The main method of oil field development in Russia is flooding. Most of the fields are at the III-IV stages of development. Production wells are mainly characterized by low oil flow rates and high water cut (90-98%). Under these conditions, development engineers are faced with the task of minimizing water production and injection while maintaining or even increasing the oil production rate. For this, measures are being taken to control and manage the oil field development. To implement such measures, a fairly simple model from a computational point of view is necessary, which at the same time takes into account all the main factors that affect the development process. The paper presents an improved mathematical model of V.S. Kovalev and M.L. Surguchev for the operational calculation of oil reservoir flooding indicators. It partially takes into account the non-piston nature of displacement (piston model of displacement is used, but the incompleteness of oil displacement by water is taken into account) and the real placement of wells, and also partially takes into account the heterogeneity of the reservoir in terms of filtration-capacitive properties. The heterogeneity of the reservoir over the area is taken into account indirectly when constructing streamlines. It is assumed to use one permeability distribution describing layer-by-layer flooding when calculating the movement of water for all stream tubes. If necessary, the calculations are possible with the adaptation of the permeability distribution for each well. An original method of constructing the distribution of streamlines is proposed for converting the flow in the well system to the flow in the curved gallery. The model is based on two methods: the stream tube method and the curved gallery method. Comparison of the results of calculations using the proposed model with the results of calculations on the commercial hydrodynamic simulator Rubis Kappa Engineering shows satisfactory accuracy from a practical point of view.

References

1. Spravochnoe rukovodstvo po proektirovaniyu razrabotki i ekspluatatsii neftyanykh mestorozhdeniy. Proektirovanie razrabotki (Reference guide for the design, development and operation of oil fields. Development design): edited by Gimatudinov Sh.K., Moscow: Nedra Publ., 1983, 464 p.

2. Borisov Yu.P., Voinov V.V., Ryabinina Z.K., Vliyanie neodnorodnosti plastov na razrabotku neftyanykh mestorozhdeniy (Influence of reservoir heterogeneity on the development of oil fields), Moscow: Nedra Publ., 1970, 288 p.

3. Kovalev V.S., Zhitomirskiy V.M., Prognoz razrabotki neftyanykh mestorozhdeniy i effektivnost' sistem zavodneniya (Oil field development forecast and waterflooding system efficiency), Moscow: Nedra Publ., 1976, 248 p.

4. Surguchev M.L., Metody kontrolya i regulirovaniya protsessa razrabotki neftyanykh mestorozhdeniy (Methods for monitoring and managing of oil fields development), Moscow: Nedra Publ., 1968, 371 p.

5. Kovalev V.S., Raschet protsessa zavodneniya neftyanoy zalezhi (Calculation of the process of waterflooding of an oil reservoir), Moscow: Nedra Publ., 1970, 137 p.

6. Akul'shin A.I., Prognozirovanie razrabotki neftyanykh mestorozhdeniy (Forecasting the development of oil fields), Moscow: Nedra Publ., 1988, 240 p.

7. Ertekin T., Abou-Kassem J.H., King G.R., Basic applied reservoir simulation, SPE Textbook Series Vol. 7, 2001, 406 p.

8. Fanchi J.R., Principles of applied reservoir simulation, Amsterdam: Elsevier, 2005, 532 p.

9. 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.

10. Sayarpour M., Zuluaga E., Kabir C.S., Lake L.W., The use of capacitance–resistance models for rapid estimation of waterflood performance and optimization, Journal of Petroleum Science and Engineering, 2009, V. 69 (3–4), pp. 227–238.

11. Houze O., Viturat D., Fjaere S.O., Dynamic data analysis, Paris: Kappa Engineering, 2020, 852 p.

12. CMG Users Guide 2018.10, Calgary: Computer Modelling Groupe LTD, 2018, 1136 p.

13. RD 39-100-91. Metodicheskoe rukovodstvo po gidrodinamicheskim, promyslovo-geofizicheskim i fiziko-khimicheskim metodam kontrolya razrabotki neftyanykh mestorozhdeniy (Methodical guidance on hydrodynamic, field-geophysical and physicochemical methods of oil field development control), Moscow: Publ. of Minneftegazprom, 1991, 540 p.

14. RD 153-39.0-10-01. Metodicheskie ukazaniya po kompleksirovaniyu i etapnosti vypolneniya geofizicheskikh, gidrodinamicheskikh i geokhimicheskikh issledovaniy neftyanykh i gazovykh mestorozhdeniy (Guidelines for the integration and staging of geophysical, hydrodynamic and geochemical studies of oil and gas fields), Moscow: Publ. of Minenergo, 2002, 76 p.

15. Brill J.P., Mukherjee H., Multiphase flow in wells, SPE Monograph, Henry L. Dogherty Series, V.17, 1999, 164 p.

16. Korolev A.V., Kats R.M., Testirovanie matematicheskikh modeley, primenyaemykh pri proektirovanii razrabotki s primeneniem gorizontal'nykh skvazhin (Testing of mathematical models used in the design of development with the use of horizontal wells), Publ. of VNIIneft, INPETRO, 1994, 26 p.

