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Abstract

Summary

In this work, we consider algorithms for solving production optimization problems that involve isothermal (constant temperature) and compositional oil production processes. The purpose of production optimization is to compute a long-term production strategy that is economically optimal. We present a thermodynamically rigorous model of isothermal oil production processes. We derive the model from first principles by applying a number of assumptions including the assumption of constant temperature. The model is based on two key principles, namely phase equilibrium and conservation of mass and energy. The conservation equations are expressed as partial differential equations, and we model the phase equilibrium as a VT flash process. It is common to formulate the phase equilibrium conditions in oil reservoir flow models as the fugacities being equal. We describe how to derive that condition from the phase equilibrium conditions from the VT flash problem. The VT flash is an adaption of the second law of thermodynamics, i.e. the entropy of a closed system in equilibrium is maximal, to isothermal systems. The VT flash can therefore be formulated as an inner optimization problem that needs to be solved for each grid cell in the discretized reservoir in the forward simulation of the oil production process. We demonstrate that it is natural to model such isothermal production processes with differential-algebraic equations in a semi-explicit index-1 form. We describe a single-shooting algorithm for solving the production optimization problem efficiently. It is key to the efficiency of such algorithms to compute gradients. For that purpose, we use an adjoint algorithm. We implement the singleshooting algorithm in C/C++ using the open-source software DUNE, the open-source thermodynamic software ThermoLib, and the numerical optimization software KNITRO. Finally, we present a numerical example that involves optimal waterflooding.

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/content/papers/10.3997/2214-4609.201802112
2018-09-03
2024-03-29
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References

  1. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Kornhuber, R., Ohlberger, M. and Sander, O.
    [2008a] A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE.Computing, 82 (2–3), 121–138.
    [Google Scholar]
  2. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M. and Sander, O.
    [2008b] A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework.Computing, 82(2–3), 103–119.
    [Google Scholar]
  3. Benjelloun-Dabaghi, Z., de Hemptinne, J.C., Jarrin, J., Leroy, J.M., Aubry, J.C., Saas, J.N. and Taravel-Condat, C.
    [2002] MOLDI™: a fluid permeation model to calculate the annulus composition in flexible pipes. Oil & Gas Science and Technology - Rev. IFP, 57(2), 177–192.
    [Google Scholar]
  4. Blatt, M. and Bastian, P.
    [2007] The iterative solver template library. In: B.Kågström et al. (Ed.) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2006, Lecture Notes in Computer Science, 4699. Springer, Berlin, Heidelberg, 666–675.
    [Google Scholar]
  5. Bukshtynov, V., Volkov, O., Durlofsky, L.J. and Aziz, K.
    [2015] Comprehensive framework for gradient-based optimization in closed-loop reservoir management. Computational Geosciences, 19(4), 877–897.
    [Google Scholar]
  6. Cabral, V.F., Castier, M. and Tavares, F.W.
    [2005] Thermodynamic equilibrium in systems with multiple adsorbed and bulk phases.Chemical Engineering Science, 60, 1773–1782.
    [Google Scholar]
  7. Callen, H.B.
    [1985] Thermodynamics and an introduction to thermostatistics. John Wiley & Sons, 2nd edn.
    [Google Scholar]
  8. Capolei, A. and Jørgensen, J.B.
    [2012] Solution of constrained optimal control problems using multiple shooting and ESDIRK methods. In: Proceedings of the 2012 American Control Conference.Fairmont Queen Elizabeth, Montréal, Canada, 295–300.
    [Google Scholar]
  9. Capolei, A., Völcker, C., Frydendall, J. and Jørgensen, J.B.
    [2012] Oil reservoir production optimization using single shooting and ESDIRK methods. In: Proceedings of the 2nd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production.Trondheim, Norway, 286–291.
    [Google Scholar]
  10. Castier, M. and Tavares, F.W.
    [2005] Centrifugation equilibrium of natural gas.Chemical Engineering Science, 60, 2927–2935.
    [Google Scholar]
  11. Codas, A., Hanssen, K.G., Foss, B., Capolei, A. and Jørgensen, J.B.
    [2017] Multiple shooting applied to robust reservoir control optimization including output constraints on coherent risk measures. Computational Geosciences, 21(3), 479–497.
