1

Ratan Mohapatra 1

Tom Al 2

Ian Clark 1

1 University of Ottawa, Ottawa, Canada

2 University of New Brunswick, Fredericton, New Brunswick, Canada

Estimation of Helium diffusion coefficients [ in low permeability sedimentary rocks ]

2

Helium

• [ Second most abundant element in the solar system!]• Mass 3 and 4 amu (1amu = 1.661×10−27kg)• Atomic radius = 1.78 x 10 −10 m• Room Temp speed: 1352 m/s (4867 km/h)• 3He/4He = 1.4 x 10 −6 (Air, Standard, RA) – a useful characteristic of volatile reservoirs • Chemically inert

Helium in Crust: • [3He/4He] ~ 2 orders of mag. Lower (~0.01RA)• 3He is produced from Li• 4He is from alpha decays (e.g., from 238U)

34Hexs (ccSTP/g)

1e-8 1e-7 1e-6 1e-5 1e-4

De

pth

(m

)

0

200

400

600

8001e-6 1e-5 1e-4 1e-3 1e-2 1e-1

400

500

600

700

800

Stepwise heating

up to 550oC

DGR-1

DGR- 3, 4

DGR-2, 4 - GW *

DGR- 2

• Kincardine, Ontario• 840m Paleozoic Sedimentary sequence• Eastern limb of Michigan Basin• Low permeability• 76mm x 200 mm cores

Deep Geologic Repository for Low & Intermediate Level Nuclear Waste

Pore water age >200 My (Ord. shales)

x Rair ( where, Rair = 1.4 x 10-6 )

0.01 0.1 1 10

De

pth

(m

)

0

200

400

600

8000.01 0.02 0.03 0.04 0.05

400

500

600

700

800

Stepwise heating

up to 550 oC

DGR-1DGR-2DGR-3,4DGR-2, 4 - GW *

4

Sampling-I

Field Sampling: 1. sub coring in the field2. encapsulation in soft 10 mm copper

tubes subsequent to evacuation (~1e-2 Torr)

Concerns: • Bulk extraction of gas (components?)

Data:3He/4He = 50 to 0.02 x RA

5

Stepwise Gas Extraction

Cumulative % release of 4He

0 20 40 60 80 100

xRa

0.00

0.02

0.04

0.06

0.08

(room temperature diffusion)

1h

4h

7h9h

29h

51h

50 C

100 C

150 C 200 C 250 C

(stepped heating)

excessmeasured

DGR-1 422.40m

My1

B

A

1. DGR-1: 35 days after drilling

2. A sub core (1 cc volume) sampled in valved ss tube

3. Gas extraction at controlled time periods and temperatures

4. ~ 1 week (11 steps)

Using Neon to correct for atmospheric contamination

6

Sampling-II• Sub-coring in the lab• Degassing in vacuum• Gas released is periodically

measured * for He and Ne (3He,4He & 20Ne)

* Cleaning by hot Ti sponge and

SAES getters He and Ne separation using a

helium cryo trap that uses a CTI Cryodyne compressor

Copper tube stainless steel tube

Parent core

1. Split into 3 pieces

Sub core(0.6cm x 3 cm)

Time = 0

15 min

2. Sub-coring

3. Evacuated and sealed

7

MAPL Noble Gas Lab @ uOttawa

Stepwise Gas Extraction

Rate of Degassing = Ci / ti (i = 1, 2, 3, 4, 5)

Modeling the gas release:

8

9

A typical expt

10513_4he

0

2e-9

4e-9

6e-9

Gas r

ele

ased

[ c

cS

TP

.g-1

.s-1

]

0

5e-17

1e-16

2e-16

2e-16

Time since core split in the Lab [ s ]

0 2e+4 4e+4 6e+4 8e+4 1e+5

0.0

6.0e-12

1.2e-11

1.8e-11

4He

3He

20Ne

Curve fitting to the gas loss rates

y = ae-bx + ce-dx

Sigma Plot

Estimating Initial Gas-I

11

Room Temp Diff

Init

ial H

e Loss dur. Sampling

Step wise heat

12

• Diffusion in 3 dimensions• Cylindrical geometry (!)• Fluid phase involved (!!)

