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
h
Q
h
QrRT 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
L
PP 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.HDR
Location: ASPO HRL, TRUE Block Scale
Elevation: 0 Reference: Ground Surface
Date: 98-09-01
UCM 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 RA TE A N D S IN GLE PO IN T R E S IS TAN C E LO GSD E P TH S OF L E AK Y FR A C TU RE SÄ S 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 point 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
on
less
Pre
ssu
re
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 1
r rr
h
r
h
t
Exponential Integral:
p r tq
T
e
xdx
q
T
r
t
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 tq
T
t
r( , ) . log
.2 3026
4
2 2462
(MKS units)
PressureDerivative: constantdp
d 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
t
r
pT
qp
D
D
1 4
2
2
Useful Definitions
T 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 M
K 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
on
less
Pre
ssu
re
3
1
2
Integer Flow Dimensions
Linear Flow:
erfc u
Cylindrical Flow
Ei
Spherical Flow
erfc
p r tqr
Kh
e
u
p r tq
Khu
p r tq
Kru
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 2
1 2
1 2
n
n
n
n
/
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)
Lo
g D
raw
do
wn
(m
)
High Intensity, Large Fractures = High Dimension, Good Boundary Connections
Near Field Domain
DomainBoundaries
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
en
sio
nle
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
en
sio
nle
ss P
ress
ure