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Development of Proxy Models for Predicting and Optimizing the Time and Recovery Factor at Breakthrough During Water Injection in Oil Reservoirs

Received: 28 December 2021     Accepted: 20 January 2022     Published: 16 February 2022
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Abstract

Numerical reservoir simulation studies can be used to plan water injection projects to delay time and maximize oil recovery at water breakthrough which is time-consuming and computationally expensive. Combining computationally inexpensive proxy models and optimization algorithms is a solution to this problem. In this study, the Box-Behnken design method and response surface methodology were used to develop two proxy models which showed the relationship between time and recovery factor at water breakthrough with six independent variables namely porosity, horizontal permeability, water viscosity, bottom-hole pressure, water injection rate and vertical permeability. A comparison of actual and predicted values for time and oil recovery factor at water breakthrough was found to be in good agreement with each other. An average absolute percentage error of 2.038% and 1.217%, a root mean square error of 0.08 and 0.0000988, and coefficients of determination, R2 of 0.9984 and 0.9946 were obtained for time and recovery factor at water breakthrough respectively. These are indications that the developed models are accurate, valid, and reliable. The models were further validated by comparing the actual and predicted water breakthrough time and recovery factor at water breakthrough using input variables that were not used in model development. These were also in close agreement with each other. The MATLAB multi-objective genetic algorithm was used to determine at a specific average porosity and permeability value, the best optimum controllable variables that maximized the objective functions. These were found to be 10.8978 years and 0.786 respectively and agreed with simulation results obtained using similar input parameter values.

Published in International Journal of Oil, Gas and Coal Engineering (Volume 10, Issue 1)
DOI 10.11648/j.ogce.20221001.12
Page(s) 17-30
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Reservoir Simulation, Proxy Model, Design of Experiments, Breakthrough Time, Recovery Factor, Optimization

References
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Cite This Article
  • APA Style

    Anthony Ogbaegbe Chikwe, Onyebuchi Ivan Nwanwe, Obinna Stanley Onyia, Ndubuisi Uchechukwu Okereke, Jude Emeka Odo. (2022). Development of Proxy Models for Predicting and Optimizing the Time and Recovery Factor at Breakthrough During Water Injection in Oil Reservoirs. International Journal of Oil, Gas and Coal Engineering, 10(1), 17-30. https://doi.org/10.11648/j.ogce.20221001.12

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    ACS Style

    Anthony Ogbaegbe Chikwe; Onyebuchi Ivan Nwanwe; Obinna Stanley Onyia; Ndubuisi Uchechukwu Okereke; Jude Emeka Odo. Development of Proxy Models for Predicting and Optimizing the Time and Recovery Factor at Breakthrough During Water Injection in Oil Reservoirs. Int. J. Oil Gas Coal Eng. 2022, 10(1), 17-30. doi: 10.11648/j.ogce.20221001.12

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    AMA Style

    Anthony Ogbaegbe Chikwe, Onyebuchi Ivan Nwanwe, Obinna Stanley Onyia, Ndubuisi Uchechukwu Okereke, Jude Emeka Odo. Development of Proxy Models for Predicting and Optimizing the Time and Recovery Factor at Breakthrough During Water Injection in Oil Reservoirs. Int J Oil Gas Coal Eng. 2022;10(1):17-30. doi: 10.11648/j.ogce.20221001.12

