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Application of Mathematical Optimization Techniques for Pattern of Horizontal Wells Selection

Authors: Khasanov M.M., Babin V.M., Melchaeva O.U., Ushmaev O.S. (Gazpromneft NTC LLC, RF, Saint-Petersburg), Echeverria Ciaurri D. (IBM Thomas J. Watson Research Center, USA, New York), Semenikhin A.S. (IBM Science and Technology Center, RF, Moscow)

Key words: optimal well pattern selection, multiobjective optimization, conceptual oilfield development, models hierarchy.

The paper describes an approach to selection of horizontal well placement. Given a field dynamic model we use advanced optimization techniques to sel ect horizontal well length, well placement, well control that improve the field economics and increase field recoveries. In order to deal with well-known problems of using optimization algorithms for field development as big number of variables and computational complexity of hydrodynamic simulation we propose multi-layer approach. First, we use chain of simulators and dynamic models (fr om analytic models to fine-scale hydrodynamic model). Second, we decompose optimal well placement and control task of high dimension into a number of optimization problems of lower dimension: selection of optimal well pattern, local well placement optimization, selection of well control. Thus we reduce number of complicated model runs. The proposed approach was implemented for FDP optimization of a Gazprom Neft JSC greenfield.
References
1. Butler R., Horizontal wells for the recovery of oil, gas and bitumen, Petroleum Society Monograph, 1992, no. 2.
2. Willhite P.G., Waterflooding, SPE Textbook, 1986, no. 3.
3. Khasanov M.M., Ushmaev O.S., Nekhaev S.A., Karamutdinova D.M.,
The optimal parameters of oil field development (In Russ.), SPE 162089, 2012.
4. Bellout M.C., Echeverría Ciaurri D., Durlofsky L.J. et al., Joint optimization of oil well placement and controls, Computational Geosciences, 2012, no. 16(4), pp. 1061–1079.
5. Isebor O.J., Durlofsky L.J., EcheverrГ­a Ciaurri D., A derivative-free methodology with local and global search for the constrained joint optimization of well locations and controls, Computational Geosciences, 2013, pp. 1–20.
6. Isebor O.J., Durlofsky L.J., EcheverrГ­a Ciaurri D., Generalized field development optimization using derivative-free procedures, SPE Journal, 2014, pp. 1–18.
7. Recham R., Bencherif D., Investigation of optimum well spacing based on
a combined simulation and economic models, Canadian International Petroleum Conference, 2003.
8. Roberts T., Economics of well spacing, SPE 240, 1961.
9. Tokunaga H. A, Hise B.R., Method to determine optimum well spacing,
SPE 1673, 1966.
10. Fletcher R., Leyffer S., Nonlinear programming without a penalty function, Mathematical Programming, 2002, no. 91(2), pp. 239–269.
11. EcheverrГ­a Ciaurri D., Isebor O.J., Durlofsky L.J., Application of derivativefree methodologies to generally con-strained oil production optimisation problems, International journal of mathematical modelling and numerical optimization, 2011, no. 2(2), pp. 134–161.
12. Audet C., Dennis J.E Jr., Analysis of generalized pattern searches, SIAM
Journal on Optimization, 2002, no. 13(3), pp. 889–903.
13. Torczon V., On the convergence of pattern search algorithms, SIAM Journal on Optimization, 1997, no. 7(1), pp. 1–25.
14. Audet C., Dennis J.E. Jr., Mesh adaptive direct search algorithms for constrained optimization, SIAM Journal on Optimization, 2002, no. 17(1),
pp. 188–217.
15. Brouwer D.R., Jansen J.D., Dynamic optimization of waterflooding with
smart wells using optimal control theory, SPE Journal, 2004, no. 9(4),
pp. 391–402.

Key words: optimal well pattern selection, multiobjective optimization, conceptual oilfield development, models hierarchy.

The paper describes an approach to selection of horizontal well placement. Given a field dynamic model we use advanced optimization techniques to sel ect horizontal well length, well placement, well control that improve the field economics and increase field recoveries. In order to deal with well-known problems of using optimization algorithms for field development as big number of variables and computational complexity of hydrodynamic simulation we propose multi-layer approach. First, we use chain of simulators and dynamic models (fr om analytic models to fine-scale hydrodynamic model). Second, we decompose optimal well placement and control task of high dimension into a number of optimization problems of lower dimension: selection of optimal well pattern, local well placement optimization, selection of well control. Thus we reduce number of complicated model runs. The proposed approach was implemented for FDP optimization of a Gazprom Neft JSC greenfield.
References
1. Butler R., Horizontal wells for the recovery of oil, gas and bitumen, Petroleum Society Monograph, 1992, no. 2.
2. Willhite P.G., Waterflooding, SPE Textbook, 1986, no. 3.
3. Khasanov M.M., Ushmaev O.S., Nekhaev S.A., Karamutdinova D.M.,
The optimal parameters of oil field development (In Russ.), SPE 162089, 2012.
4. Bellout M.C., Echeverría Ciaurri D., Durlofsky L.J. et al., Joint optimization of oil well placement and controls, Computational Geosciences, 2012, no. 16(4), pp. 1061–1079.
5. Isebor O.J., Durlofsky L.J., EcheverrГ­a Ciaurri D., A derivative-free methodology with local and global search for the constrained joint optimization of well locations and controls, Computational Geosciences, 2013, pp. 1–20.
6. Isebor O.J., Durlofsky L.J., EcheverrГ­a Ciaurri D., Generalized field development optimization using derivative-free procedures, SPE Journal, 2014, pp. 1–18.
7. Recham R., Bencherif D., Investigation of optimum well spacing based on
a combined simulation and economic models, Canadian International Petroleum Conference, 2003.
8. Roberts T., Economics of well spacing, SPE 240, 1961.
9. Tokunaga H. A, Hise B.R., Method to determine optimum well spacing,
SPE 1673, 1966.
10. Fletcher R., Leyffer S., Nonlinear programming without a penalty function, Mathematical Programming, 2002, no. 91(2), pp. 239–269.
11. EcheverrГ­a Ciaurri D., Isebor O.J., Durlofsky L.J., Application of derivativefree methodologies to generally con-strained oil production optimisation problems, International journal of mathematical modelling and numerical optimization, 2011, no. 2(2), pp. 134–161.
12. Audet C., Dennis J.E Jr., Analysis of generalized pattern searches, SIAM
Journal on Optimization, 2002, no. 13(3), pp. 889–903.
13. Torczon V., On the convergence of pattern search algorithms, SIAM Journal on Optimization, 1997, no. 7(1), pp. 1–25.
14. Audet C., Dennis J.E. Jr., Mesh adaptive direct search algorithms for constrained optimization, SIAM Journal on Optimization, 2002, no. 17(1),
pp. 188–217.
15. Brouwer D.R., Jansen J.D., Dynamic optimization of waterflooding with
smart wells using optimal control theory, SPE Journal, 2004, no. 9(4),
pp. 391–402.


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