Hydrologic Characterization of Fractured Rocks for DFN

Models

Useful Definitions and Concepts

• Transmissivity -- Properties of a conductor (aquifer, reservoir, single fracture, fracture zone) (L2/T)

• Permeability, Hydraulic Conductivity -- Property of material inside conductor (L/T)

Definitions, continued

• Storativity -- Storage of a conductor or conducting feature (dimensionless)

• Specific Storage -- Property of material in a conductor (1/L)

• Hydraulic Diffusivity -- Ratio of T/S (L2/T)– Controls speed of propagation of pressure

effect of a disturbance– Very (!!!) important for scaling results

Overview

• Useful Concepts• Steady Flow Methods

– Packer Tests– Flow Logs

• Transient Flow Methods– Boundary effects– Dimension effects

Steady Flow Methods

• Packer Testing– Falling Head Test– Constant Pressure/Lugeon Test

• Flow Logging– Heat pulse– Spinner– Hydrophysical

Steady Radial Flow

• Pressure and flow constant

• Only exists with constant pressure boundary

• Generally under-estimates due to skin

R

rw

hQ

hQrRT w

π2)ln(

Packer Test (Fixed Interval Length)

• Used in Civil Engineering

• Testing at fixed interval lengths

• Some zones have no fractures; some zones have multiple fractures

• Efficient testing has some no flows but not too many

LPP n )ln(

10

Pn - # of no flows/# of tests

L - length of test zone

Oxfilet (Osnes Extraction of Fixed Interval Length Evaluation of Transmissivity)

• Guess T and P10 of Fractures• Oxfiet generated fracture along hole• Oxfilet calculates packer test

transmissivities• Oxfilet compares measured and

simulated pacer test transmissivities

Oxfilet Interface Data and Simulated PDF’s

Data and Simulated CDF’s

Fracture Network Stats

Packer Test Stats

Oxfilet Challenges

• Results non-unique but constrained (range of combinations of distributions of T and frequency that will fit a test

• Flow logging preferred method

Flow Log Types

• Spinner• Heat pulse• Hydrophysical• Induced electromagnetic

Spinner Hydrophysical Log(1) Replace fluid with deionized water

(2) Log fluid resistivity while pumping

UCM (Electromagnetic Log)Well Name: KI0025F02File Name: C:\WELLMAC\WELLDATA\ASPO\TRUE\KI025F02.HDRLocation: ASPO HRL, TRUE Block ScaleElevation: 0 Reference: Ground Surface

Date: 98-09-01UCM Probe:9302

Metres Flow(l/min)0 60

Temp(Deg C)16.2 16.8

Fluid_Res(ohmm)0.75 2

0

-50

-100

-150

-200

Flow

Fluid Resistivity

Temp

FLO W RATE AN D SIN GLE PO IN T R ES IS TAN C E LO GSD E P TH S OF L E AK Y FR A C TU RESÄS P Ö , K I002 5F03

1E +1 1E +2 1E +3 1E +4 1E +5 1E +6

Flo w ra te (m l/h)

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

Dep

th (m

)

1E +1 1E +2 1E +3

S in gle po int resistanc e (o hm)

12 5 .45

12 4 .65

1 33.3

1 31.1

1 28.3

Heat Pulse Log Posiva (Finland) Heat Pulse Flow Log (Äspö)

Thoughts on Flow Logging

• Cumulative logging methods fast and easy

• Discrete interval logging methods provide better detail and wide range of distribution

• Complementary temperature and fluid resistivity can be useful

Image LoggingBorehole TV (BIPS) FMI (micro-resistivity)

Hydro-Testing Work Flow

• Steady tests (flow log) to identify conductors

• Image log or core analysis to geo-logically characterize conductors

• Transient tests to characterize network away from hole

-3.00E+00

-2.00E+00

-1.00E+00

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

-2.00E+00 -1.00E+00 0.00E+00 1.00E+00 2.00E+00 3.00E+00 4.00E+00 5.00E+00 6.00E+00 7.00E+00

Dimensioness Time

Dim

ensi

onle

ss P

ress

ure

3

1

2

Transient Well Tests

Overview of Transient Tests

• Important source (most important?) of geometric information on fracture plumbing system

• Cylindrical flow and beyond• Dimensions, boundaries, and reading

derivative curves

Radial Diffusion Equation(Radial Cylindrical Flow)

1 1r r

r hr

ht

Exponential Integral:

p r t qT

ex

dx qT

rt

x

r t

( , )/( )

4 4 42 4

2

Ei -

Semilog Approximation of the Exponential Integral

Ei( u u uu u u

) . ln! ! !

