GWPcalc, the Ground Water Protection Calculator - KSCST

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 

1 Field Studies and Groundwater Protection | Feb 2012

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 sources 

reported 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 

2 

Field Studies and Groundwater Protection | Feb 2012 

VIRUS ATTACHMENT AND INACTIVATION

Viruses 

DNA or RNA 

Host 

Virus 

Attachment 

Protein coat 

Penetration 

Polio Rota MS2 PRD1 

● Human viruses: host= human cells 

● Bacterial viruses: host = bacteria cells 

● Bacteriophages MS2 and PRD1 are 

model viruses 

– Harmless to humans 

– Same shape and size 

(smallest microorganisms) 

– Negative charge: Poor attachment to sand 

– Survives well at low temperature 

– Easy to enumerate 

DNA-replication 

Protein synthesis 

Assembly 

Lysis 

Mature viruses 

3 



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 medium 

with semi-solid agar 

– Solid agar plate 

– Count plaques 

4 



Major removal processes 

● Inactivation 

● Attachment 

- 

- 

- - 

- 

- 

- 

Detachment 

- 

k det 

- - 

- - - - Inactivation - 

µ 

- 

l 

- 

- 

- 

- 

k att 

- 

- - 

Attachment 

- - 

- 

- - - - 

- + - 

- 

+ - 

- - 

- - - 

+ 

Grain of sand 

+ 

- 

- 

+ 

- 

- 

- 

- 

- - - 

- 

+ 

- 

- 

- 

Inactivation 

- 

 

- 

- 

- 

- 

- 

- 

µ s 

- 

- 

5 



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 α 

measure for attachment 

and depends on surface 

properties of virus and 

sand 

6 

C/C 0 

C/C 0 

10 

1 

0.1 

0.01 

0.001 

0.0001 

0.00001 

0.000001 

10 

1 

0.1 

0.01 

0.001 

0.0001 

0.00001 

0 24 48 72 96 

Time [hours] 

0 24 48 72 96 120 144 168 

Time [hours] 


VIRUS ATTACHMENT AND INACTIVATION 

MS2 

PV1 

MS2 

CB4

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 

7 



Collision efficiency η 0 

● Collision: Interception, sedimentation, diffusion 

● Viruses: Diffusion 

0.200 

0.150 

Viruses 20-200 nm 

h 0 

0.100 

0.070 

0.050 

0.030 

Protozoa 

5-10 µm 

0.020 

0.015 

0.010 

Bacteria 

1-3 µm 

0.05 0.10 0.50 1.00 5.00 10.00 

Diameter microorganism,mm 

8 



Virus attachment 

● Attachment rate coefficient 

● Collision efficiency 

k 

η 

att 

= 

3 (1 − n) 

αηv 

2 d 

1/ 3 −2 / 3 

= 4A s 

N 

Pe 

c 

● Peclet number 

N = d nv / 

Pe 

c 

D 

BM 

● Diffusion coefficient 

D = K ( T + 273) /(3 d µ ) 

BM 

B 

π p 

● Happel’s porosity dependent parameter 

with 

γ = 

( 1 − n) 

1/ 3 

A s 

= 

2(1 − γ 

5 

) /(2 − 3γ 

+ 

3γ 

5 

− 

2γ 

6 

) 

9 



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 

log 

10 

C 

C 

0 

= −k 

att 

L 

v 

1 

ln10 

= − 

3 

2 

( 1− 

n) 

d 

c 

L 

αη 

ln10 

10 



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 Ip => negatively charged virus 

● Ip (MS2) 3.9 Ip (PRD1) 3-4 

11 



DLVO energy profile 

● Energy barrier Φ max 

– Repulsion 

● Primary minimum Φ min1 

– Irreversible attachment 

Dimensionless 

energy 

FêHk B TL 

5 

0 

PRD1-Quartz 

ÿÿÿ Electrostatic interaction 

ÿÿÿ London-van de Waals attraction 

ÿÿÿ Born repulsion 

— DLVO -profile 

F max 6.94212 z PRD1 

F min1 -4.39547 z Quartz 

F min2 -0.772816 

-17.5572 mV 

-42.1402 mV 

● Secundary minimum Φ min2 

– Reversible attachment 

-5 

-10 -9 -8 -7 -6 

Log 10 Separation distance @mD 

● 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 

12 



Virus inactivation 

● Depends on 

– Virus 

– Temperature 

– pH 

= C 

Exp 

– Other environmental conditions 

C 

● 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 µ l 

at 5-12 °C 

t 

[ − µ t] ⇒ log = − µ t = t 

– 0.023 (0.01 – 0.1) /day = 0.01 (0.0043 – 0.043) log 10 

/day 

C 

C 

t 0 l 

10 

l 

− µ 

l 

0 

ln10 2.3 

1 

1 

13 



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 

[ 

−λ −λ 

e 

t ] 

