The paper discusses the problem of increasing the discreteness of liquid flow rate measurements in a well using highly discrete pressure data at the receiving end of an electric submersible pump (ESP) unit. The «virtual flow meter» algorithm based on machine learning methods that solves the problem is presented. The numerical characteristics describing the curve of pressure change at the ESP unit inlet, as well as the components of Darcy's law and diffusivity equation are considered as features. To solve the regression problem, the authors considered single machine learning models and ensembles based on stacking method of combining the responses of single models as attributes to calculate the responses of the final model. The results of testing on field data on mechanized production wells on examples of low-permeability reservoir of Western Siberia field showed that the average relative error does not exceed 10 %. The algorithm of «virtual flow meter» was implemented in the software package for interpretation of well test «RN-VEGA» and used in preparation of data for interpretation of well-testing by the production and pressure transient analysis. To approbate the approach under consideration, the results of interpretation by the production and pressure transient analysis were compared on data sets with different discreteness of measurements of downhole pressure and liquid rate dynamics. In the first set the liquid rate series had low discreteness, the second set was obtained from the first one by applying the constructed algorithm. It is shown that the use of the «virtual flow meter» reduces the error by 10 % in determining the fracture half-length and permeability of the formation. The results of approbation allow the authors to conclude that the developed algorithm increases the reliability of data interpretation by production and pressure transient analysis, as well as increases the accuracy of determining reservoir parameters and well completion in low-permeability reservoirs.
References
1. Asalkhuzina G.F., Davletbaev A.Ya., Salakhov T.R. et al., Applying decline analysis for reservoir pressure determination (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2022, no. 10, pp. 30-33, DOI: https://doi.org/10.24887/0028-2448-2022-10-30-33
2. Asalkhuzina G.F., Bikmetova A.R., Kardopol’tsev A.S. et al., Evolution of methods and scopes of welltesting on fields with low permeability reservoir (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2023, no. 9, pp. 108–111, DOI: https://doi.org/10.24887/0028-2448-2023-9-108-111
3. Davletbaev A.Ya., Makhota N.A., Nuriev A.Kh. et al., Design and analysis of injection tests during hydraulic fracturing in low-permeability reservoirs using RN-GRID software package (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2018, no. 10, pp. 77–83, DOI: https://doi.org/10.24887/0028-2448-2018-10-77-83
4. Bukhmastova S.V., Fakhreeva R.R., Pityuk Yu.A. et al., Approbation of MLR and CRMIP methods in research of well interference (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2020, no. 8, pp. 58–62, DOI: https://doi.org/10.24887/0028-2448-2020-8-58-62
5. Afanas’ev I.S., Sergeychev A.V., Asmandiyarov R.N. et al., Automatic well test data processing: a time series wavelet analysis approach (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2012, no. 11, pp. 34-37.
6. Shabonas A.R., Gorid’ko K.A., Review of approaches to virtual flowmeter algorithm implementation in wells, equipped by electric submersible pumps (In Russ.), Neftepromyslovoe delo, 2022, no. 1(637), pp. 33–41, DOI: https://doi.org/10.33285/0207-2351-2022-1(637)-33-41
7. Stundner M., Nunes G., Production performance monitoring workflow, SPE-103757-MS, 2006, DOI: https://doi.org/10.2118/112221-MS
8. Zangl G., Graf T., Al-Kinami A., Proxy modeling in production optimization, SPE-100131-MS, 2006, DOI: https://doi.org/10.2118/100131-MS
9. Pashali A.A., Aleksandrov M.A., Kliment’ev A.G. et al., Automatization of collecting and preparation of telemetry data for well testing using ‘’virtual flowmeter’’ (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 11, pp. 60–63.
