2024-03-29T14:53:33Zhttp://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/1408062018-05-18T10:16:17Zcom_10261_5062com_10261_5col_10261_5064
Continuous time random walks for non-local radial solute transport
Dentz, Marco
Kang, Peter K.
Le Borgne, Tanguy
European Research Council
Continuous time random walks
Multirate mass transfer
Non-local transport
Radial transport
Random walk particle tracking
Stochastic modeling
This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer tests. © 2015 Elsevier Ltd.
2016-11-28T08:46:42Z
2016-11-28T08:46:42Z
2015-08-01
artículo
Advances in Water Resources 82: 16-26 (2015)
http://hdl.handle.net/10261/140806
10.1016/j.advwatres.2015.04.005
http://dx.doi.org/10.13039/501100000781
eng
Postprint
10.1016/j.advwatres.2015.04.005
Sí
info:eu-repo/grantAgreement/EC/FP7/617511
closedAccess
Elsevier