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Petrophysical properties required for typical reservoir engineering purposes include porosity, pore volume compressibility, permeability, relative-permeability-vs.-saturation curves, capillary-pressure-vs.-saturation curves, and liquid saturations. Additional data are sometimes required as well, but typically not for natural gas reservoirs. Two petrophysical properties of interest in gas engineering work are the Klinkenberg effect and non-Darcy flow.

Klinkenberg effect

Low-pressure (i.e., laboratory) measurements give rise to what is termed the Klinkenberg[1] or "slippage" effect because the mean free path of gas molecules is approximately the same size as the pores in a reservoir rock, meaning that gas molecules are so far apart that the gas does not behave as a continuum fluid, resulting in erroneously high apparent permeability. At low pressures, measured gas permeabilities can be empirically related to effective liquid (or high-pressure gas) permeabilities by

Vol5 page 0994 eq 001.png....................(1)

The effective liquid permeability can be determined in the laboratory by measuring gas permeabilities at different average core pressures. A plot of Vol5 page 0994 inline 001.png yields an intercept equal to kl (Fig. 1) of 24 md compared with 48 md at low pressure. The Klinkenberg effect is unimportant at reservoir pressures.

Non-darcy flow

At high fluid velocities, Darcy’s law may not always be accurate. An additional energy loss is often apparent above that predicted from the laminar-flow relationship suggested by Darcy’s law. This effect has sometimes been called turbulence or inertial turbulence based on analogies with pipe flow. The effect, however, is probably caused by multiple factors, including pore-scale as well as reservoir-scale phenomena. Because of the lack of understanding of the fundamental nature of such phenomena, it is usually simply referred to as non-Darcy flow.

The most common expression of the non-Darcy effect is through the Forchheimer[2] equation:

Vol5 page 0994 eq 002.png....................(2)

where β is called the non-Darcy velocity coefficient, having units of L–1, and u is the volumetric flux (q/A) through the rock.

Note that Eq. 2 introduces a velocity-squared term into Darcy’s law. This effect shows up as a flow-rate-squared term in flow relationships (e.g., well-deliverability equations) that involve Darcy’s law.

Although non-Darcy flow can occur at all points in a reservoir, in practice it is only significant in the near-well region, where gas velocities are highest owing to radial-flow effects and expansion of gas volume at low pressure. For this reason, non-Darcy flow is incorporated primarily as a flow-rate-dependent skin factor and is seldom, if ever, incorporated to calculate flow away from the wellbore. The magnitude of the non-Darcy effect must generally be measured empirically at reservoir conditions using well tests.

Nomenclature

a = empirical constant
b = empirical constant
kg = measured gas permeability, L2
kl = effective liquid permeability, L2
p = pressure, m/Lt2
Vol5 page 1033 inline 003.png = average pressure, m/Lt2
R = universal gas constant, mL2/nt2T
T = temperature, T
Vm = molar volume, L3/n
α = cubic equation-of-state parameter

References

  1. 1.0 1.1 Klinkenberg, L.J.: “The Permeability of Porous Media to Liquids and Gases,” Drill. & Prod. Prac., API (1941) 200.
  2. Forchheimer, P.: “Wasserbewegung durch Boden,” Zeitz ver deutsch Ing. (1901) 45, 1731.

Noteworthy papers in OnePetro

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External links

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See also

Natural gas properties

Petrophysics

PEH:Gas Reservoirs