APPI.IKD AND ENVIKONMI-.NTAI. MH KOHIOIIK.V, May 1W2. p. INN- IMh
IX)W.2240/V2;imfiU«M)! Y. OUYANGt
Department of Soil and Environmental Sciences; University of California, Riverside. California V252I
Received V September IWl/Accepletl 21) February 1W2
As • mull of the recently proposed mandatory groundwater disinfection requirements to Inactivate viruses
in potable water supplies, there has been Increasing interest in virus fate and transport in the subsurface.
Several models have been developed to predict the fate of viruses In groundwater, but few include transport in
the unsaturated lone and all require a constant virus inactlvation rate. These are serious limitations in the
models, as It has been well documented that considerable virus removal occurs in the unsaturaled zone and thai
the inactivatkra rate of viruses Is dependent on environmental conditions. The purpose of this research was to
develop a predictive model of virus fate and transport in unsaturaled soils thai allows the virus inactlvation rale
to vary on the basis of changes In soil temperature. The model was developed on the basis of the law of mass
conservation of a contaminant in porous media and couples the Hows of water, viruses, and heal through the
soil. Model predictions were compared with measured data of virus transport in laboratory column studies
and, with the exception of one point, were within the 95% confidence limits of the measured concentrations.
The model should be a useful tool for anyone wishing to estimate the number of viruses entering groundwater
after traveling through the soil from a contamination source. In addition, model simulations were performed
to Identify parameters that have a large effect on the results. This Information can be used to help design
experiments so that important variables are measured accurately. t
The significance of viruses as agents of groundwatcrbornc
disease in the United Stales has been well documented (3,4).
The increasing interest in preventing groundwater contami-
nation by viruses and other disease-causing microorganisms
has led to new U.S. Environmental Protection Agency
regulations regarding groundwaicr disinfection (21). the de-
velopment of wellhead protection zones, and stricter stan-
dards for the microbiological quality of municipal sludge (20)
and treated effluent (2) that arc applied to land. For many of
the new regulations, a predictive model of virus (or bacterial)
transport would be helpful in the implementation process.
For example, such a model could be used to determine
where septic tanks should be placed or where land applica-
tion of sludge or effluent should be practiced relative to
drinking water wells to minimize negative impacts on the
groundwater quality. Another application of microbial trans-
port models is related to the groundwater disinfection rule
(21). Water utilities wishing to avoid groundwater disinfec-
tion may use a pathogen transport model to demonstrate that
adequate removal of viruses in the source water occurs
during transport to the wellhead.
Several models of microbial transport have been devel-
oped during the past 15 to 20 years (6. 7, 11. 12.17, 18. 23.
27). The models range from the very simple, requiring few
input parameters, to the very complex, requiring numerous
input parameter*. For many of the more complex models (7.
11. 23), the data required for input arc noi available except
for very limited environmental conditions. They may be
useful for research purposes but would be impractical for
widespread use. The potential applications of these models
also range considerably, from being useful only for screening
purposed on a regional scale (27) to predicting virus behavior
at one specific location (6,13, 18). One limitation of almost
all of these models is that they have been developed to
' Corresponding author.
t Present iddrcss: Soil Science Department, University of Flor-
ida. Gainesville. FL.
describe virus transport in saturated soils (i.e., groundwa-
ter). However, it has been demonstrated many times thai the
potential for virus removal is greater in the unsaturated zone
than in the groundwater (°, 10, 14). If the viruses arc
transported through the unsalurated zone before entering the
groundwater, then neglecting the unsuturated /one and
assuming that the viruses immediately enter the saturated
zone in a model of virus transport could lead to inaccurately
high predictions of virus concentrations at the site of inter-
est. This omission would be especially significant in areas
with thick unsaturated zones, such as those in many western
states. The one transport model (IK) that h;is reportedly been
developed for predicting virus transport in variably saturated
media is not specific for viruses but can be used for any
contaminant. In addition, it has not been tested with data of
virus transport in unsaturated soil.
