Startseite A new algorithm for numerical modelling of impurity transport in the frame of statistically homogeneous sharply contrasting media
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

A new algorithm for numerical modelling of impurity transport in the frame of statistically homogeneous sharply contrasting media

  • Petr S. Kondratenko EMAIL logo , Leonid V. Matveev und Alexander D. Vasiliev
Veröffentlicht/Copyright: 26. Dezember 2019

Abstract

A new method is developed to calculate characteristics of contaminant transport (including non-classical regimes) in statistically homogeneous sharply contrasting media. A transport integro-differential equation in the space-time representation is formulated on the basis of the model earlier proposed by one of the authors (L. M.). Analytical expressions for transport characteristics in limiting time intervals in the one-dimensional case are derived. An interpolation form is proposed for the integral kernel of the transport equation. On a basis of this expression, an algorithm is developed for numerical modelling the contaminant transport in statistically homogeneous sharply contrasting media. Trial numerical 1D calculations are performed based on this algorithm. Good agreement was found between the numerical simulation results and the asymptotic analytical expressions.

MSC 2010: 65Z05
  1. Funding: This work was supported by the Russian Science Foundation grant 18-19-00533.

References

[1] G. Barenblatt, I. Zheltov, and I. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]. J. Appl. Math. Mechanics24 (1960), No. 5, 1286–1303.10.1016/0021-8928(60)90107-6Suche in Google Scholar

[2] J. Carrera, X. Sanchez-Vila, I. Benet, A. Medina, G. Galarza, and J. Guimera, On matrix diffusion formulations, solution methods and qualitative effects. Hydrogeol. J. 6 (1998), No. 1, 178–190.10.1007/s100400050143Suche in Google Scholar

[3] V. Cvetcovic, A general memory function for modeling mass transfer in groundwater transport. Water Resour. Res. 48 (2012), No. 4, W04528.10.1029/2011WR011657Suche in Google Scholar

[4] M. Dentz and B. Berkowitz, Transport behavior of a passive solute in continuous time random walks and multirate mass transfer. Water Resour. Res. 39 (2003), No. 5, 1111.10.1029/2001WR001163Suche in Google Scholar

[5] L. D. Donado, X. Sanchez-Vila, M. Dentz, J. Carrera, and D. Bolster, Multicomponent reactive transport in multi-continuum media. Water Resour. Res. 45 (2009), No.11, W11402.Suche in Google Scholar

[6] Ch. Dong, S. Sun, and G. A. Taylor, Numerical modeling of contaminant transport in fractured porous media using mixed finite-element and finite volume method. J. Porous Media14 (2011), No. 3, 219–242.10.1615/JPorMedia.v14.i3.30Suche in Google Scholar

[7] H. H. Gerke and M. Th. van Genuchten, A dual-porosity Model for simulating the preferential movement of water and solutes in structured porous media. Water Resour. Res. 29 (1993), No. 2, 305–319.10.1029/92WR02339Suche in Google Scholar

[8] N. M. Goltz and P. V. Roberts, Interpreting organic transport data from a field experiment using physical nonequilibrium models. J. Contam. Hydrol. 1 (1986), No. 1–2, 77–93.10.1016/0169-7722(86)90008-2Suche in Google Scholar

[9] R. Haggerty and S. M. Gorelick, Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity. Water Resour. Res. 31 (1995), No. 10, 2383–2400.10.1029/95WR10583Suche in Google Scholar

[10] R. Harvey, and S. M. Gorelick, Multiple-rate mass transfer for modeling diffusion and space reactions in media with porescale heterogeneity. Water Resour. Res. 31 (1995), No. 10, 2383–2400.10.1029/95WR10583Suche in Google Scholar

[11] P. Kekäläinen, M. Voutilainen, A. Poteri, P. Hölttä, A. Hautojärvi, and J.Timonen, Solutions to and Validation of Matrix- Diffusion Models. Transport Porous Med,. 87 (2011). No. 1, 125–149.10.1007/s11242-010-9672-ySuche in Google Scholar

[12] M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable. Nauka, Moscow, 1973 (in Russian).Suche in Google Scholar

[13] C. Masciopinto, and G. Passarella, Mass-transfer impact on solute mobility in porous media: a new mobile–immobile model. J. Contam. Hydrol. 215 (2018), 21–28.10.1016/j.jconhyd.2018.06.004Suche in Google Scholar PubMed

[14] L. V. Matveev, Impurity transport in a dual-porosity medium with sorption. JETP115 (2012), No. 5, 943–950.10.1134/S1063776112100068Suche in Google Scholar

[15] L. V. Matveev, Anomalous nonequilibrium transport simulations using a model of statistically homogeneous fracturedporous medium. Physica A406 (2014), 119–130.10.1016/j.physa.2014.03.017Suche in Google Scholar

[16] N. Muscus, and R. W. Falta, Semi-analytical method for matrix diffusion in heterogeneous and fractured systems with parent-daughter reactions. J. Contam. Hydrol. 218 (2018), 94–109.10.1016/j.jconhyd.2018.10.002Suche in Google Scholar PubMed

[17] V. V. Nair and S. G. Thampi, Numerical modeling of contaminant transport in sets of parallel fractures with fracture skin. J. Porous Media15 (2012), No. 1, 95–100.10.1615/JPorMedia.v15.i1.80Suche in Google Scholar

[18] M. Willmann, J. Carrera, X. Sanchez-Vila, O. Silva, and M. Dentz, Coupling of mass transfer and reactive transport for nonlinear reactions in heterogeneous media. Water Resour. Res. 46 (2010), No. 7, W07512.10.1029/2009WR007739Suche in Google Scholar

Received: 2019-07-16
Accepted: 2019-10-22
Published Online: 2019-12-26
Published in Print: 2019-12-18

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 2.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/rnam-2019-0029/html
Button zum nach oben scrollen