virus transport in groundwater – field studies and groundwater … · 2014. 12. 17. · jack...

1 Field Studies and Groundwater Protection | Feb 2012

Virus Transport in

Groundwater – Field Studies and Groundwater

Protection

Jack Schijven

VIRUS ATTACHMENT AND INACTIVATION

FIELD STUDIES

QMRA

GROUNDWATER PROTECTION

GWPCalc: tool for calculating the size of groundwater protection zones

Field Studies and Groundwater Protection | Feb 2012


2

Groundwater: Focus on viruses● Viruses may be transported with groundwater farther than bacteria

and protozoa

– Viruses are very small

– Viruses may attach little to sand grains

– Viruses may survive long

● Viruses may be very infectious

● Diseases outbreaks from contaminated groundwater sourcesreported in developing and developed countries

– Howard et al, WHO Groundwater Monograph, 2006, chapter 10

● Usually vulnerable geologic settings

– Fractured rock, cross connecting well bores, leaking well cases X presence of sources such as wastewater treatment facilities, septic tanks, animal manure

● Contamination may be overestimated: Mostly studies of high-risk wells



3

Viruses

Polio Rota MS2 PRD1

● Human viruses: host= human cells

● Bacterial viruses: host = bacteria cells

● Bacteriophages MS2 and PRD1 aremodel viruses

– Harmless to humans

– Same shape and size(smallest microorganisms)

– Negative charge: Poor attachment to sand

– Survives well at low temperature

– Easy to enumerate

Attachment

Penetration

Host

DNA or RNA Virus

Protein synthesis

DNA-replication

Assembly

Lysis

Mature viruses

Protein coat



4

Enumeration of viruses

● Enteroviruses

– Tissue culture (infectious virus particles)PCR (infectious+non-infectious virus particles)

● Bacteriophages

– Double Layer Agar Plate

– Tube

› 1 ml sample (bacteriophages)

› 1 ml host bacteria

› 2.5 ml growth mediumwith semi-solid agar

– Solid agar plate

– Count plaques



5

Major removal processes

● Inactivation

● Attachment

--

- - -

lµ

Grain of sand

�

�

Attachment

Inactivation

Inactivation

Detachment

-

+----

-- +-

--

--

--

+

+-

---

-

-

-

--

-

--

-

--

---

-

--

--

-

---

- -

--

- --

--

-

--

-

- --

+

+

--

sµ

detk

attk



6

Virus attachment

● Bacteriophages as model viruses

● Bacteriophages MS2 and PRD1 strongly negative => attach less than most viruses

● Poliovirus neutral

● Coxsackievirus B4 probably negative

● Sticking efficiency αmeasure for attachment and depends on surface properties of virus and sand

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

0 24 48 72 96

Time [hours]

C/C0MS2PV1

0.00001

0.0001

0.001

0.01

0.1

1

10

0 24 48 72 96 120 144 168

Time [hours]

C/C0MS2CB4



7

Colloid filtration theory

● Collision efficiency η: Probability of collision

– Physical conditions

– Diffusion, interception, sedimentation

● Sticking efficiency α: Probability of attachment

– Chemical conditions (DLVO)

● Viruses are small

– Diffusion / Brownian movement →collision efficiency η

– Surface charge → sticking efficiency α

– At lower pH, higher ionic strength →higher α



8

Collision efficiency η0

● Collision: Interception, sedimentation, diffusion

● Viruses: Diffusion

0.05 0.10 0.50 1.00 5.00 10.00

0.010

0.100

0.050

0.020

0.200

0.030

0.015

0.150

0.070

Diameter microorganism,mm

h0

Viruses 20-200 nm

Protozoa5-10 µm

Bacteria1-3 µm



9

Virus attachment

● Attachment rate coefficient

● Collision efficiency

● Peclet number

● Diffusion coefficient

● Happel’s porosity dependent parameter

with

vd

nk

catt αη)1(

2

3 −=

3/23/14 −= Pes NAη

BMcPe DnvdN /=

)3/()273( µπ pBBM dTKD +=

)2332/()1(2 655 γγγγ −+−−=sA3/1)1( n−=γ



10

CFT: Literature and spreadsheet

● Yao KM, Habibian MT, O'Melia CR, Water and waste water filtration: concepts and applications, EST, 1971, 5, 1105-1112

