Skip to main content
SpringerLink
Log in

Machine learning applied to evaluation of reservoir connectivity

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In mature reservoirs, there are hundreds or thousands of producing and injecting wells operating simultaneously, so it is important to understand the impact of injection wells on producers to maintain pressure and control water production. In this work, we propose a workflow with two strategies, reduced-physics and data-driven modeling, to monitoring producer and injector wells based on interwell connectivity. The monitoring the wells allows to increase oil production, reducing water rate, and avoiding possible fracturing or fault reactivations. Both strategies use production history data only. The inputs in both strategies are injection rates, while output are liquid production rates. The first one, the reduced-physics modeling strategy, is based on the capacitance-resistance modeling for producers (CRMP), which calculates the liquid flowrate of the producing well based on the injection rate, productivity index of producers, time constant, and the connectivity between injectors and producers. The parameters of the CRMP model are obtained by minimizing the error between the observed and calculated liquid flowrates. The optimization algorithm that minimizes the error is the Sequential Quadratic Programming (SQP) and the gradient is obtained by finite differences. The second one, the data-driven modeling strategy is based on artificial neural networks (ANNs), which only use input and output data. The parameters of the artificial neural network, weights, and biases, are adjusted during the training process. Three architectures are proposed to match the outputs based on the inputs: single-layer perceptron, deep learning with multiple layers, and convolutional neural networks. The backpropagation algorithm is used to adjust the weights and biases of the architectures during training. In this study, we propose three alternatives for calculating the connectivities based on the trained model. The first one is based on the optimal weights. The second one is based on the average error after training and shuffling the input data, and the last one is based on the gradient importance. Two synthetic models, Two-phases, and Brush Canyon Outcrop, are used to validate the proposed workflow. The results show that the connectivities calculated by the gradient importance approach are closer to the connectivities obtained by the capacitance-resistance model. On the other hand, the connectivities obtained through the optimal weights and average error strategies show differences of 4% and 5%, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

The authors declare to make available the data that were used to generate this work when required.

References

  1. Artun E (2016) Characterization reservoir connectivity and forecasting waterflood performance using data-driven and reduced-physics models. Paper presented at the SPE Western Regional Meeting, Anchorage, Alaska, USA. https://doi.org/10.2118/180488-MS

  2. Artun E (2017) Characterizing interwell connectivity in waterflooded reservoirs using data-driven and reduced-physics models: a comparative study. Neural Comput Appl 28:1729–1743. https://doi.org/10.1007/s00521-015-2152-0

    Article  Google Scholar 

  3. Canning A, Moulière-Reiser D, Weiss Y, Malkin A, Phillip E, Grinberg N, Yehezkel V (2017) Neural networks approach to spectral enhancement. Society of Exploration Geophysicists

    Book  Google Scholar 

  4. Cao F, Luo H, Lake LW (2015) Oil-rate forecast by inferring fractional-flow models from field data with Koval method combined with the capacitance-resistance model. SPE Reserv Eval Eng 18(4):534–553

    Article  Google Scholar 

  5. Cerleani M (2020) Feature importance with time series and recurrent neural network. In: Published in Towards data science. https://towardsdatascience.com/feature-importance-with-time-series-and-recurrent-neural-network-27346d500b9c

  6. Cerleani M (2021) Advanced permutation importance to explain predictions. In: Published in Towards data science. https://towardsdatascience.com/advanced-permutation-importance-to-explain-predictions-ead7de26eed4

  7. Cheng H, Vyatkin V, Osipov E, Zeng P, Yu H (2020) LSTM based EFAST global sensitivity analysis for interwell connectivity evaluation using injection and production fluctuation data. IEEE Access 8:67289–67299. https://doi.org/10.1109/ACCESS.2020.2985230

    Article  Google Scholar 

  8. Computer Modeling Group LTD (2020) IMEX: user’s guide, Calgary, Canada

  9. Davudov D, Malkov A, Venkatraman A (2020) Integration of capacitance-resistance model with reservoir simulation. Paper presented at the SPE improved oil recovery conference, Virtual. https://doi.org/10.2118/200332-MS

  10. Elzenary M, Elkatatny S, Abdelgawad KZ, Abdulraheem A, Mahmoud M, Al-Shehri D (2018) New technology to evaluate equivalent circulating density while drilling using artificial intelligence. Society of Petroleum Engineers. https://doi.org/10.2118/192282-MS

    Book  Google Scholar 

  11. Ertekin T, Sun Q (2019) Artificial intelligence applications in reservoir engineering: a status check. Energies 12:2897. https://doi.org/10.3390/en12152897

    Article  Google Scholar 

  12. Holanda RW, Gildin E, Jensen JL (2015) Improved waterflood analysis using the capacitance-resistance model within a control systems framework. Society of Petroleum Engineers. https://doi.org/10.2118/177106-MS

    Article  Google Scholar 

  13. Kaviani D, Valkó PP (2010) Inferring interwell connectivity using multiwell productivity index (MPI). J Pet Sci Eng 73(1):48–58. https://doi.org/10.1016/j.petrol.2010.05.006

    Article  Google Scholar 

  14. Kim TH (2019) Improvement of reservoir management efficiency using stochastic capacitance-resistance model. Paper presented at the SPE Western Regional Meeting, San Jose, California, USA. https://doi.org/10.2118/195322-MS

  15. Kim YD, Durlofsky LJ (2021) A recurrent neural network-based proxy model for well-control optimization with nonlinear output constraints. SPE J 26(04):1837–1857

