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