● Tufenkji N, Elimelech M. Correlation Equation for Predicting Single-Collector Efficiency in Physicochemical Filtration in Saturated Porous Media, EST, 2004, 38, 529-536

● www.yale.edu/env/elimelech/publication-pdf/TECorrelationEqn.xls

● http://biocolloid.mcgill.ca/publications.html

( ) αη10ln

1

2

3

10ln

1log

010

L

d

n

v

Lk

C

C

catt

−−=−=



11

DLVO: Derjaguin-Landau-Verwey-Overbeek theory● Double Layer force (electrostatic)

– Attractive or repulsive surface charge– Depends on pH and ionic strength (IS)

● Lifshitz-Van der Waals attractive force● Born repulsive force

– Overlap of electron clouds at <1 nm● Extended DLVO: + Hydrophobic interaction● Virus mantle

– Positively and negatively charged groups, like NH2

+, COO-

● Isoelectric point (Ip)– pH at which net charge is zero– pH<Ip => positively charged virus– pH>Ip => negatively charged virus

● Ip (MS2) 3.9 Ip (PRD1) 3-4



12

DLVO energy profile

● Energy barrier Φmax

– Repulsion

● Primary minimum Φmin1

– Irreversible attachment

● Secundary minimum Φmin2

– Reversible attachment

● Effect of pH and IS on attachment of PRD1 to sand

– pH increase: more repulsive

– IS increase: less repulsive

● Equations: e.g. Hahn and O’Melia, EST, 2004, 38, 210-220

-10 -9 -8 -7 -6

-5

0

5

Log10 Separation distance @mD

Dimensionless

energy

FêHkB TL

PRD1-Quartz

ÿÿÿ Electrostatic interaction

ÿÿÿ London-van de Waals attraction

ÿÿÿ Born repulsion

—DLVO-profile

Fmax 6.94212 zPRD1 -17.5572 mV

Fmin1 -4.39547 zQuartz -42.1402 mV

Fmin2 -0.772816



13

Virus inactivation

● Depends on

– Virus

– Temperature

– pH

– Other environmental conditions

● Literature data virus inactivation in groundwater

– Schijven JF and Hassanizadeh SM, CREST, 2000, 31, 49-127

– Pedley S, Yates M, Schijven JF, West J, Howard G, Barrett M, Pathogens: Health relevance, transport and attenuation. In: Protecting groundwater for Health, eds: Schmoll O, Howard G, Chilton J, Chorus I, WHO, 2006, chapter 3

● Inactivation rate coefficient µlat 5-12 °C

– 0.023 (0.01 – 0.1) /day = 0.01 (0.0043 – 0.043) log10

/day

[ ] ttC

CtExpCC ll

tlt µµµ

3.2

1

10ln

1log

0100 −=−=⇒−=



14

Long term inactivation study

● Objective

– Determine change of ratio of infectious to defective virus particles over time

● Experimental design

– Three enteroviruses PV1, PV2, CB4

– BGM cell culture: Infectious virus particles, Poisson-distributed plaque counts

– RT-PCR: Most Probable Number estimates

– Artificial Ground Water (AGW) + Artificial Surface Water (ASW)

– 4 °C and 22 °C– T= 0 – a year

● Biphasic inactivation ( )[ ]ttt effeCC 21 10

λλ −− −+=

De Roda Husman et al. AEM, 2009, 75(4):1050-1057



15

Inactivation curves

AGW ASW

● Bleu: RT-PCR; Green: BGM cell culture

● Ratio RT-PCR/BGM cell culture increases over time



16

Conclusions● Ratio RT-PCR/BGM cell culture

– Time dependent (increases with time)

