New concept of mathematical modeling for making reservoir engineering decisions

UDK: 622.276.1/.4.001.57
DOI: 10.24887/0028-2448-2019-4-50-53
Key words: numerical modeling, reservoir model, digital core, material balance, capacitance resistive model (CRM)
Authors: S.V. Stepanov (TNNC LLC, RF, Tyumen), T.A. Pospelova (TNNC LLC, RF, Tyumen)

The paper describes a problem of the quality of reservoir engineering mathematical modeling. It also gives the criteria for the models quality and six case studies based on real fields. The authors show that the practical value of the models is not high; therefore, the quality of mathematical modeling of reservoir engineering should be improved. To solve this problem, the authors suggest to use a new concept of mathematical modeling. This concept is based on hierarchical modeling and it takes into account the different scales of mathematical models and their specific features. Within the framework of the proposed modeling concept, it is assumed that the initial stage of it is to obtain data using the Digital Core technology, and then a gradual transition from one level of modeling to another takes place. The final stage of the concept is modeling the reservoir engineering process using the material balance equations. In the transition between the modeling levels, the obtained data are analyzed and transformed for the next level. Analysis and transformation of data at different levels of modeling implies that their form should reflect the models nature, i.e. spatial dimension, scale of heterogeneity, assumptions used, and other features. The importance of honoring the model features for the formation of a practically valuable result is demonstrated by a synthetic example of evaluating the mutual influence of production and injection wells. A solution to such an inverse problem allows to achieve similarity of the estimated and “actual” profiles, but this is achieved due to distortions of the mutual influence of wells relative to their true values. A capacitance resistive model (CRM) is used to show that the use of analytical models is an effective way to address complex challenges of reservoir engineering.

References

1. Ivantsov N.N., Stepanov S.V., Stepanov A.V., Bukhalov I.S. Assessment of possibilities of hydrodynamic simulators to imitate the development of high-viscous oil fields. Part 1. Coning (In Russ.), Neftepromyslovoe delo, 2015, no. 6, pp. 52–58.

2. Lysenko V.D., Razrabotka neftyanykh mestorozhdeniy. Proektirovanie i analiz (Development of oil fields. Design and analysis), Moscow: Nedra-Biznestsentr Publ., 2003, 638 p.

3. Sayarpour M., Development and application of capacitance-resistive models to water/CO2 floods: Ph.D Dissertation, 2008.

4. Mohaghegh Sh.D., Liu J., Gaskari R., Maysami M., Application of well-based surrogate models (SRMs) to two offshore fields in Saudi Arabia, case study, SPE 153845-MS, 2012.

5. Mohaghegh Sh.D., Amini Sh., Gholami V. et al., Grid-based surrogate reservoir modelling (SRM) for fast track analysis of numerical reservoir simulation models at the grid block level, SPE 153844-MS, 2012.

6. He Qin, Mohaghegh Sh.D., Liu Zh., Reservoir simulation using smart proxy in SACROC unit – case study, SPE 184069-MS, 2016.

7. Baykov V.A., Rabtsevich S.A., Kostrigin I.V., Sergeychev A.V., Monitoring of field development using a hierarchy of models in software package RN-KIN (In Russ.), Nauchno-tekhnicheskiy vestnik “NK “RosneftК№”, 2014, no. 2, pp. 14 –17.

8. Gavris' A.S., Kosyakov V.P., Botalov A.Yu., The concept of effective design of hydrocarbon fields development. Software solutions (In Russ.), Neftepro­myslovoe delo, 2015, no. 11, pp. 75–85.

9. Shandrygin A.N., Digital core analysis for flow process evaluation is myth or reality? (In Russ.), SPE 171216-RU, 2014.

10. Stepanov S.V., Numerical research of capillary pressure and compressibility effect on the drowning dynamics (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2008, no. 8, pp. 72–74.

11. Stepanov S.V., Stepanov A.V., Eletskiy S.V., Numerical-analytical approach towards salvation of the problem relating to on-line prediction of an oil well operation in conditions of a gas cone formation (In Russ.), Neftepromyslovoe delo, 2013, no. 2, pp. 53–58.

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. 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.

14. Stepanov S.V. Ruchkin A.A., Stepanov A.V., Analytical method of separation of liquid and oil production in reservoirs during their joint development (In Russ.), Neftepromyslovoe delo, 2018, no. 2, pp. 10–17.

15. Lysenko V.D., Razrabotka neftyanykh mestorozhdeniy. Proektirovanie i analiz (Development of oil fields. Design and analysis), Moscow: Nedra-Biznestsentr Publ., 2003, 638 p.

16. Holanda R., Gildin E., Jensen J. et al., A state-of-the-art literature review on capacitance resistance models for reservoir characterization and performance forecasting, Energies, 2018, no. 11, 46 p.

17. Chitsiripanich S., Field application of capacitance-resistance models to identify potential locations for infill drillings: Master’s Thesis, Texas: University of Texas, 2015.

