Abstract
The disposal of heat-generating nuclear waste in salt host rock generates a thermal gradient around the waste package that may cause brine inclusions in the salt grains to migrate toward the waste package. In this study, a dual-continuum model is developed to analyze such a phenomenon. In this model, fluid flow in terms of advective and diffusive fluxes in the interconnected pore space and diffusive and thermal-diffusive fluxes in the salt grains is considered. Due to the very distinct behavior of fluid flow in the interconnected pore space versus in the salt grains, this process is simulated based on a dual-continuum model. In the dual-continuum model, the mass balance of salt and water in the two continua is separately considered, and the coupling between the two continua is represented by flux associated with brine migration in one medium and out of another. The energy balance is simulated assuming thermal equilibrium among different components and phases in the whole system. For mechanical analysis, a new formulation (extended finite volume method, XFVM) is proposed and is applied with a Voronoi tessellated mesh. The coupling between the hydraulic and mechanical fields in terms of pore-volume effects is consistent with Biot’s theory, while thermal and mechanical fields are linked in terms of thermal expansion. The resulting fully coupled THM model is capable of modeling strongly nonlinear features, involving salt concentration effects on fluid mass associated with advection, and thermal effects on brine migration. A Newton-Raphson iteration formula is used to generate the linearized equations for this nonlinear problem. The model was verified step by step for each component of the coupling terms, including thermal-hydraulic (TH) and hydro-mechanical (HM) couplings, and was applied to analyze diffusion in single continuum and dual continua, small-scale brine migration, and large-scale brine migration induced by thermal gradient. The results show that the model is able to quantify brine under different conditions and thermal gradients, making it a valuable tool for performance assessment for nuclear waste disposal in salt.
Similar content being viewed by others
References
Olander, D.R.: A Study of Thermal-Gradient Induced Migration Inclusions in Salt: Final Report, BMI/ONWI-538, Regents of the University of California, Oakland, CA (1984)
Roedder, E., Belkin, H.E.: Thermal gradient migration of fluid inclusions in single crystals of salt from the Waste Isolation Pilot Plant (WIPP), Scientific Basis for Nuclear Waste Management, Vol. 2 Edited by Clyde J.M. Northrup, Jr., Plenum Publishing Corporation, New York, NY (1980)
Kuhlman, K.L., Malama, B.: Brine Flow in Heated Geologic Salt, SAND2013-1944, Sandia National Laboratory, Albuquerque, NM (2013)
Yagnik, S.K.: Interfacial stability of migrating brine inclusions in alkali halide single crystals supporting a temperature gradient. J. Cryst. Growth. 62, 612–626 (1983)
Olivella, S., Castagna, S., Alonso, E.E., Lloret, A.: Porosity variations in saline media induced by temperature gradients: experimental evidences and modeling. Transp. Porous Media. 90, 763–777 (2011)
Stauffer, P.H., Harp, D.A., Jordan, A.B., Lu, Z., Kelkar, S., Kang, Q., Ten Cate, J., Boukhalfa, H., Labyed, Y., Reimus, P.W., Caporuscio, F.A., Miller, T.A., Robinson, B.A.: Coupled model for heat and water transport in a high level waste repository in salt. LANL. Rep. LANL M2FT-13L A08180113 (2013)
Wolters, R., Lux, K.H., Düsterloh, U.: Evaluation of rock salt barriers with respect to tightness: influence of thermomechanical damage, fluid infiltration and sealing/healing. In: Proc 7th Int Conf Mech Behav Salt (SaltMech7), Paris, 425–434 (2012)
Lux, K.H., Lerche, S., Dyogtyev, O.: Intense damage processes in salt rock- a new approach for laboratory investigations, physical modelling and numerical simulation. In proceedings Mechanical Behavior of Salt IX, Hannover, Germany, 12–14 September, (2018)
Kuhlman, K.L.: Summary Results for Brine Migration Modeling Performed by LANL, LBNL, and SNL for the UFD Program, SAND2014-18217 R, Sandia National Laboratory, Albuquerque, NM (2014)
Ratigan, J.L.: A finite element formulation for brine transport in rock salt. Int. J. Numer. Anal. Methods Geomech. 8, 225–241 (1984)
Olivella, S., Carrera,, J., Gens, A., Alonso, E.E.: Nonisothermal multiphase flow of brine and gas through saline media, Transp. Porous Media 15, 271–293 (1994)
Zyvoloski, G.A., Robinson, B.A., Dash, Z.V., Kelkar, S., Viswanathan, H.S., Pawar, R.J., Stauffer, P.H.: Software Users Manual (UM) for the FEHM Application Version 3.1–3.X. Los Alamos National Laboratory, Los Alamos, NM (2011)
