permeability

Well productivity is proportional to permeability and the interval of production, with a constant fluid viscosity.

The immobile fraction of gas in a reservoir.

Sandstone permeability is well controlled by porosity, while carbonate shows a more diffuse cloud indicating other factors also influence permeability.

The maximum permeability of rock when it contains only one fluid.

Poroperm trends for different lithologies.

Because they form very connected networks that allow efficient passage of fluids.

Micro-porosity filled with chemically and physically bound water.

Size and shape of grains, grain size distribution, and capillary forces.

P_o is the outlet fluid pressure and P_i is the inlet fluid pressure (both in atmospheres absolute).

Smaller pore throats constrain fluid flow more than larger pore throats.

k = 2.25 × (S_wi)^2 / (100 - φ), where k is permeability (mD), φ is porosity (fraction), and S_wi is irreducible water saturation (fraction).

It is a directional quantity affected by heterogeneous or directional properties of pore geometry.

Porosity.

To avoid a disappointing cloud of data and to reveal individual trends.

The ease with which the rock permits the passage of fluids.

It refers to the overestimation of permeability due to gas slippage in smaller pores at low pressures.

By measuring permeability at multiple pressure differences and plotting apparent permeability against the reciprocal of mean pressure.

The permeability of the sample (millidarcy, mD).

It represents the dynamic viscosity of the fluid (centipoise, cP).

Both effective and relative permeability decrease as the saturation of that fluid decreases.

1000 mD = 1 D.

A vertical sand pack through which water flowed under gravity.

It can be calculated from the heights of manometers, providing the density of the fluid is known.

To calculate permeability based on flow rate and pressure differences.

k = 2.0 × d^2 × 10^8, where k is permeability (D) and d is channel diameter (inches).

k = 3.64 × (D_d)^2 / (3.64 + C), where k is permeability (mD), φ is porosity (fraction), D_d is modal grain size (microns), and C is sorting index.

There is no fundamental law linking the two, only empirical approximations.

Pore geometry affects permeability in a complex way.

Because laminar flow and incompressibility are almost always met at surface geological conditions.

c.g.s system and S.I. units.

The Navier-Stokes equation.

Q = ∆V/∆T (cm³/s)

Permeability to a single fluid is different from permeability with multiple fluid phases; relative permeability is used for multiple phases.

It approximates the permeability of the sample measured with liquid flowing through it.

It can lead to corrections of up to 100%, especially in tight rocks.

There is a threshold value of saturation needed for a fluid to move, indicating that fluids can become trapped in the rock.

1 millidarcy (mD).

Fair.

k = C × (S_wi)^2, where k is permeability (mD), φ is porosity (fraction), S_wi is irreducible water saturation (fraction), and C is a constant.

Porosity, connectivity of flow paths, and pore geometry of the rock.

The amount of oil that remains in a reservoir after production, typically less than 20%.

Grain size influences permeability as shown in poroperm cross-plots.

The immobile fraction of water in a reservoir.

Between the use of gaseous fluids and liquids.

A clear trend with some scatter due to other influences on permeability.

As oil saturation increases, permeability to oil increases while permeability to water decreases, and vice versa.

Permeability is generally anisotropic due to depositional effects and the in-situ stress field.

Water production does not generate revenue and increases water cut, reducing the permeability of the reservoir to oil.

Gas is a compressible fluid, leading to slower travel at high pressure compared to low pressure.

Permeability perpendicular to bedding is about a third to half of that parallel to bedding.

Permeability and the interval of the borehole that is open for production.

High porosities may not lead to high permeabilities if the pore spaces are poorly connected.

Darcy (D).

Higher permeability generally leads to higher well productivity.

Assuming that the flow is laminar.

One darcy is the permeability of a sample 1 cm long with a cross-sectional area of 1 cm², causing a fluid with a dynamic viscosity of 1 poise to flow at a rate of 1 cm³/s under a pressure difference of 1 dyne/cm².

Permeabilities of each fluid present in the rock when two or more fluids are present, always less than absolute permeability.

The permeability at which gas behaves like a near perfect liquid under infinite pressure.

1 D = 0.9869 × 10^-12 m².

Relative permeabilities are expressed as a fraction of the absolute permeability of the rock to either of the fluids present at 100% saturation.

Higher porosity generally leads to higher permeability.

Poiseuille’s equation.

Because it is commonly too large, so the millidarcy (mD) is used.

k = (ΔV / ΔT) * (μ / (P_o - P_i)) * (L / A) (adjusted for gas pressures).

Smaller grain sizes produce smaller pores and pore throats, which constrain fluid flow more than larger grains.

Henry Darcy.

From 1 nanodarcy (nD) to 1 microdarcy (μD).

It shows the relationship between grain size, porosity, and permeability for each core taken.

Exceptional.

k = (φ^3) / (c × (1 - φ)^2), where k is permeability (mD), φ is porosity (fraction), c is a constant, and d is median grain size (microns).

The correction is generally smaller for higher permeability rocks with larger pores.

Oil becomes immobile until its saturation is about 20%.

By flowing a fluid of known viscosity through a core sample and measuring the pressure drop or flow rate.

k = 0.544 × h^3 × w^8 × 10^8, where k is permeability (D), h is fracture width (inches), and w is fracture aperture (inches).

k = 1000 × (d^2) / (φ^2), where k is permeability (mD), d is weighted geometric mean grain size (microns), φ is porosity (fraction), and m is Archie cementation exponent.

Rocks with smaller grain sizes have smaller permeabilities than those with larger grain sizes.

Q = ΔV / ΔT (cm³/s).

The length of the sample (cm).

The area of the sample (cm²).

k = 4.4 × (S_wi)^2 × 136, where k is permeability (mD), φ is porosity (%), and S_wi is irreducible water saturation (%).

k = (ΔV / ΔT) * (μ / (P_o - P_i)) * (L / A)

Millidarcy (mD).

The volume of liquid flowed in time ΔT (cm³).