Review of research on modeling the geological structure and processes of field development

UDK: 622.276.1/.4
DOI: 10.24887/0028-2448-2021-10-46-51
Key words: field development, well interaction, modeling
Authors: M.M. Khasanov (Gazprom Neft PJSC, RF, Saint-Petersburg), R.R. Bakhitov (Ufa State Petroleum Technological University, RF, Ufa), I.A. Lakman (Ufa State Aviation Technical University, RF, Ufa)

In the analysis of field development processes, methods for assessing the mutual influence of wells within one development object and a model of the connectivity of reservoir systems, including the forecast of the spread of anisotropy of the geological properties of the productive layer of the studied reservoir, are especially in demand. There are several approaches to solving this problem, but they all have their limitations of applicability. The purpose of the study is to systematize and evaluate the effectiveness of various existing mathematical models, statistical algorithms for describing the geology of the reservoir, the connectivity of reservoir systems and field development processes. The main sources for the research search were the SPE database OnePetro, as well as Russian scientific library eLibrary.ru. The main selection criterion was the presence in the publication of a description of the study of the mutual influence of wells. After the selection of duplicate publications, a search for the full texts of the selected publications was carried out using Digital Object Identifier (DOI) and in the ResearchGate social network. The section "Classical Methods and Phenomenological Approaches" includes a review of 6 publications by Russian scientists describing the applicability of approaches based on hydrodynamic modeling of the material balance method and the mutual productivity matrix. In the section describing capacitive-resistive models, an analysis of 7 sources is carried out, describing the hydrodynamic connection of wells on the basis of material balance equations. The section "Statistical Methods and Machine Learning Methods" includes the analysis of 11 sources, which describe both approaches based on time series analysis and based on machine learning algorithms (support vector machine, decision tree algorithm, etc.), neural network models. A separate section contains 6 studies based on the applicability of geostatistical methods. This section discusses, in addition to traditional cricking and coking methods, methods based on spatial statistical modeling. The analysis of the sources allowed us to draw conclusions about the most promising use of hybrid approaches, since when building a model on the entire set of related time series (well productivity dynamics), it is important to support the study with synchronous analysis to identify the characteristic patterns of both each well and the existing time lag in the resulting mutual influence wells.

References

1. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1984, 208 p.

2. 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, DOI: 10.21684/2411-7978-2018-4-3-146-164.

3. Abidov D.G., Kamartdinov M.R., Material balance method as a primary tool for assessing the development indicators of a field site during waterflooding (In Russ.), Izvestiya Tomskogo politekhnicheskogo universiteta, 2013, V. 322, no. 1, pp. 90-96

4. Meerov M.V., Litvak B.L., Optimizatsiya sistem mnogosvyaznogo upravleniya (Optimization of multiply connected control systems), Moscow: Nauka Publ., 1972, 344 p.

5. Valko P.P., Doublet L.E., Blasingame T.A., Development and application of the multiwell productivity index (MPI), SPE-51793-PA, 2000, DOI: 10.2118/51793-PA.

6. Yudin E.V., Method for estimating the wells interference using field performance data (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2018, no. 8, pp. 64-69, DOI: 10.24887/0028-2448-2018-8-64-69

7. Albertoni A., Lake L.W., Inferring interwell connectivity only from well-rate fluctuations in waterfloods, SPE-83381-PA, 2003, DOI:10.2118/83381-pa

8. Lake L. W., Liang X., Edgar T. F., Al-Yousef A., Sayarpour M., Weber D., Optimization of oil production based on a capacitance model of production and injection rates, SPE-107713-MS, 2007, DOI: 10.2118/107713-ms.

9. Gentil P.H., The use of multilinear regression models in patterned water floods: Physical meaning of the regression coefficients: MS thesis, The University of Texas at Austin, Texas, 2005, DOI: 10.26153/tsw/8138

10. Yousef A.A., Gentil P.H., Jensen J.L., Lake L.W., A capacitance model to infer interwell connectivity from production and injection rate fluctuations, SPE-95322-PA, 2006, DOI:10.2118/95322-pa.

11. Sayarpour M., Development and application of capacitance-resistive models to water/CO2 floods: Doctoral dissertation, The University of Texas at Austin, 2008, DOI: 10.13140/RG.2.1.1798.3847

12. 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, no. 3-4, pp. 227-238, DOI: 10.1016/j.petrol.2009.09.006.

