Document Ex8n7aaQkyLmqvr74rGwRYEdg
2. Chiou, C.T., V.H. Freed, D.W.Schmedding, and R.L. Kohnert,1977. "Partition Coefficient and Bioaccumulation of Selected Organic Chemicals", Environ. Sci. Technol. 11(5), 475-478.
3. Farmer ,W.J., M.S. Yang, J. Letey.andW.F.Spencer, 1980. "Hexetehlorobenzene: Its Vapor Pressure and Vapor Pressure Diffusion in Soil", Soil Sci. Soc. Am. 44,676-680.
4. Goring, CAI.,and J.W. Hamaker, 1972. Organic Chemicals in the Soil Environment. Marcel Dekker, lnc.,N.Y.
5. Hamaker, J.W., 1975. "The Interpretation of Soil Leaching Experiments" in Environmental Dynamics of Pesticides, R. HaqueandV. Freed, (eds.). Plenum.
6. Hemwall, J.B., 1972, as reported on pp 373-374 of Organic Chemicals in the Soil Environment, CAI. Goring and J. W.Hamaker,(eds.)
7. Karickhoff.S.W., D.S. Brown,and T.A. Scott, 1979. "Sorption of Hydrophobic Pollutants on Natural Sediments", 13,241-248.
8. Shen, T.T., 1981. "Estimating hazardous air emissions from disposal sites". Pollution Engineering pp 31-34, August 1981.
9. Thibodeaux, L.J., 1979. Chemodynamics. Wiley. N.Y.
10. Veith.G.D., D.L.DeFoe.and B.V.Bergstedt, 1979, J. Fish. Res. Board Can., 36,1040-1048.
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DO 074446 CONFIDFNTTAl.
proper value for q, in this case 2.326. The solution for distance travelled by vapor diffusion is then:
xv=q/4Dt = w/t
(36)
where w=q/4D
(36a)
6). The time in days is calculated to reach sn arbitrary 3-meter deep groundwater with c/Cg of
0.000001 to 0.8 by adding equations (35) end (36). The combined movement with water and as
vapor is approximated as:
letting
solving for z gives: or
xx = w/t + uu-t = 3 m zl-1 wz^ + w- z - xx = 0 z^-w+Vlw^ - (4 xx uu)]}/2 uu t = z2/(60- 60- 24)
(37a) (37b) (37) (38a) (38)
CONCLUSIONS
1) . This PC computer program provides an easy way to estimate the potential of a chemical for migration in soil or groundwater. 2) . It requires 8S data only
a. aqueous solubility ( and if cpd is a solid, then preferably a MP) b. vapor pressure c. molecular weight 3) . It derives several simple parameters such as KOW, KOC.Rf, and a soil vapor diffusion coefficient, Ds.
4) . Migration patterns and fluxes for several simple situations are calculated. 5) . Because of the widely varied migration properties of different chemicals, it provides for consideration of both aqueous migration and vapor diffusion. This should be done in general.
REFERENCES 1. Banerjee.S., S.H.Yalkowski.andS.C.Valvani, 1980. Water Solubility and Octanol/Water Partition Coefficients of Organics. Limitations of the Solubility-Partition Coefficient Correlation". Environ. Sci. and Technol. 14,1227-1229.
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-iry ft'ps n ;-7! r\V:' r;
a ..
,V. :.
AA >\i Li
Figure 6. Time for Compound to Reach Groundwater Scenario.
The assumptions and derivation are as follows: 1). The compound is initially in the surface zone. 2) . Intermittent rainfall totalling 88 cm/y drives the compound downward according to the Rf value and 0.
3) . Back movement of 48 cm/y of water with evaporation moves the compound back upward according to Rf and 0. ( Actually desorption is slower snd less effective than adsorption and material left adsorbed for some time is more firmly bound).
4). We simplify the outcome of 2) and 3) as simply the net downward movement of water x Rf/0.