– Virus type dependent

– Conditions (temperature, water) dependent

● Inactivation CB4 first order; PV1 and PV2 biphasic

● Inactivation rate coefficient of 0.01 log10/day at ≈10°C from literature data not too conservative

Inactivation rate coefficient, log10/day

Water °C PV1 PV2 CB4AGW 4 0.0031 0.0031 0.0035

22 0.011 0.022 0.03ASW 4 0.0023 0.0013 0.0043

22 0.012 0.0069 0.022

De Roda Husman et al. AEM, 2009, 75(4):1050-1057



17

One site kinetic model

● Virus transport processes through saturated porous media

– Advection / dispersion / attachment / detachment / inactivation

● Governing equations

SkCCkx

Cv

x

Cv

t

C BlattL θ

ρµα det2

2

+−−∂∂−

∂∂=

∂∂

SSkCkt

S Bs

Batt

B

θρµ

θρ

θρ −−=

∂∂

det



18

One kinetic site model: breakthrough curves

0.0001

0.001

0.01

0.1

1

0 5 10 15 20 25

t(h)

C/C0

katt=0.1; kdet=0.001; mul=0; mus=0



katt=0.1; kdet=0.001; mul=0.1; mus=0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20 25

t(h)

C/C0

Log scale to show tail

(katt

+µl)C

=> Cmax

kdet

S =>level of tail

µsS =>

slope of tail



19

Two site kinetic model

● Governing equations

22det11det212

2

SkSkCCkCkx

Cv

x

Cv

t

C BBlattattL θ

ρθρµα ++−−−

∂∂−

∂∂=

∂∂

1111det11 SSkCkt

S Bs

Batt

B

θρµ

θρ

θρ −−=

∂∂

2222det22 SSkCkt

S Bs

Batt

B

θρµ

θρ

θρ −−=

∂∂

Breakthrough curve of PRD1 2-site kinetic model

0.001

0.01

0.1

1

0 1 2 3 4 5 6 7

Days

C/C0



20

Modeling breakthrough curves: one and two kinetic sites

– v and αL

from NaCl tracer

– µlfrom inactivation experiment

– CXTFIT: 1 kinetic site model

– HYDRUS-1D: 2 kinetic site model

– µs

≈ slope of tail

0.000001

0.0001

0.01

1

0 24 48 72 96 120 144 168 192

Time [hours]

C/C0

b

c

a

Rate coefficients(day-1)

Aone site

Bone site

Ctwo sites

katt1 4.8 2.6 2.0

kdet1 6.7 0.065 0.065

katt2 3.36

kdet2 13.7

µs1=µs2 5.8 0.43 0.43

Goodness of fit 98% 92% 98%

22det11det212

2

SkSkCCkCkx

Cv

x

Cv

t

C BBlattattL θ

ρθρµα ++−−−

∂∂−

∂∂=

∂∂

1111det11 SSkCkt

S Bs

Batt

B

θρµ

θρ

θρ −−=

∂∂

2222det22 SSkCkt

S Bs

Batt

B

θρµ

θρ

θρ −−=

∂∂


FIELD STUDIES

21

Field study dune recharge Castricum


FIELD STUDIES

22



FIELD STUDIES

23



FIELD STUDIES

24

Salt tracer

● NaCl

● 7 days pulse

● Pore water velocity (1.5 m/day)

● Dispersivity

800

1800

2800

3800

0 5 10 15 20 25 30 35 40Day

EC

(µS

/cm

)

CompartmentPCO3 (3.8 m)PCO5 (10 m)PCO7 (30 m)

800

1800

2800

3800

0 5 10 15 20 25 30 35 40

EC

(µS

/cm

)

CompartmentPCO2 (2.4 m)PCO4 (6.0 m)PCO6 (17 m)


FIELD STUDIES

25

Breakthrough curves

● Bacteriophages

– MS2

– PRD1

– 7 days seeding

MS2

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

0 25 50 75 100 125

C (

pfp/

l)

