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Vol. 8  No. 5

DISTRIBUTION COEFFICIENT
&
SOLINST INTERFACE METER

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Distribution Coefficient

As mentioned in the previous newsletter, the distribution coefficient, an important parameter for the calculation of the retardation coefficient, will be discussed in the current newsletter.  The distribution coefficient describes how a solute sorbs to the solid matrix in which it is located.  A thorough description of the distribution coefficient, in addition to how it is determined, and what properties it tends to have, is given below, in addition to some example values, and a calculator.

What is a distribution coefficient?

How is a distribution coefficient calculated?

Do distribution coefficients remain the same for all solutes?

What are typical values of distribution coefficients?

Distribution Coefficient Calculator for Organic Micropollutants

What is a distribution coefficient?

The distribution coefficient (Kd), relates the adsorbed concentration of a solute, to the concentration in water.  As an equation, it is given as the mass of solute on the solid phase per unit mass of solid phase divided by the concentration of solute in solution:

How is a distribution coefficient calculated?

A distribution coefficient is calculated from a sorption isotherm, which is a plot that describes the amount of a species sorbed as a function of its concentration in solution, measured at a constant temperature.  The distribution coefficient is related to the slope of the line created by this isotherm.  There are several different sorption isotherms that can be used to determine the distribution coefficient.  The three most commonly used include:

• Linear Distribution Coefficient (K_d)

m_i(ads)= K_dm_i(soln)

m_i(ads)= concentration of the species of interest adsorbed on the solid phase (commonly moles/kg of solid)

m_i(soln)= concentration of the species in solution (commonly moles/l)

K_d is therefore commonly in units of l/kg

This is the most commonly used method of using a distribution coefficient in contaminant transport models.  This is because it is linear and involves no variables other than the concentration of the species of interest it is computationally simple.

• Freundlich Isotherm (K_f)

m_i(ads)=K_fmⁿ_i(soln)

n = is a constant, usually less than 1

m_i(ads)= concentration of the species of interest adsorbed on the solid phase (commonly moles/kg of solid)

m_i(soln)= concentration of the species in solution (commonly moles/l)

K_f is therefore commonly in units of l/kg

The exponent in this equation causes the isotherm to curve, becoming less steep at higher concentrations, indicating that the high concentrations are less retarded compared to lower concentrations. This can be justified theoretically in several ways, including:

1. adsorbed species forming a non-ideal solid solution on the solid surface

2. heterogeneity in the sites to which the solute binds on the surface

 

Figure 1: A Comparison of a Linear and a Freundlich Isotherm (from Appelo and Postma, 1996)

 

• Langmuir Isotherm (K_L)

m_i(ads)=m_i(ads,max)(K_Lm_i(soln)/(1+K_Lm_i(soln)))

m_i(ads)= concentration of the species of interest adsorbed on the solid phase (commonly moles/kg of solid)

m_i(ads,max)= total concentration of sites for adsoption

m_i(soln)= concentration of the species in solution (commonly moles/l)

K_L is therefore commonly in units of l/kg

This isotherm was originally derived to describe the adsorption of a gas monolayer on a solid surface, and above is the form derived from the original for aqueous systems.  At low concentrations, the term K_Lm_i(soln) becomes small compared to 1 that the isotherm reduces to a linear form.

Do distribution coefficients remain the same for all solutes?

One of the most important properties of a distribution coefficient is that it should be measured experimentally for each system of interest, as it cannot be easily transferred from one system to another.  Each distribution coefficient is representative of that particular solute, in that particular solid, at that temperature, and cannot be easily converted to properly describe a system with a difference in any of the properties.

What are typical values of distribution coefficients?

Distribution coefficients for reactive solutes tend to range from values near zero to 1 l/kg or greater.  As these values are quite variable, it is difficult to give one general value to use as a default.  The distribution coefficient is empirical (derived from experiment), and a parameter used for one field site cannot typically be used for another, even for materials from the same site.

For organic micropollutants (typically hydrocarbons and chlorinated hydrocarbons), the distribution coefficient can be estimated by multiplying a known K_oc value, which is calculated in the lab as the organic carbon-water distribution coefficient, by the fraction of organic carbon in the soil. The following is a table of  K_oc values for some hydrocarbons (From Appelo and Postma, 1996), and a calculator for determining the K_d value based upon the fraction of organic carbon in the soil (f_oc).