Another, more important limitation of published models of
virus transport is that none of them has been validated by
using actual data of virus transport in unsaturated soils.
Most models arc developed on the basis of theory and are
fitted to data obtained from one or two experiments. Rarely
are they tested by applying the model to data collected under
a variety of conditions and by then determining how well the
model predicts what has been observed in the laboratory or
field without any fitting or calibration of the model.
The purpose of this research was to develop a model that
can be used to predict virus movement from a contamination
source through unsaturated soil to the groundwater. The
model was tested by comparing the model predictions with
the results of laboratory studies. Several model simulations
were then performed to determine the effects of different
input parameters on model predictions.
MATERIALS AND METHODS
Model development. The computer model, VIRTUS (virus
transport in unsaturated soils), is a one-dimensional numer-
ical finite difference code written in FORTRAN program-
ming language. It simultaneously solves equations dcscrib-
IMN
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1MO
YATES AND OUYANCJ
Am.. ENVIRON. Mit KOHIOI..
ing the flow of water, viruses, unit heal through unsaturatcil
soil under different climatic conditions. The equation used to
calculate the transport of water through the soil is
& (TV! (e -
- »>K'l (l)
where / is time (in hours), p» is the density of water (in grams
per cubic centimeter), 6 is the volumetric soil water content
(in cubic centimeters per cubic centimeter), iCJ(T) is the
density of water vapor at saturation al T (in grams per cubic
centimeter), T is temperature (°C). h is the relative humidity
at (he atmosphere-soil interface (dimensionless), r is the soil
porosity (in cubic centimeters of soil voids per cubic centi-
meter of soil), V, is the velocity of water in the liquid phase
(in centimeters per hour), and Vy is the velocity of water in
the vapor phase (in centimeters per hour). Heat transport
through the soil is calculated by using the equation
.1
ill
-V-
/« -t-flH,, -Mr- »)//sv|
where <•„,,„, is the specific heat of the solid (in calories per
gram per degree Celsius) (1 cal = 4.184J), |>MllK, is the density
of the solid (in grams per cubic centimeter). CM, is the
specific heat of (he air (in calories per gram per degree
Celsius). |>.,,, is the density of the air (in grams per cubic
rentimeler). CM is the specific heat of the water (in calories
l/cr gram per degree Celsius), //,„ is the transfer of heat by
conduction through the soil particles (in calories per square
centimeter per hour), //,, is the transfer of heal by conduc-
tion and convection in the liquid-phase water (in calories per
square centimeter per hour), and //„ is the transfer of heal
by conduction in the vapor-phase water and by transport in
the form of latent heat (in calories per square centimeter per
hour). The equation governing the transport of viruses
through the soil is given by:
ill
HC',)
/> / i>Ci\
- 0/>— - J -
in. \ i>z J
- e/Ti (3)
where (>,, is the bulk density of the soil (in grams per cubic
centimeter), C\ is the concentration of viruses adsorbed to
the soil (in PFUs per gram of solid), C, is the concentration
of viruses suspended in the liquid phase (in PFUs per
millililer), 1) is the hydrodynamic dispersion coefficient (in
square centimeters per hour). M., is the inactivation rale of
viruses in the liquid phase (per hour). m is the inactiyalion
rale of adsorbed viruses (per hour)./is the filtration coeffi-
cient (per centimeter), and ; is the position in space (in
centimeters). The derivations of these equations arc given by
Ouyung (13) and Yalcs ct al. (29).
The processes used in the model to describe virus fate and
transport include advection (transport by the bulk movement
of water), dispersion (spreading out of the viruses as they
move around soil particles), adsorption, inactivation. and
filtration. A complete discussion of these factors and their
effects on microbiul transport has been published recently
(2H). Some of the specific features of the model will now be
described.
In the model, adveciion and dispersion of the virus parti-
cles are allowed to vary as the viruses are transported
through the soil profile. In other words, (he rate at which
viruses are transported through the soil varies on the basis of
the velocity of the water, which depends on the flow of heat
through the system, among other factors. Another attribute
of VIRTUS is that the user may input different virus inacti-
vation rates for viruses that are adsorbed to the soil particles
as compared with freely suspended viruses, if that informa-
tion is known.
