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Using entropy modeling to analyze the effectiveness of the waterflooding system

UDK: 622.276.43.001
DOI: 10.24887/0028-2448-2020-6-62-67
Key words: entropy modeling, differential entropy, waterflooding, well interaction
Authors: S.V. Stepanov (Tyumen Petroleum Research Center LLC, RF, Tyumen; Tyumen State University, RF, Tyumen), A.N. Tyrsin (Ural Federal University, RF, Ekaterinburg), A.A. Ruchkin (Tyumen Petroleum Research Center LLC, RF, Tyumen), T.A. Pospelova (Tyumen Petroleum Research Center LLC, RF, Tyumen)

Analysis of the flooding system is the most important task when supporting the development of oil fields. The use of hydrodynamic modeling to solve this problem is resource-intensive and characterized by significant uncertainties. An effective alternative to hydrodynamic modeling for the analysis of the flooding system can be entropy modeling, the use of which for this task is first justified in this paper. Within the framework of the developed approach, the modeling object-the "reservoir-wells" system is considered as a multidimensional stochastic system with potentially interconnected elements. In this case, the system is open, which allows us to consider the differential entropy as the sum of the entropy of randomness (describes the interaction of the system with the environment) and the entropy of self-organization (describes the processes within the system). Together, this allows a more objective approach to the analysis of the flooding system than other methods.

The article presents the theory of the developed method. In particular, it is noted that the calculation of differential entropy uses the apparatus of mathematical statistics. In this case, multidimensional random vectors are the vector of producing wells and the vector of injection wells with data defined for the selected time intervals.

The article shows an example of its application to a synthetic oilfield. The oilfield is located in a reservoir with a complex distribution of permeability. Development of the oilfield is carried out by wells with complex dynamics of flow rate and injection rate. The entropy modeling is applied to analyze the interwell connectivity between producers and injectors for the entire object and between individual pairs of wells. A comparison of the coefficients obtained using entropy modeling and using the CRM model is presented. A very high level of compliance was obtained for all wells, which indicates the validity of the results of entropy modeling.

References

1. Stepanov S.V., Pospelova T.A., New concept of mathematical modeling for making reservoir engineering decisions (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 4, pp. 50–53.

2. Zakharyan A.Z., Ursegov S.O., From digital to mathematical models: a new look at geological and hydrodynamic modeling of oil and gas fields by means of artificial intelligence (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 12, pp. 144–148.

3. Mohaghegh S.D., Abdulla F., Abdou M. et al., Smart proxy: an innovative reservoir management tool; case study of a giant mature oilfield in UAE, SPE-177829-MS, 2015.

4. Khachkuruzov G.A., Osnovy obshchey i khimicheskoy termodinamiki (Fundamentals of general and chemical thermodynamics), Moscow: Vysshaya shkola Publ., 1979, 268 p.

5. Landau L.D., Lifshits E.M., Statisticheskaya fizika (Statistical physics), Moscow: Nauka Publ., 1976, 584 p.

6. Shannon C.E., A mathematical theory of communication, The Bell System Technical Journal, 1948, V. 27, pp. 379–423, 623–656.

7. Gel'fand I.M., Kolmogorov A.N., Yaglom A.M., Kolichestvo informatsii i entropiya dlya nepreryvnykh raspredeleniy (Amount of information and entropy for continuous distributions), Proceedings of III All-Union Mathematical Congress, V. 3, Moscow: Publ. of USSR Academy of science, 1958, pp. 300–320.

8. Tyrsin A.N., Entropiynoe modelirovanie mnogomernykh stokhasticheskikh sistem (Entropy modeling of multidimensional stochastic systems), Voronezh: Nauchnaya kniga Publ., 2016, 156 p.

9. Prigogine I., Introduction to thermodynamics of irreversible processes, Interscience, New York, 1961.

10. Tyrsin A.N., Sistemnyy analiz. Modeli i metody (System analysis. Models and methods), Voronezh: Nauchnaya kniga Publ., 2019, 167 p.

11. Stepanov S.V., Sokolov S.V., Ruchkin A.A. et al., Considerations on mathematical modeling of producer-injector interference (In Russ.), Vestnik Tyumenskogo gosudarstvennogo universiteta. Fiziko-matematicheskoe modelirovanie. Neft', gaz, energetika = Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, 2018, V. 4, no. 3, pp. 146–164.

12. Ruchkin A.A., Stepanov S.V., Knyazev A.V. et al., Applying CRM model to study well interference (In Russ.), Vestnik Tyumenskogo gosudarstvennogo universiteta. Fiziko-matematicheskoe modelirovanie. Neft', gaz, energetika = Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, 2018, V. 4, no. 4, pp. 148–168.

13. Zelenin D.V., Stepanov S.V., Bekman A.D., Ruchkin A.A., Research of mechanisms for accounting of wells interaction when using various methods of mathematical modeling (In Russ.), Neftepromyslovoe delo, 2019, no. 12, pp. 39–45.


