Streamline-Based Simulation of Cryptosporidium Transport in

Riverbank Filtration

Reed M. Maxwell1Claire Welty2

Andrew F.B. Tompson11Environmental Science Division

Lawrence Livermore National Laboratory

2Center for Urban Environmental Research and Educationand

Dept. of Civil and Environmental EngineeringUniversity of Maryland, Baltimore County

Objectives

• To evaluate the influence of geologic heterogeneity on field-scale microbial transport

• To incorporate any pattern of heterogeneity at any scale

• To investigate microbial transport in a simulated realistic heterogeneous setting

• To understand differences between heterogeneous microbial transport and heterogeneous solute transport

• To provide information about effectiveness of microbial filtration in a realistic setting

General Pathogen Transport Processes

kattkdet

Attached Microbe

Free Microbeadvection

attachment/filtration detachment

kds

kdc

inactivation/non-viability

inactivation/non-viability

Solid Surface

Free Microbes (C)

Attached Microbes (S)

advection dispersioninactivation

attachmentdetachment

Colloid Filtration(Rajagopalan and Tien, 1976; Martin et al, 1996; Logan et al., 1995)

katt = 32

(1−θ)d

αcη⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

vi

ρb

ρθ∂S∂t

= −kds

ρb

ρθS + kattC − kdet

ρb

ρθS

∂C∂t

= − ∂∂xi

(viC) + ∂

∂xiD

ij∂C∂xj

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟

− kdc

C − kattC + kdet

ρb

ρθS

Governing local-scale equations

Spatial Variability of Hydraulic Conductivity (K)

λ1λ3

num

ber

-5 -4 -3 -2 ln(K)

60

40

20

ln(K)

σlnK

Statistical Characterization of Heterogeneity

δ1 residual

Correlation of Colloid Parameters with Soil Type

αc

ln(K)

b1

1

•

•

••

••

••

•

•

••

αc = a1 + b1lnK + δ1η= f(lnK, vi)

Correlations explored:•Rehmann, Welty and Harvey, WRR, 35(7), 1999•Ren, Packman and Welty, WRR, 36(9), 2000•Blanc and Nasser, Water Sci &Tech, 33,1996•Harter and Wagner, ES&T, 34, 2000

-300

-225

-150Ele

vati

on

(ft

)

5000

x (ft)

15000y (ft)

-75

0

75

0

0.5

1

050100150200250Travel Time, Tau [days]

SL C

once

ntra

tion

[-]

0

50

100

150

200

250

1112131415161

Node Number [-]

Trav

el T

ime

[day

s]

τ =180 days τ =0

RiverWell

•Streamlines are mapped and used to determine origin, travel time, travel pathway and flux of water entering a well screen•Forward colloid transport simulated along each streamline using finite-difference 1-D grid: advection terms solved explicitly via high-order TVD algorithm, attach/detachment terms solved implicitly•Concentrations are mapped from each 1-D streamlines onto the 3-D grid•Breakthrough curves at the well are flux-averaged across all streamlines

Well

River

Streamline Modeling Approach

Orange County Case Study

• Domestic supply for over 2 million residents• Seek increased reliability

• augment uncertain imported supplies• hedge against growth and increased demand• protection from earthquake interruption of

surface deliveries• Now:

Active infiltration of Santa Ana River and imported water in Forebay recharge basins (equals 3/4 of annual extraction)

• Future: Supplemental recharge provided from recycled

(waste) water

Primary regulatory concerns focused on water quality implications

• Water Quality Issues• longevity of

microbiological elements in subsurface

• increase of TDS from cyclic recharge

• impacts of other organic contaminants

• Management Balances• tertiary

treatment/disinfection• wetlands development• groundwater

impacts/natural attenuation

• emerging regulatory framework

Correlated lithology indicator functions generate conditioned realizations of material categories

Carle, 1996

• Discrete representation• Honors borehole lithologies • Assume lithology categories

correlate to permeability• Representation of geologic

structure is more realistic– less bias toward high

permeability values– recreate measured transitional

probabilities between facies– recreate volumetric abundance

of individual categories – recreate representative length

scales of individual categories • Generate nonunique, equally

probable “realizations”

Tompson, Carle, Rosenberg and Maxwell, WRR 35(10), 1999.

3D Geologic Model

Reverse Streamline Traces

K

Recharge Well Locations

Predicted Mean Water Age:P5: 1.4 yr

P6: 11.9 yrP1: 0.41 yrPL4: 0.89 yr

K

1E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

0.1 1 10 100

Time [y]

C/C

0[-]

P1

P6 C/C0<1E-100

PL4

P5

Comparison among wells

Colloid breakthrough very different in character than tracer breakthrough

Tracer Transport Colloid Transport

Ren et al. correlations, 2000.1E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

0.1 1 10 100

Time [y]

C/C

0[-]

P1

P6

PL4P5

Breakthrough curves for tracer, colloids, PRD1, C.parvum- Wells P1, PL4

0

0.5

1

0 5 10 15

Time [y]

C/C

0[-]

Ren et al.- Colloid

Conservative Tracer

PL4

P1

1E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

1 10 100

Time [y]

C/C

0[-]

Ren et al. correlations

Rehmann et al. correlations

PL4

P1

Colloid

PRD1Colloid

PRD1

C. parvum C/C0<10-25

Comparing Two Streamlines

0

500

1000

1500

2000

2500

3000

0 300 600 900

Travel Time, Tau [day]

SL

Pat

h Le

ngth

[ft]

0.1

1

10

100

1000

K [f

t/d]

La Habra FmAlluvium

SL 1484, P6 B

0

500

1000

1500

2000

2500

3000

0 300 600 900

Travel Time, Tau [day]

SL

Path

Len

gth

[ft]

0.1

1

10

100

1000

K [f

t/d]

La Habra FmAlluvium

SL 259, P1 A

Same travel time, much different travel distancesDifferent amount of time spent in different formations

Comparing Two Streamlines, Transport

• Same travel time, much different travel distances

• Different time/location of filtration

0.0

0.2

0.4

0.6

0.8

1.0

0 250 500

Travel Time, Tau, [d]

C/C

0 [-]

0

20

40

60

80

100

120

Atta

ched

Col

loid

Mas

s Fr

actio

n, S

[µ

g/g]

P6-ColloidFree

P1-ColloidFree

P1-Tracer

P6-Tracer

P6-ColloidAttached

P1-ColloidAttached

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000 2500 3000

Streamwise Travel Distance [ft]

C/C

0 [-]

0

20

40

60

80

100

120

Atta

ched

Col

loid

Mas

s Fr

actio

n, S

[µ

g/g]

P6-ColloidFree P1-Colloid

Free

P1-Tracer

P6-Tracer

P6-ColloidAttached P1-Colloid

Attached

Summary

• 1D streamline approach is presented for carrying out microbial transport simulations in a large, heterogeneous 3D domain

• In high-K layers, microbes may behave as a conservative tracer

• K variability significantly affects colloid filtration • The postulated correlation between lnK and αc is very

sensitive to parameterization (slope)• Shallow wells may be more vulnerable to microbial

contamination than deeper wells (low-k unit)• C.parvum was greatly filtered due to large particle

diameter and filtration correlations

Maxwell, Welty and Tompson, Advances in Water Resources 26(10):1075-1096, 2003

Future Work

• Better model for correlation of C.parvum parameters with hydraulic conductivity

• Integrated Microbial Risk Assessment Framework

Portions of this work were conducted under the auspices of the U. S. Department of Energy by the University of California, Lawrence Livermore National Laboratory (LLNL) under contract W-7405-Eng-48.