csh_lecture9_reactive - CWR 6537 Subsurface Contaminant...

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CWR 6537 Subsurface Contaminant Hydrology 1 ADVECTIVE-DISPERSIVE TRANSPORT OF REACTIVE SOLUTES: Equilibrium Sorption Cases A. Lecture Goal: To investigate solute transport under the assumption that a contaminant will undergo equilibrium, reversible sorption to the porous medium solid matrix during transient and steady water flow. B. Reactive Solutes: Equilibrium Models We will now consider “reactive” or adsorbed solute transport through porous media. A reactive solute interacts with the solid matrix during flow, as opposed to an “ideal” solute that is transported passively through the porous medium with no interactions or reactions with the solid matrix. A sorbed solute is one that is sorbed and desorbed (if sorption is reversible) by the porous medium. The solute is therefore distributed between the fluid (solution and/or gas) and the sorbed phases. Note on terminology: See attached copy of paper for a discussion of various mechanisms responsible for sorption of solutes by the solid matrix. You will see various terms like “sorption” or “uptake” or “adsorption” or “partitioning” – depending on the mechanism responsible – to describe the phenomenon of interest to us here. The distribution of the solute between the solid phase and the solution phase. Some refer to it as simply “retention”. We will use the term “soption” throughout this course. (i) Let, S represent the mass of solute sorbed per gram of solid matrix, M M -1 . [for example, µ g/g solid; meq/g solid; etc]. (ii) Let ρ be the porous medium bulk density; M L -3 [ for example, g solids/cm 3 total]. (iii) Let C w be the solution-phase concentration; M L -3 [for example, µ g/ml ; meq/ml]. (iv) Let θ w be the volumetric water content; L 3 L -3 [for example, ml/cm 3 total] The total mass of solute, M T , per unit volume the porous medium is simply the sum of the solute mass present in the solution-phase (M w ) and that in the sorbed phase (M s ). Thus, M T = M w + M s = ( θ w C w ) + ( ρ S ) ( 1 ) g g cm g ml g cm ml µ µ µ + = 3 3 3 We have shown earlier, from the continuity equation, that x J - = t M s T
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CWR 6537 Subsurface Contaminant Hydrology 2 Substituting Eq[1] in [2], x J - = S + C t s w w ] [ ρ θ ( 3 ) Recall that for advective-dispersive solute transport, the total solute flux is given as: ] [ ] [ C q + t C D - = J w w w w s θ For steady water flow, under saturated or uniformly unsaturated conditions, in homogeneous media, (that is, with θ w and q w being constant): x C q - x C D = t S + t C w w 2 w 2 w w w ρ θ ( 4 ) x C v - x C D = t S + t C w 2 w 2 w w θ ρ ( 5 ) where ν is the average pore-water velocity, ν = (q w / θ
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csh_lecture9_reactive - CWR 6537 Subsurface Contaminant...

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