J.E. and Beckner, B.L. 2003. Integrated Optimization for RateAllocation in Reservoir Simulation. SPE Res Eval & Eng 6 (6): 426-432. SPE-87309-PA. http://dx.doi.org/10.2118/87309-PA.
Díez, M.D., Brusdal, K., Evensen, G., Barkve, T., and Mjaavatten, A. 2005.Opportunities and challenges of using sequential quadratic programming (SQP)for optimization of petroleum production networks. In 15th EuropeanSymposium on Computer Aided Process Engineering (ESCAPE-15), ed. L.Puigjaner and A. Espuña, No. 20, Paper CM-029, 169-174. Amsterdam, TheNetherlands: Computer Aided Chemical Engineering, Elsevier Science B.V.
Gao, G., Li, G., and Reynolds, A.C. 2007. A Stochastic Algorithm forAutomatic History Matching. SPE J. 12 (2): 196-208.SPE-90065-PA. http://dx.doi.org/10.2118/90065-PA.
Gill, P.E., Murray, W., and Wright, M.H. 1981. PracticalOptimization. New York: Academic Press.
Harding, T.J., Radcliffe, N.J., and King, P.R. 1998. Hydrocarbon ProductionScheduling With Genetic Algorithms. SPE J. 3 (2): 99-107.SPE-36379-PA. http://dx.doi.org/10.2118/36379-PA.
Jansen, J.D., van Doren, J.F.M., Heidary-Fyrozjaee, M., and Yortsos, Y.C.2009. Front Controllability in Two-Phase Porous Media Flow. In Model-BasedControl:: Bridging Rigorous Theory and Advanced Technology ed. P.M.J. vanden Hof, C. Scherer, and P.S.C. Heuberger, 203-219. Dordrecht, The Netherlands:Springer.
Kraaijevanger, J.F.B.M., Egberts, P.J.P., Valstar, J.R., and Buurman,H.W. 2007. Optimal Waterflood Design Using the Adjoint Method. Paper SPE 105764presented at the SPE Reservoir Simulation Symposium, Houston, 26-28 February.http://dx.doi.org/10.2118/105764-MS.
Lien, M., Brouwer, D.R., Mannseth, T., and Jansen, J.D. 2008. MultiscaleRegularization of Flooding Optimization for Smart Field Management. SPEJ. 13 (2): 195-204. SPE-99728-PA. http://dx.doi.org/10.2118/99728-PA.
Lorentzen, R.J., Berg, A.M., Nævdal, G., and Vefring, E.H. 2006. A NewApproach for Dynamic Optimization of Waterflooding Problems. Paper SPE 99690presented at the Intelligent Energy Conference and Exhibition, Amsterdam, 11-13April. http://dx.doi.org/10.2118/99690-MS.
Lorentzen, R.J., Shafieirad, A., and Nævdal, G. 2009. Closed-Loop ReservoirManagement Using the Ensemble Kalman Filter and Sequential QuadraticProgramming. Paper SPE 119101 presented at the SPE Reservoir SimulationSymposium, The Woodlands, Texas, USA, 2-4 February. http://dx.doi.org/10.2118/119101-MS.
Nævdal, G., Brouwer, D.R., and Jansen, J.-D. 2006. Waterflooding usingclosed-loop control. Comput. Geosci. 10 (1): 37-60. http://dx.doi.org/10.1007/s10596-005-9010-6.
Nocedal, J. and Wright, S.J. 2006. Numerical Optimization, secondedition. New York: Series in Operations Research and Financial Engineering,Springer.
Nwaozo, J. 2006. Dynamic optimization of a water flood reservoir. MSthesis, University of Oklahoma, Norman, Oklahoma.
Odi, U., Lane, R.H., and Barrufet, M.A. 2010. Ensemble Based Optimization ofEOR Processes. Paper SPE 132626 presented at the SPE Western Regional Meeting,Anaheim, California, USA, 27-29 May. http://dx.doi.org/10.2118/132626-MS.
Peters, L., Arts, R.J., Brouwer, G.K., et al. 2010. Results of the BruggeBenchmark Study for Flooding Optimization and History Matching. SPE Res Eval& Eng 13 (3): 391-405. SPE-119094-PA. http://dx.doi.org/10.2118/119094-PA.
Powell, M.J.D. 1978. Algorithms for nonlinear constraints that uselagrangian functions. Math. Program. 14 (1): 224-248. http://dx.doi.org/10.1007/bf01588967.
Ramakrishnan, T.S. 2007. On Reservoir Fluid-Flow Control With SmartCompletions. SPE Prod & Oper 22 (1): 4-12.SPE-84219-PA. http://dx.doi.org/10.2118/84219-PA.
Sarma, P., Aziz, K., and Durlofsky, L.J. 2005. Implementation ofAdjoint Solution for Optimal Control of Smart Wells. Paper SPE 92864 presentedat the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 31January-2 February. http://dx.doi.org/10.2118/92864-MS.
Sarma, P., Durlofsky, L.J., Aziz, K., and Chen, W.H. 2006. Efficientreal-time reservoir management using adjoint-based optimal control and modelupdating. Comput. Geosci. 10 (1): 3-36. http://dx.doi.org/10.1007/s10596-005-9009-z.
Sarma, P., Chen, W.H., Durlofsky, L.J., and Aziz, K. 2008. ProductionOptimization With Adjoint Models Under Nonlinear Control-State Path InequalityConstraints. SPE Res Eval & Eng 11 (2): 326-339.SPE-99959-PA. http://dx.doi.org/10.2118/99959-PA.
Su, H.-J. and Oliver, D.S. 2010. Smart Well Production Optimization Using AnEnsemble-Based Method. SPE Res Eval & Eng 13 (6):884-892. SPE-126072-PA. http://dx.doi.org/10.2118/126072-PA.
Tavakkolian, M., Jalali, F., and Amadi, M.A. 2004. Production OptimizationUsing Genetic Algorithm Approach. Paper SPE 88901 presented at the NigeriaAnnual International Conference and Exhibition, Abuja, Nigeria, 2-4 August. http://dx.doi.org/10.2118/88901-MS.
Wang, C., Li, G., and Reynolds, A.C. 2009. Production Optimization inClosed-Loop Reservoir Management. SPE J. 14 (3): 506-523.SPE-109805-PA. http://dx.doi.org/10.2118/109805-PA.
Yeten, B., Durlofsky, L.J., and Aziz, K. 2003. Optimization ofNonconventional Well Type, Location, and Trajectory. SPE J. 8 (3): 200-210. SPE-86880-PA. http://dx.doi.org/10.2118/86880-PA.
Not finding what you're looking for? Some of the OnePetro partner societies have developed subject- specific wikis that may help.
The SEG Wiki
The SEG Wiki is a useful collection of information for working geophysicists, educators, and students in the field of geophysics. The initial content has been derived from : Robert E. Sheriff's Encyclopedic Dictionary of Applied Geophysics, fourth edition.