One important feature of the model is that the inactivation
rate does not have to remain constant throughout the simu-
lation. Because the model simulates the flow of heat through
the soil, it allows one to compute a new value for any
heat-dependent variable as the temperature changes in the
soil profile. It has been well documented that virus inactiva-
tion rates arc temperature dependent (8, 16, 24). An equation
describing the relationship between virus inactivation rates
and subsurface temperatures has been developed previously
(25) and is
u = -0.181 + (0.0214 x 7)
(4)
where |i is the inactivation rate of the viruses (in log,,, per
day) and 7 is the temperature (°C). Thus, whenever the
temperature of the soil changes, VIRTUS calculates a new
virus inactivation rate on the basis of this equation. The user
may specify the virus inactivalion rate to he a constant or a
function of any of the variables in the program. Equation 4
was used in several of the examples that will be presented
herein.
Model testing. The model was tested for its ability to
predict virus movement measured in laboratory column
studies. Three data sets that contained sufficient information
about the soil properties for the model were obtained. In
examples 1 and 2, the data were obtained from virus trans-
port experiments using saturated soil columns conducted by
Grondin at the University of Arizona, Tucson (5). For
example 3, the data were obtained from virus transport
experiments using unsaturatcd soil columns conducted by
Powelson at the University of Arizona, Tucson, and re-
ported by Powelson ct al. (14). The data used as model input
for each example arc listed in Table 1.
In each case, the model was run by using input values
measured or reported by the respective investigator. Model
predictions were then compared with the virus concentra-
tions measured as a function of soil depth and lime in the
laboratory.
Model simulations. Several features of the model were
demonstrated by using data for two different soil types, a
loam (example 4) and a sand (example 5). Some of the input
data for these examples arc shown in Table 2. Soil data were
obtained from Ouyang (13) for the Indio loam and from Ungs
el al. (19) for the Rchovot sand. Virus data were obtained
from several sources (1, 6, 14, 26) reporting virus transport
characteristics in soils similar to those used in the model. In
all simulations, water was added to the soil columns at a rate
of 0.1 cm h"' for 6 h. The concentration of viruses in the
influent solution was 105 PFU ml"1.
In example 4. the effects of three different virus inactivu-
tion rales on model predictions were determined. For exam-
ple 4a, the virus inactivation rate varied as a function of the
soil temperature throughout the simulation. Virus inactiva-
lion rates were calculated by using equation 4. For examples
4b and 4c. the virus inactivation rales were calculated for
constant soil temperatures of 10 and 2S°C. respectively. In
these three examples, virus inaciivation was calculated only
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VOL. 58. W2
A MODI-L OF VIRUS TRANSPORT IN UNSATURATliD SOILS
1M1
TABLE 1. Data used for model testing*
Properly
Soil type
Soil hulk density (g cm ')
llydrodynamic dispersion (cnr h 'l
Soil water content (cm' cm ')
Average water velocity (cm h ')
Soil column length (cm)
Soil adsorption coefficient (A!., => CJC,\ (ml g of soil '.)
Virus type
Virus inactivation rate (login day ')
Filtration coefficient (cm )
Input virus concentration (PFU ml ')
Simulation lime
Cxjmplc 1
(inivelly sand
1.65 g
7X
0.26
48.3
1(1(1
-0.054
MS2 coliphage
0.082
0
6..1 x 10'
48 min
Input value
Example 2
Gravelly sand
1.65
5«
0.26
28.3
100
-0.07.1
MS2 coliphage
0.056
0
8.37 x 10'
48 min
lixample .1
Ld;iniy line sand
1.54
•J2.24
Variable with depth
1.54
100
0.27
MS2 coliphage
2.00
0
10'
4 days
" Krom (iromlin (Jl and P>rwelM>n cl *l. (14).
for the freely suspended viruses, while the inuctivutiun rule
(if viruses adsorbed to soil particles, u,,, was zero. In
example 4d, the inuctivution rate of adsorbed viruses wus
specified to be one-half of the rate for viruses suspended in
the water, u.,, which changed as a function of soil tempera-
ture (i.e., same as example 4a with a u,, of 0.5u,,).
