• Radek Fučík Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics, Trojanova 13, 12000, Praha, Czech Republic
  • Jakub Solovský Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics, Trojanova 13, 12000, Praha, Czech Republic
  • Michelle R. Plampin U.S. Geological Survey, Eastern Energy Resources Science Center, 12201 Sunrise Valley Drive, Reston, VA 20192, USA
  • Hao Wu Virginia Polytechnic Institute and State University, Department of Geosciences, 926 West Campus Drive, Blacksburg, VA 24061, USA
  • Jiří Mikyška Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics, Trojanova 13, 12000, Praha, Czech Republic
  • Tissa H. Illangasekare Colorado School of Mines, Center for Experimental Study of Subsurface Environmental Processes, 1500 Illinois St., Golden, CO 80401, USA



Compositional flow, two–phase flow, kinetic mass transfer, gas exsolution, gas dissolution


Exsolution and re-dissolution of CO2 gas within heterogeneous porous media are investigated using experimental data and mathematical modeling. In a set of bench-scale experiments, water saturated with CO2 under a given pressure is injected into a 2-D water-saturated porous media system, causing CO2 gas to exsolve and migrate upwards. A layer of fine sand mimicking a heterogeneity within a shallow aquifer is present in the tank to study accumulation and trapping of exsolved CO2. Then, clean water is injected into the system and the accumulated CO2 dissolves back into the flowing water. Simulated exsolution and dissolution mass transfer processes are studied using both nearequilibrium and kinetic approaches and compared to experimental data under conditions that do and do not include lateral background water flow. The mathematical model is based on the mixed hybrid finite element method that allows for accurate simulation of both advection- and diffusion- dominated processes.


S. Pacala, R. Socolow. Stabilization wedges: solving the climate problem for the next 50 years with current technologies. Science 305(5686):968–972, 2004. doi:10.1126/science.1100103.

J. A. Apps, L. Zheng, Y. Zhang, et al. Evaluation of potential changes in groundwater quality in response to CO2 leakage from deep geologic storage. Transport in Porous Media 82(1):215–246, 2010. doi:10.1007/s11242-009-9509-8.

M. R. Plampin, T. H. Illangasekare, T. Sakaki, R. J. Pawar. Experimental study of gas evolution in heterogeneous shallow subsurface formations during leakage of stored CO2. International Journal of Greenhouse Gas Control 22:47–62, 2014. doi:10.1016/j.ijggc.2013.12.020.

M. R. Plampin, R. N. Lassen, T. Sakaki, et al. Heterogeneity-enhanced gas phase formation in shallow aquifers during leakage of co2-saturated water from geologic sequestration sites. Water Resources Research 50(12):9251–9266, 2014. doi:10.1002/2014WR015715.

T. Sakaki, M. R. Plampin, R. Pawar, et al. What controls carbon dioxide gas phase evolution in the subsurface? experimental observations in a 4.5 m-long column under different heterogeneity conditions. International Journal of Greenhouse Gas Control 17:66–77, 2013. doi:10.1016/j.ijggc.2013.03.025.

M. R. Plampin, M. L. Porter, R. J. Pawar, T. H. Illangasekare. Intermediate-scale experimental study to improve fundamental understanding of attenuation capacity for leaking CO2 in heterogeneous shallow aquifers. Water Resources Research 53(12):10121–10138, 2017. doi:10.1002/2016WR020142.

M. L. Porter, M. Plampin, R. Pawar, T. Illangasekare. CO2 leakage in shallow aquifers: A benchmark modeling study of CO2 gas evolution in heterogeneous porous media. International Journal of Greenhouse Gas Control 39:51–61, 2015. doi:10.1016/j.ijggc.2015.04.017.

R. N. Lassen, M. R. Plampin, T. Sakaki, et al. Effects of geologic heterogeneity on migration of gaseous CO2 using laboratory and modeling investigations. International Journal of Greenhouse Gas Control 43:213–224, 2015. doi:10.1016/j.ijggc.2015.10.015.

R. Fučík, J. Klinkovský, J. Solovský, et al. Multidimensional mixed–hybrid finite element method for compositional two-phase flow in heterogeneous porous media and its parallel implementation on gpu. Computer Physics Communications 238:165–180, 2019. doi:10.1016/j.cpc.2018.12.004.

M. R. Plampin, M. Porter, R. Pawar, T. H. Illangasekare. Multi-scale experimentation and numerical modeling for process understanding of CO2 attenuation in the shallow subsurface. Energy Procedia 63:4824–4833, 2014. doi:10.1016/j.egypro.2014.11.513.

J. Solovský, R. Fučík, M. R. Plampin, et al. Dimensional effects of inter-phase mass transfer on attenuation of structurally trapped gaseous carbon dioxide in shallow aquifers. Journal of Computational Physics 40, 2020. doi:10.1016/

P. Bastian. Numerical Computation of Multiphase Flows in Porous Media. Habilitation thesis, Kiel University, 2000.

R. Helmig. Multiphase Flow and Transport Processes in the Subsurface, A contribution to the Modelling of Hydrosystems. Springer, 1997.

K. Mosthaf, K. Baber, B. Flemisch, et al. A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow. Water Resources Research 47(10), 2011. doi:10.1029/2011WR010685.

R. Brooks, A. Corey. Hydraulic Properties of Porous Media. Colorado State University, Hydrology Paper 3:27, 1964.

N. Burdine. Relative permeability calculations from pore size distribution data. Journal of Petroleum Technology 5:71–78, 1953. doi:10.2118/225-G.

I. Tsimpanogiannis, Y. C. Yortsos. The critical gas saturation in a porous medium in the presence of gravity. J Colloid Interface Sci 270:388–395, 2014. doi:10.1016/j.jcis.2003.09.036.

R. J. Millington, J. P. Quirk. Permeability of porous solids. Transactions of the Faraday Society 57:1200–1207, 1961.

J. Niessner, S. M. Hassanizadeh. Modeling kinetic interphase mass transfer for two-phase flow in porous media including fluid-fluid interfacial area. Transport in Porous Media 80:329–344, 2009. doi:10.1007/s11242-009-9358-5.

R. Sander. Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry. Max-Planck Inst of Chem, Mainz, Germany 1999.

C. Geuzaine, J.-F. Remacle. Gmsh: A 3-D finite element mesh generator with built-in pre- nd post-processing facilities. International Journal for Numerical Methods in Engineering 79(11):1309–1331, 2009. doi:10.1002/nme.2579.

J. Solovský, R. Fučík. Mass Lumping for MHFEM in Two Phase Flow Problems in Porous Media. In F. A. Radu, K. Kumar, I. Berre, et al. (eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017, pp. 635–643. Springer International Publishing, 2019. doi:10.1007/978-3-319-96415-7_58.

J. Solovský, R. Fučík. A Parallel mixed-hybrid finite element method for two phase flow problems in porous media using MPI. Computer Methods in Materials Science 17:84–93, 2017.






Refereed Articles