Solute Reaction Parameters

Kd

Adsorption isotherm coefficient, ks [M-1L3]

Nu

Adsorption isotherm coefficient, η [M-1L3]

Beta

Adsorption isotherm exponent, β [-]

Henry

Equilibrium distribution constant between liquid and gaseous phases, kg [-]

SinkL1

First-order rate constant for dissolved phase, μw [T-1]

SinkS1

First-order rate constant for solid phase, μs [T-1]

SinkG1

First-order rate constant for gas phase, μg [T-1]

SinkL1'

First-order rate constant for dissolved phase, μw‘ [T-1], as part of a solute decay chain

SinkS1'

First-order rate constant for solid phase, μs‘ [T-1], as part of a solute decay chain

SinkG1'

First-order rate constant for gas phase, μg‘ [T-1], as part of a solute decay chain

SinkW0

Zero-order rate constant for dissolved phase, γw  [ML-3T-1]

SinkS0

Zero-order rate constant for solid phase, γw  [T-1]

SinkG0

Zero-order rate constant for gas phase, γs  [ML-3T-1]

D_Soil

Diameter of the sand grains, dc [L]. Note that HYDRUS allow only one value (for all materials) and that this value is used only in the Depth-dependent blocking function (iPsi=4) developed by Bradford et al. [2002], which was developed for homogeneous laboratory column. It is less clear have is should be used in multi-layered systems (for other than the first layer). Also note that this blocking function depends on a vertical spatial coordinate. This means that one needs to specify the origin of the function, i.e., the inflow and inter-material interfaces. HYDRUS allows doing this for up to 2 materials using the cBnd vector as described in the help.

Then z entering the blocking function (zz) for node i is calculated as follows:

       if(M.eq.1) zz=cBnd(6)-z(i)

       if(M.eq.2) zz=cBnd(7)-z(i)

where M is the material number, cBnd(6) is the origin for the blocking function for material 1 (usually the inflow), cBnd(7) is the origin for the blocking function for material 2 (usually the first soil horizon change), and z(i) is the z-coordinate of the FE-Node. This approach was used in Bradford et al. [2004].

iPsi2

Type of blocking on the second sorption sites:

= 0: No blocking.

= 1: Langmuirian dynamics.

= 2: Ripening.

= 3: random sequential adsorption model.

= 4: depth dependent blocking coefficient.

iPsi1

Same for the first sorption sites.

SMax2

Parameter in the blocking function for the second sorption sites (smax for blocking options (1), (2) and (3), and b for (4)).

AttachSolid2

First-order deposition (attachment) coefficient, ka [T-1], for the second sorption sites.

DetachSolid2

First-order entrainment (detachment) coefficient, kd [T-1], for the second sorption sites.

SMax1

Parameter in the blocking function for the first sorption sites.

AttachSolid1

First-order deposition (attachment) coefficient, ka [T-1], for the first sorption sites.

DetachSolid1

First-order entrainment (detachment) coefficient, kd [T-1], for the first sorption sites.

D_Soil

Diameter of the sand grains, dc [L].

D_Virus

Diameter of the particle, dp (e.g., virus, bacteria) (e.g., = 0.95 μm or 0.95e-6 m) [L].

SMax2

Parameter in the blocking function for the second sorption sites (smax for model (1)).

Stick. Eff2

Sticking efficiency, a [-], for the second sorption sites.

DetachSolid2

First-order entrainment (detachment) coefficient, kd [T-1], for the second sorption sites.

SMax1

Parameter in the blocking function for the first sorption sites.

Stick. Eff1

Sticking efficiency, a [-], for the first sorption sites.

DetachSolid1

First-order entrainment (detachment) coefficient, kd [T-1], for the first sorption sites.

cBnd1

Value of the concentration for the first time-independent boundary condition [ML-3]. Set equal to zero if no time-independent boundary condition is specified. The same for cBnd2 through cBnd4

cRoot

Value of the concentration for the fifth time-independent boundary condition [ML-3]. If water uptake is considered then cRoot is automatically used for the maximum concentration of water removed from the flow region by root water uptake. When zero is specified, then all solute is left behind in the soil and only a solute-free solution is being taken up. When the concentration is lower than cRoot, all solute is taken up. When the concentration is higher than cRoot, the excess solute stays behind. Set equal to zero if no fifth time-independent boundary condition and no solute uptake by roots is considered.

cWell

Value of the concentration for the sixth time-independent boundary condition [ML-3]. If internal sources are specified, then cWell is automatically used for the concentration of water injected into the flow region through internal sources. Set equal to zero if no sixth time-independent boundary condition and no internal sources are specified.

cBnd7

Concentration of the incoming fluid for a volatile type boundary condition at the soil surface [ML-3]. Set equal to zero if no volatile boundary condition is specified.

cAtm

Concentration above the stagnant boundary layer, gatm [ML-3], for a volatile type boundary condition. Set equal to zero if no volatile boundary condition is being specified.

d

Thickness of the stagnant boundary layer, d [L], for a volatile type boundary condition. Set equal to zero if no volatile boundary condition is being specified.

