Transcript Permeability Fracture

Permeability
Q = KA dh
dl
where K = hydraulic conductivity
A = cross-sectional area
dh/dI = head gradient.
Hubbert (1940) showed that:
K = k(g/)
and
Fracture
Permeability
Q = e3 dh g
A 12D dl 
k = Nd2
where k = intrinsic permeability
 = fluid density
g = acceleration of gravity
 = fluid viscosity
N = a dimensionless coefficient
d = average constitutive grain diameter
where D = fracture spacing, the
average distance between parallel
regularly spaced fractures.
Lamb (1957)
The resultant dimensions of k are (length).
Darcy (1856)
Fracture System Permeability
(Parsons, 1966):
kfm =
km + e3 . Cos 
12D
and
kf =
e2  wg
12
w
where kfr = permeability of the fracture plus
intact-rock system
kf = permeability of a fracture
km = permeability of the intact-rock
 = angle between the axis of the
pressure gradient and the fracture planes.
Combined Permeability
After Duguid (1973)
Continuity Eq. For Fluid In Pores
(1-f)m Cw (dPm/dt) + (1-f)f Cw (dPf/dt) + r/w +    Vm  = 0
Continuity Eq. For Fluid In Fractures
(1-m) m Cw(dPm/dt) + (1-m)f Cw(dPf/dt) +    Vfm  = 0
Where:
< Vfm > = Kf/w, (w (dVfm/dt) + Pf)), Vm = - Km/Mw Pm
Written in Terms of
3 Components of
Dilation of the Medium
Fluid Velocity in Fractures
r = Cross-flow Term
Pressure in Matrix
Pressure in Fractures
Fluid Flow in Fractures & Matrix
After Parsons (1966)
Kfm = Km + e13 Cos A1 + …..
12 D1
e3
en 3Cos An
12 Dn
. w g
Kf = 12
w
For 1 - n Fracture Sets
Where K = Permeability
e = Fracture Width
D = Fracture Spacing
A = Angle Between Axis Of Pressure
Gradient and Fracture Planes
= Density
= Viscosity
g = Acc. Gravity
Subscripts:
m is Matrix
f is Fracture
fm is Matrix & Fracture Combined
w is Water (Fluid)
Flow in Multiple Fracture Sets
Parsons (1966) also shows that his Equation can
be expanded to incorporate multiple fracture sets:
kfm = km + a cos2+ b cos2 + . . . .
where
a=
e13 for Fracture Set 1
12 D1
and
b = e23 Fracture Set 2
12 D2
Fracture Widths
Some Published Natural Fracture Widths
Noorishad and others (1971)
Ohnishi and Goodman (1974)
Sharp and others (1972)
Snow (1968a)
Snow (1968b)
van Golf-Racht (1982)
Wilson and Witherspoon (1970)
3.0 X 10-1 cm
1.3-2.5 X 10-1 cm
1.0-5.0 X 10-2 cm
5.0 X 10-1 cm
0.5-1.5 X 10-2cm
1.0-4.0 X 10-3 cm
2.5 x 10-2 cm (mean)
Experimental Fracture Widths at 10,000 ft
(Simulated Depth)
(Number of Samples Not Statistically Significant)
Medium to Coarse Grained Sandstone
Fine to Medium Sandstone and
Crystalline Carbonates
Siltstones
Shales (Textural Term)
Chalks (Compositional and Textural Term
10-2 cm
10-1
10-4
10-5
10-1
cm
cm
cm
to 10-6 cm
In Situ Stress & Fracture Closure
kf & km with Stress
Hod Chalk,North Sea
k
(md)
Nelson (1985)
Confining Pressure (psi)
Calculated Fracture Width with Stress
e
(cm)
Nelson (1985)
Confining Pressure (psi)
Fracture & Matrix Porosity
Compressibility
Fracture Permeability Calculator
Nelson (1985)
% Fracture Permeability Plot
Nelson (1985)
% Fracture Porosity Plot
Nelson (1985)
Permeability Anisotropy from
Whole-Core
kv vs kh max
kh 90 vs kh max
Nelson (1985)
Permeability Anisotropy Map
Ryckman
Creek
WI # 6
Nelson (1985)
Permeability Features from Core Log
kh 90/kh max
Fractures
Bedding &
Fractures
kv/kh max
Strong
B&F
Bedding & Fractures
Fractures
Nelson
(1985)
Channeled Flow Along a Planar Fracture
Fracture
Surface
Secondary
Calcite
Navajo Ss
3 ft
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