Calculate Permeability K - NMR Log

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Permeability NMR

It is also possible to calculate permability from nuclear magnetic resonance well logs (NMR). The equation for the calculation of NMR-derived permeability, includes a constant that depends of the formation type, NMR derived porosity, and T2 distribution. The expression is the following:

Where:
• k= NMR-derived permeability
• a= a constant, depending on formation
• ɸNMR= NMR-derived effective porosity
• T2gm= geometric mean of the T2 distribution

Calculate Permeability (k)- NMR
a:		ɸnmr: Decimal
T2gm:

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Calculate Permeability K - NMR Log - Three-fluid Model - (Coates)

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NMR Permeability- Three-fluid Model - (Coates)

The autor Coates, proposed an equation known as the "three-fluid model", based on nuclear magnetica resonance well log (NMR). This equation considers the NMR derived porosity, and some constants that depend on the formation type, and the proportion of fluids filling the reservoir pores. The equation is the following:

Where:
• k= NMR-derived permeability
• ɸNMR= NMR-derived effective porosity
• C= constant, depending on formation
• FFI= proportion of moveable fluids occupying effective porosity
• BVI= proportion of capillary-bound fluids occupying effective porosity

Calculate Permeability (k)- NMR - Coates
ɸnmr: Decimal		C:
FFI:		BVI:

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Calculate Permeability K - Coates & Dumanoir (1973)

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Permeability- Coates & Dumanoir (1973)

Coates & Dumanoir (1973) proposed a more expression for permeability calculation. This equation includes water resistivity and water resistiviy of a formation at an irreducible water saturation zone values, and some constants that are related to resistivity and density values. The equation is the following:

Where:
• K= permeability in milidarcys
• Rw= formation water resistivity at formation temperature
• Rt irr= true formation resistivity from a formation at irreducible water saturation (Swirr)
• ɸ = porosity
• C= Coates and Dumanoir constant
• W= Coates and Dumanoir constant

Calculate Permeability (k) - Coates & Dumanoir (1973)
c:		ɸ: Decimal
W:		Rw: ohm-m
Rwtirr: ohm-m

Constant W

Constant W of the Coates & Dumanoir equation, is calculated considering porosity and resistivity values, and it is the following:

Where:
• Rw= formation water resistivity at formation temperature
• Rt irr= true formation resistivity from a formation at irreducible water saturation (Swirr)
• ɸ= porosity

Calculate Constant W - Coates and Dumanoir (1973)
ɸ: Decimal		Rw: ohm-m
Rwtirr: ohm-m

Constant C

In the case of constant C, this is calculated from the following expression, which only considers the hydrocarbon density value:

Where:
• ρh = hydrocarbon density in g / cm3

Calculate Constant C - Coates and Dumanoir (1973)
ρh: g/cm3

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Calculate Permeability K - Timur (1968)

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Permeability - Timur (1968)

Timur (1968) also proposed an equation for permeability calculation. It is an expression similar to the Wyllie & Rose (1950) equation, which considers the porosity and the irreducible water saturation values, but Timur did not differentiate the fluid type accumulated in the reservoir. The equation is the following:

Where:
• K= permeability in milidarcys
• ɸ = porosity
• Swirr= water saturation (Sw) of a zone at irreductible water saturation

Calculate Permeability (k) - Timur (1968)
ɸ: Decimal		Swirr: Decimal

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Calculate Permeability K - Wyllie & Rose (1950) - Dry Gas Reservoirs

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Permeability- Wyllie & Rose (1950)- Dry Gas

Wyllie & Rose (1950) also proposed an equation to calculate permeability in dry gas reservoirs, where like in the case of medium gravity oil reservoirs, this equation considers the values of porosity and irreducible water saturation. The equation is the following one:

Where:
• K = permeability in milidarcys
• ɸ = porosity
• Swirr = water saturation (Sw) of a zone at irreductible water saturation

Calculate Permeability (k) - Wyllie and Rose (1950)- Dry Gas
ɸ: Decimal		Swirr: Decimal

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Calculate Permeability K - Wyllie & Rose (1950) - Medium Gravity Oil Reservoirs

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Permeability- Wyllie & Rose (1950)- Medium Gravity Oil

Wyllie & Rose (1950) created an equation to calculate permeability in reservoirs of medium gravity oils. This equation includes the values of porosity and irreducible water saturation, and it is the following expression:

Where:
• K = permeability in milidarcys
• ɸ = porosity
• Swirr = water saturation (Sw) of a zone at irreductible water saturation

Calculate Permeability (k) - Wyllie and Rose (1950)- Medium Gravity Oil
ɸ: Decimal		Swirr: Decimal

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