CompartmentPCO2 (2.4 m)PCO3 (3.8 m)PCO4 (6.4 m)PCO5 (10 m)PCO6 (17 m)PCO7 (30 m)

PRD1

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0 25 50 75 100 125

C (

pfp/

l)

CompartmentPCO2 (2.4 m)PCO3 (3.8 m)PCO4 (6.4 m)PCO5 (10 m)PCO6 (17 m)PCO7 (30 m)


FIELD STUDIES

26

Inactivation

● Mild conditions

– near neutral pH

– low temperature

●→ First order rate decrease

MS2

0.01

0.1

1

10

0 10 20 30 40

Day

C/C

0

Obs in peptone/saline at lab

Linear fit: 0.0008 log10/day .Obs in compartment water atlabLinear fit: 0.019 log10/day

Obs in well water at lab

Linear fit: 0.028 log10/day

Obs in well water at field


PRD1

0.01

0.1

1

10

0 10 20 30 40

Day

C/C

0

Obs in peptone/saline at lab

Linear fit: 0.0026 log10/day .Obs in compartment water atlabLinear fit: 0.0032 log10/day

Obs in well water at lab


Obs in well water at field



FIELD STUDIES

27

Modeling breakthrough curvesMS2 - Well PCO2 at 2.4 m

0.1

10

1000

100000

10000000

0 20 40 60 80 100 120 140

Day

C (viruses/l)

ObservationOne-site modelTwo-site model

Rate coefficients(day-1)

one site two sites

katt1 4.1 4.2

kdet1 0.00087 0.00079

katt2 0.47

kdet2 0.54

µs1=µs2 0.085 0.085

Goodness of fit 75% 79%

Rate coefficients (day-1)

one site two sites

katt1 3.2 3.2

kdet1 0.0016 0.0022

katt2 0.17

kdet2 0.24

µs1=µs2 0.092 0.092

Goodness of fit 77% 80%

MS2 - Well PCO3 at 3.8 m

0.1

10

1000

100000

10000000

0 20 40 60 80 100 120 140

Day

C (viruses/l)

ObservationsOne-site modelTwo-site model


FIELD STUDIES

28

Deep well injection study

● Redox-zones: Attachment to iron oxyhydroxides in O2-zone

71477 R 03

- 250

m-Field LevelPP.1

3

2

1

5

55

4 4 44

3

33

22 22

1 111

IP.2WP.1

3898 0

WP.3

8

[distance to IP.2;m] [distance to IP.2;m]

WP.2

12

WP.4

22

- 260

- 270

- 280

- 290

- 300

- 310

- 320

- 330

- 340

4 4

4

4 44

2 2

2

2 22

66

6 6 66

8

88

888

10

1010

101012

12

12

12

12

10

12

5

4

3

2

1

(1)

5

6

33

ntemperature sensorscreensfine sand

coarse sand

clay, loam

71477 R 03

- 250

m-Field LevelPP.1

3

2

1

5

55

4 4 44

3

33

22 22

1 111

IP.2WP.1

3898 0

WP.3

8


WP.2

12

WP.4

22

- 260

71477 R 03

- 250

m-Field LevelPP.1

3

2

1

5

55

4 4 44

3

33

22 22

1 111

IP.2WP.1

3898 0

WP.3

8


WP.2

12

WP.4

22

- 260

- 270

- 280

- 290

- 300

- 310

- 320

- 330

- 340

- 270

- 280

- 290

- 300

- 310

- 320

- 330

- 340

4 4

4

4 44

2 2

2

2 22

66

6 6 66

8

88

888

10

1010

101012

12

12

12

12

10

12

5

4

3

2

1

(1)

4 4

4

4 44

2 2

2

2 22

66

6 6 66

8

88

888

10

1010

101012

12

12

12

12

10

12

5

4

3

2

1

(1)

5

6

33

5

6

33

ntemperature sensorscreensfine sand

coarse sand

clay, loam


FIELD STUDIES

29

Soil passage effectively removes viruses

● 8 log10 removal (non-linear with distance)

– After 25 days (30 m) dune passage

– After 40 days (38 m) deep well injection

-10

-8

-6

-4

-2

0

0 10 20 30 40

Travel time [days]

RemovalLog10(C/C0)

MS2 - dune rechargePRD1 - dune rechargeMS2 - deep well injectionPRD1 - deep well injection


FIELD STUDIES

30

Removal processes during soil passage

● Effective virus removal if sites for attachment are present (mostly iron hydroxides; sticking efficiency α∼10-3)

● Virus populationheterogeneity?

