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Predicting plume spreading during CO2 geo-sequestration: benchmarking a new hybrid finite element–finite volume compositional simulator with asynchronous time marching

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Abstract

In this paper, we present the results of benchmark simulations for plume spreading during CO2 geo-sequestration conducted with the newly developed Australian CO2 Geo-Sequestration Simulator (ACGSS). The simulator uses a hybrid finite element–finite volume (FEFVM) simulation framework, integrating an asynchronous local time stepping method for multi-phase multi-component transport and a novel non-iterative flash calculation approach for the phase equilibrium. The benchmark investigates four standard CO2 storage test cases that are widely used to assess the performance of simulation tools for carbon geo-sequestration: (A) radial flow from a CO2 injection well; (B) CO2 discharge along a fault zone; (C) CO2 injection into a layered brine formation; and (D) leakage through an abandoned well. For these applications, ACGSS gives results similar to well-established compositional simulators. Minor discrepancies can be rationalised in terms of the alternative, spatially adaptive discretisation and the treatment of NaCl solubility. While these benchmarks cover issues related to compositional simulation, they do not address the accurate representation of geologically challenging features of CO2 storage sites. An additional 3D application scenario of a complexly faulted storage site demonstrates the advantages of the FEFVM discretisation used in the ACGSS for resolving the geometric complexity of geologic storage sites. This example also highlights the significant computational benefits gained from the use of the asynchronous time marching scheme.

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References

  1. Aavatsmark, I.: An introduction to multipoint flux approximations for quadrilateral grids. Comput. Geosci. 6(3), 405–432 (2002). https://doi.org/10.1023/A:1021291114475

    Article  Google Scholar 

  2. Aavatsmark, I., Barkve, T., Bøe, Ø., Mannseth, T.: Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media. J. Comput. Phys. 127(1), 2–14 (1996). https://doi.org/10.1006/jcph.1996.0154

    Article  Google Scholar 

  3. Aavatsmark, I., Reiso, E., Teigland, R.: Control-volume discretization method for quadrilateral grids with faults and local refinements. Comput. Geosci. 5(1), 1–23 (2001). https://doi.org/10.1023/A:1011601700328

    Article  Google Scholar 

  4. Aavatsmark, I., Eigestad, G., Heimsund, B.-O., Mallison, B., Nordbotten, J., Øian, E.: A new finite-volume approach to efficient discretization on challenging grids. SPE J. 15, 04 (2013). https://doi.org/10.2118/106435-MS

    Article  Google Scholar 

  5. ANSYS\(^{{\circledR }}\): Academic ICEM CFD TM Linux 64-bit Release 17.2 (2016)

  6. Aziz, K.: Reservoir simulation grids: Opportunities and problems. Soc. Pet. Eng. 45(07). https://doi.org/10.2118/25233-PA (1993)

  7. Aziz, K., Aziz, K., Settari, A.: Petroleum reservoir simulation. Applied Science Publishers (1979)

  8. Bazr Afkan, S., Matthäi, S., Mindel, J.: The finite-element-centered finite-volume discretization method (fecfvm) for multiphase transport in porous media with sharp material discontinuities. In: 14th European Conference on the Mathematics of Oil Recovery 2014, vol. 9 (2014). https://doi.org/10.3997/2214-4609.20141841

  9. Brand, C.W., Heinemann, J.E., Aziz, K.: The grid orientation effect in reservoir simulation. Soc. Pet. Eng. 1. https://doi.org/10.2118/21228-MS (1991)

  10. Brooks, R., Corey, A.: Hydraulic properties of porous media colorado state university hydrology papers colorado state university (1964)

  11. Cao, H., Aziz, K.: Performance of impsat and impsat-aim models in compositional simulation. Soc. Pet. Eng. 01. https://doi.org/10.2118/77720-MS (2002)