1. Diffusion Coefficients2. Estimating Initial Helium conc.

Approach• Simulation of out-diffusion experiments in 3D • Numerical model MIN3P (Mayer et al. 2002)• Parameter estimation code PEST (Doherty, 2004)

– least squares approach used within PEST to estimate tf and initial He concentration (Cinitial)

– tf combined with the known D0He provides Dp(@25 °C, D0HE = 7.5e-9 m2/s; Wise and Houghton, 1966)

– Dp combined with measured water-loss porosity provides De

13

0DD fp 0DD fwe

knownFrom PEST

valve

Head Space (45 cc)

14

Sub core out-diffusion model domain

0

0.01

0.02

0.03

0.04

0.05

0.06

00.01

0.02

Distance (m)00.01

0.02

X Y

Z

- 152064 Elements

- Element Dimensions (x, y, z; metres): 0.0003 x 0.0003 x 0.001 (in sample) 0.001 x 0.001 x 0.001 (in head space)

- Zero flux boundary around the enclosing ‘box’

-Diffusion coefficient in head space = 7.5e-7 m2/s

Sub core out-diffusion-I

0 20000 40000 60000 80000 1000000.00000002

4.00000000000004E-08

6.00000000000008E-08

8.00000000000012E-08

1.00000000000002E-07

1.20000000000002E-07

ModelMeasured

Time (sec)

He in

Hea

d Sp

ace

(mol

/L)

PEST Results

tf = 4.5e-3

Cinitial = 6.4e-5 mol/L

Therefore:

Dp = 3.4e-11 m2/s

De = 2.6e-12 m2/s

Sample 484 -an example of the good match between experimental and model results that is obtained when He behaves conservatively.

15

valve

Head Space (45 cc)

Sub core out-diffusion-II

PEST Results

No realistic result obtained

Sample 612- an example of the poor match between experimental and model results - when He behaves non-conservatively.

0 20000 40000 60000 80000 1000002.0E-08

6.0E-08

1.0E-07

1.4E-07

1.8E-07

ModelMeasured

Time (sec)

He

in H

ead

Spac

e (m

ol/L

)

16

17

Diffusion Coeff. From PEST

De (m2/s)

1e-13 1e-12 1e-11

De

pth

(m

)

400

500

600

700

800

900Diffusion Coefficients from PEST

18

Initial Helium- comparison

4He (ccSTP/g)

1e-5 1e-4

Dep

th

(m

)

400

500

600

700

800

900

PESTDegassing Rates

Large (parent) core out-diffusion

Simulation of diffusion loss from the large core assuming it is open to the air. The plot shows the estimated fraction of initial He remaining in the inner volume representing the small sub core. The simulation uses DpHe values obtained from the sub core experiments.

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

Time (days)

Frac

tion

Initi

al H

e Re

mai

ning

19

Strange cases of Diffusion

21

Summary

• Helium has been measured in very low permeability sedimentary rocks by

stepwise diffusion at room temperature followed by mild (up to 250 oC)

stepwise heating

• The diffusion data were modeled to derive helium concentrations at the

time of sample preparation in the lab

• Results obtained from 2 procedures – Degassing rates and Numerical

Simulations (MIN3P PEST) – are similar within the statistical uncertainties

• However, no meaningful diffusion data were obtained from a few samples

in which helium did not behave conservatively

• Expected helium loss in the parent core during the typical “wait times” for

the analysis, a week, is within the statistical uncertainties

Acknowledgements

• Ontario Power Generation• Nuclear Waste Management

Organisation• Intera Engineering / GeoFirma• Kamel Latoui

stock

Definitions

0fwe DD

e

a

DD

0DD fp

dd K

2

L

Le

f

Tortuosity factor:

Tortuosity:

Pore water diffusion coefficient:

Effective diffusion coefficient:

Apparent diffusion coefficient:

Rock capacity factor:

w = water-loss porosity; d = diffusion-accessible porosity; = constrictivity

25

Copper tube vs Conflat Stainless steel

4He (ccSTP/g)

1e-9 1e-8 1e-7

xR

a

1

10

100measuredexcess

Air

clamped Cu tube(87 h)

valved ss tube(59 h)

DGR-1 35.2 m

Loss rates- an observation

Time (s)

0 5e+5 1e+6 2e+6 2e+6 3e+6 3e+6

4 He

Los

s cc

STP/

g/s

-5e-9

0

5e-9

1e-8

2e-8

2e-8

3e-8

3e-8

4.01 (86) x 10 -8 ccSTP/g/s

Drilling time

DGR-2 samples Loss rates from different core samples plotted against their delay in analysis wrt to the field drilling

26