Darcy velocity
v = 40 cm/y = 1.27E-6 cm/s
(35a)
Compound velocity
uu = Rf (1.27E-6)/0
(35b)
Compound travel by water
xw=uu t
(35)
5) . Vapor phase diffusion is simply included es an additive value. (This is certainly not strictly so, but gives some measure of overall effect). We need the value of Xy/v'"4Dt such that
I -erf(xy//4Dt) =C/C0
(36a)
We then define a value
q = xv//4Dt
(36b)
For any given value of C/C0, e.g., 0.001, we can obtain from a table of the error function, erf, the
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Figure 5. Stead/ State Flux Through a Soil Layer.
This solution is based on Fick's law and follows a similar treatment by Farmer et al (19xx) for
hexachlorobenzene loss through a landfill cover of clay.
J = - Dac/h
(33)
but
D=Ds
(33a)
end ac= 0 - c0 = (WS/KWA) bq ; let CX)V = Ac
(33b)
but h = 1 m = 100 cm Converting from seconds to days we get:
d=864 Ds-C0Y pg/tcm^d) (34)
(33c)
Time to Reach 3-meter Deep Groundwater
This example deals with the movement of a compound initially present in surface layers of the soil and subject to downward movement along with infiltrating water from rain and also by superimposed vapor diffusion.
n :
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Figure 4. Total Depletion from a Plane Source by Vapor Migration from Initial Exposure to Given Time, t.
C=C(y,t)
ilHiiiiiiSiijfji
c = cI.i*1S"l.*11*.1I**S*'1\%*1.Vft*.*isl*.'l*t*ls*.,,fJW_-.
^L* ijili
1
*7.***;*
vw'sW'1
It Is calculated by:
t = Cj,/-'! Dt/ir
This is derived from Pick's law: J = - D ac/ay coupled with the solution of the diffusion equation: c/c0= I - erf(y/V4 Dt)
where
erf(q)=2/Vn J^expt-n2) dn (26a)
(24) (25)
(26)
with
q=y//4Dt
then d(c/cQ)/dq = (-2/VTr)exp(-q'^)
(27)
(26b)
or ac/ay=(-1/-/DtTr)exp(-y2/4Dt)-c0
(28)
Therefore an instantaneous flux value is: J=(-/D/TTt)exp(-y^/4Dt)c0 (2g)
The average value of flux over time 8t y=0 is then Jav=J0lJdt/t=(c0/t)J0VD/irtdt
(30)
or Jav = co^D/rrt
(31)
therefore
Javt = CpvMDt/n
(32)
Stead/ State Flux Through..! Meter of Soil For the situation where a zone of soil with a concentration of the compound at a concentration, c=Cq
is covered with 1 meter of soil, such bs, for example, clay, the program calculates an estimated stead/ state flux passing through the soil. This could be illustrated as shown in Figure 5.
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u lOa dn us2
the solution of equation (10a) is: c/cq= 1 - erf(q)
(23)
where and
q = x/ / 4 Dst erf(q) = (2//ir)/^ exp(-y2)dy
(23a) (23b)
Using the estimated value of Ds from equation (22), we can solve for x at any time t, or for t for
any penetration distance, x. The program calculates values for this simple example one-dimensional migration from 0 large planar source, giving solutions of x for c/Cq of
0.000001 to 0.8, at times of 1,7,30, and 365 days. If these data are plotted they appear as follows:
Figure 3. Vapor Diffusion Migration Distances.
02
4
DISTANCE, meters
Vapor-Migration, Zero-Time to.Given Time
This example represents material depleted from a plane layer, with a concentration c=Cg , into an
adjacent region from an initial exposure time to any given time, t, as indicated in Figuyre 4. The derivation is similar to one given by Thibodeaux (19xx) for upwelling of nutrients from a lake bottom.
