Geochemical equilibrium determination using an artificial neural network in compositional reservoir flow simulation

  • Dominique GuérillotEmail author
  • Jérémie Bruyelle
Open Access
Original Paper


The fluid injection in sedimentary formations may generate geochemical interactions between the fluids and the rock minerals, e.g., CO2 storage in a depleted reservoir or a saline aquifer. To simulate such reactive transfer processes, geochemical equations (equilibrium and kinetics equations) are coupled with compositional flows in porous media in order to represent, for example, precipitation/dissolution phenomena. The aim of the decoupled approach proposed consists in replacing the geochemical equilibrium solver with a substitute method to bypass the huge consuming time required to balance the geochemical system while keeping an accurate equilibrium calculation. This paper focuses on the use of artificial neural networks (ANN) to determine the geochemical equilibrium instead of solving geochemical equations system. To illustrate the proposed workflow, a 3D case study of CO2 storage in geological formation is presented.


Reservoir simulation Compositional Heterogeneity CO2 storage Chemically reacting flows Artificial neural network 

Mathematics Subject Classification (2010)

80A32 76S05 68T05 



Open Access funding provided by the Qatar National Library.


  1. 1.
    Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Applied Science Publishers, London (1979)Google Scholar
  2. 2.
    Bethke, C.: Geochemical Reaction Modeling: Concepts and Applications. Oxford University Press, New York (1996)Google Scholar
  3. 3.
    Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)Google Scholar
  4. 4.
    Bruyelle, J., Guérillot, D.: Neural networks and their derivatives for history matching and reservoir optimization problems. Comput. Geosci. 18(3-4), 549–561 (2014)CrossRefGoogle Scholar
  5. 5.
    Carman, P.C.: Fluid flow through granular beds. Trans. Institut. Chem. Eng. London 15, 150–166 (1937)Google Scholar
  6. 6.
    Christie, M.A., Blunt, M.J.: Tenth SPE comparative solution project: A comparison of upscaling techniques. Society of petroleum engineers, SPE 66599 (2001)Google Scholar
  7. 7.
    Costa, L.A.N., Maschio, C., Schiozer, D.J.: Study of the influence of training data set in artificial neural network applied to the history matching process. In: Rio Oil & Gas Expo and Conference (2010)Google Scholar
  8. 8.
    Courant, R., Friedrichs, K., Lewy, H.: ÜBer die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100(1), 32–74 (1928)CrossRefGoogle Scholar
  9. 9.
    Cybenko, G.: Continuous Valued Neural Networks with Two Hidden Layers are Sufficient. Technical Report, Department of Computer Science Tufts University (1988)Google Scholar
  10. 10.
    Cybenko, G.: Approximation by superpositions of sigmoidal functions. Mathematics of Control, Signals, and Systems (1989)Google Scholar
  11. 11.
    Guérillot, D.: Procédé et système de modélisation dynamique d’un écoulement de fluide polyphasique, French Patent EP 2791712 A1 (WO2013087846a1) (2011)Google Scholar
  12. 12.
    Guérillot, D.: Method and system for dynamically modeling a multiphase fluid flow - US Patent App. 14/365,053 (2014)Google Scholar
  13. 13.
    Guérillot, D.R., Bruyelle, J.: Uncertainty assessment in production forecast with an optimal artificial neural network. Society of Petroleum Engineers. (2017)
  14. 14.
    Hagan, M.T., Demuth, H.B., Beale, M.H., De Jesús, O.: Neural Network Design, vol. 20. Pws Pub, Boston (1996)Google Scholar
  15. 15.
    Hammond, G.E., Lichtner, P.C., Lu, C., Mills, R.T.: PFLOTRAN: Reactive flow & transport code for use on laptops to leadership-class supercomputers. Groundwater Reactive Transport Models, 141–159 (2012)Google Scholar
  16. 16.
    Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2, 359–366 (1989)CrossRefGoogle Scholar
  17. 17.
    Hornik, K., Stinchcombe, M., White, H.: Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Netw. 3, 551–560 (1990)CrossRefGoogle Scholar
  18. 18.
    Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural Netw. 4, 251–257 (1991)CrossRefGoogle Scholar
