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Abstract

Summary

The Markowitz classical theory has been applied in the robust optimisation of petroleum engineering operations by many researchers. It involves the computation of the means and standard deviation of a specified reservoir performance measure(s), and the creation of an efficient frontier which qualifies the relationship between the optimised mean and standard deviation. However, the optimisation routine is computationally expensive as numerous simulations are required for calculating the means and standard deviations. Also, to simplify the optimisation problem many significant uncertainties are not considered in the optimisation routine. Also, previous researches have used a limited number of reservoir-model sample points of the uncertain variable(s) to calculate the means and standard deviations values. For example, if the uncertain parameter is uniformly distributed, three equiprobable (the low, median and high values) are used to correlate the uncertainty. However, this approach leads to erroneous calculations of the means and standard deviations because the actual distribution of the uncertainty is ignored.

In this study, we apply the Markowitz classical robust optimisation routine to a validated approximation model of the cumulative oil production of a case study reservoir to optimise oil recovery after waterflooding. Using this approach, we can reduce computational costs and for the first time, consider up to four geological uncertain variables in reservoir optimisation under uncertainty. We show that at least 100 sample points (realisations) of the uncertain geological parameters are required to obtain accurate computations of the means (reward) and standard deviations (risk). This allows for adequate sampling of the distribution of the uncertain parameters. We then construct an efficient frontier of the optimal solutions for various risk-aversion factors and compare the results to that obtained from a deterministic optimisation routine.

This approach was applied for the first time to optimisation under uncertainty. The result indicates that considering geological uncertainties while solving to the optimisation problem results in more realistic optimal solutions when compared to the deterministic optimisation case. This is because engineering control variables that lead to a risk-quantified strategy for the waterflooding operation are obtained.

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/content/papers/10.3997/2214-4609.202035076
2020-09-14
2024-03-28
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References

  1. Agada, S., Geiger, S., Elsheikh, A., & Oladyshkin, S.
    (2017). Data-driven surrogates for rapid simulation and optimization of WAG injection in fractured carbonate reservoirs.Petroleum Geoscience, 23(2), 270–283. https://doi.org/10.1144/petgeo2016-068
    [Google Scholar]
  2. Al-Mudhafar, W. J., Rao, D. N., & Srinivasan, S.
    (2018). Robust Optimization of Cyclic CO2 flooding through the Gas-Assisted Gravity Drainage process under geological uncertainties.Journal of Petroleum Science and Engineering, 166, 490–509. https://doi.org/10.1016/j.petrol.2018.03.044
    [Google Scholar]
  3. Ampomah, W., Balch, R. S., Cather, M., Will, R., Gunda, D., Dai, Z., & Soltanian, M. R.
    (2017). Optimum design of CO2 storage and oil recovery under geological uncertainty.Applied Energy, 195(July 2018), 80–92. https://doi.org/10.1016/j.apenergy.2017.03.017
    [Google Scholar]
  4. Arinkoola, A. O., Onuh, H. M., & Ogbe, D. O.
    (2016). Quantifying uncertainty in infill well placement using numerical simulation and experimental design: case study.Journal of Petroleum Exploration and Production Technology, 6(2), 201–215. https://doi.org/10.1007/s13202-015-0180-z
    [Google Scholar]
  5. AsadollahiM
    (2012) Waterflooding optimization for improved reservoir management, Ph.D. dissertation, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
    [Google Scholar]
  6. BrouwerD. R., JansenJ. D.
    , “Dynamic Optimization of Waterflooding With Smart Wells Using Optimal Control Theory”, paper SPE 78278 presented at the 2002SPE European Petroleum Conference, Aberdeen, U.K., 29-31 October
    [Google Scholar]
  7. Couët, B., Burridge, R., and Wilkinson, D.W.
    2000. Optimization Under Reservoir and Financial Uncertainty. Proc.European Conference on the mathematics of Oil Recovery (ECMOR), Baveno, Italy, 5–8 September.
    [Google Scholar]
  8. ECLIPSE
    ECLIPSE (2017). 2017.1. Schlumberger, Houston, Texas. 2017
    [Google Scholar]
  9. MATLAB
    MATLAB (2018), version 9.4 (R2018b). The MathWorks Inc., Natick, Massachusetts.
    [Google Scholar]
  10. Markowitz, H.M.
    , 1952. Portfolio Selection.The Journal of Finance7(1): 77–91. http://dx.doi.org/10.1111/j.1540-6261.1952.tb01525.x This work was later refined by H.M. Markowitz in Portfolio Selection: Efficient Diversification Of Investments, New York: John Wiley & Sons. 1959.
    [Google Scholar]
  11. Negash, B. M., Vel, A., & Elraies, K. A.
    (2017). Artificial neural network and inverse solution method for assisted history matching of a reservoir model.International Journal of Applied Engineering Research, 12(11), 2952–2962.
    [Google Scholar]
  12. OgbeiwiP, AladeitanY, UdebhuluDO
    (2017) An Approach to Waterflood Optimization: Case Study of the Reservoir X.J Petrol Explor Prod Technol., DOI 10.1007/s13202‑017‑0368‑5
    https://doi.org/10.1007/s13202-017-0368-5 [Google Scholar]
  13. Raghuraman, B., Couët, B., Savundararaj, P. M., Bailey, W. J., & Wilkinson, D. J.
    (2003). Valuation of technology and information for reservoir risk management.SPE Reservoir Evaluation and Engineering, 6(5), 307–316. https://doi.org/10.2118/86568-PA
    [Google Scholar]
  14. Rashid, K., Bailey, W. J., Couet, B., & Wilkinson, D.
    (2013). An efficient procedure for expensive reservoir-simulation optimization under uncertainty.SPE Economics & Management, 5(04), 21–33. https://doi.org/10.2118/167261-PA
    [Google Scholar]
  15. SchulteD. O., ArnoldD., GeigerS., DemyanovV., andSass I.
    , 2020. Multi-objective optimization under uncertainty of geothermal reservoirs using experimental design-based proxy models.Geothermics86 (2020). https://doi.org/10.1016/j.geothermics.2019.101792
    [Google Scholar]
  16. Sudaryanto, B., and Yortsos, Y.C.
    2001Optimization of Displacements in Porous Media Using Rate Control. Paper SPE 71509 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September-3 October
    [Google Scholar]
  17. van Essen, G. M., Zandvliet, M. J., Van Den Hof P. M. J.
    2006. Robust Waterflooding Optimization of Multiple Geological Scenarios. Paper SPE 102913 presented at the Annual Technical Conference and Exhibition, San Antonio, 24–27 September
    [Google Scholar]
  18. Yang, C., Card, C., Nghiem, L.X., Fedutenko, E., Bosgra, O. H., and Jansen, J. D.
    , 2011. Robust optimization of SAGD operations under geological uncertainties. In: SPE Reservoir Simulation Symposium, the Woodlands, Texas. https://doi.org/10.2118/141676-MS.
    [Google Scholar]
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