Development of multi-functional measurement devices for vadose zone characterization

Jan HopmansUniversity of California, Davis, CA, USA

Yasushi MoriShimane University, JapanAnnette Pia MortensenGeological Institute, Copenhagen University, DenmarkGerard KluitenbergKansas State UniversityCarlos VazEMBRAPA, Sao Carlos, BrazilKeith BristowCSIRO, Townsville, Australia

SOIL PROPERTIES ARE NOTORIOUSLY HETEROGENEOUS, IN BOTH SPACE AND TIME

QUESTIONS:Measurement Scale ????Measurement Types ???

Measurement Instruments ??Measurement Locations ???Measurement Times ??????

Vent Tube

PVC Dowel

Rubber Septum

Sampling Tube

Sample Bottle

Rubber Stopper

PVC Pipe

Porous Ceramic Cup

Acrylic Tube

Plug

Copper Tube

MULTI-FUNCTIONAL instruments, ensuring identical measurement volumes

Combined tensiometer-solution sampling probe

Vent Tube

PVC Dowel

Rubber

Sampling Tube

Sample Bottle

Rubber

PVC Pipe

Porous Ceramic Cup

Acrylic Tube

Plug

Copper Tube

Tensiometer

Soil Solution Sampling

Coiled Cone Penetrometer-TDR Probe

o Two parallel copper wires are wrapped around inner core (as double helix);

o Wires are connected to conductor and ground ofcoaxial cable;

o Signal is analyzed by cable tester;o Long wire length (about 30 cm) ensures accurate

travel time measurement,and

o Narrow wire spacing ensure high depth resolution

tip (steel)2.4 cm

parallelwires(steel)

Hammer penetrometer

Calibration

0.0 0.1 0.2 0.3 0.42

3

4

5

6

7

8 Columbia Yolo Sand Fit Columbia Fit Yolo Fit Sand Polynomial fit Yolo

ε coil

θ (cm3cm-3)

0.0 0.1 0.2 0.3 0.40

2

4

6

8

10

12

14

16

18

r2 = 0.72RMSE = 0.98

1.25

1.35

1.45

1.55 g cm-3 1.2 to 1.3 g cm-3

1.3 to 1.4 g cm-3

1.4 to 1.5 g cm-3

1.5 to 1.6 g cm-3

equation [3]

Pene

tratio

n R

esist

ance

(MPa

)

Water Content (cm3cm-3)

Field development, Brazil

Combined Tensiometer-TDR

0 5 10 15 20 25

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

water

sat. glass beads

dried glass beads

Refle

ctio

n Co

effic

ient

Time (ns)

Laboratory Calibration

0.0 0.1 0.2 0.3 0.4 0.5

8

10

12

14

16

18

20

22

24 Oso Flaco Ottawa SRI Columbia Lincoln

ε coil

Soil Water Content (cm3cm-3)

A heat pulse probe?

Instrumentation in the vadose zoneTDR – Time domain reflectometryTensiometersTracer experiments

Heat pulse probe – multifunctionalApply heat as tracerHeat, water and solute transport

Multifunctional heat pulse probe

Temperature, T

Thermal propertiesHeat capacity, CHeat conductivity, λ0

Thermal diffusivity, κHeat dispersion, D

Hydraulic propertiesWater flux, qw

Water content, θElectrical conductivity, ECa

same time+

same place+

same scale

same time+

same place+

same scale

Heat pulse probe design

6 needles1 mm diameter6 mm spacing28 mm long25 mm wide

Heat pulse

heater thermistor

Electrical conductivity

Wennerarray

I. Multi-step outflow experiment

Heating

Four-electrode

Thermistor

Sensitometer and Outflow

Datalogger CR10

Datalogger CR10

MFMF--HPPHPP

Multi-plexerAM416

Multiplexer AM416

Heating

Four-electrode

Thermistor

Sensitometer and Outflow

Datalogger CR10

Datalogger CR10

MFMF--HPPHPP

Multi-plexerAM416

Multiplexer AM416

Tensiometer

I. Analytical solutions of heat transport

De Vries (1952)- Thermal Conduction

( ) ( ) 0

2

0

2

;444

', ttt

rEitt

rEiC

qtrT >⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛κ

−−⎟⎟

⎠

⎞⎜⎜⎝

⎛−κ

−κπ

=∆

Ren et al. (2000) – Thermal Convection

( )0

21

0 44tt;ds

ssVrexps

CqT

t

tthd

d >⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧ −−

′=∆ ∫ −

−

κκπ

( )0

21

0 44tt;ds

ssVrexps

CqT

t

tthu

u >⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧ +−

′=∆ ∫ −

−

κκπ

II. Experimental flow column

multiplexerAM416

tensiometer and pressure transducer

datalogger CR10

HPP

multiplexerAM416

rainmakingdevicepump

II. Numerical solution heat transport

Heat conduction and convectionHomogenoues and isotropic mediaThermal equilibrium between phases

z

Waterflow

H

U

D

Tr

r

x

2 2

2 2w

wb

CT T T TVt x z C z

κ θ⎛ ⎞∂ ∂ ∂ ∂

= + −⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠

s (1 )bulk wC C Cφ θ= − +

w w w wh

bulk b

C q C VVC C

θ= =

Fitting of temperature response curve

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80 100 120

Time [s]

Tem

pera

ture

diff

eren

ce [C

]