  19. 19.
    Jatnieks, J., De Lucia, M., Dransch, D., Sips, M.: Data-driven surrogate model approach for improving the performance of reactive transport simulations. Energy Procedia 97, 447–453 (2016)CrossRefGoogle Scholar
  20. 20.
    Leal, A.M., Kulik, D.A., Saar, M.O.: Ultra-fast reactive transport simulations when chemical reactions meet machine learning: chemical equilibrium. arXiv:1708.04825 (2017)
  21. 21.
    Lichtner, P.C.: Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems. Geochim. Cosmochim. Acta 49(3), 779–800 (1985)CrossRefGoogle Scholar
  22. 22.
    Lichtner, P.C.: Continuum formulation of multicomponent–multiphase reactive transport. Reactive Transport in Porous Media. Rev. Mineral. 34, 1–81 (1996)Google Scholar
  23. 23.
    Marle, C.M.: On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media. Int. J. Eng. Sci. 20(5), 643–662 (1982)CrossRefGoogle Scholar
  24. 24.
    Merkel, B.J., Planer-Friedrich, B., Nordstrom, D.K.: Groundwater geochemistry. A practical guide to modeling of natural and contaminated aquatic systems, 2 (2005)Google Scholar
  25. 25.
    Nghiem, L., Sammon, P., Grabenstetter, J., Ohkuma, H.: Modeling CO2 storage in aquifers with a fully-coupled geochemical EOS compositional simulator. In: SPE/DOE Symposium on Improved Oil Recovery. Society of Petroleum Engineers (2004)Google Scholar
  26. 26.
    Peng, D.Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15(1), 59–64 (1976)CrossRefGoogle Scholar
  27. 27.
    Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning Internal Representations by Error Backpropagation, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, pp 318–362. MIT Press, Cambridge (1986)Google Scholar
  28. 28.
    Schou Pedersen, K., Hasdbjerg, C.: PC-SAFT equation of state applied to petroleum reservoir fluids. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (2007)Google Scholar
  29. 29.
    Soave, G.: Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 27(6), 1197–1203 (1972)CrossRefGoogle Scholar
  30. 30.
    Steefel, C.I., MacQuarrie, K.T.B.: Approaches to modeling reactive transport in porous media. Reactive Transport in Porous Media. Rev. Mineral. 34, 83–125 (1996)Google Scholar
  31. 31.
    Steefel, C.I., Appelo, C.A.J., Arora, B., Jacques, D., Kalbacher, T., Kolditz, O., Lagneau, V., Lichtner, P.C., Mayer, K.U., Meeussen, J.C.L., Molins, S., Moulton, D., Shao, H., Šimůnek, J., Spycher, N., Yabusaki, S.B., Yeh, G.T.: Reactive transport codes for subsurface environmental simulation. Comput. Geosci. 19, 445–478 (2015)CrossRefGoogle Scholar
  32. 32.
    Steefel, C.I., Molins, S.: Crunchflow, software for modeling multicomponent reactive flow and transport, USER’S MANUAL (2016)Google Scholar
  33. 33.
    Strang, G.: On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5(3), 506–517 (1968)CrossRefGoogle Scholar
  34. 34.
    Tebes-Stevens, C., Valocchi, A.J., VanBriesen, J.M., Rittmann, B.E.: Multicomponent transport with coupled geochemical and microbiological reactions: Model description and example simulations. J. Hydrol. 209(1-4), 8–26 (1998)CrossRefGoogle Scholar
  35. 35.
    Xu, T., Spycher, N., Sonnenthal, E., Zhang, G., Zheng, L., Pruess, K.: TOUGHREACT Version 2.0: A Simulator for subsurface reactive transport under non-isothermal multiphase flow conditions. Comput. Geosci. 37(6), 763–774 (2011)CrossRefGoogle Scholar
  36. 36.
    Yeh, G.T., Tripathi, V.S.: A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components. Water Resour. Res. 25(1), 93–108 (1989)CrossRefGoogle Scholar
  37. 37.
    Yeh, G.T., Tripathi, V.S.: A model for simulating transport of reactive multispecies components: Model development and demonstration. Water Resour. Res. 27(12), 3075–3094 (1991)CrossRefGoogle Scholar
  38. 38.
    Yeh, G.T., Sun, J., Jardine, P., Burgos, W.D., Fang, Y., Li, M.-H., Chunli, Siegel, M.D.: HYDROGEOCHEM 5.0: a three-dimensional model of coupled fluid flow, thermal transport, and HYDROGEOCHEMical transport through variably saturated conditions - version 5.0 (2004)Google Scholar

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Texas A&M University at QatarDohaQatar

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