    Article  Google Scholar 

  16. Li H, He J, Misra S (2018) Data-driven in-situ geomechanical characterization in shale reservoirs. Society of Petroleum Engineers. https://doi.org/10.2118/191400-MS

    Book  Google Scholar 

  17. Lins HK, Horowitz B, Tueros JAR (2017) Numerical experience using capacitance-resistance multilayered models. CILAMCE 2017, Ibero-latin American congress in computational methods in engineering, Florianópolis, Brazil. https://doi.org/10.20906/CPS/CILAMCE2017-0282 (in Portuguese)

  18. Liu W, Liu WD, Gu J (2020) A machine learning method to infer inter-well connectivity using bottom-hole pressure data. J Energy Resour Technol. https://doi.org/10.1115/1.4047304

    Article  Google Scholar 

  19. Mamghaderi A, Pourafshary P (2013) Water flooding performance prediction in layered reservoirs using improved capacitance-resistive model. J Pet Sci Eng 108:107–117. https://doi.org/10.1016/j.petrol.2020.108151

    Article  Google Scholar 

  20. Mamghaderi A, Aminshahidy B, Bazargan H (2021) Prediction of waterflood performance using a modified capacitance-resistance model: a proxy with a time-correlated model error. J Pet Sci Eng 198:108152. https://doi.org/10.1016/j.petrol.2013.06.006

    Article  Google Scholar 

  21. Moreno GA (2013) Multilayer capacitance-resistance model with dynamic connectivities. J Pet Sci Eng 109:298–307. https://doi.org/10.1016/j.petrol.2013.08.009

    Article  Google Scholar 

  22. Naudomsup N, Lake LW (2017) Extension of capacitance-resistance model to tracer flow for determining reservoir properties. Paper presented at the SPE annual technical conference and exhibition, San Antonio, Texas, USA, October 2017. https://doi.org/10.2118/187410-MS

  23. Olden J, Jackson D (2002) Illuminating the black box: a randomization approach for understanding variable contributions in artificial neural networks. Ecol Model 154(1–2):135–150. https://doi.org/10.1016/S0304-3800(02)00064-9

    Article  Google Scholar 

  24. Oliveira DFB (2006) Production optimization techniques for petroleum reservoirs: derivate free approaches to dynamic rate allocation for injection and production. Master thesis, Civil Engineering Department, UFPE, Recife, Brazil (in Portuguese)

  25. Oliveira SD, Horowitz B, Tueros JAR (2021) Ensemble-based method with combined fractional flow model for waterflooding optimization. Oil Gas Sci Technol Rev IFP Energ Nouv 76:7. https://doi.org/10.2516/ogst/2020090

    Article  Google Scholar 

  26. Panda M, Chopra A (1998) An integrated approach to estimate well interactions. In: SPE India oil and gas conference and exhibition. Society of Petroleum Engineers. https://doi.org/10.2118/39563-MS

  27. Ross C (2017) Improving resolution and clarity with neural networks. Society of Exploration Geophysicists

    Book  Google Scholar 

  28. Sayarpour M, Zuluaga E, Kabir CS, Lake LW (2009) The use of capacitance-resistive models for rapid estimation of waterflood performance and optimization. J Pet Sci Eng 69(3–4):227–238. https://doi.org/10.1016/j.petrol.2009.09.006

    Article  Google Scholar 

  29. Tueros JAR, Horowitz B, Willmersdorf R, Oliveira D (2018) Non-distance-based localization techniques for ensemble-based waterflooding optimization. J Pet Sci Eng 170:440–452. https://doi.org/10.1016/j.petrol.2018.06.089

    Article  Google Scholar 

  30. Yousef AA, Gentil PH, Jensen JL, Lake LW (2005) A capacitance model to infer interwell connectivity from production and injection rate fluctuations. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers. https://doi.org/10.2118/95322-MS

  31. Yang Z, Urdaneta AH (2015) A practical approach to history-matching water-recycling in waterflood reservoir simulation-method and case studies in south belridge diatomite waterflood. Paper presented at the SPE Western Regional Meeting, Garden Grove, California, USA, April. https://doi.org/10.2118/174006-MS

  32. Yu J, Jahandideh A, Jafarpour B (2020) Engineering design of neural network architectures for estimation of inter-well connectivity and production performance. European Association of Geoscientists & Engineers. https://doi.org/10.3997/2214-4609.202035191

    Book  Google Scholar 

  33. Weber D (2009) The use of capacitance-resistance models to optimize injection allocation and well location in water floods. Ph.D. dissertation, The University of Texas at Austin

Download references

Acknowledgements

The authors acknowledge the financial support for this research by PRH-47 Human Resources Program, PETROBRAS, FACEPE, Energi Simulation and Federal University of Pernambuco (UFPE)

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Federal University of Pernambuco, Recife, PE, 50670-901, Brazil

    Leticia Agra Mendes Ramalho, Juan Alberto Rojas Tueros & Bernardo Horowitz

Authors
  1. Leticia Agra Mendes Ramalho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juan Alberto Rojas Tueros
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bernardo Horowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Alberto Rojas Tueros.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramalho, L.A.M., Tueros, J.A.R. & Horowitz, B. Machine learning applied to evaluation of reservoir connectivity. Neural Comput & Applic 36, 731–746 (2024). https://doi.org/10.1007/s00521-023-09056-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-023-09056-0

Keywords

Search

Navigation