  12. Cavanagh, A.: Benchmark calibration and prediction of the sleipner CO2 plume from 2006 to 2012. Energy Procedia 37, 3529–3545 (2013). GHGT-11 Proceedings of the 11th International Conference on Greenhouse Gas Control Technologies

    Article  Google Scholar 

  13. Celia, M.A., Bachu, S., Nordbotten, J.M., Bandilla, K.W.: Status of CO2 storage in deep saline aquifers with emphasis on modeling approaches and practical simulations. Water Resour. Res. 51(9), 6846–6892 (2015)

    Article  Google Scholar 

  14. Chen, W.H., Durlofsky, L.J., Engquist, B., Osher, S.: Minimization of grid orientation effects through use of higher order finite difference methods. Soc. Pet. Eng. 7. https://doi.org/10.2118/22887-PA (1993)

  15. Class, H., Ebigbo, A., Helmig, R., Dahle, H.K., Nordbotten, J.M., Celia, M.A., Audigane, P., Darcis, M., Ennis-King, J., Fan, Y., Flemisch, B., Gasda, S.E., Jin, M., Krug, S., Labregere, D., Naderi Beni, A., Pawar, R.J., Sbai, A., Thomas, S.G., Trenty, L., Wei, L.: A benchmark study on problems related to CO2 storage in geologic formations. Comput. Geosci. 13(4), 409 (2009)

    Article  Google Scholar 

  16. van der Meer, L.B., Law, D.H.-S., Gunter, W.B.: Comparison of numerical simulators for greenhouse gas storage in coalbeds, part iv: History match of field micropilot test data. In: Rubin, E., Keith, D., Gilboy, C., Wilson, M., Morris, T., Gale, J., Thambimuthu, K. (eds.) Greenhouse Gas Control Technologies, vol. 7, pp 2239–2242. Elsevier Science Ltd, Oxford (2005). https://doi.org/10.1016/B978-008044704-9/50309-8

  17. Deutsch, C.: Geostatistical Reservoir Modeling. Applied geostatistics series. Oxford University Press, Oxford (2002)

    Google Scholar 

  18. Ding, Y., Lemonnier, P.: Use of corner point geometry in reservoir simulation. In: Society of Petroleum Engineers (1995)

  19. Doughty, C., Pruess, K.: A similarity solution for two-phase water, air, and heat flow near a linear heat source in a porous medium. J. Geophys. Res. Solid Earth 97(B2), 1821–1838 (1992)

    Article  Google Scholar 

  20. Driesner, T., Heinrich, C.A.: The system h2o-nacl. part i: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000c, 0 to 5000bar, and 0 to 1 xNaCL. Geochim. Cosmochim. Acta 71(20), 4880–4901 (2007)

    Article  Google Scholar 

  21. Durlofsky, L.J.: A triangle based mixed finite element-finite volume technique for modeling two phase flow through porous media. J. Comput. Phys. 105, 252–266 (1993)

    Article  Google Scholar 

  22. Durlofsky, L.J.: Upscaling of geocellular models for reservoir flow simulation: a review of recent progress. In: 7th International Forum on Reservoir Simulation, pp 23–27 (2003)

  23. Ebigbo, A., Class, H., Helmig, R.: CO2 Leakage through an abandoned well: problem-oriented benchmarks. Comput. Geosci. 11(2), 103–115 (2007)

    Article  Google Scholar 

  24. Edwards, M.G., Rogers, C.F.: Finite volume discretization with imposed flux continuity for the general tensor pressure equation. Comput. Geosci. 2(4), 259–290 (1998). https://doi.org/10.1023/A:1011510505406

    Article  Google Scholar 

  25. Forsyth, P.A.: A control-volume finite element method for local mesh refinement in thermal reservoir simulation. SPE Reserv. Eng. 5(4), 561–566 (1990)