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  • @article{10.11648/j.ogce.20221001.12,
      author = {Anthony Ogbaegbe Chikwe and Onyebuchi Ivan Nwanwe and Obinna Stanley Onyia and Ndubuisi Uchechukwu Okereke and Jude Emeka Odo},
      title = {Development of Proxy Models for Predicting and Optimizing the Time and Recovery Factor at Breakthrough During Water Injection in Oil Reservoirs},
      journal = {International Journal of Oil, Gas and Coal Engineering},
      volume = {10},
      number = {1},
      pages = {17-30},
      doi = {10.11648/j.ogce.20221001.12},
      url = {https://doi.org/10.11648/j.ogce.20221001.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ogce.20221001.12},
      abstract = {Numerical reservoir simulation studies can be used to plan water injection projects to delay time and maximize oil recovery at water breakthrough which is time-consuming and computationally expensive. Combining computationally inexpensive proxy models and optimization algorithms is a solution to this problem. In this study, the Box-Behnken design method and response surface methodology were used to develop two proxy models which showed the relationship between time and recovery factor at water breakthrough with six independent variables namely porosity, horizontal permeability, water viscosity, bottom-hole pressure, water injection rate and vertical permeability. A comparison of actual and predicted values for time and oil recovery factor at water breakthrough was found to be in good agreement with each other. An average absolute percentage error of 2.038% and 1.217%, a root mean square error of 0.08 and 0.0000988, and coefficients of determination, R2 of 0.9984 and 0.9946 were obtained for time and recovery factor at water breakthrough respectively. These are indications that the developed models are accurate, valid, and reliable. The models were further validated by comparing the actual and predicted water breakthrough time and recovery factor at water breakthrough using input variables that were not used in model development. These were also in close agreement with each other. The MATLAB multi-objective genetic algorithm was used to determine at a specific average porosity and permeability value, the best optimum controllable variables that maximized the objective functions. These were found to be 10.8978 years and 0.786 respectively and agreed with simulation results obtained using similar input parameter values.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - Development of Proxy Models for Predicting and Optimizing the Time and Recovery Factor at Breakthrough During Water Injection in Oil Reservoirs
    AU  - Anthony Ogbaegbe Chikwe
    AU  - Onyebuchi Ivan Nwanwe
    AU  - Obinna Stanley Onyia
    AU  - Ndubuisi Uchechukwu Okereke
    AU  - Jude Emeka Odo
    Y1  - 2022/02/16
    PY  - 2022
    N1  - https://doi.org/10.11648/j.ogce.20221001.12
    DO  - 10.11648/j.ogce.20221001.12
    T2  - International Journal of Oil, Gas and Coal Engineering
    JF  - International Journal of Oil, Gas and Coal Engineering
    JO  - International Journal of Oil, Gas and Coal Engineering
    SP  - 17
    EP  - 30
    PB  - Science Publishing Group
    SN  - 2376-7677
    UR  - https://doi.org/10.11648/j.ogce.20221001.12
    AB  - Numerical reservoir simulation studies can be used to plan water injection projects to delay time and maximize oil recovery at water breakthrough which is time-consuming and computationally expensive. Combining computationally inexpensive proxy models and optimization algorithms is a solution to this problem. In this study, the Box-Behnken design method and response surface methodology were used to develop two proxy models which showed the relationship between time and recovery factor at water breakthrough with six independent variables namely porosity, horizontal permeability, water viscosity, bottom-hole pressure, water injection rate and vertical permeability. A comparison of actual and predicted values for time and oil recovery factor at water breakthrough was found to be in good agreement with each other. An average absolute percentage error of 2.038% and 1.217%, a root mean square error of 0.08 and 0.0000988, and coefficients of determination, R2 of 0.9984 and 0.9946 were obtained for time and recovery factor at water breakthrough respectively. These are indications that the developed models are accurate, valid, and reliable. The models were further validated by comparing the actual and predicted water breakthrough time and recovery factor at water breakthrough using input variables that were not used in model development. These were also in close agreement with each other. The MATLAB multi-objective genetic algorithm was used to determine at a specific average porosity and permeability value, the best optimum controllable variables that maximized the objective functions. These were found to be 10.8978 years and 0.786 respectively and agreed with simulation results obtained using similar input parameter values.
    VL  - 10
    IS  - 1
    ER  - 

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Author Information
  • Department of Petroleum Engineering, Federal University of Technology, Owerri, Nigeria

  • Department of Petroleum Engineering, Federal University of Technology, Owerri, Nigeria

  • Department of Petroleum Engineering, Federal University of Technology, Owerri, Nigeria

  • Department of Petroleum Engineering, Federal University of Technology, Owerri, Nigeria

  • Department of Petroleum Engineering, Federal University of Technology, Owerri, Nigeria

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