Downstream Upstream Transverse

Parameters

Thermal conductivity λWater content θWater flux qw

Fitting

I. Analytical solutionII. Numerical solution

(HYDRUS 2D)

I and II: Calibration of MF-HPP

Needle distance, rCalibration in agar solution

heat capacity for water

no convective heat transport

Calibration in porous mediaheat capacity for materialsaturated conditions

Wenner arrayCalibration in porous media

varying EC and water content

0.0

0.2

0.4

0.6

0.8

0 20 40 60 80 100

Time [s]

Tem

pera

ture

diff

eren

ce [K

]

0

1

2

3

0 0.1 0.2 0.3 0.4 0.5θ by MFHPP (m3 m-3)

EC

b (dS

m-1

)

0.03 M0.06 M0.10 MFitted

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5Volumetric water content (m3 m-3)

-Mat

ric h

ead

(cm

)

0.03 M0.06 M0.10 M

-9

-8

-7

-6

-5

-4

Log 1

0 Hyd

raul

ic c

ondu

ctiv

ity (m

s-1

)

I.Unsaturated hydraulic functions

0

20

40

60

80

100

120

140

160

180

0 20 40 60 80Time (hours)

Cum

ulat

ive

outfl

ow (c

m3 ) a

nd -m

atric

hea

d (c

m) Cumulative outflow

Matric head

Inverse Modeling of Multi-step Outflow

I and II. Estimation of thermal conductivity, λ( heat conduction only)

0.0

0.4

0.8

1.2

1.6

2.0

0.0 0.1 0.2 0.3 0.4

Water content [cm3/cm3]

Ther

mal

con

duct

ivity

λ

[W/m

K]

Mortensen et al. [2003]Mori et al [2003]Hopmans and Dane [1986]

Thermal conductivity

Thermal diffusivity

502100

.θθλ bbb ++=

bulkC/0λκ =

II. Solute transport

Electrical conductivity

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60

Time [min]

EC

[mS/

cm]

θ=0.37

θ=0.32

θ=0.22

θ=0.20

v=0.0036 cm/s

Ψ=20 cm

solidwaterbulk ECECEC += )(θτθ

I and II: Estimation of water content, θ(Heat conduction only)

0.00

0.10

0.20

0.30

0.40

0.00 0.10 0.20 0.30 0.40

Estimated water content

Rea

l wat

er c

onte

nt

0.00

0.10

0.20

0.30

0.40

0.00 0.10 0.20 0.30 0.40

Estimated water content

Rea

l wat

er c

onte

nt

0.00

0.10

0.20

0.30

0.40

0.00 0.10 0.20 0.30 0.40Estimated water content (m3m-3)

Rea

l wat

er c

onte

nt (m

3m-3

)

StaticTransient

19.8

20.0

20.2

20.4

20.6

20.8

21.0

21.2

0 25 50 75 100

Time (s)

Tem

pera

ture

(o C)

No Flow

1 m/d, downstream needle

1 m/d, upstream needle

10 m/d, downstream needle

10 m/d, upstream needle

(B)

Water flux effect on temperature signature

I and II: Estimation of water flux, qw(heat conduction and convection)

Accurate range: 0.0001 to 0.01 cm/s or 10 to 1000 cm/day

0.E+0

1.E-5

2.E-5

3.E-5

4.E-5

5.E-5

6.E-5

7.E-5

8.E-5

0.E+0 1.E-5 2.E-5 3.E-5 4.E-5 5.E-5 6.E-5 7.E-5 8.E-5

Estimated flux [m/s]

Rea

l flu

x [m

/s]

Unsaturated Saturated

Water content error for high water fluxes

However, these high water fluxes only occur under saturated conditions

Dispersivity = 0

19.9

20.1

20.3

20.5

20.7

20.9

0 10 20 30 40 50 60

Time (s)

Tem

pera

ture

(o C) Downstream

UpstreamTransverse

Dispersivity = 0.001

19.9

20.1

20.3

20.5

20.7

20.9

0 10 20 30 40 50 60

Time (s)

Tem

pera

ture

(o C) Downstream

UpstreamTransverse

Dispersivity = 0.01

19.9

20.1

20.3

20.5

20.7

20.9

0 10 20 30 40 50 60

Time (s)

Tem

pera

ture

(o C)

DownstreamUpstreamTransverse

Dispersivity = 0.1

19.9

20.1

20.3

20.5

20.7

20.9

0 10 20 30 40 50 60

Time (s)

Tem

pera

ture

(o C) Downstream

UpstreamTransverse

Thermal dispersion effect on temperature signature (qw = 1 m d-1)

Conclusions

AdvantagesSimultaneous measurement of water flow, solute and heat transport properties within the same sample volume

LimitationsIn situ calibration of probeSensibility to needle spacingAccurate water flux range is limited to 10 - 1000 cm/day

Future workCompare heat and solute dispersivitiesImprove for water flux density < 10 cm/dayField applications

Are being developed, that

Measure approximately same volumes,

BUTIssues of probe-soil contact

Measurement interferences

What is real measurement volume, contributing to the measurement???

Multi-Functional Sensors:

SENSOR

REV (Bear) or Relativist Concept (Baveyeand Sposito, 1984) ????

Spatial weighting

function, ω:

( , , ) 1V

x y z dVω =∫

( , , ) ( , , ) ( , , )mac micV

x y z x y z x y z dVθ ω θ= ∫