13. Khatmullin I. F., Tsanda A. P., Andrianova A. M., Budenny S. A., Margarit A. S., Lushpeev V. A., Semi-analytical models for calculating well interference: limitations and applications (In Russ.), Neftyanoe Khozyaystvo = Oil Industry, 2018, no. 12, pp. 38-41, DOI: 10.24887/0028-2448-2018-12-38-41

14. Apergis N., T. Ewing B., Payne J., A time series analysis of oil production, rig count and crude oil price: Evidence from six U.S. oil producing regions, Energy, 2015, V. 97, pp. 339-349, DOI: 10.1016/j.energy.2015.12.028

15. Frausto-Solis J., Chi-Chim M., Sheremetov L., Forecasting oil production time series with a population-based simulated annealing method, Arabian Journal for Science and Engineering, 2015, V. 40, pp. 1081-1096, DOI:10.1007/S13369-015-1587-Z

16. Suhartono D., Prastyo H., Kuswanto M., Hisyam L., Comparison between VAR, GSTAR, FFNN-VAR and FFNN-GSTAR models for forecasting oil production, MATEMATIKA, 2018, V. 34, no. 1, pp. 103–111, DOI:10.11113/matematika.v34.n1.1040

17. Albertoni A., Lake L.W., Inferring interwell connectivity only from well-rate fluctuations in waterfloods, SPE-83381-PA, 2003, V. 6, no. 1, pp. 6–16, DOI: 10.2118/83381-pa

18. Yousef A.A., Investigating statistical techniques to infer interwell connectivity from production and injection rate fluctuations: Doctoral dissertation, The University of Texas at Austin, 2006.

19.  Smith R., Mukerji T., Lupo T., Correlating geologic and seismic data with unconventional resource production curves using machine learning, Geophysics, 2018, V. 84, no. 2, pp. 39-47, DOI: 10.1190/geo2018-0202.1

20. Bansal Y., Ertekin T., Karpyn Z., Ayala L., Nejad A., Forecasting well performance in a discontinuous tight oil reservoir using artificial neural networks, SPE-164542-MS, USA, 2013, DOI: 10.2118/164542-ms.

21. Akande K., Olatunji S., Owolabi T., AbdulRaheem A., Comparative analysis of feature selection-based machine learning techniques in reservoir characterization, SPE-178006-MS, 2015, DOI: 10.2118/178006-MS

22. Liu W., Liu W. D., Gu J., Reservoir inter-well connectivity analysis based on a data driven method, SPE-197654-MS, 2019, DOI: 10.2118/197654-MS

23. Artun E., Characterizing interwell connectivity in waterflooded reservoirs using data-driven and reduced-physics models: A comparative study, Neural Computing and Applications, 2017, V. 28, no. 1, pp. 1729–1743, DOI:10.1007/s00521-015-2152-0

24. Maojun C., Fuhua S., Study on inferring interwell connectivity of injection-production system based on decision tree, Proceedings of 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 2013, DOI: 10.1109/fskd.2013.6816343 

25. Kelkar M., Application of geostatistics for reservoir characterization accomplishments and challenges, Journal of Canadian Petroleum Technology, 2000, V. 39, pp. 25–29, DOI: 10.2118/00-07-DAS

26. Delfiner P., Delhomme J., Pelissier J., Application of geostatistical analysis to the evaluation of petroleum reservoirs with well logs, Proceedings of SPWLA 24th Annual Logging Symposium, 1983, June 27–30, New Orleans, LA, 1983.

27. Kammann E., Wand M., Geoadditive models, Journal of the Royal Statistical Society: Series C (Applied Statistics), 2003, V. 52, no. 1, pp. 1-18, DOI: 10.1111/1467-9876.00385.