( ) 

1 

● Biphasic inactivation = C fe 

t + 1− 

f 

C 

2 

t 

0 

14 

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



Inactivation curves 

AGW 

ASW 

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

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

15 



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, log 10 /day 

Water °C PV1 PV2 CB4 

AGW 4 0.0031 0.0031 0.0035 

22 0.011 0.022 0.03 

ASW 4 0.0023 0.0013 0.0043 

22 0.012 0.0069 0.022 

● Inactivation rate coefficient of 0.01 log 10 /day at ≈10°C from literature data 

not too conservative 

16 

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



One site kinetic model 

● Virus transport processes through saturated porous media 

– Advection / dispersion / attachment / detachment / inactivation 

● Governing equations 

∂C 

∂t 

= α v 

L 

ρB 

∂S 

= 

θ ∂t 

2 

∂ C ∂C 

− v − k 

2 

∂x 

∂x 

k 

att 

C 

− 

k 

det 

att 

ρB 

θ 

C 

− µ C 

l 

S − µ 

s 

+ 

k 

det 

ρB 

S 

θ 

ρB 

S 

θ 

17 



One kinetic site model: breakthrough curves 

Log 

scale to 

show tail 

1 

0.1 

(k att 

+µ l 

)C 

=> Cmax 

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



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

C/C 0 0.01 

0.001 

0.0001 

0.6 

0.5 

0.4 

C/C 0 0.3 

0.2 

0.1 

0 

0 5 10 15 20 25 

t(h) 

0 5 10 15 20 25 

t(h) 

k det 

S => 

level of tail 

µ s 

S => 

slope of tail 

18 



Two site kinetic model 

● Governing equations 

∂C 

∂t 

2 

∂ C ∂C 

ρB 

= α 

Lv 

− v − k 

2 

att1C 

− katt 

2C 

− µ 

lC 

+ kdet1 

S1 

+ k 

∂x 

∂x 

θ 

det2 

ρB 

θ 

S 

2 

1 

0.1 

Breakthrough curve of PRD1 

2-site kinetic model 

ρB 

θ 

ρB 

θ 

∂S 

∂t 

∂S 

∂t 

ρ 

θ 

µ 

ρ 

θ 

1 B 

B 

= k 

S 

att1C 

− kdet1 

S1 

− 

s1 

1 

ρ 

θ 

ρ 

θ 

2 B 

B 

= k 

S 

att 2C 

− kdet 2 

S2 

− µ 

s2 

2 

C/C 0 

0.01 

0.001 

0 1 2 3 4 5 6 7 

Days 

19 



Modeling breakthrough curves: one and two kinetic sites 

C/C 0 

1 

0.01 

0.0001 

b 

c 

a 

∂C 

∂t 

2 

∂ C ∂C 

ρB 

= α 

Lv 

− v − k 

2 

att1C 

− katt 

2C 

− µ 

lC 

+ kdet1 

S1 

+ k 

∂x 

∂x 

θ 

ρ 

B 

∂S 

θ ∂t 

ρB 

∂S 

θ ∂t 

ρ 

θ 

det2 

ρB 

S 

θ 

ρ 

θ 

1 B 

B 

= k 

S 

att1C 

− kdet1 

S1 

− µ 

s1 

1 

ρ 

θ 

ρ 

θ 

2 B 

B 

= k 

S 

att 2C 

− kdet 

2 

S2 

− µ 

s2 

2 

2 

0.000001 

0 24 48 72 96 120 144 168 192 

Time [hours] 

– v and α L 

from NaCl tracer 

– µ l 

from inactivation experiment 

– CXTFIT: 1 kinetic site model 

– HYDRUS-1D: 2 kinetic site model 

– µ s 

≈ slope of tail 

Rate coefficients A B C 

(day -1 ) 

one site one site two sites 

katt1 4.8 2.6 2.0 

kdet1 6.7 0.065 0.065 

katt2 3.36 

kdet2 13.7 

µ s1=µ s2 5.8 0.43 0.43 

Goodness of fit 98% 92% 98% 

20 



Field study dune recharge Castricum 

21 


FIELD STUDIES


22 


FIELD STUDIES


23 


FIELD STUDIES

Salt tracer 

● NaCl 

● 7 days pulse 

● Pore water velocity (1.5 m/day) 

