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 k = Nd2 where k = intrinsic permeability = fluid density g = acceleration of gravity = fluid viscosity N = a dimensionless coefficient d = average constitutive grain diameter The resultant dimensions of k are (length) .

PermeabilityPermeability

FractureFracturePermeabilityPermeability

Darcy (1856)

Lamb (1957)

(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.

Fracture System PermeabilityFracture System 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 (dVfm/dt) + Pf)), Vm = - Km/Mw Pm

Written in Terms of3 Components ofDilation of the MediumFluid Velocity in Fracturesr = Cross-flow TermPressure in MatrixPressure in Fractures

Combined PermeabilityCombined Permeability

Fluid Flow in Fractures & MatrixFluid Flow in Fractures & Matrix

Parsons (1966) also shows that his Equation can be expanded to incorporate multiple fracture sets: kfm = km + a cos2+ b cos2 + . . . . where a = e1

3 for Fracture Set 1 12 D1 and b = e2

3 Fracture Set 2 12 D2

Flow in Multiple Fracture SetsFlow in Multiple Fracture Sets

Fracture WidthsFracture Widths

In Situ Stress & Fracture ClosureIn Situ Stress & Fracture Closure

kf & km with Stresskf & km with Stress

Hod Chalk,North Sea

Confining Pressure (psi)

k (md)

Nelson (1985)

Calculated Fracture Width with StressCalculated Fracture Width with Stress

Confining Pressure (psi)

e (cm)

Nelson (1985)

Fracture & Matrix PorosityFracture & Matrix PorosityCompressibilityCompressibility

Fracture Permeability CalculatorFracture Permeability Calculator

Nelson (1985)

% Fracture Permeability Plot

Nelson (1985)

% Fracture Porosity Plot

Nelson (1985)

kv vs kh max

kh 90 vs kh max

Permeability Anisotropy from Permeability Anisotropy from Whole-CoreWhole-Core

Nelson (1985)

Permeability Anisotropy MapPermeability Anisotropy Map

Ryckman CreekWI # 6

Nelson (1985)

kh 90/kh max kv/kh maxPermeability Features from Core LogPermeability Features from Core Log

Fractures Bedding &Fractures

Bedding & Fractures

StrongB&F Fractures

Nelson

(1985)

Channeled Flow Along a Planar FractureChanneled Flow Along a Planar Fracture

Navajo Ss

Page Arizona3 ft

Fracture Surface

Secondary

Calcite