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Petrophysical properties of gas reservoirs
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.
Low-pressure (i.e., laboratory) measurements give rise to what is termed the Klinkenberg 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
The effective liquid permeability can be determined in the laboratory by measuring gas permeabilities at different average core pressures. A plot of 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.
Fig. 1 – Example of Klinkenberg permeability correction.
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 equation:
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.
- Klinkenberg, L.J.: “The Permeability of Porous Media to Liquids and Gases,” Drill. & Prod. Prac., API (1941) 200.
- Forchheimer, P.: “Wasserbewegung durch Boden,” Zeitz ver deutsch Ing. (1901) 45, 1731.
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