● Dispersivity 

EC (µS/cm) 

3800 

2800 

1800 

800 

Compartment 

PCO2 (2.4 m) 

PCO4 (6.0 m) 

PCO6 (17 m) 

0 5 10 15 20 25 30 35 40 

EC (µS/cm) 

3800 

2800 

1800 

Compartment 

PCO3 (3.8 m) 

PCO5 (10 m) 

PCO7 (30 m) 

800 

0 5 10 15 20 25 30 35 40 

Day 

24 


FIELD STUDIES

Breakthrough curves 

● Bacteriophages 

– MS2 

– PRD1 

C (pfp/l) 

1.E+09 

1.E+08 

1.E+07 

1.E+06 

1.E+05 

1.E+04 

1.E+03 

1.E+02 

1.E+01 

1.E+00 

MS2 

Compartment 

PCO2 (2.4 m) 

PCO3 (3.8 m) 

PCO4 (6.4 m) 

PCO5 (10 m) 

PCO6 (17 m) 

PCO7 (30 m) 

– 7 days seeding 

1.E-01 

1.E-02 

1.E-03 

0 25 50 75 100 125 

C (pfp/l) 

1.E+08 

1.E+07 

1.E+06 

1.E+05 

1.E+04 

1.E+03 

1.E+02 

1.E+01 

1.E+00 

1.E-01 

1.E-02 

PRD1 

Compartment 

PCO2 (2.4 m) 

PCO3 (3.8 m) 

PCO4 (6.4 m) 

PCO5 (10 m) 

PCO6 (17 m) 

PCO7 (30 m) 

1.E-03 

0 25 50 75 100 125 

25 


FIELD STUDIES

MS2 

Inactivation 

● Mild conditions 

– near neutral pH 

C/C0 

10 

1 

Obs in peptone/saline at lab 

Linear fit: 0.0008 log10/day 

. 

Obs in compartment water at 

lab 


Obs in well water at lab 

– low temperature 

●→ First order rate decrease 

0.1 


Obs in well water at field 


0.01 

0 10 20 30 40 

Day 

PRD1 

10 

Obs in peptone/saline at lab 

1 


. 

Obs in compartment water at 

lab 


C/C0 

Obs in well water at lab 

0.1 


Obs in well water at field 


0.01 

0 10 20 30 40 

Day 

26 


FIELD STUDIES

Modeling breakthrough curves 

C (viruses/l) 

C (viruses/l) 

10000000 

100000 

10000000 

100000 

1000 

1000 

10 

0.1 

10 

0.1 

MS2 - Well PCO2 at 2.4 m 

0 20 40 60 80 100 120 140 

Day 

MS2 - Well PCO3 at 3.8 m 

Observation 

One-site model 

Two-site model 

0 20 40 60 80 100 120 140 

Day 

Observations 

One-site model 

Two-site model 

Rate coefficients one site two sites 

(day -1 ) 

katt1 4.1 4.2 

kdet1 0.00087 0.00079 

katt2 0.47 

kdet2 0.54 

µ s1=µ s2 0.085 0.085 

Goodness of fit 75% 79% 

Rate coefficients one site two sites 

(day -1 ) 

k att1 3.2 3.2 

k det1 0.0016 0.0022 

k att2 0.17 

k det2 0.24 

µ s1 =µ s2 0.092 0.092 

Goodness of fit 77% 80% 

27 


FIELD STUDIES

Deep well injection study 

● Redox-zones: Attachment to iron oxyhydroxides in O 2 

-zone 

m-Field Level 

- 250 

PP.1 

WP.1 

WP.3 

IP.2 

WP.2 

WP.4 

- 260 

6 

- 270 

- 280 

- 290 

- 300 

- 310 

- 320 

- 330 

- 340 

2 

5 

5 

5 

2 5 

3 

2 

2 

4 

2 

2 

5 

4 

4 

4 

4 

4 

4 4 4 

4 

4 

2 

6 

6 

6 

6 

6 

6 

8 

8 

3 

3 

8 

3 

3 

10 

8 

3 

8 

1 

10 

8 

10 

12 

10 

2 

2 10 

2 

2 

2 

10 

12 

12 

clay, loam 

fine sand 

screens 

coarse sand 

temperature sensor 

n 

12 

12 

1 

12 

1 1 

(1) 