    [Google Scholar]
  12. Delshad, M. and Pope, G.A.
    [1989] Comparison of the three-phase oil relative permeability models. Transport in Porous Media, 4(1), 59–83.
    [Google Scholar]
  13. Espósito, R.O., Castier, M. and Tavares, F.W.
    [2000] Calculations of thermodynamic equilibrium in systems subject to gravitational fields.Chemical Engineering Science, 55, 3495–3504.
    [Google Scholar]
  14. Forouzanfar, F., Rossa, E.D., Russo, R. and Reynolds, A.C.
    [2013] Life-cycle production optimization of an oil field with an adjoint-based gradient approach.Journal of Petroleum Science and Engineering, 112, 351–358.
    [Google Scholar]
  15. Garipov, T.T., Tomin, P., Rin, R., Voskov, D.V. and Tchelepi, H.A.
    [2018] Unified thermo-compositional-mechanical framework for reservoir simulation.Computational Geosciences, 1–19.
    [Google Scholar]
  16. Heirung, T.A.N., Wartmann, M.R., Jansen, J.D., Ydstie, B.E. and Foss, B.A.
    [2011] Optimization of the water-flooding process in a small 2D horizontal oil reservoir by direct transcription. In: Proceedings of the 18th IFAC World Congress.Milano, Italy, 10863–10868.
    [Google Scholar]
  17. Jansen, J.D., Douma, S.D., Brouwer, D.R., Van den Hof, P.M.J., Bosgra, O.H. and Heemink, A.W.
    [2009] Closed-loop reservoir management. In: Proceedings of the 2009 SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, The Woodlands, Texas, USA.
    [Google Scholar]
  18. Jindrová, T. and Mikyška, J.
    [2013] Fast and robust algorithm for calculation of two-phase equilibria at given volume, temperature, and moles.Fluid Phase Equilibria, 353, 101–114.
    [Google Scholar]
  19. [2015a] General algorithm for multiphase equilibria calculation at given volume, temperature, and moles.Fluid Phase Equilibria, 393, 7–25.
    [Google Scholar]
  20. [2015b] Phase equilibria calculation of CO2-H2O system at given volume, temperature, and moles in CO2 sequestration. International Journal of Applied Mathematics, 45(3), 20–29.
    [Google Scholar]
  21. Kou, J., Sun, S. and Wang, X.
    [2016] An energy stable evolution method for simulating two-phase equilibria of multi-component fluids at constant moles, volume and temperature.Computational Geosciences, 20, 283–295.
    [Google Scholar]
  22. Kourounis, D., Durlofsky, L.J., Jansen, J.D. and Aziz, K.
    [2014] Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow. Computational Geosciences, 18(2), 117–137.
    [Google Scholar]
  23. Lei, Y., Li, S., Zhang, X. and Zhang, Q.
    [2012] Optimal control of polymer flooding for high temperature and high salinity reservoir. International Journal ofAdvancements in Computing Technology, 4(12), 52–60.
    [Google Scholar]
  24. Lie, K.A.
    [2014] An introduction to reservoir simulation using MATLAB. Sintef ICT, Oslo, Norway.
    [Google Scholar]
  25. Lohrenz, J., Bray, B.G. and Clark, C.R.
    [1964] Calculating viscosities of reservoir fluids from their compositions. Journal of Petroleum Engineers, 16(10), 1171–1176.
    [Google Scholar]
  26. Michelsen, M.L.
    [1999] State function based flash specifications.Fluid Phase Equilibria, 158–160, 617–626.
    [Google Scholar]
  27. Michelsen, M.L. and Mollerup, J.M.
    [2007] Thermodynamic models: fundamentals and computational aspects.Tie-Line Publications, 2nd edn.
    [Google Scholar]
  28. Mikyška, J. and Firoozabadi, A.
    [2011] A new thermodynamic function for phase-splitting at constant temperature, moles, and volume. AIChE Journal, 57(7), 1897–1904.
    [Google Scholar]
  29. Nocedal, J. and Wright, S.J.
    [2006] Numerical optimization.Springer Science & Business Media, 2nd edn.