Example 5 simulates the transport of viruses through a
sandy soil. In this example, the virus inactivation rate for
. freely suspended viruses changed as a function of tempera-
ture as described in equation 4 with a u., of 0.
RESULTS
Examples 1 and 2. Figure 1 shows the predicted virus
concentrations at several depths after 4K min of transport in
u saturated column of gravelly sand. The model predictions
were close to the measured virus concentrations and in all
cases fell within the 95% confidence limits of the measured
data. In the second example, the model predictions were
within the 95% confidence limits of the measured data at all
points except the UN)-cm depth (Fig. 2). Compared to the
measured virus concentrations, the model overpredictcd the
concentration of viruses that would be present in the column
outflow. Grondin (5) measured 0 PFU of viruses alter 4K
min. while the model predicted, on the basis of Crondin's
data, that the virus concentration would be 341 PFU ml '.
Example 3. Virus transport in an unsaturaled soil column
of loamy line sand, with measured values provided by
Powelson el ul. (14), is depicted in Fig. 3. The agreement
between model predictions and the observed dulu is very
good in this case. The model predicted that the virus
concentration in the column outflow after 4 days would he
3.54 login PFU ml"', while the measured concentration was
3.78 log,,, PFU ml '.
TABLE 2. Data used for model simulations
Inpul value"
riu|iviijr
Soil type
Soil hulk density (g cm ')
Hydrodynamic dispersion
Initial soil water content (cm1 cm ')
Residual soil water content (cm1 cm " ')
Initial soil temp (°C)
Saturated hydraulic conductivity (cm h ')
Soil column length (cm)
Soil adsorption coefficient (K,, - CVC'i) (ml g of soil' ')
Virus type
Virus inactivation rale (free) (|t,)
Example 4a
Example 4h
Example 4c
Example 4d
Virux inactivulion rale (adsorbed)
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If 12 YATHS AND OUYANG
AI'F'I.. I'NVIKCIN. MlCKOHIOI .
Depth (cm)
0
JO
40
«0
M
WO
120
1 2 3
Concentration (tog phi/ml)
FIG. 1. Comparison of mixJcl predictions with experimental dalu
of Grondin |.S) for a saturated, gravelly sand soil (example 1).
Ninety-live percent confidence limits were calculated from seven
replicates.
Depth (cm)
0
20
40
ao
SO
. 100
120
4 6
Concentration (log plu/ml)
FIG. 3. Comparison of model predictions with experimental dad
of Powclson el al. (14) for a loamy fine sand soil (example 3).
Ninety-five percent confidence limits were calculated from seven
replicates.
Example 4. Virus concentrations in the UX)-cm-long col-
umn of loam soil predicted by.using a variable inactivation
rate arc shown in Fig. 4. Four different curves arc shown,
representing snapshots of the virus concentration profile in
the column after 6. 24, 72, and 120 h of transport. Figures Sa
and b show the effects of the different inuctivation rates on
model predictions of virus transport. In Fig. Sa, the differ-
ence in the concentration of virus particles predicted by
using a variable inactivation rate and the constant rate at
WC is shown. The difference between predicted concentra-
tions by using the variable, temperature-dependent inactiva-
tion rate and the constant rate at 2S°C is shown in Fig. 5b.
The differences in virus concentrations predicted by the
model when the rule of inactivation of adsorbed viruses is
zero compared to when the rate of inactivation of adsorbed
viruses is assumed to be one-half that of the free viruses arc
shown in Fig. 6.
Example 5. Model predictions of virus transport in a soil
column of Rchovot sand with the virus inactivation rate
ocprn (om)
0.1 2 3 4 (
Concentration (log plu/ml)
FIG. 2. Comparison of model predictions with experimental data
of Grondin (5) for a saturated, gravelly Hand Mill (example 2).