1 

1 

98 38 

8 

0 

12 

22 

[distance to IP.2;m] 

[distance to IP.2;m] 

71477 R 03 

28 


FIELD STUDIES

Soil passage effectively removes viruses 

● 8 log 10 

removal (non-linear with distance) 

– After 25 days (30 m) dune passage 

– After 40 days (38 m) deep well injection 

0 

Removal 

Log 10 (C/C 0 ) 

-2 

-4 

-6 

MS2 - dune recharge 

PRD1 - dune recharge 

MS2 - deep well injection 

PRD1 - deep well injection 

-8 

-10 

0 10 20 30 40 

Travel time [days] 

29 


FIELD STUDIES

Removal processes during soil passage 

● Effective virus removal if sites for attachment are 

present (mostly iron hydroxides; sticking efficiency α∼10 -3 ) 

0 

● Virus population 

heterogeneity? 

Virus removal 

Log 10 (C/C 0 ) 

-2 

-4 

-6 

MS2 - dune recharge 

PRD1 - dune recharge 

MS2 - deep well injection 

PRD1 - deep well injection 

-8 

● 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 

0 10 20 30 40 

Travel time [days] 

30 


FIELD STUDIES

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 water 

from surface water and vulnerable groundwater 

● Index pathogens 

– Enteroviruses, Campylobacter, Cryptosporidium, Giardia 

31 


QMRA

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) 

Index pathogens 

Indicator organisms 

Enteroviruses 20-200 nm Bacteriophages 20-60 nm 

Campylobacter 1-2 µm E.coli 1-2 µm 

Cryptosporidium 5-6 µm Spores of sulphite 

Giardia 8-10 µm reducing clostridia (SSRC) 1 µm 

● 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 

32 


QMRA

QMRA from surface water to drinking water 

● C sw 

= Pathogen concentration in source water [N/liter] 

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

● Z = Fraction of microorganisms passing treatment [-] 

● C dw 

= Pathogen concentration in drinking water [N/liter] 

● V = Consumption of unboiled drinking water [liter] 

● P m 

= Infectivity of pathogen [-] 

● P inf 

= Infection risk [per person per day or year] 

● P inf,day 

= C sw 

x 1/R x Z x V x P m 

365 

● P inf,year 

= 365.25 x P inf,day 

or P = 1− 

− P 

inf, year 

1 

i= 

1 

∏( ) 

inf, dayi 

● Drinking water companies: point estimates (average values) 

● RIVM: Monte Carlo simulations (variability) 

33 


QMRA

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, C s 

● Setback distance r s 

and travel time T determine size of protection 

zone, which is the soil barrier 

● Z = fraction of pathogens 

able to pass the soil barrier 

P inf 

= C s 

x 1/R x Z x V x P m 

≤ 10 -4 

34 


QMRA

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 protection 

for a maximum infection risk of 10 -4 p -1 y -1 ? 

35 


GROUNDWATER PROTECTION

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 log 10 

/day 

● Dilution in groundwater 

– Pumping rate Q W 

at well 

36 



Steady state model 

⎛ C ⎞ 

A 

1 ⎛ 3 5/3 1 2⎞ 

log ⎜ 

⎟ 

10 

= log10 

Z = − ⎜ αk1R 

+ µ 

lk2R 

⎟ + log 

⎝ C0⎠ 

2.3⎝ 

5 2 ⎠ 

Removal = Attachment + Inactivation + Dilution 

C A 

is virus concentration at well 

C 0 

is virus concentration in wastewater 

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

µ l 

is the inactivation rate coefficient = 0.01 log 10 

/day 

k 1 

en k 2 

physical constants 

q is leakage rate of sewage pipe 

Q is abstraction rate of groundwater 

R is radial distance sourcewell 

10 

⎛ 

⎜ 

⎝ 

q 

Q 

⎞ 

⎟ 

⎠ 

● QMRA: p inf 

= C 0 

x Z x V x p m 

≤ 10 -4 

37 



Monte 

Carlo 

Simulations 

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 α=10-5 Temperature Protection zone 1-2 years 

38 



Sensitivity analysis 

● Size of protection zone most sensitive to inactivation and attachment 

Parameter 

Attachment α 

Parameter 

value 

R 95 (m) 

T 95 (day) 

T 95 (year) 

10 -5 231 603 1.7 

10 -4 132 215 0.6 

10 -3 47 29 0.3 

0.01 

280 

859 

2.4 

Inactivation µ l 

(day -1 ) 