28. Johannesson G., Cressie N., Finding large-scale spatial trends in massive, global, environmental datasets, Environmetrics, 2003, V. 15, no. 1, pp. 1-44, DOI: 10.1002/env.624

29. Zimmerman D., de Marsily G., Gotway C., Marietta M., Axness C., Beauheim R., Bras R., Carrera J. et al., A Comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow, Water Resources Research, 1998, V. 39, no. 6, pp. 1373-1413, DOI: 10.1029/98WR00003

30. Cressie N., Statistics for spatial data, J Wiley&Sons Inc., 1991, 991 p.

In the analysis of field development processes, methods for assessing the mutual influence of wells within one development object and a model of the connectivity of reservoir systems, including the forecast of the spread of anisotropy of the geological properties of the productive layer of the studied reservoir, are especially in demand. There are several approaches to solving this problem, but they all have their limitations of applicability. The purpose of the study is to systematize and evaluate the effectiveness of various existing mathematical models, statistical algorithms for describing the geology of the reservoir, the connectivity of reservoir systems and field development processes. The main sources for the research search were the SPE database OnePetro, as well as Russian scientific library eLibrary.ru. The main selection criterion was the presence in the publication of a description of the study of the mutual influence of wells. After the selection of duplicate publications, a search for the full texts of the selected publications was carried out using Digital Object Identifier (DOI) and in the ResearchGate social network. The section "Classical Methods and Phenomenological Approaches" includes a review of 6 publications by Russian scientists describing the applicability of approaches based on hydrodynamic modeling of the material balance method and the mutual productivity matrix. In the section describing capacitive-resistive models, an analysis of 7 sources is carried out, describing the hydrodynamic connection of wells on the basis of material balance equations. The section "Statistical Methods and Machine Learning Methods" includes the analysis of 11 sources, which describe both approaches based on time series analysis and based on machine learning algorithms (support vector machine, decision tree algorithm, etc.), neural network models. A separate section contains 6 studies based on the applicability of geostatistical methods. This section discusses, in addition to traditional cricking and coking methods, methods based on spatial statistical modeling. The analysis of the sources allowed us to draw conclusions about the most promising use of hybrid approaches, since when building a model on the entire set of related time series (well productivity dynamics), it is important to support the study with synchronous analysis to identify the characteristic patterns of both each well and the existing time lag in the resulting mutual influence wells.

References

1. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1984, 208 p.

2. 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, DOI: 10.21684/2411-7978-2018-4-3-146-164.

3. Abidov D.G., Kamartdinov M.R., Material balance method as a primary tool for assessing the development indicators of a field site during waterflooding (In Russ.), Izvestiya Tomskogo politekhnicheskogo universiteta, 2013, V. 322, no. 1, pp. 90-96

4. Meerov M.V., Litvak B.L., Optimizatsiya sistem mnogosvyaznogo upravleniya (Optimization of multiply connected control systems), Moscow: Nauka Publ., 1972, 344 p.

5. Valko P.P., Doublet L.E., Blasingame T.A., Development and application of the multiwell productivity index (MPI), SPE-51793-PA, 2000, DOI: 10.2118/51793-PA.

6. Yudin E.V., Method for estimating the wells interference using field performance data (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2018, no. 8, pp. 64-69, DOI: 10.24887/0028-2448-2018-8-64-69

7. Albertoni A., Lake L.W., Inferring interwell connectivity only from well-rate fluctuations in waterfloods, SPE-83381-PA, 2003, DOI:10.2118/83381-pa

8. Lake L. W., Liang X., Edgar T. F., Al-Yousef A., Sayarpour M., Weber D., Optimization of oil production based on a capacitance model of production and injection rates, SPE-107713-MS, 2007, DOI: 10.2118/107713-ms.

9. Gentil P.H., The use of multilinear regression models in patterned water floods: Physical meaning of the regression coefficients: MS thesis, The University of Texas at Austin, Texas, 2005, DOI: 10.26153/tsw/8138

10. Yousef A.A., Gentil P.H., Jensen J.L., Lake L.W., A capacitance model to infer interwell connectivity from production and injection rate fluctuations, SPE-95322-PA, 2006, DOI:10.2118/95322-pa.

11. Sayarpour M., Development and application of capacitance-resistive models to water/CO2 floods: Doctoral dissertation, The University of Texas at Austin, 2008, DOI: 10.13140/RG.2.1.1798.3847

12. 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, no. 3-4, pp. 227-238, DOI: 10.1016/j.petrol.2009.09.006.

