Continuous time random walks for non-local radial solute transport |
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| Institution: | 1. Institute of Environmental Assessment and Water Research (IDÆA), Spanish National Research Council (CSIC), 08034 Barcelona, Spain;2. Massachusetts Institute of Technology, 77 Massachusetts Ave, Building 48, Cambridge, MA 02139, USA;3. Université de Rennes 1, CNRS, Geosciences Rennes, UMR 6118, Rennes, France;1. Chevron Energy Technology Co., 1500 Louisiana St., Houston, TX 77002, USA;2. Dept. of Mathematics, Texas A&M, College Station, TX 77843-3368, USA;3. Dept. of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA;1. Department of Electrical and Computer Engineering, Tufts University, 196 Boston Avenue, Medford, MA 02155, United States;2. Department of Civil and Environmental Engineering, Yang & Yamazaki Environment & Energy Building, 473 Via Ortega, Stanford, CA 94305, United States;3. Institute for Computational and Mathematical Engineering, Huang Engineering Center, 475 Via Ortega, Stanford, CA 94305, United States;1. Centre for Water Management and Reuse, School of Natural and Built Environments, University of South Australia, Mawson Lakes, SA 5095, Australia;2. Department of Civil and Environmental Engineering, United Arab Emirates University, Al Ain 15551, United Arab Emirates;1. Eawag – Swiss Federal Institute of Aquatic Science and Technology, Department of Water Resources and Drinking Water, Dübendorf, Switzerland;2. Centre for Hydrogeology and Geothermics (CHYN), University of Neuchâtel, Neuchâtel, Switzerland;3. Department ICEA and International Center for Hydrology “Dino Tonini”, University of Padova, Padua, Italy;1. Department of Geology and Geological Engineering, Colorado School of Mines, United States;2. Integrated GroundWater Modeling Center, United States;3. Department of Applied Mathematics and Statistics, Colorado School of Mines, United States;4. Climate Change Water and Society (CCWAS), Integrative Graduate Education and Research Traineeship (IGERT), United States |
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| Abstract: | 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. |
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| Keywords: | Continuous time random walks Multirate mass transfer Radial transport Random walk particle tracking Stochastic modeling Non-local transport |
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