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Alternative concept of monitoring and optimization water flooding of oil reservoirs in the conditions of instability of the displacement front

UDK: 622.276.43
DOI: 10.24887/0028-2448-2019-12-118-123
Key words: filtration of multiphase fluids, flooding system, regulation of well operation modes, growth models, discriminant analysis
Authors: A.Kh. Shakhverdiev (Sergo Ordzhonikidze Russian State Geological Prospecting University, RF, Moscow), Yu.V. Shestopalov (University of Gävle, Sweden, Gävle), I.E. Mandrik (LUKOIL PJSC, RF, Moscow), S.V. Arefiev (LUKOIL – Western Siberia LLC, Kogalym)

It has always been an urgent issue for the oil and gas industry to improve oil, gas, and condensate recovery at liquid and gaseous hydrocarbon fields developed with the use of artificial formation pressure maintenance techniques that involve injection of water or water combined with other displacement agents. Therefore, due to the aforesaid issues, permanent attention should still be paid to the practical problem of optimizing the non-stationary hydrodynamic pressure applied to a reservoir by regulating the operating conditions of the production and injection wells, development process optimization in general, and water flooding in particular. The theory of Buckley and Leverett, does not take into account the loss of stability of the displacement front, which provokes a stepwise change and the triple value of water saturation. Traditionally a mathematically simplified approach was proposed - a repeatedly differentiable approximation to eliminate the “jump” in water saturation. Such a simplified solution led to negative consequences well-known from the water flooding practice, recognized by experts as “viscous instability of the displacement front” and “fractal geometry of displacement front”.

The core of the issue is an attempt to predict the beginning of the stability loss of the front of oil displacement by water and to prevent its negative consequences on the water flooding process under difficult conditions of interaction of hydro-thermodynamics, capillary, molecular, inertial, and gravitational forces. In this study, catastrophe theory methods applied for the analysis of nonlinear polynomial dynamical systems are used as a novel approach. Namely, a mathematical growth model is developed and an inverse problem is formulated so that the initial coefficients of the system of differential equations for a two-phase flow can be determined using this model. A unified control parameter has been selected, which enables one to propose and validate a discriminant criterion for oil and water growth models for monitoring and optimizing.

References

1. Kreyg F.F., Razrabotka neftyanykh mestorozhdeniy pri zavodnenii (Applied waterflood field development), Moscow: Nedra Publ., 1974, 191 p.

2. Buckley I., Leverett M.С., Mechanism of fluid displacement in sands, Trans. AIME, 1942, V. 146, no. 1, pp. 107–116.

3. Dake L.P., The practice of reservoir engineering, Elsevier Science, 2001, 570 p.

4. Aziz Kh., Settari A., Petroleum reservoir simulation, Applied Science Publishers, 1979, 476 p.

5. Shaohua Gu, Yuetian Liu, Zhangxin Chen, Cuiyu Ma, A method for evaluation of water flooding performance in fractured reservoirs, Journal of Petroleum Science and Engineering, 2014, V. 120, pp. 130–140.

6. Wang Dashun, Di Niu, Huazhou Andy Li, Predicting waterflooding performance in low-permeability reservoirs with linear dynamical systems, SPE-185960-PA, 2017.

7. Yonggang Duan, Ting Lu, Mingqiang Wei et al., Leverett analysis for transient two-phase flow in fractal porous medium, CMES, 2015, V. 109–110, no. 6, pp. 481–504.

8. Charnyy I.A., Podzemnaya gidrogazodinamika (Underground fluid dynamics), Moscow: Gostoptekhizdat Publ., 1963, 397 p.

9. Nigmatullin R.I., Dinamika mnogofaznykh sred (The dynamics of multiphase media), Part 2, Moscow: Nauka Publ., 1987, 360 p.

10. Shakhverdiev A.Kh., Sistemnaya optimizatsiya protsessa razrabotki neftyanykh mestorozhdeniy (System optimization of oil field development process), Moscow: Nedra Publ., 2004, 452 p.