Blanco-Martín, L., Rutqvist, J., Birkholzer, J.T.: Long-term modelling of the thermal-hydraulic-mechanical response of a generic salt repository for heat-generating nuclear waste. Eng. Geol. 193, 198–211 (2015)
Blanco-Martín, L., Wolters, R., Rutqvist, J., Lux, K.H., Birkholzer, J.T.: Comparison of two simulators to investigate thermal-hydraulic-mechanical processes related to nuclear waste isolation in saliniferous formations. Comput. Geotech. 66, 219–229 (2015)
Blanco-Martín, L., Wolters, R., Rutqvist, J., Lux, K.H., Birkholzer, J.T.: Thermal–hydraulic–mechanical modeling of a large-scale heater test to investigate rock salt and crushed salt behavior under repository conditions for heat-generating nuclear waste. Comput. Geotech. 77, 120–133 (2016)
Blanco-Martín, L., Rutqvist, J., Birkholzer, J.T.: Extension of TOUGH-FLAC to the finite strain framework. Comput. Geosci. 108, 64–71 (2017)
Blanco-Martín, L., Rutqvist, J., Battistelli, A., Birkholzer, J.T.: Coupled processes modeling in rock salt and crushed salt including halite solubility constraints: application to disposal of heat-generating nuclear waste. Transp. Porous Media. 124, 159–182 (2018)
Rutqvist, J. Tsang, C.F.: TOUGH-FLAC: a numerical simulator for analysis of coupled thermal-hydrologic-mechanical processes in fractured and porous geological media under multi-phase flow conditions. In: Proceedings of the TOUGH Symposium 2003, Berkeley, CA, USA, 12 pp (2003)
Rutqvist, J., Blanco Martin, L., Houseworth, J., Birkholzer, J.: Modeling Coupled THMC Processes and Brine Migration in Salt at High Temperatures, LBNL-6718E, Lawrence Berkeley National Laboratory, Berkeley, CA (2014)
Rutqvist, J.: Status of the TOUGH-FLAC simulator and recent applications related to coupled fluid flow and crustal deformations. Comput. Geosci. 37, 739–750 (2011)
Rutqvist, J., Wu, Y.S., Tsang, C.F., Bodvarsson, G.: A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. Int. J. Rock Mech. Min. Sci. 39, 429–442 (2002)
Doughty, C.: Investigation of conceptual and numerical approaches for evaluating moisture, gas, chemical, and heat transport in fractured unsaturated rock. J. Contam. Hydrol. 38(1–3), 69–106 (1999)
Gerke, H.H., Van Genuchten, M.T.: A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resour. Res. 24, 1225–1236 (1993)
Pruess, K., Oldenburg, C., Moridis, G.: TOUGH2 User’s Guide, Version 2, Lawrence Berkeley National Laboratory Report LBNL-43134 (2011)
Wu, Y.S., Pruess, K.: A multiple-porosity method for simulation of naturally fractured petroleum reservoirs. SPE Reserv. Eng. 3, 327–336 (1988)
Silva, O., Carrera, J., Dentz, M., Kumar, S., Alcolea, A., Willmann, M.: A general real-time formulation for multi-rate mass transfer problems. Hydrol. Earth Syst. Sci. 13, 1399–1411 (2009)
Dold, A.: Partitions of unity in the theory of fibrations. Ann. Math. 78, 223–255 (1963)
Hu, M., Wang, Y., Rutqvist, J.: Fully coupled hydro-mechanical numerical manifold modeling of porous rock with dominant fractures. Acta Geotech. 12(2), 231–252 (2017)
Wu, Y.S., Qin, G.: A generalized numerical approach for modeling multiphase flow and transport in fractured porous media. Commun Comput Phys. 6, 85–108 (2009)
Hu, M., Rutqvist, J., Wang, Y.: A numerical manifold method model for analyzing fully coupled hydro-mechanical processes in porous rock masses with discrete fractures. Adv. Water Resour. 102, 111–126 (2017)
Rutenberg, M., Feierabend, J., Lux, K.H., Maßmannn, J., Sentís, M.L., Graupner, B.J., Hansmann, J., Czaikowski, O., Wieczorek, K., Friedenberg, L., Hotzel, S., Kock, I., Rutqvist, J., Hu, M., Rinaldi, A.P.: BENVASIM—A Benchmarking of simulators for modeling TH2M processes in the context of radioactive waste disposal. In Proceedings TOUGH Symposium 2018, Berkeley, 8–10 October (2018)
Biot, M.A.: General theory of three dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941)
Caporuscio, F.A., Boukhalfa, H., Cheshire, M.C., Jordan, A.B., Ding, M.: Brine Migration Experimental Studies for Salt Repositories, LA-UR-13-27240, Los Alamos National Laboratory, Los Alamos, NM (2013)
Acknowledgments
Funding for this work has been provided by the Used Fuel Disposition Campaign, Office of Nuclear Energy of the US Department of Energy, under Contract Number DE-AC02-05CH11231 with Berkeley Lab. Additionally, this work was partially supported by Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hu, M., Rutqvist, J. Finite volume modeling of coupled thermo-hydro-mechanical processes with application to brine migration in salt. Comput Geosci 24, 1751–1765 (2020). https://doi.org/10.1007/s10596-020-09943-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-020-09943-8