Ninety-five percent confidence limits were calculated from seven
replicates.
calculated as a function of temperature as described in
equation 4 arc shown in Fig. 7.
DISCUSSION
Model testing. The ultimate measure of the usefulness of a
model as a predictive tool is its ability to accurately predict
field observations of virus transport under a variety of
environmental conditions. However, most models that have
been developed to predict microbial transport have not been
tested by using lie Id or laboratory data. There arc a few
exceptions to this. For example, Tcutsch ct al. (17) devel-
oped a one-dimensional model to describe microbial trans-
port that includes decay, growth, filtration, and adsorption.
The model predictions compared closely with the measured
Virus Concentration (PFU/ml)
10° 10' ioj io3 10* 10*
o
4-t
fr
Q
20
40
60
80
100
FIG. 4. Virus concentration as a function of soil depth when u
temperature-dependent inactivation rale was used with an Indio
loam noil (example 4n).
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Vol.. 58. 1W2 A MODEL OF VIRUS TRANSPORT IN UNSATURATED SOILS 1M.1
a CCT - C10 (PFU/ml) C^ - C^ (PFU/ml)
-12000 -9000 -6000 -3000
0
O
^ 10
Q
•6 20
30
•—•t • 24 h
«-«• I » 72 h
' t - 120 h
- C25 (PFU/ml)
2000 4000 6000 8000
•5 20
CO
30
•—•t » 24 h
»-»t - 72 h
I - 120 h
FIG. 5. (a) Differences in predicted virus concentration when a
temperature-dependent (Ccl) or a constant (C,,,) inactivation rate
was used with an Indio loam soil (example 4a versus 4b). (b)
Differences in predicted virus concentration when a temperature-
dependent (C,.,) or constant (C,,) inactivation rate was used with an
Indio loam soil (example 4a versus 4c).
results of a high-Row-ratc experiment of MS2 transport.
However, at low flow rates, microbial behavior could not be
.simulated closely by using the name transport equation.
Harvey and Garabcdian (7) simulated bacterial transport by
using a colloid filtration model that had been modified to
include advcction, storage, dispersion, and adsorption. They
compared model predictions with measurements of bacterial
transport in a sandy aquifer in Cape Cod. Mas.s. While the
model wan able to simulate the bacterial transport measured
at a sampling point at a depth of 9.1 m, model predictions for
a sampling point at a depth of 8.5 m were not very close to
the measured concentrations, especially at later limes.
1000 2000 3000 4000 5000
t « 24 h
«-« t • 72 h
t = 120 h
FIG. ft. Effects of assuming no inaclivalion of adsorbed viruses
(C'nu.) or of assuming a nonzero inaclivalion rale of adsorbed viruses
(£',„,) '>n model predictions for an Indio loam soil (example 4a
versus 4d).
Both of these models were developed for use by the
investigators to simulate their own data. In the case of the
colloid filtration model, extensive fitting of the required input
parameters was performed by calibrating different solutions
of the transport equation to the observed bacterial break-
through curves (7). Thus, while these models may be able to
simulate the data of the investigator reasonably well, they
may not be able to predict the results of the transport
Virus Concentration (PFU/ml)
K>° 10' 102 103 10* 10*
u
O
to
FIO. 7. Virus concentration as a function of noil depth when a
temperature-dependent Inactlvalion rate wax used with a Rehovoi
rand soil (example 5).
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1M4 YATES AND OUYANG
Am.. ENVIKON. MiotoHioi..
experiments uf other investigators. If a model is to be used
for purposes other than research, such as community plan-
ning or making regulatory decisions, it must be able to
predict microbial transport by using data obtained by anyone
under a wide range of environmental conditions.