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To estimate the diffusion coefficient of a compound in air, Shen gives an equation 3; D* = D(M/M'),/2
tic;
This leads here to Dcpd= Dajr/MWajr/vrMWCpCj =0.1849 (/28.8)/('/MW)
or: D = D " 1//MW a cpd
D=. Soil Diffusion Coefficient
(19) (19a)
(20)
The program calculates a soil vapor diffusion coefficient, Ds, following the general lines of the
treatment of Goring and Hamaker (1972). It is simply the air diffusion coefficient reduced by the fraction of compound in the soil air space and by a tortuosity factor (Hemwall in G&H).
Ds - 0.66 Fa- Da
..
(21)
( 0.66 ) 0 Da Dg = --------------------------------------------------------------
(22)
0a+BD-KOC-OC*0w+_0w- KWA
A Vapor Diffusion Application
The diffusion equation (10), if restricted to one dimension, for a situation such as indicated below,
becomes: (dc/dt)x =Ds(d'i:c/dx^)
(10a)
Figure 2. One-Dimensional Vapor Diffusion.
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r\ n r-T ;wJ* tij A "LaH^-J *t*.<----3 -Ji ` V\y'Au:i
r% V**"
*a,. t. /a' 73;^.i &3 ' "c * V
-(i -(.'T& L'^/ c-`
VAPOR DIFFUSION
The equation governing movement as vapor in the air pososity of the soil is the general diffusion
equation:
ac/at = D-a^c/ax^ + a^c/ay^ + a^c/az^
^ wj
An appropriate o value and 6 typical applications ere generated Dy the program. Movement can oe ) UUU to 1 uuuu times taster then the dittusion ot a lew cm/month observed m liquids.
Fraction in the 3 Soil Phases
Following the general treatment in Goring & Hamaker (1972), the amount of compound/ml of soil for each phase can be expressed as:
in water, xw=
(,,a)
in air, Xg = cg0g = (Cy^/KWAj'Og
(11b)
in solids, xs = c$- 0S* dg = KOOOC-c^dgflg)^- KOC- 0C- BD
(lie)
TOTAL * xw + xa + x$ * Cyy-TOT (11)
where
TOT -0W + 0Q/KWA + KOC OC* BD
The fraction of compound in each phase is then given by:
in water, Fw =xw/T0TAL
(12)
(lid)
in air, Fa = xa/T0TAL
(13)
in solids, Fs =x$/TOTAL
(14)
Cp-Soil. maximum soil concentration without a 2nd liquid phase.
C0-Soil= WS TOT DlF-AtR. an. air diffusion coefficient This is estimated simply as Da * 1 / -/MW; the derivation is as follows:
(15)
An equation for estimating the diffusion of one gas in another is given by T. T, Shen (Shen, 1981, eqn 2);
D*0.001T175 /( 1/Mj + !/M2) /{P[(iv,)1/3 + (zv2)1/3)2}
(16)
For Bir in air using V, =V2=20.1 (Shen) ,M|=M2-28.8,endT=20 *C gives:
Dfljr= 0.1849 cm2/sec
(17)
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ASSUMED TYPICAL SOIL PROPERTIES
The following typical soil properties are used by the program:
CLAY.
LOAM
SAND
Porosity, 0
0.40
0.50
0.30
Air fraction, 0a
0.20
0.25
0.15
Water fraction, 0W
0.20
Bulk density, BD,g/ml
1.50
Permeability, k,cm/s
1.0e-7
% Organic carbon, OC - 100 0.10 1.45
0.25
1.25 1.0e-4 0.10
0.15
1.75 1.0e-3 0.01
GRAVEL 0.50 0.25
0.25 1.25 1.0
AQUEOUS MIGRATION The program estimates the movement of a compound through the soil by water convection as modified by adsorption. It does this by combining a water velocity from Darcy's law and an estimated Rf for the compound vs the water.
Rf-Soil Column This is estimated by use of an equation given by J. W. Hamaker (1975) (his equation #4):
1 / Rf = 1 +
* OC/100)ds( 1 /0^/'5-1)
(6)
where ds=soil particle density=2.50 g/ml= BD/0. This equation
was derived by Hamaker for soil TLC. He gave 8 slightly rearranged equation expressed ss an "R" value giving the compound movement in the soil relative to the water entry rate into the soil for soil columns. The latter showed excellent agreement with experimental values for flow rates of <0.1 in/hr. The single form used here seems appropriate for both situations.
