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
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