● Little removal if attachment sites are absent(e.g. when oxygen deficient aquifer) → conservative value for attachment to be used in calculation of protection zones (sticking efficiency α∼10-5)

-10

-8

-6

-4

-2

0

0 10 20 30 40

Travel time [days]

Virus removalLog10(C/C0)

MS2 - dune rechargePRD1 - dune rechargeMS2 - deep well injectionPRD1 - deep well injection


QMRA

31

Dutch Drinking Water Act 2001

● No pathogens in drinking water in concentrations that adversely affect public health ≠ zero => risk

● Quantitative Microbiological Risk Assessment (QMRA)

– WHO Drinking Water Guidelines (eds 3+4): Health based target

– The Netherlands: Max infection risk = 10-4 per person per year

– Drinking water concentration ≈ 1 pathogen in 1 000 000 liter

● QMRA required for drinking waterfrom surface water and vulnerable groundwater

● Index pathogens

– Enteroviruses, Campylobacter, Cryptosporidium, Giardia


QMRA

32

Environmental Inspectorate Guideline 5318 (2006)● How to do QMRA

● QMRA from surface water to drinking water

– Quality of source water (index pathogens)

– Treatment efficiency (indicator organisms)

● QMRA from vulnerable groundwater to drinking water

– Is protection zone of 60 days an adequate barrier (natural treatment)?

● Unconfined sandy aquifers and karst aquifers are vulnerable

– No protective confining (clay) layers

– Karst: fast flow paths

Index pathogens Indicator organismsEnteroviruses 20-200 nm Bacteriophages 20-60 nmCampylobacter 1-2 µm E.coli 1-2 µmCryptosporidium 5-6 µm Spores of sulphiteGiardia 8-10 µm reducing clostridia (SSRC) 1 µm


QMRA

33

QMRA from surface water to drinking water● Csw = Pathogen concentration in source water [N/liter]

● R = Recovery = fraction of detected pathogens [-]

● Z = Fraction of microorganisms passing treatment [-]

● Cdw = Pathogen concentration in drinking water [N/liter]

● V = Consumption of unboiled drinking water [liter]

● Pm = Infectivity of pathogen [-]

● Pinf = Infection risk [per person per day or year]

● Pinf,day = Csw x 1/R x Z x V x Pm

● Pinf,year = 365.25 x Pinf,day or

● Drinking water companies: point estimates (average values)

● RIVM: Monte Carlo simulations (variability)

( )∏=

−−=365

1inf,inf, 11

idayyear i

PP


QMRA

34

QMRA from groundwater to drinking water

● Guideline 5318

– Unconfined sandy and karst aquifers are considered vulnerable therefore QMRA required

● Protection zone:

– No sources of contamination allowed within that zone

● Source concentration, Cs

● Setback distance rs and travel time T determine size of protection zone, which is the soil barrier

● Z = fraction of pathogensable to pass the soil barrier

Pinf = Cs x 1/R x Z x V x Pm ≤ 10-4



35

History of 60-days protection zone

● Knorr, Das Gas- und Wasserfach 1937, 80: 330-334

– Survival of bacteria in a bottle of water

– No bacteria detected after 60 days

● 60-days protection zone

– After 50-60 days no danger to public health

● Austria, Denmark, Germany, Ghana,Indonesia,The Netherlands, UK

● But viruses (and other pathogens)may survive longer

● Is 60-days enough protectionfor a maximum infection risk of 10-4 p-1y-1?