Bulk.d.

Bulk density, ρ [ML-3]

Dw

Molecular diffusion coefficient in free water, Dw [L2T-1]

Disper.L.

Longitudinal dispersivity, DL  [L]

Disper.T.

Transverse dispersivity, DT  [L]

CEC

Cation exchange capacity, CEC [meq/kg]

Calc.SA

Calcite surface area [m2/dm3]

Dol.SA

Dolomite surface area [m2/dm3]

DOC

Dissolved organic carbon [mmol/dm3]

K[Ca/Mg]

Gapon constant for exchange of calcium and magnesium

K[Ca/Na]

Gapon constant for exchange of calcium and sodium

K[Ca/K]

Gapon constant for exchange of calcium and potassium

No

Parameter

Notation

Description

1

Kd

Kd

Should be equal to 0. This parameter is usually reserved for the sorption parameter Kd, which is not used with colloid transport [L3/M].

2

Nu

h

Should be equal to 0 (commonly used for Langmuir h  [L3/M]).

3

Beta

b

Should be equal to 1 (commonly used for Freundlich exponent b).

4

Henry

KH

Should be equal to 0 (commonly used for the Henry's law constant KH, which is not used with colloid transport).

5

SinkL1

mcw

Should be equal to 0 (commonly used for colloid immobilization in the liquid phase mcw).

6

SinkS1

msw

Should be equal to 0 (commonly used for colloid immobilization in the solid phase msw).

7

Not used

Not used.

8

Not used

Not used.

9

RefImCol

yi

Parameter adjusting the sorption rate to the number of immobile colloids present.

10

AttImCol

kaic

Solute adsorption rate to immobile colloids [T-1].

11

DetImCol

kdic

Solute desorption rate from immobile colloids [T-1].

12

RefMobCol

ym

Parameter adjusting the sorption rate to the number of mobile colloids present.

13

AttMobCol

kamc

Solute adsorption rate to mobile colloids [T-1].

14

DetMobCol

kdmc

Solute desorption rate from mobile colloids [T-1].

No

Parameter

Notation

Description

1

Kd

Kd

The sorption distribution parameter Kd [L3/M].

2

Nu

h

The sorption (Langmuir) parameter h  [L3/M]).

3

Beta

b

The sorption (Freundlich exponent) parameter b.

4

Henry

KH

Henry's law constant KH.

5

SinkL1

mw

Degradation rate for contaminant dissolved in the liquid phase mw [T-1].

6

SinkS1

msw

Degradation rate for contaminant dissolved in the solid phase ms [T-1].

7

Not used

Not used.

8

Not used

Not used.

9

Not used

Not used.

10

Not used

Not used.

11

Not used

Not used.

12

Not used

Not used.

13

Not used

Not used.

14

Alpha

w

First-order rate coefficient for one-site or two-site nonequilibrium adsorption [T-1].

No

Parameter

Notation

Description

1

Kdm

Kd

Adsorption isotherm (distribution) coefficient for the matrix [L3/M].

2

Nu

h

Adsorption isotherm (Langmuir) coefficient (used for both matrix and fracture domains)  [L3/M].

3

Beta

b

Adsorption isotherm (Freundlich) exponent [-] (used for both matrix and fracture domains).

4

AlphaM

w

First-order rate coefficient for nonequilibrium adsorption in the matrix [T-1].

5

SinkL1

mw

First-order degradation rate constant for dissolved phase  [T-1] (used for both matrix and fracture domains).

6

SinkS1

ms

First-order degradation rate constant for solid phase  [T-1] (used for both matrix and fracture domains).

7

Disp.F.

lL

Longitudinal dispersivity in the fracture domain [L]

8

SinkL1'

mw'

First-order degradation rate constant (representing the chain reaction) for dissolved phase [T-1] (used for both matrix and fracture domains).

9

SinkS1'

ms'

First-order degradation rate constant (representing the chain reaction) for solid phase [T-1] (used for both matrix and fracture domains).

10

Frac.F.

f

Dimensionless fraction of adsorption sites classified as type-1 sites, i.e., sites with instantaneous sorption when the chemical nonequilibrium option is considered [-] in the fracture domain. Set this parameter equal to 1 when equilibrium transport is considered. Frac becomes the dimensionless fraction of adsorption sites in contact with mobile water when the physical nonequilibrium option is considered [-]. In that case Frac should be set equal to 1 when all sorption sites are in contact with mobile water.

11

SinkS0

gw

Zero-order (production) rate constant for dissolved phase [ML-3T-1].

12

SinkL0

gs

Zero-order (production) rate constant for solid phase [T-1].

13

KdF

Kd

Adsorption isotherm (distribution) coefficient for the fracture domain [L3/M].

14

AlphaF

w

First-order rate coefficient for nonequilibrium adsorption in the fracture domain [T-1].