Tim and Mostaghimi (18) attempted to simulate the results
of a saturated-flow column transport experiment using po-
liovirus I conducted by Lance and Gcrba (10). They used a
conventional equation for describing solute transport, i.e.,
the advcction-dispcrsion equation, in their studies. The
difficulty encountered by these investigators was that insuf-
ficient data were reported by Lance and Gcrba (10) to fulfill
the input requirements of the model. Therefore, they had to
estimate values for the virus adsorption coefficient, the virus
inactivation rate, the saturated hydraulic conductivity, the
hydrodynamic dispersion coefficient, the moisture content at
saturation, and the average porosity of the soil. The model
simulation of virus concentrations compared closely to the
measured virus concentrations in the top 80 cm of the soil
column; however, because so many of the input values were
estimated, it is difficult to assess the accuracy of the model.
In this research, a model to describe virus transport was
developed on the basis of the factors known to affect virus
Cute in the subsurface. A survey of the literature was
conducted to locate data sets in which the investigators
made measurements of not only virus properties but also soil
and hydraulic properties. Three data sets were located and
used to lest VIRTUS. No fitting or calibration of the model
was performed; the data and measurements as reported by
the respective investigators were used as model input.
When the predictions of VIRTUS were compared with the
results obtained by Grondin (5) by using a saturated gravelly
sand column, the model predictions were within the 95%
confidence limits of the measured virus concentrations for
one trial (Fig. 1). For the second trial, the model predicted
that more than 3(X) viruses ml"' would appear in the column
effluent after 48 min. although none were detected in the
laboratory study (Fig. 2). The discrepancy between the
model predictions and the laboratory measurements may be
due to the reported value for the adsorption coefficient
(-O.S4 ml g of soil"'). This value was not measured by the
investigators by using a batch adsorption isotherm study;
rather, the value was used as a fitting parameter for their
data. In the model, a negative value for the adsorption
coefficient would have the effect of transporting the viruses
at a more rapid rate through the soil (on average) than the
average velocity of the water and resulted in viruses being
present in the column effluent. If, in reality, there was
adsorption of the viruses to the soil particles, this would
retard their movement through the column and result in no
viruses being detected in the outflow.
In the case in which VIRTUS wan tested by using the data
of Powclson ct al. (14), model predictions were very close to
the measured virus concentration profiles (Fig. 3). However,
this is only one example of a comparison to one laboratory
transport study in unsaturatcd soil by using a single soil type
and a single virus type. More testing of the model in required
before it should be used for any purposes other than re-
search.
Unfortunately, in these examples, the temperature-depen-
dent inuclivation rate capabilities of the model could not be
tested. This is due to the fact that the experiments were
conducted under constant temperature conditions in the
laboratory, and. thus, the virus inactivation rate remained
constant (theoretically) throughout the course of the exper-
iment. To tckt the capacity of the model to calculate new
virus inactivation rates as a function of the changing soil
temperature, data from a laboratory study in which (he
temperature is allowed to change (and is closely monitored)
or from a field study in which the temperature is monitored
will be required. This will allow an assessment of the
capability of the model to accurately calculate heat flow
through the soil, which affects water flow (and thus virus
transport) as well as the rate of virus inactivation during
transport.
Model simulations. In addition to being predictive tools,
models are useful for demonstrating the effects of different
variables on model results. Because it is not feasible to
perform experiments on all possible combinations of viruses,
soil types, and environmental conditions to determine their
transport behavior, models can serve as a useful alternative.
The value of input variables can be easily changed, and the
results on model outputs can be determined. For example,
the model can be run by using different values for tempera-
ture while holding constant all other values. By using this
technique, a quantitative measure of the influence of tem-
perature on model results can be obtained. If it is shown that
a given variable has a considerable effect on the mode!
predictions, this indicates that experiments should be de-
signed in such a way that the variable is measured accu-
rately. Several factors that affect the transport and fate of
viruses in the unsaturatcd zone, and which thus affect model
predictions, were investigated by using model simulations
and arc discussed below.
(I) Effects of temperature-dependent inactlvalion rates.