11. Mirzadzhanzade A.Kh., Shakhverdiev A.Kh., Dinamicheskie protsessy v neftegazodobyche: sistemnyy analiz, diagnoz, prognoz (Dynamic processes in the oil and gas production: systems analysis, diagnosis, prognosis), Moscow: Nauka Publ., 1997, 254 p.

12. Mandrik I.E., Panakhov G.M., Shakhverdiev A.Kh., Nauchno-metodicheskie i tekhnologicheskie osnovy optimizatsii protsessa povysheniya nefteotdachi plastov (Scientific and methodological and technological basis for EOR optimization), Moscow: Neftyanoe khozyaystvo Publ., 2010, 288 p.

13. Shakhverdiev A.Kh., Once again about oil recovery factor (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2014, no. 1, pp. 44–48.

14. Shakhverdiev A.Kh., System optimization of non-stationary floods for the purpose of increasing oil recovery (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 1, pp. 44–50.

15. Shakhverdiev A.Kh., Innovative potential of non-stationary flooding for increase in oil recovery of layers (In Russ.), Vestnik Azerbaydzhanskoy Inzhenernoy Akademii = Herald of the Azerbaijan Engineering Academy, 2019, no. 1, pp. 32–41.

16. Shakhverdiev A.Kh., Shestopalov Yu.V., Qualitative analysis of quadratic polynomial dynamical systems associated with the modeling and monitoring of oil fields, Lobachevskii Journal of Mathematics, 2019, V. 40, no. 10, pp. 1695–1710.

17. Shakhverdiev A.Kh., Shestopalov Yu.V., Kachestvennyy analiz dinamicheskoy sistemy podderzhaniya plastovogo davleniya s tsel'yu povysheniya nefteotdachi zalezhey (Qualitative analysis of a dynamic system for maintaining reservoir pressure in order to increase oil recovery), Proceedings of 14 International Conference “Novye idei v naukakh o Zemle” (New ideas in earth sciences), Moscow, 2–5 April 2019.

18. Anishchenko V.S., Deterministic chaos (In Russ.), Sorosovskiy obrazovatel'nyy zhurnal, 1997, no. 6, pp. 70–76.

19. Arnol'd V.I., Teoriya katastrof (Catastrophe theory), Moscow: Nauka Publ., 1990, 128 p.

It has always been an urgent issue for the oil and gas industry to improve oil, gas, and condensate recovery at liquid and gaseous hydrocarbon fields developed with the use of artificial formation pressure maintenance techniques that involve injection of water or water combined with other displacement agents. Therefore, due to the aforesaid issues, permanent attention should still be paid to the practical problem of optimizing the non-stationary hydrodynamic pressure applied to a reservoir by regulating the operating conditions of the production and injection wells, development process optimization in general, and water flooding in particular. The theory of Buckley and Leverett, does not take into account the loss of stability of the displacement front, which provokes a stepwise change and the triple value of water saturation. Traditionally a mathematically simplified approach was proposed - a repeatedly differentiable approximation to eliminate the “jump” in water saturation. Such a simplified solution led to negative consequences well-known from the water flooding practice, recognized by experts as “viscous instability of the displacement front” and “fractal geometry of displacement front”.

The core of the issue is an attempt to predict the beginning of the stability loss of the front of oil displacement by water and to prevent its negative consequences on the water flooding process under difficult conditions of interaction of hydro-thermodynamics, capillary, molecular, inertial, and gravitational forces. In this study, catastrophe theory methods applied for the analysis of nonlinear polynomial dynamical systems are used as a novel approach. Namely, a mathematical growth model is developed and an inverse problem is formulated so that the initial coefficients of the system of differential equations for a two-phase flow can be determined using this model. A unified control parameter has been selected, which enables one to propose and validate a discriminant criterion for oil and water growth models for monitoring and optimizing.

References

1. Kreyg F.F., Razrabotka neftyanykh mestorozhdeniy pri zavodnenii (Applied waterflood field development), Moscow: Nedra Publ., 1974, 191 p.