10. Andrianova A.M., Loginov A.A., Khabibullin R.A., Kobzar’ O.S., Virtual metering as a tool for ESP-equipped wells monitoring (In Russ.), PRONEFT’’. Professional’no o nefti, 2020, no. 4(18), pp. 75–80, DOI: https://doi.org/10.7868/S2587739920040114
11. Bikmukhametov T., Jäschke J., First principles and machine learning virtual flow metering: A literature review, J. of Petroleum Science and Engineering, 2020, V. 184, DOI: https://doi.org/10.1016/j.petrol.2019.106487.
12. RN-DIGITAL: Analiz i interpretatsiya gidrodinamicheskikh issledovaniy skvazhin (GDIS) (RN-DIGITAL: Analysis and interpretation of hydrodynamic well testing), URL: https://rn.digital/rnvega
13. Sarapulova V.V., Davletbaev A.Ya., Kunafin A.F. et al., The RN-VEGA program complex for well test analysis and interpretation (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2023, no. 12, pp. 124 –129, DOI: https://doi.org/10.24887/0028-2448-2023-12-124-129
14. Abramenkova I.V., Kruglov V.V., Methods for recovering gaps in data sets (In Russ.), Programmnye produkty i sistemy, 2005, no. 2, URL: https://cyberleninka.ru/article/n/metody-vosstanovleniya-propuskov-v-massivah-dannyh
15. Kayumov E., Metody vosstanovleniya propuskov v dannykh (Methods for recovering gaps in data), MachineLearning.ru: professional’nyy informatsionno-analiticheskiy resurs, 2015, URL: http://www.machinelearning.ru/wiki/images/4/48/Methods_for_missing_value.pdf
16. Sharma V., Yuden K., Imputing missing data in hydrology using machine learning models, International Journal of Engineering Research & Technology, 2021, no. 10, pp. 78-82, DOI: http://doi.org/10.17577/IJERTV10IS010011
17. Mariani M.C., Basu K., Spline interpolation techniques applied to the study of geophysical data, Physica A: Statistical Mechanics and its Applications, 2015, V. 428(C), pp. 68–79, DOI: http://doi.org/10.1016/j.physa.2015.02.014
18. Schaff D.P., Waldhauser F., Waveform cross correlation based differential travel-time measurements at the northern California Seismic Network, Bull. Seismol. Soc. Am., 2005, V. 95, no. 95, pp. 2446–2461, DOI: http://doi.org/10.1785/0120040221
19. Honghai F., Guoshun C., Cheng Y. et al., A SVM regression based approach to filling in missing values, Knowledge-Based Intelligent Information and Engineering Systems, 2005, V. 3683, pp. 581–587, DOI: http://doi.org/10.1007/11553939_83
20. Gao Y., Merz C., Lischeid G., Schneider M., A review on missing hydrological data processing, Environmental Earth Sciences, 2018, V. 77,
DOI: http://doi.org/10.1007/s12665-018-7228-6
21. Tian C., Horne R.N., Machine learning applied to multiwell test analysis and flow rate reconstruction, SPE-175059-MS, 2015, DOI: https://doi.org/10.2118/175059-MS
22. Yudin E.V., Andrianova A.M., Ganeev T.A. et al., Production monitoring using a virtual flow meter for an unstable operating well stock (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2023, no. 8, pp. 82–87, DOI: https://doi.org/10.24887/0028-2448-2023-8-82-87
23. Davletbaev A.Ya., Fluid filtration in porous media with vertically fractured wells (In Russ.), Inzhenerno-fizicheskiy zhurnal, 2012, V. 85, no. 5, pp. 919–924.
24. Dorogush A.V., Ershov V., Gulin A., CatBoost: gradient boosting with categorical features support, Workshop on ML Systems at NIPS, 2017.
25. Horichreiter S., Schmidhuber J., Long short-term memory, Neural Computation, 1997, V. 9(8), DOI: https://doi.org/10.1162/neco.1997.9.8.1735
26. Sill J., Takacs G., Mackey L., Feature-weighted linear stacking, Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2009, pp. 845–854.