36

Protection zones that comply with 10-4 infection risk

● Shallow, unconfined sandy aquifers

● Viruses leaking from a sewage pipe

● Horizontal transport to the pumping well

● Literature data distributions of parameters (Monte Carlo simulation)

● Removal processes

– Little attachment (field data at anoxic conditions), α=10-5

– Extensive literature data on virus inactivation, µ=0.01 log10/day

● Dilution in groundwater

– Pumping rate QW at well



37

Steady state model

Removal = Attachment + Inactivation + Dilution

CA

is virus concentration at well

C0

is virus concentration in wastewater

α is sticking efficiency (attachment parameter) = 10-5

µlis the inactivation rate coefficient = 0.01 log

10/day

k1

en k2

physical constants

q is leakage rate of sewage pipe

Q is abstraction rate of groundwater

R is radial distance source<=>well

● QMRA: pinf

= C0

x Z x V x pm≤ 10-4

+

+−==

Q

qRkRkZ

C

Cl

A10

22

3/5110

010 log

2

1

5

3

3.2

1loglog µα



38

MonteCarloSimulations

VIRUS PROPERTIES AQUIFER PROPERTIES RISK ASSESSMENT

Sewage: 100 Enteroviruses/L Aquifer thickness Consumption 0.27 L/day

Leakage rate q=1m3/day Grain size Rotavirus infectivity

Inactivation 0.01 log10/day Porosity Protection zone 200-400m

Sticking efficiency αααα=10-5 Temperature Protection zone 1-2 years



39

Sensitivity analysis

● Size of protection zone most sensitive to inactivation and attachment

0.0829550.4

0.31091050.1

2.48592800.01

Inactivation µl

(day-1)

0.3294710-3

0.621513210-4

1.760323110-5

Attachment α

T95(year)T95(day)R95 (m)Parameter value

Parameter



40

Conclusions

● Shallow unconfined sandy aquifers (20-35 m deep)

– Travel time of 1 to 2 years (206 - 418 m setback distance)

– Infection risk below 10-4 per person per year with 95% certainty

● Most sensitive model parameters for size of protection zone

– Attachment and inactivation

● A smaller protection zone

– Demonstrate aquifer properties that lead to more virus removal

– Location specific investigation

● Only horizontal transport considered

– If vertical transport is significant thenprotection zone may be overestimated



41

Vulnerability● Environmental Inspectorate Guideline 5318 (2006)

– All unconfined sandy aquifers and karst aquifers are vulnerable

– QMRA of drinking water from vulnerable groundwater

● Groundwater companies

– Deeper unconfined aquifers should be less vulnerable

● Vulnerability

– Ability of viruses to be transported with the groundwater

– Less attenuation of virus in a more vulnerable aquifer

– Attenuation depends on properties of viruses and aquifer

● Size of protection zone:

– Maximum risk level (health based target) [risk]

– Virus source concentration [source]

– Attenuation of virus concentration [vulnerability]



42

Properties of viruses

● Significant threat to public health

– Very infectious

– Commonly gastroenteritis, but also more severe illness

● Can be very persistent

– survive well = inactivate slow; µ=0.01 log10/day

● Usually little attachment to sand grains

– Many viruses are negatively charged; α=10-5

● Very small

– 20-200 nm

– Negligible straining

● λ= virus removal rate coefficient(inactivation + attachment)



43

Properties of unconfined sandy aquifers● No confining layers

● High permeability

● In the Netherlands often shallow

● Properties relevant to virus attachment and inactivation = λ– porosity, grain size, iron hydroxides, temperature, pH, ionic

strength, ion composition, organic content, etc.

