Conservative and Reactive Solutes
Conservativedo not react with soil / groundwater
Chloride is a good example
Sorbed onto mineral grains as well as organic matter
Solute Transport
Reactive
Retardation
Slows the rate of transport
Divalent ions more strongly adsorbed than monovalent ions
Cations more likely than anions to be adsorbed
Size of ion mattersif too large not adsorbed
HCO3-
SO4 2-
NO3-
Particularly true of clays, tend to possess excess negative charge
Surfaces of solids can possess an electrical charge
DL2Cx2
- vxC x
=C t
DL = coefficient of longitudinal hydrodynamic dispersionC = solute concentration in liquid phasevx = average linear groundwater velocityt = timeb = bulk density of aquifer= porosity (saturated aquifer)C* = amount of solute sorbed per unit weight of solid
- b
dispersion advection sorption
C* t
One dimension advection - dispersion with sorption
Direct linear relationship between amount of solute sorbed onto solid (C*) and the concentration of the solute (C)
C* = KdC
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)
Kd = distribution coefficient (L/kg)
Slope of linear isotherm = KdC*
C
(1 + Kd)
DL2Cx2
- vxC x
=C t
- b
C* t
C* = KdC
One dimension advection – dispersion with sorption
Substitute into advection – dispersion equation
DL2Cx2
- vxC x
=C t
- b
(KdC)
t
DL2Cx2
- vxC x
=C t
(1 + Kd) = rf = retardation factorb
b
If solute is reactive, it will travel slower than groundwater rate due to adsorption
vc = vx / [1 + (b / ) (Kd)] = vx / rf
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 Kf
C* = Kf Cj
C* = mass of solute sorbed per bulk unit dry mass of soilC = solute concentrationKf, 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 Kf
Log C* = j log C + log Kf
DL2Cx2
- vxC x
=C t
- b
(KfCj)
t
(1 + ) DL2Cx2
- vxC x
=C t
bKf 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
CC*
112
C2
C = equilibrium concentration of the ion in contact with soilC* = amount of ion adsorbed per unit weight of soil1 = adsorption constant related to the binding energy2 = adsorption maximum for the soil (mg/kg)
Limited number of sorption sites
When all sorption sites filled, no more sorption
= +
1 + b
( )12
(1 + 1C)2= rf
Langmuir Sorption Isotherm
1 + b
( )12
(1 + 1C)2= rf
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 slope1 = slope of line divided by intercept
C*
CCC*
C
Effect of retardation on solute transport
Lower peak value and peak arrives later
DNAPL (Denser)DNAPL (Denser)
Density of ContaminantDensity of Contaminant
If Denser If Denser than Waterthan Water
TransportTransportWith WaterWith Water
Leaking Gas TanksLeaking Gas Tanks