17. Odeh A.S., Comparison of solutions to a three-dimensional black-oil reservoir simulation problem, SPE-9723-PA, 1981.

The main method of oil field development in Russia is flooding. Most of the fields are at the III-IV stages of development. Production wells are mainly characterized by low oil flow rates and high water cut (90-98%). Under these conditions, development engineers are faced with the task of minimizing water production and injection while maintaining or even increasing the oil production rate. For this, measures are being taken to control and manage the oil field development. To implement such measures, a fairly simple model from a computational point of view is necessary, which at the same time takes into account all the main factors that affect the development process. The paper presents an improved mathematical model of V.S. Kovalev and M.L. Surguchev for the operational calculation of oil reservoir flooding indicators. It partially takes into account the non-piston nature of displacement (piston model of displacement is used, but the incompleteness of oil displacement by water is taken into account) and the real placement of wells, and also partially takes into account the heterogeneity of the reservoir in terms of filtration-capacitive properties. The heterogeneity of the reservoir over the area is taken into account indirectly when constructing streamlines. It is assumed to use one permeability distribution describing layer-by-layer flooding when calculating the movement of water for all stream tubes. If necessary, the calculations are possible with the adaptation of the permeability distribution for each well. An original method of constructing the distribution of streamlines is proposed for converting the flow in the well system to the flow in the curved gallery. The model is based on two methods: the stream tube method and the curved gallery method. Comparison of the results of calculations using the proposed model with the results of calculations on the commercial hydrodynamic simulator Rubis Kappa Engineering shows satisfactory accuracy from a practical point of view.

References

1. Spravochnoe rukovodstvo po proektirovaniyu razrabotki i ekspluatatsii neftyanykh mestorozhdeniy. Proektirovanie razrabotki (Reference guide for the design, development and operation of oil fields. Development design): edited by Gimatudinov Sh.K., Moscow: Nedra Publ., 1983, 464 p.

2. Borisov Yu.P., Voinov V.V., Ryabinina Z.K., Vliyanie neodnorodnosti plastov na razrabotku neftyanykh mestorozhdeniy (Influence of reservoir heterogeneity on the development of oil fields), Moscow: Nedra Publ., 1970, 288 p.

3. Kovalev V.S., Zhitomirskiy V.M., Prognoz razrabotki neftyanykh mestorozhdeniy i effektivnost' sistem zavodneniya (Oil field development forecast and waterflooding system efficiency), Moscow: Nedra Publ., 1976, 248 p.

4. Surguchev M.L., Metody kontrolya i regulirovaniya protsessa razrabotki neftyanykh mestorozhdeniy (Methods for monitoring and managing of oil fields development), Moscow: Nedra Publ., 1968, 371 p.

5. Kovalev V.S., Raschet protsessa zavodneniya neftyanoy zalezhi (Calculation of the process of waterflooding of an oil reservoir), Moscow: Nedra Publ., 1970, 137 p.

6. Akul'shin A.I., Prognozirovanie razrabotki neftyanykh mestorozhdeniy (Forecasting the development of oil fields), Moscow: Nedra Publ., 1988, 240 p.

7. Ertekin T., Abou-Kassem J.H., King G.R., Basic applied reservoir simulation, SPE Textbook Series Vol. 7, 2001, 406 p.

8. Fanchi J.R., Principles of applied reservoir simulation, Amsterdam: Elsevier, 2005, 532 p.

9. 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.

10. Sayarpour M., Zuluaga E., Kabir C.S., Lake L.W., The use of capacitance–resistance models for rapid estimation of waterflood performance and optimization, Journal of Petroleum Science and Engineering, 2009, V. 69 (3–4), pp. 227–238.

11. Houze O., Viturat D., Fjaere S.O., Dynamic data analysis, Paris: Kappa Engineering, 2020, 852 p.

12. CMG Users Guide 2018.10, Calgary: Computer Modelling Groupe LTD, 2018, 1136 p.

13. RD 39-100-91. Metodicheskoe rukovodstvo po gidrodinamicheskim, promyslovo-geofizicheskim i fiziko-khimicheskim metodam kontrolya razrabotki neftyanykh mestorozhdeniy (Methodical guidance on hydrodynamic, field-geophysical and physicochemical methods of oil field development control), Moscow: Publ. of Minneftegazprom, 1991, 540 p.

14. RD 153-39.0-10-01. Metodicheskie ukazaniya po kompleksirovaniyu i etapnosti vypolneniya geofizicheskikh, gidrodinamicheskikh i geokhimicheskikh issledovaniy neftyanykh i gazovykh mestorozhdeniy (Guidelines for the integration and staging of geophysical, hydrodynamic and geochemical studies of oil and gas fields), Moscow: Publ. of Minenergo, 2002, 76 p.

15. Brill J.P., Mukherjee H., Multiphase flow in wells, SPE Monograph, Henry L. Dogherty Series, V.17, 1999, 164 p.

16. Korolev A.V., Kats R.M., Testirovanie matematicheskikh modeley, primenyaemykh pri proektirovanii razrabotki s primeneniem gorizontal'nykh skvazhin (Testing of mathematical models used in the design of development with the use of horizontal wells), Publ. of VNIIneft, INPETRO, 1994, 26 p.

17. Odeh A.S., Comparison of solutions to a three-dimensional black-oil reservoir simulation problem, SPE-9723-PA, 1981.