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PERMEABILITY

PERMEABILITY. Some slides in this section are from NExT PERF Short Course Notes , 1999. Some slides appear to have been obtained from unknown primary sources that were not cited by NExT. Note that some slides have a notes section. . Permeability. Definition (ABW, Ref: API 27)

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PERMEABILITY

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  1. PERMEABILITY Some slides in this section are from NExTPERF Short Course Notes, 1999. Some slides appear to have been obtained from unknown primary sources that were not cited by NExT. Note that some slides have a notes section.

  2. Permeability • Definition (ABW, Ref: API 27) • … permeability is a property of the porous medium and is a measure of the capacity of the medium to transmit fluids • … a measure of the fluid conductivity of the particular material • Permeability is an INTENSIVE property of a porous medium (e.g. reservoir rock)

  3. Sources for Permeability Determination • Core analysis • Well test analysis (flow testing) • RFT (repeat formation tester) provides small well tests • Production data • production logging measures fluid flow into well • Log data • MRI (magnetic resonance imaging) logs calibrated via core analysis

  4. Examples, Typical Permeability-Porosity Relationship From Tiab and Donaldson, 1996

  5. A Darcy’sApparatus for DeterminingPermeability WATER h1-h2 q A h1 h2 (Sand Pack Length) L • Flow is Steady State • q = KA (h1-h2)/L • K is a constant of proportionality • h1>h2 for downward flow q WATER

  6. PERMEABILITY (k) • Darcy’s “K” has a unit of m/s and is called hydraulic conductivity • Permeability can be easily obtained from K: • or hydraulic conductivity can be easily obtained from k

  7. Review - Derived Units • Consider Newton’s 2nd Law for constant mass, F=ma • SI Units are Absolute and Coherent • Absolute: Force is a derived unit, 1 N = 1 (kg*m/s2) • Coherent (consistent): No conversion constants needed • So: F[N] = m[kg]*a[m/s2]

  8. Review - Derived Units • What if we want F to be in [lbf ]? • Then, F[lbf]*4.448[ N/lbf] = m[kg]*a[m/s2] • Adding the conversion factor restores the original formula (a true statement in SI units)

  9. Review - Derived Units • For: F in [lbf ], m in [lbm ], a in [ft/s2] • Then, F[lbf ]*4.448222[N / lbf] = m[lbm ]*0.4535924[kg/lbm] * a[ft/s2]*0.3048[m/ft] • Or, F[lbf ] = m[lbm ] * a[ft/s2] / 32.17405[(lbmft)/(lbf s2)] • Remember: 1[N] / 1[kg*m/s2] = 1; dimensionless

  10. Permeability Dimensions & Units • Permeability is a derived dimension • From Darcy’s equation, the dimension of permeability is length squared • This is not the same as area, even though for example, it is m2 in SI units • In Darcy and SI Units, this equation is coherent • Oilfield units are non-coherent, a unit conversion constant is required

  11. Darcy Units (Obsolete) • Peremebility in d • viscosity in cp • length in cm • volume in cm3 • pressure in atm • time in s

  12. SI Units • Permeability has a derived dimension L2 based on Darcy’s Equation: • The SI unit of permeability is 1 m2 • The oilfield unit is millidarcy • 1 md = 9.87×10-16 m2 • If you have 1 m long core with 9.87×10-16 m2 permeability and you apply 105 Pa pressure difference to the two ends, the Darcy velocity of water (μ=0.001 Pa·s) will be vs = 9.87×10-8 m/s • If the core has a cross sectional area 0.1 m2, the flow rate will be q = A vs = 9.87×10-9 m3/s

  13. English Units • If you have 3 ft long core with 1 md permeability and you apply 14.7 psi pressure difference to the two ends, the Darcy velocity of water (μ = 1 cP) will be vs = 3.59×10-7 ft/s • If the core has a cross sectional area 1 ft2, the flow rate will be 3.59×10-7 ft3/s ft / s md / cp psi / ft

  14. Field Units • If you have 3 ft long core with 1 md permeability and you apply 14.7 psi pressure difference to the two ends, and the flowing fluid is water (μ = 1 cP) and the core has a cross sectional area 1 ft2, the flow rate will be 0.00552 bbl/day bbl / day ft2 md /cP psi / ft

  15. Differential Form - Darcy’s Law • Darcy’s Equation rearranged as Darcy velocity (volumetric flux) vs = q/A = (k/m) (Dp/L) • This equation applies for any L,  as L0 vs = q/A = -(k/m) (dp/ds) where, vs Darcy velocity, (volumetric flux) s distance along flow path (0s  L), in the direction of decreasing pressure (note negative sign) • The differential form is Darcy’s Law

  16. Flow Potential s • The generalized form of Darcy’s Law includes pressure and gravity terms to account for horizontal or non-horizontal flow • The gravity term has dimension of pressure / length • Flow potential includes both pressure and gravity terms, simplifying Darcy’s Law •  = p - gZ/c ; Z+; Z is elevation measured from a datum •  has dimension of pressure

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