    Article  Google Scholar 

  26. Fung, L.S.-K., Collins, D.A., Nghiem, L.X.: An adaptive-implicit switching criterion based on numerical stability analysis. Soc. Pet. Eng. 02. https://doi.org/10.2118/16003-PA (1989)

  27. Geiger, S., Roberts, S., Matthäi, S.K., Zoppou, C., Burri, A.: Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media. Geofluids 4(4), 284–299 (2004)

    Article  Google Scholar 

  28. Geiger, S., Driesner, T., Heinrich, C., Matthäi, S.: Multiphase thermohaline convection in the earth’s crust: I. a new finite element - finite volume solution technique combined with a new equation of state for nacl-h2o. Transp. Porous Media 63(3), 399–434 (2006). https://doi.org/10.1007/s11242-005-0108-z

    Article  Google Scholar 

  29. Goovaerts, P., Goovaerts, D.: Geostatistics for Natural Resources Evaluation. Applied geostatistics series. Oxford University Press, Oxford (1997)

    Google Scholar 

  30. Grabenstetter, J., Li, Y.-K., Collins, D.A., Nghiem, L.X.: Stability-based switching criterion for adaptive-implicit compositional reservoir simulation. Soc. Pet. Eng. 01. https://doi.org/10.2118/21225-MS (1991)

  31. Gringarten, E., Arpat, G., Haouesse, M., Dutranois, A., Deny, L., Jayr, S., Tertois, A.-L., Mallet, J.-L., Bernal, A., Nghiem, L.: New grids for robust reservoir modeling. Soc. Pet. Eng. 01. https://doi.org/10.2118/116649-MS (2008)

  32. Gringarten, E., Haouesse, M., Arpat, G., Nghiem, L.: Advantages of using vertical stair step faults in reservoir grids for flow simulation. Soc. Pet. Eng. 01. https://doi.org/10.2118/119188-MS (2009)

  33. Heinemann, Z., von Hantelmann, G., Gerken, G., Montanuniversitat, L.: Using local grid refinement in a multiple-application reservoir simulator. Soc. Pet. Eng. J., SPE 11255, 11 (1983)

    Google Scholar 

  34. Helmig, R.: Multiphase flow and transport processes in the subsurface: a contribution to the modeling of hydrosystems. Environmental engineering springer (1997)

  35. Huber, R., Helmig, R.: Multiphase flow in heterogeneous porous media: a classical finite element method versus an implicit pressure–explicit saturation-based mixed finite element–finite volume approach. Int. J. Numer. Methods Fluids 29(8), 899–920 (1999)

    Article  Google Scholar 

  36. Huppert, H.E., Neufeld, J.A.: The fluid mechanics of carbon dioxide sequestration. Ann. Rev. Fluid Mech. 46(1), 255–272 (2014). https://doi.org/10.1146/annurev-fluid-011212-140627

    Article  Google Scholar 

  37. Issautier, B., Viseur, S., Audigane, P., Nindre, Y. -M.: Impacts of fluvial reservoir heterogeneity on connectivity: Implications in estimating geological storage capacity for co2. Int. J. Greenh. Gas Con. 20, 333–349 (2014). https://doi.org/10.1016/j.ijggc.2013.11.009

    Article  Google Scholar 

  38. Journel, A., Huijbregts, C.: Mining Geostatistics. Blackburn Press, Caldwell (2003)

    Google Scholar 

  39. Juanes, R., Kim, J., Matringe, S.F., Thomas, K.: Implementation and application of a hybrid multipoint flux approximation for reservoir simulation on corner-point grids. In: SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA. Society of Petroleum Engineers. https://doi.org/10.2118/95928-MS (2005)

  40. Kim, J.G., Deo, M.D.: Comparison of the performance of a discrete fracture multiphase model with those using conventional models. In: SPE Reservoir Simulation Symposium, SPE51928, pp 14–17 (1999)

