Abstract
This paper takes a new approach to the modelling and visualisation of sequestered CO\(_2\) in subsurface reservoirs and its migration pathways. We model the gas as discretised packets moving along paths within a graph or network. The movement of the packets will be governed by chip-firing. This new approach provides a new insight into the modelling of CO\(_2\) migration in porous media with complex geological architectures. We compare and contrast this new graph theoretic approach with traditional methods and demonstrate that similar results are obtained, with the added advantage that the new methods are quick to implement and execute. In addition, the new methods are more flexible and can more accurately capture the variation in the stratification of the encasing rock.
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References
Bachu, S.: Sequestration of CO\(_2\) in geological media in response to climate change: capacity of deep saline aquifers to sequester CO\(_2\) in solution. Energy Convers. Manag. 44(20), 3151–3175 (2003). https://doi.org/10.1016/S0196-8904(03)00101-8
Björner, A., Lovász, L., Shor, P.W.: Chip-firing games on graphs. Eur. J. Comb. 12, 283–291 (1991)
Bruant Jr., R.G., Celia, M.A., Guswa, A.J., Peters, C.A.: Safe storage of CO\(_2\) in deep saline aquifers. Environ. Sci. Technol. 36(11), 240A–245A (2002). https://doi.org/10.1021/es0223325
Bryant, D., Francetić, N., Gordinowicz, P., Pike, D.A., Prałat, P.: Brushing without capacity restrictions. Discrete Appl. Math. 170, 33–45 (2014)
CMG: GEM User’s Guide. CMG, Calgary (2012)
Dai, Z., Middleton, R., Viswanathan, H., Fessenden-Rahn, J., Bauman, J., Pawar, R., McPherson, B.: An integrated framework for optimizing CO\(_2\) sequestration and enhanced oil recovery. Environ. Sci. Technol. Lett. 1(1), 49–54 (2014). https://doi.org/10.1021/ez4001033
Deng, H., Stauffer, P.H., Dai, Z., Jiao, Z., Surdam, R.C.: Simulation of industrial-scale CO\(_2\) storage: multi-scale heterogeneity and its impacts on storage capacity, injectivity and leakage. Int. J. Greenh. Gas Control 10, 397–418 (2012). https://doi.org/10.1016/j.ijggc.2012.07.003
Gershenzon, N.I., Ritzi Jr., R.W., Dominic, D.F., Soltanisan, M., Mehnert, E., Okwen, R.: Influence of small-scale fluvial architecture on CO\(_2\) trapping processes in deep brine reservoirs. Water Resour. Res. 51, 8240–8256 (2015)
Holloway, S.: Storage of fossil fuel-derived carbon dioxide beneath the surface of the earth. Annu. Rev. Environ. Resour. 26, 145–166 (2001)
Holroyd, A.E., Levine, L., Mészáros, K., Peres, Y., Propp, J., Wilson, D.B.: Chip-firing and rotor-routing on directed graphs. Prog. Probab. 60, 331–364 (2008)
Kopp, A., Class, H., Helmig, R.: Investigations on CO\(_2\) storage capacity in saline aquifers: part 1. Dimensional analysis of flow processes and reservoir characteristics. Int. J. Greenh. Gas Control 3(3), 263–276 (2009)
Kovscek, A.R., Cakici, M.D.: Geologic storage of carbon dioxide and enhanced oil recovery. II. Cooptimization of storage and recovery. Energy Convers. Manag. 46, 1941–1956 (2005). https://doi.org/10.1016/j.enconman.2004.09.009
Kovscek, A.R., Wang, Y.: Geologic storage of carbon dioxide and enhanced oil recovery. I. Uncertainty quantification employing a streamline based proxy for reservoir flow simulation. Energy Convers. Manag. 46, 1920–1940 (2005). https://doi.org/10.1016/j.enconman.2004.09.008
Pruess, K., Garcıa, J.: Multiphase flow dynamics during CO\(_2\) disposal into saline aquifers. Environ. Geol. 42(2–3), 282–295 (2002). https://doi.org/10.1007/s00254-001-0498-3
Ren, B., Bryant, S.L., Lake, L.W.: Fast Modeling of local capillary trapping during CO\(_2\) injection into a saline aquifer. In: Carbon Management Technology Conference, Carbon Management Technology Conference (2015)
Ren, B., Jeongb, H.: Influence of injection strategies on local capillary trapping during geological carbon sequestration in saline aquifers. J. CO2 Utilization 27, 441–449 (2018)
Schnaar, G., Digiulio, D.C.: Computational modeling of the geologic sequestration of carbon dioxide. Vadose Zone J. 8(2), 389–403 (2009)
Webb, S.W.: Gas transportation mechanisms. In: Ho, C.K., Webb, S.W. (eds.) Gas Transport in Porous Media. Springer, Amsterdam (2006)
West, D.B.: Introduction to Graph Theory, vol. 2. Prentice Hall, Upper Saddle River (2001)
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The fourth author would like to acknowledge the support of the School of Mathematics and Physics, the University of Queensland, through the awarding of an Ethel Raybould Visiting Fellowship.
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All authors were involved in the formalisation of the problem, the discussion of the solution and the editing of the manuscript. TAMC implemented the code and provided the chip-firing visualisation; VB suggested the problem and provided the geological expertise and discussion; FZ implemented the process on the commercial package, CMG, providing the model visualisation; DP provided the graph theory background and suggested the chip-firing approach and mathematical expertise; DD oversaw the project and team, provided mathematical insights and drafted and edited the manuscript.
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McCourt, T.A., Zhou, F., Bianchi, V. et al. Chip-Firing on a Graph for Modelling Complex Geological Architecture in CO\(_2\) Injection and Storage. Transp Porous Med 129, 281–294 (2019). https://doi.org/10.1007/s11242-019-01287-x
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DOI: https://doi.org/10.1007/s11242-019-01287-x