0.1 

0.4 

105 

55 

109 

29 

0.3 

0.08 

39 



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 then 

protection zone may be overestimated 

40 



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] 

41 



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 log 10 

/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) 

42 



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 

– z t 

=top of well screen 

– z b 

=bottom of well screen 

43 



Model development 

● Vulnerability parameters 

– Virus+aquifer properties 

● Dimensionless model 

– Model parameters are dimensionless 

– Lower number of model parameters 

● Numerical calculations (FlexPDE) 

– Calculate r s* 

= dimensionless setback distance 

to achieve a required virus removal 

● Empirical formula 

– Fit a formula to values of r s* 

as a function of the vulnerability 

parameters 

● r s* 

= dimensionless setback distance = vulnerability index 

– Different combinations of the vulnerability parameters leading to 

the same virus attenuation have the same r 

* 

s 

r * 

1 

0 

-1 

-2 

-3 

æ 

æ 

à 

à 

æ 

æ 

àà æ 

æ 

àààààà æ ææ æ 

æ 

æ 

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-2 -1 0 1 2 3 

l * 

æ 

æ 

æ 

æ 

à 

æ 

æ 

æ 

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44 



Model domain 

Well screen 

C * =10 -8 

Q 

r s * = r s 

/H 

Vulnerability index 

* 

Setback distance 

Contamination 

source 

H/H=1 

● 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 H 3 /Q 

45 



Radial water flow under steady state conditions 

● Governing equation 

k 

z 

2 

∂ h 

2 

∂z 

– where, t [T] is the time, h [L]is the hydraulic head, k r 

[LT -1 ] is the 

hydraulic conductivity in the r-direction and k z 

[LT -1 ] is the 

hydraulic conductivity in the z-direction 

+ 

k 

r 

r 

∂ 

∂r 

∂h 

r 

∂r 

= 

0 

● Dimensionless flow equation 

1 

m 

2 

∂ h 

∂z 

* 

*2 

+ 

1 

r 

* 

∂ 

∂r 

* 

⎛ 

⎜r 

⎝ 

* 

∂h 

∂r 

* 

* 

⎞ 

⎟ 

⎠ 

= 

0 

– Division of governing equation by k r 

and scaling to H [L] which is 

the total thickness of all aquifer layers 

46 



Virus transport 

● Governing equation 

v 

z 

∂ 2 

C ∂C 

∂ C 

+ vr 

− Dzz 

− 

1 

2 

∂z 

∂r 

∂z 

r 

∂ 

∂r 

⎛ 

⎜ 

⎝ 

D 

rr 

r 

∂C 

∂r 

⎞ 

⎟ 

⎠ 

= −λC 

– where, v r 

and v z 

are the vertical and radial pore water velocities 

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

attachment and inactivation. 

– D rr 

≈α r 

v r 

and D zz 

≈α z 

v z 

[L 2 T -1 ] are the dispersion coefficients in r and 

z directions. 

● Dimensionless virus transport equation 

v 

∂ 

∂z 

∂ 

∂r 

∂ 

∂z 

* 

* 

2 * 

* 

* C * C 

* * C 1 * * * C 

* * 

z 

+ v 0.1 

v 

v r 

C 

* r 

− α 

* 

r r 

− α 

*2 * r 

⎜ 

* r 

⎟ = −λ 

* 

r 

∂ 

∂r 

⎛ 

⎜ 

⎝ 

∂ 

∂r 

⎞ 

⎟ 

⎠ 

47 



Parameter 

Description 

* * 

A = 2r 

l 

Leakage area 

s 

s 

s 

Dimensionless 

parameters 

48 

Varied in numerical simulations 

* A 

Cross sectional area of the screen of the abstraction well 

w 

Aw 

= 

2 

πH 

* r 

* 

α = α 

r 

0.005rs 

H = 

Dispersivity in the r -direction. 

* α 

* 

Dispersivity in the z -direction 

z 

α 

z 

= = 0.1α 

r 

H 

* C 

Virus concentration with C 

R 

[L -3 ] the concentration at the 

C = 

abstraction well at R [L] from the source of contamination. 

* 

C 

s 

C R 

Virus concentration at the contamination source 

* h 

Aquifer thickness 

h = 

H 

πH 

2 πH 

Horizontal hydraulic conductivity, 

* 

kr 

= kr 

= ∑tri 

Q Q 

where tr 

i 

[m 2 day -1 ] is the transmissivity of i-th aquifer layer. 