14. Ayvazyan S.A., Enyukov I.S., Meshalkin L.D., Prikladnaya statistika: Issledovanie zavisimostey (Applied statistics: Dependency research), Moscow: Finansy i statistika Publ., 1985, 488 p.

Analysis of the flooding system is the most important task when supporting the development of oil fields. The use of hydrodynamic modeling to solve this problem is resource-intensive and characterized by significant uncertainties. An effective alternative to hydrodynamic modeling for the analysis of the flooding system can be entropy modeling, the use of which for this task is first justified in this paper. Within the framework of the developed approach, the modeling object-the "reservoir-wells" system is considered as a multidimensional stochastic system with potentially interconnected elements. In this case, the system is open, which allows us to consider the differential entropy as the sum of the entropy of randomness (describes the interaction of the system with the environment) and the entropy of self-organization (describes the processes within the system). Together, this allows a more objective approach to the analysis of the flooding system than other methods.

The article presents the theory of the developed method. In particular, it is noted that the calculation of differential entropy uses the apparatus of mathematical statistics. In this case, multidimensional random vectors are the vector of producing wells and the vector of injection wells with data defined for the selected time intervals.

The article shows an example of its application to a synthetic oilfield. The oilfield is located in a reservoir with a complex distribution of permeability. Development of the oilfield is carried out by wells with complex dynamics of flow rate and injection rate. The entropy modeling is applied to analyze the interwell connectivity between producers and injectors for the entire object and between individual pairs of wells. A comparison of the coefficients obtained using entropy modeling and using the CRM model is presented. A very high level of compliance was obtained for all wells, which indicates the validity of the results of entropy modeling.

References

1. Stepanov S.V., Pospelova T.A., New concept of mathematical modeling for making reservoir engineering decisions (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 4, pp. 50–53.

2. Zakharyan A.Z., Ursegov S.O., From digital to mathematical models: a new look at geological and hydrodynamic modeling of oil and gas fields by means of artificial intelligence (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 12, pp. 144–148.

3. Mohaghegh S.D., Abdulla F., Abdou M. et al., Smart proxy: an innovative reservoir management tool; case study of a giant mature oilfield in UAE, SPE-177829-MS, 2015.

4. Khachkuruzov G.A., Osnovy obshchey i khimicheskoy termodinamiki (Fundamentals of general and chemical thermodynamics), Moscow: Vysshaya shkola Publ., 1979, 268 p.

5. Landau L.D., Lifshits E.M., Statisticheskaya fizika (Statistical physics), Moscow: Nauka Publ., 1976, 584 p.

6. Shannon C.E., A mathematical theory of communication, The Bell System Technical Journal, 1948, V. 27, pp. 379–423, 623–656.

7. Gel'fand I.M., Kolmogorov A.N., Yaglom A.M., Kolichestvo informatsii i entropiya dlya nepreryvnykh raspredeleniy (Amount of information and entropy for continuous distributions), Proceedings of III All-Union Mathematical Congress, V. 3, Moscow: Publ. of USSR Academy of science, 1958, pp. 300–320.

8. Tyrsin A.N., Entropiynoe modelirovanie mnogomernykh stokhasticheskikh sistem (Entropy modeling of multidimensional stochastic systems), Voronezh: Nauchnaya kniga Publ., 2016, 156 p.

9. Prigogine I., Introduction to thermodynamics of irreversible processes, Interscience, New York, 1961.

10. Tyrsin A.N., Sistemnyy analiz. Modeli i metody (System analysis. Models and methods), Voronezh: Nauchnaya kniga Publ., 2019, 167 p.

11. Stepanov S.V., Sokolov S.V., Ruchkin A.A. et al., Considerations on mathematical modeling of producer-injector interference (In Russ.), Vestnik Tyumenskogo gosudarstvennogo universiteta. Fiziko-matematicheskoe modelirovanie. Neft', gaz, energetika = Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, 2018, V. 4, no. 3, pp. 146–164.

12. Ruchkin A.A., Stepanov S.V., Knyazev A.V. et al., Applying CRM model to study well interference (In Russ.), Vestnik Tyumenskogo gosudarstvennogo universiteta. Fiziko-matematicheskoe modelirovanie. Neft', gaz, energetika = Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, 2018, V. 4, no. 4, pp. 148–168.

13. Zelenin D.V., Stepanov S.V., Bekman A.D., Ruchkin A.A., Research of mechanisms for accounting of wells interaction when using various methods of mathematical modeling (In Russ.), Neftepromyslovoe delo, 2019, no. 12, pp. 39–45.


14. Ayvazyan S.A., Enyukov I.S., Meshalkin L.D., Prikladnaya statistika: Issledovanie zavisimostey (Applied statistics: Dependency research), Moscow: Finansy i statistika Publ., 1985, 488 p.


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