    [Google Scholar]
  30. Onwunalu, J.E. and Durlofsky, L.J.
    [2010] Application of a particle swarm optimization algorithm for determining optimum well location and type. Computational Geosciences, 14(1), 183–198.
    [Google Scholar]
  31. Polívka, O. and Mikyška, J.
    [2014] Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification.Journal of Computational Physics, 272, 149–169.
    [Google Scholar]
  32. Ritschel, T.K.S., Capolei, A., Gaspar, J. and Jørgensen, J.B.
    [2017a] An algorithm for gradient-based dynamic optimization of UV flash processes.Computers and Chemical Engineering. In Press. DOI: doi:http://https://doi.org/10.10167j.compchemeng.2017.10.007.
    [Google Scholar]
  33. Ritschel, T.K.S., Gaspar, J., Capolei, A. and Jørgensen, J.B.
    [2016] An open-source thermodynamic software library. Tech. Rep. DTU Compute Technical Report-2016-12, Department of Applied Mathematics and Computer Science, Technical University of Denmark.
    [Google Scholar]
  34. Ritschel, T.K.S., Gaspar, J. and Jørgensen, J.B.
    [2017b] A thermodynamic library for simulation and optimization of dynamic processes. In: Proceedings of the 20th IFAC World Congress.
    [Google Scholar]
  35. Ritschel, T.K.S. and Jørgensen, J.B.
    [2017] Computation of phase equilibrium and phase envelopes. Tech. Rep. DTU Compute Technical Report-2017-11, Department of Applied Mathematics and Computer Science, Technical University of Denmark.
    [Google Scholar]
  36. [2018a] Computation of phase equilibrium in reservoir simulation and optimization. In: Proceedings of the 3rd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production. Esbjerg, Denmark. Accepted.
    [Google Scholar]
  37. [2018b] The extended Kalman filter for state estimation of dynamic UV flash processes. In: Proceedings of the 3rd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production.Esbjerg, Denmark. Accepted.
    [Google Scholar]
  38. [2018c] Nonlinear filters for state estimation of UV flash processes. In: Proceedings of the 2nd IEEE Conference on Control Technology and Applications.Copenhagen, Denmark. Accepted.
    [Google Scholar]
  39. [2018d] Production optimization of a rigorous thermal and compositional reservoir flow model. In: Proceedings of the 3rd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production.Esbjerg, Denmark. Accepted.
    [Google Scholar]
  40. Santori, G. and Luberti, M.
    [2016] Thermodynamics of thermally-driven adsorption compression.Sustainable Materials and Technologies, 10, 1–9.
    [Google Scholar]
  41. Saputelli, L., Malki, H., Canelon, J. and Nikolaou, M.
    [2002] A critical overview of artificial neural network applications in the context of continuous oil field optimization. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, San Antonio, Texas.
    [Google Scholar]
  42. Thomson, G.H.
    [1996] The DIPPR® databases. International Journal of Thermophysics, 17(1), 223–232.
    [Google Scholar]
  43. Völcker, C., Jørgensen, J.B., Thomsen, P.G. and Stenby, E.H.
    [2010] Explicit singly diagonally implicit Runge-Kutta methods and adaptive stepsize control for reservoir simulation. In: Proceedings of the 12th European Conference on the Mathematics of Oil Recovery.Oxford, England.
    [Google Scholar]
  44. Zaydullin, R., Voskov, D.V., James, S.C., Henley, H. and Lucia, A.
    [2014] Fully compositional and thermal reservoir simulation.Computers and Chemical Engineering, 63, 51–65.
    [Google Scholar]
  45. Zhang, X. and Li, S.
    [2007] Optimal control solving of polymer flooding in enhanced oil recovery with 2-D models. In: Proceedings of the 2007 IEEE International Conference on Control and Automation.Guangzhou, China, 1981–1986.
    [Google Scholar]
  46. Zhao, H., Tang, Y.W., Li, Y., Shi, Y.B., Cao, L., Gong, R.X. and Shang, G.H.
    [2016] Reservoir production optimization using general stochastic approximate algorithm under the mixed-linear-nonlinear constraints.Journal of Residuals Science & Technology, 13(8).
    [Google Scholar]
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