Most models of contaminant transport consider the move-
ment of water and the transport of the contaminant in (heir
development and assume that the thermal conditions in the
soil remain constant. In reality, under field conditions, this is
not generally the case. Temperature fluctuations in soil can
be considerable throughout the course of a 24-h period,
especially near the soil surface. Because the effects of
temperature on virus inactivation rates in the environment
can be quite significant, it seems logical to use a model of
contaminant transport that also models heat flow.
The effects of allowing the virus inactivation rate to vary
as a function of soil temperature in comparison with the
effects of holding it constant arc graphically shown in Fig. 5a
and b. In the case where the virus inactivation rate was held
constant at 0.033 log,,, day"1 (10°C), the model predicted
higher concentrations of viruses than would be predicted if
the inactivation rate was allowed to vary as a function of
temperature (Fig. Sa). The opposite predictions were ob-
tained in the case of a constant inactivation rate of 0.354
log,,, day"1 (25°C), as shown in Fig. 5b. When the inactiva-
tion rate was considered to be a constant at 2S°C an
underprediction in the concentration of viruses resulted as
compared with that predicted when the inactivation rate was
considered to be temperature dependent.
The reasons for these predictions become apparent upon
observation of the predicted change in soil temperature that
occurs as applied water is infiltrated through the soil column.
Figure 8 shows the soil temperature as a function of time for
the model simulations discussed for example 4 above. At the
soil surface, over a 24-h period, the soil temperature (which
started at 8.7*0) decreased to 3°C at 6 h during the addition
of cold water and increased to 3S°C at 12 h because of the
effects of solar radiation. Similar patterns would be expected
at the 5- and 10-cm depths, although the magnitude of the
variation would not be as large. In example 4b, the virus
inactivation rate was held constant at a value that would be
expected for constant 10°C soil conditions. The fact that the
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VOL. 58, 1992
A MODEL OF VIRUS TRANSPORT IN UNSATURATED SOILS
1615
40
O 30
0)
a
10
•—• 0 cm
12
24
36
48
Time (h)
FIG. 8. Soil temperature as a°'function of time for an Indio kxim
soil (example 4).
soil temperature rose above 10°C for more than 12 h in a 24-h
period resulted in a prediction of virus inactivation at rela-
tively high rates (compared to the rate at a constant temper-
ature of 10°C) for that period. Overall, maintaining the
inactivation rate at a constant value had the effect of
increasing the predicted concentration of viruses that were
transported in the soil column by more than 4 orders of
magnitude (Fig. 5a).
In example 4c, the soil temperature was considered to be
constant at 25°C; consequently, the virus inactivaiion was
maintained at a relatively high rale throughout the transport
process. In actuality, the soil temperature was at or above
25°C for a relatively short period of time (less than 6 h), so
viruses were inactivated at or above that high rate for only 6
h in the simulation where the rate was temperature depen-
dent. In this case (Fig. 5b), an assumption of a constant
inactivation rate would lead to a prediction that thousands of
viruses fewer than the actual number (assuming that the
variable inactivation rate simulation predicts the actual
number) would be transported in the column.
The sensitivity of model predictions to changes in the
temperature-dependent, inactivation rate was determined by
changing the inactivation rate while keeping all other varia-
bles constant. This sensitivity analysis showed that changing
the value of the inactivation rate by 50% resulted in a 33%
change in the predicted concentration of viruses being
transported through the soil. A high sensitivity of model
predictions to the virus inactivation rate has also been
observed by Tim and Mostaghimi (18) and Park et al. (12).
These results demonstrate the need to accurately monitor
virus inactivation and/or temperature during experiments of
virus transport in the subsurface.
(U) Effects of inactivation rates for adsorbed vcnos those of
(rcc viruses. There have been reports in the literature of
differences in the measured rates of virus inactivation for
viruses that arc adsorbed to soil particles as compared with
those for viruses that are freely suspended in the liquid
medium (8, IS, 22). Therefore, this model was developed to
allow the user to input different values for inactivation rates
for viruses in these two states. When u value fur the
inactivation rate of adsorbed viruses is specified. Ihc model
calculates the number of viruses adsorbed at a given time on
the basis of the adsorption coefficient specified by ihe user
and determines accordingly the number of viruses inacti-
vated.
