Hydraulic Conductivity Characterisation and Effects of Scale in Fractured Rock

James R. Kunkel

Outline

Hydraulic Conductivity Measurement

Scale of Hydraulic Conductivity

Conclusions

Questions

2

Hydraulic Conductivity Measurement

Methods

3

Source: USEPA, 1998 and 2001; Burbey and

Murdoch, 2010 and Burbey et al., 2011

Hydraulic Conductivity Measurement

Scale of Measurement

4

Hydraulic Conductivity Measurement

Fractured Rock Characterization Issues

5

After Marchal, Dewandel and Subrahmanyam, 2004

LEGEND

CFZ = Conductive Fractures

Zone

PFN = Primary Fracture

Network

SFN = Secondary Fracture

Network

HSFN = Horizontal Fractures of

SFN

VSFN = Subvertical Fractures

of SFN

Kx = Hydraulic Conductivity

in x-type of

fracture/material

Sx = Storativity

in x-type of

fracture/material

Hydraulic Conductivity Measurement

6

0

100

200

300

400

500

600

700

800

900

1.00E-071.00E-061.00E-051.00E-041.00E-03

Dep

th (

m-b

gs)

Hydraulic Conductivity (cm/s)

Dacite Porphyry (P1*) Dacite Porphyry (P2) Andesite Porphyry (P4*)

Diorite Porphyry Schist Unidentified

Dacite Porphyry (P1) Basalt Linear (Trend)

Lugeon Tests (Various

Fractured Rock Types) Marmato Mine, Colombia

Hydraulic Conductivity Measurement

7

Time (sec)

Norm

alize

d H

ea

d

No

rma

lize

d H

ea

d

No

rma

lize

d H

ea

d

Falling Head Tests

(Fractured Gneiss) Edgar Experimental Mine,

Colorado USA (GEGN 581)

Hydraulic Conductivity Measurement

8

0

5

10

15

20

25

30

0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 5.00E-05

Dep

th (

mb

gs)

Hydraulic Conductivity (m/s)

0

5

10

15

20

25

30

0 1000 2000 3000 4000 5000 6000

Dep

th (

mb

gs)

Seismic Velocity (m/s)

1.00E-06

1.00E-05

1.00E-04

0 1000 2000 3000 4000 5000 6000

Hyd

rau

lic

Con

du

ctiv

ity (

m/s

)

Seismic Velocity (m/s)

Downhole Seismic Surveys Source: Urban and Pasquarell, 1992

Hydraulic Conductivity Measurement

9

0.1

1

10

100

0.1 1 10 100 1000 10000

Dra

wd

ow

n (

ft)

Time Since Pumping Started (min)

Pumping Well Y-2 Observation Well Y-1 Observation Well T-1 Observation Well T-2 Observation Well T-3

Pumping Tests (Fractured Basalt) Source: Paschis, Kunkel and Koenig, 1988

Hydraulic Conductivity Measurement

10

Tracer Test (Fractured

Basalt) Source: Kunkel and Way, 1992

Hydraulic Conductivity Measurement

Scale of Hydraulic Conductivity by Measurement Method

METHOD

LABORATORY TESTING

SLUG/LUGEON TESTS

BOREHOLE GEOPHYSICS

DOWNHOLE SEISMIC SURVEYS

STRAIN-DEFORMATION SURVEYS

PUMPING TESTS

TRACER TESTS

COMPUTER MODELS

11

INC

RE

AS

ING

SC

AL

E

Scale of Hydraulic Conductivity

What is SCALE?

12

Source: Kunkel, Way and McKee, 1988

REV = Representative

Elementary Volume (of

fractured rock)

Scale of Hydraulic Conductivity

What is SCALE?

A common scale measure is distance (m)

Valid for dispersivity and perhaps storativity

A better scale measure for K is volume (m3)

Volume measures eliminate the issues of length between field and laboratory testing for slug tests vs. laboratory core test

13

Source: Schulze-Makuch and Cherkauer, 1995

Scale of Hydraulic Conductivity

14

Source: Marchal, Dewandel and Subrahmanyam, 2004

PFN = Primary Fracture Network

SFN = Secondary Fracture Network

Scale of Hydraulic Conductivity

15

Source: Schulze-Makuch and Cherkauer, 1995

Scale of Hydraulic Conductivity

K = aLn where:

K = hydraulic conductivity in appropriate units

L = a characteristic length (volume) in appropriate units

a = a fit parameter whose physical meaning is a measure of the medium-characteristic (log hydraulic conductivity of fractured rock, for example)

n = the scale coefficient

16

Source: Kunkel, Way and McKee, 1988

C

o

n

c

e

p

t

u

a

l

l

y

Scale of Hydraulic Conductivity

17

Formation Type

Scale Coefficient

n (1)

Medium Characteristic

a (2)

L Lower

Bound (3)

L Upper

Bound (3)

Porous Flow 0.51 -5.7 >1 100,000

Fracture Flow 0.96 -8.0 50 106

(1) Average scale coefficient of all data.

(2) Average medium-characteristic parameter given as log value (m/s)

(3) Upper and lower bound of the average relationships in m3 of tested formation

Scale as a Volume

Source: Schulze-Makuch and others, 1999

Scale of Hydraulic Conductivity

18

Marmato Mine, Colombia

Hydraulic Conductivity in Fractured Rock Characterisation and Scale

Hydraulic conductivity measurement in fractured rock can include direct and indirect methods, as well as methods which measure at various scales

The most common methods are direct measurement using pumping tests for far-field results and slug/Lugeon tests for near-field results

Hydraulic conductivity in fractured rock may involve identification of various flow boundaries, heterogeneities, and directional issues

19

Hydraulic Conductivity in Fractured Rock

Characterisation and Scale

Use the characterization method appropriate for the scale of the problem

Typically, an order of magnitude change in the characteristic length scale results in about an order of magnitude change in hydraulic conductivity

A REV may not exist if large-scale features such as fracture zones or barrier boundaries exist. Additionally, several REVs may be necessary to adequately characterize a mine site.

20

Hydraulic Conductivity in Fractured Rock

21

FIN

??