Compound	log Koc
3-methyl choanthrene	6.09
Dibenz[a,h]anthracene	6.22
7,12-dimethylbenz[a]anthracene	5.35
Tetracene	5.81
9-methylantracene	4.71
Pyrene	4.83
Penanthrene	4.08
Anthracene	4.20
Naphthalene	2.94
Benzene	1.78
1,2-dichloroethane	1.51
1,1,2,2-tetrachloroethane	1.90
1,1,1-tricholorethane	2.25
Tetrachloroethylene	2.56
Lindane	3.30
Atrazine	2.33
Propazine	2.56
Simazine	2.13
Trietazine	2.74
Ipazine	3.22
Cyanazine	2.26
Carbaryl	2.36
Carboturan	1.46
Chlorpropham	2.77
Malathion	3.25
Parathion	3.68
Methylparathion	3.71
Chlorpyrifos	4.13
Diuron	2.60
Fenuron	1.43
Linuron	2.91
Monolinuron	2.30
Monuron	2.00
Flometuron	2.24

 

Distribution Coefficient Calculator for Organic Micropollutants

Kd can be estimated by the following equation:

K_d = K_oc x f_oc 
where: 
f_{oc = fraction of organic carbon in soil (as %)}
K_{oc = octonol water partitioning coefficient}

 

log K_oc:   

f_oc: 

K_d:   

The following is an example calculation for the distribution coefficient (from Appelo and Postma, 1996).

Given: log Koc = 3.30 (Lindane)

foc = 0.3%

Calculation:

Kd = 10^3.3 x 0.3/100

Kd = 1995.26 x 0.003

Kd = 5.98

As mentioned previously, the distribution coefficient is an important part of the retardation coefficient calculation. Retardation coefficients are often used to determine the location of a plume, based upon groundwater velocity.  There are also field methods of determining the location of a plume, such as the use of the Solinst Interface meter.

References

Appelo, C.A.J., and Postma, D. (1996). Geochemistry, Groundwater and Pollution. Published by A.A. Balkema, Brookfield, VT.

Drever, J.I. (2002). The Geochemistry of Natural Waters; Third Edition. Published by Prentice-Hall, Inc. Englewood Cliffs, NJ.

Fetter, C.W. (1994). Applied Hydrogeology; Third Edition.  Published by Prentice-Hall, Inc. , Englewood Cliffs, NJ.

Langmuir, D. (1997). Aqueous Environmental Geochemistry. Published by Prentice-Hall, Inc., Englewood Cliffs, NJ.

Zhu, C. and Anderson, G. (2002). Environmental Applications of Geochemical Modeling. Published by Cambridge University Press, New York, NY.

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Solinst Interface Meter

The Solinst Oil/Water Interface Meters give accurate measurements of product level and the thickness in wells and tanks. Determination of both floating non-aqueous liquids (LNAPL) and sinking non-aqueous liquids (DNAPL) is quick and easy. The Model 122 Interface Meter has been approved by the Canadian Standards Association (CSA) for use in explosive environments. 

How does the Solinst Interface Meter work?

To detect liquids, Solinst Interface Meters use an infra-red beam and detector. When the probe enters a liquid the beam is refracted away from the detector which activates an audible tone and light. If the liquid is a non-conductive oil/product the signals are steady. If the liquid is water, the conductivity of the water completes a conductive circuit. This overrides the intra-red circuit and the tone and light are intermittent.

Both sensors use exactly the same zero point giving accuracy as good as 1/100' or 1mm. The circuits are powered by 2 standard 9V batteries (one for the Mini) which are housed in easy access drawers on the faceplate of the reel.

What are the Main Features of the Solinst Interface Meter?

• Designed for rugged field use

• Tape uses stranded stainless steel conductors for strength

• Rugged, free-standing reel with carrying handle

• 5/8" (16mm) diameter 122/P1 probe

• Easy access batteries; minimum 120 hours for life

• Sensor accuracy to 1/100' or 1 mm

• Clear signals

• Automatic shut-off after 10 minutes

• Inexpensive, simple repairs

• Lengths from 50-1500' (15-450 m)

• Carrying bag and Tape Guide included

For more info click here:  Solinst Interface Meter
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