Conservative and Reactive Solutes Conservative do not react with soil / groundwater Chloride is a good example Sorbed onto mineral grains as well as organic.
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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
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
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
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
(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
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?
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 …
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
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
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
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
Effect of retardation on solute transport Lower peak value and peak arrives later