  41. Li, B., Benson, S.: Influence of small-scale heterogeneity on upward co2 plume migration in storage aquifers. Adv. Water Resour. 83, 389–404 (2015). https://doi.org/10.1016/j.advwatres.2015.07.010

    Article  Google Scholar 

  42. Lindeberg, E., Bergmo, P. Gale, J., Kaya, Y. (eds.): The Long- Term Fate of CO2 Injected into an Aquifer. Pergamon, Oxford (2003)

  43. Lu, P., Shaw, J.S., Eccles, T.K., Mishev, I.D., Beckner, B.L.: Experience with numerical stability, formulation, and parallel efficiency of adaptive implicit methods. Soc. Pet. Eng. 01. https://doi.org/10.2118/118977-MS (2009)

  44. Mathias, S.A., Hardisty, P.E., Trudell, M.R., Zimmerman, R.W.: Approximate solutions for pressure buildup during co2 injection in brine aquifers. Transp. Porous Media 79(2), 265 (Dec 2008). https://doi.org/10.1007/s11242-008-9316-7

    Article  Google Scholar 

  45. Moortgat, J.: Adaptive implicit finite element methods for multicomponent compressible flow in heterogeneous and fractured porous media. Water Resour. Res. 53(1), 73–92 (2017). https://doi.org/10.1002/2016WR019644

    Article  Google Scholar 

  46. Mouton, T., Borouchaki, H., Bennis, C.: Hybrid mesh generation for reservoir flow simulation: Extension to highly deformed corner point geometry grids. Finite Elem. Anal. Des. 46(1), 152–164 (2010). https://doi.org/10.1016/j.finel.2009.06.033. Mesh Generation - Applications and Adaptation

    Article  Google Scholar 

  47. Muron, P.: Méthodes Numériques 3-D De Restauration Des Structures Géologiques Faillées. PhD thesis, Institut National Polytechnique de Lorraine (2005)

  48. Muskat, M., Wyckoff, R.D., Botset, H.G., Meres, M.W.: Flow of gas-liquid mixtures through sands. Trans. AIME 123(01), 69–96 (1937)

    Article  Google Scholar 

  49. Nacul, E., S.U.D. of Petroleum Engineering: Use of Domain Decomposition and Local Grid Refinement in Reservoir Simulation Number v. 2 in Use of Domain Decomposition and Local Grid Refinement in Reservoir Simulation. Stanford University (1991)

  50. Nick, H., Matthäi, S.: Comparison of three fe-fv numerical schemes for single- and two-phase flow simulation of fractured porous media. Transp. Porous Media 90, 421–444 (2011)

    Article  Google Scholar 

  51. Niessner, J., Helmig, R.: Multi-scale modelling of two-phase–two-component processes in heterogeneous porous media. Numer. Linear Algebra Appl. 13, 699–715 (2006). https://doi.org/10.1002/nla.497

    Article  Google Scholar 

  52. Nilsen, H., Lie, K. -A., Natvig, J., Krogstad, S.: Accurate modeling of faults by multipoint, mimetic, and mixed methods. SPE J. 17, 568–579 (2012). https://doi.org/10.2118/149690-PA

    Article  Google Scholar 

  53. Nordbotten, J.M., Celia, M.A., Bachu, S.: Injection and storage of co2 in deep saline aquifers: Analytical solution for co2 plume evolution during injection. Transp. Porous Media 58(3), 339–360 (2005a). https://doi.org/10.1007/s11242-004-0670-9

    Article  Google Scholar 

  54. Nordbotten, J.M., Celia, M.A., Bachu, S., Dahle, H.K.: Semianalytical solution for co2 leakage through an abandoned well. Environ. Sci. Technol. 39(2), 602–611 (2005b). https://doi.org/10.1021/es035338i. PMID: 15707061

    Article  Google Scholar 

  55. O’Sullivan, M.J.: A similarity method for geothermal well test analysis. Water Resour. Res. 17 (2), 390–398 (1981)

    Article  Google Scholar 

  56. Paluszny, A., Matthäi, S. K., Hohmeyer, M.: Hybrid finite element-finite volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks. Geofluids 7(2), 186–208 (2007)

