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Conservative and Reactive Solutes Conservative do not react with soil / groundwater Chloride is a good example Sorbed onto mineral grains as well as organic matter Solute Transport Reactive

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Retardation Slows the rate of transport

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Divalent ions more strongly adsorbed than monovalent ions Cations more likely than anions to be adsorbed Size of ion matters if too large not adsorbed HCO 3 - SO 4 2- NO 3 - Particularly true of clays, tend to possess excess negative charge Surfaces of solids can possess an electrical charge

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DLDL 2Cx22Cx2 - vxvx C x = C t D L = coefficient of longitudinal hydrodynamic dispersion C = solute concentration in liquid phase v x = average linear groundwater velocity t = time b = bulk density of aquifer = porosity (saturated aquifer) C* = amount of solute sorbed per unit weight of solid - bb dispersion advectionsorption C* t One dimension advection - dispersionwith sorption

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Direct linear relationship between amount of solute sorbed onto solid (C*) and the concentration of the solute (C) C* = K d C C* = mass of solute sorbed per dry unit weight of solid (mg/kg) C = concentration of solute in solution in equilibrium with the mass of solute sorbed onto the solid (mg/L) K d = distribution coefficient (L/kg) Slope of linear isotherm = K d C* C

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(1 + K d ) DLDL 2Cx22Cx2 - vxvx C x = C t - bb C* t C* = K d C One dimension advection – dispersion with sorption Substitute into advection – dispersion equation DLDL 2Cx22Cx2 - vxvx C x = C t - bb (K d C) t DLDL 2Cx22Cx2 - vxvx C x = C t (1 + K d ) = r f = retardation factor bb bb

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If solute is reactive, it will travel slower than groundwater rate due to adsorption v c = v x / [1 + ( b / ) (K d )] = v x / r f Linear isotherm has no upper limit to amount of sorption What if data don’t fit linear?

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Freundlich isotherm Log C* = j log C + log K f C* = K f C j C* = mass of solute sorbed per bulk unit dry mass of soil C = solute concentration K f, j = coefficients Nonlinear relationship If you plot C* vs C … data will be curvilinear Linearize the data by plotting log …

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Plot of log C* vs log C … straight line Log C* Log C Slope is j intercept log K f Log C* = j log C + log K f

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DLDL 2Cx22Cx2 - vxvx C x = C t - bb (K f C j ) t (1 + ) DLDL 2Cx22Cx2 - vxvx C x = C t b K f j C j-1 Retardation factor for Freundlich sorption isotherm If j = 1 this becomes the linear isotherm Still no upper limit Plug into advection – dispersion equation

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C C* 112112 C2C2 C = equilibrium concentration of the ion in contact with soil C* = amount of ion adsorbed per unit weight of soil 1 = adsorption constant related to the binding energy 2 = adsorption maximum for the soil (mg/kg) Limited number of sorption sites When all sorption sites filled, no more sorption =+ 1 + bb ( ) 1212 (1 + 1 C) 2 = r f Langmuir Sorption Isotherm

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1 + bb ( ) 1212 (1 + 1 C) 2 = r f If you plot C* verses C will have curved shape that reaches a maximum If you plot C/C* vs C data will plot on straight line 2 = reciprocal of the slope 1 = slope of line divided by intercept C* C C C* C

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Effect of retardation on solute transport Lower peak value and peak arrives later

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DNAPL (Denser)

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Density of Contaminant

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If Denser than Water Transport With Water

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Leaking Gas Tanks

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