It is difficult to obtain a quantitative value for the relative
difference between inactivation rates for adsorbed viruses
and those for freely suspended viruses. For the purposes of
illustration, a simulation with a value for adsorbed viruses
equal to one-half that of free viruses (temperature depen-
dent) was compared with a simulation in which the inactiva-
tion rate for adsorbed viruses was zero. As one would
expect, the concentration of viruses transported through the
soil column is larger when the solid-phase inactivaiion rate is
zero than when it is one-half the liquid-phase rate. The
difference increases with time, as shown in Fig. 6. In a
system in which the inactivation rate of adsorbed viruses is
equal to that of free viruses, the differences would he even
greater.
This example demonstrates the importance of knowing the
inactivation rate for viruses in the adsorbed and liquid
phases. If the inactivation rate for adsorbed viruses is
actually lower than that of suspended viruses, it would be
important to incorporate that information in a model so that
accurate predictions could be made.of virus concentration
profiles. If the model assumes the same inactivation rate for
all viruses, it would predict that fewer viruses arc being
transported than Ihc actual number.
(til) Effects of soil type. A simulation of virus transport by
using data for a Rchovot sand was run to illustrate the effects
of soil properties on transport. The Rchovot sand has a much
higher hydraulic conductivity (Table 2) than that of the Indio
loam, and, thus, water and contaminants can move through
this soil more rapidly. As shown in Fig. 7, the viruses were
transported more rapidly and in higher concentrations in this
soil than in Ihe loam soil of ihc previous examples. After 6 h,
the viruses in the loam soil had been transported only 11 cm
(Fig. 4), in comparison to more than 35 cm in the sandy soil
(Fig. 7). The differences between the two columns become
more apparent at longer times: after 5 days, approximately
30 viruses ml~' had been transported 15 cm in the loam soil,
whereas more than 10r viruses ml"' were being recovered in
the sand column effluent after the same length of time.
Another reason for the relatively higher concentrations of
viruses being transported through this soil, in addition to the
higher hydraulic conductivity, is related to the adsorption
coefficient. For this sand, on the basis of reported values for
virus adsorption to other sandy soils, an adsorption coeffi-
cient of zero was chosen. Thus, the rate at which the viruses
were transported through the soil was not decreased as a
result of adsorption to the soil particles, unlike the case for
the loam soil.
Condusioas. A model of virus transport, VIRTUS, that
simultaneously solves equations describing the transport of
water, heat, and viruses through the unsaturatcd zone of the
soil has been developed. The effects of a temperature-
dependent inactivation rate versus a constant inactivation
rate were shown to be considerable in terms of the concen-
trations of viruses that are predicted to be transported, in
addition, it was shown that different inactivation rates for
adsorbed versus freely suspended viruses may have a con-
siderable effect on model predictions. More data on the
relative inactivation rates for viruses in these two states ;ire-
necessary so that model input "ilucs arc as accurate as
possible.
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1616 YATES AND OUYANG
AHPL. ENVIRON. MICROHIOI..
VIRTUS was tested by using three data sets obtained
during laboratory studies of coliphagc transport and was
found to produce reasonable predictions in comparison with
measured results. However, before this or any model of
contaminant transport can be used with confidence for any
purpose other than research, considerable testing is re-
quired. VIRTUS must be tested by using field data collected
in a wide variety of environmental and hydrogeologic set-
tings, so that its limitations can be assessed. Few, if any,
data sets containing both virus data and the appropriate
hydrogeologic data are currently available so that this, or
any, model can be tested. More transport studies using
human viruses that have been implicated in waterborne
disease outbreaks and bacteriophages must be conducted to
assess the appropriateness of using phages or other micro-
organisms as surrogates for animal viruses in environmental
fate studies.
ACKNOWLEDGMENT
This research was supported by intcragency agreement DW
12933820-0 from the R. S. Kerr Environmental Research Labora-
tory, U.S. Environmental Protection Agency.
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