3 

* nπH 

Dimensionless removal rate coefficient, 

λ = λ 

Q 

k 

Anisotropy ratio 

r 

m = 

k 

z 

* q 

Dilution, where q = 1 m 3 day -1 (Schijven et al., 2006). 

Q = 

Q 

* r * z 

Radial and vertical coordinate 

r = , z = 

H H 

2 

2 

* nπH 

* nπH 

Radial and vertical pore water velocity 

vr = v r 

, vz 

= vz 

Q 

Q 

* zb 

* z Bottom and top of the well screen 

t 

zb 

= 1− 

, zt 

= 1− 

H H 



Numerical simulations (FlexPDE) 

● Dutch groundwater database 

– Dimensionless parameter values of 35 unconfined aquifers 

– λ=0.03 day -1 (α =10 -5 , µ l =0.01 log 10 /day) 

Dimensionless parameter Mean Min Max Values for numerical simulation 

λ* removal rate coefficient 45 0.79 645 0.01, 0.1, 1, 10, 100, 1000 

Q* dilution factor 0.00012 0.000037 0.0019 0.0001, 0.001 

k r * horizontal hydraulic conductivity 500 4.4 6900 10, 100, 1000 

m anisotropy factor 1.6 1 3.5 1, 2, 5, 10 

z t * top of well screen 0.72 0.31 1 1, 0.85, 0.75, 0.5 

z t *-z b * length of well screen 0.43 0.042 0.82 025, 0.5 

H (m) aquifer depth 116 23 334 - 

C s * virus source concentration 10 4 …10 8 

● 212 cases simulated 

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

● No effect of k r * 

● Fit r s * to vulnerability parameters 

49 



First fitting step: If z t* 

=1 (horizontal transport) 

● Numerical simulations => 

Linear relation lnr s * and lnλ * 

● Steady state solution, 

neglecting dispersion 

ln r 

* 

s 

1 

= ln ln 

s 

Q 

2 

1 

2 

[ 

* *] * 

C + ln − ln 

r 

* 2 

s 

= 

λ 

C 

Q 

* * 

s 

* 

λ 

* 

● Fit data to 

ln r 

● R 2 =99.9% 

● a 1 = 0.557 

● a 2 = 0.467 

● Empirical formula 

[ 

* *] * 

C + lnQ 

a ln 

* 

s 

= a1 

ln ln 

s 

+ 

r 

* 

s 

2 

λ 

[ 

* * 

( )] 0.557 * −0. 

467 

ln C Q 

= λ 

s 

50 



Second fitting step: If z t *

Empirical formula 

r 

* 

s 

= 

( ) − ⎡ 

− − * 2.19 * 

* * 0.557 * 0.467 * 0.227 * 0.383 −1.17 

zt 

1.64 

* 

* 

lnC 0.207( −1) [ 0.529 − 2.99 ] * ⎤ 

sQ 

λ Exp Cs 

Q λ m zt 

Exp zt 

zb 

⎥ ⎦ 

⎢⎣ 

● R 2 =97.9% 

52 



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 

53 



GWPCalc 

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 

screen 

Aquifer 

thickness H 

Required removal: 

Source 100 vir/L=> 

8 log 10 

removal=> 

Groundwater 10 -6 vir/L=> 

Infection risk

Example 0 

● 

● 

Unconfined / shallow / well screen high 

Most sensitive aquifer thickness, pumping rate 

and removal rate coefficient 

55 


GWPCalc

Example 1 

● 

● 

Unconfined / less shallow / well screen high 

Most sensitive aquifer thickness, pumping rate 

and removal rate coefficient 

56 


GWPCalc

Example 2 

● 

● 

Unconfined / less shallow / well screen deep 

Also sensitive to changes in anisotropy 

57 


GWPCalc

Example 3 

● 

Confined / less shallow / well screen deep 

58 


GWPCalc

Example 4 

● 

● 

● 

Well screen crosses a confining layer 

Virus transport in upper aquifer 

Dilution with water from lower, clean aquifer 

59 


GWPCalc

Conclusions 

● GWPCalc is a tool with a quickand-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 

60 


GWPCalc

QUESTIONS? 

● GWPCalc is for free 

● QMRAspot@rivm.nl 

● Jack.Schijven@rivm.nl 

61 Field Studies and Groundwater Protection | Feb 2012

GWPcalc, the Ground Water Protection Calculator - KSCST

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