Abstract
Matrix diffusion is a phenomenon in which tracer particles convected along a flow channel can diffuse into porous walls of the channel, and it causes a delay and broadening of the breakthrough curve of a tracer pulse. Analytical and numerical methods exist for modeling matrix diffusion, but there are still some features of this phenomenon, which are difficult to address using traditional approaches. To this end we propose to use the lattice-Boltzmann method with point-like tracer particles. These particles move in a continuous space, are advected by the flow, and there is a stochastic force causing them to diffuse. This approach can be extended to include particle-particle and particle-wall interactions of the tracer. Numerical results that can also be considered as validation of the LBM approach, are reported. As the reference we use recently-derived analytical solutions for the breakthrough curve of the tracer.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Foster, S.: The Chalk groundwater tritium anomaly – A possible explanation. Journal of Hydrology 25(1-2), 159–165 (1975)
Neretnieks, I.: Diffusion in the rock matrix: An important factor in radionuclide retardation? Journal of Geophysical Research 85(B8), 4379–4397 (1980)
Bodin, J., Delay, F., de Marsily, G.: Solute transport in a single fracture with negligible matrix permeability: 1. fundamental mechanisms. Hydrogeology Journal 11(4), 418–433 (2003)
Barten, W., Robinson, P.: Contaminant transport in fracture networks with heterogeneous rock matrices: The PICNIC code. Technical Report NTB 01-03, NAGRA (February 2001) ISSN: 1015-2636
McDermott, C., Walsh, R., Mettier, R., Kosakowski, G., Kolditz, O.: Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion. Computational Geosciences 13(3), 349–361 (2009)
Succi, S.: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Clarendon Press, Oxford (2001)
Ma, Y., Bhattacharya, A., Kuksenok, O., Perchak, D., Balazs, A.C.: Modeling the transport of nanoparticle-filled binary fluids through micropores. Langmuir 28(31), 11410–11421 (2012)
Kekäläinen, P., Voutilainen, M., Poteri, A., Hölttä, P., Hautojärvi, A., Timonen, J.: Solutions to and validation of matrix-diffusion models. Transport in Porous Media 87, 125–149 (2011)
Frisch, U., Hasslacher, B., Pomeau, Y.: Lattice-gas automata for the Navier-Stokes equation. Physical Review Letters 56(14), 1505–1508 (1986)
Qian, Y.H., D’Humiéres, D., Lallemand, P.: Lattice BGK models for Navier-Stokes equation. Europhysics Letters 17(6), 479–484 (1992)
Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94(3), 511–525 (1954)
Mattila, K., Hyväluoma, J., Rossi, T., Aspnäs, M., Westerholm, J.: An efficient swap algorithm for the lattice Boltzmann method. Computer Physics Communications 176(3), 200–210 (2007)
Ladd, A.J.C., Verberg, R.: Lattice-Boltzmann simulations of particle-fluid suspensions. Journal of Statistical Physics 104(5), 1191–1251 (2001)
Verberg, R., Yeomans, J.M., Balazs, A.C.: Modeling the flow of fluid/particle mixtures in microchannels: Encapsulating nanoparticles within monodisperse droplets. The Journal of Chemical Physics 123(22), 224706 (2005)
Szymczak, P., Ladd, A.J.C.: Boundary conditions for stochastic solutions of the convection-diffusion equation. Physical Review E 68(3), 036704 (2003)
Vidal, D., Roy, R., Bertrand, F.: On improving the performance of large parallel lattice Boltzmann flow simulations in heterogeneous porous media. Computers & Fluids 39(2), 324–337 (2010)
Starikovičius, V., Čiegis, R., Iliev, O.: A parallel solver for the design of oil filters. Mathematical Modelling and Analysis 16(2), 326–341 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Toivanen, J.I., Mattila, K., Hyväluoma, J., Kekäläinen, P., Puurtinen, T., Timonen, J. (2013). Simulation Software for Flow of Fluid with Suspended Point Particles in Complex Domains: Application to Matrix Diffusion. In: Manninen, P., Öster, P. (eds) Applied Parallel and Scientific Computing. PARA 2012. Lecture Notes in Computer Science, vol 7782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36803-5_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-36803-5_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36802-8
Online ISBN: 978-3-642-36803-5
eBook Packages: Computer ScienceComputer Science (R0)