Guidelines on remediation of contaminated sites
Appendix
5.9
Example of calculation of soil-water concentration based on soil concentration
The following provides an example of the use of the principle of fugacity to calculate the soil-water concentration of a contaminant on the basis of known soil contamination; i.e. a calculation of the soil-water phase transition.
The example given concerns benzene spill in clayey till. The values used in these calculations are the same values used in one of the examples of a risk assessment (Appendix 5.8 – calculation example 1).
1 Background
Calculations are carried out by means of the formulae given in Appendix 5.3 - section 3. The calculations are analogous to calculations in Appendix 5.4 - section 2, where calculations are carried out to determine contaminant contents in soil gas on the basis of know contaminant content in soil (the soil gas phase transition).
The following table shows values used in the calculation.
2 Calculations
The total volume of soil can be seen as the sum of the soil-phase volumes.
Equation 1
VL + VV + VJ = 1
| where: | VL | = | relative volumetric proportion of air in soil (in this case 0.10), |
| VV | = | relative volumetric proportion of water in soil (in this case 0.30), | |
| and | V | = | relative volumetric proportion of soil particles in soil (0.60). |
Table 1
Parameters used in calculations
Relative volumetric proportion of air, VL |
0.10* |
Relative volumetric proportion of water, VV |
0.30* |
Relative volumetric proportion of soil, VJ |
0.60* |
Soil temperature, T |
281 K = 8o C |
Soil particle density, d |
2.7 kg/l* |
Soil benzene concentration, CT |
1.0 mg/kg |
Soil density, r |
1.8 kg/l* |
Soil content of organic matter, foc |
0.001* |
Benzene partial pressure, p |
12,700 N/m2¤ |
Benzene molecular weight, m |
78.1 g/mol¤ |
Gas constant, R |
8,314 J/mol× K |
Benzene solubility, S |
1,760,000 mg/m3¤ |
Benzene octanol-water proportion, Kow |
102.1 l/kg¤ |
*: cf. Appendix 5.3 - Table 1
¤: cf. Appendix 5.5 - Table 1
The maximum benzene content in one cubic metre (1 m3) of soil distributed on the three phases of the soil can be calculated as follows:
In the air phase of soil (soil gas)
Equation 2
ML, max = VL · CL, max = 0.10 × 425,000 mg/m3 = 42,500 mg/m3
| where: | ML,max | = | maximum benzene content in soil gas (mg/m3 soil volume) |
| CL,max | = | saturated vapour concentration of contaminant (mg/m3 soil gas). |
By means of the law of ideal gases, CL,max is calculated on the basis of the
partial pressure of benzene:
Equation 3
| where: | p | = | benzene partial pressure (12,700 N/m2) |
| m | = | benzene molecular weight (78.1 g/mol) | |
| R | = | gas constant (8.314 J/mol · K) | |
| T | = | temperature (281 K = 8o C). |
In the water phase of soil (soil water)
Equation 4
MV,max = VV · S = 0.30 × 1,760,000 mg/m3 = 528,000 mg/m3
where:
MV,max = maximum benzene content in soil water (mg/m3 soil volume)
S = benzene solubility in water (1,760,000 mg/m3 soil water).
In the partial phase of soil
Equation 5
| MJ,max | = | VJ · d · Koc · foc · S (mg/m3) |
| = | 0.60 × 2.7 kg/l × 101.344 l/kg × 0.001 × 1,760,000 mg/m3 | |
| = | 63,000 mg/m3 |
| where: | MJ,max | = | maximum amount of benzene adsorbed to the organic fraction of soil particles (mg/m3 soil volume) |
| d | = | soil particle density (2.7 kg/l) | |
| Koc | = | benzene distribution between organic carbon and water (1/kg) | |
| foc | soil content of organic carbon (0.001). |
The distribution of benzene between organic carbon and water (Koc) can be
estimated on the basis of the octanol/water proportion Kow, by means of
Abdul’s formula /1/:
Equation 6
log Koc = 1.04 × log Kow – 0.84 = 1.04 × 2.1 – 0.84 = 1.344
The maximum soil capacity for benzene (just before NAPL occurs), will then be:
Equation 7
ML,max + MV,max + MJ,max
= 42,500 mg/m3 + 528,000 mg/m3 + 63,000 mg/m3
= 633,500 mg/m3
Based on the assumption (cf. the concept of fugacity in Appendix 5.3) that the relative distribution of the three phases in soil is independent of on total concentration in soil, the distribution of benzene on the three soil phases can be calculated.
The following applies to the water phase of soil:
Equation 8
where fV = relative benzene proportion in soil water in relation to total soil content (calculated per m3 soil).
ML, MV, MJ = actual amount of benzene in each of the three phases (mg/m3 soil).
With a total concentration in soil CT (in this example 1.0 mg benzene/kg soil volume) the amount of benzene in soil water MV can then be determined as:
Equation 9
MV = fV · CT · r = 0.833 × 1.0 mg/kg × 1.8 kg/l
= 1.5 mg/l soil volume
where:
CT = benzene concentration in soil (1 mg/kg)
r = soil density (1.8 kg/l)
The benzene concentration in the soil water, CV, is then calculated on the basis of the benzene concentration in soil, CT.
References
| /1/ | Kemiske stoffers opførsel i soil og grundwater
(‘Chemical Substance Behaviour in Soil and Groundwater’) Projekt om soil og
grundwater (‘Project on Soil and Groundwater’), No. 20. The Environmental
Protection Agency, 1996. [Tilbage] |