1887

Abstract

Summary

Parameterization of element balance formulation in reactive compositional flow and transport

K. Kala1, D. Voskov1,2

1 Department of Geoscience and Engineering, TU Delft

2 Department of Energy Resources Engineering, Stanford University

We present a novel nonlinear formulation for modeling reactive-compositional transport in the presence of complex phase behavior related to dissolution and precipitation in multi-phase systems. This formulation is based on the consistent element balance reduction of the molar (overall composition) formulation. To predict a complex phase behavior in such systems, we include the chemical equilibrium constraints to the multiphase multicomponent negative flash calculations and solve the thermodynamic and chemical phase equilibrium simultaneously. In this solution, the phase equilibrium is represented by the partition coefficients whereas the chemical equilibrium reaction is represented by the activity coefficients model. This provides a generic treatment of chemical and thermodynamic equilibrium within an EOS SSI loop by modification of the multiphase flash to accommodate chemical equilibrium. Using the Equilibrium Rate Annihilation matrix allows us to reduce the governing unknowns to the primary set only while the coupling between chemical and thermodynamic equilibrium is captured by a simultaneous solution of modified multiphase flash equations. An input in this thermodynamic computation is an element composition of the mixture when an output contains fractions of components in each phase, including solids. This element balance molar formulation along with the modified formulation for multiphase flash has been tested in a simple transport model with dissolution and precipitation reactions. The same approach will be later used to model a system involving kinetic reactions. The simulation of more general practical models is performed using the recently developed Operator-Based Linearization (OBL) technique. In the modified version of the OBL, the nonlinear element based governing equations are formulated in terms of space and state-dependent parameters constrained by the solution of the extended multiphase flash based on molar element compositions. This approach helps us to add equilibrium reaction capabilities to the computationally efficient OBL technique.

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/content/papers/10.3997/2214-4609.201802113
2018-09-03
2020-03-28
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References

  1. Acs, G., Doleschall, S. and Farkas, E.
    [1985] General Purpose Compositional Model.SPE Journal, 25(04), 543–553. SPE-10515-PA.
    [Google Scholar]
  2. Coats, K.
    [1980] An Equation of state compositional model.SPE Journal, SPE 8284.
    [Google Scholar]
  3. Collins, D., Nghiem, L., Li, Y.K. and Grabonstotter, J.
    [1992] An Efficient Approach to Adaptive-Implicit Compositional Simulation With an Equation of State. SPE, 15133-PA.
    [Google Scholar]
  4. Fan, Y.
    [2010] Chemical reaction modeling in a subsurface flow simulator with application to in-situ upgrading and CO2 Mineralization PhD Thesis Stanford University.SPE, 3, 1–2.
    [Google Scholar]
  5. Farshidi, S., Fan, Y., Durlofsky, L. and Tchelepe, H.A.
    [2013] Chemical Reaction modeling in a compositional reservoir simulation framework.SPE 163677.
    [Google Scholar]
  6. Iranshahr, A., Voskov, D. and Tchelepi, H.
    [2010] Generalized negative flash method for multiphase muticomponent systems.Fluid Phase Equilibria, 299, 272–283.
    [Google Scholar]
  7. Khait, M. and Voskov, D.
    [2018a] Operator-based linearization for efficient modeling of geothermal processes.Geothermics, 74, 7–18.
    [Google Scholar]
  8. Khait, M. and Voskov, D.V.
    [2017] Operator-based linearization for general purpose reservoir simulation.Journal of Petroleum Science and Engineering, 157, 990–998.
    [Google Scholar]
  9. [2018b] Adaptive Parameterization for solving of Thermal/Compositional Nonlinear flow and transport with Buoyancy.SPEJ, 182685.
    [Google Scholar]
  10. Lake, L.
    [1989] Enhanced Oil Recovery.Prentice Hall.
    [Google Scholar]
  11. Li, Y.K. and Nghiem, L.X.
    [1982] The Development of a General Phase Envelope Construction Algorithm for Reservoir Fluid Studies.SPE 11198.
    [Google Scholar]
  12. Lichtner, P., Steefel, C. and Oelkers, E.
    [1996] Reactive transport in porous media. Reviews in mineralogy. Mineralogical Society of America.
    [Google Scholar]
  13. Lichtner, P.C.
    [1985] Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems.Geochimica et Cosmochimica Acta, 49(3), 779–800.
    [Google Scholar]
  14. Lucia, A., Henley, H. and Thomas, E.
    [2015] Multiphase equilibrium flash with salt precipitation in systems with multiple salts.Chemical Engineering Research and Design, 93, 662–674.
    [Google Scholar]
  15. Michelsen, M.L.
    [1982a] The Isothermal Flash Problem. Part I Stability.Fluid Phase Equilibria, 9, 1–9.
    [Google Scholar]
  16. [1982b] The Isothermal Flash Problem. Part II Phase Split Calculations.Fluid Phase Equilibria, 9(1982) 21–40, 9, 21–40.
    [Google Scholar]
  17. Nghiem, L.X., Shrivastava, V.K., Kohse, B.F. and Tripathi, V.
    [2011] Modeling Aqueous Phase Behavior and Chemical Reactions in Compositional Simulation.SPE, 141417-MS.
    [Google Scholar]
  18. Orr, F.
    [2007] Theory of gas injection processes.Tie-Line Publications.
    [Google Scholar]
  19. Peng, D.Y. and Robinson, D.B.
    [1976] A New Two-Constant Equation of State. Industrial & Engineering Chemistry Fundamentals, 15(1), 59–64.
    [Google Scholar]
  20. Peters, E., Arts, R., Brouwer, G., Geel, C., Cullick, S., Lorentzen, R., Chen, Y., Dunlop, K., Vossepoel, F., Xu, R., Sarma, P., Alhutali, A. and Reynolds, A.
    [2010] Results of the brugge benchmark study for flooding optimization and history matching. SPE Reservoir Evaluation and Engineering, 13(3), 391–405.
    [Google Scholar]
  21. Rachford, H. and Rice, J.
    [1952] Procedure for use of electronic digital computers in calculating flash vaporization at hydrocarbon equilibrium.Petroleum Transactions AIME Vol.152 (1952) 327–328, 152, 327–328.
    [Google Scholar]
  22. Sriyanong, P.
    [2013] Element based formulations for coupled flow, transport and chemical reactions.MSc Thesis, Department of Energy Resources Engineering, Stanford University.
    [Google Scholar]
  23. Voskov, D.V.
    [2017] Operator-based linearization approach for modeling of multiphase multi-component flow in porous media.Journal of Computational Physics, 337, 275–288.
    [Google Scholar]
  24. Voskov, D.V., Henley, H. and Lucia, A.
    [2017] Fully compositional multi-scale reservoir simulation of various CO2 sequestration mechanisms.Computers and Chemical Engineering, 96, 183–195.
    [Google Scholar]
  25. Voskov, D.V. and Tchelepi, H.A.
    [2012] Comparison of nonlinear formulations for two-phase multi-component EoS based simulation.Journal of Petroleum Science and Engineering, 82–83, 101–111.
    [Google Scholar]
  26. Whitson, C.H. and Michelsen, M.L.
    [1989] The Negative Flash.Fluid Phase Equilibria, 53, 51–71.
    [Google Scholar]
  27. Yeh, G. and Tripathi, V.
    [1989] A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components. Water Resources Research, 25(1), 93–108.
    [Google Scholar]
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