    Article  Google Scholar 

  57. Pellerin, J., Botella, A., Bonneau, F., Mazuyer, A., Chauvin, B., Lévy, B., Caumon, G.: Ringmesh: a programming library for developing mesh-based geomodeling applications. Comput. Geosci. 104, 93–100 (2017). https://doi.org/10.1016/j.cageo.2017.03.005

    Article  Google Scholar 

  58. Prevost, M.: Accurate Coarse Reservoir Modeling Using Unstructured Grids, Flow-based Upscaling and Streamline Simulation Stanford University (2004)

  59. Pruess, K.: ECO2N: A TOUGH2 Fluid Property Module for Mixtures of Water, NaCl, and CO2. Lawrence Berkeley Natl. Lab. berkeley, CA USA (2005)

  60. Pruess, K.: On CO2 fluid flow and heat transfer behavior in the subsurface, following leakage from a geologic storage reservoir. Environ. Geol. 54(8), 1677–1686 (2008). Copyright - Springer-Verlag 2008; Document feature - ; Last updated - 2011-05-26

    Article  Google Scholar 

  61. Pruess, K., García, J.: Multiphase flow dynamics during CO2 disposal into saline aquifers. Environ. Geol. 42(2), 282–295 (2002)

    Article  Google Scholar 

  62. Pruess, K., Garcia, J., Kovscek, T., Oldenburg, C., Rutqvist, J., Steefel, C., Xu, T.: Intercomparison of numerical simulation codes for geologic disposal of CO2. Lawrence Berkeley National Laboratory 11 (2002)

  63. Pruess, K., Garcia, J., Kovscek, T., Oldenburg, C., Rutqvist, J., Steefel, C., Xu, T.: Code intercomparison builds confidence in numerical simulation models for geologic disposal of CO2. Energy 29(9), 1431–1444 (2004). 6th International Conference on Greenhouse Gas Control Technologies

    Article  Google Scholar 

  64. Quandalle, P., Besset, P.: The use of flexible gridding for improved reservoir modeling. Soc. Pet. Eng. SPE-11239, 11 (1983)

    Google Scholar 

  65. Shao, Q., Matthäi, S., Gross, L.: Efficient Modelling of Co2 Injection and Plume Spreading with Discrete Event Simulation (Des). In: 14th International Conference on Greenhouse Gas Control Technologies Conference Melbroune 21-26 October 2018 (GHGT-14), vol. 10 (2018)

  66. Shao, Q., Matthäi, S., Gross, L.: Efficient modelling of solute transport in heterogeneous media with discrete event simulation. J. Comput. Phys. 384, 134–150 (2019)

    Article  Google Scholar 

  67. Spycher, N., Pruess, K., Ennis-King, J.: Co2-h2o mixtures in the geological sequestration of co2. i. assessment and calculation of mutual solubilities from 12 to 100c and up to 600 bar. Geochim. Cosmochim. Acta 67(16), 3015–3031 (2003)

    Article  Google Scholar 

  68. Stéphenne, K.: Start-up of world’s first commercial post-combustion coal fired ccs project: Contribution of shell cansolv to saskpower boundary dam iccs project. Energy Procedia 63, 6106–6110 (2014). https://doi.org/10.1016/j.egypro.2014.11.642. 12th International Conference on Greenhouse Gas Control Technologies, GHGT-12

    Article  Google Scholar 

  69. Stüben, K.: Algebraic Multigrid (AMG): An Introduction with Applications. GMD-report GMD-forschungszentrum Informationstechnik (1999)

  70. Tan, T.B.: Implementation of an improved adaptive-implicit method in a thermal compositional simulator. Soc. Pet. Eng. 11. https://doi.org/10.2118/16028-PA (1988)

