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### 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.

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)

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

Examples, Typical Permeability-Porosity Relationship

From Tiab and Donaldson, 1996

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

PERMEABILITY

- Darcy’s “K” was determined to be a combination of
- k, permeability of the sand pack (porous medium, e.g. reservoir rock)
- , viscosity of the liquid

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]

- SI Units are Absolute and Coherent

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)

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[(lbmft)/(lbf s2)]
- Remember: 1[N] / 1[kg*m/s2] = 1; dimensionless

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

- See handout: Darcy, {SI}, and [Oilfield] units
- In Darcy and SI Units, this equation is coherent
- Oilfield units are non-coherent, a unit conversion constant is required

Darcy Units

- Permeability is a derived dimension based on Darcy’s Equation
k = (q m L) / (A Dp)

- The unit of permeability is the Darcy [d]
- The oilfield unit is millidarcy [md]

- The Darcy is defined from Darcy’s Equation, where:
q [cm3/s]

m [cp]

L [cm]

A [cm2]

Dp [atm]

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 L0
vs = q/A = -(k/m) (dp/ds)

where,

vs Darcy velocity, (volumetric flux)

s distance along flow path (0s L), in the direction of decreasing pressure (note negative sign)

- The differential form is Darcy’s Law

Flow Potential

- 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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