● Properties relevant to virus advection, dispersion, dilution

– m = anisotropy factor

– Q = Pumping rate of abstraction well

– H= thickness of aquifer

– zt=top of well screen

– zb=bottom of well screen



44

Model development● Vulnerability parameters

– Virus+aquifer properties

● Dimensionless model

– Model parameters are dimensionless

– Lower number of model parameters

● Numerical calculations (FlexPDE)

– Calculate rs* = dimensionless setback distance

to achieve a required virus removal

● Empirical formula

– Fit a formula to values of rs* as a function of the vulnerability

parameters

● rs* = dimensionless setback distance = vulnerability index

– Different combinations of the vulnerability parameters leading to the same virus attenuation have the same rs

*

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-2 -1 0 1 2 3

-3

-2

-1

0

1

l*

r*



45

● Steady state

– Constant pumping rate and constant leakage rate of virus from sewer

● Horizontal radial and vertical transport

● Dimensionless model

– The model domain was scaled=divided by H, the aquifer thickness

● Dimensional virus removal rate coefficient

– Inactivation + attachment: λ*= λ n π H3/Q

Model domainrs

*= rs /H

H/H=1

Q

*Contamination

source

Well screen

C*=10-8

Vulnerability index

Setback distance



46

Radial water flow under steady state conditions● Governing equation

– where, t [T] is the time, h [L]is the hydraulic head, kr[LT-1] is the

hydraulic conductivity in the r-direction and kz[LT-1] is the

hydraulic conductivity in the z-direction

● Dimensionless flow equation

– Division of governing equation by krand scaling to H [L] which is

the total thickness of all aquifer layers

02

2

=∂∂

∂∂+

∂∂

r

hr

rr

k

z

hk r

z

011

*

**

**2*

*2

=

∂∂

∂∂+

∂∂

r

hr

rrz

h

m



47

Virus transport

● Governing equation

– where, vrand v

zare the vertical and radial pore water velocities

– λ [T-1] is the virus removal rate coefficient, which entails both attachment and inactivation.

– Drr

≈αrvrand D

zz≈α

zvz[L2T-1] are the dispersion coefficients in r and

z directions.

● Dimensionless virus transport equation

Cr

CrD

rrz

CD

r

Cv

z

Cv rrzzrz λ−=

∂∂

∂∂−

∂∂−

∂∂+

∂∂ 1

2

2

***

***

**

*2*

*2**

*

**

*

** 1

1.0 Cr

Crv

rrz

Cv

r

Cv

z

Cv rrrrrz λαα −=

∂∂

∂∂−

∂∂−

∂∂+

∂∂



48

Dimensionlessparameters

Parameter Description

sss lrA ** 2= Leakage area

2

*

H

AA w

w π=

Cross sectional area of the screen of the abstraction well

** 005.0 sr

r rH

== αα Dispersivity in the r -direction.

** 1.0 rz

z Hααα ==

Dispersivity in the z -direction

RC

CC =*

Virus concentration with RC [L-3] the concentration at the abstraction well at R [L] from the source of contamination.

*sC Virus concentration at the contamination source

H

hh =*

Aquifer thickness

∑== irr trQ

H

Q

Hkk

ππ 2*

Horizontal hydraulic conductivity, where itr [m2 day-1] is the transmissivity of i-th aquifer layer.

Q

Hn 3* πλλ =

Dimensionless removal rate coefficient,

z

r

k

km =

Anisotropy ratio

Q

qQ =*

Dilution, where 1=q m3 day-1 (Schijven et al., 2006).

H

rr =* ,

H

zz =*

Radial and vertical coordinate

rr vQ

Hnv

2* π= , zz v

Q

Hnv

2* π=

Radial and vertical pore water velocity

H

zz b

b −= 1* , H

zz t

t −= 1* Bottom and top of the well screen

Varie

d in n

um

eric

al sim

ula

tio

ns



49

Numerical simulations (FlexPDE)● Dutch groundwater database

– Dimensionless parameter values of 35 unconfined aquifers

– λ=0.03 day-1 (α =10-5, µl=0.01 log10/day)

● 212 cases simulated

● Set vulnerability index rs* to get required removal (such that C* at well =1)