  71. Thomas, G.W., Thurnau, D.H.: The mathematical basis of the adaptive implicit method. Soc. Pet. Eng. 01. https://doi.org/10.2118/10495-MS (1982)

  72. Thomas, G.W., Thurnau, D.H.: Reservoir simulation using an adaptive implicit method. Soc. Pet. Eng. 10. https://doi.org/10.2118/10120-PA (1983)

  73. Tran, L., Kim, J., Matthäi, S.: Simulation of two-phase flow in porous media with sharp material discontinuities. Adv. Water Resour. 142, 103636 (2020). https://doi.org/10.1016/j.advwatres.2020.103636

    Article  Google Scholar 

  74. van Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils1. Soil Sci. Soc. Am. J. 44, 892–898 (1980). https://doi.org/10.2136/sssaj1980.03615995004400050002x

    Article  Google Scholar 

  75. Verma, A., Pruess, K.: Thermohydrological conditions and silica redistribution near high-level nuclear wastes emplaced in saturated geological formations. J. Geophys. Res. Solid Earth 93(B2), 1159–1173 (1988). https://doi.org/10.1029/JB093iB02p01159

    Article  Google Scholar 

  76. Verma, S.K.: Flexible grids for reservoir simulation. Phd thesis, Stanford University, Stanford, CA USA (1996)

  77. von Rosenberg, D.: Local mesh refinement for finite difference methods. Soc. Pet. Eng., SPE 10974, 9 (1982)

    Google Scholar 

  78. Weis, P., Driesner, T., Coumou, D., Geiger, S.: Hydrothermal, multiphase convection of h2o-nacl fluids from ambient to magmatic temperatures: a new numerical scheme and benchmarks for code comparison. Geofluids 14(3), 347–371 (2014). https://doi.org/10.1111/gfl.12080

    Article  Google Scholar 

  79. Wheeler, M.F., Yotov, I.: A multipoint flux mixed finite element method. SIAM J. Numer. Anal. 44(5), 2082–2106 (2006). https://doi.org/10.1137/050638473

    Article  Google Scholar 

  80. Young, L.C.: Rigorous treatment of distorted grids in 3d. Soc. Pet. Eng. 1–14. https://doi.org/10.2118/51899-MS9 (1999)

  81. Young, L.C., Russell, T.F.: Implementation of an adaptive implicit method. Soc. Pet. Eng. 01. https://doi.org/10.2118/25245-MS (1993)

  82. Zhou, Q., Birkholzer, J.T., Tsang, C.-F., Rutqvist, J.: A method for quick assessment of co2 storage capacity in closed and semi-closed saline formations. Int. J. Greenh. Gas Con. 2(4), 626–639 (2008). https://doi.org/10.1016/j.ijggc.2008.02.004. TCCS-4: The 4th Trondheim Conference on CO2 Capture, Transport and Storage

    Article  Google Scholar 

  83. Zhou, Y., Tchelepi, H.A., Mallison, B.T.: Automatic differentiation framework for compositional simulation on unstructured grids with multi-point discretization schemes. Soc. Pet. Eng. J. 1. https://doi.org/10.2118/141592-MS (2011)

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Acknowledgements

ANLEC R & D is supported by Australian Coal Association Low Emissions Technology Limited and the Australian Government through the Clean Energy Initiative.

Funding

The authors received financial assistance provided through Australian National Low Emissions Coal Research and Development (ANLEC R & D). More important was the support by the CCS-RD grant CCS49356 by the Australian federal government which allowed us to implement the ACGSS in the first place.

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Shao, Q., Matthai, S., Driesner, T. et al. Predicting plume spreading during CO2 geo-sequestration: benchmarking a new hybrid finite element–finite volume compositional simulator with asynchronous time marching. Comput Geosci 25, 299–323 (2021). https://doi.org/10.1007/s10596-020-10006-1

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