2. Buckley I., Leverett M.С., Mechanism of fluid displacement in sands, Trans. AIME, 1942, V. 146, no. 1, pp. 107–116.

3. Dake L.P., The practice of reservoir engineering, Elsevier Science, 2001, 570 p.

4. Aziz Kh., Settari A., Petroleum reservoir simulation, Applied Science Publishers, 1979, 476 p.

5. Shaohua Gu, Yuetian Liu, Zhangxin Chen, Cuiyu Ma, A method for evaluation of water flooding performance in fractured reservoirs, Journal of Petroleum Science and Engineering, 2014, V. 120, pp. 130–140.

6. Wang Dashun, Di Niu, Huazhou Andy Li, Predicting waterflooding performance in low-permeability reservoirs with linear dynamical systems, SPE-185960-PA, 2017.

7. Yonggang Duan, Ting Lu, Mingqiang Wei et al., Leverett analysis for transient two-phase flow in fractal porous medium, CMES, 2015, V. 109–110, no. 6, pp. 481–504.

8. Charnyy I.A., Podzemnaya gidrogazodinamika (Underground fluid dynamics), Moscow: Gostoptekhizdat Publ., 1963, 397 p.

9. Nigmatullin R.I., Dinamika mnogofaznykh sred (The dynamics of multiphase media), Part 2, Moscow: Nauka Publ., 1987, 360 p.

10. Shakhverdiev A.Kh., Sistemnaya optimizatsiya protsessa razrabotki neftyanykh mestorozhdeniy (System optimization of oil field development process), Moscow: Nedra Publ., 2004, 452 p.

11. Mirzadzhanzade A.Kh., Shakhverdiev A.Kh., Dinamicheskie protsessy v neftegazodobyche: sistemnyy analiz, diagnoz, prognoz (Dynamic processes in the oil and gas production: systems analysis, diagnosis, prognosis), Moscow: Nauka Publ., 1997, 254 p.

12. Mandrik I.E., Panakhov G.M., Shakhverdiev A.Kh., Nauchno-metodicheskie i tekhnologicheskie osnovy optimizatsii protsessa povysheniya nefteotdachi plastov (Scientific and methodological and technological basis for EOR optimization), Moscow: Neftyanoe khozyaystvo Publ., 2010, 288 p.

13. Shakhverdiev A.Kh., Once again about oil recovery factor (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2014, no. 1, pp. 44–48.

14. Shakhverdiev A.Kh., System optimization of non-stationary floods for the purpose of increasing oil recovery (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 1, pp. 44–50.

15. Shakhverdiev A.Kh., Innovative potential of non-stationary flooding for increase in oil recovery of layers (In Russ.), Vestnik Azerbaydzhanskoy Inzhenernoy Akademii = Herald of the Azerbaijan Engineering Academy, 2019, no. 1, pp. 32–41.

16. Shakhverdiev A.Kh., Shestopalov Yu.V., Qualitative analysis of quadratic polynomial dynamical systems associated with the modeling and monitoring of oil fields, Lobachevskii Journal of Mathematics, 2019, V. 40, no. 10, pp. 1695–1710.

17. Shakhverdiev A.Kh., Shestopalov Yu.V., Kachestvennyy analiz dinamicheskoy sistemy podderzhaniya plastovogo davleniya s tsel'yu povysheniya nefteotdachi zalezhey (Qualitative analysis of a dynamic system for maintaining reservoir pressure in order to increase oil recovery), Proceedings of 14 International Conference “Novye idei v naukakh o Zemle” (New ideas in earth sciences), Moscow, 2–5 April 2019.

18. Anishchenko V.S., Deterministic chaos (In Russ.), Sorosovskiy obrazovatel'nyy zhurnal, 1997, no. 6, pp. 70–76.

19. Arnol'd V.I., Teoriya katastrof (Catastrophe theory), Moscow: Nauka Publ., 1990, 128 p.


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