The distance travelled by the center of mass of the concentration for several times (1,7.30, and
365 days), three typical hydrsulic gradients (H0)(0.001,0.01 ,and 0.10), for 4 soil types
(clay, loam, sand, gravel) are estimated for a no dispersion condition. The equations used are:
v= ~k HG
Darcy velocity (7)
u= Rf v/ 0 Compound velocity
(8)
XAQ= u * (t sec)/100 cm/m Compound travel
(9)
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FIGURE 1
MIGRT DATA FLOW SHEET
PROPERTIES OF THE CHEMICAL
MODEL SOIL PROPERTIES
SITE PROPERTIES
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V
It the chemical is a solid with unknown MP, the Chiou relation (Chiou, 1977) is used:
log KOW = 5.00-0.67 log S (2)
or In KOW = 11.513-0.67 x In S
(2a)
An option is provided in the input prompts to allow the bypass of the correlation equations and directly enter a known KOW.
KOCf the soil adsorption coefficient
This is obtained from KOW by the Karickhoff/Brown relation, their eqn 5 (Karickhoff/Brown,
1979):
KOC = 0.63 x KOW
(3)
BCF. Bioconcentration Factor
While not directly involved in the partitions that are used in groundwater calculations, this
partition coefficient is readily available from KOW, and is useful in environmental evaluations.
The equation is from Yeith/Oefoe, 1979.
log BCF = 0.85 log KOW - 0.70 (A)
or In BCF= 0.85 In KOW - 1.612
(4a)
KWA. water to air partition coefficient
This is the reciprocal of the dimensionless Henry's Law constant, i.e.:
KWA = Cy/Cg
(5a) where c^, Is the
saturation concentration in water at, say 20* C,
or:
Cyy = (WS mg/L)/(( 1000 mg/g)(MW))
(5b)
and ca is the saturation concentration in air at, say 20 *C,
or: ca = (VP,mmHg/760)/((0.082 L atm mol~1 *K~1)( 293 *)) or: KWA= 18.26 WS/(VP x MW) (5)
(5c)
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t
MIGRT, a Computer Program to Estimate Migration Properties of Chemicals in Soil and Groundwater FABlanchard
For meeting regulatory requirements 8nd for doing an adequate job of product stewardship, including both proper use as well as proper disposal, it is vital to be able to make reasonable estimates of the migration potential of chemicals.
This report describes a simple PC computer program which requires as input only the physical chemical properties of molecular weight (MW), water solubility (WS), vapor pressure (VP) and melting point (MP) to make such estimates. Correlation equations provide the partition coefficients KOW, KOC, snd KWA. An air diffusion coefficient Is estimated from MW. When these are combined with typical assumed soil hydrogeological properties we can obtain estimates of the fractional distribution of a chemical among the air, water, end solids fractions of the soil. These also lead to an estimated soil column Rf ( or its reciprocal, a retardation coefficient), and a soil vapor diffusion coefficient. Several different scenarios sre then used to indicate the potential for migration by vapor diffusion through the soil and by movement along with water movement in the soil. These steps are illustrated as a flow sheet in Figure 1.
To operate the program itself, after placing the diskette into an operating PC, simply type in : BASICA A:MIGRT.BA$, (assuming the diskette is in the A drive), Then respond to prompts. An example printout is given 83 Appendix A. The program itself is given as Appendix B.
PARTITION COEFFICIENTS KOW. the octanol/water partition coefficient. If a MP is provided or if the compound is a liquid at 25* C, the program uses the Banerjee/Yalkowsky Eqn 6 (Banerjee/Yalkowsky, 1980):
where
log K0W=6.5 - 0.89 log S - 0.015 x MP S ,inpmol/L = 1000WS/MW (la)
(D
The calculation is actually done with natural logs: In K0W= 14.97 - 0.89 In S - 0.035 x MP
(lb)
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