Estimation of characteristic relations for unsaturated flow through rock fractures

 

Jerker Jarsjö

Department of Physical Geography and Quaternary Geology, Stockholm University, 106 91 Stockholm, Sweden.

jerker.jarsjo@natgeo.su.se

Areas of fundamental research

(1) Characteristics of multiphase flow in fractured rock under different ambient conditions

(2) Dependence on quantifiable fracture characteristics (aperture distribution, connectivities)

(3) Multiphase flow in soil and fractured rock: Similarities and differences. -Are parameter translations of characteristic curves possible?

Relevance?

Useful for prediction of…• Conductivity of gas or non-aqueous phase liquids (NAPLS) in

fractured media

• Immobilization and trapping of NAPLS in fractured media

Application examples:• Storage of waste /oil in bedrock

• Storage of carbon dioxide storage in deep saline aquifers and potential return flows

• Movement of accidental oil spills in fractured media (Granite, karst, glaciers)

Experimental determination of pressure – saturation (- conductivity) – relations

in soil

A

B

C

D

E

Step A-E: succesively increased underpressure (-)

* S = Vw/Vtot (Vw=vol. water, Vtot=total vol.)

Water saturation, S*

atmospheric pressure

Experimental determination of pressure – saturation (- conductivity) – relations

in soil

A

B

C

D

E

Step A-E: succesively increased underpressure (-)

Water saturation, S*

atmospheric pressure

underpressure (-m.water column)

S =n

0

The water saturation is a function of the underpressure, i.e. S= S(). Straightforward to determine experimentally

A BC

DE

Empirical vG relation

for h<0

K(h)=Ks for h0

where , pc=capillary pressure

, n, m = fitting parameters

nmn

nnn

s

h

hhKhK

/11

2/111

1

11)(

gph c /

Empirical vG relation

for h<0

K(h)=Ks for h0

where , pc=capillary pressure

, n, m = fitting parameters

nmn

nnn

s

h

hhKhK

/11

2/111

1

11)(

Related to bubble pressure

Related to width of soil psd

m=0.5 usually assumed

gph c /

The cubic law for water flow in a fracture

• Single fractures: relation between aperture (a) and fracture transmissivity T:

3

12a

gT

a aDirection of

flow

Direction of

flow

”Cubic law”

( =density, och µ =viscosity, and g=graviational constant)

Cubic law: exact relation Cubic law: approximately true

Fracture aperture relation1 h 5 h 48 h

Darker areas=wider aperture; gas=white (SKB TR-98-17 & 01-13 )

The fracture aperture distribution (and the mean aperture) can be measured in situ or in the lab

Distribution of water and air in a fracture

Water occupies the tighter parts, and air the wider parts. Similar to the porous medium case

aperture, a

pro

ba

bili

ty d

en

sit

y f

un

cti

on

fl

n(a

)

water

gas

a cu

water

air (gas)

cut-off aperture (ac) assumption

ac =2w/ pc

Fracture aperture relationFor unsaturated fracture flow

Predict relative fracture transmissivity through consideration of the cubic law (TR-98-17)

0

lnlnln3

0

lnlnln3

lnln

),;(

),;(

),;(

daafa

daafa

pT

aa

a

aa

aacrel

c

Ts

Tus (w)

us=unsaturateds=saturatedw=water

Fitting procedure Fitted van Genuchten parameter: n_fit 2.242

_fit 1.966

0 2 4 6

0.2

0.4

0.6

0.8

1Fracture based relation (eq. 5)

van Genuchten- relation (eq. 6)

Tre

l and

Kre

l [-]

Capillary pressure, pc [kPa]

Trel=0.05

Considered T-data

Hydraulic aperture*, ah Mean aperture**, a5-1 *assuming one single fracture **assuming a/ah=1.7RFMxxx ZFMxxxx or FFMxxSec-up Sec-low Elev-up Elev-low No.PFL-f ST:PFL-F (cubic law)RFM029 FFM02 102 203 –98 –199 23 1.92E-07 6.1719E-05 0.10492228RFM029 FFM01 203 216 –199 –212 0 0 0 0RFM029 Possible(G) 216 224 –212 –220 0 0 0 0RFM029 FFM01 224 267 –220 –262 2 7.09E-10 9.53968E-06 0.016217456RFM029 ZFMENE1192 267 285 –262 –280 2 7.79E-10 9.84383E-06 0.016734515RFM029 FFM01 285 386 –280 –380 7 4.76E-09 1.79965E-05 0.030594002RFM029 ZFMENE1192 386 412 –380 –406 0 0 0 0RFM029 FFM01 412 639 –406 –630 0 0 0 0RFM029 ZFMENE2254 639 684 –630 –674 0 0 0 0RFM029 FFM01 684 1,001 –674 –982 0 0 0 0

T-values estimated from hydraulic testing(R-07-48)

Estimation of corresponding hydraulic apertureand mean aperture

(b)

(b)

Conclusions• Simple patterns emerge from the matching of

seemingly complex curves • Fracture roughness related to the n-value of the

van Genuchten-formulation: the rougher the fracture, the lower the matching n-value

• Implies that characteristic curves derived from measurable aperture statistics can be described with soil-based van Genuchten parameters (standard description in most computer codes)

Geological storage in deep saline aquifers

Quaternary

CO2 injection

Geological CO2 storage

Rock fractures (potential escape route)

1500 m

Feasable if return flows are sufficiently small (min 95% retained after 100 years)

Cap rock:confining unit –low permeability

Storage formation:high permeability high porosity

Storage potential in Sweden and investigation site

Target: sandstone aquifer at 1670 m depth

Representation in the TOUGH2 code

Stratigraphic uncertainty

Parameter value uncertainty

…confidence interval for k

Uncertainties addressed through scenario analyses

+ simulations for different injection pressures

Considered scenarios:

A) Base case

B) No upper barrier (thin claystone layer not continuous)

C) High permeability (95% confidence limit)

D) Combination B+C

Resulting plume migration (1000 days)

Volumetricgas saturation [-]

Salt precipitation – injectivity effects

Permeabilityreductionfactor k/k0 [-]

Summary of plume behaviour

Summary of plume behaviour

Conclusions

Stratigraphic uncertainty leads to large differences in predicted CO2 storage in target formation

Parameter uncertainty (permeability) has small impact on CO2 storage predictions but affects injectivity

Salt precipitation at the border of the target formation affects CO2 injectivity

At low injection rates, salt precipitates within the target formation, decreasing its storage ability

Journal reference: Chasset, C., Jarsjö, J., Erlström, M., Cvetkovic, V. and Destouni, G., 2011. Scenario simulations of CO2 injection feasibility, plume migration and storage in a saline aquifer, Scania, Sweden. International Journal of Greenhouse Gas Control, 5(5), 1303-1318.

March 15, 2012Airplane crash and kerosene spill on top of Kebnekaise mountain (Rabots glacier) Sweden

/

2101.3 m2096.3 m

PROCESSES DETERMINING THE FATE OF THE HYDROCARBON POLLUTION

Sampling of water 1/week + passive

15, 18 July traced og naftalen & PAH in Rabot jokk

13-14 July 160 mm precipitation (TRS)