18. Baykov V.A., Gazizov R.K., Latypov A.R., Yakovlev A.A., Problems of development: from kiloв€’ to nanometer (In Russ.), Nauchno-tekhnicheskiy vestnik OAO “NK “Rosneft'”, 2011, no. 23, pp. 30–32.

The paper describes a problem of the quality of reservoir engineering mathematical modeling. It also gives the criteria for the models quality and six case studies based on real fields. The authors show that the practical value of the models is not high; therefore, the quality of mathematical modeling of reservoir engineering should be improved. To solve this problem, the authors suggest to use a new concept of mathematical modeling. This concept is based on hierarchical modeling and it takes into account the different scales of mathematical models and their specific features. Within the framework of the proposed modeling concept, it is assumed that the initial stage of it is to obtain data using the Digital Core technology, and then a gradual transition from one level of modeling to another takes place. The final stage of the concept is modeling the reservoir engineering process using the material balance equations. In the transition between the modeling levels, the obtained data are analyzed and transformed for the next level. Analysis and transformation of data at different levels of modeling implies that their form should reflect the models nature, i.e. spatial dimension, scale of heterogeneity, assumptions used, and other features. The importance of honoring the model features for the formation of a practically valuable result is demonstrated by a synthetic example of evaluating the mutual influence of production and injection wells. A solution to such an inverse problem allows to achieve similarity of the estimated and “actual” profiles, but this is achieved due to distortions of the mutual influence of wells relative to their true values. A capacitance resistive model (CRM) is used to show that the use of analytical models is an effective way to address complex challenges of reservoir engineering.

References

1. Ivantsov N.N., Stepanov S.V., Stepanov A.V., Bukhalov I.S. Assessment of possibilities of hydrodynamic simulators to imitate the development of high-viscous oil fields. Part 1. Coning (In Russ.), Neftepromyslovoe delo, 2015, no. 6, pp. 52–58.

2. Lysenko V.D., Razrabotka neftyanykh mestorozhdeniy. Proektirovanie i analiz (Development of oil fields. Design and analysis), Moscow: Nedra-Biznestsentr Publ., 2003, 638 p.

3. Sayarpour M., Development and application of capacitance-resistive models to water/CO2 floods: Ph.D Dissertation, 2008.

4. Mohaghegh Sh.D., Liu J., Gaskari R., Maysami M., Application of well-based surrogate models (SRMs) to two offshore fields in Saudi Arabia, case study, SPE 153845-MS, 2012.

5. Mohaghegh Sh.D., Amini Sh., Gholami V. et al., Grid-based surrogate reservoir modelling (SRM) for fast track analysis of numerical reservoir simulation models at the grid block level, SPE 153844-MS, 2012.

6. He Qin, Mohaghegh Sh.D., Liu Zh., Reservoir simulation using smart proxy in SACROC unit – case study, SPE 184069-MS, 2016.

7. Baykov V.A., Rabtsevich S.A., Kostrigin I.V., Sergeychev A.V., Monitoring of field development using a hierarchy of models in software package RN-KIN (In Russ.), Nauchno-tekhnicheskiy vestnik “NK “RosneftК№”, 2014, no. 2, pp. 14 –17.

8. Gavris' A.S., Kosyakov V.P., Botalov A.Yu., The concept of effective design of hydrocarbon fields development. Software solutions (In Russ.), Neftepro­myslovoe delo, 2015, no. 11, pp. 75–85.

9. Shandrygin A.N., Digital core analysis for flow process evaluation is myth or reality? (In Russ.), SPE 171216-RU, 2014.

10. Stepanov S.V., Numerical research of capillary pressure and compressibility effect on the drowning dynamics (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2008, no. 8, pp. 72–74.

11. Stepanov S.V., Stepanov A.V., Eletskiy S.V., Numerical-analytical approach towards salvation of the problem relating to on-line prediction of an oil well operation in conditions of a gas cone formation (In Russ.), Neftepromyslovoe delo, 2013, no. 2, pp. 53–58.

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. 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.

14. Stepanov S.V. Ruchkin A.A., Stepanov A.V., Analytical method of separation of liquid and oil production in reservoirs during their joint development (In Russ.), Neftepromyslovoe delo, 2018, no. 2, pp. 10–17.

15. Lysenko V.D., Razrabotka neftyanykh mestorozhdeniy. Proektirovanie i analiz (Development of oil fields. Design and analysis), Moscow: Nedra-Biznestsentr Publ., 2003, 638 p.

16. Holanda R., Gildin E., Jensen J. et al., A state-of-the-art literature review on capacitance resistance models for reservoir characterization and performance forecasting, Energies, 2018, no. 11, 46 p.

17. Chitsiripanich S., Field application of capacitance-resistance models to identify potential locations for infill drillings: Master’s Thesis, Texas: University of Texas, 2015.

18. Baykov V.A., Gazizov R.K., Latypov A.R., Yakovlev A.A., Problems of development: from kiloв€’ to nanometer (In Russ.), Nauchno-tekhnicheskiy vestnik OAO “NK “Rosneft'”, 2011, no. 23, pp. 30–32.


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