........057722 2 3 3 4 4

2 3 4

p r t qT

tr

( , ) . log .2 3026

42 246

2

(MKS units)

PressureDerivative: constantdpd t(log )

Exponential Integral Function

0

2

4

6

8

10

12

14

-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

log tD

pD

0

0

1

10

100

-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

log tD

log pD

Semilog Log-Log

Derivative Methods

• Plots P/log(t)• Intent to make semi-line unambiguous• Effect is a very powerful tool to interpret

geometry from tests• Derivative is a map of transmissivity versus

distance from the well• Shape of derivative constrains network

geometry

Exponential Integral and Derivative

0.01

0.1

1

10

100

0 5 10 15 20 25 30 35

log tD

log

pD

Calculating Pressure Derivative in Spreadsheets

A B CTime Head or Pressure Change Derivative

5 2.33E-02 6.15E+016 2.47E-02 6.37E+01 3.68E+017 3.16E-02 7.38E+01 4.47E+018 3.98E-02 8.52E+01 5.27E+019 4.67E-02 9.39E+01 5.72E+01

10 5.08E-02 9.86E+01 5.78E+0111 6.32E-02 1.13E+02 6.89E+0112 7.96E-02 1.30E+02 7.95E+0113 9.46E-02 1.44E+02 8.69E+0114 9.73E-02 1.46E+02 8.23E+0115 1.03E-01 1.51E+02 154.4430288

Formula in Cell C8: t p/ t, or approximately =a8*(b9-b7)/(a9-a7)

If the derivative is noisy, calculate derivative over a larger spread, for example, at C7 calculate using rows 10 and 4

Note: Averaging deteriorates at beginning and end of data especially if a larger is used

Dimensionless Variables(Radial Cylindrical Flow)

Dimensionless Time:

Dimensionless Pressure:

tu

tr

p Tq

p

D

D

1 4

2

2

Useful DefinitionsT kh L FT

T K h L T

S c h L T M

T S L T

FT L

c L F

S S h LT MK k

t

t

s

transmissibility = (

transmissivity =

storativity = (

diffusivity (

viscosity (porosity (-)

compressibility

specific storage = ( conductivity = g

/ / )

( / )

/ )

/ / )

/ )

( / )

/ / )/

* *

5

2

2 2

2

2

2

2

Generalized Radial Flow

p r tqr

Khv u

n

n

n n( , ) ( , )

/

/

2

2 341 2

Dimension Information from Well Tests

-3.00E+00

-2.00E+00

-1.00E+00

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

-2.00E+00 -1.00E+00 0.00E+00 1.00E+00 2.00E+00 3.00E+00 4.00E+00 5.00E+00 6.00E+00 7.00E+00

Dimensioness Time

Dim

ensi

onle

ss P

ress

ure

3

1

2

Integer Flow Dimensions

Linear Flow:

erfc u

Cylindrical Flow

Ei

Spherical Flow

erfc

p r tqr

Khe

u

p r tqKh

u

p r tqKr

u

u

( , )

( , )

( , )

2

4

4

2

Linear (1-D), x-section area r0

Cylindrical (2-D)

x-section area r1

Spherical (3-D)

x-section area r2

Generalized Flow, x-section area rn-1

Log Slope and Dimension

Log Slope = = - /< <

Log Slope = = all

1 21 2

1 2

nn

nn

/For

For Log Plots of Pressure or Inverse Flow Verus Time

For Log Plots of Pressure or Inverse Flow Derivative

Boundary and Dimension Effects

1-D1-D 2-D2-D

3-D3-D

Reservoir geometryReservoir geometry Network/Flow geometryNetwork/Flow geometry

Fracture Intensity (Fracture Area/Rock Mass Volume) Can Influence Dimension

0.1

1

10

100

0.1 1.0 10.0 100.0 1000.0

Time, seconds

Hea

d, m

eter

s

0.175

0.5

.06

0.1

0.25

0.1

Boundary Effect

Geometric Information From Well Tests

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-2 -1 0 1 2 3 4 5 6 7

Log Time (s)

Log

Dra

wdo

wn

(m)

High Intensity, Large Fractures = High Dimension, Good Boundary Connections

Near Field DomainDomainBoundaries

Lower Intensity, Smaller Fractures = Low Dimension, Compartments

1.00E-02

1.00E-01

1.00E+00

1.00E+01

1.00E+02

1.00E+03

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08

Dimensionless Time

Dim

ensi

onle

ss P

ress

ure

Linear Flow

Composite Boundary

Spherical Flow

Composite Dimension

Comments on Interference Tests

• Radius of Investigation (very handy !!!)• Estimate diffusivity from response time• Independent of dimension

tr 2

Important Notes on Tests

• Transmissivity can be determined only from pumping wells in fractured or heterogeneous rock without assuming uniform flow over region of influence

• Storativity (diffusivity) can only be obtained from observation responses

• Observation wells give geometric information for areas farther from pumping source than themselves

Composite Dimension

• Dimesional Variation Reflect Local Scale versus Larger Scale Effects

• May Reflect Borehole Geometry as Well as Conductive Geometry

Parts of Composite Dimension Curves

• Early Time Effects (Wellbore Storage, Finite Borehole)

• Inner Shell (n1)• Transition (changes in area, property)• Outer Shell (n2)• Boundary Effects

Composite Interference Response

• Response depends on relative distances of transition radius and observation well radius

• Inner zone not observed for observation points near or beyond the transition radius

Rd=1, n1=1.5, n2=2.5

1E-1

1E+0

1E+1

1E+2

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08

Dimensionless Time

Dim

ensi

onle

ss P

ress

ure

Rd=85, RD1=100, n1=1.5, n2=2.5

1E-1

1E+0

1E+1

1E+2

1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07

Dimensionless Time

Dim

ensi

onle

ss P

ress

ure