● No effect of kr*

● Fit rs* to vulnerability parameters

Mean Min Max Values for numerical simulationλ* removal rate coefficient 45 0.79 645 0.01, 0.1, 1, 10, 100, 1000Q* dilution factor 0.00012 0.000037 0.0019 0.0001, 0.001kr* horizontal hydraulic conductivity 500 4.4 6900 10, 100, 1000m anisotropy factor 1.6 1 3.5 1, 2, 5, 10zt* top of well screen 0.72 0.31 1 1, 0.85, 0.75, 0.5

zt*-zb* length of well screen 0.43 0.042 0.82 025, 0.5H (m) aquifer depth 116 23 334 -Cs* virus source concentration 104…108

Dimensionless parameter



50

First fitting step: If zt*=1 (horizontal transport)

● Numerical simulations =>Linear relation lnrs

* and lnλ*

● Steady state solution,neglecting dispersion

● Fit data to

● R2=99.9%

● a1 = 0.557

● a2 = 0.467

● Empirical formula

*

[ ] **** ln2

1lnlnln

2

1ln λ−+= QCr ss

[ ] *2

**1

* lnlnlnlnln λaQCar ss ++=

( )[ ] 467.0*557.0*** ln−= λQCr ss

*

**2*

λQC

r ss =



51

Second fitting step: If zt*<1, vertical transport significant

● Strong decreaseof lnrs

* for large lnλ*

(vertical transport dominates)

● Add (1-zt*) x (terms of

vulnerability parameters with coefficients)

*



52

Empirical formula

● R2=97.9%

( ) ( ) [ ]

−−=

−−−− ***64.117.119.2*383.0*227.0*467.0*557.0*** 99.2529.01207.0ln*

btt

z

sss zzExpzmQCExpQCr tλλ



53

Conclusions

● Empirical formula developed to calculate vulnerability index (dimensionless setback distance) and setback distance of an unconfined sandy aquifer to protect against virus contamination

● Deeper unconfined aquifers with deep well screen are less vulnerable and even more is anisotropy factor m>1

● A higher pumping rate Q increases dilution and flow rate, the net effect is increased vulnerability

● Integral part of Quantitative Microbial Risk Assessment

● Next steps:

– Incorporate in Inspectorate Guideline 5318

– Compare calculated with actual setback distances


GWPCalc

54

GWPCalc

● Computable Document File, Mathematica version 8 (Wolfram Inc, Champaign, Illinois)

● Runs in Mathematica and the free CDF Player (add-on or internet browser)

Empirical formula from

numerical calculations,

including vertical

transport

(Schijven et al., 2010)

Virus source

(leaking sewer or

septic tank at

groundwater table)

or any other

contaminant

Well

screenAquifer

thickness H

Setback

distance rs

Required removal:

Source 100 vir/L=>

8 log10

removal=>

Groundwater 10-6 vir/L=>

Infection risk <10-4 pppy

Vulnerability

rs*=r

s/H


GWPCalc

55

Example 0

● Unconfined / shallow / well screen high● Most sensitive aquifer thickness, pumping rate

and removal rate coefficient


GWPCalc

56

Example 1

● Unconfined / less shallow / well screen high● Most sensitive aquifer thickness, pumping rate

and removal rate coefficient


GWPCalc

57

Example 2

● Unconfined / less shallow / well screen deep● Also sensitive to changes in anisotropy


GWPCalc

58

Example 3

● Confined / less shallow / well screen deep


GWPCalc

59

Example 4

● Well screen crosses a confining layer● Virus transport in upper aquifer● Dilution with water from lower, clean aquifer


GWPCalc

60

Conclusions● GWPCalc is a tool with a quick-

and-easy to use formula to identify vulnerable sandy aquifers and situations that require attention

● GWPCalc be used to identify sources of contamination

● One removal rate coefficient: GWPCalc can be used for any contaminant

GWPCalc

61 Field Studies and Groundwater Protection | Feb 2012

QUESTIONS?

● GWPCalc is for free

● [email protected]

● [email protected]

virus transport in groundwater – field studies and groundwater … · 2014. 12. 17. · jack...

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