13. Khatmullin I. F., Tsanda A. P., Andrianova A. M., Budenny S. A., Margarit A. S., Lushpeev V. A., Semi-analytical models for calculating well interference: limitations and applications (In Russ.), Neftyanoe Khozyaystvo = Oil Industry, 2018, no. 12, pp. 38-41, DOI: 10.24887/0028-2448-2018-12-38-41

14. Apergis N., T. Ewing B., Payne J., A time series analysis of oil production, rig count and crude oil price: Evidence from six U.S. oil producing regions, Energy, 2015, V. 97, pp. 339-349, DOI: 10.1016/j.energy.2015.12.028

15. Frausto-Solis J., Chi-Chim M., Sheremetov L., Forecasting oil production time series with a population-based simulated annealing method, Arabian Journal for Science and Engineering, 2015, V. 40, pp. 1081-1096, DOI:10.1007/S13369-015-1587-Z

16. Suhartono D., Prastyo H., Kuswanto M., Hisyam L., Comparison between VAR, GSTAR, FFNN-VAR and FFNN-GSTAR models for forecasting oil production, MATEMATIKA, 2018, V. 34, no. 1, pp. 103–111, DOI:10.11113/matematika.v34.n1.1040

17. Albertoni A., Lake L.W., Inferring interwell connectivity only from well-rate fluctuations in waterfloods, SPE-83381-PA, 2003, V. 6, no. 1, pp. 6–16, DOI: 10.2118/83381-pa

18. Yousef A.A., Investigating statistical techniques to infer interwell connectivity from production and injection rate fluctuations: Doctoral dissertation, The University of Texas at Austin, 2006.

19.  Smith R., Mukerji T., Lupo T., Correlating geologic and seismic data with unconventional resource production curves using machine learning, Geophysics, 2018, V. 84, no. 2, pp. 39-47, DOI: 10.1190/geo2018-0202.1

20. Bansal Y., Ertekin T., Karpyn Z., Ayala L., Nejad A., Forecasting well performance in a discontinuous tight oil reservoir using artificial neural networks, SPE-164542-MS, USA, 2013, DOI: 10.2118/164542-ms.

21. Akande K., Olatunji S., Owolabi T., AbdulRaheem A., Comparative analysis of feature selection-based machine learning techniques in reservoir characterization, SPE-178006-MS, 2015, DOI: 10.2118/178006-MS

22. Liu W., Liu W. D., Gu J., Reservoir inter-well connectivity analysis based on a data driven method, SPE-197654-MS, 2019, DOI: 10.2118/197654-MS

23. Artun E., Characterizing interwell connectivity in waterflooded reservoirs using data-driven and reduced-physics models: A comparative study, Neural Computing and Applications, 2017, V. 28, no. 1, pp. 1729–1743, DOI:10.1007/s00521-015-2152-0

24. Maojun C., Fuhua S., Study on inferring interwell connectivity of injection-production system based on decision tree, Proceedings of 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 2013, DOI: 10.1109/fskd.2013.6816343 

25. Kelkar M., Application of geostatistics for reservoir characterization accomplishments and challenges, Journal of Canadian Petroleum Technology, 2000, V. 39, pp. 25–29, DOI: 10.2118/00-07-DAS

26. Delfiner P., Delhomme J., Pelissier J., Application of geostatistical analysis to the evaluation of petroleum reservoirs with well logs, Proceedings of SPWLA 24th Annual Logging Symposium, 1983, June 27–30, New Orleans, LA, 1983.

27. Kammann E., Wand M., Geoadditive models, Journal of the Royal Statistical Society: Series C (Applied Statistics), 2003, V. 52, no. 1, pp. 1-18, DOI: 10.1111/1467-9876.00385.

28. Johannesson G., Cressie N., Finding large-scale spatial trends in massive, global, environmental datasets, Environmetrics, 2003, V. 15, no. 1, pp. 1-44, DOI: 10.1002/env.624

29. Zimmerman D., de Marsily G., Gotway C., Marietta M., Axness C., Beauheim R., Bras R., Carrera J. et al., A Comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow, Water Resources Research, 1998, V. 39, no. 6, pp. 1373-1413, DOI: 10.1029/98WR00003

30. Cressie N., Statistics for spatial data, J Wiley&Sons Inc., 1991, 991 p.


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